Anhydrous and Hydrated Protein Models Derived from High-Resolution and Low-Resolution Techniques

the model also shows that waters are preferentially bound to charged and polar residues, while hydrophobic residues are avoided.


Introduction
High-resolution crystallography provides information on the precise 3D structure of proteins or other (bio)macromolecules, including ligands and several water molecules. In the case of small proteins, NMR techniques may be equally purposive. Reconstructions from cryo-electron microscopy may also supply precise anhydrous models. The most intimate structural details of proteins can be visualized from application of these high-resolution techniques (Creighton, 2010a(Creighton, , 2010bSerdyuk et al., 2007).
In general, however, only a small fraction of preferentially bound water molecules is identified by crystallographic techniques, owing to insufficient resolution and hydrogen bond network building. Discrete waters should have hydrogen bonded contact(s) to other solvent molecules or to protein; poorly placed waters tend to drift away during refinement (Rupp, 2010). Further deficiencies/errors in crystallographic work are due to missing parts (amino acid (AA) residues) and the occurrence of various radiation damages (Ravelli & Garman, 2006). By contrast, the data from low-resolution solution techniques, such as small-angle X-ray scattering (SAXS) and hydrodynamics (analytical ultracentrifugation, viscometry etc.), inherently contain hydration and yield hydrated protein models Zipper & Durchschlag, 2010b). For many reasons, knowledge of hydration is essential for understanding the behaviour of proteins in solution and manifold interactions.
Water is important for structure, stability, dynamics, and function of native proteins; it is also involved in guiding protein folding, and, consequently, needs to be involved in protein structure predictions and modelling of folding pathways (Levy & Onuchic, 2006;Papoian et al., 2004). Minimizing the number of hydrophobic side-chains exposed to aqueous solvent is a major driving force behind protein structure formation. In a typical protein, a tightly packed core contains more than 80 % of the non-polar side chains and water molecules are www.intechopen.com Protein Structure 70 generally excluded from protein interiors. There is a clear correlation between the hydrophobicities of AA residues and their tendency to occur in the interior (Creighton, 2010b). Water soluble proteins have all ionized groups on the surface, exposed to the solvent. Polar groups tend to be paired in hydrogen bonds. Fixed, preferentially bound water molecules occur in positions where they can build hydrogen bonds to polar groups. Overall, to some extent both bound and free waters are of relevance for the structure of proteins and their formation. Only the existence of water leads to the distinction between hydrophobic and hydrophilic parts. Water is the 'lubricant of life'.
Biophysically relevant hydration details are mandatorily required in certain cases: understanding protein interactions as precondition for flexibility, dynamics and functionality (Creighton, 2010a(Creighton, , 2010bSerdyuk et al., 2007); very precise comparisons of high-resolution 3D structures and molecular parameters with data from solution techniques Durchschlag & Zipper, 2008;Zipper & Durchschlag, 2010b); gaining insight into radiation damage events ; construction of tailor-made nano-compounds in context with drug-design projects and the development of functionalized surfaces and polymers by mimicking proteins (Durchschlag & Zipper, 2008); improvement/check of crystallographic/NMR data with regard to hydration waters .
Experimental determinations of volume, surface, and hydration properties of proteins by SAXS or other low-resolution techniques turned out to be rather inaccurate, whereas the hydration numbers for individual AA residues, derived from NMR spectroscopy or thermodynamic considerations, seem to be rather precise (Durchschlag & Zipper, 2001, 2008. For different pH values, of course, different hydration numbers for the AA residues have been found. Unlike experimental data, calculations of volume and surface properties of simple and complex proteins proved to yield reliable results, if based on the properties of the molecular constituents and the coordinates , 2008. Modern analytical procedures and programs yield the anhydrous volume (van der Waals volume), summing up the contributions of the constituents. For analyzing the surface area of proteins, rollingball mechanisms were most effective, characterizing either an anhydrous or a hydrated protein. Prediction of the values for hydrated volume and surface requires assumptions/estimations/findings for the amount of water bound to the protein, e.g. application of a shell model, blowing up (surface) AA residues, and use of individual waters. For the precise prediction of structural and hydrodynamic parameters (volume, surface, radius of gyration, sedimentation and diffusion coefficients, intrinsic viscosity etc.) realistic assumptions or estimations are sufficient, whereas visualization of biophysically realistic hydrated protein models obviously necessitates more sophisticated, advanced modelling techniques.
A critical inspection of anhydrous and hydrated protein models obtained by crystallography with models derived from quite different experimental techniques and calculation approaches allows a scrutinized comparison of the models under analysis. Among a variety of problems, the amount of hydration and the position of the individual water molecules turned out to be the most crucial points. To meet this challenge, a variety of techniques and approaches were examined and both models and molecular parameters were analyzed: (i) Anhydrous and Hydrated Protein Models Derived from High-Resolution and Low-Resolution Techniques

