Free-energy-based framework for early forecasting of stem cell differentiation.

Commitment of stem cells to different lineages is inherently stochastic but regulated by a range of environmental bio/chemo/mechanical cues. Here, we develop an integrated stochastic modelling framework for predicting the differentiation of hMSCs in response to a range of environmental cues, including sizes of adhesive islands, stiffness of substrates and treatment with ROCK inhibitors in both growth and mixed media. The statistical framework analyses the fluctuations of cell morphologies over approximately a 24 h period after seeding the cells in the specific environment and uses the cytoskeletal free-energy distribution to forecast the lineage the hMSCs will commit to. The cytoskeletal free energy which succinctly parametrizes the biochemical state of the cell is shown to capture hMSC commitment over a range of environments while simple morphological factors such as cell shape, tractions on their own are unable to correlate with lineages hMSCs adopt.

The homeostatic ensemble for cells.

Cells are quintessential examples of out-of-equilibrium systems, but they maintain a homeostatic state over a timescale of hours to days. As a consequence, the statistics of all observables is remarkably consistent. Here, we develop a statistical mechanics framework for living cells by including the homeostatic constraint that exists over the interphase period of the cell cycle. The consequence is the introduction of the concept of a homeostatic ensemble and an associated homeostatic temperature, along with a formalism for the (dynamic) homeostatic equilibrium that intervenes to allow living cells to evade thermodynamic decay. As a first application, the framework is shown to accurately predict the observed effect of the mechanical environment on the in vitro response of smooth muscle cells. This includes predictions that both the mean values and diversity/variability in the measured values of observables such as cell area, shape and tractions decrease with decreasing stiffness of the environment. Thus, we argue that the observed variabilities are inherent to the entropic nature of the homeostatic equilibrium of cells and not a result of in vitro experimental errors.