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Ribosome assembly in eukaryotes requires approximately 200 essential assembly factors (AFs) and occurs through ordered events that initiate in the nucleolus and culminate in the cytoplasm. Here, we present the electron cryo-microscopy (cryo-EM) structure of a late cytoplasmic 40S ribosome assembly intermediate from Saccharomyces cerevisiae at 18 angstrom resolution. We obtained cryo-EM reconstructions of preribosomal complexes lacking individual components to define the positions of all seven AFs bound to this intermediate. These late-binding AFs are positioned to prevent each step in the translation initiation pathway. Together, they obstruct the binding sites for initiation factors, prevent the opening of the messenger RNA channel, block 60S subunit joining, and disrupt the decoding site. These redundant mechanisms probably ensure that pre-40S particles do not enter the translation pathway, which would result in their rapid degradation.

The phase-selective crystallization of acetaminophen (ACM) using insoluble polymers as heteronuclei was investigated in a combined experimental and computational effort to elucidate the mechanism of polymer-induced heteronucleation (PIHn). ACM heteronucleates from supersaturated aqueous solution in its most thermodynamically stable monoclinic form on poly(n-butyl methacrylate), whereas the metastable orthorhombic form is observed on poly(methyl methacrylate). When ACM crystals were grown through vapor deposition, only the monoclinic polymorph was observed on each polymer. Each crystallization condition leads to a unique powder X-ray diffraction pattern with the major preferred orientation corresponding to the crystallographic faces in which these crystal phases nucleate from surfaces of the polymers. The molecular recognition events leading to these outcomes are elucidated with the aid of computed polymer-crystal binding energies using docking simulations. This investigation illuminates the mechanism by which phase selection occurs during the crystallization of ACM using polymers as heteronuclei, paving the way for the improvement of methods for polymorph selection and discovery based on heterogeneous nucleation promoters., (© 2011 American Chemical Society)

The long wavelength, low-frequency modes of motion are the relevant motions for understanding the continuum mechanical properties of biomolecules. By examining these low-frequency modes, in the context of a spherical harmonic basis set, we identify four elastic moduli that are required to describe the two-dimensional elastic behavior of capsids. This is in contrast to previous modeling and theoretical studies on elastic shells, which use only the two-dimensional Young's modulus (Y) and the bending modulus (κ) to describe the system. Presumably, the heterogeneity of the structure and the anisotropy of the biomolecular interactions lead to a deviation from the homogeneous, isotropic, linear elastic shell theory. We assign functional relevance of the various moduli governing different deformation modes, including a mode primarily sensed in atomic force microscopy nanoindentation experiments. We have performed our analysis on the T = 3 cowpea chlorotic mottle virus and our estimate for the nanoindentation modulus is in accord with experimental measurements., (Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Accompanying recent advances in determining RNA secondary structure is the growing appreciation for the importance of relatively simple topological constraints, encoded at the secondary structure level, in defining the overall architecture, folding pathways, and dynamic adaptability of RNA. A new view is emerging in which tertiary interactions do not define RNA 3D structure, but rather, help select specific conformers from an already narrow, topologically pre-defined conformational distribution. Studies are providing fundamental insights into the nature of these topological constraints, how they are encoded by the RNA secondary structure, and how they interplay with other interactions, breathing new meaning to RNA secondary structure. New approaches have been developed that take advantage of topological constraints in determining RNA backbone conformation based on secondary structure, and a limited set of other, easily accessible constraints. Topological constraints are also providing a much-needed framework for rationalizing and describing RNA dynamics and structural adaptation. Finally, studies suggest that topological constraints may play important roles in steering RNA folding pathways. Here, we review recent advances in our understanding of topological constraints encoded by the RNA secondary structure., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

We apply two-dimensional elasticity theory to viral capsids to develop a framework for calculating elastic properties of viruses from equilibrium thermal fluctuations of the capsid surface in molecular dynamics and elastic network model trajectories. We show that the magnitudes of the long wavelength modes of motion available in a simulation with all atomic degrees of freedom are recapitulated by an elastic network model. For the mode spectra to match, the elastic network model must be scaled appropriately by a factor which can be determined from an icosahedrally constrained all-atom simulation. With this method we calculate the two-dimensional Young's modulus Y, bending modulus κ, and Föppl-von Kármán number γ, for the T=1 mutant of the Sesbania mosaic virus. The values determined are in the range of previous theoretical estimates.

Riboswitches are cis-acting RNA fragments that regulate gene expression by sensing cellular levels of the associated small metabolites. In bacteria, the class I preQ(1) riboswitch allows the fine-tuning of queuosine biosynthesis in response to the intracellular concentration of the queuosine anabolic intermediate preQ(1). When binding preQ(1), the aptamer domain undergoes a significant degree of secondary and tertiary structural rearrangement and folds into an H-type pseudoknot. Conformational "switching" of the riboswitch aptamer domain upon recognizing its cognate metabolite plays a key role in the regulatory mechanism of the preQ(1) riboswitch. We investigate the folding mechanism of the preQ(1) riboswitch aptamer domain using all-atom Go̅-model simulations. The folding pathway of such a single domain is found to be cooperative and sequentially coordinated, as the folding proceeds in the 5' → 3' direction. This kinetically efficient folding mechanism suggests a fast ligand-binding response in competition with RNA elongation.

Dynamic motions of human purine nucleoside phosphorylase (hPNP) in complex with transition-state analogues and reactants were studied using 10 ns explicit solvent molecular dynamics simulations. hPNP is a homotrimer that catalyzes the phosphorolysis of purine 6-oxynucleosides. The ternary complex of hPNP includes the binding of a ligand and phosphate to the active site. Molecular dynamics simulations were performed on the ternary complex of six ligands including the picomolar transition-state analogues, Immucillin-H (K(d) = 56 pM), DADMe-Immucillin-H (K(d) = 8.5 pM), DATMe-Immucillin-H (K(d) = 8.6 pM), SerMe-Immucillin-H (K(d) = 5.2 pM), the substrate inosine, and a complex containing only phosphate. Protein-inhibitor complexes of the late transition-state inhibitors, DADMe-Imm-H and DATMe-Imm-H, are inflexible. Despite the structural similarity of SerMe-Imm-H and DATMe-Imm-H, the protein complex of SerMe-Imm-H is flexible, and the inhibitor is highly mobile within the active sites. All inhibitors exhibit an increased number of nonbonding interactions in the active site relative to the substrate inosine. Water density within the catalytic site is lower for DADMe-ImmH, DATMe-Imm-H, and SerMe-Imm-H than that for the substrate inosine. Tight binding of the picomolar inhibitors results from increased interactions within the active site and a reduction in the number of water molecules organized within the catalytic site relative to the substrate inosine.

