A metabolite-sensitive, thermodynamically-constrained model of\ud cardiac cross-bridge cycling: Implications for force development during ischemia

We present a metabolically regulated model of cardiac active force generation with which we investigate the effects of ischemia on maximum forceproduction. Our model, based on the Rice et al. (2008) model of cross-bridge kinetics, reproduces many of the observed effects of MgATP, MgADP, Pi and H+ on force development while still retaining the force/length/Ca2+ properties of the original model. We introduce three new parameters to account for the competitive binding of H+ to the Ca2+ binding site on troponin C and the binding of MgADP within the cross-bridge cycle. These parameters along with the Pi and H+ regulatory steps within the cross-bridge cycle were constrained using data from the literature and validated using a range of metabolic and sinusoidal length perturbation protocols. The placement of the MgADP binding step between two strongly-bound and force-generating states leads to the emergence of an unexpected effect on the force-MgADP curve, where the trend of the relationship (positive or negative) depends on the concentrations of the other metabolites and [H+]. The model is used to investigate the sensitivity of maximum force production to changes in metabolite concentrations during the development of ischemia

A thermodynamic framework for modelling membrane transporters

Membrane transporters contribute to the regulation of the internal environment of cells by translocating substrates across cell membranes. Like all physical systems, the behaviour of membrane transporters is constrained by the laws of thermodynamics. However, many mathematical models of transporters, especially those incorporated into whole-cell models, are not thermodynamically consistent, leading to unrealistic behaviour. In this paper we use a physics-based modelling framework, in which the transfer of energy is explicitly accounted for, to develop thermodynamically consistent models of transporters. We then apply this methodology to model two specific transporters: the cardiac sarcoplasmic/endoplasmic Ca$^{2+}$ ATPase (SERCA) and the cardiac Na$^+$/K$^+$ ATPase

Differentiable Physics-based Greenhouse Simulation

We present a differentiable greenhouse simulation model based on physical processes whose parameters can be obtained by training from real data. The physics-based simulation model is fully interpretable and is able to do state prediction for both climate and crop dynamics in the greenhouse over very a long time horizon. The model works by constructing a system of linear differential equations and solving them to obtain the next state. We propose a procedure to solve the differential equations, handle the problem of missing unobservable states in the data, and train the model efficiently. Our experiment shows the procedure is effective. The model improves significantly after training and can simulate a greenhouse that grows cucumbers accurately.Comment: Accepted at the Machine Learning and the Physical Sciences workshop, NeurIPS 2022. 7 pages, 2 figure