Mathematical models and synthetic gene circuits are powerful tools to develop novel treatments for patients with drug-resistant infections and cancers. Mathematical modeling guides the rational design of synthetic gene circuits. These systems are then assembled into unified constructs from existing and/or modified genetic components from a range of organisms. In this chapter, we describe modeling tools for the design and characterization of chemical- and light-inducible synthetic gene circuits in different organisms and highlight how synthetic gene circuits are advancing biomedical research. Specifically, we demonstrate how these quantitative model systems are being used to study drug resistance in microbes and to probe the spatial–temporal dimensions of cancer in mammalian cells.
- antimicrobial resistance
- synthetic gene circuits
- mathematical models
A primary goal of synthetic biology is to rationally design and engineer synthetic gene circuits as tools to advance basic research [1, 2], optimize the production of chemicals or biofuels [3, 4], build biocomputational systems , and enhance clinical therapeutics . Control of synthetic gene circuits at the transcriptional level (transcription is the process of transcribing mRNA from a DNA template) has been demonstrated through chemical- and light-based stimuli [7, 8]. The transcriptional network architecture (how genes are connected to and regulate each other through transcription factor proteins) affects the properties of gene expression, in terms of average expression levels as well as the degree of expression variability inside a single cell or across a cell population . Throughout this chapter, we will use the term “synthetic gene circuits” to describe synthetic systems and the term “gene networks” to described natural systems.
Fluctuations in the biochemical processes of transcription and translation (translation is the process of translating amino acid-based proteins from a nucleotide-based mRNA template) are referred to as gene expression noise . Gene expression noise leads to heterogeneity among genetically identical cells in the same environment and can affect the survival of microorganisms . For instance, gene expression noise has been shown to promote drug resistance in microbes . Similarly, gene expression noise is thought to play an important role in tumorigenesis and the development of resistance during cancer chemotherapy . Mathematical models and synthetic gene circuits have established that the architecture of the gene network modulates gene expression noise .
Electronic circuits inspired the development of synthetic gene circuits, with mathematical representations of natural and synthetic networks successfully predicting their effects on gene expression . A milestone study in
Optogenetics is the control of cellular components using electromagnetic radiation. Like other synthetic systems, optogenetic components can be engineered into gene circuits to precisely control cellular processes such as gene expression or protein activity in prokaryotic and eukaryotic cells; the performance of optogenetic gene circuits can be optimized in an iterative model-experiment cycle. However, unlike previous gene circuits, optogenetics offers the ability to control gene expression at a single-cell resolution. The fast temporal and single-cell spatial resolutions that light provides as a stimulus for gene circuits is unmatched; chemical stimulus regulates transcription on longer timescales and at a cell-population level. Like their gene circuit predecessors, optogenetic gene circuits can be used to control functional proteins. Optogenetic tools are especially suited to investigate gene function at the single-cell level. For instance, researchers can take a gene of interest, such as KRAS which is often found mutated in cancers , and integrate it into an optogenetic gene circuit to explore the transcriptional and translational effects on cellular phenotypes by stimulating individual cells with visible light. It is worth noting that although in this chapter we focus on optogenetic applications involving visible light, some optogenetic tools have been developed using other regions of the electromagnetic spectrum, including near-infrared  and UV  radiation.
This chapter describes the construction and characterization of synthetic gene circuits in yeast and mammalian cells (Section 2) and optogenetic gene circuits in mammalian cells (Section 3) with various transcriptional network architectures, along with their applications in biomedical research. The mathematical approaches to model synthetic and optogenetic gene circuits are also discussed.
2. Synthetic gene circuits
2.1 Positive feedback gene circuits in yeast
A positive feedback synthetic gene circuit was first constructed in yeast to convert a continuous gradient of a constitutively expressed transcriptional activator into a cell phenotype switch, resembling analog to digital signal conversion . Subsequently, a positive feedback (PF) gene circuit was genomically integrated into the budding yeast
In the PF gene circuit, the regulator reverse tetracycline-controlled trans-activator (rtTA) binds to its own promoter in the presence of tetracyclines (Figure 1A, top left) . The genetic engineering approaches mirrored the assembly of a negative feedback (NF) circuit in yeast . Unlike the NF circuit, toxicity exists after activating the regulator gene rtTA, which sequesters general transcription factors from vital cellular processes . Additionally, the construct controlled the drug resistance gene ZeoR, which confers resistance to the antibiotic Zeocin (Figure 1A, top right).
