Jeremy L. England

Statistical physics of self-replication

Self-replication is a capacity common to every species of living thing, and simple physical intuition dictates that such a process must invariably be fueled by the production of entropy. Here, we undertake to make this intuition rigorous and quantitative by deriving a lower bound for the amount of heat that is produced during a process of self-replication in a system coupled to a thermal bath. We find that the minimum value for the physically allowed rate of heat production is determined by the growth rate, internal entropy, and durability of the replicator, and we discuss the implications of this finding for bacterial cell division, as well as for the pre-biotic emergence of self-replicating nucleic acids.

Thoroughly sampling sequence space: Large‐scale protein design of structural ensembles

Modeling the inherent flexibility of the protein backbone as part of computational protein design is necessary to capture the behavior of real proteins and is a prerequisite for the accurate exploration of protein sequence space. We present the results of a broad exploration of sequence space, with backbone flexibility, through a novel approach: large‐scale protein design to structural ensembles. A distributed computing architecture has allowed us to generate hundreds of thousands of diverse sequences for a set of 253 naturally occurring proteins, allowing exciting insights into the nature of protein sequence space. Designing to a structural ensemble produces a much greater diversity of sequences than previous studies have reported, and homology searches using profiles derived from the designed sequences against the Protein Data Bank show that the relevance and quality of the sequences is not diminished. The designed sequences have greater overall diversity than corresponding natural sequence alignments, and no direct correlations are seen between the diversity of natural sequence alignments and the diversity of the corresponding designed sequences. For structures in the same fold, the sequence entropies of the designed sequences cluster together tightly. This tight clustering of sequence entropies within a fold and the separation of sequence entropy distributions for different folds suggest that the diversity of designed sequences is primarily determined by a structures overall fold, and that the designability principle postulated from studies of simple models holds in real proteins. This has important implications for experimental protein design and engineering, as well as providing insight into protein evolution.

Structural determinant of protein designability

Here we present an approximate analytical theory for the relationship between a protein structures contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of low energy in a structure on the eigenvalues of the structures contact matrix, and then use a Monte Carlo simulation to test the applicability of this analytical result to cubic lattice proteins. We find that the lattice structures with the most low-energy sequences are the same as those predicted by the theory. We argue that, given sufficiently strict requirements for foldability, these structures are the most designable, and we propose a simple means to test whether the results in this paper hold true for real proteins.

Natural selection of more designable folds: A mechanism for thermophilic adaptation

An open question of great interest in biophysics is whether variations in structure cause protein folds to differ in the number of amino acid sequences that can fold to them stably, i.e., in their designability. Recently, we have shown that a novel quantitative measure of a folds tertiary topology, called its contact trace, strongly correlates with the folds designability. Here, we investigate the relationship between a folds contact trace and its relative frequency of usage in mesophilic vs. thermophilic eubacteria. We observe that thermophilic organisms exhibit a bias toward using folds of higher contact trace when compared with mesophiles. We establish this difference both for the distributions of folds at the whole-proteome level and also through more focused structural comparisons of orthologous proteins. Our findings suggest that thermophilic adaptation in bacterial genomes occurs in part through natural selection of more designable folds, pointing to designability as a key component of protein fitness.

Dissipation bounds all steady-state current fluctuations

Near equilibrium, small current fluctuations are described by a Gaussian distribution with a linear-response variance regulated by the dissipation. Here, we demonstrate that dissipation still plays a dominant role in structuring large fluctuations arbitrarily far from equilibrium. In particular, we prove a linear-response-like bound on the large deviation function for currents in Markov jump processes. We find that nonequilibrium current fluctuations are always more likely than what is expected from a linear-response analysis. As a small-fluctuations corollary, we derive a recently conjectured uncertainty bound on the variance of current fluctuations.

A Role for Confined Water in Chaperonin Function

Chaperonins engulf other proteins and accelerate their folding by an unknown mechanism. Here, we combine all-atom molecular dynamics simulations with data from experimental assays of the activity of the bacterial chaperonin GroEL to demonstrate that a chaperonin’s ability to facilitate folding is correlated with the affinity of its interior surface for water. Our results suggest a novel view of the behavior of confined water for models of in vivo protein folding scenarios.

Morphogen Gradient from a Noisy Source

We investigate the effect of time-dependent noise on the shape of a morphogen gradient in a developing embryo. Perturbation theory is used to calculate the deviations from deterministic behavior in a simple reaction-diffusion model of robust gradient formation, and the results are confirmed by numerical simulation. It is shown that such deviations can disrupt robustness for sufficiently high noise levels, and the implications of these findings for more complex models of gradient-shaping pathways are discussed.

Rattling the cage: computational models of chaperonin-mediated protein folding.

Chaperonins are known to maintain the stability of the proteome by facilitating the productive folding of numerous misfolded or aggregation-prone proteins and are thus essential for cell viability. Despite their established importance, the mechanism by which chaperonins facilitate protein folding remains unknown. Computer simulation techniques are now being employed to complement experimental ones in order to shed light on this mystery. Here we review previous computational models of chaperonin-mediated protein folding in the context of the two main hypotheses for chaperonin function: iterative annealing and landscape modulation. We then discuss new results pointing to the importance of solvent (a previously neglected factor) in chaperonin activity. We conclude with our views on the future role of simulation in studying chaperonin activity as well as protein folding in other biologically relevant confined contexts.

Allostery in Protein Domains Reflects a Balance of Steric and Hydrophobic Effects

Allosteric conformational change underlies biological function in many proteins. Allostery refers to a conformational event in which one region of a protein undergoes structural rearrangement in response to a stimulus applied to a different region of the same protein. Here, I show for a variety of proteins that a simple, phenomenological model of the dependence of protein conformation on hydrophobic burial energy allows one to compute low-energy conformational fluctuations for a given sequence by using linear programming to find optimized combinations of sequence-specific hydrophobic burial modes that satisfy steric constraints. From these fluctuations one may calculate allosteric couplings between different sites in a protein domain. Although the physical basis of protein structure is complex and multifactorial, a simplified description of conformational energy in terms of the hydrophobic effect alone is sufficient to give a mechanistic explanation for many biologically important allosteric events.

Potential for Modulation of the Hydrophobic Effect Inside Chaperonins

Despite the spontaneity of some in vitro protein-folding reactions, native folding in vivo often requires the participation of barrel-shaped multimeric complexes known as chaperonins. Although it has long been known that chaperonin substrates fold upon sequestration inside the chaperonin barrel, the precise mechanism by which confinement within this space facilitates folding remains unknown. We examine the possibility that the chaperonin mediates a favorable reorganization of the solvent for the folding reaction. We discuss the effect of electrostatic charge on solvent-mediated hydrophobic forces in an aqueous environment. Based on these physical arguments, we construct a simple, phenomenological theory for the thermodynamics of density and hydrogen-bond order fluctuations in liquid water. Within the framework of this model, we investigate the effect of confinement inside a chaperonin-like cavity on the configurational free energy of water by calculating solvent free energies for cavities corresponding to the different conformational states in the ATP-driven catalytic cycle of the prokaryotic chaperonin GroEL. Our findings suggest that one function of chaperonins may involve trapping unfolded proteins and subsequently exposing them to a microenvironment in which the hydrophobic effect, a crucial thermodynamic driving force for folding, is enhanced.