Calculation of Proteins' Total Side-Chain Torsional Entropy and Its Influence on Protein-Ligand Interactions

Despite the high density within a typical protein fold, the ensemble of sterically permissible side-chain repackings is vast. Here, we examine the extent of this variability that survives energetic biases due to van der Waals interactions, hydrogen bonding, salt bridges, and solvation. Monte Carlo simulations of an atomistic model exhibit thermal fluctuations among a diverse set of side-chain arrangements, even with the peptide backbone fixed in its crystallographic conformation. We have quantified the torsional entropy of this native-state ensemble, relative to that of a noninteracting reference system, for 12 small proteins. The reduction in entropy per rotatable bond due to each kind of interaction is remarkably consistent across this set of molecules. To assess the biophysical importance of these fluctuations, we have estimated side-chain entropy contributions to the binding affinity of several peptide ligands with calmodulin. Calculations for our fixed-backbone model correlate very well with experimentally determined binding entropies over a range spanning more than 80 kJ/(mol·308 K)

Remembering the work of Phillip L. Geissler: A coda to his scientific trajectory

Phillip L. Geissler made important contributions to the statistical mechanics of biological polymers, heterogeneous materials, and chemical dynamics in aqueous environments. He devised analytical and computational methods that revealed the underlying organization of complex systems at the frontiers of biology, chemistry, and materials science. In this retrospective, we celebrate his work at these frontiers

Long-Range Intra-Protein Communication Can Be Transmitted by Correlated Side-Chain Fluctuations Alone

Allosteric regulation is a key component of cellular communication, but the way in which information is passed from one site to another within a folded protein is not often clear. While backbone motions have long been considered essential for long-range information conveyance, side-chain motions have rarely been considered. In this work, we demonstrate their potential utility using Monte Carlo sampling of side-chain torsional angles on a fixed backbone to quantify correlations amongst side-chain inter-rotameric motions. Results indicate that long-range correlations of side-chain fluctuations can arise independently from several different types of interactions: steric repulsions, implicit solvent interactions, or hydrogen bonding and salt-bridge interactions. These robust correlations persist across the entire protein (up to 60 Å in the case of calmodulin) and can propagate long-range changes in side-chain variability in response to single residue perturbations

Structure and Dynamics of Adsorbed Dopamine on Solvated Carbon Nanotubes and in a CNT Groove

Advanced carbon microelectrodes are being developed for the in vivo detection of neurotransmitters, such as dopamine (DA), including many carbon nanotube (CNT) based electrodes. Our prior simulations of DA and dopamine-o-quinone (DOQ) on pristine, flat graphene showed rapid surface diffusion for all adsorbed species, but it is not known how CNT surfaces affect dopamine adsorption and surface diffusivity. In this work, we use molecular dynamics simulations to investigate the adsorbed structures and surface diffusion dynamics of DA and DOQ on CNTs of varying curvature and helicity. In addition, we study DA dynamics in a groove between two aligned CNTs to model the spatial constraints at the junctions within CNT assemblies. We find that the adsorbate diffusion on a solvated CNT surface depends upon curvature. However, this effect cannot be attributed to changes in the surface energy roughness because the lateral distributions of the molecular adsorbates are similar across curvatures, diffusivities on zigzag and armchair CNTs are indistinguishable, and the curvature dependence disappears in the absence of solvent. Instead, adsorbate diffusivities correlate with the vertical placement of the adsorbate\u27s moieties, its tilt angle, its orientation along the CNT axis, and the number of waters in its first hydration shell -- all of which will influence its effective hydrodynamic radius. Finally, DA diffuses into and remains in the groove between a pair of aligned and solvated CNTs, enhancing diffusivity along the CNT axis. These first studies of surface diffusion on a CNT electrode surface are important for understanding the changes in diffusion dynamics of dopamine on nanostructured carbon electrode surfaces

Structure and Dynamics of Adsorbed Dopamine on Solvated Carbon Nanotubes and in a CNT Groove

Advanced carbon microelectrodes, including many carbon-nanotube (CNT)-based electrodes, are being developed for the in vivo detection of neurotransmitters such as dopamine (DA). Our prior simulations of DA and dopamine-o-quinone (DOQ) on pristine, flat graphene showed rapid surface diffusion for all adsorbed species, but it is not known how CNT surfaces affect dopamine adsorption and surface diffusivity. In this work, we use molecular dynamics simulations to investigate the adsorbed structures and surface diffusion dynamics of DA and DOQ on CNTs of varying curvature and helicity. In addition, we study DA dynamics in a groove between two aligned CNTs to model the spatial constraints at the junctions within CNT assemblies. We find that the adsorbate diffusion on a solvated CNT surface depends upon curvature. However, this effect cannot be attributed to changes in the surface energy roughness because the lateral distributions of the molecular adsorbates are similar across curvatures, diffusivities on zigzag and armchair CNTs are indistinguishable, and the curvature dependence disappears in the absence of solvent. Instead, adsorbate diffusivities correlate with the vertical placement of the adsorbate’s moieties, its tilt angle, its orientation along the CNT axis, and the number of waters in its first hydration shell, all of which will influence its effective hydrodynamic radius. Finally, DA diffuses into and remains in the groove between a pair of aligned and solvated CNTs, enhancing diffusivity along the CNT axis. These first studies of surface diffusion on a CNT electrode surface are important for understanding the changes in diffusion dynamics of dopamine on nanostructured carbon electrode surfaces

