The analysis of correlation dimensions of Lorenz chaos time series
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The aim of this chapter is to answer the essence of SEMG and to explore the potential use of nonlinear analysis as a tool in the clinical and biomechanical applications. The technical tools include nonlinear time series test, time series analysis based on chaos theory, multifractal analysis.
In Section 2, we discuss the two methods of nonlinear time series test: surrogate data test method and Volterra-Wiener-Korenberg (VWK) model test method. Theoretically, the two methods can detect the nonlinearity of the data indirectly. The surrogate data method is used to analyze the SEMG. The result shows that the SEMG has deterministic nonlinear components. Meanwhile, we introduce the VWK model test method and compare it with the surrogate data method. The nonlinearity of SEMG during muscle fatigue can be detected by the VWK.
In Section3, we describe the time series analysis based on chaos theory. The chaos definition and chaotic characteristics are discussed. The embedding theory of the attractor reconstruction is investigated for the dynamical system. From the view of the fractal structure of the chaotic attractor, the correlation dimension is used to test the chaotic characteristics of the SEMG during arm movements. The Largest Lyapunov exponent is also studied. Then, we investigate the influence of measure noise, internal noise and sampling interval on the principal components of chaotic time series. The symplectic principal component analysis is given. We illustrate the feasibility of this method and give the embedding dimension of the action surface EMG signal.
In Section4, the self-affine fractal definition and nature are described. The power spectrum and frequency relationship is used to calculate the self-affine fractal dimension of the time series, such as SEMG. Then, the multifractal dimension is given for the SEMG.
The conclusion and future research are shown in Section5.Here, it is necessary to note that this chapter is actually the result of many years work. The new methods presented here build on a broad and strong foundation of nonlinear time series analysis and chaotic dynamical theory.
In many areas of science and engineering, it is a critical issue to determine whether an observed time series is purely stochastic, or deterministic nonlinear, even chaotic. One may know about the intrinsic properties of the observed phenomenon by distinguishing between nonlinear deterministic dynamics and noisy dynamics from a time series. In this section, we review and discuss the surrogate data test method[1] and Volterra-Wiener-Korenberg (VWK) model test method[2] for identifying the nonlinearity of a time series. These methods have been successfully used to detect and characterize nonlinear dynamics from recordings in biology and medicine[2-5].
Surrogate analysis is currently an important empirical technique of testing nonlinearity for a time series. The aim is to test whether the dynamics are consistent with linearly filtered noise or a nonlinear dynamical system[1, 6]. The basic idea of the surrogate data method is to first specify some kind of linear stochastic process as a null hypothesis that mimics “linear properties” of the original data. According to the null hypothesis, surrogate data sets are generated. Then, a discriminating statistic is calculated for the original and for each of the surrogate data sets. If the statistic of the original data is significantly different from those of surrogate data sets, the null hypothesis can be rejected within a certain confidence level. It shows that the original data is from a nonlinear dynamical system. The method is demonstrated for numerical time series generated by known chaotic systems and applied to the analysis of SEMG.
VWK test method is a kind of nonlinear detection of time series based on linear and nonlinear Volterra-Wiener-Korenberg model [2, 5]. That is, it first produces the linear and nonlinear predicted data from the original time series and then compares their information criterions to detect the nonlinearity of the raw data. VWK test technique is capable of robust and highly sensitive statistical detection of deterministic dynamics, including chaotic dynamics, in experimental time series. This method is superior to other techniques when applied to short time series, either continuous or discrete, even when heavily contaminated with noise or in the presence of strong periodicity. Later, an extension of the Volterra algorithm (called the numerical titration algorithm) was given to detect and quantify chaos in noisy time series[7]. Here, the surrogate data method and VWK test approach are used to analyze the nonlinearity of surface EMG signals.
Surrogate data method includes two parts: a null hypothesis and a test statistic. The null hypothesis is a specific process which may or may not adequately explain an origin of the data. The test statistic provides a quantitative description to demonstrate the data sources.
The null hypotheses usually specify some certain properties of the original data that reflect some structure characteristics of the dynamical system, such as mean and variance, and possibly also the Fourier power spectrum. Different null hypotheses describe different specific dynamical systems. In terms of the corresponding null hypothesis, the surrogate data can be generated so as to test the corresponding specific dynamical system class.
Null hypothesis 1 The observed data is produced by independent and identically distributed (IID) random variables.
For this hypothesis, the corresponding surrogate data can be generated by shuffling the time-order of the original time series so that it has the same mean, variance and amplitude distribution as the original data. But any temporal correlations of the original data are destroyed in the surrogate data. Schienkman and LeBaron[8] applied this hypothesis to analyze stock market returns. Breeden and Packard also used this hypothesis to demonstrate that a time series of quasar data which were sampled nonuniformly in time has some dynamics structure[9].
The algorithm of the null hypothesis is that one first create gaussian random numbers from 1 to N, where N is the length of the original data x. Then, the original data x is permuted by the random numbers to generate the surrogate data.
Null hypothesis 2 The observed data is produced by the Ornstein-Uhlenbeck process.
The surrogate data generated by the Ornstein-Uhlenbeck process is a sequence that has the simplest time correlation. The Ornstein-Uhlenbeck process can be given as follows.
whereet is a Gaussian random with zero mean and unit variance. The coefficients a0, a1, and σ work together to determine the mean, variance, and autocorrelation time of the time series xt. In this case, its autocorrelation function is exponential form. Let
In order to generate the surrogate data that is consistent with this hypothesis, the algorithm is that one first calculates the mean
Null hypothesis 3 The observed data is produced by the linear autocorrelatedgaussian process with the mean and variance of the original time series.
The hypothesis has been usually used to test whether the original time series contains nonlinear components. It can be described by using a linear autoregressive (AR) model.
There are the two algorithms to produce the surrogate data in accord with this hypothesis.One algorithm is to directly use Eq.3.That is, the coefficients are firstly identified by using the original data.Then, the surrogate data is generated by repeatedly iterating Eq.3. However, the performance of this algorithm is very unstable. If the values of the coefficients are mis-estimated slightly, this algorithm may lead to the iterative results which easily diverge to infinity. The alternative algorithm is that a surrogate data is generated by randomizing the phases of a Fourier transform. According to the Weiner-Khintchine theorem, the two algorithms are equivalent in essence[1, 10]. The surrogate data has the same Fourier spectrum as the original data. Meanwhile, the algorithm based on the Fourier transform is stabler in the numerical calculation than the first algorithm. The following is the steps of this algorithm.
Let an observed data as
The Fourier transform has a complex amplitude at each frequency. One can randomize the phases of the Fourier transform by multiplying
where
This point can be easily proved[11].
Proof:
According to the nature of DFT of a real time series x(n), if
where
In order to ensure that the inverse Fourier transform results are real values, there must be
In practical, if the data length N is odd,φ(f1)=0,φ(fi) =-φ(fk), i=2~(N+1)/2, k=N~(N+1)/2+1; If N is even, φ(f1)=0, φ(fN/2+1)=0,φ(fi)=-φ(fk), i=2~N/2, k=N~N/2+2. Thus, the surrogate datax‘(n) given by the inverse Fourier transform is a sequence of real numbers.
The imaginary components of surrogate data by our (a) and previous (b) FT algorithm
Thus, there are no imaginary components (see Fig.(1a)). The values of the imaginary parts are very little (magnitude 10-14) so that they can be regarded as computing precision errors. The surrogate data has the same Fourier transform spectrum as the original data by using this algorithm. The reproduced “pure” frequencies are very well. Fig.(1b)shows that the previous FT algorithm[1] cannot make the imaginary components of Fourier inverse transform to be zero. So, if one only uses the real part of Fourier inverse transform as surrogate data and omit its imaginary components, the obtained surrogates would have the two limitations[1, 12].
Null hypothesis 4 The observed data is produced by the static nonlinear transform of linear gaussian process.
The static nonlinear transform is that the observation or measure function is nonlinear. The static means that the measure data xt only depends on the state yt of the dynamic process at the timet,not on derivatives or values in the past. Let h be a measure function, then
The generated surrogate data not only contain the linear correlated characteristic, but also can reflect the static, monotonic nonlinearity of the original data.Strictly speaking, time series in this class are nonlinear.But this nonlinearity is not from the dynamics.This hypothesis can be used to indicate whether the nonlinearity is from the dynamical system or the amplitude distribution (i.e. the measure process).
For generating surrogate data corresponding to this null hypothesis, an algorithm is described.The aimis to shuffle the time-order of the dataxtand to preserve the linear correlations of the underlying time series yt = h-1(xt). The first step is to make a Gaussian time series yt, where each element is generated independently from a Gaussian pseudorandom number generator.Next, we rescale yt in accordance with the time-order of the original data xt. The re-ordered yt has a time series which “follows” the static, monotonic nonlinearity of the original data. Then, the data
The test statistic isa value which estimates some certain aspects of the time series.To compare the raw data to its surrogate data sets, a suitable test statistic must be selected. A useful statistic should be pivotal and independent of the way that surrogate data sets are generated. In other words, for every data set z and every realization zi of any Fi∈Fϕ, their test statistics should be different, i.e.
whereFϕ represents the null hypothesis process. Meanwhile, the distribution of T under the null hypothesis does not depend on μor σ. Here we give two discriminating statistics as follows:
where“¯” denotes the average of the data. The mean μand varianceσhave no effect on the T value in Eq. (13). Therefore, some linear structure characteristics can be determined except for the mean and variance.The T value in Eq.(14) can judge if the surrogate data are consist with the raw data in the view of the correlation with the mean and variance. The T value in Eq.(15) is a simple skewed difference statistic that is both rapidly computable and often quite powerful.
where
The surrogate data method is suitable to detect the nonlinearity of a short, noisy time series. Here, a Gaussian data and a Logistic chaotic time series are used to study the performance of surrogate data method. For a two-sided test, the probability of rejecting the null hypothesis is given by the confidence level p, the surrogate data sets B must be at least as large as
A Gaussian data x is a random time series with zero mean and unit variance produced by the pseudorandom generator. The data length is 1000 points. According to the null hypothesis 3, 39 sets of surrogate data are generated by using our above FT algorithm. The T value is calculated by Eq. (13) and Eq. (14), respectively. In the Figure (2a and b), there are no statistical discrepancy between the test statistic T of the raw data x and those of surrogate data.
The statistic T values of the raw data are on the range of the empirical distribution of T given by the surrogate data. The results show that the generated surrogate data has the same Fourier transform spectrum as the raw data besides the same mean and variance as the raw data because the T value in Eq. (14)is a measure of the time irreversibility of the data. The null hypothesis 3 is accepted at the confidence level 95%. The raw data is consistent with the stochastic process of the null hypothesis 3. The surrogate data produced by the above FT algorithm is equivalent to theraw data.The generated surrogate data reflects the null hypothesis 3.
The histogram is T distribution of surrogate data given by FT algorithm, * is T value of the original data, where abscissa is T, ordinate is the number of surrogate data sets
where
T calculated by Eq.(13), histogram is T distribution of surrogate data, * is T value of the original data, where abscissa is T, ordinate is the number of surrogate data sets
For the case without noise e = 0, we use Eq. (16) to compute the two Logistic chaotic time series with the length of 5000 points and 500 points. 39 surrogate data generated by the above FT algorithm contain the linear properties of the original data in terms of the null hypothesis 3. In Fig.3, we can see the obvious difference between the original data and its surrogate data, regardless of the length of 5000 points or 500 points. The null hypothesis can be rejected in 95% confidence level. The original data has nonlinear components. The results show that the data length has little effect on the surrogate data method based on the above FT algorithm. In Figure 4, we study the nonlinear test of Logistic chaotic time series with measure noise and interior noise, respectively. The data length is 1000 points. According to the null hypothesis, 39 sets of surrogate data are generated. The statistic T for the original data is significantly different from the values obtained for the surrogate data sets. The null hypothesis 3 can also be rejected in 95% significance. The nonlinearity of the original data can be detected. To sum up, the length and noise has no impact on the surrogate data method based on our FT algorithm.
T calculated by Eq.(13), histogram is T distribution of surrogate data, * is T value of the original data, where abscissa is T, ordinate is the number of surrogate data sets
The nature of SEMG plays an important role in neuromuscular disorder diagnosis, muscle fatigue monitoring, prosthesis control, etc. Here the analyzed data are collected from physiological instruments. Humid surface electrode and AD12-16LG collecting card of physiology signal are used in the whole experiment that was done at HuaShanHospital in Shanghai. The data are sampled at 1kHz for the action surface EMG (ASEMG)[3]and the fatigue surface EMG (FSEMG)when one hand carries a 1kg heavy thing [15](see Fig. 5). The length of data for ASEMG is 1000 points during the beginning of action because this time span contains the information of the forearm movement. In the case of carrying a 1kg heavy thing, the length of FSEMG data is also 1000 points when the arm has been fatigue.
For these surface EMG signals, 39 surrogate data are produced by the null hypothesis 2. The surrogate data analysis is given for the action surface EMG signal and the fatigue surface EMG signal, respectively(see Fig. 6).The results show that for action surface EMG signal and fatigue surface EMG signal, their T values are obviously different from those of surrogate data in terms of Eq.13. The null hypothesis 2 can be rejected in 95% degree of confidence. The action surface EMG signal and fatigue surface EMG signal is not stochastic signal produced by a linear stochastic process, but contains nonlinear components.However, this result could not ensure that this nonlinearity must be from the dynamic system.
The surface EMG signals
Surrogate data analysis of surface EMG signal. * is Torig, histogram is Tsurr distribution of surrogate data
Surrogate data test of surface EMG signal during movement, where surrogate data sets are 39 sets; * is T value of surrogate data by the nullhypothesis 4, +is T value of EMG signal,where T is calculated by Eq. 15
In order to test that the nonlinear components are intrinsic deterministic, we further assume that ASEMG is stochastic signal consistent with the null hypothesis 4. Fig.7 gives the T values of ASEMG and surrogate data calculated by Eq.15. This statistic indicates the asymmetry between rise and fall times in the time series. From this figure, we can see that there is the difference between data and surrogates, and the null hypothesis 4 is rejected in 95% credibility. This result shows that the nonlinearity of ASEMG is intrinsic and deterministic.
For a dynamic system, an observed time series
where the memory k and combination degree d correspond to the embedding dimension and the degree of nonlinearity of the model, respectively. The coefficients am are recursively estimated through a Gram-Schmidt procedure from linear and nonlinear autocorrelations of the data itself with a total dimensionM=(k+d)!/(d!k!).
There is the following information criterion in accordance with the parsimony principle:
where
For each data series, there is the following numerical procedure to search for the optimal pair {kopt, dopt}:
when d=1, search for kopt which minimizes C(r).
with k=kopt, increasing d>1, search for dopt which minimizes C(r).
calculate Clin(r) with d=1 and k=M-1, and Cnl(r) with d=dopt and k=kopt.
Compare Clin(r) and Cnl(r), if Cnl(r) is obviously smaller than Clin(r), then the original system dynamics is nonlinear, the obtained time series is nonlinear, even chaos; otherwise, the original system dynamics is linear, the raw data is linear.
Note that when kopt is rather large, M is quite large, too, then the computational time will rapidly go up. In this case, k and d should be adjusted synchronously to search for kopt and doptso as to make Cnl(r) <Clin(r). Furthermore, one can obtain the corresponding linear and nonlinear models for surrogate data generated by the FT algorithm according to the null hypothesis 3 so that
Here, the VWK method is used to deal with the surface EMG signals in Fig.5. For the action surface EMG signal, Clin(r) is almost equal to Cnl(r), i.e.
