Steven M. Kreuzer

Catch bond-like kinetics of helix cracking: network analysis by molecular dynamics and milestoning.

The first events of unfolding of secondary structure under load are considered with Molecular Dynamics simulations and Milestoning analysis of a long helix (126 amino acids). The Mean First Passage Time is a non-monotonic function of the applied load with a maximum of 3.6 ns at about 20 pN. Network analysis of the reaction space illustrates the opening and closing of an off-pathway trap that slows unfolding at intermediate load levels. It is illustrated that the nature of the reaction networks changes as a function of load, demonstrating that the process is far from one-dimensional.

Coiled-Coil Response to Mechanical Force: Global Stability and Local Cracking

Coiled coils are important structural motifs formed by two or more amphipathic α-helices that twist into a supercoil. These motifs are found in a wide range of proteins, including motor proteins and structural proteins, that are known to transmit mechanical loads. We analyze atomically detailed simulations of coiled-coil cracking under load with Milestoning. Milestoning is an approach that captures the main features of the process in a network, quantifying kinetics and thermodynamics. A 112-residue segment of the β-myosin S2 domain was subjected to constant-magnitude (0-200 pN) and constant-direction tensile forces in molecular dynamics simulations. Twenty 20 ns straightforward simulations at several load levels revealed that initial single-residue cracking events (Ψ > 90°) at loads <100 pN were accompanied by rapid refolding without either intra- or interhelix unfolding propagation. Only initial unfolding events at the highest load (200 pN) regularly propagated along and between helices. Analysis of hydrophobic interactions and of interhelix hydrogen bonds did not show significant variation as a function of load. Unfolding events were overwhelmingly located in the vicinity of E929, a charged residue in a hydrophobic position of the heptad repeat. Milestoning network analysis of E929 cracking determined that the mean first-passage time ranges from 20 ns (200 pN) to 80 ns (50 pN), which is ∼20 times the mean first-passage time of an isolated helix with the same sequence.

Analyzing milestoning networks for molecular kinetics: definitions, algorithms, and examples.

Network representations are becoming increasingly popular for analyzing kinetic data from techniques like Milestoning, Markov State Models, and Transition Path Theory. Mapping continuous phase space trajectories into a relatively small number of discrete states helps in visualization of the data and in dissecting complex dynamics to concrete mechanisms. However, not only are molecular networks derived from molecular dynamics simulations growing in number, they are also getting increasingly complex, owing partly to the growth in computer power that allows us to generate longer and better converged trajectories. The increased complexity of the networks makes simple interpretation and qualitative insight of the molecular systems more difficult to achieve. In this paper, we focus on various network representations of kinetic data and algorithms to identify important edges and pathways in these networks. The kinetic data can be local and partial (such as the value of rate coefficients between states) or an exact solution to kinetic equations for the entire system (such as the stationary flux between vertices). In particular, we focus on the Milestoning method that provides fluxes as the main output. We proposed Global Maximum Weight Pathways as a useful tool for analyzing molecular mechanism in Milestoning networks. A closely related definition was made in the context of Transition Path Theory. We consider three algorithms to find Global Maximum Weight Pathways: Recursive Dijkstras, Edge-Elimination, and Edge-List Bisection. The asymptotic efficiency of the algorithms is analyzed and numerical tests on finite networks show that Edge-List Bisection and Recursive Dijkstras algorithms are most efficient for sparse and dense networks, respectively. Pathways are illustrated for two examples: helix unfolding and membrane permeation. Finally, we illustrate that networks based on local kinetic information can lead to incorrect interpretation of molecular mechanisms.

Publisher's Note: “Catch bond-like kinetics of helix cracking: Network analysis by molecular dynamics and Milestoning” [J. Chem. Phys. 139, 121902 (2013)]

This article was originally published online on 1 July 2013 with the second authors name omitted. The authors now appear correct as seen above. There has also been an update to the “Acknowledgments” section. This update is shown below:

Publisher's Note: “Catch bond-like kinetics of helix cracking: Network analysis by molecular dynamics and Milestoning”.

This article was originally published online on 1 July 2013 with the second authors name omitted. The authors now appear correct as seen above. There has also been an update to the “Acknowledgments” section. This update is shown below: