Introduction:: Most nucleated cells in mammals exhibit consistent 24-hour cycles of protein expression. In various mouse tissues, for instance, between 2 and 10% of proteins show such periodic expression1. These oscillations are driven by the cells’ Circadian clock, a network of positive and negative feedback loops between the expression of Circadian proteins such as PER, CRY, BMAL1, and CLOCK. Multiple recent studies have shown that mechanotransduction pathways, such as nuclear translocation of myocardin-related transcription factor (MRTF) or YAP/TAZ, may also affect expression of some Circadian proteins and perturb Circadian oscillations2,3. For instance, treatment of cells with various actomyosin inhibitors consistently led to increases in the period and amplitude of Circadian oscillations3. Here, we use mathematical modeling to examine mechanotransduction-Circadian coupling, demonstrating that recent data is consistent with a model in which YAP/TAZ and MRTF nuclear translocation induce the expression of Circadian proteins.
Materials and Methods:: Our model of YAP/TAZ and MRTF mechanotransduction derives from previous models of YAP/TAZ mechanosensing4,5. In this iteration of the model, we include newly calibrated parameters for nuclear translocation of MRTF. Our simplified model of the cell Circadian clock consists of a system of two delay differential equations, representing the positive (BMAL1/CLOCK) and negative (PER/CRY) components of the mammalian Circadian clock (Fig 1a). In this model, BMAL1 provides time-delayed feedback, leading to inhibition of its own expression and upregulation of PER expression. In turn, PER provides additional negative feedback by promoting breakdown of BMAL1. We couple mechanotransduction to these oscillations by adding additional terms for YAP/TAZ and MRTF dependent expression of BMAL1 and PER/CRY. Bayesian parameter calibration was used to fit our model to experimental data of changes in PER2 oscillation period and amplitude in fibroblasts seeded on different substrate stiffnesses or treated with cytoskeletal inhibitors3.
Results, Conclusions, and Discussions:: Under control conditions in our coupled mathematical model, PER and BMAL1 oscillate in antiphase with a period close to 24 hours, consistent with experimental data. Linear stability analysis of our system shows that sustained oscillations occur more often with increased baseline expression of PER, but can be eliminated by increased expression of BMAL1. We find that inhibiting actin polymerization or myosin activity results in prolonged periods of oscillation and enhanced oscillation amplitudes, in agreement with our calibration datasets3. We then generated a population of model cells with parameters drawn from probability distributions and measured how changes in cell density are predicted to impact the regularity of oscillations at a population level. As measured in experiments2, cells seeded at higher densities showed consistent Circadian oscillations, whereas at low densities, more cells in the population exhibited decaying oscillations over time.
In alignment with recent experiments, our mathematical model demonstrates that feedback between YAP/TAZ and MRTF nuclear translocation and the expression of Circadian proteins can affect Circadian oscillations in single cells and populations of cells. Given that altered Circadian rhythms are associated with diseases from diabetes to cancer, predictions from this model may provide novel insights about disease progression. For instance, changes in tissue stiffness associated with tumor growth could disrupt local Circadian oscillations.
Acknowledgements (Optional): : This material is based upon work supported by the National Science Foundation under Grant # EEC-2127509 to the American Society for Engineering Education. Diagram in Fig 1a created with BioRender.com.
