Analysis of single molecule folding studies with replica correlation functions

Abstract

Single molecule experiments that can track individual trajectories of biomolecular processes provide a challenge for understanding how these stochastic trajectories relate to the global energy landscape. Using trajectories from a native structure based simulation, we use order parameters that accurately distinguish between protein folding mechanisms that involve a simple, single set of pathways versus a complex one with multiple sets of competing pathways. We show how the folding dynamics can be analyzed with replica correlation functions in a way compatible with single molecule experiments.

Figure 1

Protein folding with multiple sets of pathways. (left) A ribbon diagram is shown of 1N0Q with clouds representing the folded ensemble of the pathway where the c-terminal (top) or n-terminal (bottom) folds first. (right) A free energy profile is projected to the fraction of native contacts of the n-terminal [Q(n-term)] and the c-terminal [Q(c-term)] with two example trajectories overlaid.

Figure 2

Histogram of folding times for 1SRL (top) and 1N0Q (bottom).

Figure 3

The distribution of q as function of Q. Data shown are for bins of width 0.02 (continuously interpolated) centered around Q =0.19, 0.28, 0.41, 0.44 for 1SRL (top) and for 1N0Q (bottom). For 1N0Q the distribution starts to be bimodal around Q = 0.24 (data not shown). For Q > 0.44 the distribution becomes unimodal. The q-distribution of 1SRL is unimodal for all 0.26 < Q < 0.81.

Figure 4

Distribution of q for given Q for 1N0Q. Data are shown for fast trajectories (top) and slow trajectories (bottom). Fast trajectories find the folded states within 330 steps, slow ones need more the 660 steps. As one sees the q-distribution is sharper for the fast trajectories.

Figure 5

The Laplace transform of the replica correlation function q^αβ(s) for 1N0Q (solid black) and 1SRL (dashed red) as determined numerically from the simulation data (time unit=1 simulation step).