One- and two-body decomposable Poisson-Boltzmann methods for protein design calculations

Research progress on unique paratope structure, antigen binding modes, and systematic mutagenesis strategies of single-domain antibodies

Single-domain antibodies (sdAbs) showed the incredible advantages of small molecular weight, excellent affinity, specificity, and stability compared with traditional IgG antibodies, so their potential in binding hidden antigen epitopes and hazard detection in food, agricultural and veterinary fields were gradually explored. Moreover, its low immunogenicity, easy-to-carry target drugs, and penetration of the blood-brain barrier have made sdAbs remarkable achievements in medical treatment, toxin neutralization, and medical imaging. With the continuous development and maturity of modern molecular biology, protein analysis software and database with different algorithms, and next-generation sequencing technology, the unique paratope structure and different antigen binding modes of sdAbs compared with traditional IgG antibodies have aroused the broad interests of researchers with the increased related studies. However, the corresponding related summaries are lacking and needed. Different antigens, especially hapten antigens, show distinct binding modes with sdAbs. So, in this paper, the unique paratope structure of sdAbs, different antigen binding cases, and the current maturation strategy of sdAbs were classified and summarized. We hope this review lays a theoretical foundation to elucidate the antigen-binding mechanism of sdAbs and broaden the further application of sdAbs.

Intrinsic basis of thermostability of prolyl oligopeptidase from Pyrococcus furiosus

Salt-bridges play a key role in the thermostability of proteins adapted in stress environments whose intrinsic basis remains to be understood. We find that the higher hydrophilicity of PfP than that of HuP is due to the charged but not the polar residues. The primary role of these residues is to enhance the salt-bridges and their ME. Unlike HuP, PfP has made many changes in its intrinsic property to strengthen the salt-bridge. First, the desolvation energy is reduced by directing the salt-bridge towards the surface. Second, it has made bridge-energy more favorable by recruiting energetically advantageous partners with high helix-propensity among the six possible salt-bridge pairs. Third, ME-residues that perform intricate interactions have increased their energy contribution by making major changes in their binary properties. The use of salt-bridge partners as ME-residues, and ME-residues' overlapping usage, predominant in helices, and energetically favorable substitution are some of the favorable features of PfP compared to HuP. These changes in PfP reduce the unfavorable, increase the favorable ME-energy. Thus, the per salt-bridge stability of PfP is greater than that of HuP. Further, unfavorable target ME-residues can be identified whose mutation can increase the stability of salt-bridge. The study applies to other similar systems.

Stability of buried and networked salt-bridges (BNSB)in thermophilic proteins

Thermophilic proteins function at high temperature, unlike mesophilic proteins. Thermo-stability of these proteins is due to the unique buried and networked salt-bridge (BNSB). However, it is known that the desolvation cost of BNSB is too high compared to other favorable energy terms. Nonetheless, it is known that stability is provided generally by hydrophobic isosteres without the need for BNSB. We show in this analysis that the BNSB is the optimal evolutionary design of salt-bridge to offset desolvation cost efficiently. Hence, thermophilic proteins with a high level of BNSB provide thermo-stability.

Trends in therapeutic antibody affinity maturation: From in-vitro towards next-generation sequencing approaches

Current advances in antibody engineering driving the strongest growth area in biotherapeutic agents development. Affinity improvement that is mainly important for biological activity and clinical efficacy of therapeutic antibodies, has still remained a challenging task. In the human body, during a course of immune response affinity maturation increase antibody activity by several rounds of somatic hypermutation and clonal selection in the germinal center. The final outputs are antibodies representing higher affinity and specificity against a particular antigen. In the realm of biotechnology, exploring of mutations which improve antibody affinity while preserving its specificity and stability is an extremely time-consuming and laborious process. Recent advances in computational algorithms and DNA sequencing technologies help researchers to redesign antibody structure to achieve desired properties such as improved binding affinity. In this review, we briefly described the principle of affinity maturation and different corresponding in vitro techniques. Also, we recapitulated the most recent advancements in the field of antibody affinity maturation including computational approaches and next-generation sequencing (NGS).