The PF gene circuit exhibits a sigmoidal gene expression dose response at the population level (Figure 1B). The expression dose–responses for low- and high-expressing subpopulations were determined using a bimodality detection algorithm . The gene expression noise level peaked at an intermediate inducer (anhydrotetracycline or ATc) concentration (Figure 1C). The shift in the gene expression distribution peaks over increasing inducer levels is reflected by the subpopulation ratio changes (Figure 1D). The gene expression distributions for the ATc dose response display bimodality (Figure 1E).
Testing multiple levels of inducer and drug determined a “fitness landscape” that quantitatively mapped population growth rates to unique combinations of ATc and Zeocin concentrations. The yeast PF system demonstrated the need to incorporate the cellular memory associated with gene expression states (Figure 1A, bottom) to computationally predict the fitness landscape ; the growth rate under Zeocin treatment was the highest at the minimal level of induction that lead to bimodal expression . These computational predictions guided laboratory experiments to identify environmental conditions that defined a “sweet spot” of drug resistance, which balanced the costs of expressing rtTA with benefits of expressing ZeoR.
The yeast PF synthetic gene circuit was subsequently used to study evolutionary dynamics under various levels of induction and drug treatment . This microbial evolution experiment included conditions at one edge or both edges (saturating molecular levels or none) of the fitness landscape, as well as at intermediate levels of induction with or without Zeocin. The evolved populations were frozen at specific time points and subsequently reestablished to test in various conditions compared to ancestral cells. Additionally, the evolution experiments were combined with simulations to predict the types of mutations that could arise under induction and drug treatment .
Full induction without drug treatment led to breakdown of the regulator rtTA over time through full and partial knock-out mutations, which improved fitness without Zeocin . Yet, during follow-up evolution experiments in high induction with Zeocin partial rtTA knockout mutants regained function . Full Zeocin treatment without induction eventually established populations with higher expression, potentially through mutations in the drug resistance gene and promoter linked with extra-circuit mutations. High induction with Zeocin led to accumulated mutations in rtTA, possibly lowering the effectiveness of the regulator as shown by decreased inducer sensitivity . After intermediate induction with Zeocin, experiments on evolved populations during reintroduction of drug under intermediate induction uncovered the two expression distribution peaks shifting towards each other leading to a single fitness peak; this highlighted the role of noise in driving evolution through the trade-off between rtTA toxicity and drug resistance.
2.2 Experiments and computational models of positive feedback and feedforward circuits in yeast
Along with positive feedback and negative feedback circuit architectures, feedforward loop (FFL) architectures (a three-gene network composed of two input transcription factors, one of which regulates the other, both jointly regulating a target gene) may have evolved in natural gene regulatory networks to enhance fitness [26, 33]. In
Mathematical models of gene regulatory networks can predict biological responses, which is essential to optimally design synthetic gene circuits and to guide experiments. A minimal model of the PDR network found that the positive feedback and feedforward loop architectures sustain transcription and can stabilize expression of the network when the drug is transient or fluctuating . The minimal model also predicted increased gene expression noise (in terms of increased noise magnitude and longer cellular memory timescales) in the FFL and FFL + PF networks. Overall, the FFL and FFL + PF network architectures were found to enhance drug resistance
The minimal model of the PDR network was described by the following system of coupled ordinary differential equations (ODEs) :
where PDR1 was treated as an adjustable parameter. and are the maximum levels of activated protein production for the variables PDR3 and PDR5, respectively. The Boolean parameter describes the activation of PDR3 by PDR1. Here the dilution and degradation rates of PDR3 and PDR5 were set to unity. The functions that describe how PDR3 and PDR5 are regulated are given by:
where, and are the Hill coefficient and half-maximal activation parameter, respectively. The Boolean parameter describes the presence or absence of positive feedback regulation on PDR3. The minimal model and a more comprehensive model (presented below) were translated into biochemical reactions that were simulated using the Gillespie stochastic simulation algorithm [36, 37].
A more comprehensive model, known as the PDR5 transcriptional network model, incorporated the dynamics of the PDR5 efflux protein pump and the negative feedback produced when PDR5 eliminates the drug from the cell . The PDR5 transcriptional network model can be described by the following system of coupled ODEs:
where PDR1 and the intracellular drug concentration () were incorporated as variables. is the basal rate of PDR1 transcription, the extracellular drug concentration, the rate of passive diffusion of the drug across the cellular membrane, half-maximum saturation coefficient for the PDR5 efflux pump, and the efflux rate of the drug via PDR5 efflux pump. It was assumed that drug entry and exit from the cells occurred through a combination of passive and active transport, and that the activation of PDR1 by the drug can be described by Michaelis–Menten kinetics. The PDR5 transcriptional network model predicted that PDR5 expression level would increase after application of the drug and that cell population fitness would oscillate before stabilizing during drug treatment.
