An improved relaxed complex scheme for receptor flexibility in computer-aided drug design
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The interactions among associating (macro)molecules are dynamic, which adds to the complexity of molecular recognition. While ligand flexibility is well accounted for in computational drug design, the effective inclusion of receptor flexibility remains an important challenge. The relaxed complex scheme (RCS) is a promising computational methodology that combines the advantages of docking algorithms with dynamic structural information provided by molecular dynamics (MD) simulations, therefore explicitly accounting for the flexibility of both the receptor and the docked ligands. Here, we briefly review the RCS and discuss new extensions and improvements of this methodology in the context of ligand binding to two example targets: kinetoplastid RNA editing ligase 1 and the W191G cavity mutant of cytochrome c peroxidase. The RCS improvements include its extension to virtual screening, more rigorous characterization of local and global binding effects, and methods to improve its computational efficiency by reducing the receptor ensemble to a representative set of configurations. The choice of receptor ensemble, its influence on the predictive power of RCS, and the current limitations for an accurate treatment of the solvent contributions are also briefly discussed. Finally, we outline potential methodological improvements that we anticipate will assist future development.
KeywordsClustering Docking Ensemble-based docking Kinetoplastid RNA editing ligase 1 Molecular dynamics Non-redundant ensemble Protein–ligand binding Relaxed complex method Representative ensemble Virtual screening W191G cytochrome c peroxidase
Kinetoplastid RNA editing ligase 1
Relaxed complex scheme
W191G cavity mutant of cytochrome c peroxidase
A full understanding of molecular recognition presents a problem of intense interest to the field of computer-aided drug design and molecular sciences in general. The interactions between ligand molecules and their corresponding receptors are dynamic and complex. Techniques that best address these issues must account for the conformational flexibility of both the ligand and the receptor and do so in an accurate and efficient manner. While the ability to explore ligand flexibility is well established, computer-aided drug design methodologies have only recently begun to take receptor flexibility into account when searching for and optimizing functional inhibitors. Since it is widely accepted that ligands may bind to receptor conformations that occur infrequently in the receptor’s dynamics, and that the local motions of active site residues can drastically alter the binding and specificity of ligands to their target, the ability to efficiently sample these rare dynamics and furthermore, to incorporate the resulting conformations into the drug design protocol, remains an important challenge (reviewed in references [1, 2, 3, 4, 5]).
A closely related challenge is the development of effective methods to predict the binding propensity for series of compounds or flexible peptides to a given receptor [6, 7, 8, 9, 10, 11]. Approaches based on scoring functions or compound libraries require large amounts of data to be available a priori. These methods include computational virtual screening [12, 13, 14, 15, 16, 17, 18], docking [18, 19, 20, 21, 22, 23], and similarity searching [24, 25]. More advanced treatments of receptor–ligand binding can be achieved using molecular dynamics (MD) simulations. Free energy changes can then be estimated based on coupling-parameter approaches, such as thermodynamic integration (TI) and free energy perturbation (FEP) [11, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], which describe a higher physical complexity of the binding process and include an extensive sampling of receptor, ligand, and solvent phase spaces. Importantly, the latter methods provide not only binding free energy estimates, but also a reliable measure of their accuracy. Yet, they are typically too computationally expensive to be applied to extensive sets (∼105) of compounds, which is the usual scenario for newly discovered biological targets.
The RCS is a promising computational methodology that combines the advantages of docking algorithms with dynamic structural information provided by MD simulations, explicitly accounting for the flexibility of both the receptor and docked ligands. This procedure is appealing as a large variety of conformational changes may characterize ligand binding processes of biochemical and medical interest and, more generally, molecular recognition. The RCS has been developed in combination with various MD software packages and AutoDock for the ligand docking. Although other docking programs can be considered, all RCS applications to date have employed AutoDock, a widely distributed and tested docking program that has been shown to be successful in a variety of docking studies [20, 21, 22]. The RCS was first applied to the FKBP binding protein  and tested using improved re-scoring functions based on MM-PBSA models . Applications of the RCS identified a novel-binding trench in HIV integrase . In this work, we sketch the philosophy underlying the RCS, describe new improvements, and present recent applications to exemplify the type of problems that can be tackled with this computational scheme.