Robustness and Efficiency of Poisson-Boltzmann Modeling on Graphics Processing Units

Poisson-Boltzmann equation (PBE) based continuum electrostatics models have been widely used in modeling electrostatic interactions in biochemical processes, particularly in estimating protein-ligand binding affinities. Fast convergence of PBE solvers is crucial in binding affinity computations as numerous snapshots need to be processed. Efforts have been reported to develop PBE solvers on graphics processing units (GPUs) for efficient modeling of biomolecules, though only relatively simple successive over-relaxation and conjugate gradient methods were implemented. However, neither convergence nor scaling properties of the two methods are optimal for large biomolecules. On the other hand, geometric multigrid (MG) has been shown to be an optimal solver on CPUs, though no MG have been reported for biomolecular applications on GPUs. This is not a surprise as it is a more complex method and depends on simpler but limited iterative methods such as Gauss-Seidel in its core relaxation procedure. The robustness and efficiency of MG on GPUs are also unclear. Here we present an implementation and a thorough analysis of MG on GPUs. Our analysis shows that robustness is a more pronounced issue than efficiency for both MG and other tested solvers when the single precision is used for complex biomolecules. We further show how to balance robustness and efficiency utilizing MG's overall efficiency and conjugate gradient's robustness, pointing to a hybrid GPU solver with a good balance of efficiency and accuracy. The new PBE solver will significantly improve the computational throughput for a range of biomolecular applications on the GPU platforms.

Computational affinity maturation of camelid single-domain intrabodies against the nonamyloid component of alpha-synuclein

Improving the affinity of protein-protein interactions is a challenging problem that is particularly important in the development of antibodies for diagnostic and clinical use. Here, we used structure-based computational methods to optimize the binding affinity of V_HNAC1, a single-domain intracellular antibody (intrabody) from the camelid family that was selected for its specific binding to the nonamyloid component (NAC) of human α-synuclein (α-syn), a natively disordered protein, implicated in the pathogenesis of Parkinson's disease (PD) and related neurological disorders. Specifically, we performed ab initio modeling that revealed several possible modes of V_HNAC1 binding to the NAC region of α-syn as well as mutations that potentially enhance the affinity between these interacting proteins. While our initial design strategy did not lead to improved affinity, it ultimately guided us towards a model that aligned more closely with experimental observations, revealing a key residue on the paratope and the participation of H4 loop residues in binding, as well as confirming the importance of electrostatic interactions. The binding activity of the best intrabody mutant, which involved just a single amino acid mutation compared to parental V_HNAC1, was significantly enhanced primarily through a large increase in association rate. Our results indicate that structure-based computational design can be used to successfully improve the affinity of antibodies against natively disordered and weakly immunogenic antigens such as α-syn, even in cases such as ours where crystal structures are unavailable.

Design of catalytic polypeptides and proteins

The first part of this review article lists examples of complete, empirical de novo design that made important contributions to the development of the field and initiated challenging projects. The second part of this article deals with computational design of novel enzymes in native protein scaffolds; active designs were refined through random and site-directed mutagenesis producing artificial enzymes with nearly native enzyme- like activities against a number of non-natural substrates. Combining aspects of de novo design and biological evolution of nature's enzymes has started and will accelerate the development of novel enzyme activities.

Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

Recent Developments and Applications of the MMPBSA Method

The Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) approach has been widely applied as an efficient and reliable free energy simulation method to model molecular recognition, such as for protein-ligand binding interactions. In this review, we focus on recent developments and applications of the MMPBSA method. The methodology review covers solvation terms, the entropy term, extensions to membrane proteins and high-speed screening, and new automation toolkits. Recent applications in various important biomedical and chemical fields are also reviewed. We conclude with a few future directions aimed at making MMPBSA a more robust and efficient method.

Computational design of membrane proteins using RosettaMembrane

Computational membrane protein design is challenging due to the small number of high-resolution structures available to elucidate the physical basis of membrane protein structure, multiple functionally important conformational states, and a limited number of high-throughput biophysical assays to monitor function. However, structural determination of membrane proteins has made tremendous progress in the past years. Concurrently the field of soluble computational design has made impressive inroads. These developments allow us to tackle the formidable challenge of designing functional membrane proteins. Herein, Rosetta is benchmarked for membrane protein design. We evaluate strategies to cope with the often reduced quality of experimental membrane protein structures. Further, we test the usage of symmetry in design protocols, which is particularly important as many membrane proteins exist as homo-oligomers. We compare a soluble scoring function with a scoring function optimized for membrane proteins, RosettaMembrane. Both scoring functions recovered around half of the native sequence when completely redesigning membrane proteins. However, RosettaMembrane recovered the most native-like amino acid property composition. While leucine was overrepresented in the inner and outer-hydrophobic regions of RosettaMembrane designs, it resulted in a native-like surface hydrophobicity indicating that it is currently the best option for designing membrane proteins with Rosetta.

