Simulating force-induced conformational transitions in polysaccharides with the SMD replica exchange method

Mechanical and Structural Tuning of Reversible Hydrogen Bonding in Interlocked Calixarene Nanocapsules

We present force probe molecular dynamics simulations of dimers of interlocked calixarene nanocapsules and study the impact of structural details and solvent properties on the mechanical unfolding pathways. The system consists of two calixarene "cups" that form a catenane structure via interlocked aliphatic loops of tunable length. The dimer shows reversible rebinding, and the kinetics of the system can be understood in terms of a two-state model for shorter loops (≤14 CH₂ units) and a three-state model for longer loops (≥15 CH₂ units). The various conformational states of the dimer are stabilized by networks of hydrogen bonds, the mechanical susceptibility of which can be altered by changing the polarity and proticity of the solvent. The variation of the loop length and the solvent properties in combination with changes in the pulling protocol allows to tune the reversibility of the conformational transitions.

Equilibrium sampling for biomolecules under mechanical tension

In the studies of force-induced conformational transitions of biomolecules, the large timescale difference from experiments presents the challenge of obtaining convergent sampling for molecular dynamics simulations. To circumvent this fundamental problem, an approach combining the replica-exchange method and umbrella sampling (REM-US) was developed to simulate mechanical stretching of biomolecules under equilibrium conditions. Equilibrium properties of conformational transitions can be obtained directly from simulations without further assumptions. To test the performance, we carried out REM-US simulations of atomic force microscope (AFM) stretching and relaxing measurements on the polysaccharide pustulan, a (1-->6)-beta-D-glucan, which undergoes well-characterized rotameric transitions in the backbone bonds. With significantly enhanced sampling convergence and efficiency, the REM-US approach closely reproduced the equilibrium force-extension curves measured in AFM experiments. Consistent with the reversibility in the AFM measurements, the new approach generated identical force-extension curves in both stretching and relaxing simulations-an outcome not reported in previous studies, proving that equilibrium conditions were achieved in the simulations. REM-US may provide a robust approach to modeling of mechanical stretching on polysaccharides and even nucleic acids.

Quantifying multiscale noise sources in single-molecule time series

When analyzing single-molecule data, a low-dimensional set of system observables typically serves as the observational data. We calibrate stochastic dynamical models from time series that record such observables. Numerical techniques for quantifying noise from multiple time scales in a single trajectory, including experimental instrument and inherent thermal noise, are demonstrated. The techniques are applied to study time series coming from both simulations and experiments associated with the nonequilibrium mechanical unfolding of titin's I27 domain. The estimated models can be used for several purposes, (1) detect dynamical signatures of "rare events" by analyzing the effective diffusion and force as a function of the monitored observable, (2) quantify the influence that conformational degrees of freedom, which are typically difficult to directly monitor experimentally, have on the dynamics of the monitored observable, (3) quantitatively compare the inherent thermal noise to other noise sources, for example, instrument noise, variation induced by conformational heterogeneity, and so forth, (4) simulate random quantities associated with repeated experiments, and (5) apply pathwise, that is, trajectory-wise, hypothesis tests to assess the goodness-of-fit of the models and even detect conformational transitions in noisy signals. These items are all illustrated with several examples.

Single-Molecule Experiments in Vitro and in Silico

Single-molecule force experiments in vitro enable the characterization of the mechanical response of biological matter at the nanometer scale. However, they do not reveal the molecular mechanisms underlying mechanical function. These can only be readily studied through molecular dynamics simulations of atomic structural models: "in silico" (by computer analysis) single-molecule experiments. Steered molecular dynamics simulations, in which external forces are used to explore the response and function of macromolecules, have become a powerful tool complementing and guiding in vitro single-molecule experiments. The insights provided by in silico experiments are illustrated here through a review of recent research in three areas of protein mechanics: elasticity of the muscle protein titin and the extracellular matrix protein fibronectin; linker-mediated elasticity of the cytoskeleton protein spectrin; and elasticity of ankyrin repeats, a protein module found ubiquitously in cells but with an as-yet unclear function.

Improved sampling methods for molecular simulation

Molecular simulation has broad application in the biological sciences. One of the greatest challenges in molecular simulation is the limited conformational sampling due to slow barrier crossing on the rugged energy landscape of complex biomolecules and to the relatively short simulation time. Many enhanced sampling techniques have been developed over the years to alleviate this problem. Significant progress has been made in the past couple of years, with emerging methods targeting specific aspects of the potential energy surface and new variants of the replica exchange method.