Materials and methods
Relaxed complex scheme: short overview
AutoDock is used to carry out the docking experiments and full ligand flexibility is employed. One of the major advantages of AutoDock is its use of a hybrid genetic algorithm (GA) to perform an efficient and effective global search for the ligand . Genetic algorithms are optimization schemes that use the language of natural genetics and evolution, and in the case of AutoDock, the optimization problem is molecular docking between a ligand and a receptor. Typically, the receptor is fixed and the translation, orientation, and conformation of the ligand are explored. Genetically derived terms such as the AutoDock “chromosome,” which describes the ligand state, define its “genotype” and the atomic coordinates of the ligand, which describes its “phenotype,” undergo genetic events such as “selection, crossover, and mutation” during the optimization procedure.
The AutoDock chromosome consists of a string of real-valued genes containing three cartesian coordinates for ligand translation, four variables defining a quaternion that specifies the ligand orientation, and one real-value for each ligand torsion . The global search is carried out on the genotype level and performed with the GA, which allows selection, crossover, and mutation. The ligand-receptor fitness is evaluated based on a semi-empirical scoring function including an empirical estimate for the ligand configurational entropy . The global search is followed by an adaptive-stepping local search that performs energy minimizations on the atomic coordinates. Afterwards, the optimized phenotype is fed back to the genotype, in accordance with “Lamarckian” genetics, from which the algorithm derives its name. Ultimately, solutions better suited to specific interactions have a better score, therefore reproduce and persist, whereas poorer suited ones die off.
The re-docking of the ligands across the ensemble of receptor structures results in a range of predicted binding affinities for each ligand, based on the AutoDock scoring function. The resulting “binding spectrum” for each ligand is then used to reorder the ligands and better predict relative affinity. Various post-processing options can be considered beyond the initial affinity estimate provided by AutoDock, including the application of MM-PBSA, single-step perturbation, LIE, FEP, or TI (Fig. 2). Although more rigorous free energy estimates increase the confidence in the predicted binding energies, they can be prohibitively computationally expensive.
Improved relaxed complex scheme
A first set of improvements involves the docking algorithm itself as implemented in AutoDock version 4.0: (i) a more complete thermodynamic cycle, where the unbound (gas phase) ligand enthalpy is computed, (ii) an improved desolvation term that accounts for a larger number of atom types than in the previous versions, and (iii) a charge model that allows fast calculation of the charge distribution  and compatibility of partial charges between the ligand and the receptor structures . The studies presented here employed this new and improved version of AutoDock (freely available at http://www.autodock.scripps.edu/).
A second set of improvements involves the RCS methodology itself, as described in the following, based on recent applications. The first extension to the RCS we present here is the application of the method for virtual screening, which involves an essential enzyme for the protozoan parasite Trypanosoma brucei. The discovery of several new inhibitors was the result of a streamlined RCS method, providing a concrete example of its success when trying to discover new inhibitors from a large database of compounds . The second methodological advancement for RCS involves accounting for both local-induced and global effects of ligand binding. This is shown with the well-characterized binding of a set of heterocyclic cation ligands to the W191G cavity mutant of cytochrome c peroxidase . The third improvement attempts to define two general algorithms to reduce the number of MD trajectory snapshots for the docking experiments, which increases computational efficiency by orders of magnitude without decreasing its accuracy. First, the KREL1 application uses the QR factorization method available in the MultiSeq plugin in VMD . Second, the W191G cavity mutant of cytochrome c peroxidase (W191G) uses an atom-positional root-mean-square deviation (RMSD) clustering algorithm  as implemented in the rmsdmat2 and cluster2 programs of the GROMOS++ analysis software . Last, we discuss the importance and the difficulties of including explicit water molecules within the binding sites in the RCS docking experiments.
RCS as a tool for enhanced virtual screening
Given a novel protein target, the goal of identifying a new set of potential inhibitors with drug-like properties can be achieved using virtual screening type approaches. Typically these large-scale virtual screens are carried out by evaluating the predicted affinities of thousands of molecules against a single static crystal structure [15, 72]. Here we report on the success of porting the RCS into a virtual screen type application in the search for inhibitors against an essential kinetoplastid RNA editing ligase 1 (KREL1) in T. brucei, the parasite responsible for the devastating tropical disease African sleeping sickness . KREL1 is required for survival of both the insect and bloodstream forms of the parasite , and it is a particularly attractive drug target as there are no known human homologues. The high-resolution crystal structure  provides an excellent platform for computer-aided drug design as well as for MD simulations and the RCS application.
