Early Events in Helix Unfolding under External Forces: A Milestoning Analysis

Abstract

Initial events of helix breakage as a function of load are considered using Molecular Dynamics simulations and Milestoning analysis. A helix length of ~100 amino acids is considered as a model for typical helices found in molecular machines and as a model that minimizes end effects for early events of unfolding. Transitions of individual amino acids (averaged over the helix’s interior residues) are examined and its surrounding hydrogen bonds are considered. Dense kinetic networks are constructed that, with Milestoning analysis, provide the overall kinetics of early breakage events. Network analysis and selection of MaxFlux pathways illustrate that load impacts unfolding mechanisms in addition to time scales. At relatively high (100pN) load levels, the principal intermediate is the 310-helix, while at relatively low (10pN) levels the π-helix is significantly populated, albeit not as an unfolding intermediate. Coarse variables are examined at different levels of resolution; the rate of unfolding illustrates remarkable stability under changes in the coarsening. Consistent prediction of about ~5ns for the time of a single amino-acid unfolding event are obtained. Hydrogen bonds are much faster coarse variables (by about 2 orders of magnitude) compared to backbone torsional transition, which gates unfolding and thereby provides the appropriate coarse variable for the initiation of unfolding.

Catch bond-like kinetics of helix cracking: Network analysis by molecular dynamics and Milestoning

“…While different force fields could have been used to describe the solvated helix, the choice here ensures efficiency and consistency with our earlier study. 15 System charge neutrality was enforced by adding 102 Na + and 91 Cl − counter-ions at a concentration of 0.1 mole/liter, resulting in a full system containing 1290 protein atoms and 49 605 water molecules, in addition to these counter-ions. Periodic boundary conditions were used throughout all phases of the 0 7 5 5 2 8 10 28 15 50 20 60 25 83 30 28 40 24 70 30 100 20 MD simulations as was the parallel processing version of the LINCS constraint on fast bond dynamics.…”

“…Load magnitudes tested included 0, 5,10,15,20,25,30,40,70, and 100 pN. The load direction, fixed throughout the simulations, was set in the [0 0 1] direction corresponding to the helix's nominal axis as defined by the vector between the center of mass of the load end groups.…”

“…We used an exact and discrete MaxFlux approach 40 to determine the maximum flux pathways from the folded (α3) to unfolded ( > 90) states on the network. 15 Recall that the transition matrix allows the calculation of the stationary reactive flux vector (q stat ). When using directional milestones there are two milestones (αβ and βα) between anchors "α" and "β," each with their own stationary reactive fluxes: q αβ and q βα .…”

“…15 That study hinted that the Mean First Passage Time (MFPT) of the initiation of unfolding was a non-monotonic function of the applied load magnitude. This non-monotonic behavior is reminiscent of the "catch-bond" phenomenon observed in some inter-molecular structures in which intermediate loads induce unfolding more slowly than either low or high loads.…”

“…In the analysis, we use the Milestoning theory in a network formulation to obtain a comprehensive view of the kinetics and thermodynamics of the unfolding process. Compared to our earlier study, 15 we consider a larger number of load levels to better resolve the molecular mechanism (ten load levels instead of three). The network model was adjusted with respect to the earlier study to make it a directed graph, which is more detailed and accurate.…”