Equilibrium simulations of proteins using molecular fragment replacement and NMR chemical shifts

Abstract

Methods of protein structure determination based on NMR chemical shifts are becoming increasingly common. The most widely used approaches adopt the molecular fragment replacement strategy, in which structural fragments are repeatedly reassembled into different complete conformations in molecular simulations. Although these approaches are effective in generating individual structures consistent with the chemical shift data, they do not enable the sampling of the conformational space of proteins with correct statistical weights. Here, we present a method of molecular fragment replacement that makes it possible to perform equilibrium simulations of proteins, and hence to determine their free energy landscapes. This strategy is based on the encoding of the chemical shift information in a probabilistic model in Markov chain Monte Carlo simulations. First, we demonstrate that with this approach it is possible to fold proteins to their native states starting from extended structures. Second, we show that the method satisfies the detailed balance condition and hence it can be used to carry out an equilibrium sampling from the Boltzmann distribution corresponding to the force field used in the simulations. Third, by comparing the results of simulations carried out with and without chemical shift restraints we describe quantitatively the effects that these restraints have on the free energy landscapes of proteins. Taken together, these results demonstrate that the molecular fragment replacement strategy can be used in combination with chemical shift information to characterize not only the native structures of proteins but also their conformational fluctuations.

Biophysical experiments and biomolecular simulations: A perfect match?

“…Indeed, this "pseudoenergy" approach underlies most structure-determination algorithms in which a physical energy function (often a simplified force field) is combined with an "experimental energy function" that measures the deviation between experiment and simulation (52). These integrative approaches enable accurate proteinstructure determination when using chemical shifts (53) (Fig. 3A) or when using sparse, uncertain, and ambiguous experimental data (54).…”

Molecular simulations minimally restrained by experimental data

“…12) at different values of N . 3,4,5 ) in the restrained ensemble simulations for different values of N , using the values of λ j and the corresponding D λj and Σ λj in different biased simulations as inputs. The largest N (N max ) for which the predicted values of all the restrained observables are within the statistical uncertainty from the experimental values is determined for each j.…”

Efficient Ensemble Refinement by Reweighting

“…8). These methods either treat experimental observables as strict constraints 20,22,61,62 or consider errors explicitly 25,30,60 . If solutions for these methods exist then they correspond to di↵erent choices of the value of the confidence parameter ✓: The BioEn optimal ensemble approaches the traditional MaxEnt solution with strict constraints forcing deviations from the experimental values to vanish, i.e., 2 = 0, in the limit of ✓ !…”

“…For BioEn optimal ensembles, we plot the reduced 2 and the relative entropy S KL parameterized by the confidence parameter ✓ (blue). The solution of Gull-Daniell-type 60 methods is given by the intersection of this curve with 2 = 1 (orange), of traditional MaxEnt methods 20,22,61,62 by the intersection with 2 = 0 (green), and of the method of Cesari et al 25,30 by the BioEn solution for ✓ = 1 (red). is rougher, we often have to apply enhanced sampling methods to obtain good coverage.…”