A Continuum Poisson-Boltzmann Model for Membrane Channel Proteins

Membrane proteins constitute a large portion of the human proteome and perform a variety of important functions as membrane receptors, transport proteins, enzymes, signaling proteins, and more. Computational studies of membrane proteins are usually much more complicated than those of globular proteins. Here, we propose a new continuum model for Poisson-Boltzmann calculations of membrane channel proteins. Major improvements over the existing continuum slab model are as follows: (1) The location and thickness of the slab model are fine-tuned based on explicit-solvent MD simulations. (2) The highly different accessibilities in the membrane and water regions are addressed with a two-step, two-probe grid-labeling procedure. (3) The water pores/channels are automatically identified. The new continuum membrane model is optimized (by adjusting the membrane probe, as well as the slab thickness and center) to best reproduce the distributions of buried water molecules in the membrane region as sampled in explicit water simulations. Our optimization also shows that the widely adopted water probe of 1.4 Å for globular proteins is a very reasonable default value for membrane protein simulations. It gives the best compromise in reproducing the explicit water distributions in membrane channel proteins, at least in the water accessible pore/channel regions. Finally, we validate the new membrane model by carrying out binding affinity calculations for a potassium channel, and we observe good agreement with the experimental results.

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

Numerical interpretation of molecular surface field in dielectric modeling of solvation

Continuum solvent models, particularly those based on the Poisson-Boltzmann equation (PBE), are widely used in the studies of biomolecular structures and functions. Existing PBE developments have been mainly focused on how to obtain more accurate and/or more efficient numerical potentials and energies. However to adopt the PBE models for molecular dynamics simulations, a difficulty is how to interpret dielectric boundary forces accurately and efficiently for robust dynamics simulations. This study documents the implementation and analysis of a range of standard fitting schemes, including both one-sided and two-sided methods with both first-order and second-order Taylor expansions, to calculate molecular surface electric fields to facilitate the numerical calculation of dielectric boundary forces. These efforts prompted us to develop an efficient approximated one-dimensional method, which is to fit the surface field one dimension at a time, for biomolecular applications without much compromise in accuracy. We also developed a surface-to-atom force partition scheme given a level set representation of analytical molecular surfaces to facilitate their applications to molecular simulations. Testing of these fitting methods in the dielectric boundary force calculations shows that the second-order methods, including the one-dimensional method, consistently perform among the best in the molecular test cases. Finally, the timing analysis shows the approximated one-dimensional method is far more efficient than standard second-order methods in the PBE force calculations. © 2017 Wiley Periodicals, Inc.

Automated protein design: Landmarks and operational principles

Protein design has an eventful history spanning over three decades, with handful of success stories reported, and numerous failures not reported. Design practices have benefited tremendously from improvements in computer hardware and advances in scientific algorithms. Though protein folding problem still remains unsolved, the possibility of having multiple sequence solutions for a single fold makes protein design a more tractable problem than protein folding. One of the most significant advancement in this area is the implementation of automated design algorithms on pre-defined templates or completely new folds, optimized through deterministic and heuristic search algorithms. This progress report provides a succinct presentation of important landmarks in automated design attempts, followed by brief account of operational principles in automated design methods.