To confirm the predictions from the PDR5 transcriptional network model, a synthetic gene circuit (Figure 2b) was constructed with molecular cloning techniques  and integrated into a yeast strain without a native PDR5 gene . The construction technique ran multiple overlap PCR steps, where two fragments with overlapping regions on their ends were amplified together initially without primers, using the overlapping sequence as a
The PDR synthetic gene circuit was experimentally compared to simplified PDR circuit components, like direct activation (DA: PDR1 directly activates PDR5), cascade (CAS: PDR1 activates PDR5 through PDR3), a cascade with positive feedback loop (CAS + PF: PDR1 activates PDR5 through PDR3, with PDR3 activating its own expression), and a feedforward loop (FFL: PDR1 activates PDR5 directly as well as indirectly through PDR3) . The FFL + PF circuit represented the PDR network. This separation of components tested the effect of specific network motifs in drug resistance and gene expression compared to the full PDR synthetic circuit. Direct activation in the FFL circuit was found experimentally to increase the speed of expression changes compared to indirect activation of PDR5. Direct activation was required for PDR5-mediated drug resistance. Indirect activation enhanced drug resistance, which provided evidence that the delayed reduction in PDR5 expression protected cells from the toxic effects of drug (Cycloheximide) exposure (Figure 3a). Figure 3b shows that strains carrying a gene circuit with a positive feedback loop grew faster in the presence of drug compared to strains in which this circuit architecture was missing. This provided evidence that the positive feedback regulation of PDR5 expression protects cells from drug exposure. Finally, reducing the strength of positive feedback regulation through mutation decreased drug resistance (Figure 3c).
Overall, the PDR network was recapitulated in mathematical and synthetic gene circuit models that demonstrated that the network architecture is optimized for drug resistance, with gene expression noise making important contributions to fitness during drug treatment.
2.3 Experiments and computational models of mammalian negative and positive feedback gene circuits
The yeast NF gene circuit was transferred to mammalian cells to test an organism transfer workflow using design and optimization cycles aided by computational modeling . This workflow led to updates to the yeast NF gene circuit, including the optimization of the tet promoter operator site locations, the introduction of an intron upstream of the regulator, codon optimization for mammalian translation, and the addition of a Kozak sequence near the start codon, which was stably but randomly transfected into MCF-7 breast cancer cells. This NF circuit in mammalian cells exhibited a linear dose response with low gene expression noise, similar to the NF circuit in yeast cells . Though the adaptability of the yeast NF circuit to mammalian cells did not require any additional design features, optimization of parts responsible for gene expression and protein location was required to replicate the features of the yeast NF circuit. These results support the “abstraction principle” in the field of synthetic biology, namely that different parts of a biological network can be optimized for improved functionality in new settings, while leaving the original network design intact .
In a subsequent study, the yeast PF circuit was transferred to mammalian cells, which was coupled with a Flp-recombinase site-specific integration system (Figure 4a) . This mammalian positive feedback (mPF) circuit displayed a sigmoidal mean gene expression dose response (Figure 4b). Gene expression noise increased at intermediate inducer (Doxycycline) levels (Figure 4c), with broad unimodal gene expression distributions (Figure 4d). A lack of bimodality is unexpected for an induced bistable circuit and may have been attributed to similar cellular growth and cellular memory time scales.
The previously reported mammalian negative feedback circuit was also connected to the Flp-In integration system in Chinese Hamster Ovary (CHO) cells (Figure 5a) . This negative feedback circuit was separately integrated into the same genomic site as the mPF circuit and subsequently called the mammalian negative feedback (mNF) circuit. The mNF circuit displayed a linear dose response in mean gene expression (Figure 5b). Gene expression noise was low across all inducer (Doxycycline) levels (Figure 5c) with narrow gene expression distributions (Figure 5d).
The mPF and mNF gene circuits controlled the EGFP fluorescent protein and the PuroR drug resistance gene each separated by self-cleaving 2A motifs [39, 40]. The, the integration into the same genomic site and the introduction of self-cleaving 2A motifs and the PuroR drug resistance gene did not affect the function of these circuits.
