Catalysis of protein folding by chaperones accelerates evolutionary dynamics in adapting cell populations

Abstract

Although molecular chaperones are essential components of protein homeostatic machinery, their mechanism of action and impact on adaptation and evolutionary dynamics remain controversial. Here we developed a physics-based ab initio multi-scale model of a living cell for population dynamics simulations to elucidate the effect of chaperones on adaptive evolution. The 6-loci genomes of model cells encode model proteins, whose folding and interactions in cellular milieu can be evaluated exactly from their genome sequences. A genotype-phenotype relationship that is based on a simple yet non-trivially postulated protein-protein interaction (PPI) network determines the cell division rate. Model proteins can exist in native and molten globule states and participate in functional and all possible promiscuous non-functional PPIs. We find that an active chaperone mechanism, whereby chaperones directly catalyze protein folding, has a significant impact on the cellular fitness and the rate of evolutionary dynamics, while passive chaperones, which just maintain misfolded proteins in soluble complexes have a negligible effect on the fitness. We find that by partially releasing the constraint on protein stability, active chaperones promote a deeper exploration of sequence space to strengthen functional PPIs, and diminish the non-functional PPIs. A key experimentally testable prediction emerging from our analysis is that down-regulation of chaperones that catalyze protein folding significantly slows down the adaptation dynamics.

Figure 1. Pictorial depictions of molecular interactions, chaperone interaction surface, and free energy-reaction coordinates diagram.

(A) A schematic representation of molecular interactions in the model cell. The folded (red cubes) and MG state (blue cubes) proteins in the cytosol of model cell are allowed to interact with each other to form functional (red solid lines) and non-functional (black dashed lines) interactions, which include homodimeric self-interactions (black dashed loops). Black solid lines represent the PPI network of chaperone (green square). (B) Chaperone interaction surface. A single face of cube, consisting of nine amino acid residues is used to model the interaction between chaperone and unfolded proteins. (C) Reaction (rxn) coordinate vs. free energy diagram for protein folding with and without chaperones, highlighting the catalytic activity of chaperones.

Figure 2. The time evolution of the fitness ratios (i.e. the ratio of birth rates with chaperones and without chaperones) are presented for the active in (A) and passive model in (B) for three different temperatures.

The fitness ratios and evolutionary time are in log scale to convey the events clearly across all time scales. All data here and in the subsequent figures are ensemble averages over 100 independent stochastic trajectories.

Figure 3. The time evolution of mean protein stabilities and mean interaction probabilities of functional dimers in the absence and presence of chaperones, i.e. for (blue lines) and (red lines), respectively, at temperature T = 0.85.

(A) The time evolution of stability for monomeric proteins. (B) The time evolution of mean stability, for heterodimer proteins. (C) The time evolution of mean stability, for date triangle proteins. (D) The time evolution of interaction probability, for the heterodimer complexes. (E) The time evolution of mean interaction probability, for the date triangle complexes.

Figure 4. The time evolution of the mean value of the fractions of proteins involved in NFP-PPIs to their total concentrations for (blue lines) and (red lines), at temperature T = 0.85.

(A) NF-PPI for functional monomer (B) average NF-PPI for heterodimers and (C) NF-PPI for date triangles where

Figure 5. The time evolution of mean and in the absence and presence of chaperones, i.e. for (blue lines) and (red lines), respectively.

The dashed line at represents the neutral evolution. The time evolution of is plotted in (A) for the monomer , in (B) for the heterodimer , and in (C), for the date triangle . The time evolution of is plotted in (D) for the monomer , in (E) for the heterodimer , and in (F) for the date triangle .

Figure 6. The time evolution of mean sequence entropy is plotted in the absence and presence of chaperones, i.e. for (blue lines) and (red lines), respectively, at temperature T = 0.85.

The time evolution of mean sequence entropy is given in (A) for the monomer , in (B) for the heterodimer , and in (C) for date triangle proteins .