How Fast Is Too Fast in Force-Probe Molecular Dynamics Simulations?

Steven Sheridan,Frauke Gräter,Csaba Daday

doi:10.1021/acs.jpcb.9b01251

Abstract

While molecular dynamics (MD) simulations are routinely used to interpret atomic force microscopy (AFM) experiments of protein unfolding, computational cost in MD simulations still mostly imposes a large difference in loading rates and time scales in this comparison. Loading rate dependencies of unfolding forces and mechanisms have been studied in depth in experiments, simulations, and theory. One potential additional implication of the larger MD pulling velocity that remains to be assessed is that regions of the proteins that are close to the point of force application will be under force earlier or under more force than more shielded regions, resulting in a bias of the protein unfolding sequence which is likely marginal at the slower AFM velocities. We here, for the first time, quantify the parameters of this bias using a model system of four tandem spectrin repeats (SRs) linked with long, flexible poly-glycine linkers. We subject the system to seven different pulling velocities ranging from 0.01 to 10 m/s and find that for the fastest velocities, down to 1 m/s, the outer domains preferentially unfold; in fact, at 10 m/s, this happened in 100 cases out of 100. On the basis of these data, and also through analyzing the amount of partial unfolding in the beginning of the simulations, we show that the bias is equivalent to an effective signal propagation of 5-100 m/s, which is about 2 orders of magnitude slower than the expected speed of sound. Our results can help in identifying and removing this bias from future simulations.

Highlights

Single molecule force spectroscopy is an established technique to study biomolecules under pulling forces
We subjected the protein construct, four spectrin domains separated by short glycine linkers, to a total of 430 force-probe molecular dynamics simulations at four different speeds between 0.01 and 10 m/s
We present the preferential unfolding of the outer spectrin repeats in Table 1 and Figure 2

Summary

Introduction

Single molecule force spectroscopy is an established technique to study biomolecules under pulling forces. Molecular dynamics simulations are routinely used to interpret these force spectroscopy experiments but, due to computational restrictions, typically use pulling velocities on the order of 10−3 to 1 m/ s, as compared to those used in force spectroscopy experiments, approximately 10−5 to 10−8 m/s. This difference of several orders of magnitude holds for the applied loading rate, i.e., the product of the pulling velocity and the system’s spring constant. High-speed AFM has reached MD pulling velocities and loading rates, resulting in a good agreement between the experiments and simulations in terms of unfolding forces.[1,2] One alternative method that can attempt to bridge this gap is through boxed molecular dynamics (BXD)[3] at the cost of losing exact time scale information and additional approximations.

Methods

Results

Conclusion