Sameer Varma

Structural Transitions in Ion Coordination Driven by Changes in Competition for Ligand Binding.

Transferring Na(+) and K(+) ions from their preferred coordination states in water to states having different coordination numbers incurs a free energy cost. In several examples in nature, however, these ions readily partition from aqueous-phase coordination states into spatial regions having much higher coordination numbers. Here we utilize statistical theory of solutions, quantum chemical simulations, classical mechanics simulations, and structural informatics to understand this aspect of ion partitioning. Our studies lead to the identification of a specific role of the solvation environment in driving transitions in ion coordination structures. Although ion solvation in liquid media is an exergonic reaction overall, we find it is also associated with considerable free energy penalties for extracting ligands from their solvation environments to form coordinated ion complexes. Reducing these penalties increases the stabilities of higher-order coordinations and brings down the energetic cost to partition ions from water into overcoordinated binding sites in biomolecules. These penalties can be lowered via a reduction in direct favorable interactions of the coordinating ligands with all atoms other than the ions themselves. A significant reduction in these penalties can, in fact, also drive up ion coordination preferences. Similarly, an increase in these penalties can lower ion coordination preferences, akin to a Hofmeister effect. Since such structural transitions are effected by the properties of the solvation phase, we anticipate that they will also occur for other ions. The influence of other factors, including ligand density, ligand chemistry, and temperature, on the stabilities of ion coordination structures are also explored.

Perspectives on: ion selectivity: design principles for K+ selectivity in membrane transport.

Selection among competing alternatives is always interesting, but when organisms select between K+ and Na+ for transport across biological membranes, it is especially intriguing for a couple of reasons (Hille, 2001). First, the results are physiologically significant. Second, K+ and Na+ are nearly as similar as they could be while not being the same things. Perhaps the separation of isotopes of the same chemical species is more demanding. Despite decades of research, the question remains: how do K+-selective ion channels catalyze K+ movement but recognize the detailed molecular-scale differences of Na+ and discriminate against it? Suggestions based on channel size and coordination chemistry (Bezanilla and Armstrong, 1972; Eisenman and Horn, 1983) have been available for a long time, but the determination of a KcsA K+ channel crystal structure (Doyle et al., 1998) enabled molecularly specific modeling studies of this K+/Na+ selectivity. In the subsequent flood of computational studies, finding consistency in results and interpretations has proven challenging. Here, we describe our perspective on how molecular modeling has advanced our understanding of the specific chemical and structural design elements of biological molecules that enable selective ion transport.

Ionization States of Residues in OmpF and Mutants: Effects of Dielectric Constant and Interactions between Residues

To understand ion permeation, one must assign correct ionization states to titratable amino acid residues in protein channels. We report on the effects of physical and methodological assumptions in calculating the protonation states at neutral bulk pH of titratable residues lining the lumen of the native Escherichia coli OmpF channel, and five mutants. We systematically considered a wide range of assumed protein dielectric constants and all plausible combinations of protonation states for electrostatically interacting side chains, and three different levels of accounting for solute shielding: 1), full nonlinear Poisson-Boltzmann; 2), linearized Poisson-Boltzmann; and 3), neglect of solute shielding. For this system we found it acceptable to neglect solute shielding, a result we postulate to be generalizable to narrow lumens of other protein channels. For the large majority of residues, the protonation state at neutral bulk pH was found to be independent of the assumed dielectric constant of the protein, and unambiguously determined by the calculation; for native OmpF only Asp-127 has a protonation state that is sensitive to the assumed protein dielectric constant. Our results are significant for understanding two published experimental observations: the structure of the narrow part of the channel, and the ionic selectivity of OmpF mutants.

Multibody Effects in Ion Binding and Selectivity

Selective binding of ions to biomolecules plays a vital role in numerous biological processes. To understand the specific role of induced effects in selective ion binding, we use quantum chemical and pairwise-additive force-field simulations to study Na(+) and K(+) binding to various small molecules representative of ion binding functional groups in biomolecules. These studies indicate that electronic polarization significantly contributes to both absolute and relative ion-binding affinities. Furthermore, this contribution depends on both the number and the specific chemistries of the coordinating molecules, thus highlighting the complexity of ion-ligand interactions. Specifically, multibody interactions reduce as well as enhance the dipole moments of the ion-coordinating molecules, thereby affecting observables like coordination number distributions of ions. The differential polarization induced in molecules coordinating these two equivalently charged, but different-sized, ions also depends upon the number of coordinating molecules, showing the importance of multibody effects in distinguishing these ions thermodynamically. Because even small differences in ionic radii (0.4 Å for Na(+) and K(+)) produce differential polarization trends critical to distinguishing ions thermodynamically, it is likely that polarization plays an important role in thermodynamically distinguishing other ions and charged chemical and biological functional groups.

Role of methyl-induced polarization in ion binding

The chemical property of methyl groups that renders them indispensable to biomolecules is their hydrophobicity. Quantum mechanical studies undertaken here to understand the effect of point substitutions on potassium (K-) channels illustrate quantitatively how methyl-induced polarization also contributes to biomolecular function. K- channels regulate transmembrane salt concentration gradients by transporting K+ ions selectively. One of the K+ binding sites in the channel’s selectivity filter, the S4 site, also binds Ba2+ ions, which blocks K+ transport. This inhibitory property of Ba2+ ions has been vital in understanding K-channel mechanism. In most K-channels, the S4 site is composed of four threonine amino acids. The K channels that carry serine instead of threonine are significantly less susceptible to Ba2+ block and have reduced stabilities. We find that these differences can be explained by the lower polarizability of serine compared with threonine, because serine carries one less branched methyl group than threonine. A T→S substitution in the S4 site reduces its polarizability, which, in turn, reduces ion binding by several kilocalories per mole. Although the loss in binding affinity is high for Ba2+, the loss in K+ binding affinity is also significant thermodynamically, which reduces channel stability. These results highlight, in general, how biomolecular function can rely on the polarization induced by methyl groups, especially those that are proximal to charged moieties, including ions, titratable amino acids, sulfates, phosphates, and nucleotides.

Measurement of Elastic Modulus of Collagen Type I Single Fiber

Collagen fibers are the main components of the extra cellular matrix and the primary contributors to the mechanical properties of tissues. Here we report a novel approach to measure the longitudinal component of the elastic moduli of biological fibers under conditions close to those found in vivo and apply it to type I collagen from rat tail tendon. This approach combines optical tweezers, atomic force microscopy, and exploits Euler-Bernoulli elasticity theory for data analysis. This approach also avoids drying for measurements or visualization, since samples are freshly extracted. Importantly, strains are kept below 0.5%, which appear consistent with the linear elastic regime. We find, surprisingly, that the longitudinal elastic modulus of type I collagen cannot be represented by a single quantity but rather is a distribution that is broader than the uncertainty of our experimental technique. The longitudinal component of the single-fiber elastic modulus is between 100 MPa and 360 MPa for samples extracted from different rats and/or different parts of a single tail. Variations are also observed in the fibril-bundle / fibril diameter with an average of 325±40 nm. Since bending forces depend on the diameter to the fourth power, this variation in diameter is important for estimating the range of elastic moduli. The remaining variations in the modulus may be due to differences in composition of the fibril-bundles, or the extent of the proteoglycans constituting fibril-bundles, or that some single fibrils may be of fibril-bundle size.

Nonintercalating Nanosubstrates Create Asymmetry between Bilayer Leaflets

The physical properties of lipid bilayers can be remodeled by a variety of environmental factors. Here we investigate using molecular dynamics simulations the specific effects of nanoscopic substrates or external contact points on lipid membranes. We expose palmitoyl-oleoyl phosphatidylcholine bilayers unilaterally and separately to various model nanosized substrates differing in surface hydroxyl densities. We find that a surface hydroxyl density as low as 10% is sufficient to keep the bilayer juxtaposed to the substrate. The bilayer interacts with the substrate indirectly through multiple layers of water molecules; however, despite such buffered interaction, the bilayers exhibit certain properties different from unsupported bilayers. The substrates modify transverse lipid fluctuations, charge density profiles, and lipid diffusion rates, although differently in the two leaflets, which creates an asymmetry between bilayer leaflets. Other properties that include lipid cross-sectional areas, component volumes, and order parameters are minimally affected. The extent of asymmetry that we observe between bilayer leaflets is well beyond what has been reported for bilayers adsorbed on infinite solid supports. This is perhaps because the bilayers are much closer to our nanosized finite supports than to infinite solid supports, resulting in a stronger support-bilayer electrostatic coupling. The exposure of membranes to nanoscopic contact points, therefore, cannot be considered as a simple linear interpolation between unsupported membranes and membranes supported on infinite supports. In the biological context, this suggests that the exposure of membranes to nonintercalating proteins, such as those belonging to the cytoskeleton, should not always be considered as passive nonconsequential interactions.