An influx of experimental and theoretical studies of ion transport protein structure has inspired efforts to understand underlying determinants of ionic selectivity. Design principles for selective ion binding can be effectively isolated and interrogated using simplified models composed of a single ion surrounded by a set of ion-ligating molecular species. While quantum mechanical treatments of such systems naturally incorporate electronic degrees of freedom, their computational overhead typically prohibits thorough dynamic sampling of configurational space and, thus, requires approximations when determining ion-selective free energy. As an alternative, we employ dynamical simulations with a polarizable force field to probe the structure and K(+)/Na(+) selectivity in simple models composed of one central K(+)/Na(+) ion surrounded by 0-8 identical model compounds: N-methylacetamide, formamide, or water. In the absence of external restraints, these models represent gas-phase clusters displaying relaxed coordination structures with low coordination number. Such systems display Na(+) selectivity when composed of more than ∼3 organic carbonyl-containing compounds and always display K(+) selectivity when composed of water molecules. Upon imposing restraints that solely enforce specific coordination numbers, we find all models are K(+)-selective when ∼7-8-fold ion coordination is achieved. However, when models composed of the organic compounds provide ∼4-6-fold coordination, they retain their Na(+) selectivity. From these trends, design principles emerge that are of basic importance in the behavior of K(+) channel selectivity filters and suggest a basis not only for K(+) selectivity but also for modulation of block and closure by smaller ions.

Building reliable structural models of G protein-coupled receptors (GPCRs) is a difficult task because of the paucity of suitable templates, low sequence identity, and the wide variety of ligand specificities within the superfamily. Template-based modeling is known to be the most successful method for protein structure prediction. However, refinement of homology models within 1-3 A C alpha RMSD of the native structure remains a major challenge. Here, we address this problem by developing a novel protocol (foldGPCR) for modeling the transmembrane (TM) region of GPCRs in complex with a ligand, aimed to accurately model the structural divergence between the template and target in the TM helices. The protocol is based on predicted conserved inter-residue contacts between the template and target, and exploits an all-atom implicit membrane force field. The placement of the ligand in the binding pocket is guided by biochemical data. The foldGPCR protocol is implemented by a stepwise hierarchical approach, in which the TM helical bundle and the ligand are assembled by simulated annealing trials in the first step, and the receptor-ligand complex is refined with replica exchange sampling in the second step. The protocol is applied to model the human beta(2)-adrenergic receptor (beta(2)AR) bound to carazolol, using contacts derived from the template structure of bovine rhodopsin. Comparison with the X-ray crystal structure of the beta(2)AR shows that our protocol is particularly successful in accurately capturing helix backbone irregularities and helix-helix packing interactions that distinguish rhodopsin from beta(2)AR., ((c) 2010 Wiley-Liss, Inc.)

The arenavirus genome encodes for a Z-protein, which contains a RING domain that coordinates two zinc ions, and has been identified as having several functional roles at various stages of the virus life cycle. Z-protein binds to multiple host proteins and has been directly implicated in the promotion of viral budding, repression of mRNA translation, and apoptosis of infected cells. Using homology models of the Z-protein from Lassa strain arenavirus, replica exchange molecular dynamics (MD) was used to refine the structures, which were then subsequently clustered. Population-weighted ensembles of low-energy cluster representatives were predicted based upon optimal agreement of the chemical shifts computed with the SPARTA program with the experimental NMR chemical shifts. A member of the refined ensemble was identified to be a potential binder of budding factor Tsg101 based on its correspondence to the structure of the HIV-1 Gag late domain when bound to Tsg101. Members of these ensembles were docked against the crystal structure of human eIF4E translation initiation factor. Two plausible binding modes emerged based upon their agreement with experimental observation, favorable interaction energies and stability during MD trajectories. Mutations to Z are proposed that would either inhibit both binding mechanisms or selectively inhibit only one mode. The C-terminal domain conformation of the most populated member of the representative ensemble shielded protein-binding recognition motifs for Tsg101 and eIF4E and represents the most populated state free in solution. We propose that C-terminal flexibility is key for mediating the different functional states of the Z-protein., ((c) 2010 Wiley-Liss, Inc.)

Mature antibodies (Abs) that are exquisitely specific for virtually any foreign molecule may be produced by affinity maturation of naïve (or germline) Abs. However, the finite number of germline Abs available suggests that, in contrast to mature Abs, germline Abs must be broadly polyspecific so that they are able to recognize a wide range of ligands. Thus, affinity maturation must play a role in mediating Ab specificity. One biophysical property that distinguishes polyspecificity from specificity is protein flexibility; a flexible combining site is able to adopt different conformations that recognize different foreign molecules (or antigens), while a rigid combining site is locked into a conformation that is specific for a given antigen. Recent studies (Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 8821-8826) have examined, at the atomic level, the structural properties that mediate changes in flexibility at four stages of affinity maturation in the 4-4-20 Ab. These studies employed molecular dynamics simulations to reveal a network of residue interactions that mediate the flexibility changes accompanying maturation. The flexibility of the Ab combining sites in these molecular systems was originally measured using three-pulse photon echo spectroscopy (3PEPS). The present investigation extends this work by providing a concrete link between structural properties of the Ab molecules and features of the spectroscopic measurements used to characterize their flexibility. Results obtained from the simulations are in good qualitative agreement with the experimental measurements and indicate that the spectroscopic signal is sensitive to protein dynamics distributed throughout the entire combining site. Thus, the simulations provide a molecular-level interpretation of the changes induced by affinity maturation of the Ab. The results suggest that 3PEPS spectroscopy in combination with molecular dynamics simulations can provide a detailed description of protein dynamics and, in this case, how it is evolved for biological function.