The KREL1 crystal structure revealed a deep active site pocket with several water molecules coordinated to the ATP substrate and the protein. Two 20 ns simulations in explicit solvent were carried out with KREL1, both with and without the bound ATP in order to generate the receptor ensembles . A screen of the crystal structure against the NCI diversity set (containing 1,900 compounds) using AutoDock version 4.0 was performed, and the top twenty-five compounds that obeyed most of Lipinski’s “rules of 5”  were selected for application of the RCS method. The top 25 ligands were then re-docked into the full receptor ensemble as well as a reduced representative set (discussed in further detail below) and these compounds were then re-ranked based on their average binding energy of the most populated cluster.
The results of the RCS virtual screen with KREL1 are particularly promising. Several new inhibitors have been identified with the RCS and an in vitro inhibition assay of the first step in the binding reaction, the adenylation step, was used to verify the computational predictions. These experiments confirmed two of the eight tested compounds found in the initial screen were inhibitory . Importantly, the RCS method resulted in a reordering of the twenty-five compounds that identified inhibitors that would not have otherwise been tested, based on their rank from the static crystal structure screen. Specifically, the best hit as experimentally verified was initially ranked fifteenth, and after RCS reordering became first. In the case of limited resources and low-throughput experimental procedures, where only a handful of the best compounds identified in the screen could be experimentally tested, the application of the RCS method provided a measurable and important enrichment of the initial ranked set.
Accounting for induced fit and the global effects of ligand binding
In nature, a great number of protein–ligand recognition processes are only possible when accompanied by local (i.e., the reorganization of residues upon induced-fit binding) or global (i.e., larger scale conformational changes occurring also in remote structural elements of the receptor upon binding) effects. Our current structural knowledge of biomolecular association phenomena is predominantly based on X-ray crystallography ensemble-averaged structures. Although these experiments provide critical binding information, they typically capture only one state involved in the binding process, which may be a dominant configuration, but not necessarily exclusive. Dynamic information at the atomistic level, as provided by MD simulations, is of fundamental importance and may reveal binding modes and relevant biophysical information otherwise inaccessible to standard experimental techniques.
A relevant example of the importance of predicting receptor-flexibility effects resulted from the application of RCS to HIV integrase. MD simulations of the integrase protein bound to a known inhibitor revealed a new cavity adjacent to the active site . RCS docking of ligands into this newly discovered pocket indicated favorable binding of ligands to this area. This new structural insight was exploited in the development of raltegravir (MK-0518), the first of a new class of antiretroviral agents active against the enzyme integrase that has recently been approved by the FDA .
As the binding propensity defining a given molecular association reflects the relative stabilities of the possible conformations of the receptor, effective drug-design protocols should be based on a distribution of receptor conformations. In this respect, RCS has the advantage of requiring the generation of only one MD ensemble per receptor macro-state (e.g., the open or closed state of a loop gating the binding pocket). This has recently been systematically investigated in the case of the W191G cavity mutant of cytochrome c peroxidase by analyzing the docking of small ligands into alternative ensembles of receptor conformations .
RCS calculations were performed on different gating-loop and binding states: the closed-gate apo, the closed-gate holo (i.e., the complex with the best binder), and the open-gate apo structure, allowing the investigation of the correlation between each compound’s binding affinity and the closed/open state of the gating loop (Fig. 3b) . Additional in silico experiments evaluated the benefits of using non-standard MD trajectories to enhance the conformational sampling (e.g., simulations at high temperature using atom-positional restraining potentials) or simulate an unphysical generalized-ligand interaction encompassing the characteristics of all potential binders . In the case of 2a5mt, the optimal binding spectrum occurs when docked into the receptor conformations from the holo ensemble. Although both the holo and apo receptor ensembles generate ligand-binding poses (i.e., the geometry of a docked ligand into the binding site) that are similar to those determined experimentally, the 2a5mt binding affinities are closer to the experimental results for the holo ensemble (Fig. 3c). This illustrates that the holo ensemble is the best choice to perform RCS calculations for the 2a5mt ligand, and suggests the same is likely the case for other ligands with similar chemical and electrostatic properties .