Effect of intrinsic and extrinsic factors on the simulated D‐band length of type I collagen

A signature feature of collagen is its axial periodicity visible in TEM as alternating dark and light bands. In mature, type I collagen, this repeating unit, D, is 67 nm long. This periodicity reflects an underlying packing of constituent triple‐helix polypeptide monomers wherein the dark bands represent gaps between axially adjacent monomers. This organization is visible distinctly in the microfibrillar model of collagen obtained from fiber diffraction. However, to date, no atomistic simulations of this diffraction model under zero‐stress conditions have reported a preservation of this structural feature. Such a demonstration is important as it provides the baseline to infer response functions of physiological stimuli. In contrast, simulations predict a considerable shrinkage of the D‐band (11–19%). Here we evaluate systemically the effect of several factors on D‐band shrinkage. Using force fields employed in previous studies we find that irrespective of the temperature/pressure coupling algorithms, assumed salt concentration or hydration level, and whether or not the monomers are cross‐linked, the D‐band shrinks considerably. This shrinkage is associated with the bending and widening of individual monomers, but employing a force field whose backbone dihedral energy landscape matches more closely with our computed CCSD(T) values produces a small D‐band shrinkage of < 3%. Since this force field also performs better against other experimental data, it appears that the large shrinkage observed in earlier simulations is a force‐field artifact. The residual shrinkage could be due to the absence of certain atomic‐level details, such as glycosylation sites, for which we do not yet have suitable data. Proteins 2015; 83:1800–1812.

Discerning intersecting fusion-activation pathways in the Nipah virus using machine learning.

The fusion of Nipah with host cells is facilitated by two of their glycoproteins, the G and the F proteins. The binding of cellular ephrins to the G head domain causes the G stalk domain to interact differently with F, which activates F to mediate virus–host fusion. To gain insight into how the ephrin‐binding signal transduces from the head to the stalk domain of G, we examine quantitatively the differences between the conformational ensembles of the G head domain in its ephrin‐bound and unbound states. We consider the human ephrins B2 and B3, and a double mutant of B2, all of which trigger fusion. The ensembles are generated using molecular dynamics, and the differences between them are quantified using a new machine learning method. We find that the portion of the G head domain whose conformational density is altered equivalently by the three ephrins is large, and comprises ∼25% of the residues in the G head domain. This subspace also includes the residues that are known to be important to F activation, which suggests that it contains at least one common signaling pathway. The spatial distribution of the residues constituting this subspace supports the model of signal transduction in which the signal transduces via the G head dimer interface. This study also adds to the growing list of examples where signaling does not depend solely on backbone deviations. In general, this study provides an approach to filter out conserved patterns in protein dynamics. Proteins 2014; 82:3241–3254.

Quantifying Changes in Intrinsic Molecular Motion Using Support Vector Machines.

The ensemble of three-dimensional (3-D) configurations exhibited by a molecule, that is, its intrinsic motion, can be altered by several environmental factors, and also by the binding of other molecules. Quantification of such induced changes in intrinsic motion is important because it provides a basis for relating thermodynamic changes to changes in molecular motion. This task is, however, challenging because it requires comparing two high-dimensional data sets. Traditionally, when analyzing molecular simulations, this problem is circumvented by first reducing the dimensions of the two ensembles separately, and then comparing summary statistics from the two ensembles against each other. However, since dimensionality reduction is carried out prior to ensemble comparison, such strategies are susceptible to artifactual biases from information loss. Here, we introduce a method based on support vector machines that yields a normalized quantitative estimate for the difference between two ensembles after comparing them directly against one another. While this method can be applied to any molecular system, including nonbiological molecules and crystals, here, we show how it can be applied to identify the specific regions of a paramyxovirus G protein that are affected by the binding of its preferred human receptor, Ephrin B2. This protein-protein interaction initiates the fusion of the virus with the host cell. Specifically, for every residue in the G protein, we obtain separately a quantitative difference between the ensemble of configurations they sample in the presence and in the absence of Ephrin B2. These ensembles were generated using molecular dynamics simulations. Rank-ordering and then mapping the residues that undergo the greatest change in motion onto the 3-D structure of the G protein reveals that they are clustered primarily on a single contiguous facet of the protein and include the set that is known experimentally to play a vital role in regulating viral fusion.