Orthogonal aminoacyl-tRNA synthetase/tRNA pairs from archaea have been evolved to facilitate site specific in vivo incorporation of unnatural amino acids into proteins in Escherichia coli. Using this approach, unnatural amino acids have been successfully incorporated with high translational efficiency and fidelity. In this study, CHARMM-based molecular docking and free energy calculations were used to evaluate rational design of specific protein-ligand interactions for aminoacyl-tRNA synthetases. A series of novel unnatural amino acid ligands were docked into the p-benzoyl-L-phenylalanine tRNA synthetase, which revealed that the binding pocket of the enzyme does not provide sufficient space for significantly larger ligands. Specific binding site residues were mutated to alanine to create additional space to accommodate larger target ligands, and then mutations were introduced to improve binding free energy. This approach was used to redesign binding sites for several different target ligands, which were then tested against the standard 20 amino acids to verify target specificity. Only the synthetase designed to bind Man-alpha-O-Tyr was predicted to be sufficiently selective for the target ligand and also thermodynamically stable. Our study suggests that extensive redesign of the tRNA synthatase binding pocket for large bulky ligands may be quite thermodynamically unfavorable.

The thermodynamic hypothesis of Anfinsen postulates that structures and stabilities of globular proteins are determined by their amino acid sequences. Chain topology, however, is known to influence the folding reaction, in that motifs with a preponderance of local interactions typically fold more rapidly than those with a larger fraction of nonlocal interactions. Together, the topology and sequence can modulate the energy landscape and influence the rate at which the protein folds to the native conformation. To explore the relationship of sequence and topology in the folding of beta alpha-repeat proteins, which are dominated by local interactions, we performed a combined experimental and simulation analysis on two members of the flavodoxin-like, alpha/beta/alpha sandwich fold. Spo0F and the N-terminal receiver domain of NtrC (NT-NtrC) have similar topologies but low sequence identity, enabling a test of the effects of sequence on folding. Experimental results demonstrated that both response-regulator proteins fold via parallel channels through highly structured submillisecond intermediates before accessing their cis prolyl peptide bond-containing native conformations. Global analysis of the experimental results preferentially places these intermediates off the productive folding pathway. Sequence-sensitive Gō-model simulations conclude that frustration in the folding in Spo0F, corresponding to the appearance of the off-pathway intermediate, reflects competition for intra-subdomain van der Waals contacts between its N- and C-terminal subdomains. The extent of transient, premature structure appears to correlate with the number of isoleucine, leucine, and valine (ILV) side chains that form a large sequence-local cluster involving the central beta-sheet and helices alpha2, alpha 3, and alpha 4. The failure to detect the off-pathway species in the simulations of NT-NtrC may reflect the reduced number of ILV side chains in its corresponding hydrophobic cluster. The location of the hydrophobic clusters in the structure may also be related to the differing functional properties of these response regulators. Comparison with the results of previous experimental and simulation analyses on the homologous CheY argues that prematurely folded unproductive intermediates are a common property of the beta alpha-repeat motif., ((c) 2010 Elsevier Ltd. All rights reserved.)

Hexameric helicases are molecular motor proteins that utilize energy obtained from ATP hydrolysis to translocate along and/or unwind nucleic acids. In this study, we investigate the dynamic behavior of the Simian Virus 40 hexameric helicase bound to DNA by performing molecular dynamics simulations employing a coarse-grained model. Our results elucidate the two most important molecular features of the helicase motion. First, the attractive interactions between the DNA-binding domain of the helicase and the DNA backbone are essential for the helicase to exhibit a unidirectional motion along the DNA strand. Second, the sequence of ATP binding at multiple binding pockets affects the helicase motion. Specifically, concerted ATP binding does not generate a unidirectional motion of the helicase. It is only when the binding of ATP occurs sequentially from one pocket to the next that the helicase moves unidirectionally along the DNA. Interestingly, in the reverse order of sequential ATP binding, the helicase also moves unidirectionally but in the opposite direction. These observations suggest that in nature ATP molecules must distinguish between different available ATP binding pockets of the hexameric helicase in order to function efficiently. To this end, simulations reveal that the binding of ATP in one pocket induces an opening of the next ATP-binding pocket and such an asymmetric deformation may coordinate the sequential ATP binding in a unidirectional manner. Overall, these findings may provide clues toward understanding the mechanism of substrate translocation in other motor proteins., (Copyright 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Background: For survival, most natural viruses depend upon the existence of spherical capsids: protective shells of various sizes composed of protein subunits. So far, general evolutionary pressures shaping capsid design have remained elusive, even though an understanding of such properties may help in rationally impeding the virus life cycle and designing efficient nano-assemblies., Principal Findings: This report uncovers an unprecedented and species-independent evolutionary pressure on virus capsids, based on the the notion that the simplest capsid designs (or those capsids with the lowest "hexamer complexity", C(h)) are the fittest, which was shown to be true for all available virus capsids. The theories result in a physically meaningful periodic table of virus capsids that uncovers strong and overarching evolutionary pressures, while also offering geometric explanations to other capsid properties (rigidity, pleomorphy, auxiliary requirements, etc.) that were previously considered to be unrelatable properties of the individual virus., Significance: Apart from describing a universal rule for virus capsid evolution, our work (especially the periodic table) provides a language with which highly diverse virus capsids, unified only by geometry, may be described and related to each other. Finally, the available virus structure databases and other published data reiterate the predicted geometry-derived rules, reinforcing the role of geometry in the natural selection and design of virus capsids.

The prediction of intramolecular contacts has a useful application in predicting the three-dimensional structures of proteins. The accuracy of the template-based contact prediction methods depends on the quality of the template structures. To reduce the false positive predictions associated with using the entire set of template-derived contacts, we develop selection filters that use sequence conservation information to predict subsets of contacts more likely to be structurally conserved between the template and the target. The method is developed specifically for protein families with few available templates such as the G protein-coupled receptor (GPCR) family. It is validated on a test set of 342 template-target pairs from three protein families, and applied to one template-target pair from the GPCR family. We find that the filter selection method increases the accuracy of contact prediction with sufficient coverage for structure prediction.

Incorporating receptor flexibility into molecular docking should improve results for flexible proteins. However, the incorporation of explicit all-atom flexibility with molecular dynamics for the entire protein chain may also introduce significant error and "noise" that could decrease docking accuracy and deteriorate the ability of a scoring function to rank native-like poses. We address this apparent paradox by comparing the success of several flexible receptor models in cross-docking and multiple receptor ensemble docking for p38α mitogen-activated protein (MAP) kinase. Explicit all-atom receptor flexibility has been incorporated into a CHARMM-based molecular docking method (CDOCKER) using both molecular dynamics (MD) and torsion angle molecular dynamics (TAMD) for the refinement of predicted protein-ligand binding geometries. These flexible receptor models have been evaluated, and the accuracy and efficiency of TAMD sampling is directly compared to MD sampling. Several flexible receptor models are compared, encompassing flexible side chains, flexible loops, multiple flexible backbone segments, and treatment of the entire chain as flexible. We find that although including side chain and some backbone flexibility is required for improved docking accuracy as expected, docking accuracy also diminishes as additional and unnecessary receptor flexibility is included into the conformational search space. Ensemble docking results demonstrate that including protein flexibility leads to to improved agreement with binding data for 227 active compounds. This comparison also demonstrates that a flexible receptor model enriches high affinity compound identification without significantly increasing the number of false positives from low affinity compounds.

