Proteins evolve at different rates. What drives the speed of protein sequence changes? Two main factors are a protein's folding stability and aggregation propensity. By combining the hydrophobic-polar (HP) model with the Zwanzig-Szabo-Bagchi rate theory, we find that: (i) Adaptation is strongly accelerated by selection pressure, explaining the broad variation from days to thousands of years over which organisms adapt to new environments. (ii) The proteins that adapt fastest are those that are not very stably folded, because their fitness landscapes are steepest. And because heating destabilizes folded proteins, we predict that cells should adapt faster when put into warmer rather than cooler environments. (iii) Increasing protein abundance slows down evolution (the substitution rate of the sequence) because a typical protein is not perfectly fit, so increasing its number of copies reduces the cell's fitness. (iv) However, chaperones can mitigate this abundance effect and accelerate evolution (also called evolutionary capacitance) by effectively enhancing protein stability. This model explains key observations about protein evolution rates.

Recent experiments demonstrate molecular chemotaxis or altered diffusion rates of enzymes in the presence of their own substrates. We show here an important implication, namely, that if a nanoscale catalyst A produces a small-molecule ligand product L which is the substrate of another catalyst B, the two catalysts will attract each other. We explore this nonequilibrium producer recruitment force (ProRec) in a reaction-diffusion model. The predicted cat-cat association will be the strongest when A is a fast producer of L and B is a tight binder to it. ProRec is a force that could drive a mechanism (the catpath mechanism) by which catalysts could become spatially localized into functional pathways, such as in the biochemical networks in cells, which can achieve complex goals.

It is not known how life arose from prebiotic physical chemistry. How did fruitful cell-like associations emerge from the two polymer types-informational (nucleic acids, xNAs = DNA or RNA) and functional (proteins)? Our model shows how functional networks could bootstrap from random sequence-independent initial states. For proteins, we adopt the foldamer hypothesis: through persistent nonequilibrium prebiotic syntheses, short random peptides fold and catalyze the elongation of others. The xNAs enter through random binding to the peptides, and all chains can mutate. Chains grow inside colloids that split when they're large, coupling faster growth speeds to bigger populations. Random and useless at first, these folding and binding events grow protein-xNA networks that resemble today's protein-protein networks.

Ever since Clausius in 1865 and Boltzmann in 1877, the concepts of entropy and of its maximization have been the foundations for predicting how material equilibria derive from microscopic properties. But, despite much work, there has been no equally satisfactory general variational principle for nonequilibrium situations. However, in 1980, a new avenue was opened by E.T. Jaynes and by Shore and Johnson. We review here maximum caliber, which is a maximum-entropy-like principle that can infer distributions of flows over pathways, given dynamical constraints. This approach is providing new insights, particularly into few-particle complex systems, such as gene circuits, protein conformational reaction coordinates, network traffic, bird flocking, cell motility, and neuronal firing.

Cells adapt to changing environments. Perturb a cell and it returns to a point of homeostasis. Perturb a population and it evolves toward a fitness peak. We review quantitative models of the forces of adaptation and their visualizations on landscapes. While some adaptations result from single mutations or few-gene effects, others are more cooperative, more delocalized in the genome, and more universal and physical. For example, homeostasis and evolution depend on protein folding and aggregation, energy and protein production, protein diffusion, molecular motor speeds and efficiencies, and protein expression levels. Models provide a way to learn about the fitness of cells and cell populations by making and testing hypotheses.

We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they are inter-connected. We use Maximum Caliber as an inference principle. The combinatorial challenge of high-dimensional data is handled using two different approximations to the pairwise couplings. We show two proofs of principle: in a nonlinear genetic toggle switch circuit, and in a toy neural network.