A different picture emerges when bzi binds to the same cavity. In this case, the best agreement between RCS affinities and the experimental free energies is found when using the apo-open receptor ensemble. This agrees with the experimental observation that bzi shifts the propensity of the gating-loop configurations towards the open-gate state. Again, the ligand-binding poses (i.e., the relative orientation of the docked ligand into the W191G artificial cavity) are very similar between the RCS method and the crystallographic complexes (Fig. 3c). Although a false negative is found when docking bzi to the ensemble of apo receptor structures, bzi binds favorably and with a binding mode similar to experiment when using the closed-gate holo ensemble (Fig 3d). These promising results suggest that it may be possible to capture different binding propensities depending on both local and global receptor rearrangements upon binding.
Effective reduction of the receptor ensemble
In the original RCS, the computational docking experiments were carried out using snapshots extracted at equal time intervals from the MD trajectories. As the simulations are carried out for several nanoseconds, this typically sums up to ∼104 to 105 receptor structures, many of which may be conformationally redundant. Two recent studies have investigated alternative methods to distill the structural information to a reduced, yet meaningful set.
A novel method to distill the ensemble of structures to a non-redundant set is the so-called “QR factorization” method. This technique was originally developed to remove inherent bias in structure databases and distill, from a vast quantity of redundant information, a minimal basis set of protein structures that accurately spans the evolutionary phase space of a particular protein . It has also been applied to an ensemble of NMR structures in order to determine a small, representative subset of structures from a larger experimental dataset  and to create non-redundant sequence alignments . This technique has most recently been incorporated into the RCS, where a multiple structural alignment of the receptor ensemble is performed with STAMP . This alignment algorithm operates progressively: all possible pair-wise alignments are computed, followed by a hierarchical clustering analysis based on a structural similarity measure to build the multiple structural alignment. The measure of structural similarity applied here is QH, which essentially measures the distance between all pairs of Cα atoms among all aligned structures. Although the development of QH was motivated by the need to include gaps in order to build a similarity measure for more distantly related proteins, in the case of aligning the receptor ensemble, the gap term is unnecessary as structures of the same protein are aligned. The structural alignment is stored in a multidimensional matrix of dimension maln × nreceptor structures × d, where d encodes the rotated Cα atoms coordinates. In this matrix, each receptor structure is represented in a column and the rows represent the multiple alignment. Finally, a multi-dimensional QR factorization algorithm is applied to the encoded alignment of receptor structures, which results in a reordering of the structures based on increasing linear dependence. This reordering subsequently allows the construction of non-redundant sets of structures at some user-defined cutoff, representing a certain dynamical configuration space.
An alternative method is clustering based on a matrix of all pair-wise RMSD of the aligned structures in the receptor ensemble. If the binding region of the receptor is known a priori the clustering algorithm can focus on this particular subset of residues that constitute the binding site. The employed algorithm was originally developed to capture the dominant configurations of an ensemble of structures for flexible peptides  and its application has been further extended to flexible molecules [86, 87] and protein surface loops . After removing overall rotation and translations, the atoms of the binding region are superimposed using their Cα atoms coordinates. A matrix that contains all pair-wise RMSD values among all the structures in the trajectory is created. Next, the matrix is divided into batches corresponding to similar structures using the RMSD values, with a clustering algorithm  and a user-defined cutoff. This clustering allows docking trials to be performed on a reduced number of significant conformations, while retaining the dominant characteristics of the entire spectrum of binding modes.
In the case of the W191G cavity mutant of cytochrome c peroxidase, re-docking into the entire ensemble of structures would require docking to 104 snapshots. However, when these trajectory snapshots were clustered into groups of similar configurations with a RMSD similarity criterion of 0.1 nm for the cavity residues, the resulting two most dominant clusters of trajectory structures represented 36 and 16%, 81 and 10%, 48 and 23% of the structures for the apo, holo, and apo-open ensembles, respectively (Fig. 4b). This RMSD clustering resulted in a 99% reduction of computational cost for the RCS docking stage .
In addition to improving the computational efficiency of the RCS, clustering analyses can also supply useful information about the flexibility of the receptor, by analyzing the number of structures representing a certain QH or RMSD threshold cutoff (in the QR factorization method) or the cluster population versus the number of clusters populated (in the RMSD clustering method). This type of information gives quantitative insight about the local and global flexibility of the receptor. The computational gain due to these types of clustering schemes seems particularly useful when screening large compound databases.