Cellobiohydrolases are the dominant components of the commercially relevant Trichoderma reesei cellulase system. Although natural cellulases can totally hydrolyze crystalline cellulose to soluble sugars, the current enzyme loadings and long digestion times required render these enzymes less than cost effective for biomass conversion processes. It is clear that cellobiohydrolases must be improved via protein engineering to reduce processing costs. To better understand cellobiohydrolase function, new simulations have been conducted using charmm of cellobiohydrolase I (CBH I) from T.reesei interacting with a model segment (cellodextrin) of a cellulose microfibril in which one chain from the substrate has been placed into the active site tunnel mimicking the hypothesized configuration prior to final substrate docking (i.e., the +1 and +2 sites are unoccupied), which is also the structure following a catalytic bond scission. No tendency was found for the protein to dissociate from or translate along the substrate surface during this initial simulation, nor to align with the direction of the cellulose chains. However, a tendency for the decrystallized cellodextrin to partially re-anneal into the cellulose surface hints that the arbitrary starting configuration selected was not ideal.

Free energy calculations are fundamental to obtaining accurate theoretical estimates of many important biological phenomena including hydration energies, protein-ligand binding affinities and energetics of conformational changes. Unlike traditional free energy perturbation and thermodynamic integration methods, lambda-dynamics treats the conventional "lambda" as a dynamic variable in free energy simulations and simultaneously evaluates thermodynamic properties for multiple states in a single simulation. In the present article, we provide an overview of the theory of lambda-dynamics, including the use of biasing and restraining potentials to facilitate conformational sampling. We review how lambda-dynamics has been used to rapidly and reliably compute relative hydration free energies and binding affinities for series of ligands, to accurately identify crystallographically observed binding modes starting from incorrect orientations, and to model the effects of mutations upon protein stability. Finally, we suggest how lambda-dynamics may be extended to facilitate modeling efforts in structure-based drug design., (2009 Wiley Periodicals, Inc.)

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983., (Copyright 2009 Wiley Periodicals, Inc.)

To provide utility in understanding the molecular evolution of ion-selective biomembrane channels/transporters, globular proteins, and ionophoric compounds, as well as in guiding their modification and design, we present a statistical mechanical basis for deconstructing the impact of the coordination structure and chemistry of selective multidentate ionic complexes. The deconstruction augments familiar ideas in liquid structure theory to realize the ionic complex as an open ion-ligated system acting under the influence of an "external field" provided by the host (or surrounding medium). Using considerations derived from this basis, we show that selective complexation arises from exploitation of a particular ion's coordination preferences. These preferences derive from a balance of interactions much like that which dictates the Hofmeister effect. By analyzing the coordination-state space of small family IA and VIIA ions in simulated fluid media, we derive domains of coordinated states that confer selectivity for a given ion upon isolating and constraining particular attributes (order parameters) of a complex comprised of a given type of ligand. We demonstrate that such domains may be used to rationalize the ion-coordinated environments provided by selective ionophores and biological ion channels/transporters of known structure, and that they can serve as a means toward deriving rational design principles for ion-selective hosts.

Spherical capsids are shells of protein subunits that protect the genomes of many viral strains. Although nature displays a range of spherical capsid sizes (reflected by the number of subunits in the formation), specific strains display stringent requirements for forming capsids of specific sizes, a requirement that appears crucial to infectivity. Despite its importance in pathogenicity, little is known regarding the determinants of capsid size. Still less is known about exactly which capsids can undergo maturation events such as buckling transitions--postcapsid-assembly events that are crucial to some virus strains. We show that the exclusive determinant of capsid size is hexamer shape, as defined by subunit-subunit dihedral angles. This conclusion arises from considering the dihedral angle patterns within hexamers belonging to natural canonical capsids and geometric capsid models (deltahedra). From simple geometric models and an understanding of endo angle propagation discussed here, we then suggest that buckling transitions may be available only to capsids of certain size (specifically, T < 7 capsids are precluded from such transformations) and that T > 7 capsids require the help of auxiliary mechanisms for proper capsid formation. These predictions, arising from simple geometry and modeling, are backed by a body of empirical evidence, further reinforcing the extent to which the evolution of the atomistically complex virus capsid may be principled around simple geometric design/requirements.

The macroscopic ion-selective behavior of K(+) channels is mediated by a multitude of physiological factors. However, considering the carbonyl-lined binding site of a conductive K(+) channel as a canonical eightfold coordinated construct can be useful in understanding the principles that correlate the channel's structure with its function. We probe the effects of structure and chemical composition on the K(+)/Na(+) selectivity provided by a variety of simplified droplet-like ion binding site models. We find that when carbonyl- and water-based models capture the qualitative structural features of the K(+) channel binding site, a selective preference for K(+) emerges. Thus our findings suggest that the preference for K(+) over Na(+) exhibited by such models is principally built-in, and is not due to a unique K(+)-selective property of carbonyl functional groups. This suggestion is confirmed by a general thermodynamic assessment, which provides a basis for using simplified models to study the design principles underlying the molecular evolution of K(+) channels.

Exploring the landscape of large scale conformational changes such as protein folding at atomistic detail poses a considerable computational challenge. Coarse-grained representations of the peptide chain have therefore been developed and over the last decade have proved extremely valuable. These include topology-based Gō models, which constitute a smooth and funnel-like approximation to the folding landscape. We review the many variations of the Gō model that have been employed to yield insight into folding mechanisms. Their success has been interpreted as a consequence of the dominant role of the native topology in folding. The role of local contact density in determining protein dynamics is also discussed and is used to explain the ability of Gō-like models to capture sequence effects in folding and elucidate conformational transitions.