Modeling Membrane Protein-Ligand Binding Interactions: The Human Purinergic Platelet Receptor

Membrane proteins, due to their roles as cell receptors and signaling mediators, make prime candidates for drug targets. The computational analysis of protein-ligand binding affinities has been widely employed as a tool in rational drug design efforts. Although efficient implicit solvent-based methods for modeling globular protein-ligand binding have been around for many years, the extension of such methods to membrane protein-ligand binding is still in its infancy. In this study, we extended the widely used Amber/MMPBSA method to model membrane protein-ligand systems, and we used it to analyze protein-ligand binding for the human purinergic platelet receptor (P2Y12R), a prominent drug target in the inhibition of platelet aggregation for the prevention of myocardial infarction and stroke. The binding affinities, computed by the Amber/MMPBSA method using standard parameters, correlate well with experiment. A detailed investigation of these parameters was conducted to assess their impact on the accuracy of the method. These analyses show the importance of properly treating the nonpolar solvation interactions and the electrostatic polarization in the binding of nucleotide agonists and non-nucleotide antagonists to P2Y12R. On the basis of the crystal structures and the experimental conditions in the binding assay, we further hypothesized that the nucleotide agonists lose their bound magnesium ion upon binding to P2Y12R, and our computational study supports this hypothesis. Ultimately, this work illustrates the value of computational analysis in the interpretation of experimental binding reactions.

Calculating protein-ligand binding affinities with MMPBSA: Method and error analysis

Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) methods have become widely adopted in estimating protein-ligand binding affinities due to their efficiency and high correlation with experiment. Here different computational alternatives were investigated to assess their impact to the agreement of MMPBSA calculations with experiment. Seven receptor families with both high-quality crystal structures and binding affinities were selected. First the performance of nonpolar solvation models was studied and it was found that the modern approach that separately models hydrophobic and dispersion interactions dramatically reduces RMSD's of computed relative binding affinities. The numerical setup of the Poisson-Boltzmann methods was analyzed next. The data shows that the impact of grid spacing to the quality of MMPBSA calculations is small: the numerical error at the grid spacing of 0.5 Å is already small enough to be negligible. The impact of different atomic radius sets and different molecular surface definitions was further analyzed and weak influences were found on the agreement with experiment. The influence of solute dielectric constant was also analyzed: a higher dielectric constant generally improves the overall agreement with experiment, especially for highly charged binding pockets. The data also showed that the converged simulations caused slight reduction in the agreement with experiment. Finally the direction of estimating absolute binding free energies was briefly explored. Upon correction of the binding-induced rearrangement free energy and the binding entropy lost, the errors in absolute binding affinities were also reduced dramatically when the modern nonpolar solvent model was used, although further developments were apparently necessary to further improve the MMPBSA methods. © 2016 Wiley Periodicals, Inc.

Dead-End Elimination with a Polarizable Force Field Repacks PCNA Structures

A balance of van der Waals, electrostatic, and hydrophobic forces drive the folding and packing of protein side chains. Although such interactions between residues are often approximated as being pairwise additive, in reality, higher-order many-body contributions that depend on environment drive hydrophobic collapse and cooperative electrostatics. Beginning from dead-end elimination, we derive the first algorithm, to our knowledge, capable of deterministic global repacking of side chains compatible with many-body energy functions. The approach is applied to seven PCNA x-ray crystallographic data sets with resolutions 2.5-3.8 Å (mean 3.0 Å) using an open-source software. While PDB_REDO models average an Rfree value of 29.5% and MOLPROBITY score of 2.71 Å (77th percentile), dead-end elimination with the polarizable AMOEBA force field lowered Rfree by 2.8-26.7% and improved mean MOLPROBITY score to atomic resolution at 1.25 Å (100th percentile). For structural biology applications that depend on side-chain repacking, including x-ray refinement, homology modeling, and protein design, the accuracy limitations of pairwise additivity can now be eliminated via polarizable or quantum mechanical potentials.

Computational design of enzyme-ligand binding using a combined energy function and deterministic sequence optimization algorithm

Enzyme amino-acid sequences at ligand-binding interfaces are evolutionarily optimized for reactions, and the natural conformation of an enzyme-ligand complex must have a low free energy relative to alternative conformations in native-like or non-native sequences. Based on this assumption, a combined energy function was developed for enzyme design and then evaluated by recapitulating native enzyme sequences at ligand-binding interfaces for 10 enzyme-ligand complexes. In this energy function, the electrostatic interaction between polar or charged atoms at buried interfaces is described by an explicitly orientation-dependent hydrogen-bonding potential and a pairwise-decomposable generalized Born model based on the general side chain in the protein design framework. The energy function is augmented with a pairwise surface-area based hydrophobic contribution for nonpolar atom burial. Using this function, on average, 78% of the amino acids at ligand-binding sites were predicted correctly in the minimum-energy sequences, whereas 84% were predicted correctly in the most-similar sequences, which were selected from the top 20 sequences for each enzyme-ligand complex. Hydrogen bonds at the enzyme-ligand binding interfaces in the 10 complexes were usually recovered with the correct geometries. The binding energies calculated using the combined energy function helped to discriminate the active sequences from a pool of alternative sequences that were generated by repeatedly solving a series of mixed-integer linear programming problems for sequence selection with increasing integer cuts.