VWK test analysis of surface EMG signal
VWK combined with surrogate analysis of surface EMG signal. solid isCsurrnl(r), * is Corignl(r)
In order to detect the nonlinearity of the action surface EMG signal, 39 FT-based surrogate data are used according to the null hypothesis 3. The generated surrogate data contain the linear properties of the raw data.Figure 9 is the analysis of surface EMG signal based on VWK with surrogate data. We can see that no matter whether it is the action or fatigue EMG signal,
The discovery of chaotic phenomena is the third major breakthrough in the 20th century physics scientific community following the creation of relativity and quantum mechanics.It organically combines the two major theoretical systems of determinism and probabilism that have long been debated to create a scientific model ofa new paradigm, so that people can use some simple rules to explain seemingly stochastic information in the past[17-19].The practical significance that finds chaotic phenomena is to recognize that a deterministic nonlinear system can have inherent uncertainty. Perhaps asystemhas only a few degrees of freedom, but it can produce complex, similar to the random output signal.In the past, one could only denote a random-looking data as a random process from the view of the traditional time series analysis. The statistical methods or random time series models were used to analyze the data. Since the chaotic phenomenon was discovered by Lorenz[17], people have begun to reunderstand and restudy these random-looking signalsso as to reveal the inherent deterministic mechanismsof these signals. That is, it is to explore that the systems which generate these signals may contain essentially deterministic characteristics. Chaos phenomenon breaks the path that the regularity is found in a lot of completely different systems. This willlead to a revolution in the field of influence of various disciplines. It is chaos to lead people to explore the complexity in nature.
At present, the idea of Chaos has been introduced into the analysis of time series to create the field of chaotic time series analysis.Since the inception of chaotic time series analysis, it hasquickly been penetrated into other disciplines and engineering fields.Thus it becomes the most active branch of the modern nonlinear dynamics.This section describes the chaos definition and the phase space reconstruction of chaotic time series, discusses some parameters that are used to analysis chaotic time series, such as the correlation dimension and Lyapunov exponent, study the principal component analysis methods based on SVD, and propose the symplectic principal component method based on symplectic geometry. Then we use these methods to investigate the surface EMG signals.
Chaos is “order in disorder”. The order means its deterministic nature. The disorder means that the final results can be unpredictable for a long time. As a scientific concept, chaos generally denotes that the long-term dynamical behavior of a deterministic nonlinear system manifests as a random-looking behavior. Mathematically speaking, “chaos” has not been a unified strict definition.For the definition of chaos, there are at least nine different definitions, where the three definitions given by Li-Yorke, Devaney, Marotto are more commonly used. Here describes the definition of chaos by Li-Yorke[18].
Li-Yorke Theorem: Let
This is the famous period 3 theorem. It becomes a milestone in thedevelopment history of chaos theory and promotes the creation and development of chaos theory. From this theorem, the first formal mathematical definition of the chaos is given.
Chaos definition: Let
where
The period of periodic point of f has no upper bound.
There is an uncountable set
where
This definition explains “existence” of chaos in mathematics. According to the above theorem and the definition, the description of chaotic motion is different from the general periodic and quasi-periodic motion. Its motion is not a single periodic orbit but an envelope for a bunch of tracks, where the infinite number of countable stable periodic orbits and uncountable stable aperiodic orbits are embedded densely. Meanwhile, there is at least one unstable aperiodic orbit. Overall, the chaos not only contains some inherent regularity, but also shows that the system has ergodicity. That is, the system has a long-term unpredictability.In other words, the long-term behavior of the system can not be predicted if the system displays the so-called “sensitive dependence on initial conditions”.The meaning of this definition is that the aperiodicity of chaotic system is exhibited accurately. For a dynamical system, the observable behaviour was called stochastic in the past. In fact, it can be random-looking, i.e. “stochastic behaviour occurring in a deterministic system”. Therefore, it is challenging to quantitatively describe the nature of chaotic dynamics and distinguish between the so-called random and chaotic motions from a time series, especially from an experimental time series. At present, chaotic time series analysis methods have been widely attention in fields of mathematics, physics, biology, biomedicine, robotics, geology, engineering, economics, finance, and so on.
Phase space reconstruction is generally the first step of chaotic time series analysis from a time series data. The dynamic characteristic of the system can be explored through phase space reconstruction of the original time series so that the mechanism of the original system can be revealed from the original time series[20]. It has been proved by the so-called Takens’ embedding theorem[21]. According to the theorem, the reconstructed phase space can maintain the invariance of geometry for the original dynamical system[22], such as the characteristic value of the fixed point, the fractal dimension of the attractor, the Lyapunov exponent in the phase space orbit, and so on.
Definition 1: Let
Definition 2: If
In terms of the above definitions and theorem,
For a time series x(t) observed by the measure function h, i.e.
the vector
where
Takens’ embedding theorem offers in the absence of noise, the possibility of reconstructing n-dimensional dynamics from one-dimensional infinite data of one observable-measurable system.This means that in the case of any delay time,a time series can always be embedded into the state space of the system, and when the embedding dimension is sufficiently large, reconstructed space and embedded space is almost one-to-one correspondence. Therefore, one canreconstruct aphase spacefrom an experimental time series so as to estimate dynamical invariants of the time series, such as dimensions, Lyapunov exponents, entropies[21, 23, 24] and so on. However, the embedding theorem does not directly answer how to choose embedding dimension d and delay time t. In practical application, the experimental data is always limited and noisy so that the estimation of the above parameters presents some difficulties[25, 26]. Accuracy of the phase space reconstruction is critically important to the estimation of invariant measures characterizing system behavior. The choice of delay time
Some researchers have studied the choice of delay time
For the embedding dimension d, there are three methods that are usually used to choose the appropriate embedding dimension, including the correlation dimension, singular value decomposition(SVD), the false neighbors[21, 31, 32]. The correlation dimension method is to estimate appropriate dimension d in terms of the correlation theorem[8, 21, 33]. By increasing the embedding dimension, one notes an appropriate dimension d when the value of the correlation dimension stops changing. Broomhead and King[31] used the singular value decomposition (SVD) technique to determine an appropriate embedding dimension d directly from the raw time series.The false neighbor method is based on the fact that choosing a too low embedding dimension results in points,which are far apart in the original phase space, being moved closer together in the reconstruction space[32].Besides, there are also some other methods and modified extensions developed based on the above methods.However, there are still problems on how to determine the appropriate embedding dimension from a scalar time series[34-38].
If a system is chaotic, the strange attractor in a region of the phase space constitutes an infinite hierarchy of self-similar structure, i.e. a fractal structure. One can use quantitative measures to define the fractal nature. The correlation dimension is a useful measurement. Grassberger and Proccacia give a kind of computation method, called GP algorithm[33, 39, 40].
Let X1, X2,..., Xnbe a point of the attractor in phase space. Cl(Xj) is denoted as a hypersurface sphere with the radius l at the reference pointXj. μ[Cl(Xi)] is the probability that Xi (i=1,..., n) falls intoCl(Xj), as follows.
where
Then a correlation integral function is defined as
withl→0, there are a scaling relation
In practical computation, D2 is the slope of log Cvs log l curve over a selected straight line range.
where
The theorem says that with the embedding dimension increasing, the slope of corresponding correlation integral curve will converge to the correlation dimension
Chaos has a fractal structure so that the corresponding correlation dimensionD2 is a fractional value. The estimation of correlation dimensionD2 from a time series can be used to determine whether the time series is chaotic. If D2is fractional, the original time series can have chaotic features, otherwise, it cannot be chaotic. According to the correlation dimension theorem, when the embedding dimension d of the reconstructed phase space is increased to a certain value, the correlation dimension D2 will be saturated. Then, the optimal embedding dimension d will be given from a time series. The corresponding correlation dimensionD2 is called as the correlation dimension of this time series.
Lorenz chaotic time series is given by the state variable x of Lorenz system as follows.
where σ=10, b=8/3, γ=28, initial conditions: x(0)=5, y(0)=5, z(0)=15.The sampling intervalτ=0.1. The sampling points N=1000. For delay time τd=τ, the corresponding correlation dimension values are given in Table 1 when the embedding dimension d is increased from 2 to 12. From this table, we can see that the correlation dimension of the time series is about 2.07. The result shows that the reconstructed attractor has a fractal structure to reflect the chaotic feature of the system. The time series can reconstruct the state space of the original system when the embedding dimension d=6.
Logistic chaotic time series
For finite sampling number (e.g.N=1000), the reconstructed attractor will be broken when the embedding dimension d is increased continuously to a higher value. The estimation of correlation dimension will fail during computation. Therefore, embedding dimension d should not be unlimitedly increased.
d | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
D2 | 1.8009 | 1.9284 | 1.9718 | 2.0389 | 2.0737 | 2.0966 | 2.086 | 2.0788 | 2.0705 | 2.0760 | 2.0753 |
The analysis of correlation dimensions of Lorenz chaos time series
d | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
D2 | 0.9598 | 0.9718 | 0.9689 | 0.9713 | 0.9718 | 0.9591 | 0.9774 | 0.9621 | 0.9827 | 0.9826 | 0.9839 |
The analysis of correlation dimensions of Logistic chaos time series
From the above analysis, we can see that the surface EMG signal has deterministic nonlinear component. Here, the correlation dimension is further used to study whether its nonlinear component are chaotic. Figure 10a shows a raw data for forearm pronation. Figure 10b gives the correlation integral curve of the data under the embedding dimension from 2 to 12. In the recontructed phase space,the delay time
The correlation dimension analysis of surface EMG signal
The corresponding slope value is the correlation dimension of the surface EMG signal, about
d | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
D2 | 1.9315 | 2.7037 | 3.2808 | 3.4837 | 3.8047 | 3.7597 | 3.8511 | 3.8864 | 3.8129 | 3.7160 | 3.8039 |
The analysis of correlation dimension of surface EMG signal during movement
The correlation dimension is a quantitative index that describes the fractal structure of chaotic attractor. It measures the freedom degree and complexity of the system. For the raw data and all dataof
When the sampling intervalτ=1, Figure 11a and b show the results of the surrogate data test analysis for Lorenz chaotic time series based on correlation dimension. There are significant differences between the original data and its surrogate data in m = 5 (see Fig.11a). This result explains that the null hypothesis can be rejected in confidence level 95%. The differences disappear between the raw data and its surrogate data in m = 10 (see Fig.11b). This illustrates that the reconstructed attractor appears broken. The reconstructed phase space is similar to that of the surrogate data with linear stochastic noise characteristics.
Figure 11c and d show the results withτ=0.1. The differences between the raw data and its surrogate data can be seen in Fig.11c (m = 4). Whenm>2, these differences become larger as m increases. Figure 11e and f show the results withτ=0.005. Figure 11e shows the surrogate data testhistogram in m = 2. The correlation dimension curves of the raw data and its surrogate data are given in m = 2 ~ 10 (see Fig.11f). Even in the case of oversampling, the correlation dimension as test statistic can also make the surrogate data methodvery effective.
The surrogate data test analysis based on correlation dimensionfor Lorenz chaos time series by sampling intervals
Figure 12 shows the surrogate dataanalysis for the surface EMG signal in Fig.12a based on correlation dimension. When m = 6, the correlation dimension value of the raw data is different from those of its surrogate data generated by the null hypothesis 3. The correlation dimensioncurves of the raw data and its surrogate data are given when m = 2 ~ 8 in Fig.12b. We can see the differences between the original data and its surrogate data. The null hypothesis 3 can be rejected in confidence level 95%. The result indicates that the surface EMG signal has deterministic nonlinear components, even chaotic.
The surrogate data test analysis based on correlation dimension for surface EMG signal.
The Lyapunov exponent method is to directly identify whether a system is chaotic. If the system is chaotic,the Lyapunov exponent is positive. Otherwise, the Lyapunov exponent is negative. For this, the Lyapunov exponent can be used to test the chaotic feature of a signal under study. The first algorithms developed computed the whole Lyapunov spectrum by Wolf et al.[43] and Sano et al. [44]. Meanwhile, the largest Lyapunov exponent is sufficientfor assessing the presence of chaos. At present, there are many algorithms to estimate the largest Lyapunov exponent from a time series, such as an algorithm given by Rosenstein et al.[45]. This algorithm is aimed specifically at estimating the largest Lyapunov exponent from short data.
For a short time series, Rosenstein et al. present a robust estimation algorithm of the largest Lyapunov exponent. First, the attractor is reconstructed, refer to Eq. 25. Next, the algorithm locates the closest neighbor of each pointXion the trajectory, with respect to the Euclidian distance. Then, one defines the distance between two neighboring points at instantn=0 by:
where
According to time, the average distance between two neighboring vectors can be simply
Assume that the system is controlled by the largest Lyapunov exponent only. Then, the distance between two neighbor points obey the following relationship:
where
y(n) curves of signals, abscissa is n, ordinate isy(n)
Then, the Lyapunov exponent can be given by using a least-squares fit to the “average” line:
where
This method is deduced directly from the largest Lyapunov exponent definition. The accurate evaluation of λdepends on the full use of the data. In practice, the curvey(n) will tend to saturation. The largest Lyapunov exponent λ is given by computing the slope of the linear part in the curve y(n).
In general, if the signal is chaotic, the slope of the curvey(n) will be independent of the embedding dimension. Otherwise, if the signal is not chaotic, the slope of the curve y(n) will depend on the embedding dimension. When the embedding dimension m is chosen from 2 to 8, the Lyapunov exponent of the curve y(n) of the signal is shown in Figure 13. For a chaotic signal, a good illustration is given (see Figure 13a, b and c). The y(n) curves are different from those of a non-chaotic signal (compare with Figure 13d and e). However, even for chaotic signals, the y(n) curves are not always parallel. For example, in the case of undersampling (
Figure 14 gives the curves of Lyapunove exponent y(n) for the surface EMG signal. The y(n) curves are not very parallel for the surface EMG signal. It is difficult to distinguish thecurves of y(n) for the surface EMG signal from those of Figure 13d, f and g. The surface EMG signal can not be determined as chaotic, or as stochastic. But it can be a high-dimensional system.
y(n) curves of surface EMG signal, embedding dimension m=2~8, abscissa is n,ordinate is y(n)
Broomhead and King[31] proposed the idea of singular system analysis that determines an appropriate embedding dimension d directly from the raw time series. It provides its convenience for the further analysis of the given system. Numerical experience, however, led several authors to express some doubts about reliability of singular system analysis in the attractor reconstruction[46-48]. Palus and Dvorak[37] explain why singular-value decomposition(SVD), the heart of the singular system analysis and by nature a linear method, may become misleading technique when it is used in nonlinear dynamics studies that reconstruction parameters are time-delay, embedding dimension (or embedding windows). For this, we propose a novel nonlinear analysis method based symplectic geometry, called symplectic principal component analysis(SPCA)[49].
Let a time seriesx1, x2,..., xnbe the measured signal by sampling intervalts, n is the number of samples. According to Takens’ embedding theorem, a trajectory matrix X can be given by time delay coordinates method, refer to Eq. 25(τd=1):
whered is embedding dimension. m=n-d+1 is the number of points in d-dimension reconstruction attractor,
where S is d×ddiagonal matrix, whose elements are defined
Since the matrix V is orthogonal, then
Meanwhile, for the matrix U, there are
In order to facilitate the calculation, Broomhead et al. applies the covariance matrix C of the matrix X to replace the matrix X. The details are as follows:
Its values reflect the degree of correlation between the time delay coordinate variable i and j.