Directed self-assembly of designed viral capsids holds significant potential for applications in materials science and medicine. However, the complexity of preparing these systems for assembly and the difficulty of quantitative experimental measurements on the assembly process have limited access to critical mechanistic questions that dictate the final product yields and isomorphic forms. Molecular simulations provide a means of elucidating self-assembly of viral proteins into icosahedral capsids and are the focus of the present study. Using geometrically realistic coarse-grained models with specialized molecular dynamics methods, we delineate conditions of temperature and coat protein concentration that lead to the spontaneous self-assembly of T = 1 and T = 3 icosahedral capsids. In addition to the primary product of icosahedral capsids, we observe a ubiquitous presence of nonicosahedral yet highly symmetric and enclosed aberrant capsules in both T = 1 and T = 3 systems. This polymorphism in assembly products recapitulates the scope and morphology of particle types that have been observed in mis-assembly experiments of virus capsids. Moreover, we find that this structural polymorphism in the end point structures is an inherent property of the coat proteins and arises from condition-dependent kinetic mechanisms that are independent of the elemental mechanisms of capsid growth (as long as the building blocks of the coat proteins are all monomeric, dimeric, or trimeric) and the capsid T number. The kinetic mechanisms responsible for self-assembly of icosahedral capsids and aberrant capsules are deciphered; the self-assembly of icosahedral capsids requires a high level of assembly fidelity, whereas self-assembly of nonicosahedral capsules is a consequence of an off-pathway mechanism that is prevalent under nonoptimal conditions of temperature or protein concentration during assembly. The latter case involves kinetically trapped dislocations of pentamer-templated proteins with hexameric organization. These findings provide insights into the complex processes that govern viral capsid assembly and suggest some features of the assembly process that can be exploited to control the assembly of icosahedral capsids and nonicosahedral capsules.

Using an extensive series of TIBO compounds that are non-nucleoside inhibitors of HIV-1 reverse transcriptase, we have systematically evaluated the quality of recently developed ligand parameters that are consistent with the CHARMM22 force field. Thermodynamic integration simulations for 44 pairs of TIBO compounds achieve a high level of success with an overall average unsigned error (AUE) in the relative binding affinities of 1.3 kcal/mol; however, the accuracy is strongly dependent on the size differential between the substituents sampled as well as the class of functional group. Low errors are observed among the alkyl, allyl, aldehyde, nitrile, trifluorinated methyl, and halide TIBO derivatives and large systematic errors among thioether derivatives. We have also investigated how different charge assignment schemes for small molecules impact the quality of computed binding affinities for a subset of this series. This study demonstrates the advantage of using model compounds to derive physically meaningful charge distributions and bond-charge increments for rapidly expanding fragment libraries for drug development applications. Specifically, in the absence of a bond-charge increment for a given pair of atom types, the strategy of adopting CHELPG charges from localized regions of model compounds provides reliable results when modeling with the CHARMM force field.

VIPERdb (http://viperdb.scripps.edu) is a relational database and a web portal for icosahedral virus capsid structures. Our aim is to provide a comprehensive resource specific to the needs of the virology community, with an emphasis on the description and comparison of derived data from structural and computational analyses of the virus capsids. In the current release, VIPERdb(2), we implemented a useful and novel method to represent capsid protein residues in the icosahedral asymmetric unit (IAU) using azimuthal polar orthographic projections, otherwise known as Phi-Psi (Phi-Psi) diagrams. In conjunction with a new Application Programming Interface (API), these diagrams can be used as a dynamic interface to the database to map residues (categorized as surface, interface and core residues) and identify family wide conserved residues including hotspots at the interfaces. Additionally, we enhanced the interactivity with the database by interfacing with web-based tools. In particular, the applications Jmol and STRAP were implemented to visualize and interact with the virus molecular structures and provide sequence-structure alignment capabilities. Together with extended curation practices that maintain data uniformity, a relational database implementation based on a schema for macromolecular structures and the APIs provided will greatly enhance the ability to do structural bioinformatics analysis of virus capsids.

The protein shells, called capsids, of nearly all spherical viruses adopt icosahedral symmetry; however, self-assembly of such empty structures often occurs with multiple misassembly steps resulting in the formation of aberrant structures. Using simple models that represent the coat proteins preassembled in the two different predetermined species that are common motifs of viral capsids (i.e., pentameric and hexameric capsomers), we perform molecular dynamics simulations of the spontaneous self-assembly of viral capsids of different sizes containing T = 1,3,4,7,9,12,13,16, and 19 proteins in their icosahedral repeating unit. We observe, in addition to icosahedral capsids, a variety of nonicosahedral yet highly ordered and enclosed capsules. Such structural polymorphism is demonstrated to be an inherent property of the coat proteins, independent of the capsid complexity and the elementary kinetic mechanisms. Moreover, there exist two distinctive classes of polymorphic structures: aberrant capsules that are larger than their respective icosahedral capsids, in T = 1-7 systems; and capsules that are smaller than their respective icosahedral capsids when T = 7-19. Different kinetic mechanisms responsible for self-assembly of those classes of aberrant structures are deciphered, providing insights into the control of the self-assembly of icosahedral capsids.

Viral capsids are composed of multiple copies of one or a few chemically distinct capsid proteins and are mostly stabilized by inter subunit protein-protein interactions. There have been efforts to identify and analyze these protein-protein interactions, in terms of their extent and similarity, between the subunit interfaces related by quasi- and icosahedral symmetry. Here, we describe a new method to map quaternary interactions in spherical virus capsids onto polar angle space with respect to the icosahedral symmetry axes using azimuthal orthographic diagrams. This approach enables one to map the nonredundant interactions in a spherical virus capsid, irrespective of its size or triangulation number (T), onto the reference icosahedral asymmetric unit space. The resultant diagrams represent characteristic fingerprints of quaternary interactions of the respective capsids. Hence, they can be used as road maps of the protein-protein interactions to visualize the distribution and the density of the interactions. In addition, unlike the previous studies, the fingerprints of different capsids, when represented in a matrix form, can be compared with one another to quantitatively evaluate the similarity (S-score) in the subunit environments and the associated protein-protein interactions. The S-score selectively distinguishes the similarity, or lack of it, in the locations of the quaternary interactions as opposed to other well-known structural similarity metrics (e.g., RMSD, TM-score). Application of this method on a subset of T = 1 and T = 3 capsids suggests that S-score values range between 1 and 0.6 for capsids that belong to the same virus family/genus; 0.6-0.3 for capsids from different families with the same T-number and similar subunit fold; and <0.3 for comparisons of the dissimilar capsids that display different quaternary architectures (T-numbers). Finally, the sequence conserved interface residues within a virus family, whose spatial locations were also conserved have been hypothesized as the essential residues for self-assembly of the member virus capsids.

