[39][41] www.pnas.org/cgi

The emergence and continuing global spread of the highly virulent avian influenza H5N1 has raised concerns of a possible human pandemic. 1 Several approved anti-influenza drugs effectively target the neuraminidase (NA), a surface glycoprotein that cleaves terminal sialic acid residues and facilitates the release of viral progeny from infected cells. 2 The first crystal structures of group-1 NAs in apo form and in complex with currently available drugs 3 revealed that although the binding pose of oseltamivir (Tamiflu) was similar to that seen in previous crystallographic complexes, 4,5 the 150-loop adopted a distinct conformation, opening a new cavity adjacent to the active site. This open form of the 150-loop was proposed as a new opportunity for drug design. 3 However, under certain crystallization conditions, the 150-loop was found to adopt the same closed conformation as previously seen in group-2 structures, suggesting a slow conformational change may occur upon inhibitor binding. 3 The possible transience of the 150-loop cavity and its proximity to the inhibitor-binding site underscores the importance of dynamic biophysical studies to complement static crystal structures in NA drug discovery efforts. Through explicitly solvated molecular dynamics (MD) simulations of the apo and oseltamivir-bound forms of tetrameric N1, here we show that the 150-loop is able to open into significantly wider conformations than seen in the crystal structures. We find this motion in the 150-loop is coupled to motion in the neighboring 430-loop, which expands the active site cavity even further. In addition, we see that the 150-loop approaches the closed conformation in simulations of the oseltamivir-bound system, suggesting that the loop switching motion may be more rapid than previously proposed.Two separate MD simulations were carried out using apo and oseltamivir-bound crystal structures. 3 The tetramer structures are exceptionally stable over the course of the 40 ns simulations (Supporting Information Figure S1). A principal components analysis over all the chains for both systems reveals that the monomer subunits within each tetramer sample different regions of configurational space, establishing that their motion can be considered independent of one another ( Figure S2). On average, the apo N1 exhibits slightly higher overall per residue C R rootmean-square fluctuation (rmsf) values than the oseltamivir-bound system ( Figure S3). Further analysis reveals that the residues exhibiting the largest rmsf differences between the two systems are located at least 5.0 Å distal to the catalytic pocket, suggesting that the largest conformational changes are due to motions of surface-exposed loops rather than local changes directly within the active site pocket.Most notably, the MD trajectories suggest that the 150-loop is even more flexible than observed in the crystal structures. Although we do not sample the completely closed conformation, salt bridge and hydrogen bond interactions between oseltamivir and residues Asp151 and Arg15...

An optimized method for estimating path-ensemble averages using data from processes driven in opposite directions is presented. Based on this estimator, bidirectional expressions for reconstructing free energies and potentials of mean force from single-molecule force spectroscopy-valid for biasing potentials of arbitrary stiffness-are developed. Numerical simulations on a model potential indicate that these methods perform better than unidirectional strategies.Crooks' path-ensemble average theorem (Eq. 1) encompasses a set of exact results in nonequilibrium statistical mechanics pertinent to systems driven from thermal equilibrium by a time-dependent external potential [1]. These include Jarzynski's equality [2] and the Crooks fluctuation theorem [3], which relate equilibrium free energy differences to the nonequilibrium work distribution, as well as reweighting relations that allow one to recover arbitrary equilibrium ensemble averages from measurements of driven nonequilibrium processes [1]. Because of the intimate connection between such processes and molecular force spectroscopy, these theorems have been widely invoked to extract free energies and potentials of mean force (PMFs) from single-molecule pulling experiments [4][5][6][7][8].While formally correct, the practical utility of these relations is limited by the presence of exponential averages of the work, which are dominated by rare events and therefore have notoriously slow convergence properties [9]. In order to improve their convergence, strategies such as work-weighted trajectory sampling [10][11][12] have been proposed. Here we suggest another method to accelerate the convergence of these averages: including trajectories from the reverse process in the forward path-ensemble. This is motivated in part by the observation that the exponential average of the work in the forward process is dominated by those rare trajectories that resemble time-reversed counterparts ("conjugate twins") of typical trajectories generated by the reverse protocol [13]. Thus, our goals are to construct optimized forward pathensemble average estimators that explicitly include such trajectories, and apply them to the problem of estimating free energies and potentials of mean force from single-molecule pulling experiments.The starting point of our analysis is Crooks' path-ensemble average theorem, which relates the forward average of an arbitrary functional of the phase space trajectory Γ = {q(t), p (t)} to its work-weighted average in the reverse process, namely [1] (1)In the above, the forward average 〈…〉 F is an average over all trajectories (path-ensemble average) generated in the forward process, wherein an external parameter (e.g. the position of * Electronic Address:

High macromolecular concentrations, or crowded conditions, have been shown to affect a wide variety of molecular processes, including diffusion, association and dissociation, and protein folding and stability. Here, we model the effect of macromolecular crowding on the internal dynamics of a protein, HIV-1 protease, using Brownian dynamics simulations. HIV-1 protease possesses a pair of flaps which are postulated to open in the early stages of its catalytic mechanism. Compared to low concentrations, close-packed concentrations of repulsive crowding agents are found to significantly reduce the fraction of time that the protease flaps are open. Macromolecular crowding is likely to have a major effect on in vivo enzyme activity, and may play an important regulatory role in the viral life cycle.

In aqueous solution some proteins undergo large-scale movements of secondary structures, subunits or domains -referred to as protein 'breathing' -that define a native-state ensemble of structures. These fluctuations are sensitive to the nature and concentration of solutes and other proteins and are thereby expected to be different in the crowded interior of a cell than in dilute solution. Here we use a combination of wide angle x-ray scattering (WAXS) and computational modeling to derive a quantitative measure of the spatial scale of conformational fluctuations in a protein solution. Concentration-dependent changes in the observed scattering intensities are consistent with a model of structural fluctuations in which secondary structures undergo rigid-body motions relative to one another. This motion increases with decreasing protein concentration or increasing temperature. Analysis of a set of five structurally and functionally diverse proteins reveals a diversity of kinetic behaviors. Proteins with multiple disulfide bonds exhibit little or no increase in breathing in dilute solutions. The spatial extent of structural fluctuations appears highly dependent on both protein structure and concentration and is universally suppressed at very high protein concentrations.

We demonstrate the feasibility of estimating protein-ligand binding free energies using multiple rigid receptor configurations. Based on T4 lysozyme snapshots extracted from six alchemical binding free energy calculations with a flexible receptor, binding free energies were estimated for a total of 141 ligands. For 24 ligands, the calculations reproduced flexible-receptor estimates with a correlation coefficient of 0.90 and a root mean square error of 1.59 kcal/mol. The accuracy of calculations based on Poisson-Boltzmann/Surface Area implicit solvent was comparable to previously reported free energy calculations.

Existing optimal estimators of nonequilibrium path-ensemble averages are shown to fall within the framework of extended bridge sampling. Using this framework, we derive a general minimalvariance estimator that can combine nonequilibrium trajectory data sampled from multiple path-ensembles to estimate arbitrary functions of nonequilibrium expectations. The framework is also applied to obtain asymptotic variance estimates, which are a useful measure of statistical uncertainty. In particular, we develop asymptotic variance estimates pertaining to Jarzynski's equality for free energies and the Hummer-Szabo expressions for the potential of mean force, calculated from uni-or bidirectional path samples. These estimators are demonstrated on a model single-molecule pulling experiment. In these simulations, the asymptotic variance expression is found to accurately characterize the confidence intervals around estimators when the bias is small. Hence, the confidence intervals are inaccurately described for unidirectional estimates with large bias, but for this model it largely reflects the true error in a bidirectional estimator derived by Minh and Adib.

The internal dynamics of proteins inside of cells may be affected by the crowded intracellular environments. Here, we test a novel approach to simulations of crowding, in which simulations in the absence of crowders are postprocessed to predict crowding effects, against the direct approach of simulations in the presence of crowders. The effects of crowding on the flap dynamics of HIV-1 protease predicted by the postprocessing approach are found to agree well with those calculated by the direct approach. The postprocessing approach presents distinct advantages over the direct approach in terms of accuracy and speed and is expected to have broad impact on atomistic simulations of macromolecular crowding.