Let Y=XU, then:
where UTCUis the covariance matrix of the matrix Y. Its elements are zero, except that the diagonal elements are equal to σi. This means that the variables i and j of the matrix Y are independent. The coordinate system is orthogonal, which is constituted from the variables of the matrix Yafter the above transformed. The σi is called the principal component or singular value in accordance with the order of the largest to the smallest. The orthogonal vectorUi corresponding to the principal componentσi is called the principal axis. The principal component describes the distribution of the signal energy. That is, the value of the principal component reflects the projection of the signal energy in the corresponding principal axis. In the different principal axes, a distribution value is given as
In order to filter out noise, the trajectory matrix X is first projected into the coordinate system U.
The variables in the matrix Y are independent. Then, the original coordinate system is updated by using the matrix Y:
That is,
Figure 15a shows the principal component spectrum of Logistic attractor from a Logistic chaotic time series without noise. The principal component spectrum has not a significant noise level. When the interior noise is Gaussian noise with zero mean and 0.0012 variance, the principal component spectrum is given for Logistic attractor. Figure 15c and d give the principal component spectrum of Logistic attractor with the measurement noise σ2=0.0012 and σ2=0.82, respectively. It can be seen that the Logistic attractor with the internal noise has the same principal component spectrum as the attractor without noise. The curves of the principal component spectrum are also slanting. The total energy is significantly distributed into each principal axes. The principal components are declining with the index i so that there is no noise floor. It is difficult to choose an appropriate embedding dimension d. For the larger measurement noise, the corresponding principal component spectrum of Logistic attractor slant into a floor area with increasing the embedding dimension. In the floor area, the principal components keep unchanged and do not decline with the index i, called noise floor. Broomhead and King[31] have suggested that this noise floor can be used to determine the embedding dimension and filter out noise from the data. The signal energy will be focused on the truncated principal components and the corresponding principal axes when the principal components above noise floor are only held. The number of the principal components above the noise floor is the optimal embedding dimension.
The principal component analysis of Logistic chaos series with differentnoises based on SVD, d=3 : 2 : 23, abscissa is d, ordinate is log(σi/tr(σi))
Besides, the new coordinate system corresponding to the principal axes can eliminate the noise floor to reduce the noise from the data. However, the truncated position of the principal components depends on the signal-noise-ratio, especially for the measurement noise. The principal components of the chaotic time series based on SVD spectrum more easily subject to the measurement noise so that the embedding dimension estimation isdirectly affected. For the smaller noise, there is the more number of principal components above the noise floor. For the larger noise, the number of the corresponding principal components will be reduced. Here, the above calculation accuracy is 2.2204e-016, which does not consider the numerical calculation error.
The Lorenz chaotic system is considered to give the state variable x in order to study the influence of sampling interval on the principal component spectrum. The principal component spectrum slant and have no floor for the chaotic time series x with τ=0.005 (see Fig.16a). When τ=0.1 (see Fig.16b), the principal component spectrum are basically similar to those in the Figure 16a. When τ=1, each line is separated from each other and tends to horizontal line in the case of different embedding dimensions(see Fig.16c). It shows that thedistribution of the total energy has little difference in each principal axis, like the Gaussian noise (see Fig.16d). For the Gaussian noise, its principal component spectrum curves are horizontal lines, where N=10000. It shows that every principal component is equal to each other. The energy distributes into every principal axis averagely. Therefore, it can be seen that sampling interval affects the determination of embedding dimension. When the sampling interval is not undersampling, the determination of embedding dimension depends the amount of signal-noise-ratio. In the case of undersampling, the chaotic time series is similar to noise so that the embedding dimension seems to be estimated as 1.
The principal component analysis of gaussian noise and Lorenz chaos time series by different sampling intervals based on SVD, d=3 : 2 : 23,abscissa is d, ordinate is log(σi/tr(σi))
The symplectic geometry is a kind of phase space geometry. Its nature is nonlinear. It can describe the system structure, especially nonlinear structure, very well. It has been used to study various nonlinear dynamical systems[50-52] since Feng Kang[53]has proposed a symplectic algorithm for solvingsymplectic differential.However, from the view of data analysis, few literatures have employed symplectic geometry theory to explore the dynamics of the system. Our previous works have proposed the estimation of the embedding dimension based on symplectic geometry from a time series[49, 54-56]. Subsequently, Niu et al. have used our method to evaluate sprinter’s surface EMG signals[57]. Xie et al[58] have proposed a kind of symplectic geometry spectra based on our work. Subsequently, we show that SPCA can well represent chaotic time series and reduce noise in chaotic data[59, 60].
In SPCA, a fundamental step is to build the multidimensional structure (attractor) in symplectic geometry space. Here, in terms of Taken’s embedding theorem, we first construct an attractor in phase space, i.e. the trajectory matrix X from a time series. That is, fora measured data (the observable of the system under study)x1, x2,..., xnrecorded with sampling intervalts, the corresponding d-dimension reconstruction attractor, Xm×dcan be given (refer to Eq.40).Then we describethe symplectic principal component analysis (SPCA) based on symplectic geometry theory and give its corresponding algorithm.
SPCA is a kind of PCA approaches based on symplectic geometry. Its idea is to map the investigated complex system in symplectic space and elucidate the dominant features underlying the measured data. The first few larger components capture the main relationship between the variables in symplectic space. The remaining components are composed of the less important components or noise in the measured data. In symplectic space, the used geometry is called symplectic geometry. Different from Eulid geometry, symplectic geometry is the even dimensional geometry with a special symplecticstructure. It is dependent on a bilinear antisymmetricnonsingular cross product——symplectic cross product:
where,
When
The measurement of symplectic space is area scale. In symplectic space, the length of arbitrary vectorsalways equals zero and without signification, and there is the concept of orthogonal cross-course.In symplecticgeometry, the symplectic transform is the nonlinear transform in essence, which is also called canonical transform, since it has measure preserving characteristics and can keep the natural properties of the original data unchanged.It is fit for nonlinear dynamics systems.
The symplectic principal components are given by symplectic similar transform. It is similar to SVD-based PCA. The corresponding eigenvalues can be obtainedby symplecticQR method. Here, we first construct the autocorrelation matrix Ad×d of the trajectory matrix Xm×d. Then the matrix A can be transformed as a Hamilton matrix M in symplectic space.
Definition 1 Let S is a matrix, if
Definition 2 Let H is a matrix, if
Theorem 1 Anyd×d matrix can be made into a Hamilton matrix. Let a matrix as A, so
Theorem 2Hamilton matrixM keeps unchanged at symplectic similar transform. (Proof refers to appendix A)
Theorem 3Let
Theorem 4Let
Theorem 5The product of sympletcic matrixes is also a symplectic matrix. (Proof refers to appendix A)
Theorem 6 Suppose Household matrix H is:
where
so, H issymplectic unitary matrix.
For Hamilton matrix M,itseigenvalues can be given by symplectic similar transform and the primary 2d dimension space can be transformed into
Construct a symplectic matrix Q,
where Bis up Hessenberg matrix(bij=0, i>j+1). The matrix Qmay be a symplecticHousehold matrix H. If the matrix M is a real symmetry matrix, M can be considered as N. Then one can get an upper Hessenberg matrix (referred to equ. 13), namely,
where H is the symplectic Householder matrix.
Calculate eigenvalues
These eigenvalues
Thus the calculation of 2d dimension space is transformed into that of that of d dimension space. The μ is the symplecticprincipal component spectrumsof A with relevant symplectic orthonormal bases. In the so-called noise floor, values of
For a measured datax1, x2,..., xn, our proposed algorithm consists of the following steps:
Reconstruct the attractor Xm×d from the measured time series, where d is the embedding dimension of the matrix X, and m = n-d+1.
Remove the mean values Xmean of each row of the matrix X.
Build the real d×d symmetry matrix A, that is,
Here, d should be larger than the dimension of the system in terms of Taken’s embedding theorem.
Calculate the symplectic principal components of the matrix A by QR decomposition, and choose the Householder matrix H instead of the transform matrix Q.It is easy to prove that H is a symplectic unitary matrix(Proof refers to appendix A) and H can be constructed from real matrix (refer to appendix B).
Construct the corresponding principal eigenvalue matrix W according to the number k of the chosen symplectic principal components of the matrix A, where W⊆Q. That is, when k=d, W=Q, otherwise W⊂Q. In use, k can be chosen according to Eq.63.
Get the transformed coefficients S = {S1, S2, …, Sm}, where
Reestimate theXsfrom S,
Then the reestimation data
For the noisy time series, the first estimation of data is usually not good. Here, one can go back to the step (6) and let Xi =Xsin Eq.(65) to do step (6) and (7) again. Generally, the second estimated data will be better than the first estimated data.
Besides, it is necessary to note that for the clean time series, the step (8) is unnecessary to handle.
SPCA, like PCA, can not only represent the original data by capturing the relationship between the variables, but also reduce the contribution of errors in the original data. Here, the performance analysis of SPCA is studied from the two views, i.e. representation of chaotic signals and noise reduction in chaotic signals.
Representation. of chaotic signals
We first show that for the clean chaotic time series, SPCA can perfectly reconstruct the original data in a high-dimensional space. We first embed the original time series to a phase space. Considering the dimension of the Lorenz system(see Eq.30) is 3, d of the matrix A is chosen as 8 in our SPCA analysis. To quantify the difference between the original data and the SPCA-filtered data, we employ the root-mean-square error (RMSE) as a measure:
where
When k = d, the RMSE values are lower than 10-14 (see Figure 17). In Figure 17, the original data are generated by Eq. 30. The estimated data is obtained by SPCA with k=d. The results show that the SPCA method is better than the PCA. Since the real systems are usuallyunknown, it is necessary to study the effect of sampling time, data length, and noise to the SPCA approach. From the Figure 17 and 18, we can see that the sampling time and data length have less effect on SPCA method in the case of free-noise.
Color online) RMSE vs. Samplingtime curves for the SPCA and PCA.
Color online) RMSE vs. data length curves for the SPCA and PCA.
For analyzing noisy data, we use the percentage of principal components (PCs) to study the occupancy rate of each PC in order to reduce noise. The percentage of PCs is defined by
whered is the embedding dimension,
Next, we study the reduced space spanned by a few largest symplectic principal components (SPCs) to estimate the chaotic Lorenz time series (see Fig.20). In Figure 20, thedata x is given with a sampling time of 0.01 from chaotic Lorenz system. The estimated data is calculated by the first three largest SPCs. The average error and standard deviation between the original data and the estimated data is -6.55e-16 and 1.03e-2, respectively. The
Color online) The percentage of principal components for the SPCA and PCA.
Colour online) Chaotic signal reconstructed by the proposed SPCA algorithm with k=3, where (a) the time series of the original Lorenz data x without noise and the estimated data; (b) phase diagrams with L =11 for the original Lorenz data x without noise and the estimated data. The sampling time ts = 0.01.
estimated data is very close to the original data not only in time domain (see Figure 20a) but also in phase space (see Figure 20b). We further explore the effect of sampling time in different number of PCs. When the PCs number k =1 and k =7, respectively, the SPCA and PCA give the change of RMSE values with the sampling time in Figure 21. We can see that the RMSE values of the SPCA are smaller than those of the PCA. The sampling time has less impact on the SPCA than the PCA. In the case of k = 7, the data length has also less effect on the SPCA than the PCA(see Fig. 22).
Comparing with PCA, the results of SPCA are better in the above Figures. We can see that the SPCA method keep the essential dynamical character of the primary time seriesgenerated by chaotic continuous systems. These indicate that the SPCA can reflect intrinsic nonlinear characteristics of the original time series. Moreover, the SPCA can elucidate the dominant features underlying the observed data. This will help to retrieve dominantpatterns from the noisy data. For this, we study the feasibility of the proposed algorithm to reduce noise by using the noisy chaotic Lorenz data.
The RMSE values vs. the sampling time for the SPCA and PCA, where (a)the PCs number k =7; (b)k =1.
The RMSE vs. the data length for the SPCA and PCA, where k =7. The sampling time is 0.1.
Noise. reduction in chaotic signals
For the noisy Lorenz data x, the phase diagrams of the noisy and clean data are given in Figure 23a and 23b. The clean data is the chaotic Lorenz data x with noise-free (see Eq.30).
The noise reduction analysis of the proposed SPCA algorithm and PCA for the noisy Lorenz time series, where L=11.
The noisy data is the chaotic Lorenz data x with Gaussian white noise of zero mean and one variance (see Eq.30). The sampling time is 0.01. The time delay L is 11 in Figure 23. It is obvious that noise is very strong. The first denoised data is obtained in terms of the proposed SPCA algorithm (see Figure 23c- f). Here, we first build an attractor X with the embedding dimension of 8. Then the transform matrix W is constructed when k=1. The first denoised data is generated by Eq.(65) and (66). In Figure 23c, the first denoised data is compared with the noisy Lorenz data x from the view of time field. Figure 23d shows the corresponding phase diagram of the first denoised data. Compared with Fig.23a, the first denoised data can basically give the structure of the original system. In order to obtain better results, this denoised data is reduced noise again by the step (8). We can see that after the second noise reduction, the results are greatly improved in Fig.23e and 23f, respectively. The curves of the second denoised data are better than those of the first denoised datawhether in time domain or in phase space by contrast with Fig.23c and 23d. Figure 23g shows that the PCA technique gives the first denoised result. We refer to our algorithm to deal with the first denoised data again by the PCA (see Figure 23h).Some of noise has been further reduced but the curve of PCA is not better than that of SPCA in Figure 23e. The reason is that the PCA is a linear method indeed. When nonlinear structures have to be considered, it can be misleading, especially in the case of a large sampling time (see Figure 24). The used program code of the PCA comes from the TISEAN tools (http://www.mpipks–dresden.mpg.de/~tisean).
Color online) D2 vs. embedding dimension d
Figure 24 shows the variation of correlation dimension D2 with embedding dimension d in the sampling time of 0.1 for the clean, noisy, and denoised Lorenz data. We can observe that for the clean and SPCA denoised data, the trend of the curves tends to smooth in the vicinity of 2. For the noisy data, the trend of the curve is constantly increasing and has no platform. For the PCA denoised data, the trend of the curve is also increasing and trends to a platform with 2. However, this platform is smaller than that of SPCA. It is less effective than the SPCA algorithm. This indicates that it is difficult for the PCA to describe the nonlinear structure of a system, because the correlation dimension D2 manifests nonlinear properties of chaotic systems. Here, the correlation dimension D2 is estimated by the Grassberger-Procaccia’salgorithm[33, 40].
In terms of Eq.63, the values ofμi, i=k+1,..., d, are far smaller thanμk. These values form a noise floor.Therefore, the embedding dimension of the reconstruction system can be determined by the noise floor. Here, the noise and nonlinear time series are used to investigate the feasibility of the embedding dimension estimation based on symplectic geometry.
For noise (which is generally regarded as Gauss white noise with mean value 0 and variance 1 in practical systems), symplectic geometry spectrums of this noise give the even distribution of its total energy (see Fig. 25a). From this figure, we can see that the symplectic geometry spectrums of noise can reflect the characteristic of noise very well when N=1000. This shows SG method can reflect noise level in the condition of short data length. For the time series of state variable x in Logistic chaos system without noise interference, the symplectic geometry spectrums (see Fig. 25b) are slant in the beginning then turn into plane area with the increase of index i. In other words, the distribution of total energy on the different axes is obviously different and with increasing the embedding dimension, the slants of symplectic geometry spectrums transit into noise floor. So one can determine embedding dimension from the number of symplectic geometry spectrums over noise floor, in which its determining criterion is similar to that in [37]. From Fig. 25b, the embedding dimension of Logistic chaotic time series can be estimated at 4 because the symplectic geometry spectrums begin to turn into noise floor at index 5. In a similar way, for Lorenz chaos time series without noise, when sampling intervalτ=0.005, the embedding dimension can be estimated at 6 (see Fig. 25c).