The relationship between the folding landscape and function of evolved proteins is explored by comparison of the folding mechanisms for members of the flavodoxin fold. CheY, Spo0F, and NtrC have unrelated functions and low sequence homology but share an identical topology. Recent coarse-grained simulations show that their folding landscapes are uniquely tuned to properly suit their respective biological functions. Enhanced packing in Spo0F and its limited conformational dynamics compared to CheY or NtrC lead to frustration in its folding landscape. Simulation as well as experimental results correlate with the local density of native contacts for these and a sample of other proteins. In particular, protein regions of low contact density are observed to become structured late in folding; concomitantly, these dynamic regions are often involved in binding or conformational rearrangements of functional importance. These observations help to explain the widespread success of Gō-like coarse-grained models in reproducing protein dynamics.

The folding of multidomain proteins often proceeds in a hierarchical fashion with individual domains folding independent of one another. A large single-domain protein, however, can consist of multiple modules whose folding may be autonomous or interdependent in ways that are unclear. We used coarse-grained simulations to explore the folding landscape of the two-subdomain bacterial response regulator CheY. Thermodynamic and kinetic characterization shows the landscape to be highly analogous to the four-state landscape reported for another two-subdomain protein, T4 lysozyme. An on-pathway intermediate structured in the more stable nucleating subdomain was observed, as were transient states frustrated in off-pathway contacts prematurely structured in the weaker subdomain. Local unfolding, or backtracking, was observed in the frustrated state before the native conformation could be reached. Nonproductive frustration was attributable to competition for van der Waals contacts between the two subdomains. In an accompanying article, stopped-flow kinetic measurements support an off-pathway burst-phase intermediate, seemingly consistent with our prediction of early frustration in the folding landscape of CheY. Comparison of the folding mechanisms for CheY, T4 lysozyme, and interleukin-1 beta leads us to postulate that subdomain competition is a general feature of large single-domain proteins with multiple folding modules.

We have developed a set of orientational restraint potentials for solid-state NMR observables including (15)N chemical shift and (15)N-(1)H dipolar coupling. Torsion angle molecular dynamics simulations with available experimental (15)N chemical shift and (15)N-(1)H dipolar coupling as target values have been performed to determine orientational information of four membrane proteins and to model the structures of some of these systems in oligomer states. The results suggest that incorporation of the orientational restraint potentials into molecular dynamics provides an efficient means to the determination of structures that optimally satisfy the experimental observables without an extensive geometrical search.

Virus capsids are highly specific assemblies that are formed from a large number of often chemically identical capsid subunits. In the present paper we ask to what extent these structures can be viewed as mathematically tilable objects using a single two-dimensional tile. We find that spherical viruses from a large number of families-eight out of the twelve studied-qualitatively possess properties that allow their representation as two-dimensional monohedral tilings of a bound surface, where each tile represents a subunit. This we did by characterizing the extent to which individual spherical capsids display subunit-subunit (1) holes, (2) overlaps, and (3) gross structural variability. All capsids with T numbers greater than 1 from the Protein Data Bank, with homogeneous protein composition, were used in the study. These monohedral tilings, called canonical capsids due to their platonic (mathematical) form, offer a mathematical segue into the structural and dynamical understanding of not one, but a large number of virus capsids. From our data, it appears as though one may only break the long-standing rules of quasiequivalence by the introduction of subunit-subunit structural variability, holes, and gross overlaps into the shell. To explore the utility of canonical capsids in understanding structural aspects of such assemblies, we used graph theory and discrete geometry to enumerate the types of shapes that the tiles (and hence the subunits) must possess. We show that topology restricts the shape of the face to a limited number of five-sided prototiles, one of which is the "bisected trapezoid" that is a platonic representation of the most ubiquitous capsid subunit shape seen in nature (the trapezoidal jelly-roll motif). This motif is found in a majority of seemingly unrelated virus families that share little to no host, size, or amino acid sequence similarity. This suggests that topological constraints may exhibit dominant roles in the natural design of biological assemblies, while having little effect on amino acid sequence similarity.

The structures of four integral membrane proteins from the Mycobacterium tuberculosis (TB) gene, Rv2433c, Rv1861, Rv1616, and Rv3069, have been de novo predicted by combining a generalized Born implicit solvent/membrane model with replica exchange molecular dynamics simulations to sample the conformational space of each protein.

Two-component signal transduction systems with membrane-embedded sensor histidine kinases are believed to recognize environmental signals and transduce this information over the cellular membrane to influence the activity of a transcription factor to which they are mated. The YycG sensor kinase of Bacillus subtilis, containing two transmembrane helices, is subject to a complicated activity-control circuit involving two other proteins with N-terminal transmembrane helices, YycH and YycI. Truncation studies of YycH and YycI demonstrated that the individual transmembrane helices of these proteins are sufficient to adjust YycG activity, indicating that this control is achieved at the membrane level. A replica exchange molecular dynamics computational approach generated in silico structural models of the transmembrane helix complex that informed mutagenesis studies of the YycI transmembrane helix supporting the accuracy of the in silico model. The results predict that signal recognition by any of the extracellular domains of the sensor histidine kinase YycG or the associated proteins YycH and YycI is transmitted across the cellular membrane by subtle alterations in the positions of the helices within the transmembrane complex of the three proteins.

This article examines ab initio methods for the prediction of protein loops by a computational strategy of multiscale conformational sampling and physical energy scoring functions. Our approach consists of initial sampling of loop conformations from lattice-based low-resolution models followed by refinement using all-atom simulations. To allow enhanced conformational sampling, the replica exchange method was implemented. Physical energy functions based on CHARMM19 and CHARMM22 parameterizations with generalized Born (GB) solvent models were applied in scoring loop conformations extracted from the lattice simulations and, in the case of all-atom simulations, the ensemble of conformations were generated and scored with these models. Predictions are reported for 25 loop segments, each eight residues long and taken from a diverse set of 22 protein structures. We find that the simulations generally sampled conformations with low global root-mean-square-deviation (RMSD) for loop backbone coordinates from the known structures, whereas clustering conformations in RMSD space and scoring detected less favorable loop structures. Specifically, the lattice simulations sampled basins that exhibited an average global RMSD of 2.21 +/- 1.42 A, whereas clustering and scoring the loop conformations determined an RMSD of 3.72 +/- 1.91 A. Using CHARMM19/GB to refine the lattice conformations improved the sampling RMSD to 1.57 +/- 0.98 A and detection to 2.58 +/- 1.48 A. We found that further improvement could be gained from extending the upper temperature in the all-atom refinement from 400 to 800 K, where the results typically yield a reduction of approximately 1 A or greater in the RMSD of the detected loop. Overall, CHARMM19 with a simple pairwise GB solvent model is more efficient at sampling low-RMSD loop basins than CHARMM22 with a higher-resolution modified analytical GB model; however, the latter simulation method provides a more accurate description of the all-atom energy surface, yet demands a much greater computational cost., ((c) 2007 Wiley Periodicals, Inc.)

