Protein Folding Kinetics and Thermodynamics from Atomistic Simulations

Determining protein folding kinetics and thermodynamics from all-atom molecular dynamics (MD) simulations without using experimental data represents a formidable scientific challenge because simulations can easily get trapped in local minima on rough free energy landscapes. This necessitates the computation of multiple simulation trajectories, which can be independent from each other or coupled in some manner, as, for example, in the replica exchange MD method. Here we present results obtained with a new analysis tool that allows the deduction of faithful kinetics data from a heterogeneous ensemble of simulation trajectories. The method is demonstrated on the decapeptide Chignolin for which we predict folding and unfolding time constants of $1.0\pm 0.3$ and $2.6\pm 0.4\mu \mathrm{s}$, respectively. We also derive the energetics of folding, and calculate a realistic melting curve for Chignolin.

Figure 1

(a) Extended (generated) conformation of Chignolin, used as starting structure for the simulations. N- and C termini are indicated. (b) Folded conformation of Chignolin from NMR data (red) [20] and from our simulations (yellow) [1]. (c) Schematic flowchart of replica exchange molecular dynamics in which multiple systems evolve simultaneously in time and in temperature; x marks a sample trajectory. (d) Root mean square deviation of interatomic distances (for all nonhydrogens) with respect to the experimental structure [20], averaged over all 20 simulations. (e) Distribution of RMSD values in all simulations; folded ($F$) and unfolded ($U$) states are indicated. The red peak at a RMSD of 0.25 nm corresponds to compact misfolded conformations, usually found at low temperatures.

Figure 2

Fraction of folded protein as a function of time $F(t)$, averaged over all 20 simulations, with the fit $\Phi (t)$ obtained by minimizing ${\chi }^2$ [Eq. (5)], and employing the definition that the unfolded state comprises everything that is not folded ($U=1-F$). The backreaction (i.e., transition from folded to unfolded state) is taken into account explicitly.

Figure 3

(a) Melting curve (fraction of folded protein as a function of temperature) from experiment [20] in black and from predictions based on Eq. (6) (in red), and directly from the REMD simulations at the individual temperatures, averaged over the last 200 ns (blue squares). (b) Gibbs energy of folding derived from the melting curves.