Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

Partial Order Optimum Likelihood (POOL): Maximum Likelihood Prediction of Protein Active Site Residues Using 3D Structure and Sequence Properties

A new monotonicity-constrained maximum likelihood approach, called Partial Order Optimum Likelihood (POOL), is presented and applied to the problem of functional site prediction in protein 3D structures, an important current challenge in genomics. The input consists of electrostatic and geometric properties derived from the 3D structure of the query protein alone. Sequence-based conservation information, where available, may also be incorporated. Electrostatics features from THEMATICS are combined with multidimensional isotonic regression to form maximum likelihood estimates of probabilities that specific residues belong to an active site. This allows likelihood ranking of all ionizable residues in a given protein based on THEMATICS features. The corresponding ROC curves and statistical significance tests demonstrate that this method outperforms prior THEMATICS-based methods, which in turn have been shown previously to outperform other 3D-structure-based methods for identifying active site residues. Then it is shown that the addition of one simple geometric property, the size rank of the cleft in which a given residue is contained, yields improved performance. Extension of the method to include predictions of non-ionizable residues is achieved through the introduction of environment variables. This extension results in even better performance than THEMATICS alone and constitutes to date the best functional site predictor based on 3D structure only, achieving nearly the same level of performance as methods that use both 3D structure and sequence alignment data. Finally, the method also easily incorporates such sequence alignment data, and when this information is included, the resulting method is shown to outperform the best current methods using any combination of sequence alignments and 3D structures. Included is an analysis demonstrating that when THEMATICS features, cleft size rank, and alignment-based conservation scores are used individually or in combination THEMATICS features represent the single most important component of such classifiers

Diffusion of hydrophobin proteins in solution and interactions with a graphite surface

<p>Abstract</p> <p>Background</p> <p>Hydrophobins are small proteins produced by filamentous fungi that have a variety of biological functions including coating of spores and surface adhesion. To accomplish these functions, they rely on unique interface-binding properties. Using atomic-detail implicit solvent rigid-body Brownian dynamics simulations, we studied the diffusion of HFBI, a class II hydrophobin from <it>Trichoderma reesei</it>, in aqueous solution in the presence and absence of a graphite surface.</p> <p>Results</p> <p>In the simulations, HFBI exists in solution as a mixture of monomers in equilibrium with different types of oligomers. The oligomerization state depends on the conformation of HFBI. When a Highly Ordered Pyrolytic Graphite (HOPG) layer is present in the simulated system, HFBI tends to interact with the HOPG layer through a hydrophobic patch on the protein.</p> <p>Conclusions</p> <p>From the simulations of HFBI solutions, we identify a tetrameric encounter complex stabilized by non-polar interactions between the aliphatic residues in the hydrophobic patch on HFBI. After the formation of the encounter complex, a local structural rearrangement at the protein interfaces is required to obtain the tetrameric arrangement seen in HFBI crystals. Simulations performed with the graphite surface show that, due to a combination of a geometric hindrance and the interaction of the aliphatic sidechains with the graphite layer, HFBI proteins tend to accumulate close to the hydrophobic surface.</p

NMR Characterizations of the Ice Binding Surface of an Antifreeze Protein

Antifreeze protein (AFP) has a unique function of reducing solution freezing temperature to protect organisms from ice damage. However, its functional mechanism is not well understood. An intriguing question concerning AFP function is how the high selectivity for ice ligand is achieved in the presence of free water of much higher concentration which likely imposes a large kinetic barrier for protein-ice recognition. In this study, we explore this question by investigating the property of the ice binding surface of an antifreeze protein using NMR spectroscopy. An investigation of the temperature gradient of amide proton chemical shift and its correlation with chemical shift deviation from random coil was performed for CfAFP-501, a hyperactive insect AFP. A good correlation between the two parameters was observed for one of the two Thr rows on the ice binding surface. A significant temperature-dependent protein-solvent interaction is found to be the most probable origin for this correlation, which is consistent with a scenario of hydrophobic hydration on the ice binding surface. In accordance with this finding, rotational correlation time analyses combined with relaxation dispersion measurements reveals a weak dimer formation through ice binding surface at room temperature and a population shift of dimer to monomer at low temperature, suggesting hydrophobic effect involved in dimer formation and hence hydrophobic hydration on the ice binding surface of the protein. Our finding of hydrophobic hydration on the ice binding surface provides a test for existing simulation studies. The occurrence of hydrophobic hydration on the ice binding surface is likely unnecessary for enhancing protein-ice binding affinity which is achieved by a tight H-bonding network. Subsequently, we speculate that the hydrophobic hydration occurring on the ice binding surface plays a role in facilitating protein-ice recognition by lowering the kinetic barrier as suggested by some simulation studies