Comparison of the results of our method (see Fig. 25b and 25c) and the results of SVD method (see Fig. 25d and 25e) shows that in SG method, the position of the noise floor is determined by the intrinsic dynamical structure of the nonlinear dynamic system rather than the numerical accuracy of the input data and the computation precision, but in SVD method, the noise floor was determined reversely[8, 37, 61].
In a word, the numerical experiments discuss that for the nonlinear dynamic systems, SG method can give the appropriate embedding dimension from their time series but SVD method cannot. So SG method is fit to deal with nonlinear systems.
It is well known that the recent methods about embedding dimension are almost more or less subjective, or are affected by changes of the data length, noise, time lag, or sampling time, etc. Here, it is necessary that the robustness of the SG method is studied.
The. effect of data length
In order to avoid the effect of the characteristics of the nonlinear system, this paper only considers and uses the noise to analyze the effect of data length. For Gauss white noise with mean value 0 and variance 1, when N=1000, the SG method can give better results than the SVD method (see Fig. 26a) because the total energy is distributed equably (see Fig. 25a).
The study of embedding dimension based on symplectic geometry algorithm, N=1000, d=3, 8, 13, 18, 23, abscissa is d, ordinate is log(μi/tr(μi))
And yet when N is rather large, e.g. N=10000, the SVD method can just have the similar results (see Fig. 26b) with Fig. 25a. These show that the SG method is more robust to changes of the data length than the SVD method. Then the SG method is fitter to the analysis of short time series.
The analysis of SVD principal components of noise with different data length, d=3, 8, 13, 18, 23, abscissa is d, ordinate is log(μi/tr(μi))
The study of symplecticgeometry spectrum analysis in different noises, N=1000, d=3, 8, 13, 18, 23, abscissa is d, ordinate is log(μi/tr(μi))
The. effect of noise
At present, there are many estimators of appropriate embedding dimension, but it has gradually been realized that such estimators are useful only for low-dimensional noise-free systems; such systems, however, seem hardly to occur in the real life. Therefore, this paper studies the robustness of the SG method under noise. For the signal obtained from the real system, it is always contaminated by noise (inner noise or/and outer noise). Although contaminated by inner or/and outer noise, the embedding dimension of Logistic system can always be noted at 4 by using the SG method because the noise floor begins at the embedding dimension 5 (see Fig. 27a and 27b). These show either inner noise or outer noise has little impact on the symplectic geometry spectrums. On the further increase of noise, the position of noise floor is obviously raised from the Figure 27c, but the appropriate embedding dimension 2 can still be obtained. In the similar way, for Lorenz chaos time series without and with noise, when sampling intervalτ=0.005, the embedding dimension is 6 without noise and 3 with noise, respectively (see Fig. 25c and Fig. 27d). These results show that the SG method is useful for Lorenz system with noise, too. Meanwhile, we find that the SG method can obtain the results similar to nonlinear high singular spectrum algorithm[62]. Thus, it further shows that the SG method can reflect intrinsic nonlinear characteristics of the raw data.
The symplectic geometry spectrum analysis of Lorenz chaos series by different sampling intervals, N=1000, d=3, 8, 13, 18, 23, abscissa is d, ordinate is log(μi/tr(μi))
The. effect of sampling interval
For the changes of the sampling interval from τ=0.005to τ=0.1, this paper finds that the embedding dimension can be estimated at 6 from the correspondingsymplectic geometry spectrums of Lorenz chaos time series (see Fig.25c and Fig. 28a), although the position of noise floor is constantly driven up. However, in the same condition, SVD method cannot give the appropriate embedding dimension (see Fig. 25e and 28b), the results of which are similar to the results of the literature[61]. Besides, no matter the sampling interval is over sampling or under sampling, SG method can always give the appropriate embedding dimension d of Lorenz chaos time series (see Fig. 28c and 28d) because the correlation dimension m of Lorenz system is 2.07, in general, if d>m, d is viable.
For the action surface EMG signal (ASEMG) collected from a normal person, SVD method cannot give its appropriate embedding dimension (see Fig. 29a). The method based on correlation theory can do it but costs much time for computation. Here, SG method can fast obtain its embedding dimension. Figure 29b is the symplectic geometry spectrums of action surface EMG signal. The embedding dimension can be chosen as 6, which is the same as that of correlation dimension analysis[3]. This further shows that the SG method has stronger practicability for the small sets of experiment data.
The analysis of action surface EMG signal, d=3, 8, 13, 18, 23, abscissa is d, ordinate is log(μi/tr(μi))
Fractal is a kind of geometry structures that have similarity in structure, form or function between the local and the whole. In nature, almost every objectis very complex and performs a self-organization phenomenon that is a spatiotemporal structure or state phenomenonby forming spontaneously. From the view of geometry structure,this object has its own self-similarity properties in many parts, called a multifractal system. This structure can often be characterized by a set of coefficients, such as multifractal dimension, wavelet multifractal energy dimension. The multifractal theory reflects the complexity and richness of the nature in essence.
Definition 1 Let the mapping
where T is a linear transformation on Rn. b is a vector in Rn. Thus, S is a combination of a translation, rotation, dilation and, perhaps, a reflection, called an affine mapping. Unlike similarities, affine mappings contract with differing ratios in different directions.
Theorem 1 Consider the iterated function system given by the contractions{
Moreover, if we define a transformation S on the class φ of non-empty compact sets by
For E∈φ, and write Sk for the kth iterate of S (so
for every set E∈φ such that
If an IFS consists of affine contractions {
Since self-affine time series have a power-law dependence of the power-spectral density function on frequency,.self-affine time series exhibit long-range persistence. For a practical data, one can use the relationship of power spectrum and frequency to determine if the data has the self-affine fractal characteristic.
Let a time series be
where f is frequency. The power spectrum of f is defined by
If the power spectrum obeys a power law
for large f, the time seriesx(t) has the self-affine fractal characteristic. The self-affine fractal dimension D is given
S(f) is plotted as a function of f with log-log scaling. β is the negative of the slope of the best-fit straight line in the range of large f. Note that the value of β is a measure of the strength of persistence in a time series. β>1 reflects strong persistence and nonstationary. 1>β>0 describes weak persistence and stationary. β=0 shows uncorrelated stationary. β<0 indicates antipersistence and stationary. In all cases, however, a self-affine time series with a non-zero β has long-range (as well as short-range) persistence and anti-persistence. For small β, the correlations with large lag are small but are non-zero. This can be contrasted with time series that are not self-affine; these may have only short-range persistence (either strong or weak).
Although the self-affine mapping are varied in a continuous way, the dimension of the self-affine set need not change continuously. Unfortunately, the self-affine fractal situation is much more complicated. It is quite difficult to obtain a general formula for the dimension of self-affine sets. It is not enough that only one fractal dimension is used to describe the self-affine fractal time series. The multifractal dimensions have been proposed to describe this kind of the time series[67-72].
For a measured time series of a multifractal system, its trajectory in phase space is often attracted to a bounded fractal object called strange attractor for which a whole set of dimension Dq has been introduced which generalize the concept of the Hausdorff dimension. Let X1,..., Xn be a point of the attractor in the phase space. The probability that the trajectory point is found within a ball of radius l around one of the inhomogeneously distributed points of the trajectory is denoted by
where
The q-order correlation integral is defined by
The multifractal dimension Dq can be computed by the following equation:
The above Dq is the multifractal dimension method based on Grassberger and Procaccia. The generalized correlation integral
The surface EMG signal is a complicated physiological signal.Its distribution is clearly uneven (see Figure 30). When the surface EMG signal is studied by using the fractal method, one should first determine if the surface EMG signal is fractal. Then, its corresponding fractal dimension D can be estimatedby Eq.(77) under a certain resolution. Figure 30 shows the self-affine fractal analysis of the surface EMG signals from Channel 1 during finger flexion, finger tension, forearm pronation and forearm supination (the results of Channel 2 are similar to those of Channel 1). It can be seen that the surface EMG signals have self-affine fractal characteristics. The results explain the physiological mechanism of the surface EMG signals.
In view of self-affine fractal characteristics, only one single fractal dimension is not easy to characterize the dynamics of surface EMG signals for different actions (see Table 4). There is little difference for the self-affine fractal dimensions of the four actions, where each type ofaction signals was chosen 100 sets of the data. The data length is 1000 points.In other words, it is difficult to identify the surface EMG signals of the different actions by using a single fractal dimension.The multifractal dimension values should be used to describe the action surface EMG signals during the arm movements.
Finger flexion | Finger tension | Forearm pronation | Forearm supination | |
Channel 1 | -0.2402±0.0725 | -0.2571±0.0947 | -0.0280±0.3250 | 0.0692±0.1418 |
Channel 2 | 0.0738±0.5734 | -0.3199±0.2842 | -0.0901±0.2591 | -0.2343±0.2134 |
The self-affine D of surface EMG signals during movements
The analysis study of self-affine of surface EMG signal: Curve is power spectrum of surface EMG signal, line is straight line fit related part of curve; Abscissa is lg(f), ordinate is lg(Psd)
Here, we use the above multifractal dimension theory to analyze the action surface EMG signals. For the surface EMG signals of the four actions in channel 1, the multifractal analysis results are shown in Figure31. The results of channel 2 are omitted since they are similar to those of channel 1. In the figure, theDq-q curves are calculated under q =8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8. It can be seen that theDq-q curves have a certain range. The results indicate that the surface EMG signals are non-uniform fractal structure signals. These are consistent with the results of the above self-affine fractal analysis. The parameter values with q can be used to classify the data. In theory, it will be more reasonable that multifractal dimensions are used to describe the surface EMG signals. However, the actual calculation process of the multifractal dimensions is very time-consuming. For the surface EMG signals, it is extremely difficult to meet the requirements of real-time classification.
The multi-fractal analysis of surface EMG signals during movements
In order to investigate whether the essence of the surface EMG signal is stochastic or deterministic nonlinear (even chaotic), some emerging nonlinear time series analysis approaches are discussed in this chapter. These techniques are based on detecting and describing determinisitic structure in the signal, such as surrogate data method, VWK model method, chaotic analysis method, symplectic geometry method, fractal analysis method, and so on.
The surrogate data method and VWK model mehtod are used to detect the surface EMG signal for arm movement and muscle fatigue. The results show that the surface EMG signal has deterministic nonlinear components. Moreover, our algorithm of surrogate data based on the null hypothesis 3 is proved that can completely satisfy the requirment of the null hypothesis 3. The VWK method with surrogate data can illuminate that not only the action but also fatigue surface EMG signals contain nonlinear dynamic properties.
Chaotic analysis techniques are reviewed and applied to investigate the surface EMG signals. The results show that the surface EMG signals have high-dimension chaotic dynamics by using correlation dimension and largest Lyapunovexpoent techniques. For the estimation of embedding dimension, symplectic principal component analysis method is introduced and discussed. In comparison with correlation dimension algorithm and SVD analysis, symplectic geometry analysis is both very simple and reliable. The results show that symplectic geometry method is useful for determining of the system attractor from the experiment data.
The fractal theory is applied to study the fractal feature of the action surface EMG signal collected from forearm of normal person. The results show that he action surface EMG signal possesses the self-affine fractal characteristic.So, it is difficult to describe the surface EMG signals by using a single fractal dimension.The multifractal dimensionsare used to analyzethe action surface EMG signals during the arm movements. The results indicate that the surface EMG signals are non-uniform fractal structure signals. The multifractal dimension values can be used to identify the surface EMG signals for different movements.
For the nonlinear characteristics of the surface EMG signals, chaos and fractal theories will play the leading role in the nonlinear study of the surface EMG signals. The related methods need to be further researched and developed although these techniques have been applied to analyze the surface EMG signals. It provides a new way for the study of the quantitative analysis of physiology and pathology, sports medicine,clinical medical diagnostics and bionics of robot limb motion.
Theorem 1 proof:
Theorem 2 proof:
Let S as a symplectic transform matrix, M as a Hamilton matrix. Then
So Hamilton matrix M keeps unchanged at symplectic similar transform.
Theorem 5 proof:
Let S1, S2,…, Sn as symplectic matrix, respectively. According Definition 1, there are
So the product of sympletcic matrixes is also a symplectic matrix.
Theorem 6 proof:
In order to prove that H matrix is symplectic matrix, we only need to prove
where
Plugging Eq.(87) into Eq.(86), we have:
Theorem 7 suppose x and yare two unequal ndimension vectors, and
It can be easily deduced from theorem 5, fornon zerondimension vector
It’s easy to testify, elementary reflective arrayHis symmetry matrix
For realsymmetrical matrix A,Householder matrix H can be constructed as follows[73]. NotesA:
First, suppose
select elementary reflective array H(1):
where
so, after H(1)transform, A is changed to a matrix with the first column is all zero except the first element is
Second, the same method is adopted to the second column vector of A(2), let
construct H(2) matrix:
where,
Using H(2), the second column of A(2) can be changed to all zero vector except the first and second elements, namely:
Householder matrix H can be obtained by repeating above mentioned method until A(n) becomes an upper triangle matrix:
This work was supported by the National Natural Science Foundation of China (No. 10872125 and No.69675002), Science Fund for Creative Research Groups of the National Natural Science Foundation of China(no. 50821003), State Key Lab of Mechanical System and Vibration,Project supported by the Research Fund of State Key Lab of MSV, China (Grant no. MSV-MS-2010-08), Key Laboratory of Hand Reconstruction, Ministry of Health, Shanghai, People’s Republic of China, Shanghai Key Laboratory of Peripheral Nerve and Microsurgery, Shanghai, People’s Republic of China, Science and Technology Commission of Shanghai Municipality (no.06ZR14042).We also thank Chinese Academy of Engineering GU Yudong and Professor Zhang Kaili very much for providing related data and valuable discussions.
The human gastrointestinal tract has various microorganisms, and “gut microbiota” has received attentions recently because the microbe population living in human intestine has significant effects to human health. Gut microbiota plays important roles in human, involving in many activities in a host body, for example, metabolism of xenobiotic compounds, immune system, nutrition, inflammation, and behavior. The delivery of prebiotics and probiotics to the human gastrointestinal tract, via dietary products or supplements, is one of the tools for management of microbiota in order to improve host health [1]. Moreover, gut microbiome has interactions with drugs and natural products, producing metabolites, which give effects on efficacy, metabolism, and toxicity of drugs. Gut microbiota plays a role in the metabolism of drugs and natural products, as well as nutrients in diet or food. The conversion of a dietary soybean isoflavone, daidzein (1) or genistein (2), to a bioactive compound, S-equol (3) (Figure 1) [2, 3], is a good example for the role of gut bacteria in the production of pharmacologically active agent in human because S-equol (3) is a potent ligand for estrogen receptor β [4]. Daidzein (1) is also derived from its corresponding isoflavone glycoside, daidzin (4), by Bifidobacterium, a representative of major bacterial species of human origin; this bacterium could transform daidzin (4) to daidzein (1) by cell-associated β-glucosidases (Figure 1) [5]. Moreover, O-desmethylangolensin (5) is also found as an intestinal bacterial metabolite of daidzein (1) [6, 7].
Bioconversion of soybean isoflavones, daidzein (1), genistein (2), and daidzin (4), to S-equol (3) and O-desmethylangolensin (5) by intestinal bacteria.
The transformation of achiral molecule daidzein (1) to a chiral molecule equol, which has one chiral center in its molecule, should provide two possible enantiomers of S-equol (3) and R-equol (3R) (Figure 2). However, gut bacteria selectively gives only S-equol (3), not R-equol (3R); this is interesting because only S-equol (3) has a high affinity to bind with estrogen receptor β, while R-equol (3R) has much less activity [4]. Therefore, S-equol (3), but not R-equol (3R), has high affinity for estrogen receptor β in human, and S-equol (3) has more potent estrogenic activity than estradiol [4]. In animal model, although a mixture of the two enantiomers of equol have the ability to inhibit bone loss in ovariectomized mice [8], S-equol (3) has better inhibitory effects on bone fragility than the racemic mixture containing both S-equol (3) and R-equol (3R) [9].