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Conventional and ab initio modelling approaches signify satisfactory agreement between crystal-and SAXS-based protein models, provided hydration contributions and other precautions are taken into account . (ii) Recourse to crystallographic or model data also allows scattering and hydrodynamic modelling; in the case of multibead structures novel modelling refinements (e.g., efficient bead reductions) have to be adopted , 2010a, 2010b. (iii) The creation of hydrated models from cryo-electron microscopy data necessitates qualified assumptions regarding hydration, e.g. in terms of voxel densities . (iv) Combining the exact surface topography (molecular dot surface; derived from atomic or amino acid coordinates of proteins or appropriate models) and our recent hydration algorithms (program HYDCRYST) allows the prediction of individual water molecules preferentially bound to certain amino acid residues (Durchschlag & Zipper, 2001, 2005, 2008).

Coarse-grained models
Sphere (S), prolate and oblate ellipsoids of revolution (PE, OE) of different axial ratios, and hollow spheres (HS) of different hollowness may serve as approximations for simple anhydrous protein structures. Selected structures were modelled by assemblies of equalsized densely packed beads (Zipper & Durchschlag, 2010a). By variation of the bead radius (r b ), the number of beads (N b ), i.e. the extent of the reduction process, can be varied systematically. The coordinates of the beads were generated by an in-house program.

Proteins: Recourse to experimental results and data banks
SAXS experiments yield scattering intensity profiles, I(h), and pair-distance distribution functions, p(r), in addition to a variety of molecular parameters such as radius of gyration, R G , hydrated volume, V, and maximum particle diameter, d max (Glatter & Kratky, 1982). Shape reconstructions may be obtained by conventional modelling or advanced ab initio modelling approaches, preferably by programs based on simulated annealing or on a genetic algorithm . Hydrodynamic properties such as sedimentation coefficient, s, translational diffusion coefficient, D, and intrinsic viscosity, [], are determined by analytical ultracentrifugation and viscometry, respectively. Atomic coordinates and masses of proteins were obtained from the PDB and SWISS-PROT data banks (Berman et al., 2000;Boeckmann et al., 2003). For hydration predictions by HYDCRYST, only the coordinates of the protein were taken, i.e. in this case all crystallographically found waters were discarded.

Model construction, data reduction, and prediction of structures and molecular parameters
Size, shape and properties of simple and complex proteins can be calculated by bead modelling procedures: in context with solution techniques, but also in the case of crystallographic and EM data Byron, 2008). Pilot tests applying wholebody approaches yield rough estimates of scattering and hydrodynamic molecular parameters and allow estimates of partial specific volume, molecular volume and overall hydration . Among the more advanced approaches applied, Debye modelling (Glatter & Kratky, 1982) and the program CRYSOL (Svergun et al., 1995) may be used for the calculation of scattering profiles from (atomic) coordinates. For hydrodynamic modelling, the HYDRO program suite (consisting of several programs and many modern adaptations; e.g., programs HYDRO++ and HYDROPRO) (García de la Torre et al., 1994Torre et al., , 2000Torre et al., , 2007Torre et al., , 2010Ortega et al., 2011aOrtega et al., , 2011b, and ZENO (Kang et al., 2004;Mansfield & Douglas, 2008) should be emphasized. Filling-model strategies (instead of shell models usually applied for hydrodynamic modelling) have to be used for analyzing both scattering and hydrodynamic quantities.
In a broad range of circumstances, models composed of a multitude of beads have to be handled, in particular when resorting to (atomic) coordinates of huge macromolecules or if the biophysically relevant fine structure of hydrated models is required. Various programs, e.g. AtoB (Byron, 1997), SOMO (Brookes et al., 2010a(Brookes et al., , 2010bRai et al., 2005), PDB2AT, PDB2AM, and MAP2GRID  have been developed to transform crystallographic/NMR data information to bead models (unreduced initial models based on atoms, atomic groups, or amino acid residues, and reduced models at certain reduction levels). The hydration program HYDCRYST allows the efficient prediction of individual water molecules preferentially bound to proteins provided the accessible surface area has been calculated previously by a surface calculation program. Several complementary tools may be required, e.g., for conversion between data formats, calculation of scattering functions, or for a correct visualization of reduced and/or hydrated structures by RASMOL (Sayle & Milner-White, 1995).

