ALBERT

Description: Time-resolved wide-angle X-ray scattering (TR-WAXS) is an emerging experimental technique used to track chemical reactions and conformational transitions of proteins in real time. Thanks to increased time resolution of the method, anisotropic TR-WAXS patterns were recently reported, which contain more structural information than isotropic patterns. So far, however, no method has been available to compute anisotropic WAXS patterns of biomolecules, thus limiting the structural interpretation. Here, we present a method to compute anisotropic TR-WAXS patterns from molecular dynamics simulations. The calculations accurately account for scattering of the hydration layer and for thermal fluctuations. For many photo-excitable proteins, given a low intensity of the excitation laser, the anisotropic pattern is described by two independent components: (i) an isotropic component, corresponding to common isotropic WAXS experiments and (ii) an anisotropic component depending on the orientation of the excitation dipole of the solute. We present a set of relations for the calculation of these two components from experimental scattering patterns. Notably, the isotropic component is not obtained by a uniform azimuthal average on the detector. The calculations are illustrated and validated by computing anisotropic WAXS patterns of a spheroidal protein model and of photoactive yellow protein. Effects due to saturated excitation at high intensities of the excitation laser are discussed, including opportunities to extract additional structural information by modulating the laser intensity.

Description: In order to identify two-step chemical mechanisms, we propose a method based on a small temperature modulation and on the analysis of the concentration oscillations of a single tagged species involved in the first step. The thermokinetic parameters of the first reaction step are first determined. Then, we build test functions that are constant only if the chemical system actually possesses some assumed two-step mechanism. Next, if the test functions plotted using experimental data are actually even, the mechanism is attributed and the obtained constant values provide the rate constants and enthalpy of reaction of the second step. The advantage of the protocol is to use the first step as a probe reaction to reveal the dynamics of the second step, which can hence be relieved of any tagging. The protocol is anticipated to apply to many mechanisms of biological relevance. As far as ligand binding is considered, our approach can address receptor conformational changes or dimerization as well as competition with or modulation by a second partner. The method can also be used to screen libraries of untagged compounds, relying on a tracer whose concentration can be spectroscopically monitored

Description: A steady-state analysis for the catalytic turnover of molecules containing two substrate sites is presented. A broad class of Markovian dynamic models, motivated by the action of DNA modifying enzymes and the rich variety of translocation mechanisms associated with these systems (e.g., sliding, hopping, intersegmental transfer, etc.), is considered. The modeling suggests an elementary and general method of data analysis, which enables the extraction of the enzyme’s processivity directly and unambiguously from experimental data. This analysis is not limited to the initial velocity regime. The predictions are validated both against detailed numerical models and by revisiting published experimental data for EcoRI endonuclease acting on DNA.

Description: Importance sampling of trajectories has proved a uniquely successful strategy for exploring rare dynamical behaviors of complex systems in an unbiased way. Carrying out this sampling, however, requires an ability to propose changes to dynamical pathways that are substantial, yet sufficiently modest to obtain reasonable acceptance rates. Satisfying this requirement becomes very challenging in the case of long trajectories, due to the characteristic divergences of chaotic dynamics. Here, we examine schemes for addressing this problem, which engineer correlation between a trial trajectory and its reference path, for instance using artificial forces. Our analysis is facilitated by a modern perspective on Markov chain Monte Carlo sampling, inspired by non-equilibrium statistical mechanics, which clarifies the types of sampling strategies that can scale to long trajectories. Viewed in this light, the most promising such strategy guides a trial trajectory by manipulating the sequence of random numbers that advance its stochastic time evolution, as done in a handful of existing methods. In cases where this “noise guidance” synchronizes trajectories effectively, as the Glauber dynamics of a two-dimensional Ising model, we show that efficient path sampling can be achieved for even very long trajectories.

Description: The Saffman-Delbrück hydrodynamic model for lipid-bilayer membranes is modified to account for the periodic boundary conditions commonly imposed in molecular simulations. Predicted lateral diffusion coefficients for membrane-embedded solid bodies are sensitive to box shape and converge slowly to the limit of infinite box size, raising serious doubts for the prospects of using detailed simulations to accurately predict membrane-protein diffusivities and related transport properties. Estimates for the relative error associated with periodic boundary artifacts are 50% and higher for fully atomistic models in currently feasible simulation boxes. MARTINI simulations of LacY membrane protein diffusion and LacY dimer diffusion in DPPC membranes and lipid diffusion in pure DPPC bilayers support the underlying hydrodynamic model.

Description: The dynamics of the human oligonucleotide AG 3 (T 2 AG 3 ) 3 has been investigated by incoherent neutron scattering in the sub-nanosecond timescale. A hydration-dependent dynamical activation of thermal fluctuations in weakly hydrated samples was found, similar to that of protein powders. The amplitudes of such thermal fluctuations were evaluated in two different exchanged wave-vector ranges, so as to single out the different contributions from intra- and inter-nucleotide dynamics. The activation energy was calculated from the temperature-dependent characteristic times of the corresponding dynamical processes. The trends of both amplitudes and activation energies support a picture where oligonucleotides possess a larger conformational flexibility than long DNA sequences. This additional flexibility, which likely results from a significant relative chain-end contribution to the average chain dynamics, could be related to the strong structural polymorphism of the investigated oligonucleotides.

Description: Predicting conformational changes of proteins is needed in order to fully comprehend functional mechanisms. With the large number of available structures in sets of related proteins, it is now possible to directly visualize the clusters of conformations and their conformational transitions through the use of principal component analysis. The most striking observation about the distributions of the structures along the principal components is their highly non-uniform distributions. In this work, we use principal component analysis of experimental structures of 50 diverse proteins to extract the most important directions of their motions, sample structures along these directions, and estimate their free energy landscapes by combining knowledge-based potentials and entropy computed from elastic network models. When these resulting motions are visualized upon their coarse-grained free energy landscapes, the basis for conformational pathways becomes readily apparent. Using three well-studied proteins, T4 lysozyme, serum albumin, and sarco-endoplasmic reticular Ca 2+ adenosine triphosphatase (SERCA), as examples, we show that such free energy landscapes of conformational changes provide meaningful insights into the functional dynamics and suggest transition pathways between different conformational states. As a further example, we also show that Monte Carlo simulations on the coarse-grained landscape of HIV-1 protease can directly yield pathways for force-driven conformational changes.

Description: Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the Smoluchowski equation. The role of the particle mobility center is determined and discussed.

Description: We present a general framework to predict the excess solubility of small molecular solids (such as pharmaceutical solids) in binary solvents via molecular simulation free energy calculations at infinite dilution with conventional molecular models. The present study used molecular dynamics with the General AMBER Force Field to predict the excess solubility of acetanilide, acetaminophen, phenacetin, benzocaine, and caffeine in binary water/ethanol solvents. The simulations are able to predict the existence of solubility enhancement and the results are in good agreement with available experimental data. The accuracy of the predictions in addition to the generality of the method suggests that molecular simulations may be a valuable design tool for solvent selection in drug development processes.