Structures of two enantiomers of S-equol (3) and R-equol (3R) and the bioconversion of daidzein (1) to S-equol (3) by the bacterium Lactococcus sp. through the metabolites (R)-dihydrodaidzein (6), (S)-dihydrodaidzein (7), and trans-tetrahydrodaidzein (8).
The ability of gut bacteria to selectively produce the correct bioactive isomer of S-equol (3) needed for human is intriguing. Shimada and co-workers identified enzymes involved in the bioconversion of daidzein (1) to S-equol (3) by the bacterium Lactococcus sp. strain 20–92, which was isolated from feces of healthy human [10]. The enzyme daidzein reductase catalyzes the transformation of daidzein (1) to (R)-dihydrodaidzein (6), which is in turn converted to (S)-dihydrodaidzein (7) by the enzyme dihydrodaidzein racemase (Figure 2). The enzyme dihydrodaidzein reductase catalyzes the conversion of (S)-dihydrodaidzein (7) to trans-tetrahydrodaidzein (8), which is converted to S-equol (3) by the enzyme tetrahydrodaidzein reductase [10]. The bioconversion of daidzein (1) selectively to S-equol (3), not R-equol (3R), by gut bacteria provides human the correct enantiomer for binding with estrogen receptor β; this may be host-bacterial mutualism in human intestine. An isoflavone daidzein (1) is found in leguminous plants such as soybeans and other legumes, which have been used as food for human since ancient times. Therefore, it is possible that gut bacteria have experienced with daidzein (1) long time ago, and their enzymatic evolutions lead to the selective bioconversion of daidzein (1) to S-equol (3), which has biological activity for human. Interestingly, many studies revealed that there is the intestinal microbiota-to-host relationship, i.e., a cross talk, between gut microbiota and human host and interactions between gene products from the microbiome with metabolic systems of human diseases such as obesity and diabetes [11].
The conversion of a dietary soybean isoflavone, daidzein (1) or genistein (2), to S-equol (3), by gut bacteria has been known for many years; however, scientists might not be aware of the importance of gut microorganisms in the past. Recently, a number of studies have revealed many essential roles of gut microbiota in human health and diseases. Gut microbiome can transform nutrients and dietary fibers to produce bioactive metabolites, for example, short-chain fatty acids (SCFAs) and nicotinamide, which have a significant impact on human health and diseases. There have been reports on interactions of gut microbiome and compounds, e.g., drugs and natural products, after humans take these compounds as drugs for the treatment of diseases. The metabolites obtained from the metabolism of drugs/natural products by the activities of gut microbiome have either positive or negative effects on therapeutic efficiency. This chapter provides the information of recent studies on the influence of the metabolites produced by gut microbiome on human health and diseases and on the interactions of microbiome and drugs/natural products.
The human gastrointestinal tract has trillions of microorganisms with a complex and diverse community. Gut microbiome is recognized as an “organ” because gut microorganisms have metabolic activities similar to an organ and have several essential functions to human health [12]. It is estimated that microbial cells in the human body are 10 times more than human cells and that gut microbiome has 150 times more genes than human genome [13]. Perturbation of gut microbial communities leads to the imbalance of gut microorganisms, by either reducing or increasing particular microbial species or altering the relative abundance of certain microorganisms; this is collectively known as “dysbiosis.” Microbial dysbiosis can cause certain diseases such as irritable bowel syndrome, diabetes, cancer, inflammatory bowel diseases, and obesity [14, 15, 16]. Gut microorganisms are able to produce many metabolites, which give substantial contributions to human health because they are involved in various physiological processes, i.e., host immunity, cell-to-cell communication, and energy metabolism [17, 18]. The metabolites produced by gut microbiome are linked with human diseases, for example, colorectal cancer [19], depression [20], inflammation and cancer [21], and cardiovascular and metabolic diseases [22, 23]. Among the metabolites produced by gut microbiome, SCFAs considerably play critical roles in human health. Gut microbiome produces acetate (9), propionate (10), and butyrate (11) (Figure 3), the respective conjugate bases of acetic acid, propionic acid, and butyric acid; these SCFAs are from saccharolytic fermentation of dietary fibers by gut microorganisms [24]. Butyrate (11) from the metabolism of gut microbiome could induce differentiation of colonic regulatory T cells in mice, suggesting that gut microorganisms are substantially involved in immunological homeostasis in the gastrointestinal tract of human [25]. SCFAs produced by gut microbiota are significantly linked with hypertension and kidney diseases [26]. SCFAs are vital fuels for intestinal epithelial cells and can maintain intestinal homeostasis; they are involved in the regulation of gut epithelial cells and immunity that is relevant to inflammatory bowel diseases [27, 28]. SCFAs are able to activate G-protein-coupled receptor, for example, GPR43, which has a role in intestinal inflammatory diseases, i.e., inflammatory bowel diseases [29]. Moreover, SCFAs produced by gut microbiome are energy source for colonocytes and can inhibit histone deacetylases, the enzymes catalyzing the removal of acetyl groups from the lysine residue of histone [30]. Recent study revealed that butyrate (11) from the metabolism of gut microbiome could promote histone crotonylation in colon epithelial cells and that the reduction of the gut microbiota leads to many changes in histone crotonylation in the colon [31].
Structures of SCFAs including acetate (9), propionate (10), and butyrate (11).
Recent study revealed that SCFAs produced by gut microbiome had relationships with metabolic diseases [32]. The level increase of butyrate (11) (Figure 3) by gut microbiome can improve insulin response after an oral glucose tolerance test; moreover, the defects in the production or absorption of propionate (10) led to an increased risk of type 2 diabetes [32]. Previous study also demonstrated that type 2 diabetes is linked with changes in the composition of gut microbiome because the profile of gut microorganisms in human with type 2 diabetes is different from that without type 2 diabetes (a control group) [33]. SCFAs are known to have a significant impact on the energy homeostasis, i.e., controlling the energy metabolism; therefore, modulation of SCFAs could be a nutritional target to prevent diseases associated with metabolism disorders, for example, type 2 diabetes and obesity [34]. Gut microbiome is also linked with food allergy in human, and changes in the population and composition of gut microbiota might cause food allergy [35], and the use of gut microbiome is a potential innovative strategy to prevent food allergy in human [36]. In an animal model, certain gut bacteria, e.g., Clostridia species, might be useful for prevention or therapy of food allergy [37]. Recent investigation led by Nagler showed that butyrate (11) (Figure 3) produced by the gut bacterium, Anaerostipes caccae, could contribute to the prevention of milk allergy in children [38]. Germ-free mice colonized with bacteria in feces of healthy infants can protect mice against milk allergy, while those colonized with bacteria in feces of milk allergic infants could not protect mice from milk allergy; this result indicates that gut microbiotas are involved in milk allergy. Detailed analysis revealed that compositions of gut bacteria in healthy infants were different from milk allergic infants, and the gut bacterium, A. caccae, was the key agent to protect against an allergic response to food [38]. A. caccae is a saccharolytic intestinal bacterium producing butyrate (11) [39]. It is known that butyrate (11) is a key energy source for colonic epithelial cells, regulating energy metabolism and autophagy in the mammalian colon [40]. Therefore, butyrate (11) is likely to be the key metabolite responsible for the protection of milk allergy [38]. An independent study revealed that a dietary supplemented with the bacterium Lactobacillus rhamnosus could promote tolerance in infants with cow’s milk allergy by enrichment of butyrate-producing bacterial strains [41]. The increased levels of butyrate (11) in feces of infants who received the supplement with L. rhamnosus were observed in the most tolerant infants against milk allergy [41].
Nicotinamide (12) is an amide derivative of vitamin B3 or niacin or nicotinic acid (13) (Figure 4) and is a substrate for nicotinamide adenine dinucleotide (NAD), a coenzyme in many important enzymatic oxidation–reduction reactions, for example, electron transport chain, citric acid cycle, and glycolysis. Nicotinamide (12) is known to have a role in neuronal systems in the central nervous system, thus implicating in neuronal death and neuroprotection [42]. Recent study led by Elinav revealed that nicotinamide (12) produced by the gut bacterium, Akkermansia muciniphila, significantly protected the progression of the neurodegenerative disease, amyotrophic lateral sclerosis (ALS) [43]. The experiment demonstrated that removal of gut microorganisms by treating mice with antibiotics could promote the ALS symptoms in mice, indicating that gut microbiome modulated the progress of ALS disease [43]. The study showed that the species of gut bacteria in healthy human were different from that in ALS patients; A. muciniphila was abundant in healthy people, while Ruminococcus torques and Parabacteroides distasonis were relatively abundant in ALS patients. Remarkably, transplantation of gut bacteria from human gut to germ-free mice revealed that the gut bacterium A. muciniphila improved the ALS symptoms, while the gut bacteria R. torques and P. distasonis worsened the ALS symptoms [43]. Detailed analysis found that the gut bacterium A. muciniphila provided nicotinamide (12) as a bioactive metabolite that improves the ALS symptoms. Indeed, a direct injection of nicotinamide (12) into mice with ALS could improve a motor-neuron function. The study in 37 patients with ALS revealed that the levels of nicotinamide (12) in cerebrospinal fluid of ALS patients were lower than that in people without ALS. Moreover, analysis of microbial genes involved in nicotinamide synthesis in feces of ALS patients revealed that people with ALS had less number of the genes for nicotinamide synthesis; these genes were mainly from the gut bacterium A. muciniphila. Therefore, it is likely that ALS patients might have less abundance of A. muciniphila in their gastrointestinal tract [43]. This work suggests that gut microbiome has a significant link with human disease pathophysiology and that there is an opportunity to use microbial therapeutic targets for certain diseases. Indeed, a clinical trial on human using the gut bacterium, A. muciniphila, in overweight and obese insulin-resistant volunteers demonstrated that the gut bacterium could reduce insulin resistance indices and could lower the levels of circulating insulin and blood cholesterol, thus improving the profile of blood lipid and insulin sensitivity [44]. This microbial therapeutic approach is safe and may be applied for the treatment of overweight or obese insulin-resistant people.
Structures of nicotinamide (12) and niacin or nicotinic acid (13).
It is known that gut microbiota is significantly associated with autism spectrum disorder, a form of mental disorder with difficulties in social communication and interaction [45]. Intriguingly, a recent study led by Sharon and Mazmanian revealed that gut microbiota could produce neuroactive metabolites which contribute to the pathophysiology of autism spectrum disorder, thus regulating behaviors in mice [46]. The experiment showed that germ-free mice receiving gut microbiota from human donors with autism spectrum disorder could induce autistic behaviors in mice. The metabolites produced by gut bacteria, 5-aminovaleric acid (14) and taurine (15) (Figure 5), were found to modulate behaviors related to autism spectrum disorder. Both 5-aminovaleric acid (14) and taurine (15) are GABAA receptor agonists [47, 48]. Levels of 5-aminovaleric acid (14) in mice with autism spectrum disorder were significantly lower than that in the control mice, while levels of taurine (15) in mice with autism spectrum disorder were ca. 50% less than the control group [46]. Administration of 5-aminovaleric acid (14) and taurine (15) to mice with autism spectrum disorder could improve repetitive and social behaviors, i.e., modulating neuronal excitability in mice brain and improving behavioral abnormalities [46]. This finding suggests that autism spectrum disorder is also related to the influence of gut microbiota; therefore microbiome interventions using fecal microbiota transplantation, as well as supplementation with metabolites produced by gut microorganisms or with probiotics, may improve the quality of life for people with autism spectrum disorder.
Structures of 5-aminovaleric acid or 5-aminopentanoic acid (14) and taurine or 2-aminoethanesulfonic acid (15).
Gut microbiome substantially contributes to human health and diseases, and the metabolites produced by gut microbiome mentioned earlier underscore the importance of gut microorganisms in health and certain diseases in human. Health and diseases of individuals partly rely on the conditions of gut microbiome whether they have healthy gut microbiota or unhealthy ones. Gut microbiota is therefore considered as a “hidden” or “forgotten” human organ [12], involving in pathology of Alzheimer’s disease [49], endocrine organ involving metabolic diseases [50], and chronic gastrointestinal disease [51]. Moreover, gut microbiota is also considered as an “invisible” organ that controls and manipulates the function of drugs [52]. The imbalance of gut microbiota, or known as dysbiosis, leads to unhealthy conditions for human or even causes certain diseases. Therefore, the use of gut microbiota as a therapeutic target for treatments of human diseases is an emerging approach for many diseases, for example, Parkinson’s disease [53], cardiovascular disease [54], metabolic disorders [55], hepatocellular carcinoma [56], nonalcoholic fatty liver disease [57], food allergy [58], and heart failure [59]. Supplementation with probiotics or with health-promoting bacteria is a possible therapeutic method and may widely be used in the near future. Fecal microbiota transplantation or supplementation with metabolites from gut microorganism needs more clinical studies; the two approaches will be a challenging research on gut microbiota in the near future.
It is estimated that a total mass of bacteria in the human body is around 0.2 kg (for people with a weight of 70 kg) and that the densities of commensal microorganisms in the human gastrointestinal tract ranged from 108 to 1011 bacterial cells/g [60]. Oral administration of drugs delivers drugs to the gastrointestinal tract that contains high densities of gut microorganisms, which could encode 150-fold more genes than those of the human genome [61]; therefore, gut microbes are able to encode many enzymes with drug-metabolizing potential [62]. Gut microbiota is recognized as an “invisible organ” responsible for controlling drug functions and modulation of drug metabolism processes [52]. Normally, antibiotic drugs give direct effects toward microorganisms in the human gastrointestinal tract, providing either negative or positive (beneficial) effects to the composition of gut microbiota [63]. However, intestinal microbiota have many important roles in maintenance of human health; therefore, perturbation of gut microbiome by antibiotics could give negative impact to human, for example, loss of colonization resistance that can prevent invading microorganisms colonizing in the human gastrointestinal tract [64]. In addition to antibiotic drugs, a recent study led by Typas demonstrated that nonantibiotic drugs also gave extensive impact on human gut bacteria because around 24% of 1197 drugs showed antibacterial activity toward at least one strain of gut bacteria [65]. This is considered as “antibiotic-like side effects” of nonantibiotic drugs, which could potentially promote antibiotic resistance that is one of the major public health problems worldwide. This finding provides essential information for drug discovery research, i.e., addressing a potential new side effect of drugs and repurposing of nonantibiotic drugs as antibacterial agents.
The next sections will highlight the interactions of gut microbiome, especially the chemistry of the drug metabolites produced by gut microorganisms, toward certain drugs and natural products. The metabolism of drugs or natural products by gut microbiome could lead to the production of bioactive metabolites, which have either beneficial effects or negative properties (i.e., reducing efficacy of drugs or natural products). The study on the interactions of gut microbiota and drugs or natural products as part of drug development process is discussed in the next sections.