A three-dimensional model of the human Calcium-sensing receptor (CaSR) seven transmembrane domain was built via a novel sequence alignment method based on the conserved contacts in proteins using the crystal structure of bovine rhodopsin as the template. This model was tested by docking NPS 2143, the first identified allosteric antagonist of CaSR. In our model, Glu837 plays a critical role in anchoring the protonated nitrogen atom and hydroxy oxygen atom of NPS 2143. The phenyl moiety of the ligand contacts residues Phe668, Pro672, and Ile841. The naphthalene moiety is surrounded by several hydrophobic residues, including Phe684, Phe688, and Phe821. Our model appears to be consistent with all six residues that have been demonstrated to be critical for NPS 2143 binding, in contrast with existing homology models based on traditional sequence alignment of CaSR to rhodopsin. This provides validation of our sequence alignment method and the use of the rhodopsin backbone as the initial structure in homology modeling of other G protein-coupled receptors that are not members of the rhodopsin family., ((c) 2007 Wiley-Liss, Inc.)

Implicit solvent-based methods play an increasingly important role in molecular modeling of biomolecular structure and dynamics. Recent methodological developments have mainly focused on the extension of the generalized Born (GB) formalism for variable dielectric environments and accurate treatment of nonpolar solvation. Extensive efforts in parameterization of GB models and implicit solvent force fields have enabled ab initio simulation of protein folding to native or near-native structures. Another exciting area that has benefited from the advances in implicit solvent models is the development of constant pH molecular dynamics methods, which have recently been applied to the calculations of protein pK(a) values and the studies of pH-dependent peptide and protein folding.

Accurate description of the solvent environment is critical in computer simulations of protein structure and dynamics. An implicit treatment of solvent aims to capture the mean influence of water molecules on the solute via direct estimation of the solvation free energy. It has emerged as a powerful alternative to explicit solvent, and provides a favorable compromise between computational cost and level of detail. We review the current theory and techniques for implicit modeling of nonpolar solvation in the context of simulating protein folding and conformational transitions, and discuss the main directions for further development. It is demonstrated that the current surface area based nonpolar models have severe limitations, including insufficient description of the conformational dependence of solvation, over-estimation of the strength of pair-wise nonpolar interactions, and incorrect prediction of anti-cooperativity for three-body hydrophobic associations. We argue that, to improve beyond current level of accuracy of implicit solvent models, two important aspects of nonpolar solvation need to be incorporated, namely, the length-scale dependence of hydrophobic association and solvent screening of solute-solute dispersion interactions. We recognize that substantial challenges exist in constructing a sufficiently balanced, yet reasonably efficient, implicit solvent protein force field. Nonetheless, most of the fundamental problems are understood, and exciting progress has been made over the last few years. We believe that continual work along the frontiers outlined will greatly improve one's ability to study protein folding and large conformational transitions at atomistic detail.

Carboxylic acid dimers are useful model systems for understanding the interplay of hydrogen bonding, hydrophobic effects, and entropy in self-association and assembly. Through extensive sampling with a classical force field and careful free energy analysis, it is demonstrated that both hydrogen bonding and hydrophobic interactions are indeed important for dimerization of carboxylic acids (except formic acid). The dimers are only weakly ordered, and the degree of ordering increases with stronger hydrophobic interactions between longer alkyl chains. Comparison of calculated and experimental dimerization constants reveals a systematic tendency for excessive self-aggregation in current classical force fields. Qualitative and quantitative information on the thermodynamics of hydrogen bonding and hydrophobic interactions derived from these simulations is in excellent agreement with existing results from experiment and theory. These results provide a verification from first principles of previous estimations based on two statistical mechanical hydrophobic theories. We also revisit and clarify the fundamental statistical thermodynamics formalism for calculating absolute binding constants, external entropy, and solvation entropy changes upon association from detailed free energy simulations. This analysis is believed to be useful for a wide range of applications including computational studies of protein-ligand and protein-protein binding.

Large-scale conformational changes in proteins are often associated with the binding of a substrate. Because conformational changes may be related to the function of an enzyme, understanding the kinetics and energetics of these motions is very important. We have delineated the atomically detailed conformational transition pathway of the phosphotransferase enzyme adenylate kinase (AdK) in the absence and presence of an inhibitor. The computed free energy profiles associated with conformational transitions offer detailed mechanistic insights into, as well as kinetic information on, the ligand binding mechanism. Specifically, potential of mean force calculations reveal that in the ligand-free state, there is no significant barrier separating the open and closed conformations of AdK. The enzyme samples near closed conformations, even in the absence of its substrate. The ligand binding event occurs late, toward the closed state, and transforms the free energy landscape. In the ligand-bound state, the closed conformation is energetically most favored with a large barrier to opening. These results emphasize the underlying dynamic nature of the enzyme and indicate that the conformational transitions in AdK are more intricate than a mere two-state jump between the crystal-bound and -unbound states. Based on the existence of the multiple conformations of the enzyme in the open and closed states, a different viewpoint of ligand binding is presented. Our estimated activation energy barrier for the conformational transition is also in reasonable accord with the experimental findings.

Growing evidence suggests that the beta-amyloid (Abeta) peptides of Alzheimer's disease are generated in early endosomes and that small oligomers are the principal toxic species. We sought to understand whether and how the solution pH, which is more acidic in endosomes than the extracellular environment, affects the conformational processes of Abeta. Using constant pH molecular dynamics simulations of two model peptides, Abeta(1-28) and Abeta(10-42), we found that the folding landscape of Abeta is strongly modulated by pH and is most favorable for hydrophobically driven aggregation at pH 6. Thus, our theoretical findings substantiate the possibility that Abeta oligomers develop intracellularly before secretion into the extracellular milieu, where they may disrupt synaptic activity or act as seeds for plaque formation.