Calculation of volumes and surfaces
Volume and surface properties of protein molecules can be calculated using crystallographic data sets as those deposited in the PDB. The molecular volumes thus obtained are either anhydrous volumes or, because of scarce waters, poorly hydrated volumes (Durchschlag & Zipper, 2008). Surface characteristics of proteins are obtained by using analytical surface calculation programs such as SIMS based on the rolling-ball strategy (Vorobjev & Hermans, 1997), yielding molecular surface and solvent-accessible surface areas (i.e. anhydrous and hydrated surfaces), in addition to a smooth 'molecular dot surface' required for values for the solvent-excluded volume and appliance of advanced hydration modelling strategies. The program SIMS may be applied either to the atomic coordinates or newly-created coordinates (e.g., gravity centres of AA residues) (Durchschlag & Zipper, 2008).

Calculation of hydration
The water molecules bound preferentially to proteins have properties different from those of the bulk water (higher order, lower mobility, higher density) . For roughly estimating the overall hydration (Durchschlag & Zipper, 2004, 2008, the hydration numbers found for the individual AA residues (Kuntz, 1971) may be used.
Knowledge of the exact anhydrous surface topography in terms of dot surface points, as obtained by SIMS, however, enables usage of advanced hydration algorithms. The normal vectors at these anhydrous dot surface points allow the creation of a huge amount of hypothetical points for potential positions of water molecules; these waters are located at the normal distance above the anhydrous protein surface, i.e. at a distance usually corresponding to the water radius (probe radius). For the selection of preferential positions for bound water molecules, a new version of our in-house program HYDCRYST (now including also essentials of the related program HYDMODEL) is applied (creation of models based on the initial atomic coordinates of the protein or reduced models derived from the coordinates of AA residues) (Durchschlag & Zipper, 2001. The selected waters, assigned to the accessible AA residues, are then attached to the dry protein models. Overall, the method is based on geometrical and energetic constraints, owing to the placing of definite hydration numbers to definite AA residues. The extent of hydration can be modulated step by step by several input parameters, in particular by variation of the dot density and a scaling factor acting on the hydration numbers used. Thereby different extents of water binding (minimum, medium, and maximum hydration) may be simulated.

Calculation of SAXS functions and of structural and hydrodynamic parameters
Radius of gyration, R G , and the pair-distance distribution function, p(r), of the protein models were calculated from the radii and coordinates of the constituent beads and the bead volume as statistical weight. The p(r) function gives the relative number of distances of two points inside a particle as a function of the distance r. Calculation approaches and the prediction of structural and hydrodynamic parameters have been described in detail previously .

Results
In the first instance, whole-body models of different shape were selected, to test the applicability of the reduction and calculation approaches applied. Based on these findings, anhydrous models for many proteins were constructed and their predicted structural and hydrodynamic properties were compared to experimental data. Because of obvious deficiencies of the anhydrous (dry) protein models, sophisticated hydration strategies had to be developed in the following, to account for the hydration contributions of the protein structures in solution. Application of our advanced hydration algorithms to various proteins revealed the effectiveness of the approaches applied.

Coarse-grained models
Models of quite different shape were selected, to prove the effectiveness of the approaches under consideration. Fig. 1 depicts a few illustrative examples: a sphere (S), a hollow sphere (HS), a prolate ellipsoid (PE) and an oblate ellipsoid (OE), composed of a multitude of beads, together with a set of the reduced models. As may be expected, the distance distribution functions, p(r), of the different model structures vary considerably (Fig. 2), with respect to their form, position of maximum, and particle diameter. However, the profiles of unreduced and reduced models coincide nearly completely, proving the applicability of the model reduction process applied. As may be taken from the structural and hydrodynamic parameters presented in Table 1, the comparison of whole-body and multibead models indicates good accordance (data for R G , D (and therefore also for s), and []). As shown previously (Zipper & Durchschlag, 2010a), choice of [] RVC represents a reasonable approximation for the value of the intrinsic viscosity.