Once drugs enter the human gastrointestinal tract, they encounter trillions of microorganisms, which are able to encode 150-fold more genes than human genome [61]. A number of enzymes encoded by gut microbial genes catalyze the biotransformation of drugs, producing bioactive metabolites, which have effects on human health [60]. Advances in liquid chromatography-mass spectrometry (LC–MS) technology allow the identification of the metabolites produced by gut microbiome, as well as detailed study of pharmacokinetics of drugs and their metabolites, while genome sequencing substantially assists the identification of genes encoding enzymes in gut microorganisms. Zimmermann and co-workers investigated the drug metabolism of an antiviral nucleoside drug, brivudine (16), which is used for the treatment of herpes zoster virus; the study was performed using mice inoculated with mutant microbiota [66]. It was found that the bioconversion of brivudine (16) to bromovinyluracil (18) (or 5-(E)-(2-bromovinyl)uracil) was achieved by enzymes from both mammalian cells and gut microbial communities isolated from mice, suggesting that both host and microbiota are capable of such biotransformation (Figure 6). Previously, intestinal anaerobic bacteria were found to convert another antiviral drug, sorivudine (17), to bromovinyluracil (18) (Figure 6) [67].
Biotransformation of antiviral drugs brivudine (16) and sorivudine (17) to bromovinyluracil (18) by gut bacteria.
Gut bacteria, Bacteroides thetaiotaomicron and B. ovatus, were the major species having the highest metabolic activity to convert brivudine (16) to bromovinyluracil (18) [66]. Comparison of serum kinetics of brivudine (16) and bromovinyluracil (18) in conventional (a control with bacteria) and germ-free mice after feeding with the drug brivudine (16) suggested that intestinal bacteria contributed to the amount of bromovinyluracil (18) in serum because the level of bromovinyluracil (18) in conventional mice serum was five times higher than that of germ-free mice [66]. The gene, bt4554, encoding the enzyme purine nucleoside phosphorylase necessary for the metabolism of brivudine (16) is present in B. ovatus and conserved in the bacterial phylum Bacteroidetes; the expression of the gene bt4554 is a rate-limiting step [66]. The gut bacterium, B. thetaiotaomicron, was found to completely metabolize the drug brivudine (16) to bromovinyluracil (18), which is absorbed from both the cecum and colon. This study was also able to predict the levels in serum and sources of the metabolite bromovinyluracil (18) derived from a drug sorivudine (17) (Figure 6) [66].
Zimmermann and co-workers also used clonazepam (19) (Figure 7), an anticonvulsant and antianxiety drug, as a model [66]; the metabolism of this drug in rats gave metabolic products through nitroreduction, oxidation, glucuronidation, and enterohepatic cycling [68]. After an oral administration of a drug clonazepam (19) to mice, 7-NH2-clonazepam (20) and 7-NH2-3-OH-clonazepam (21) were found as major metabolites in serum of the conventional mice (Figure 7). The host-microbiome pharmacokinetic model revealed that 7-NH2-clonazepam (20) in serum was substantially from a microbial contribution. Experiments also revealed that intestinal microbes could convert glucuronyl-3-OH-clonazepam (23) to 3-OH-clonazepam (22), which in turn transformed to 7-NH2-3-OH-clonazepam (21) by microbial reduction (Figure 7) [66]. The study established a pharmacokinetic model that can predict microbiome or host (human) contributions to drug metabolism, e.g., the ability to distinguish drug-metabolizing activity by human or gut bacteria [66]. This research model is particularly useful for the study on drug metabolism in an animal model.
Biotransformation of clonazepam (19) to the metabolites 20–23 by human intestinal microbes.
Gut microbiome has potential ability to metabolite many drugs, thus affecting the therapeutic efficacy due to lower concentrations of drugs. The study on the drug metabolism of 271 commonly used drugs by gut bacteria revealed that, after incubation of drugs with gut bacteria, the levels of 176 drugs (accounting for two thirds of 271 drugs) were significantly reduced, indicating that these drugs were metabolized by gut bacteria [62]. Intriguingly, each bacterial strain (from 76 human gut bacterial strains) could metabolize up to 11–95 drugs [62]. This result suggests that, when designing the drug molecules, the drug metabolism by gut microbes should be seriously considered, particularly the drugs delivered by an oral administration. Therefore, the action of gut microbiome toward individual drug candidates should also be evaluated during the drug development process. Untargeted metabolomics analysis is used to identify products derived from drug metabolism by gut bacteria, and it could properly identify the metabolites from microbial metabolism of drugs [62]. Some drugs, for example, paliperidone, sulfasalazine, and pantoprazole, were previously investigated for their metabolism by gut microbes [69]. Detailed analysis by high-resolution mass spectrometry (HRMS) revealed that drugs with an acetyl ester or an alkene functional group, such as norethisterone acetate (24), drospirenone (25), and roxatidine acetate (26), were metabolized through either deacetylation (removing C2H2O) or hydrogenation (adding H2) by gut bacteria (Figure 8) [62]. Gut bacteria metabolized drugs with aliphatic hydroxyl or amine functional group such as dasatinib (27), fluphenazine (28), and primaquine (29) through propionylation (adding C3H4O), giving their corresponding O- or N-propionyl products 30, 31, and 32, respectively (Figure 8). The HRMS data clearly indicated the mass difference of 56.026 unit of a propionyl group between the drug and its corresponding derivative [62].
Structures of the drugs, norethisterone acetate (24), drospirenone (25), and roxatidine acetate (26) and biotransformation of dasatinib (27), fluphenazine (28), and primaquine (29) to their corresponding products 30, 31, and 32, respectively, by gut bacteria.
Zimmermann and co-workers investigated the metabolism of drug in mice model and in human gut microbial communities using a corticosteroid drug, dexamethasone (33), as a model (Figure 9) [62]. It is known that this class of drug is metabolized by the bacterium Clostridium scindens through the side-chain cleavage, known as the desmolytic activity, to produce the active androgen form of the drug, dexamethasone-desmo (34) (Figure 9) [70, 71]. Levels of dexamethasone-desmo (34) were measured after an oral administration of dexamethasone (33) to germ-free mice and to mice that have only one bacterial species of C. scindens, technically known as gnotobiotic mice (GNC. scindens). Although dexamethasone (33) was found in the cecum of germ-free mice and gnotobiotic mice, the levels of the drug were significantly reduced in gnotobiotic mice, suggesting that the bacterium C. scindens associated in these mice is involved in the drug metabolism. Accordingly, levels of the androgen form of the drug, dexamethasone-desmo (34), which are derived from the metabolism of dexamethasone (33), were higher in both serum and cecum of gnotobiotic mice than that of germ-free mice [62]. Moreover, similar corticosteroid drugs, i.e., prednisone (35), prednisolone (36), cortisone (37), and cortisol (38), were also metabolized by the intestinal bacterium C. scindens through the desmolytic activity, giving the metabolite products of prednisone-desmo (39), prednisolone-desmo (40), cortisone-desmo (41), and cortisol-desmo (42), respectively (Figure 9). However, when incubating the drug dexamethasone (33) with gut bacterial community isolated from 28 healthy human participants under anaerobic condition, the drug-metabolizing activity had considerable interpersonal variation as suggested by level variations of the drug metabolite, dexamethasone-desmo (34) [62]. This result implies that dexamethasone (33) is also metabolized by other gut bacterial species, not only C. scindens.
Gut bacterial metabolism of corticosteroid drugs, dexamethasone (33), prednisone (35), prednisolone (36), cortisone (37), and cortisol (38), to their respective products 34, 39, 40, 41, and 42 via the desmolytic activity.
Systematic identification of drug-metabolizing genes encoded by gut bacteria provides the mechanistic insights into drug metabolism in human [62]. Genes of the gut bacterium Bacteroides thetaiotaomicron were cloned into Escherichia coli, leading to the identification of new 16 gene products, which were able to metabolite 18 drugs to 41 different metabolites [62]. Certain gene products have specificity and cross-activity, and gene deletion and complementation techniques revealed the mechanisms of individual gene products. For instance, the bt2068 gene encodes the enzyme that could reduce (adding H2) norethisterone acetate (24) (Figure 8), as well as other similar steroid drugs such as levonorgestrel and progesterone, while the bt2367 gene encodes acyltransferase that converts the drug pericyazine (43) to both acetyl- and propionyl-pericyazine products, e.g., acetyl-O-pericyazine (44) and propionyl-O-pericyazine (45), respectively (Figure 10) [62]. It is known that the metabolism products of a drug diltiazem (46) are N-desmethyldiltiazem (47), N,N-didesmethyldiltiazem (48), O-desmethyldiltiazem (49), N,O-didesmethyldiltiazem (50), desacetyldiltiazem (51), desacetyl-N-desmethyldiltiazem (52), desacetyl-N,N-didesmethyldiltiazem (53), desacetyl-O-desmethyldiltiazem (54), and desacetyl-N,O-didesmethyldiltiazem (55) (Figure 10) [72]. The gene bt4096 in gut bacteria is responsible for the deacetylation of diltiazem (46) and its metabolites 47–50 to give their corresponding deacetylated products 51–55, respectively (Figure 10) [62]. This study suggests that gut bacteria substantially contribute to drug metabolism in the human gastrointestinal tract, and the metabolism of drug candidates by gut microbiome should be studied as a part of the drug development processes.
Metabolism of pericyazine (43) to acetyl-O-pericyazine (44) and propionyl-O-pericyazine (45) and metabolism of diltiazem (46) to the metabolite products 47–55 by gut bacteria.
The drug metabolism by gut microbiome can give negative effects to drug efficacy, thus leading to the decrease in efficiency and potency of certain drugs. L-dopa or levodopa (56) (Figure 11) is the first-line drug for the treatment of Parkinson’s disease; the metabolism of this drug by gut microbiome provides negative effects for Parkinson’s patients. The drug L-dopa (56) can cross the blood–brain barrier, entering the central nervous system and then transforming to a neurotransmitter, dopamine (57), by the enzyme pyridoxal phosphate
Bioconversion of L-dopa (56) to dopamine (57) and m-tyramine (58) by gut bacteria and structures of inhibitors of amino acid decarboxylases, carbidopa (59), (S)-α-fluoromethyltyrosine (60), benserazide (61), and methyldopa (62).
Recent study led by Prof. Balskus revealed that the gut bacterium Enterococcus faecalis has the tyrDC gene encoding the enzyme tyrosine decarboxylase that is able to decarboxylate both L-dopa (56) and an amino acid, tyrosine [77]. Moreover, the gut bacterium Eggerthella lenta has the dadh gene encoding a molybdenum cofactor-dependent dopamine dehydroxylase, which is the enzyme responsible for the dehydroxylation of dopamine (57) to m-tyramine (58) (Figure 11). The metabolism of L-dopa (56) and dopamine (57) in complex gut microbiotas of Parkinson’s patients is dependent on the tyrDC and dadh genes [77]. The study demonstrated that carbidopa (59), an inhibitor of pyridoxal phosphate
Gut microbiota can improve therapeutic efficiency of certain drugs for particular treatments. Cancer immunotherapy is relatively new for cancer treatment using human immune system to control and eradicate cancer cells, and it is more precise and personalized, thus providing more effectiveness with fewer side effects than other cancer treatments. Gut microbiota was found to play a role in cancer immunotherapy targeting CTLA-4, a protein receptor downregulating the immune system, because anticancer effects of CTLA-4 blockade were found to depend on gut bacteria of Bacteroides species, e.g., Bacteroides thetaiotaomicron or B. fragilis [79]. The study demonstrated that germ-free mice did not show the response to CTLA blockade, thus defecting an anticancer property of the drug. Indeed, this drug deficiency could be improved by gavage with the gut bacterium B. fragilis through immunization with the bacterium polysaccharides or by adoptive transfer of B. fragilis-specific T cells. Therefore, this research study demonstrates that the gut bacterium could help patients treated with a monoclonal antibody drug for the treatment of cancer targeting CTLA-4 [79].
Gut microbiome also improves therapeutic effect of a cancer immunotherapy targeting immune checkpoint inhibitor via the PD-1/PD-L1 pathway [59]. Antibiotics are found to give negative effects for patients treated with cancer immunotherapies as they inhibit the efficacy of immune checkpoint inhibitor drug that targets the programmed cell death receptor of the PD-1/PD-L1 pathway [59]. Moreover, suppression of growth of gut bacteria by antibiotic drugs leads to the decrease of drug efficacy, suggesting that gut microorganisms are important for this cancer therapy. The study demonstrated that gut microbiota provided significant effects on cancer immunotherapies targeting the PD-1/PD-L1 interaction because there was substantial association between commensal microorganisms and therapeutic response of anticancer drug that inhibits the activity of PD-1 and PD-L1 immune checkpoint proteins [80]. Gut bacteria including Collinsella aerofaciens, Enterococcus faecium, and Bifidobacterium longum were found to be associated with the improvement of this cancer immunotherapy. Intriguingly, reconstitution of germ-free mice with fecal samples from patients with good drug response could help to control tumor, leading to better efficacy of anti-PD-L1 cancer therapy [80]. An independent study revealed that the gut bacterium Akkermansia muciniphila assists cancer immunotherapy targeting the PD-1/PD-L1 interaction toward epithelial tumors [81]. The study on fecal microbiota transplantation demonstrated that germ-free or antibiotic-treated mice receiving gut bacteria from patients with good response to cancer immunotherapy have significant therapeutic improvement, while those receiving the samples from nonresponding patients do not have such improvement for cancer immunotherapy [81]. Restoration of the drug efficacy in germ-free mice receiving the samples from nonresponding patients was simply achieved by oral supplementation with the gut bacterium A. muciniphila, indicating the benefit of gut microbiota for this cancer immunotherapy. Another independent research also found similar benefits of gut microbiota on anti-PD-1 immunotherapy in melanoma patients; this study investigated microbiome samples from 112 patients with metastatic melanoma and found that there were substantial differences in the composition and diversity of gut microbiome obtained from patients with good drug response and from nonresponding patients [82]. Patients with good response to immunotherapeutic PD-1 blockade have abundance of gut bacteria of the family Ruminococcaceae and Faecalibacterium, while patients with poor response to immunotherapeutic PD-1 blockade tend to have relative abundance of Bacteroidales. It is possible that patients with a favorable gut microbiome, e.g., Ruminococcaceae and Faecalibacterium, toward the immunotherapeutic PD-1 blockade therapy have improved systemic and immune responses mediated by certain factors such as improvement of effector T cell function in the periphery, increase of antigen production, and improvement of the tumor microenvironment [82].
Gut microbiota also has an important role in chemotherapy for cancer treatment because they can modulate drug efficacy, for example, eliminating the anticancer properties of the drug or mediating toxicity [83]. Cyclophosphamide (63) (Figure 12) is a drug used in cancer chemotherapy for many types of cancers, as well as for autoimmune diseases, and its mechanism is through the stimulation of anticancer immune responses. In a mouse model, the composition of gut microbiota is changed after administration of cyclophosphamide (63), and this drug induces the translocation of certain Gram-positive bacteria into secondary lymphoid organs. Gut bacteria could stimulate certain immune responses beneficial to cancer therapy. Germ-free mice carrying tumor treated with antibiotics to kill Gram-positive bacteria had less therapeutic response, and their tumors exhibited resistance to the drug cyclophosphamide (63), suggesting that gut microbiota improves anticancer immune response [84]. Gut bacteria, Enterococcus hirae and Barnesiella intestinihominis, were found to help cyclophosphamide-induced therapeutic immunomodulatory response, thus improving the efficacy of this alkylating immunomodulatory drug [85].
Structure of an anticancer drug, cyclophosphamide (63).
