Coupling hydrophobic, dispersion, and electrostatic contributions in continuum solvent models

Recent studies of the hydration of micro- and nanoscale solutes have demonstrated a strong {\it coupling} between hydrophobic, dispersion and electrostatic contributions, a fact not accounted for in current implicit solvent models. We present a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy with respect to a solvent volume exclusion function. The solvent accessible surface is output of our theory. Our method is illustrated with the hydration of alkane-assembled solutes on different length scales, and captures the strong sensitivity to the particular form of the solute-solvent interactions in agreement with recent computer simulations.Comment: 11 pages, 2 figure

Simple estimation of absolute free energies for biomolecules

One reason that free energy difference calculations are notoriously difficult in molecular systems is due to insufficient conformational overlap, or similarity, between the two states or systems of interest. The degree of overlap is irrelevant, however, if the absolute free energy of each state can be computed. We present a method for calculating the absolute free energy that employs a simple construction of an exactly computable reference system which possesses high overlap with the state of interest. The approach requires only a physical ensemble of conformations generated via simulation, and an auxiliary calculation of approximately equal central-processing-unit (CPU) cost. Moreover, the calculations can converge to the correct free energy value even when the physical ensemble is incomplete or improperly distributed. As a "proof of principle," we use the approach to correctly predict free energies for test systems where the absolute values can be calculated exactly, and also to predict the conformational equilibrium for leucine dipeptide in implicit solvent.Comment: To appear in J. Chem. Phys., 10 pages, 6 figure

Substrate concentration dependence of the diffusion-controlled steady-state rate constant

The Smoluchowski approach to diffusion-controlled reactions is generalized to interacting substrate particles by including the osmotic pressure and hydrodynamic interactions of the nonideal particles in the Smoluchoswki equation within a local-density approximation. By solving the strictly linearized equation for the time-independent case with absorbing boundary conditions, we present an analytic expression for the diffusion-limited steady-state rate constant for small substrate concentrations in terms of an effective second virial coefficient B_2*. Comparisons to Brownian dynamics simulations excluding HI show excellent agreement up to bulk number densities of B_2* rho_0 < 0.4 for hard sphere and repulsive Yukawa-like interactions between the substrates. Our study provides an alternative way to determine the second virial coefficient of interacting macromolecules experimentally by measuring their steady-state rate constant in diffusion-controlled reactions at low densities.Comment: 7 pages, 3 figure

Coupling nonpolar and polar solvation free energies in implicit solvent models

Recent studies on the solvation of atomistic and nanoscale solutes indicate that a strong coupling exists between the hydrophobic, dispersion, and electrostatic contributions to the solvation free energy, a facet not considered in current implicit solvent models. We suggest a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy of the solvent with respect to a solvent volume exclusion function. The resulting differential equation is similar to the Laplace-Young equation for the geometrical description of capillary interfaces, but is extended to microscopic scales by explicitly considering curvature corrections as well as dispersion and electrostatic contributions. Unlike existing implicit solvent approaches, the solvent accessible surface is an output of our model. The presented formalism is illustrated on spherically or cylindrically symmetrical systems of neutral or charged solutes on different length scales. The results are in agreement with computer simulations and, most importantly, demonstrate that our method captures the strong sensitivity of solvent expulsion and dewetting to the particular form of the solvent-solute interactions.Comment: accpted in J. Chem. Phy

Enhanced conformational space sampling improves the prediction of chemical shifts in proteins.

A biased-potential molecular dynamics simulation method, accelerated molecular dynamics (AMD), was combined with the chemical shift prediction algorithm SHIFTX to calculate (1)H(N), (15)N, (13)Calpha, (13)Cbeta, and (13)C' chemical shifts of the ankyrin repeat protein IkappaBalpha (residues 67-206), the primary inhibitor of nuclear factor kappa-B (NF-kappaB). Free-energy-weighted molecular ensembles were generated over a range of acceleration levels, affording systematic enhancement of the conformational space sampling of the protein. We have found that the predicted chemical shifts, particularly for the (15)N, (13)Calpha, and (13)Cbeta nuclei, improve substantially with enhanced conformational space sampling up to an optimal acceleration level. Significant improvement in the predicted chemical shift data coincides with those regions of the protein that exhibit backbone dynamics on longer time scales. Interestingly, the optimal acceleration level for reproduction of the chemical shift data has previously been shown to best reproduce the experimental residual dipolar coupling (RDC) data for this system, as both chemical shift data and RDCs report on an ensemble and time average in the millisecond range

Functional dynamics of the folded ankyrin repeats of I kappa B alpha revealed by nuclear magnetic resonance.

Inhibition of nuclear factor kappaB (NF-kappaB) is mainly accomplished by IkappaB alpha, which consists of a signal response sequence at the N-terminus, a six-ankyrin repeat domain (ARD) that binds NF-kappaB, and a C-terminal PEST sequence. Previous studies with the ARD revealed that the fifth and sixth repeats are only partially folded in the absence of NF-kappaB. Here we report NMR studies of a truncated version of IkappaB alpha, containing only the first four ankyrin repeats, IkappaB alpha(67-206). This four-repeat segment is well-structured in the free state, enabling full resonance assignments to be made. H-D exchange, backbone dynamics, and residual dipolar coupling (RDC) experiments reveal regions of flexibility. In addition, regions consistent with the presence of micro- to millisecond motions occur periodically throughout the repeat structure. Comparison of the RDCs with the crystal structure gave only moderate agreement, but an ensemble of structures generated by accelerated molecular dynamics gave much better agreement with the measured RDCs. The regions showing flexibility correspond to those implicated in entropic compensation for the loss of flexibility in ankyrin repeats 5 and 6 upon binding to NF-kappaB. The regions showing micro- to millisecond motions in the free protein are the ends of the beta-hairpins that directly interact with NF-kappaB in the complex

Enzyme Localization, Crowding, and Buffers Collectively Modulate Diffusion-Influenced Signal Transduction: Insights from Continuum Diffusion Modeling

Biochemical reaction networks consisting of coupled enzymes connect substrate signaling events with biological function. Substrates involved in these reactions can be strongly influenced by diffusion “barriers” arising from impenetrable cellular structures and macromolecules, as well as interactions with biomolecules, especially within crowded environments. For diffusion-influenced reactions, the spatial organization of diffusion barriers arising from intracellular structures, non-specific crowders, and specific-binders (buffers) strongly controls the temporal and spatial reaction kinetics. In this study, we use two prototypical biochemical reactions, a Goodwin oscillator, and a reaction with a periodic source/sink term to examine how a diffusion barrier that partitions substrates controls reaction behavior. Namely, we examine how conditions representative of a densely packed cytosol, including reduced accessible volume fraction, non-specific interactions, and buffers, impede diffusion over nanometer length-scales. We find that diffusion barriers can modulate the frequencies and amplitudes of coupled diffusion-influenced reaction networks, as well as give rise to “compartments” of decoupled reactant populations. These effects appear to be intensified in the presence of buffers localized to the diffusion barrier. These findings have strong implications for the role of the cellular environment in tuning the dynamics of signaling pathways