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Register a new userThe cardiac Na$^+$/K$^+$ ATPase: An updated, thermodynamically consistent model
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The Na$^+$/K$^+$ ATPase is an essential component of cardiac electrophysiology, maintaining physiological Na$^+$ and K$^+$ concentrations over successive heart beats. Terkildsen et al. (2007) developed a model of the ventricular myocyte Na$^+$/K$^+$ ATPase to study extracellular potassium accumulation during ischaemia, demonstrating the ability to recapitulate a wide range of experimental data, but unfortunately there was no archived code associated with the original manuscript. Here we detail an updated version of the model and provide CellML and MATLAB code to ensure reproducibility and reusability. We note some errors within the original formulation which have been corrected to ensure that the model is thermodynamically consistent, and although this required some reparameterisation, the resulting model still provides a good fit to experimental measurements that demonstrate the dependence of Na$^+$/K$^+$ ATPase pumping rate upon membrane voltage and metabolite concentrations. To demonstrate thermodynamic consistency we also developed a bond graph version of the model. We hope that these models will be useful for community efforts to assemble a whole-cell cardiomyocyte model which facilitates the investigation of cellular energetics.
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We give the alternative formulation of quasiparticle model of quark gluon plasma with medium dependent dispersion relation. The model is thermodynamically consistent provided the medium dependent contribution to the energy density is taken in to account. We establish the connection of our model with other variants of quasiparticle models which are thermodynamically consistent. We test the model by comparing the equation of state with the lattice gauge theory simulations of SU(3) pure gluodynamics .
The Ca-sensitive regulatory switch of cardiac muscle is a paradigmatic example of protein assemblies that communicate ligand binding through allosteric change. The switch is a dimeric complex of troponin C (TnC), an allosteric sensor for Ca, and troponin I (TnI), an allosteric reporter. Time-resolved equilibrium FRET measurements suggest that the switch activates in two steps: a TnI-independent Ca-priming step followed by TnI-dependent opening. To resolve the mechanistic role of TnI in activation we performed stopped-flow FRET measurements of activation following rapid addition of a lacking component (Ca or TnI) and deactivation following rapid chelation of Ca. The time-resolved measurements, stopped-flow measurements, and Ca-titration measurements were globally analyzed in terms of a new quantitative dynamic model of TnC-TnI allostery. The analysis provided a mesoscopic parameterization of distance changes, free energy changes, and transition rates among the accessible coarse-grained states of the system. The results reveal (i) the Ca-induced priming step, which precedes opening, is the rate limiting step in activation, (ii) closing is the rate limiting step in deactivation, (iii) TnI induces opening, (iv) an incompletely deactivated population when regulatory Ca is not bound, which generates an accessory pathway of activation, and (v) incomplete activation by Ca--when regulatory Ca is bound, a 3:2 mixture of dynamically inter-converting open (active) and primed-closed (partially active) conformers is observed (15 C). Temperature-dependent stopped-flow FRET experiments provide a near complete thermo-kinetic parametrization of opening. <Abstract Truncated>
Thermodynamic and structural properties of the tangent diatomic fluid are studied in the framework provided by the Reference Interaction Site Model (RISM) theory, coupled with a Modified Hypernetted Chain closure. The enforcement of the internal thermodynamic consistency of the theory is described in detail. The results we obtain almost quantitatively agree with available or newly generated simulation data. We envisage the possibility to extend the consistent RISM formalism to generic, more realistic molecular fluids.
Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems. These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of thermodynamics. In contrast, here we rigorously prove that local master equations are consistent with thermodynamics and its laws without resorting to a microscopic model, as done in previous works. In particular, we consider a quantum system in contact with multiple baths and identify the relevant contributions to the total energy, heat currents and entropy production rate. We show that the second law of thermodynamics holds when one considers the proper expression we derive for the heat currents. We confirm the results for the quantum heat currents by using a heuristic argument that connects the quantum probability currents with the energy currents, using an analogous approach as in classical stochastic thermodynamics. We finally use our results to investigate the thermodynamic properties of a set of quantum rotors operating as thermal devices and show that a suitable design of three rotors can work as an absorption refrigerator or a thermal rectifier. For the machines considered here, we also perform an optimisation of the system parameters using an algorithm of reinforcement learning.
The $alpha$ and $beta$ subunits comprising the hexameric assembly of F1-ATPase share a high degree of structural identity, though low primary identity. Each subunit binds nucleotide in similar pockets, yet only $beta$ subunits are catalytically active. Why? We re-examine their internal symmetry axes and observe interesting differences. Dividing each chain into an N-terminal head region, a C-terminal foot region, and a central torso, we observe (1) that while the foot and head regions in all chains obtain high and similar mobility, the torsos obtain different mobility profiles, with the $beta$ subunits exhibiting a higher motility compared to the $alpha$ subunits, a trend supported by the crystallographic B-factors. The $beta$ subunits have greater torso mobility by having fewer distributed, nonlocal packing interactions providing a spacious and soft connectivity, and offsetting the resultant softness with local stiffness elements, including an additional $beta$ sheet. (2) A loop near the nucleotide binding-domain of the $beta$ subunits, absent in the $alpha$ subunits, swings to create a large variation in the occlusion of the nucleotide binding region. (3) A combination of the softest three eigenmodes significantly reduces the RMSD between the open and closed conformations of the $beta$ subnits. (4) Comparisons of computed and observed crystallographic B-factors suggest a suppression of a particular symmetry axis in an $alpha$ subunit. (5) Unexpectedly, the soft intra-monomer oscillations pertain to distortions that do not create inter-monomer steric clashes in the assembly, suggesting that structural optimization of the assembly evolved at all levels of complexity.
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