The research studies mentioned earlier demonstrate the interactions of drugs and gut microbiome that provide beneficial effects on cancer therapy. However, interactions of gut microbiome and drugs can also give negative influence in cancer treatment, for example, the treatment of an anticancer drug, gemcitabine (64) or 2′,2′-difluorodeoxycytidine (Figure 13), which is a derivative of cytidine nucleoside base. A research led by Straussman showed that the bacterium Mycoplasma hyorhinis was found to be the cause of gemcitabine (64) resistance in colon carcinoma models [86]. In a colon cancer mouse model, M. hyorhinis could metabolize gemcitabine (64) to the corresponding deaminated derivative, 2′,2′-difluorodeoxyuridine (65), that does not have anticancer activity (Figure 13). The conversion of gemcitabine (64) to 2′,2′-difluorodeoxyuridine (65) was previously reported [87], and the nucleoside-catabolizing enzymes, i.e., cytidine deaminase, in the bacterium, M. hyorhinis, were also identified [88]. Straussman and co-workers analyzed genes and genomes of 2674 bacterial species and found that most of the Gammaproteobacteria class had the gene coding for the enzyme cytidine deaminase, thus potentially mediating gemcitabine resistance [86]. In a mouse model of colon carcinoma, mice receiving an antibiotic, ciprofloxacin, showed a good response to the anticancer drug gemcitabine (64), indicating that suppression of the growth of certain bacteria led to the improvement of the drug efficacy. Investigation of human pancreatic ductal adenocarcinoma collected from pancreatic cancer surgery revealed that there were intratumor bacteria, mainly belonging to the class Gammaproteobacteria such as Enterobacteriaceae and Pseudomonadaceae families in these samples; the intratumor bacteria can mediate resistance to chemotherapy of the drug gemcitabine (64) [86]. Therefore, the metabolism of the drug gemcitabine (64) to 2′,2′-difluorodeoxyuridine (65) by gut microbiota provides the negative effects for cancer treatment. This study underscores the importance of the research on drug metabolism by gut microbiome, which should be investigated for the new drug candidates during the drug development processes.
Biotransformation of gemcitabine (64) to its metabolite 2′,2′-difluorodeoxyuridine (65); structures of anticancer drugs, oxaliplatin (66) and fluorouracil or 5-FU (67), and autophagy lysosomal inhibitor, chloroquine (68).
Additional example for the negative effects of gut microbiota for cancer chemotherapy is the treatment of colorectal cancer with the drugs, oxaliplatin (66) and fluorouracil or 5-FU (67) (Figure 13); the gut bacterium Fusobacterium nucleatum was found to promote resistance to chemotherapy for colorectal cancer [89]. Analysis of colorectal cancer tissues collected from patients with recurrence or without recurrence of cancer revealed that the bacterium F. nucleatum is associated with the recurrence of colorectal cancer, which is derived from chemoresistance toward the drugs [89]. Cultivation of colorectal cancer cells co-cultured with F. nucleatum revealed that the bacterium potentially activated an autophagy pathway in colorectal cancer cells. An addition of a known autophagy lysosomal inhibitor, chloroquine (68) (Figure 13), could inhibit autophagic flux in the F. nucleatum-cultured cells, confirming the autophagy activation induced by the gut bacterium F. nucleatum [89]. Moreover, this bacterium reduced cell apoptosis of colorectal cancer cells, indicating that it specifically induced resistance toward the drugs oxaliplatin (66) and fluorouracil (67). Co-cultured cancer cells with the bacterium F. nucleatum and treated cancer cells with the drugs oxaliplatin (66) and fluorouracil (67) in the presence of autophagy lysosomal inhibitor, chloroquine (68), could eradicate chemoresistant effect, strongly confirming that the bacterium F. nucleatum induced chemoresistance through the autophagy pathway [89]. Detailed mechanistic study revealed that the bacterium F. nucleatum mediated chemoresistance through the TLR4 and MYD88 signaling pathway [89]. An independent study showed that the gut bacterium F. nucleatum is a diagnostic marker of colorectal cancer because patients with this cancer generally have high density of this bacterium in tumor cells [90]. Several studies have shown the prevalence of the bacterium F. nucleatum in colorectal tissues and fecal samples of patients, and those with high density of this bacterium tend to have lower rate of survival [91]. Therefore, manipulation of the bacterial population of F. nucleatum might be useful for the treatment of colorectal cancer, and this bacterium is potentially a diagnostic and/or prognostic marker for colorectal cancer.
In addition to drug metabolism, gut microbiota is also involved in drug–drug interactions when patients take two drugs at the same time, particularly when using antibiotics together with other drugs. Several studies have demonstrated the effects of antibiotic drugs on the metabolic activities of gut microbiota toward drugs and phytochemicals [92]. An example of a drug–drug interaction is the contribution of an antibiotic drug, amoxicillin (69), to a nonsteroidal anti-inflammatory drug aspirin (70) (Figure 14) [93]. It is worth mentioning that aspirin (70) is used not only for a pain reliever but also for primary prevention of cardiovascular disease [94] and cancer chemoprevention [95]. Recent study showed that amoxicillin (69) potentially affected the composition of gut microbiota by reducing number and species of intestinal bacteria in rats; the abundance of the gut bacteria, Prevotella copri and Helicobacter pylori, was reduced significantly after rats receiving amoxicillin (69) [93]. Gut microorganisms in rats could metabolite aspirin (70) to salicylate or salicylic acid (71) (Figure 14). Salicylate is a conjugate base of salicylic acid (71). It is known that the drug aspirin (70) is not responsible for a pain relief, but its metabolite, salicylic acid (71), is the active metabolite responsible for a pain relief with anti-inflammatory effect [96]. Therefore, gut microbiota plays an important role in the biotransformation of the drug aspirin (70) into the active metabolite, salicylic acid (71). After an oral administration of an antibiotic drug amoxicillin (69) to rats, the reduction of the metabolism of aspirin (70) into salicylic acid (71) was observed, suggesting the decrease of gut microbiota by amoxicillin (69) led to the reduction of the biotransformation of aspirin (70) into salicylic acid (71). Further study on the pharmacokinetics of aspirin (70) in rats revealed that amoxicillin (69) significantly affected the pharmacokinetic properties of aspirin (70) [93]. This study indicates that changes of the composition of gut microbiome by antibiotic drugs could substantially disturb the therapeutic effect of other drugs.
Structures of amoxicillin (69), aspirin (70) and its metabolite, salicylate or salicylic acid (71), and nifedipine (72).
Previous study also showed that antibiotics substantially reduced the metabolic activity of gut microbiota toward aspirin (70), leading to the reduction of an antithrombotic effect of aspirin (70) [97]. Moreover, environmental changes, e.g., high-altitude hypoxia, also give effects on the pharmacokinetics and pharmacodynamics of aspirin (70) because of the changes in gut microbiota [98]. In an animal model, the plateau hypoxic environment affected the composition of gut microbiome because it increased the bacterial species of Bacteroides in rat feces but reduced numbers of the bacteria of the genus Prevotella, Coprococcus, and Corynebacterium. Changes in gut microbiome affected the metabolism of aspirin (70), thus altering the bioavailability of aspirin (70) in patients [98]. Plateau hypoxic environment also has the effects on the drug nifedipine (72), which could be metabolized by gut microorganisms (Figure 14) [99]. Nifedipine (72) is a drug for the treatment of hypertension, precordial angina, and certain vascular diseases. Plateau hypoxic environment was found to alter the composition of gut microbiota in an animal model, thus affecting the bioavailability of nifedipine (72) [99].
Recent study led by Kittakoop revealed that valproic acid or valproate (73) (Figure 15), an anticonvulsive drug used for treatments of epilepsy and bipolar disorder, had effects on the biosynthesis of fatty acids in microorganisms including representative gut microbiome [100]. Valproic acid (73) is also an epigenetic modulator, acting as an inhibitor of histone deacetylase [101]. Initially, Kittakoop and co-workers employed “One strain many compound” (OSMAC) approach using the marine fungus Trichoderma reesei treated with an epigenetic modulator, valproic acid (73), aiming to modulate the fungus T. reesei to produce new natural products, which are secondary metabolites. However, valproic acid (73) was found to have the effects on the biosynthesis of fatty acids, which are primary metabolites, instead of natural products that are secondary metabolites [100]. The study revealed that valproic acid (73) at a concentration of 100 μM could either inhibit or induce the biosynthesis of certain fatty acids in fungi, yeast, and bacteria. Valproic acid (73) inhibited the biosynthesis of palmitoleic acid (C16:1), α-linolenic acid (C18:3), arachidic acid (C20:0), and lignoceric acid (C24:0) in the fungus Fusarium oxysporum, while it induced the production of α-linolenic acid (C18:3) in the fungus Aspergillus aculeatus [100]. The bacterium of the genus Pediococcus is commonly found as gut microbiome in humans and animals [102]; valproic acid (73) was found to inhibit the production of lignoceric acid (C24:0) in the bacterium, Pediococcus acidilactici [100]. The yeast Candida utilis was found as gut microbiome in pediatric patients with inflammatory bowel disease [103]; valproic acid (73) inhibited the biosynthesis of palmitoleic acid (C16:1) and α-linolenic acid (C18:3) in C. utilis [100]. The yeast Saccharomyces cerevisiae was previously found as a prevalent gut microbiome in human [104], and the drug valproic acid (73) was found to inhibit the production of α-linolenic acid (C18:3) in the yeast S. cerevisiae [100]. Interestingly, valproic acid (73) could induce the biosynthesis of trans-9-elaidic acid (74) (Figure 15) in the yeast Saccharomyces ludwigii [100]. In human, trans-9-elaidic acid (74) could increase intracellular Zn2+ in macrophages and inhibit β-oxidation in peripheral blood macrophages [105, 106]; this suggests that the production of trans-9-elaidic acid (74) in gut microorganisms induced by the drug valproic acid (73) may indirectly give the effects to human. Valproic acid (73) also had effects on the biosynthesis of polyketides because it substantially reduced the production of austdiol (75) (90% reduction) and quadricinctone A (76) (50% reduction) (Figure 15), which are the polyketides of the fungus Dothideomycetes sp. [100]. The biosynthesis of fatty acids is considerably similar to that of polyketides, i.e., sharing the same catalytic roles and biosynthetic precursors [107]. Therefore, the drug valproic acid (73) possibly gives effects on the biosynthetic pathways of both fatty acids and polyketides because of their biosynthetic similarities. Gut microbes have biosynthetic gene clusters involving in the biosynthesis of many bioactive natural products including polyketides [108]; some natural products produced by gut microbiome have biological activities. This study suggests that commonly used drugs could potentially give the effects on the biosynthesis of secondary metabolites (natural products) of gut microbiome.
Structures of valproic acid or valproate (73), trans-9-elaidic acid (74), austdiol (75), and quadricinctone A (76).
Traditional medicine and natural products have significant interactions with gut microbiome. Many studies revealed that dietary natural products modulating gut microbiota are useful for prevention and management of diabetes mellitus [109]. Recent study revealed that a traditional Chinese herbal formula and an antidiabetic drug, metformin (77) (Figure 16), could improve the treatment of type 2 diabetes with hyperlipidemia by enriching certain beneficial species of gut bacteria, for example, Faecalibacterium sp. and Blautia [110]. The study was carried out in 450 patients with type 2 diabetes and hyperlipidemia, and the profiles of gut microbiota were analyzed using fecal samples in patients treated with metformin and a traditional Chinese herbal formula. An antidiabetic drug metformin (77) and herbal medicine significantly changed the gut microbiota profile that led to the enhancement of therapeutic effects of the drugs [110]. The traditional Chinese herbal formula used in the study contains the plants including Coptis chinensis, Momordica charantia, Rhizoma anemarrhenae, and Aloe vera, as well as red yeast rice from the fermentation; this herbal recipe is practically used in clinical application [110]. Among the plants used in this formula, Coptis chinensis contains an alkaloid berberine (78) (Figure 16). An independent study revealed that berberine (78) could significantly change the composition of gut microbiota in high-fat diet-fed rats [111]. An alkaloid berberine (78) was able to enrich selectively short-chain fatty acid-producing bacteria such as the genus Blautia and Allobaculum [111]. Another independent study also revealed that both metformin (77) and berberine (78) could change profiles of gut microbiota in high-fat diet-induced obesity in rats [112]. Substantial reduction of the diversity of gut microbiota was observed by both metformin (77) and berberine (78) because 60 out of the 134 operational taxonomic units were decreased after treatment with both drugs. However, there were considerable increases in short-chain fatty acid-producing bacteria, e.g., the genus Butyricicoccus, Blautia, Allobaculum, Phascolarctobacterium, and Bacteroides, after treatment with both metformin (77) and berberine (78) [112]. Therefore, in addition to the direct benefit toward the treatment of diabetes and obesity, the drugs, metformin (77) and berberine (78), could also improve gut microbiota profile by increasing short-chain fatty acid-producing bacteria and thus mediating their useful effects on the host [112]. As mentioned earlier in Section 2, gut microbiomes that produce short-chain fatty acids provide many beneficial effects on human health [24, 25].
Structures of metformin (77), berberine (78), and theobromine (79).
Recent study revealed that berberine (78) could prevent ulcerative colitis by modifying gut microbiota and regulating T regulatory cell and T helper 17 cell in a dextran sulfate sodium-induced ulcerative colitis mouse model [113]. The diversity of gut microbiota was reduced by berberine (78), which markedly interfered the abundance of certain bacterial genus such as Bacteroides, Desulfovibrio, and Eubacterium. Therefore, the mechanisms of berberine (78) for the prevention of ulcerative colitis are by regulating the balance of T regulatory cell and T helper 17 cell, as well as by modifying gut microbiota [113]. Theobromine (79) (Figure 16) is a xanthine alkaloid of cocoa beans and found in chocolate, and its structure is closely related to caffeine. A cocoa-enriched diet containing theobromine (79) could decrease the intestinal immunoglobulin A secretion and immunoglobulin A-coating bacteria, i.e., the genus of Bacteroides, Staphylococcus, and Clostridium [114]. A cocoa-enriched diet had effects on a differential toll-like receptor pattern, which led to changes in the intestinal immune system [114]. Moreover, further experiments in rats revealed that a diet containing 10% cocoa and a diet supplemented with 0.25% theobromine (79) could reduce the gut bacterium Escherichia coli, while a diet with 0.25% theobromine (79) reduced the gut bacterial community of Clostridium histolyticum, C. perfringens, Streptococcus sp., and Bifidobacterium sp. [115]. The amounts of short-chain fatty acids increased after feeding rats with a diet containing 10% cocoa and that supplemented with 0.25% theobromine (79), while both diets decreased the abundance of immunoglobulin A (IgA)-coated bacteria. It is worth mentioning that gut IgA-coated bacteria could potentially cause intestinal disease such as inflammatory bowel disease, and eradication of these bacteria may prevent or reduce intestinal disease development [116]. Therefore, the active natural product theobromine (79) in cocoa able to reduce the amounts of immunoglobulin A-coated bacteria, and to modify the profile of gut microbiota, provides beneficial effects on human health [115].
