The membrane permeability coefficient of a solute can be estimated using the solubility-diffusion model. This model requires the diffusivity profile (D(z)) of the solute as it moves along the transmembrane axis, z. The generalized Langevin equation provides one strategy for calculating position-dependent diffusivity from straightforward molecular dynamics simulations where the solute is restrained to a series of positions on the z-coordinate by a harmonic potential. The diffusivity of the solute is calculated from its correlation functions, which are related to the friction experienced by the solute. Roux and Hummer have derived expressions for the diffusion coefficient from the velocity autocorrelation function (VACF) and position autocorrelation function (PACF), respectively. In this work, these methods are validated by calculating the diffusivity of HO and O in homogeneous liquids. These methods are then used to calculate transmembrane diffusivity profiles. The VACF method is less sensitive to thermostat forces and has incrementally lower errors but is more sensitive to the spring constant of the harmonic restraint. For the permeation of a solute through a lipid bilayer, the diffusion coefficients calculated using these methods provided significantly different results. Long-lived correlations of the restrained solute due to inhomogeneities in the bilayer can result in spuriously low diffusivity when using the PACF method. The method based on the VACF does not have this issue and predicts higher rates of diffusion inside the bilayer.
Biomolecular structure determination has long relied on heuristics based on physical insight; however, recent efforts to model conformational ensembles and to make sense of sparse, ambiguous, and noisy data have revealed the value of detailed, quantitative physical models in structure determination. We review these two key challenges, describe different approaches to physical modeling in structure determination, and illustrate several successes and emerging technologies enabled by physical modeling.
There is a pressing need for new computational tools to integrate data from diverse experimental approaches in structural biology. We present a strategy that combines sparse paramagnetic solid‐state NMR restraints with physics‐based atomistic simulations. Our approach explicitly accounts for uncertainty in the interpretation of experimental data through the use of a semi‐quantitative mapping between the data and the restraint energy that is calibrated by extensive simulations. We apply our approach to solid‐state NMR data for the model protein GB1 labeled with Cu2+‐EDTA at six different sites. We are able to determine the structure to 0.9 Å accuracy within a single day of computation on a GPU cluster. We further show that in some cases, the data from only a single paramagnetic tag are sufficient for accurate folding.
Replica exchange is a widely used sampling strategy in molecular simulation. While a variety of methods exist to optimize parameters for temperature replica exchange, less is known about how to optimize parameters for more general Hamiltonian replica exchange simulations. We present an algorithm for the online optimization of total acceptance for both temperature and Hamiltonian replica exchange simulations using stochastic gradient descent. We optimize the total acceptance, a heuristic objective function capturing the efficiency of replica exchange. Our approach is general and has several desirable properties, including: (1) it makes few assumptions about the system of interest, (2) optimization occurs online without the requirement of presimulation, and (3) most importantly, it readily generalizes to systems where there are multiple control parameters (e.g., temperatures, force constants, etc.) that determine the Hamiltonian of each replica. We explore some general properties of the algorithm on a simple harmonic oscillator system, and demonstrate its effectiveness on a more complex data-guided protein folding simulation.
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