Anhydrous and hydrated protein models
Bovine pancreatic trypsin inhibitor (BPTI), a nonconjugated protein, was chosen as a small model protein, to demonstrate different types of anhydrous models and descriptions of reduction procedures to be applied in scattering and hydrodynamic modelling. Fig. 3 compares the initial anhydrous model, the unreduced BPTI model based on atomic coordinates (A), with several approaches for reduced models (B-E). The most straightforward types of reduced models are based on AA residue coordinates, either on the entire residue or on parts of it (such as main chain and side chain, a concept adopted from SOMO). Procedures, such as SOMO and AtoB, are used in the program UltraScan II (Brookes et al., 2010a(Brookes et al., , 2010b; D e m e l e r , 2 0 0 5 ) . A n i n s p e c t i o n o f t h e p(r) functions (Fig. 4) clearly proves that the straightforward procedures result in perfect agreement with the initial model, while the applied versions of SOMO, and in particular of AtoB, lead to remarkable discrepancies. This is partly due to the fast, but unprecise modus operandi for calculation of p(r) in the present versions of UltraScan II (the errors caused by neglecting the bead radii increase with decreasing bead numbers). However, part of the disagreement of the p(r) functions of SOMO and AtoB models with those of the initial and straightforward reduction procedures seems to be caused by the models themselves. The models created by SOMO and AtoB tend to be rather artificial and far from space-filling ( Fig. 3) because of avoidance of overlapping beads. Our straightforward approaches, on the other hand, do not prevent the occurrence of bead overlaps. Even overlapping unequal-sized beads can be used for hydrodynamic modelling, either by applying a special expression for the interaction tensor in HYDRO (Zipper & Durchschlag, 1997, 1999 or by using ZENO. However, in principle, all types of anhydrous model constructions may be used as starting points for the creation of hydrated models. For obvious reasons, however, in the following we will restrict our considerations to our straightforward in-house approaches for the model reduction process. The 30 S ribosomal subunit of Thermus thermophilus was used as a representative of a conjugated protein. It is a nucleoprotein composed of protein and ribonucleic acid moieties. As may be taken from Fig. 5, also in this case modelling may be achieved on the level of atomic coordinates (unreduced model: 51792 beads) and by applying AA and nucleotide residue coordinates (reduced model: 3917 beads) as well. Different approaches for the reduction process (running mean and grid reductions) and varying input parameters were applied, to test the applicability of the reduction procedures. The overall impression of the images obtained for all the models is satisfactory (Fig. 6). The comparison of the p(r) functions, however, reveals that use of the cubic grid approach and equal-sized beads on lattice points (CLE) may fail (Fig. 7). And the same conclusion can be drawn from a meticulous inspection of the molecular parameters listed in Table 2. Again, the CLE variant rather leads to erroneous predictions of structural and hydrodynamic parameters. The normal vectors at these points are used for the localization of potential water points (C). Selecting water molecules on the protein surface by HYDCRYST yields the water molecules to be tracked on the protein surface, eventually establishing a realistic hydrated protein model, revealing, however, no complete water shell (D). In comparison to this calculated model, the structure based on crystal data demonstrates only a few bound water molecules (E). . Note that CG implicitly means CGU since the G approach is only applicable together with unequal-sized beads.