Biological applications of classical electrostatics methods

Continuum electrostatics modeling of solvation based on the Poisson–Boltzmann (PB) equation has gained wide acceptance in biomolecular applications such as energetic analysis and structural visualization. Successful application of the PB solvent models requires careful calibration of the solvation parameters. Extensive testing and validation is also important to ensure accuracy in their applications. Limitation in the continuum modeling of solvation is also a known issue in certain biomolecular applications. Growing interest in membrane systems has further spurred developmental efforts to allow inclusion of membrane in the PB solvent models. Despite their past successes due to careful parameterization, algorithm development and parallel implementation, there is still much to be done to improve their transferability from the small molecular systems upon which they were developed and validated to complex macromolecular systems as advances in technology continue to push forward, providing ever greater computational resources to researchers to study more interesting biological systems of higher complexity.

Pairwise decomposition of an MMGBSA energy function for computational protein design

Computational protein design (CPD) aims at predicting new proteins or modifying existing ones. The computational challenge is huge as it requires exploring an enormous sequence and conformation space. The difficulty can be reduced by considering a fixed backbone and a discrete set of sidechain conformations. Another common strategy consists in precalculating a pairwise energy matrix, from which the energy of any sequence/conformation can be quickly obtained. In this work, we examine the pairwise decomposition of protein MMGBSA energy functions from a general theoretical perspective, and an implementation proposed earlier for CPD. It includes a Generalized Born term, whose many-body character is overcome using an effective dielectric environment, and a Surface Area term, for which we present an improved pairwise decomposition. A detailed evaluation of the error introduced by the decomposition on the different energy components is performed. We show that the error remains reasonable, compared to other uncertainties.

Design and application of implicit solvent models in biomolecular simulations

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Implicit solvent replaces explicit water by a potential of mean force.

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Popular models are SASA, VOL and Generalized Born.

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Implicit solvent is used in MD, protein modelling, folding, design, prediction and drug screening.

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Large-scale simulations allow for parametrisation via force matching.

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Application to nucleic acids and membranes is challenging.

We review implicit solvent models and their parametrisation by introducing the concepts and recent devlopments of the most popular models with a focus on parametrisation via force matching. An overview of recent applications of the solvation energy term in protein dynamics, modelling, design and prediction is given to illustrate the usability and versatility of implicit solvation in reproducing the physical behaviour of biomolecular systems. Limitations of implicit modes are discussed through the example of more challenging systems like nucleic acids and membranes.

Optimization of affinity, specificity and function of designed influenza inhibitors using deep sequencing

We show that comprehensive sequence-function maps obtained by deep sequencing can be used to reprogram interaction specificity and to leapfrog over bottlenecks in affinity maturation by combining many individually small contributions not detectable in conventional approaches. We use this approach to optimize two computationally designed inhibitors against H1N1 influenza hemagglutinin and, in both cases, obtain variants with subnanomolar binding affinity. The most potent of these, a 51-residue protein, is broadly cross-reactive against all influenza group 1 hemagglutinins, including human H2, and neutralizes H1N1 viruses with a potency that rivals that of several human monoclonal antibodies, demonstrating that computational design followed by comprehensive energy landscape mapping can generate proteins with potential therapeutic utility.

Adapting Poisson-Boltzmann to the self-consistent mean field theory: application to protein side-chain modeling

We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ(1) for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains.

