Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently-developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.Comment: 15 pages, 2 figures, and 2 table

Towards Automated Benchmarking of Atomistic Forcefields: Neat Liquid Densities and Static Dielectric Constants from the ThermoML Data Archive

Atomistic molecular simulations are a powerful way to make quantitative predictions, but the accuracy of these predictions depends entirely on the quality of the forcefield employed. While experimental measurements of fundamental physical properties offer a straightforward approach for evaluating forcefield quality, the bulk of this information has been tied up in formats that are not machine-readable. Compiling benchmark datasets of physical properties from non-machine-readable sources require substantial human effort and is prone to accumulation of human errors, hindering the development of reproducible benchmarks of forcefield accuracy. Here, we examine the feasibility of benchmarking atomistic forcefields against the NIST ThermoML data archive of physicochemical measurements, which aggregates thousands of experimental measurements in a portable, machine-readable, self-annotating format. As a proof of concept, we present a detailed benchmark of the generalized Amber small molecule forcefield (GAFF) using the AM1-BCC charge model against measurements (specifically bulk liquid densities and static dielectric constants at ambient pressure) automatically extracted from the archive, and discuss the extent of available data. The results of this benchmark highlight a general problem with fixed-charge forcefields in the representation low dielectric environments such as those seen in binding cavities or biological membranes

Exploring the Free Energy Landscape: From Dynamics to Networks and Back

The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers are, how the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times or rate constants, and the hierarchical relationship among basins, complete the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, the dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press

A weak characterization of slow variables in stochastic dynamical systems

We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordinates in molecular dynamical applications, where they play a key role in system analysis and coarse graining. The defining characteristics of these slow variables is that they parametrize a so-called transition manifold, a low-dimensional manifold in a certain density function space that emerges with progressive equilibration of the system's fast variables. The existence of said manifold was previously predicted for certain classes of metastable and slow-fast systems. However, in the original work, the existence of the manifold hinges on the pointwise convergence of the system's transition density functions towards it. We show in this work that a convergence in average with respect to the system's stationary measure is sufficient to yield reaction coordinates with the same key qualities. This allows one to accurately predict the timescale preservation in systems where the old theory is not applicable or would give overly pessimistic results. Moreover, the new characterization is still constructive, in that it allows for the algorithmic identification of a good slow variable. The improved characterization, the error prediction and the variable construction are demonstrated by a small metastable system

Turning high-throughput structural biology into predictive inhibitor design

Peer reviewe

Why are MD simulated protein folding times wrong?

The question of significant deviations of protein folding times simulated using molecular dynamics from experimental values is investigated. It is shown that in the framework of Markov State Model (MSM) describing the conformational dynamics of peptides and proteins, the folding time is very sensitive to the simulation model parameters, such as forcefield and temperature. Using two peptides as examples, we show that the deviations in the folding times can reach an order of magnitude for modest variations of the molecular model. We, therefore, conclude that the folding rate values obtained in molecular dynamics simulations have to be treated with care

Supplementary guidance: listening to staff: Autumn 2017

Kinases play a critical role in cellular signaling and are dysregulated in a number of diseases, such as cancer, diabetes, and neurodegeneration. Therapeutics targeting kinases currently account for roughly 50% of cancer drug discovery efforts. The ability to explore human kinase biochemistry and biophysics in the laboratory is essential to designing selective inhibitors and studying drug resistance. Bacterial expression systems are superior to insect or mammalian cells in terms of simplicity and cost effectiveness but have historically struggled with human kinase expression. Following the discovery that phosphatase coexpression produced high yields of Src and Abl kinase domains in bacteria, we have generated a library of 52 His-tagged human kinase domain constructs that express above 2 μg/mL of culture in an automated bacterial expression system utilizing phosphatase coexpression (YopH for Tyr kinases and lambda for Ser/Thr kinases). Here, we report a structural bioinformatics approach to identifying kinase domain constructs previously expressed in bacteria and likely to express well in our protocol, experiments demonstrating our simple construct selection strategy selects constructs with good expression yields in a test of 84 potential kinase domain boundaries for Abl, and yields from a high-throughput expression screen of 96 human kinase constructs. Using a fluorescence-based thermostability assay and a fluorescent ATP-competitive inhibitor, we show that the highest-expressing kinases are folded and have well-formed ATP binding sites. We also demonstrate that these constructs can enable characterization of clinical mutations by expressing a panel of 48 Src and 46 Abl mutations. The wild-type kinase construct library is available publicly via Addgene

Evaluation of gait symmetry in poliomyelitis subjects : Comparison of a conventional knee ankle foot orthosis (KAFO) and a new powered KAFO.

Background: Compared to able-bodied subjects, subjects with post polio syndrome and poliomyelitis demonstrate a preference for weight-bearing on the non-paretic limb, causing gait asymmetry. Objectives: The purpose of this study was to evaluate the gait symmetry of the poliomyelitis subjects when ambulating with either a drop- locked knee ankle foot orthosis (KAFO) or a newly developed powered KAFO. Methods: Seven subjects with poliomyelitis who routinely wore conventional KAFOs participated in this study, and received training to enable them to ambulate with the powered KAFO on level ground, prior to gait analysis. Results: There were no significant differences in the gait symmetry index (SI) of step length (P=0.085), stance time (P=0.082), double limb support time (P=0.929) or speed of walking (p=0.325) between the two test conditions. However, using the new powered KAFO improved the SI in step width (P=0.037), swing time (P=0.014), stance phase percentage (P=0.008) and knee flexion during swing phase (p≤0.001) compared to wearing the dropped locked KAFO. Conclusion: The use of a powered KAFO for ambulation by poliomyelitis subjects affects gait symmetry in the base of support, swing time, stance phase percentage and knee flexion during swing phase

Variational Approach to Molecular Kinetics

The eigenvalues and eigenvectors of the molecular dynamics propagator (or transfer operator) contain the essential information about the molecular thermodynamics and kinetics. This includes the stationary distribution, the metastable states, and state-to-state transition rates. Here, we present a variational approach for computing these dominant eigenvalues and eigenvectors. This approach is analogous the variational approach used for computing stationary states in quantum mechanics. A corresponding method of linear variation is formulated. It is shown that the matrices needed for the linear variation method are correlation matrices that can be estimated from simple MD simulations for a given basis set. The method proposed here is thus to first define a basis set able to capture the relevant conformational transitions, then compute the respective correlation matrices, and then to compute their dominant eigenvalues and eigenvectors, thus obtaining the key ingredients of the slow kinetics