Nanomechanics of β-rich proteins related to neuronal disorders studied by AFM, all-atom and coarse-grained MD methods

Abstract

Computer simulations of protein unfolding substantially help to interpret force-extension curves measured in single-molecule atomic force microscope (AFM) experiments. Standard all-atom (AA) molecular dynamics simulations (MD) give a good qualitative mechanical unfolding picture but predict values too large for the maximum AFM forces with the common pulling speeds adopted here. Fine tuned coarse-grain MD computations (CG MD) offer quantitative agreement with experimental forces. In this paper we address an important methodological aspect of MD modeling, namely the impact of numerical noise generated by random assignments of bead velocities on maximum forces (F(max)) calculated within the CG MD approach. Distributions of CG forces from 2000 MD runs for several model proteins rich in β structures and having folds with increasing complexity are presented. It is shown that F(max) have nearly Gaussian distributions and that values of F(max) for each of those β-structures may vary from 93.2 ± 28.9 pN (neurexin) to 198.3 ± 25.2 pN (fibronectin). The CG unfolding spectra are compared with AA steered MD data and with results of our AFM experiments for modules present in contactin, fibronectin and neurexin. The stability of these proteins is critical for the proper functioning of neuronal synaptic clefts. Our results confirm that CG modeling of a single molecule unfolding is a good auxiliary tool in nanomechanics but large sets of data have to be collected before reliable comparisons of protein mechanical stabilities are made.

Figure

Computational strechnings of single protein modeules leads to broad distributions of unfolding forces

Fig. 1

The initial all-atom and coarse-grained structures of the β-rich protein domains and their topologies: a Fibroin-H motif (f–H), b FnIII₃ CNTN4 (CNT), c FnIII₉ of fibronectin 1 (FN1), d LNS₅ of NRXN1α (NRX). The figure was prepared using the VMD program [34] and Pro-origami server [35]

Fig. 2

Maximum force histograms as established in CG SMD simulations (each data set contains at least N >2000 simulations)

Fig. 3

Averaged curves with standard deviations (in gray) for each model obtained from 500 random CG SMD simulations (v = 0.025 Å/ps)

Fig. 4

Averaged curves with standard deviations (in gray) for each model obtained from 5 AA SMD simulations (v = 0.025 Å/ps)

Fig. 5

Force vs. extension curves for f–H from: a CG SMD (v = 0.001 Å/ps), b CG SMD (v = 0.025 Å/ps), c all-atom SMD simulation (v = 0.025 Å/ps). Running averages were used

Fig. 6

Force vs. extension curves for CNT from: a AFM measurements, b CG SMD (v = 0.001 Å/ps), c CG SMD (v = 0.0025 Å/ps), d CG SMD (v = 0.025 Å/ps), e all-atom SMD simulation (v = 0.025 Å/ps). Running averages for simulation curves were used. Two maxima in AFM spectrum are indicated by stars

Fig. 7

Force vs. extension curves for FN1 from: a AFM measurements, b CG SMD (v = 0.001 Å/ps), c CG SMD (v = 0.025 Å/ps), d all-atom SMD simulation (v = 0.025 Å/ps). Running averages for simulation curves were used

Fig. 8

Force vs. extension curves for NRX from: a AFM measurements, b CG SMD (v = 0.001 Å/ps), c CG SMD (v = 0.025 Å/ps), d all-atom SMD simulation (v = 0.025 Å/ps). Running average for simulation curves were used

Fig. 9

A rough classification scheme of mechanical unfolding scenarios. When protein modules are pulled by a force attached to the C-terminus, alternate paths are possible: a uniform unfolding without clear intermediates (type 0), a dominant unfolding at the C-terminus with an intermediate (or intermediates) located close to the N-terminus (type C), a similar scenario but with the N-terminus part unfolding at the initial stage (type N). On rare occasions unfolding happens symmetrically at both ends (type NC, not shown)