Computational protein design with a generalized Born solvent model: application to Asparaginyl-tRNA synthetase

Computational Protein Design (CPD) is a promising method for high throughput protein and ligand mutagenesis. Recently, we developed a CPD method that used a polar-hydrogen energy function for protein interactions and a Coulomb/Accessible Surface Area (CASA) model for solvent effects. We applied this method to engineer aspartyl-adenylate (AspAMP) specificity into Asparaginyl-tRNA synthetase (AsnRS), whose substrate is asparaginyl-adenylate (AsnAMP). Here, we implement a more accurate function, with an all-atom energy for protein interactions and a residue-pairwise generalized Born model for solvent effects. As a first test, we compute aminoacid affinities for several point mutants of Aspartyl-tRNA synthetase (AspRS) and Tyrosyl-tRNA synthetase and stability changes for three helical peptides and compare with experiment. As a second test, we readdress the problem of AsnRS aminoacid engineering. We compare three design criteria, which optimize the folding free-energy, the absolute AspAMP affinity, and the relative (AspAMP-AsnAMP) affinity. The sequences and conformations are improved with respect to our previous, polar-hydrogen/CASA study: For several designed complexes, the AspAMP carboxylate forms three interactions with a conserved arginine and a designed lysine, as in the active site of the AspRS:AspAMP complex. The conformations and interactions are well maintained in molecular dynamics simulations and the sequences have an inverted specificity, favoring AspAMP over AsnAMP. The method is not fully successful, since experimental measurements with the seven most promising sequences show that they do not catalyze at a detectable level the adenylation of Asp (or Asn) with ATP. This may be due to weak AspAMP binding and/or disruption of transition-state stabilization.

Structural synthetic biotechnology: from molecular structure to predictable design for industrial strain development

The future of industrial biotechnology requires efficient development of highly productive and robust strains of microorganisms. Present praxis of strain development cannot adequately fulfill this requirement, primarily owing to the inability to control reactions precisely at a molecular level, or to predict reliably the behavior of cells upon perturbation. Recent developments in two areas of biology are changing the situation rapidly: structural biology has revealed details about enzymes and associated bioreactions at an atomic level; and synthetic biology has provided tools to design and assemble precisely controllable modules for re-programming cellular metabolic circuitry. However, because of different emphases, to date, these two areas have developed separately. A linkage between them is desirable to harness their concerted potential. We therefore propose structural synthetic biotechnology as a new field in biotechnology, specifically for application to the development of industrial microbial strains.

Computer-aided design of functional protein interactions

Predictive methods for the computational design of proteins search for amino acid sequences adopting desired structures that perform specific functions. Typically, design of 'function' is formulated as engineering new and altered binding activities into proteins. Progress in the design of functional protein-protein interactions is directed toward engineering proteins to precisely control biological processes by specifically recognizing desired interaction partners while avoiding competitors. The field is aiming for strategies to harness recent advances in high-resolution computational modeling-particularly those exploiting protein conformational variability-to engineer new functions and incorporate many functional requirements simultaneously.

An improved pairwise decomposable finite-difference Poisson-Boltzmann method for computational protein design

Our goal is to develop accurate electrostatic models that can be implemented in current computational protein design protocols. To this end, we improve upon a previously reported pairwise decomposable, finite difference Poisson-Boltzmann (FDPB) model for protein design (Marshall et al., Protein Sci 2005, 14, 1293). The improvement involves placing generic sidechains at positions with unknown amino acid identity and explicitly capturing two-body perturbations to the dielectric environment. We compare the original and improved FDPB methods to standard FDPB calculations in which the dielectric environment is completely determined by protein atoms. The generic sidechain approach yields a two to threefold increase in accuracy per residue or residue pair over the original pairwise FDPB implementation, with no additional computational cost. Distance dependent dielectric and solvent-exclusion models were also compared with standard FDPB energies. The accuracy of the new pairwise FDPB method is shown to be superior to these models, even after reparameterization of the solvent-exclusion model.

An object-oriented library for computational protein design

Recent advances in computational protein design have established it as a viable technique for the rational generation of stable protein sequences, novel protein folds, and even enzymatic activity. We present a new and object-oriented library of code, written specifically for protein design applications in C(++), called EGAD Library. The modular fashion in which this library is written allows developers to tailor various energy functions and minimizers for a specific purpose. It also allows for the generation of novel protein design applications with a minimal amount of code investment. It is our hope that this will permit labs that have not considered protein design to apply it to their own systems, thereby increasing its potential as a tool in biology. We also present various uses of EGAD Library: in the development of Interaction Viewer, a PyMOL plug-in for viewing interactions between protein residues; in the repacking of protein cores; and in the prediction of protein-protein complex stabilities.