Choice of MD receptor ensemble and RCS predictive power
One of the major challenges for hybrid docking techniques is the possibility to screen large compound databases and extract potential binders based on very limited a priori knowledge of the binding process itself. In this context, the W191G cytochrome c peroxidase system is used as a platform to investigate how the choice of MD receptor ensemble for RCS calculations affects the predictive power of this methodology . To reflect the different amounts of knowledge that may be available on the binding process, different typical scenarios in drug discovery were considered, including cases in which: (i) no information is available on the location of the binding site, (ii) X-ray structures of the protein–ligand complexes and knowledge on potential binders is not available, and (iii) the X-ray structures known for the protein–ligand complex do not define unique ligand-binding poses. Corresponding to the above scenarios: (i) the RCS technique using the holo-receptor ensemble finds true positives using a docking grid that encompasses the entire W191G cytochrome c peroxidase structure; (ii) the number of true positives and true negatives can be significantly increased versus the number of false positives and false negatives by employing an MD receptor ensemble containing a generalized type of unphysical ligand that reflects the main structural properties of the compounds in the database, when compared to equivalent docking calculations performed on the apo MD receptor ensemble; and (iii) the multiple binding orientations characterizing the true positives do not necessarily correspond to non-accurate docking results when compared to the raw electron density data from X-ray crystallography. The quality of the binding poses can be judged by a combined evaluation of (i) the distribution of the docked-ligand cluster populations versus the cluster number, (ii) RMSD from the corresponding experimental complex after superimposing the structures as described above, and (iii) the comparison of the different poses for a same ligand. These results open new possibilities for enhancing the predictive power of RCS calculations in so-called “blind” test cases (when information is missing concerning the binding process), and they also suggest that the best possible choice of MD ensemble may depend on the amount of knowledge available case by case. Additional scenarios can be considered as well, for example including homology-modeling type of approaches to generate the initial receptor structural configuration.
Accurate description of solvent contributions
An effective representation of the solvent during the docking trials is a major factor limiting the accuracy of docking calculations. Until recently, RCS calculations have been performed using only the receptor structure and ligand, even when the MD trajectory structures were generated in combination with explicit water models. Accounting for the specific role of conserved water molecules is highly relevant as they may perturb the flexibility of a bound ligand, significantly alter the electrostatic environment experienced by a small molecule, and even occlude potential areas of binding. The explicit inclusion of these contributions will certainly improve the accuracy of the ligand-binding description, similarly to what recently reported for protein–protein docking . Here, we present two new applications of the RCS that tested docking of the ligands into MD generated receptor structures with and without cavity water molecules. What emerges from both examples is the important (thermo)dynamic role of specific waters for the binding process.
In the W191G cytochrome c peroxidase application, several docking calculations were performed to investigate the influence of the crystallographic water sites on AutoDock binding affinities and ligand poses. The tests were performed with rigid-protein docking calculations on different receptor models, alternatively including or excluding water site 308, which was suggested to be a highly conserved location for a bound water based on X-ray structures for a large group of compounds . The results from the docking calculations are in agreement with what was previously suggested by similar tests based on AutoDock version 3.0, which showed that the introduction of even a single water molecule can significantly perturb the binding propensity of most of the ligands .
While the effect on the predicted binding affinities and poses is at variance with the specific ligand, a systematic consequence of the introduction of one water molecule into the W191G cavity is the significant reduction of the configurational space available to the ligand during the docking trials. MD simulations of the W191G cavity predict the location of the highly favorable water sites (within X-ray crystallography resolution and refinement assumptions) compared with the available experimental data (Fig. 5b). Additionally, MD simulations reveal a larger number of favorable water sites, and allow the description of the dynamic behavior of the solvent, including the swapping of water molecules between highly favorable regions . Based on these observations we suggest that the significant effects of including explicit water in the static dockings may be an artificial consequence of the introduction of bound (static) water molecules in the cavity, whereas locally disordered (dynamically swapping among the favorable sites) water molecules should be considered instead. We note that an accurate sampling of receptor, ligand, and solvent phase spaces is, in principle, reached by more expensive free energy calculations [11, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36].