It is known that berberine (78) has poor solubility; however, it can show effectiveness for the treatment of certain diseases; therefore, there might be a specific mechanism to deliver berberine (78) to an organ system. In an animal model, berberine (78) was found to convert to dihydroberberine (80) in an intestinal ecosystem of rats (Figure 17); the metabolite dihydroberberine (80) exhibited much better absorption rate than its parent drug, berberine (78) [117]. Incubation of berberine (78) with human gut bacteria isolated from gastrointestinal human specimens also produced dihydroberberine (80), and the amounts of dihydroberberine (80) obtained from the biotransformation of gut bacteria were higher than that obtained from other bacteria, which were not gut bacteria and used as the control. This experiment confirmed that gut microbiota could convert berberine (78) into its absorbable form, dihydroberberine (80); therefore intestinal microbiota is considered to be a “tissue” or an “organ” that is able to transform berberine (78) into an absorbable form, dihydroberberine (80) [117]. Mechanistic study revealed that gut microbiome uses the enzyme nitroreductases to catalyze the conversion of berberine (78) to dihydroberberine (80) (Figure 17). Dihydroberberine (80) was found to be absorbed in intestinal epithelia, but it was reverted to the active form berberine (78) soon after entering tissues of the intestinal wall. Detailed analysis showed that the conversion of dihydroberberine (80) back to berberine (78) was by a nonenzymatic oxidation through multi-faceted factors, for example, superoxide anion and metal ions, which occurred in intestinal epithelial tissues (Figure 17) [117]. Previous report demonstrated that dihydroberberine (80) in its sulfate form, e.g., dihydroberberine sulfate, also showed better absorption in the intestine than its parent drug, berberine (78) [118]. Recent independent studies revealed that dihydroberberine (80) has interesting biological activities, for example, anti-inflammatory activity through dual modulation of NF-κB and MAPK signaling pathways [119], synergistic effects with an anticancer drug sunitinib on human non-small cell lung cancer cell lines by inflammatory mediators and repressing MAP kinase pathways [120], and inhibition of ether-a-go-go-related gene (hERG) channels expressed in human embryonic kidney 293 (HEK293) cells [121]. It is worth mentioning that the metabolite products from gut biomicrobiota, i.e., dihydroberberine (80), have different biological activity from its parent drug, berberine (78). Therefore, the drug development process should include a research study on the metabolism of natural products (as drug candidates) by gut microbiota.
Bioconversion of berberine (78) into an absorbable form, dihydroberberine (80), by gut bacteria; absorption of dihydroberberine (80) into the intestine wall and nonenzymatic conversion of dihydroberberine (80) to the active form berberine (78).
Demethyleneberberine (81), berberrubine (82), jatrorrhizine (83), and thalifendine (84) were found as major metabolites in rats after an oral administration of berberine (78) (Figure 18) [122]. Comparison of the levels of these metabolites in conventional rats (a control group) and pseudo germ-free rats revealed that liver and intestinal bacteria were involved in the metabolism and disposition of berberine (78) in vivo. It is worth mentioning that some metabolites from this biotransformation exert important biological activities. For example, demethyleneberberine (81) inhibits oxidative stress, steatosis, and mitochondrial dysfunction in a mouse model, which is a potential therapy for alcoholic liver disease [123]. Berberrubine (82) was found to reduce inflammation and mucosal lesions in dextran sodium sulfate-induced colitis in mice, which might be useful for the treatment of ulcerative colitis [124]. Jatrorrhizine (83) could reduce the uptake of 5-hydroxytryptamine and norepinephrine by the inhibition of uptake-2 transporters, thus exerting antidepressant-like action in mice [125]. Therefore, the biotransformation of berberine (78) by gut bacteria leads to the production of bioactive metabolites, which have interesting pharmacological properties; this underscores the impact of gut microbiota in the drug development process for natural products.
Biotransformation of berberine (78) to demethyleneberberine (81), berberrubine (82), jatrorrhizine (83), and thalifendine (84) by gut bacteria.
Since there are interactions between gut microbiota and natural products, efforts have been made to use natural compounds for the treatment of gut microbiota dysbiosis, which is the imbalance of microorganisms in the human gastrointestinal tract. Dysbiosis of gut microbiota is strongly associated with some diseases such as type 2 diabetes, inflammatory bowel disease, obesity, and nonalcoholic fatty liver disease [16, 126]. Alkaloids of a medicinal plant, Corydalis saxicola, were used to prevent gut microbiota dysbiosis in an animal model [127]. Major alkaloids in Corydalis saxicola are berberine (78), jatrorrhizine (83), dehydrocavidine (85), palmatine (86), and chelerythrine (87) (Figures 18 and 19). Among these alkaloids, berberine (78), palmatine (86), and chelerythrine (87) are the main active principles for the treatment of antibiotic-induced gut microbiota dysbiosis through the key enzyme, CYP27A1, which is involved in the biosynthesis of bile acid [127]. This study provides insights for the discovery of natural products for the treatment of gut microbiota dysbiosis.
Structures of dehydrocavidine (85), palmatine (86), and chelerythrine (87).
Xanthohumol (88) is a prenylflavonoid in hops (Humulus lupulus), which is responsible bitter flavor in beer (Figure 20). Xanthohumol (88) has interesting pharmacological properties, for example, improving cognitive flexibility in young mice [128] and having beneficial effects toward metabolic syndrome-related diseases such as type 2 diabetes and obesity [129]. The comparative study on germ-free and human microbiota-associated rats toward the metabolism of xanthohumol (88) revealed that gut bacteria could transform xanthohumol (88) to isoxanthohumol (89) and 8-prenylnaringenin (90), respectively (Figure 20) [130]. The metabolism of xanthohumol (88) was further studied using human intestinal bacteria, Eubacterium ramulus and E. limosum. It is worth mentioning that an independent study revealed that the bacteria of the genus Eubacterium are normally abundant in the human gastrointestinal tract; their densities in human gut are up to 1010 colony-forming units/g of intestinal content [131]. Xanthohumol (88) is spontaneously converted to isoxanthohumol (89), which is in turn bioconverted to 8-prenylnaringenin (90) by the gut bacterium, E. limosum (Figure 20) [132]. 8-Prenylnaringenin (90) is biotransformed to O-desmethylxanthohumol (91) by the bacterium E. ramulus; this bacterium could also convert O-desmethylxanthohumol (91) to desmethyl-α,β-dihydroxanthohumol (92). Moreover, the bacterium E. ramulus was able to transform xanthohumol (88) to α,β-dihydroxanthohumol (93) (Figure 20) [132]. An independent study in healthy women volunteers revealed that isoxanthohumol (89) could be bioconverted to 8-prenylnaringenin (90) in human intestine and that the bacterial microbiota isolated from fecal samples of female volunteers could also biotransform isoxanthohumol (89) to 8-prenylnaringenin (90) [133]. Another study demonstrated that 8-prenylnaringenin (90) has potent estrogenic property, and it could relieve climacteric symptoms, i.e., vasomotoric complaints and osteoporosis, and may be useful for the treatment of menopausal complaints [134]. These studies conclusively show that the metabolites produced by gut microbiome, i.e., 8-prenylnaringenin (90), are actually bioactive compounds, not the parent natural products, and they have different pharmacological activities from their parent natural products. Gut microbiome is therefore important for in vivo biotransformation of natural products, providing bioactive metabolites responsible for therapeutic effects.
Bioconversion of xanthohumol (88) to isoxanthohumol (89), 8-prenylnaringenin (90), O-desmethylxanthohumol (91), desmethyl-α,β-dihydroxanthohumol (92), and α,β-dihydroxanthohumol (93) by human gut bacteria.
Gut microbiome can biotransform natural products to bioactive metabolite essentially for therapeutic effects, for example, the biotransformation of isoxanthohumol (89) to bioactive 8-prenylnaringenin (90) [133]. However, gut microbiome can also produce toxic metabolites from the biotransformation of natural products, thus giving negative side effects. Camptothecin (CPT) is a natural alkaloid of a plant, Camptotheca acuminata, and has anticancer property with topoisomerase inhibitory activity [135]. Irinotecan or CPT-11 (94) is an alkaloid derivative of camptothecin and used as anticancer drug (Figure 21). Irinotecan (94) is a prodrug, which is transformed in vivo through hydrolysis by carboxylesterase enzymes, giving an active metabolite, SN-38 (95) (Figure 21) [136]. Uridine diphosphate-glucuronosyltransferase enzymes catalyze the conversion of SN-38 (95) to a glucuronidated derivative, SN-38G (96) (Figure 21). The metabolite SN-38G (96) is inactive for cancer cells and is excreted into the gastrointestinal tract [137], where the gut bacteria use β-glucuronidase enzymes to convert SN-38G (96) to SN-38 (95) that causes severe diarrhea in patients (Figure 21) [138]. This side effect reflects the significant negative effects of gut bacteria in the drug metabolism. However, the use of antibiotics, e.g., levofloxacin, to reduce the population of gut bacteria in the gastrointestinal tract is not recommended for patients because it has many consequent problems [139]. Gut microbiotas are important for a healthy gastrointestinal tract, and they play many essential roles in dietary metabolisms [140, 141]; the treatment of cancer should not give any effects to gut microorganisms. Therefore, the use of antibiotic drugs, which affect gut microbiota, is not recommended. To reduce the diarrhea side effect without affecting gut microorganisms, a research led by Redinbo employed appropriate inhibitors of gut bacterial β-glucuronidase enzymes, in order to prevent the formation of SN-38 (95), a causative agent of severe diarrhea in patients [142]. Certain inhibitors exhibited β-glucuronidase inhibitory activity in living bacterial cells without disturbing the growth of gut bacteria or giving any damaging effects toward mammalian cells. Indeed, in a mouse model, mice treated with both irinotecan (94) and a β-glucuronidase inhibitor had less diarrhea and bloody diarrhea than the group receiving only the drug irinotecan (94). Therefore, the inhibition of microbial β-glucuronidases could prevent the production of toxic metabolite, SN-38 (95), during the treatment of anticancer drug, irinotecan (94) [142]. This is an example of a toxic drug metabolite produced by the activity of gut microbiome, and the manipulation of the enzyme activity of gut bacteria could be done by using another drug (an inhibitor of bacterial enzyme).
Structures of irinotecan or CPT-11 (94) and its metabolites, SN-38 (95) and SN-38G (96), and the bioconversion of SN-38G (96) to SN-38 (95) by gut bacterial β-glucuronidase.
Some natural products can alter the composition of gut microbiome, and changes in gut microbiome lead to the drug-induced negative side effects on certain treatments. Paclitaxel or Taxol (97) is an anticancer drug for the treatment of many types of cancers (Figure 22), and it is a natural product isolated from a Pacific yew tree, Taxus brevifolia. In a mouse model, paclitaxel (97) chemotherapy could change the composition of gut bacterial community and induce negative effects such as sickness behaviors, i.e., fatigue and anorexia, increased central and peripheral inflammation, and impaired cognitive performance [143]. These negative effects might be associated with changes in gut bacteria because paclitaxel (97) therapy decreased the abundance of gut bacteria including Lachnospiraceae bacteria and butyrate-producing bacteria, which are necessary for human gut health [143]. Therefore, the negative effects of cancer chemotherapy may be attenuated by improving the composition of gut microbiota, for example, the use of prebiotic or probiotic supplements, which has become one of the emerging approaches to change the microbiota composition, thus improving therapeutic outcome for patients treated with anticancer drugs [144].
Structure of an anticancer drug paclitaxel or Taxol (97).
Antibiotic drugs have significant effects on the metabolism of drugs and phytochemicals because they could suppress enzymatic activities of gut microbiome [92]. Therefore, if patients are treated with an antibiotic drug together with another drug, there are possible drug–drug interactions due to changes of gut microbiota caused by antibiotic drugs. Lovastatin (98) (Figure 23), a natural polyketide isolated from the fungus Aspergillus terreus [145], is a cholesterol-lowering drug, which is a member of the statin family. Lovastatin (98) has the interactions with antibiotics through the mediation of gut microbiome [146]. Incubation of lovastatin (98) with human and rat fecalase revealed the biotransformation of this drug by gut microbiota, giving four major metabolites including demethylbutyryl-lovastatin (99), hydroxylated-lovastatin (100), hydroxy acid-lovastatin (101), and OH-hydroxy acid-lovastatin (102) (Figure 23) [146]. These four metabolites were also found in rat plasma, and they might be from gut microbiota-mediated metabolism of the drug lovastatin (98). Among the drug metabolites, hydroxy acid-lovastatin (101) is the active form, which could effectively inhibit 3-hydroxy-3-methylglutaryl coenzyme-A reductase, the target enzyme of this cholesterol-lowering drug [147].
Structures of major metabolites of lovastatin (98) including demethylbutyryl-lovastatin (99), hydroxylated-lovastatin (100), hydroxy acid-lovastatin (101), and OH-hydroxy acid-lovastatin (102).
In an animal model, rats with an oral administration of lovastatin (98) were compared with those treated with lovastatin (98) and antibiotics; the pharmacokinetic study revealed that the levels of the active metabolite hydroxy acid-lovastatin (101) in antibiotic-treated rats were lower than that without antibiotics. This result indicates that antibiotic drugs reduce the biotransformation of the drug lovastatin (98) to its active form, hydroxy acid-lovastatin (101), because antibiotics affect gut microbiome. The in vivo metabolism of lovastatin (98) to its active form, hydroxy acid-lovastatin (101), is important for the therapeutic efficacy of this drug; therefore antibiotic intake of patients treated with lovastatin (98) would lead to the decrease of the active form, hydroxy acid-lovastatin (101), thus decreasing its therapeutic effects [146]. This study clearly demonstrates the drug–drug interaction mediated by changes of gut microbiome.
Intriguingly, gut microbiome is very important for human health and diseases, and it is therefore recognized as an “organ” or a “tissue” in the human body. Gut microorganisms have much more genes encoding enzymes than those of human genome; therefore, enzymes of these microbes are involved in many biochemical processes, i.e., metabolism of xenobiotics (compounds not produced in human host, e.g., drugs and pollutants) and dietary sources. Metabolites produced by gut microbiome play significant roles in human health and diseases; these metabolites include short-chain fatty acids such as butyrate (11), as well as other metabolites, e.g., nicotinamide (12), 5-aminovaleric acid (14), and taurine (15) (see Section 2). Since gut microbiome and its metabolites substantially contribute to human health and diseases, a therapy by intervention strategies using gut microbiota can potentially be useful for some diseases, for example, metabolic disorders, cardiovascular disease, food allergy, and neurological disorders. Supplementation with probiotics or certain gut bacteria, as well as their metabolites, may be a new therapeutic method in the future. Fecal microbiota transplantation, e.g., transferring gut bacteria from healthy individuals into patients, is a challenging research study in the near future.
Gut microbiome can metabolite commonly used drugs and natural products. Drug metabolism by gut microorganisms decreases the levels of drugs in serum, thus disturbing the drug pharmacokinetics, which can lead to alteration of therapeutic efficiency. Moreover, metabolites produced by the drug metabolism of gut microbiome contribute considerably to the drug efficacy. For example, the levels of the drug L-dopa (56) are substantially reduced by the metabolic activity of gut microbiome, and this results in the requirement of higher doses for the Parkinson’s patients with gut microbiome that has high metabolic activity toward the drug L-dopa (56) (see Section 3.1). This example well demonstrates the role of gut microorganisms on treatment outcomes of the commonly used drugs. Gut microbiome could improve many drug therapies, for example, cancer immunotherapy targeting CTLA-4 blockade and immune checkpoint inhibitor via the PD-1/PD-L1 pathway. Moreover, the metabolism of gut microbiome improves drug efficacy because it assists the bioconversion of some drugs into their active forms, for example, a biotransformation of lovastatin (98) to its active form, hydroxy acid-lovastatin (101), and a bioconversion of aspirin (70) to salicylic acid (71) that actively reduces pain. Interestingly, gut microbiome involves in a biotransformation of an alkaloid natural product berberine (78) to an absorbable form, dihydroberberine (80), which is absorbed at the intestine system (see Section 3.2). This result demonstrates that gut microbiome facilitates drug delivery of berberine (78) that has poor solubility by a biotransformation to an absorbable form, dihydroberberine (80), which is in turn converted to its active form berberine (78) in the human body. Since gut microbiome plays many important roles in drugs and natural products, the metabolism of natural products and drug candidates by gut microbiome should therefore be studied, and it should be a part of the drug development process. Gut microbiome can potentially play a crucial role for the improvement of drug safety and efficacy.
The author thanks the Center of Excellence on Environmental Health and Toxicology, Science & Technology Postgraduate Education and Research Development Office (PERDO), Ministry of Education, for the support of research that leads to this book chapter.
The author declares no competing interests or no conflict of interest.
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