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.

SignificanceSome biological evolution is slow (millions of years), and some is fast (months to years). The speed at which a protein evolves depends on how stable a protein’s folded structure is, how well it avoids aggregation, and how well-chaperoned it is. What are the mechanisms? We compute fitness landscapes by combining a model of protein-folding equilibria with sequence-change dynamics. We find that adapting to a new environment is fastest for proteins that are least stably folded, because those sit on steep downhill parts of fitness potentials. The modeling shows that cells should adapt to warmer environments faster than to colder ones, explains why increasing a protein’s abundance slows cell evolution, and explains how chaperones accelerate evolution by mitigating this effect.

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.

What were the physico-chemical forces that drove the origins of life? We discuss four major prebiotic ‘discoveries’: persistent sampling of chemical reaction space; sequence-encodable foldable catalysts; assembly of functional pathways; and encapsulation and heritability. We describe how a ‘proteins-first’ world gives plausible mechanisms. We note the importance of hydrophobic and polar compositions of matter in these advances.