Polarizable Atomic Multipole Solutes in a Generalized Kirkwood Continuum

The generalized Born (GB) model of continuum electrostatics is an analytic approximation to the Poisson equation useful for predicting the electrostatic component of the solvation free energy for solutes ranging in size from small organic molecules to large macromolecular complexes. This work presents a new continuum electrostatics model based on Kirkwood's analytic result for the electrostatic component of the solvation free energy for a solute with arbitrary charge distribution. Unlike GB, which is limited to monopoles, our generalized Kirkwood (GK) model can treat solute electrostatics represented by any combination of permanent and induced atomic multipole moments of arbitrary degree. Here we apply the GK model to the newly developed Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field, which includes permanent atomic multipoles through the quadrupole and treats polarization via induced dipoles. A derivation of the GK gradient is presented, which enables energy minimization or molecular dynamics of an AMOEBA solute within a GK continuum. For a series of 55 proteins, GK electrostatic solvation free energies are compared to the Polarizable Multipole Poisson-Boltzmann (PMPB) model and yield a mean unsigned relative difference of 0.9%. Additionally, the reaction field of GK compares well to that of the PMPB model, as shown by a mean unsigned relative difference of 2.7% in predicting the total solvated dipole moment for each protein in this test set. The CPU time needed for GK relative to vacuum AMOEBA calculations is approximately a factor of 3, making it suitable for applications that require significant sampling of configuration space.

Progress in computational protein design

Current progress in computational structure-based protein design is reviewed in the areas of methodology and applications. Foundational advances include new potential functions, more efficient ways of computing energetics, flexible treatments of solvent, and useful energy function approximations, as well as ensemble-based approaches to scoring designs for inclusion of entropic effects, improvements to guaranteed and to stochastic search techniques, and methods to design combinatorial libraries for screening and selection. Applications include new approaches and successes in the design of specificity for protein folding, binding, and catalysis, in the redesign of proteins for enhanced binding affinity, and in the application of design technology to study and alter enzyme catalysis. Computational protein design continues to mature and advance.

Potential energy functions for protein design

Different potential energy functions have predominated in protein dynamics simulations, protein design calculations, and protein structure prediction. Clearly, the same physics applies in all three cases. The differences in potential energy functions reflect differences in how the calculations are performed. With improvements in computer power and algorithms, the same potential energy function should be applicable to all three problems. In this review, we examine energy functions currently used for protein design, and look to the molecular mechanics field for advances that could be used in the next generation of design algorithms. In particular, we focus on improved models of the hydrophobic effect, polarization and hydrogen bonding.

Accurate, conformation-dependent predictions of solvent effects on protein ionization constants

Predicting how aqueous solvent modulates the conformational transitions and influences the pKa values that regulate the biological functions of biomolecules remains an unsolved challenge. To address this problem, we developed FDPB_MF, a rotamer repacking method that exhaustively samples side chain conformational space and rigorously calculates multibody protein-solvent interactions. FDPB_MF predicts the effects on pKa values of various solvent exposures, large ionic strength variations, strong energetic couplings, structural reorganizations and sequence mutations. The method achieves high accuracy, with root mean square deviations within 0.3 pH unit of the experimental values measured for turkey ovomucoid third domain, hen lysozyme, Bacillus circulans xylanase, and human and Escherichia coli thioredoxins. FDPB_MF provides a faithful, quantitative assessment of electrostatic interactions in biological macromolecules.

CIRSE: a solvation energy estimator compatible with flexible protein docking and design applications

We present the Coordinate Internal Representation of Solvation Energy (CIRSE) for computing the solvation energy of protein configurations in terms of pairwise interactions between their atoms with analytic derivatives. Currently, CIRSE is trained to a Poisson/surface-area benchmark, but CIRSE is not meant to fit this benchmark exclusively. CIRSE predicts the overall solvation energy of protein structures from 331 NMR ensembles with 0.951+/-0.047 correlation and predicts relative solvation energy changes between members of individual ensembles with an accuracy of 15.8+/-9.6 kcal/mol. The energy of individual atoms in any of CIRSE's 17 types is predicted with at least 0.98 correlation. We apply the model in energy minimization, rotamer optimization, protein design, and protein docking applications. The CIRSE model shows some propensity to accumulate errors in energy minimization as well as rotamer optimization, but these errors are consistent enough that CIRSE correctly identifies the relative solvation energies of designed sequences as well as putative docked complexes. We analyze the errors accumulated by the CIRSE model during each type of simulation and suggest means of improving the model to be generally useful for all-atom simulations.