Structural characterization of the bacterial channel, AmtB, provides a glimpse of how members of its family might control the protonated state of permeant ammonium to allow for its selective passage across the membrane. In a recent study, we employed a combination of simulation techniques that suggested ammonium is deprotonated and reprotonated near dehydrative phenylalanine landmarks (F107 and F31, respectively) during its passage from the periplasm to the cytoplasm. At these landmarks, ammonium is forced to maintain a critical number ( approximately 3) of hydrogen bonds, suggesting that the channel controls ammonium (de)protonation by controlling its coordination/hydration. In the work presented here, a free energy-based analysis of ammonium hydration in dilute aqueous solution indicates, explicitly, that at biological pH, the transition from ammonium (NH(4)(+)) to ammonia (NH(3)) occurs when these species are constrained to donate three hydrogen bonds or less. This result demonstrates the viability of the proposal that AmtB indirectly controls ammonium (de)protonation by directly controlling its hydration.

Recent advances in efficient and accurate treatment of solvent with the generalized Born approximation (GB) have made it possible to substantially refine the protein structures generated by various prediction tools through detailed molecular dynamics simulations. As demonstrated in a recent CASPR experiment, improvement can be quite reliably achieved when the initial models are sufficiently close to the native basin (e.g., 3-4 A C(alpha) RMSD). A key element to effective refinement is to incorporate reliable structural information into the simulation protocol. Without intimate knowledge of the target and prediction protocol used to generate the initial structural models, it can be assumed that the regular secondary structure elements (helices and strands) and overall fold topology are largely correct to start with, such that the protocol limits itself to the scope of refinement and focuses the sampling in vicinity of the initial structure. The secondary structures can be enforced by dihedral restraints and the topology through structural contacts, implemented as either multiple pair-wise C(alpha) distance restraints or a single sidechain distance matrix restraint. The restraints are weakly imposed with flat-bottom potentials to allow sufficient flexibility for structural rearrangement. Refinement is further facilitated by enhanced sampling of advanced techniques such as the replica exchange method (REX). In general, for single domain proteins of small to medium sizes, 3-5 nanoseconds of REX/GB refinement simulations appear to be sufficient for reasonable convergence. Clustering of the resulting structural ensembles can yield refined models over 1.0 A closer to the native structure in C(alpha) RMSD. Substantial improvement of sidechain contacts and rotamer states can also be achieved in most cases. Additional improvement is possible with longer sampling and knowledge of the robust structural features in the initial models for a given prediction protocol. Nevertheless, limitations still exist in sampling as well as force field accuracy, manifested as difficulty in refinement of long and flexible loops., (2007 Wiley-Liss, Inc.)

We evaluate the pK(a) of dihydrofolate (H(2)F) at the N(5) position in three ternary complexes with Escherichia coli dihydrofolate reductase (ecDHFR), namely ecDHFR(NADP(+):H(2)F) in the closed form (1), and the Michaelis complexes ecDHFR(NADPH:H(2)F) in the closed (2) and occluded (3) forms, by performing free energy perturbation with molecular dynamics simulations (FEP/MD). Our simulations suggest that in the Michaelis complex the pK(a) is modulated by the Met20 loop fluctuations, providing the largest pK(a) shift in substates with a "tightly closed" loop conformation; in the "partially closed/open" substates, the pK(a) is similar to that in the occluded complex. Conducive to the protonation, tightly closing the Met20 loop enhances the interactions of the cofactor and the substrate with the Met20 side chain and aligns the nicotinamide ring of the cofactor coplanar with the pterin ring of the substrate. Overall, the present study favors the hypothesis that N(5) is protonated directly from solution and provides further insights into the mechanism of the substrate protonation.

The selectivity filter of K+ channels provides specific coordinative interactions between dipolar carbonyl ligands, water, and the permeant cation, which allow for selective flow of K+ over (most importantly) Na+ across the cell membrane. Although a structural viewpoint attributes K+ selectivity to coordination geometry provided by the filter, recent molecular dynamics simulation studies attribute it to dynamic and unique chemical/electrostatic properties of the filter's carbonyl ligands. Here we provide a simple theoretical analysis of K+ and Na+ complexation with water in the context of simplified binding site models and bulk solution. Our analysis reveals that water molecules and carbonyl groups can both provide K+ selective environments if equivalent constraints are imposed on the coordination number of the complex. Absence of such constraints annihilates selectivity, demonstrating that whether a coordinating ligand is a water molecule or a carbonyl group, "external" or "topological" constraints/forces must be imposed on an ion-coordinated complex to elicit selective binding. These forces must inevitably originate from the channel protein, because in bulk water, which, by definition, presents a nonselective medium, the coordination number is allowed to relax to suit the ion. We show that the coordination geometry of K+ channel binding sites is replicated by 8-fold complexation of K+ in both water and simplified binding site models due to dominance of local interactions within a complex and is thus a requirement for topologically constraining the coordination number to a specific value.

The immune system responds to the introduction of foreign antigens by rapidly evolving antibodies with increasing affinity for the antigen (i.e., maturation). To investigate the factors that control this process at the molecular level, we have assessed the changes in flexibility that accompany ligand binding at four stages of maturation in the 4-4-20 antibody. Our studies, based on molecular dynamics, indicate that increased affinity for the target ligand is associated with a decreased entropic cost to binding. The entropy of binding is unfavorable, opposing favorable enthalpic contributions that arise during complex formation. Computed binding free energies for the various antibody-ligand complexes qualitatively reproduce the trends observed in the experimentally derived values, although the absolute magnitude of free-energy differences is overestimated. Our results support the existence of a correlation between high-affinity interactions and decreased protein flexibility in this series of antibody molecules. This observation is likely to be a general feature of molecular association processes and key to the molecular evolution of antibody responses.

The kinetics of amyloid fibril formation are in most cases explained by classical nucleation theory, yet the mechanisms behind nucleation are not well understood. We show using molecular dynamics simulations that the hydrophobic cooperativity in the self-association of the model amyloidogenic peptide STVIYE is sufficient to allow for nucleation-dependent polymerization with a pentamer critical nucleus. The role of electrostatics was also investigated. Novel considerations of the electrostatic solvation energy using the Born-Onsager equation are put forth to rationalize the aggregation of charged peptides and provide new insight into the energetic differences between parallel and antiparallel beta-sheets. Together these results help explain the influence of molecular charge in the class of fibril-forming hexapeptides recently designed by Serrano and collaborators.