Model
Parameter Nb: number of beads, V: total volume, RG: radius of gyration, : goodness of the fit, D: translational diffusion coefficient, s: sedimentation coefficient, []: intrinsic viscosity; PDB2AT: program generating running-mean models by merging as many atoms in sequential order as fit into a bead of given diameter BD, PDB2AM: program generating running-mean models by merging a given number (compression index ICOM) of AA and nucleotide residues in sequential order to one bead, MAP2GRID: program generating bead models by mapping a given model onto a cubic or hexagonal grid of given edge length (voxel size) VS; CG, CLU, CLE: cubic grid models composed of unequal-sized beads placed on local centres of gravity (CG) or on lattice points (CLU) or of equal-sized beads placed on lattice points (CLE). a The values given in the first line were obtained from the reduction program, the values given in the second line were obtained by the ZENO approach. Discrepancies in V are mainly due to the overlap of beads; the discrepancies in RG for the models reduced with MAP2GRID (calculation mode CLE) result from the neglect of the special weights of the beads of these models by the ZENO approach. b The values were obtained by comparing the calculated p(r) function of the reduced models with the p(r) function of the initial model. For computing the p(r) functions weighting by volume was assumed throughout. c The values are accurate to about ± 0.03 x 10 -7 cm 2 /s. d The values are accurate to about ± 0.3 x 10 -13 s. e The values are accurate usually to about ± 0.06 cm 3 /g, except for the models reduced by MAP2GRID where broader error bands are encountered (for mode CLU up to ± 0.08 cm 3 /g, for mode CLE up to ± 0.09 cm 3 /g).  Fig. 7. Comparison of distance distribution functions p(r) of selected unreduced and reduced bead models for the Thermus thermophilus 30 S ribosomal subunit (1FJG) as explained and shown in Fig. 6. The term 'V weighting' means that in the calculation of p(r) the beads are weighted according to their volume. This kind of weighting is correct for grid models of type CG and CLU, but obviously not for type CLE . Some characteristics of BPTI and the model under discussion are outlined in Table 3, together with the properties of some other selected proteins discussed later on. In the following, our hydration approaches were applied to several proteins differing in size and complexity.
Carbonmonoxide myoglobin has been used as an example of a liganded protein (ligands haem and carbonmonoxide CMO). The hydration approach is demonstrated both for the unreduced model based on atomic coordinates and the reduced model utilizing AA residue coordinates (Fig. 9). Evidently, the approach works in both cases.  A representative of large proteins, apoferritin, is shown in Fig. 10, highlighting some further aspects of particular interest. Water molecules are bound both to the outer and inner surface of this hollow protein; in addition, a few waters seem to occur also in some channels between interior and outside. Again, the number of waters predicted by HYDCRYST exceeds the number found by crystallography (Table 3).
A comparison of structural and hydrodynamic parameters of anhydrous and hydrated models for apoferritin (Table 4) reveals that the properties of the hydrated protein (V, R G , D, s, []) considerably deviate from those of the anhydrous one. It is quite obvious that a critical comparison of crystallographic data with the findings of solution techniques requires strict consideration of hydration contributions.
There is compelling evidence that water molecules can also be visualized in typical water channels of membrane proteins. The aquaporins shown in Fig. 11 are illustrative examples showing that the existence of a water channel as predicted by HYDCRYST is in full agreement with the crystallographic waters found in this case (Table 3). Some pilot tests also showed that the width of channels can be determined by variation of the probe radius.
Quantifying the results of anhydrous and hydrated proteins in terms of distance distribution functions p(r) again demonstrates that the properties of hydrated models differ significantly from anhydrous models. For the proteins selected (BPTI, apoferritin, aquaporin 1, aquaporin Z), this is shown in Fig. 12. The profiles for the proteins plus the HYDCRYST waters deviate significantly from those of the anhydrous proteins. This effect is most pronounced in the case of small proteins (such as BPTI), whereas, due to the size ratio between protein and waters, the difference is rather insignificant with large molecules (such as apoferritin). For a given protein, owing to the scarce numbers of waters in the crystal data set, generally the functions obtained on the basis of the proteins plus crystal waters rather resemble the anhydrous proteins.
www.intechopen.com Model  The multidrug resistance transporter Sav1866 is another example of a membrane protein. In this case crystallography was able to identify only very few water molecules, while our calculative approach HYDCRYST reveals many waters (Fig. 13). In context of membrane proteins, it has to be mentioned, however, that the preferential water molecules identified only indicate that at these positions individual waters could exist in principle, provided that they have contact with water. On the other hand, the model also shows that waters are preferentially bound to charged and polar residues, while hydrophobic residues are avoided.
Finally, modelling of the giant protein Lumbricus terrestris haemoglobin calls for tough measures. Fig. 14 demonstrates SAXS-based experimental scattering intensities, I(h), and distance distribution functions, p(r), of the native HBL complex and of its dodecameric subunit, respectively. The two profiles render information of the molecules under investigation in the reciprocal space and real space, respectively. The two profiles also show impressively the inverse relation between particle size (real space) and the decay of scattering intensity (reciprocal space) by reflecting the different size of the subunit and the complex.
Modelling of the anhydrous and hydrated HBL complexes requires consideration of several measures and precautions regarding model reduction and careful attention of AA residues missing in the crystal structure. Additional, appropriately located beads may serve as substitutes for the missing residues. Figs. 15 and 16 demonstrate that all structural features are retained through the reduction process, and the possibility to generate hydrated objects in both cases. Fig. 13. Space-filling models and slabs for the hydrated multidrug resistance transporter Sav1866 (2ONJ), based on crystallographic data (A, B) and HYDCRYST modelling procedures (C, D). Groups of special AA residues are highlighted in bluetint (hydrophobic residues), yellow (polar residues), or orange (charged residues). Waters localized by crystallography are shown in red, and waters identified by HYDCRYST are displayed in blue.