Simple electrostatic model improves designed protein sequences

Electrostatic interactions are important for both protein stability and function, including binding and catalysis. As protein design moves into these areas, an accurate description of electrostatic energy becomes necessary. Here, we show that a simple distance-dependent Coulombic function parameterized by a comparison to Poisson-Boltzmann calculations is able to capture some of these electrostatic interactions. Specifically, all three helix N-capping interactions in the engrailed homeodomain fold are recovered using the newly parameterized model. The stability of this designed protein is similar to a protein forced by sequence restriction to have beneficial electrostatic interactions.

Affinity enhancement of an in vivo matured therapeutic antibody using structure-based computational design

Improving the affinity of a high-affinity protein-protein interaction is a challenging problem that has practical applications in the development of therapeutic biomolecules. We used a combination of structure-based computational methods to optimize the binding affinity of an antibody fragment to the I-domain of the integrin VLA1. Despite the already high affinity of the antibody (Kd approximately 7 nM) and the moderate resolution (2.8 A) of the starting crystal structure, the affinity was increased by an order of magnitude primarily through a decrease in the dissociation rate. We determined the crystal structure of a high-affinity quadruple mutant complex at 2.2 A. The structure shows that the design makes the predicted contacts. Structural evidence and mutagenesis experiments that probe a hydrogen bond network illustrate the importance of satisfying hydrogen bonding requirements while seeking higher-affinity mutations. The large and diverse set of interface mutations allowed refinement of the mutant binding affinity prediction protocol and improvement of the single-mutant success rate. Our results indicate that structure-based computational design can be successfully applied to further improve the binding of high-affinity antibodies.

Electrostatics calculations: latest methodological advances

Electrostatics plays a major role in the stabilization and function of biomolecules; as such, it remains a major focus of theoretical and computational studies of macromolecules. Electrostatic interactions are long range, and strongly dependent on the solvent and ions surrounding the biomolecule under study. During the past year, progress has been reported in the treatment of electrostatics in explicit and implicit solvent models. Interesting new developments of explicit solvent models include more efficient Ewald summation methods, as well as alternative approaches based on reaction field theory, periodic images and Euler summations. Implicit solvent models remain divided into those that solve the Poisson-Boltzmann equation numerically and those based on the generalized Born formalism. Both approaches are now included in molecular dynamics simulations and their accuracies may be assessed by direct comparison against experimental data. It is worth mentioning the recent development of web interfaces that facilitate access to and usage of existing tools for computing electrostatic interactions.

A Residue-Pairwise Generalized Born Scheme Suitable for Protein Design Calculations

We describe an efficient generalized Born (GB) approximation for proteins, in which the interaction energy between two amino acids depends on the whole protein structure, but can be accurately computed from residue-pairwise information. Two results make the scheme pairwise. First, an accurate expression exists for the interaction energy between two residues R and R' that depends on the product B = BRBR' of their residue Born solvation radii. Second, this expression is accurately fitted by a parabolic function of B; the (three) fitting coefficients depend only on the pair RR', not on its environment. In effect, the quantity B captures all the information that is relevant about the pair's dielectric environment. The method is tested with calculations on several hundred structures of the proteins trpcage, BPTI, ubiqutin, and thoredoxin. It yields solvation energies in better agreement with Poisson calculations than a traditional GB formulation. We also compute the effect of the protein/solvent environment on the interactions between pairs of charged residues in the active site of the enzyme aspartyl-tRNA synthetase. Our method captures this effect as accurately as traditional GB. Because it is residue-pairwise, the method can be incorporated into efficient protocols for rotamer placement and computational protein design.

Electrostatics in computational protein design

Catalytic activity and protein-protein recognition have proven to be significant challenges for computational protein design. Electrostatic interactions are crucial for these and other protein functions, and therefore accurate modeling of electrostatics is necessary for successfully advancing protein design into the realm of protein function. This review focuses on recent progress in modeling electrostatic interactions in computational protein design, with particular emphasis on continuum models.