We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics—such as the Green-Kubo fluctuation-dissipation relations, Onsager’s reciprocal relations, and Prigogine’s minimum entropy production—are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Significance: How do brains adapt to changing resource constraints? This is particularly relevant in the aging brain, for which the ability of neurons to utilize their primary energy source, glucose, is diminished. Through experiments and modeling, we find that changes to brain activity patterns with age can be understood in terms of decreasing metabolic activity. Specifically, we find that older brains approach a critical point in our model, enabling small changes in metabolic activity to give rise to an abrupt reconfiguration of functional brain networks.

Purpose: The genetic intratumoral heterogeneity observed in human osteosarcomas poses challenges for drug development and the study of cell fate, plasticity, and differentiation, which are processes linked to tumor grade, cell metastasis, and survival. Experimental Design: To pinpoint errors in osteosarcoma differentiation, we transcriptionally profiled 31,527 cells from a tissue-engineered model that directs mesenchymal stem cells toward adipogenic and osteoblastic fates. Incorporating preexisting chondrocyte data, we applied trajectory analysis and non-negative matrix factorization to generate the first human mesenchymal differentiation atlas. Results: This “roadmap” served as a reference to delineate the cellular composition of morphologically complex osteosarcoma tumors and quantify each cell’s lineage commitment. Projecting a bulk RNA-sequencing osteosarcoma dataset onto this roadmap unveiled a correlation between a stem-like transcriptomic phenotype and poorer survival outcomes. Conclusions: Our study quantifies osteosarcoma differentiation and lineage, a prerequisite to better understanding lineage-specific differentiation bottlenecks that might someday be targeted therapeutically.

Recently, both microfluidic and fluorescence correlation spectroscopy experiments have revealed that diffusion coefficients of active biological catalysts (enzymes) rise proportionately to their catalytic rate. Similar effects have also been observed for active material catalysts, such as platinum nanocatalysts in hydrogen peroxide solution. While differences in diffusion coefficients have recently been cleverly exploited to spatially separate active from inactive catalysts, here we investigate the consequences of these novel findings on the spatiotemporal organization of catalysts. In particular, we show that chemical reactions—such as coupled catalytic reactions—may drive effective attraction or repulsion between catalysts which in turn drives their spatiotemporal organization. This, we argue, may have implications for internal cell signaling.