In an evolution experiment with multiple drug (Puromycin) concentrations, the mNF and mPF circuits were tuned to the same mean expression level to decouple gene expression noise from the mean gene expression prior to drug treatment . After adaptation, the drug was removed while induction was either maintained or removed. Finally, the adapted populations were retreated with the previous level of drug to uncover potential adaptation mechanisms. The evolution experiment demonstrated that low gene expression noise from the mNF circuit was beneficial in adaptation compared to mPF under low levels of drug . In contrast, the high noise from the mPF circuit was beneficial compared to the mNF circuit under high levels of drug.
Mutations were found in the TetR regulator gene from the mNF circuit that knocked out repression, which explained why the mNF populations maintained high expression with or without inducer after the temporary removal of the drug. The mPF circuits did not mutate, which was consistent with the drug retreatment period where uninduced mPF populations struggled to adapt while the induced populations adapted faster . Overall, the decoupling of gene expression noise from the mean demonstrated the power of using synthetic gene circuits to uncover novel insights into mammalian drug resistance.
A stochastic population dynamics model was developed to predict the emergence and switching dynamics of persister (
3. Optogenetic gene circuits
A major focus of synthetic biology has been to engineer gene circuits to control cellular processes. This has mainly been achieved through small molecules that activate or inactivate various components of synthetic gene circuits [17, 19, 41, 42, 43, 44, 45, 46]. Chemical stimuli has many advantages, including easy titration for inducing gene expression over large dynamic ranges, characterized affinity for existing proteins, and minimal off-target effects . However, controlling gene circuits with chemicals is often not instantaneous and makes it difficult to control individual cells in a population.
Light stimulus can achieve many of the same advantages as chemicals without the above limitations. Like the cellular proteins that respond to chemical stimuli, proteins have been found in nature that respond to light [47, 48]. The discovery of light-activated proteins provided the elements necessary to build optogenetic gene circuits. By engineering light-responsive elements with existing components in gene circuits, synthetic biologists were able to adapt endogenous proteins from natural organisms to experimental model organisms, including yeast  and mammalian cell lines .
The use of light-inducible systems in eukaryotic organisms has expanded to cover nearly as many applications as chemical systems, including the control of gene expression, protein alterations, metabolic reactions, epigenetic states, and animal behavior [50, 51, 52, 53, 54, 55]. A common theme among light-activated and chemical-induced circuits is the genetic architecture of the system. For chemically regulated gene circuits, classic engineering architectures  have been produced including negative regulation, positive regulation, positive feedback, negative feedback, and many others [39, 40, 42, 56, 57, 58, 59]. Optogenetic systems have begun to incorporate these circuit architectures [49, 60]. Optogenetic tools respond to a variety of wavelengths of light [61, 62] and can be used transiently [63, 64] or as stable systems .
Negative feedback is an important gene circuit architecture that has been implemented in optogenetic circuits. Negative feedback is a desirable architecture in synthetic biology because it provides two advantages: 1) negative feedback reduces gene expression noise and 2) negative feedback allows tunability of system output to a “transfer function”, which describes the relationship between an input and an output function [65, 66]. In synthetic biology, many systems are designed with desired inputs and outputs in mind and therefore knowing the relationship or transfer function between these variables is crucial . Additionally, such features also occur in natural systems [68, 69], which synthetic systems are often designed to mimic . The negative feedback circuit architecture has been engineered into synthetic gene circuits in bacterial, fungal, and mammalian systems, all controllable by small chemical molecules [29, 40, 70, 71]. This circuit architecture was recently engineered in an optogenetic system and found to offer many of the same advantages as the chemical-induced negative feedback gene circuits; namely, low gene circuit noise, wide system tunability, and a characterized transfer function between input and output (i.e., light and a fluorescence reporter) .
The optogenetic NF system (Figure 7A) was inspired from previous chemical gene circuits  and from computational modeling . A well-known tetracycline-responsive system [72, 73] provided the foundation to engineer a light-responsive system, by fusing the TetR protein with a LOV2 domain [52, 74, 75] and either a degradation tag  or a small peptide  that inhibits TetR (Figure 7B). When light is absent, the degradation tag or the inhibitory peptide remains hidden. When blue light is present, the LOV2 protein undergoes a confirmational change and reveals one of the two domains. By employing this engineered light protein, an optogenetic gene circuit can be constructed with operator sites upstream of the gene for this protein to allow down regulation of its own expression (as well as another functional gene). The light stimulus can then be used to control gene expression output with the benefits of low noise and titratable expression levels.