Crystallographic model HYDCRYST model
Advanced 3D reconstructions of the HBL complex, obtained from cryoelectron microscopy (Krebs et al., 1998), yield a voxel density distribution that can be interpreted in terms of anhydrous and hydrated protein volumes (Fig. 17). Thus, the EM-based data allow construction of anhydrous protein models and hydrated models as well (Fig. 18). The resemblance between the crystallography-based and EM-based protein models is striking.

Discussion
Several classes of coarse-grained models and biologically relevant proteins of different size and complexity have been used, to test the applied approaches concerning bead reduction and hydration algorithms, and to compare protein structures and molecular parameters obtained by quite different high-resolution and low-resolution techniques in the crystal, solid state or solution.
With all models and proteins, the bead reduction steps applied were successful, provided the reduction process was not too excessive and grid approaches with beads on lattice points are avoided. Reductions by a factor of 10 provided parameter predictions identical to the initial models, while reductions exceeding this factor can lead to slight deviations.
In the case of proteins, usage of precise anhydrous 3D models (derived from atomic or amino acid coordinates or appropriate models) along with computation of the exact surface topography (molecular dot surface) and our recent hydration approaches (program HYDCRYST) allow the prediction of discrete water molecules preferentially bound to particular residues. In this context, various approaches and procedural methods were tested: sequence of assignment to accessible residues, atomic vs. amino acid coordinates, original vs. coarse-grained models, fine-tuning of input parameters, variation of channel characteristics (e.g., width), rugosity effects. A critical comparison of the water sites on the surface, in active centres, ligand binding sites, interior, crevices, channels, contact areas etc. proves far-reaching identity of crystallographic data, if available, and our predictions. Examples presented include proteins ranging from simple to complex, multisubunit, liganded proteins and water-channels in membrane proteins (e.g., aquaporins) as well. Our hydration algorithms allow the prediction of the number and position of discrete water molecules, even in those cases where no or scant crystallographic waters or water channels have been identified. Our approaches may be used in the future as useful tools for improving crystal data.
The good agreement of the results found for hydrated models by crystallography, SAXS, and other techniques offers the possibility to complement different techniques and to predict details such as the localization of potential water sites -even in those cases where no or insufficient amounts of waters, water clusters or water channels have been identified by crystallography. Variation of input parameters (such as probe radius) should also allow the width and type of channels (other than water channels) to be established. Visualization of protein sites of special concern (charged, hydrophilic and hydrophobic residues and patches, radiosensitive groups, active centres of enzymes, ligand binding sites, docking sites and contact areas) together with individual waters provides the basis for a much deeper understanding of the mechanisms of biological action and effective biotechnological application.
Considering quite different proteins, it can be stated that the majority of waters is bound to polar AA residues, located primarily outside. Some hydrophobic patches on the protein surface prevent the formation of a perfect, uniform water shell. The hydrated models also reveal that some water molecules can be found in the protein interior (e.g. in crevices, clefts, cavities or between subunits).
Both structural and hydrodynamic parameters and scattering profiles proved good agreement between observed and predicted quantities. In conclusion, about two water molecules were found per AA residue, corresponding to about 0.35 g of water per g of protein.
Anhydrous and hydrated models differ substantially in their volume-to-mass ratios ( 1 . 2 v s . 1 . 6 -1 . 7 ) . D e t a i l e d d a t a o n v a r i o u s p r o t e i n s m a y b e f o u n d i n p r e v i o u s p a p e r s Durchschlag & Zipper, 2001, 2005, 2008, 2010b.