The Interaction Properties of the Human Rab GTPase Family – A Comparative Analysis Reveals Determinants of Molecular Binding Selectivity

Rab GTPases constitute the largest subfamily of the Ras protein superfamily. Rab proteins regulate organelle biogenesis and transport, and display distinct binding preferences for effector and activator proteins, many of which have not been elucidated yet. The underlying molecular recognition motifs, binding partner preferences and selectivities are not well understood.Comparative analysis of the amino acid sequences and the three-dimensional electrostatic and hydrophobic molecular interaction fields of 62 human Rab proteins revealed a wide range of binding properties with large differences between some Rab proteins. This analysis assists the functional annotation of Rab proteins 12, 14, 26, 37 and 41 and provided an explanation for the shared function of Rab3 and 27. Rab7a and 7b have very different electrostatic potentials, indicating that they may bind to different effector proteins and thus, exert different functions. The subfamily V Rab GTPases which are associated with endosome differ subtly in the interaction properties of their switch regions, and this may explain exchange factor specificity and exchange kinetics.We have analysed conservation of sequence and of molecular interaction fields to cluster and annotate the human Rab proteins. The analysis of three dimensional molecular interaction fields provides detailed insight that is not available from a sequence-based approach alone. Based on our results, we predict novel functions for some Rab proteins and provide insights into their divergent functions and the determinants of their binding partner selectivity

Probing the Flexibility of Large Conformational Changes in Protein Structures through Local Perturbations

Protein conformational changes and dynamic behavior are fundamental for such processes as catalysis, regulation, and substrate recognition. Although protein dynamics have been successfully explored in computer simulation, there is an intermediate-scale of motions that has proven difficult to simulate—the motion of individual segments or domains that move independently of the body the protein. Here, we introduce a molecular-dynamics perturbation method, the Rotamerically Induced Perturbation (RIP), which can generate large, coherent motions of structural elements in picoseconds by applying large torsional perturbations to individual sidechains. Despite the large-scale motions, secondary structure elements remain intact without the need for applying backbone positional restraints. Owing to its computational efficiency, RIP can be applied to every residue in a protein, producing a global map of deformability. This map is remarkably sparse, with the dominant sites of deformation generally found on the protein surface. The global map can be used to identify loops and helices that are less tightly bound to the protein and thus are likely sites of dynamic modulation that may have important functional consequences. Additionally, they identify individual residues that have the potential to drive large-scale coherent conformational change. Applying RIP to two well-studied proteins, Dihdydrofolate Reductase and Triosephosphate Isomerase, which possess functionally-relevant mobile loops that fluctuate on the microsecond/millisecond timescale, the RIP deformation map identifies and recapitulates the flexibility of these elements. In contrast, the RIP deformation map of α-lytic protease, a kinetically stable protein, results in a map with no significant deformations. In the N-terminal domain of HSP90, the RIP deformation map clearly identifies the ligand-binding lid as a highly flexible region capable of large conformational changes. In the Estrogen Receptor ligand-binding domain, the RIP deformation map is quite sparse except for one large conformational change involving Helix-12, which is the structural element that allosterically links ligand binding to receptor activation. RIP analysis has the potential to discover sites of functional conformational changes and the linchpin residues critical in determining these conformational states

The Beneficial Effects of Antifreeze Proteins in the Vitrification of Immature Mouse Oocytes

Antifreeze proteins (AFPs) are a class of polypeptides that permit organismal survival in sub-freezing environments. The purpose of this study was to investigate the effect of AFP supplementation on immature mouse oocyte vitrification. Germinal vesicle-stage oocytes were vitrified using a two-step exposure to equilibrium and vitrification solution in the presence or absence of 500 ng/mL of AFP III. After warming, oocyte survival, in vitro maturation, fertilization, and embryonic development up to the blastocyst stage were assessed. Spindle and chromosome morphology, membrane integrity, and the expression levels of several genes were assessed in in vitro matured oocytes. The rate of blastocyst formation was significantly higher and the number of caspase-positive blastomeres was significantly lower in the AFP-treated group compared with the untreated group. The proportion of oocytes with intact spindles/chromosomes and stable membranes was also significantly higher in the AFP group. The AFP group showed increased Mad2, Hook-1, Zar1, Zp1, and Bcl2 expression and lower Eg5, Zp2, Caspase6, and Rbm3 expression compared with the untreated group. Supplementation of the vitrification medium with AFP has a protective effect on immature mouse oocytes, promoting their resistance to chilling injury. AFPs may preserve spindle forming ability and membrane integrity at GV stage. The fertilization and subsequent developmental competence of oocytes may be associated with the modulation of Zar1, Zp1/Zp2, Bcl2, Caspase6, and Rbm3

