Sampling of Protein Folding Transitions: Multicanonical Versus Replica Exchange Molecular Dynamics

Abstract

We compare the efficiency of multicanonical and replica exchange molecular dynamics for the sampling of folding/unfolding events in simulations of proteins with end-to-end β-sheet. In Go-model simulations of the 75-residue MNK6, we observe improvement factors of 30 in the number of folding/unfolding events of multicanonical molecular dynamics over replica exchange molecular dynamics. As an application, we use this enhanced sampling to study the folding landscape of the 36-residue DS119 with an all-atom physical force field and implicit solvent. Here, we find that the rate-limiting step is the formation of the central helix that then provides a scaffold for the parallel β-sheet formed by the two chain ends.

A Monte Carlo Study of the Early Steps of Functional Amyloid Formation

“…For the dimer simulations we experienced severe convergence problems and experimented with various enhanced sampling algorithms in our efforts to obtain reliable free energy estimates. One method that turned out to be particularly well suited for this problem is a recently developed generalized ensemble technique based on flattening the energy-specific diffusion profile [ 62 , 63 ]. Below, we briefly introduce the method and compare its performance to the commonly used parallel tempering (replica exchange) technique.…”

Multicanonical molecular dynamics simulations of the N-terminal domain of protein L9

“…This allows one to calculate thermodynamic averages of any physical quantity $\mathrm{scriptA}$ at a temperature T by re-weighting [20,21]: $${<\mathrm{scriptA}>}_T=\frac{\int \mathit{dx}\mathcal{A}\left(x\right)w^{-1}\left(E\right(x\left)\right)e^{-E\left(x\right)∕\mathit{RT}}}{\int \mathit{dx}{w}^{-1}\left(E\right(x\left)\right)e^{-E\left(x\right)∕\mathit{RT}}}.$$ Application of the method has been limited by the need to determine iteratively estimators of the weights w ( E ) [18,19]. We have shown recently [6] that the additional workload may be worthwhile for proteins with strong cooperative transitions. Another problem is that the implementation for molecular dynamics [21, 22] is less straightforward than that for Monte Carlo sampling [19,23].…”

“…However, while the use of this technique has become ubiquitous, its usefulness deteriorates for first-order like transitions. We have recently demonstrated [6] that in cases where folding/unfolding transitions are rare events, techniques such as multicanonical sampling may be more appropriate. For Go-model simulations of the 75 residue protein MNK6 and all-atom simulations of the 36 residue DS119 we show that multicanonical molecular dynamics lead to improvements of factors ≈ 30 over that of replica exchange molecular dynamics in the sampling of folding/unfolding transitions.…”

“…Extending our series of investigations into the folding of proteins with end-to-end β -sheets [6,7] we choose as our test system the 39-residue N-terminal domain of ribosomal protein L9 (Protein Data Bank Identifier 2HBB); as this protein allows comparison of our work with that of other groups that used different sampling techniques [8]. …”

Parallel continuous simulated tempering and its applications in large-scale molecular simulations

“…Multicanonical ensemble has already been shown to be very effective in the simulation of many complex systems such as the spin glass, 3,5 simple liquid systems, 6 small peptides, 7 and structure-based model of proteins. 8 Another typical approach of generalized ensemble is called simulated tempering (ST), 9 which generates a flat histogram of temperature, i.e., W (T ) = const. or a flat histogram of reciprocal temperature, i.e., W (β) = const.…”