Long-Range Intra-Protein Communication Can Be Transmitted by Correlated Side-Chain Fluctuations Alone

Allosteric regulation is a key component of cellular communication, but the way in which information is passed from one site to another within a folded protein is not often clear. While backbone motions have long been considered essential for long-range information conveyance, side-chain motions have rarely been considered. In this work, we demonstrate their potential utility using Monte Carlo sampling of side-chain torsional angles on a fixed backbone to quantify correlations amongst side-chain inter-rotameric motions. Results indicate that long-range correlations of side-chain fluctuations can arise independently from several different types of interactions: steric repulsions, implicit solvent interactions, or hydrogen bonding and salt-bridge interactions. These robust correlations persist across the entire protein (up to 60 Å in the case of calmodulin) and can propagate long-range changes in side-chain variability in response to single residue perturbations

Atomistic simulations of dopamine diffusion dynamics on a pristine graphene surface

Carbon microelectrodes enable in vivo detection of neurotransmitters, and new electrodes are being developed to optimize the carbon surface. However, the work is mainly empirical and there have not been corresponding theoretical studies using molecular-level simulations of the diffusion and orientation of neurotransmitters near these surfaces. Here, we employ molecular dynamics simulations to investigate in atomistic detail the surface diffusion of dopamine (DA), its oxidation product dopamine-o-quinone (DOQ), and their protonated forms on the pristine basal plane of flat graphene. All DA species rapidly adsorb to the surface and remain adsorbed for the full length of the equilibrium simulations, even without a holding potential or graphene surface defects. The diffusivities of the adsorbed and the fully solvated DA are similar, and all molecular diffusion on the surface is slower than that of an adatom of comparable molecular weight. The protonated species diffuse more slowly than their corresponding neutral forms, and the oxidized species diffuse more rapidly. The underlying hexagonal graphene structure has little influence over the molecular adsorbate\u27s lateral position. The vertical placement of the amine group on dopamine is highly dependent upon its charge, and the protonated amine prefers to be above the surface near the solvating waters. Solvation has a large effect on surface diffusivities when diffusion is compared to that in a vacuum. These are the first results of molecular dynamics simulations of dopamine diffusion at the aqueous-graphene interface, and they show that dopamine diffuses quickly on graphene surfaces, even without an applied potential. These calculations provide a basis for future simulations to predict the behavior of neurotransmitter diffusion on advanced carbon materials electrodes

Structural representations of extended crystalline calmodulin.

<p>The crystal structure (a) and contact map (b) of calcium-bound calmodulin (3cln <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002168#pcbi.1002168-Babu1" target="_blank">[39]</a>). The calcium ions are shown in yellow, and several residues are labeled in both panels for reference. The distance between each pair of atoms is indicated by color (see scale bar) in (b), where - and -axes run over residue labels. The residue labeling corresponds to the full sequence, however residues that do not possess torsional degrees of freedom in our model (A, G, P, and all residues bound to the calcium ions) are excluded from the contact map.</p

Single-residue perturbations in barstar.

<p>Changes in the Gibbs entropy of each residue in barstar (1a19 <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002168#pcbi.1002168-Ratnaparkhi1" target="_blank">[47]</a>) that resulted from perturbations to single side-chains. Residues whose entropy changes by a significant amount, according to Student's t-test at the 90% level, are shown in color. Red indicates increased entropy, blue indicates decreased entropy (see scale bar). Although side-chains are depicted in their crystallographic arrangements for graphical simplicity, note that is a measure of the extent of fluctuations among a wide variety of distinct packings. For the results presented in panel (a), I86 (shown in black and circled) was mutated to G. For those of panel (b) E46 (shown in black and circled) was constrained to its crystallographic configuration.</p

Mutual information of residue pairs in calmodulin.

<p>The mutual information, , associated with side-chain fluctuations of residue pairs in calmodulin. Plots (b)–(f) display the mutual information signal∶noise ratio, (upper left triangles) and the excess mutual information (lower right triangles), as indicated in (a). The - and -axes run over labels, and respectively, of residues in the amino acid sequence, excluding those lacking rotameric freedom in our model. Scale bars for the signal∶noise ratio and the excess mutual information are presented on the top and bottom left, respectively. Results are shown for the following combinations of interactions: (b) repulsive sterics (S), (c) implicit solvent (IS) (d) Lennard-Jones (LJ) interaction comprising repulsive sterics and van der Waals attractions, (e) hydrogen bonding and salt-bridges (HBSB), and (f) the full potential (LJ+HBSB+IS). Residue 30K, which we scrutinize in detail later (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002168#pcbi-1002168-g005" target="_blank">Fig. 5</a>), is highlighted in (f) for reference.</p