Hydrogen bond networks determine emergent mechanical and thermodynamic properties across a protein family

<p>Abstract</p> <p>Background</p> <p>Gram-negative bacteria use periplasmic-binding proteins (bPBP) to transport nutrients through the periplasm. Despite immense diversity within the recognized substrates, all members of the family share a common fold that includes two domains that are separated by a conserved hinge. The hinge allows the protein to cycle between open (apo) and closed (ligated) conformations. Conformational changes within the proteins depend on a complex interplay of mechanical and thermodynamic response, which is manifested as an increase in thermal stability and decrease of flexibility upon ligand binding.</p> <p>Results</p> <p>We use a distance constraint model (DCM) to quantify the give and take between thermodynamic stability and mechanical flexibility across the bPBP family. Quantitative stability/flexibility relationships (QSFR) are readily evaluated because the DCM links mechanical and thermodynamic properties. We have previously demonstrated that QSFR is moderately conserved across a mesophilic/thermophilic RNase H pair, whereas the observed variance indicated that different enthalpy-entropy mechanisms allow similar mechanical response at their respective melting temperatures. Our predictions of heat capacity and free energy show marked diversity across the bPBP family. While backbone flexibility metrics are mostly conserved, cooperativity correlation (long-range couplings) also demonstrate considerable amount of variation. Upon ligand removal, heat capacity, melting point, and mechanical rigidity are, as expected, lowered. Nevertheless, significant differences are found in molecular cooperativity correlations that can be explained by the detailed nature of the hydrogen bond network.</p> <p>Conclusion</p> <p>Non-trivial mechanical and thermodynamic variation across the family is explained by differences within the underlying H-bond networks. The mechanism is simple; variation within the H-bond networks result in altered mechanical linkage properties that directly affect intrinsic flexibility. Moreover, varying numbers of H-bonds and their strengths control the likelihood for energetic fluctuations as H-bonds break and reform, thus directly affecting thermodynamic properties. Consequently, these results demonstrate how unexpected large differences, especially within cooperativity correlation, emerge from subtle differences within the underlying H-bond network. This inference is consistent with well-known results that show allosteric response within a family generally varies significantly. Identifying the hydrogen bond network as a critical determining factor for these large variances may lead to new methods that can predict such effects.</p

Dendritic Cells in Chronic Mycobacterial Granulomas Restrict Local Anti-Bacterial T Cell Response in a Murine Model

Background: Mycobacterium-induced granulomas are the interface between bacteria and host immune response. During acute infection dendritic cells (DCs) are critical for mycobacterial dissemination and activation of protective T cells. However, their role during chronic infection in the granuloma is poorly understood. Methodology/Principal Findings: We report that an inflammatory subset of murine DCs are present in granulomas induced by Mycobacteria bovis strain Bacillus Calmette-guerin (BCG), and both their location in granulomas and costimulatory molecule expression changes throughout infection. By flow cytometric analysis, we found that CD11c + cells in chronic granulomas had lower expression of MHCII and co-stimulatory molecules CD40, CD80 and CD86, and higher expression of inhibitory molecules PD-L1 and PD-L2 compared to CD11c + cells from acute granulomas. As a consequence of their phenotype, CD11c + cells from chronic lesions were unable to support the reactivation of newly-recruited, antigen 85Bspecific CD4 + IFNc + T cells or induce an IFNc response from naïve T cells in vivo and ex vivo. The mechanism of this inhibition involves the PD-1:PD-L signaling pathway, as ex vivo blockade of PD-L1 and PD-L2 restored the ability of isolated CD11c + cells from chronic lesions to stimulate a protective IFNc T cell response. Conclusions/Significance: Our data suggest that DCs in chronic lesions may facilitate latent infection by down-regulating protective T cell responses, ultimately acting as a shield that promotes mycobacterium survival. This DC shield may explai