Computational modeling was used to investigate how system performance could be enhanced in the optogenetic NF system . This methodology of build, model, improve is crucial when developing synthetic gene circuits. To achieve this, the design and construction of the optogenetic NF system focused on changes that could decrease gene circuit noise, lower basal expression of the circuits, increase fold-change of the circuit, and enhance the range of circuit response to stimuli. A quantitative gene expression model identified parameters that optimized the performance of the optogenetic NF system. The “pipeline” for modeling the NF optogenetic gene circuit is shown in Figure 8. The NF optogenetic circuit was represented by a network schematic of the main optogenetic gene circuit’s components (Figure 8A). These components were formalized as a set of chemical reactions (Figure 8B). The chemical reactions were then described by a system of ordinary differential equations (Figure 8C), which was solved numerically . Lastly, the equations describing each reaction were explored to investigate whether a given optogenetic gene circuit component should be changed experimentally (Figure 8D). The design of the optogenetic NF system was improved by changing the transcription and translation rates of the optogenetic inhibitory protein.
In addition to validation and improving optogenetic gene circuits, various architectures can be utilized for expressing functional proteins at precise levels inside of single cells. Controlling gene expression in single cells can allow for exploration of phenotypic landscapes as a function of protein levels and time. For example, the optogenetic NF system was used to control the mutated oncogene KRAS (G12V), which showed expression and function could be controlled in a dose-responsive manner with low optogenetic gene circuit noise . This system can be modified to contain any functional gene allowing single-cell gene expression studies using microscopy equipment such as digital mirror device (DMD) . DMD technology can allow system feedback for controlling optogenetic gene circuits
Overall, optogenetic gene circuits allow researchers to perturb single cells to distinguish between individual and population-level behavior. Optogenetic tools are anticipated to be important for elucidating mechanisms in drug resistance and cancer metastasis, where single-cell behavior and spatial–temporal factors may dictate biological fate.
The ability of synthetic gene circuits to fulfill engineered design principles and facilitate scientific discoveries is expected to grow over time. However, evolutionary forces can undermine the integrity of synthetic gene circuits [25, 32]. It will be crucial to design gene circuits in the future to mitigate the effects of evolution to maintain their functional integrity. One approach is to use DNA sponges to change the response of gene circuits while lowering protein toxicity . Another approach is to use evolution itself to repair broken synthetic gene circuit components, resulting in more robust gene circuits . Overall, as the library of biological parts increases, the discovery of new “BioBricks” (standardized and interchangeable gene circuits components) will aid in resolving the integrity issues presently associated with synthetic gene circuits. Genomic mining is a promising approach for discovering BioBricks, including identifying novel TetR-family regulators from prokaryotic genomes  and CRISPR-Cas systems in microbes .
Clinical applications of synthetic gene circuits will continue to expand and could lead to successful treatments for various diseases, including autoimmune disorders  and cancers . CAR-T technologies to fight cancer increasingly include synthetic gene circuits and synthetic intercellular pathways to avoid adverse inflammatory reactions that damage healthy cells and to improve the targeting of cancer cells [83, 84]. Additionally, investigating drug resistance in microbial pathogens will require gene circuits that can be introduced into pathogens, which have native gene networks relevant to drug resistance that are complex and incompletely characterized. Relatedly, increasing complexity in gene circuits remains a challenge and will require multiple orthogonal components [80, 85] as well as more advanced computational methods to predict the dynamics of large-scale, nonlinear networks . Ultimately, improvements in our ability to model, design, and construct synthetic gene circuits will benefit biomedical applications as well as increase our understanding of natural gene networks.
Optogenetic gene circuits allow researchers to utilize the strengths that have been developed through two decades of synthetic biology research, as well as to achieve more precise control of living cells. The use of light as a stimulus enables the single-cell control of gene circuit response, which can complement existing systems to study cell populations. The generation of single-cell data will allow researchers to address questions on how individual cells give rise to population level phenomenon and how neighboring cells affect adjacent or distal cells. Answering such questions will be important for extracting information on biological processes such as tissue development , epithelial-to-mesenchymal transition , and the effects of the microenvironment on cancer progression [89, 90].
While using optogenetic tools will be important for answering a broad range biological questions and for biomedical applications, challenges remain in terms of the scalability and precision of cellular control. There have been applications of optogenetic technology that address these challenges individually. For instance, the light plate apparatus (LPA)  is a simple to construct and inexpensive system that can be adapted and used for scaling light-induced conditions
DC was supported by funding from the Government of Canada’s New Frontiers in Research Fund – Exploration grant program (NFRFE-2019-01208) and the University of Alberta. GB was supported by the National Institutes of Health, NIGMS MIRA Program (R35 GM122561) and by the Laufer Center for Physical and Quantitative Biology. MTG was supported by the National Defense Science and Engineering Graduate Fellowship Program.