Future methodological improvements
The development of computational tools for computer-aided drug design depends on the critical compromise between accuracy and computational costs. Ideally, the most reliable prediction of molecular affinity can be obtained through rigorous free energy calculations of the ligand-binding process [11, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]. In practice, however, the CPU time typically required to perform such free energy calculations on a few candidates (bottom of the funnel diagram in Fig. 1) is comparable to that involved in rough geometrical recognition over a pool of molecules more than five orders of magnitude larger (top of the funnel diagram in Fig. 1). Although the theory and methods are well established for calculating free energy in practice, they are still prohibitively expensive to be employed in high-throughput screening of drug-like databases. The future development of hybrid techniques, and especially the RCS, is therefore twofold.
First, it will certainly involve the refinement of the underlying physical models describing ligand-binding (thermo)dynamics in increased detail, especially during the docking stage. Although the results presented here include the unbound (gas phase) ligand enthalpy term at the docking stage , a complete description of the thermodynamic cycle of binding is still far from being explicitly treated in RCS. Previous studies investigated the benefits of rescoring the docked complexes using a more accurate (implicit solvent) description of the solvent contributions . More recently, the role of ligand entropy in the refinement of protein–ligand docking predictions has been evaluated [90, 91]. Additionally, accurate configurational entropy calculations from MD simulations and a complete quasi-harmonic analysis have demonstrated that the thermodynamic role of receptor flexibility is generally underestimated . Alternative strategies based on MM-PBSA-type thermodynamic estimates, which involve the implicit description of the solvation and desolvation thermodynamic effects involved in protein–ligand binding, are being pursued. These terms are currently implemented in the AutoDock 4.0 scoring functions on empirical basis only. Using a more generally parameterized MD-type force field to evaluate and rescore the docked complexes should lead to more accurate estimates of the binding affinities, as well as allow for increased transferability of the RCS to a more diverse set of systems.
Second, concerning the final refinement procedure (bottom of the funnel in Fig. 1): the application of accurate (explicit solvent) free energy calculations for a larger number of ligands and receptors of increasing size will primarily be influenced by force field accuracy, the ability to attain extensive sampling, and an improved description of the enthalpy–entropy compensation thermodynamics. Although the computational determination of free energy changes has become a standard procedure for which a variety of techniques have been developed, absolute entropies and their differences are still rarely computed. The rapid development of computer resources accompanied by force field refinement and improved simulation algorithms will naturally extend the range of problems that free energy calculations can directly assess.
Accounting for receptor flexibility in computer-aided drug design is still a major challenge. Recent examples illustrate the importance of predicting and including induced-fit effects upon receptor–ligand binding. MD simulations of receptors in complex with known and potential inhibitors provide relevant biochemical insights, which are otherwise not accessible through standard experimental techniques. Despite this, a general and highly transferable procedure that reliably and efficiently accommodates receptor flexibility is still lacking. The extensions and methodological improvements to the RCS presented here take important steps toward offering such a streamlined procedure. Our examples indicate that alternative choices of receptor ensembles can significantly alter the predictive power of RCS calculations, and that it is possible to reduce the receptor ensemble to a non-redundant set of configurations by various techniques without losing relevant binding information. Furthermore, both example systems indicate that the role of explicit water molecules in molecular association remains one of the key components of computer-aided drug design methods to be further investigated. A summary of the crucial points that we anticipate will help drive the future development of the RCS was presented and what emerges is that a clear and pressing challenge, closely coupled to receptor flexibility, is the development of methods to better estimate ligand and receptor entropy. Their subsequent application to molecular association thermodynamics will allow an increased accuracy in the description of enthalpy-entropy compensation effects during the ligand binding process.
We thank Justin Gullingsrud, William “Lindy” Lindstrom, and Jung-Hsin Lin for fruitful discussions. R. E. A. is funded by National Institutes of Health (NIH) Grant 1F32 GM077729 and National Science Foundation (NSF) MRAC Grant CHE060073N. Funding by NIH GM31749, NSF MCB-0506593 and MCA93S013 (to J. A. M.) also supports this work. Additional support from the Howard Hughes Medical Institute, San Diego Supercomputing Center, Accelrys, Inc., the W. M. Keck Foundation, the National Biomedical Computational Resource and the Center for Theoretical Biological Physics is gratefully acknowledged.
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