Competing interactions give rise to two-state behavior and switch-like transitions in charge-rich intrinsically disordered proteins

The most commonly occurring intrinsically disordered proteins (IDPs) are polyampholytes, which are defined by the duality of low net charge per residue and high fractions of charged residues. Recent experiments have uncovered surprises regarding sequence-ensemble relationships of model polyampholytic IDPs. These include differences in conformational preferences for sequences with lysine vs. arginine, and the suggestion that well-mixed sequences either form globules or conformations with ensemble averages that are reminiscent of ideal chains wherein intra-chain and chain-solvent interactions are counterbalanced. Here, we explain these observations by analyzing results from atomistic simulations. We find that polyampholytic IDPs generally sample two distinct stable states, namely globules and self-avoiding walks. Globules are favored by electrostatic attractions between oppositely charged residues, whereas self-avoiding walks are favored by favorable free energies of hydration of charged residues. We find sequence-specific temperatures of bistability at which globules and self-avoiding walks can coexist. At these temperatures, ensemble averages over coexisting states give rise to statistics that resemble ideal chains without there being an actual counterbalancing of intra-chain and chain-solvent interactions. At equivalent temperatures, arginine-rich sequences tilt the preference toward globular conformations whereas lysine-rich sequences tilt the preference toward self-avoiding walks. This stems from intrinsic differences in free energies of hydration between arginine and lysine. We also identify differences between aspartate and glutamate containing sequences, whereby the shorter aspartate sidechain engenders preferences for metastable, necklace-like conformations. Finally, although segregation of oppositely charged residues within the linear sequence maintains the overall two-state behavior, compact states are highly favored by such systems.

Nonreversible Markov Chain Monte Carlo Algorithm for Efficient Generation of Self-Avoiding Walks

We introduce an efficient nonreversible Markov chain Monte Carlo algorithm to generate self-avoiding walks with a variable endpoint. In two dimensions, the new algorithm slightly outperforms the two-move nonreversible Berretti-Sokal algorithm introduced by H. Hu, X. Chen, and Y. Deng, while for three-dimensional walks, it is 3–5 times faster. The new algorithm introduces nonreversible Markov chains that obey global balance and allow for three types of elementary moves on the existing self-avoiding walk: shorten, extend or alter conformation without changing the length of the walk.

Off-lattice and parallel implementations of the pivot algorithm

The pivot algorithm is the most efficient known method for sampling polymer configurations for self-avoiding walks and related models. Here we introduce two recent improvements to an efficient binary tree implementation of the pivot algorithm: an extension to an off-lattice model, and a parallel implementation.