Information thermodynamics of cellular ion pumps

Abstract

The framework of bipartite stochastic thermodynamics is a powerful tool to analyze a composite system's internal thermodynamics. It has been used to study the components of different molecular machines such as ATP synthase. However, this approach has not yet been used to describe ion-transporting proteins despite their high-level functional similarity. Here we study the bipartite thermodynamics of the sodium-potassium pump in the nonequilibrium steady state. Using a physically intuitive partition between the ATP-consuming subsystem and the ion-transporting subsystem, we find considerable information flow comparable to other molecular machines, and Maxwell-demon behavior in the ATP-consuming subsystem. We vary ion concentrations and transmembrane voltage in a range including the neuronal action potential, and find that the information flow inverts during depolarization.

Figures (5)

• Figure 1: Albers-Post cycle of the sodium-potassium pump, encompassing a main path exchanging sodium and potassium, an alternative path releasing one sodium ion to the extracellular medium, and four dead-end states corresponding to mixed ion binding. Gray: states and transitions removed in this paper; red: added reverse transitions. Adapted from clarke_quantitative_2013.
• Figure 2: Two different bipartite partitions. Red blocks: subsystem $X$ states; blue blocks subsystem $Y$ states. a) The principal partition in this paper. b) An alternative partition to assess the robustness of our results.
• Figure 3: Global probability current (a), internal energy ($k_\text{B}T/$cycle) and information (nats/cycle) flows from subsystem $X$ to subsystem $Y$ (b), and subsystem efficiencies (c) as a function of the ratio $\gamma \equiv \frac{R_{0,1}}{R_{7,8}}$ of introduced reverse rates. Environmental parameters taken from Table \ref{['tab:concentrations']}.
• Figure 4: Relative change $(P-P_0)/P_0$ in probability current as a function of the relative change $([X^+]-[X^+]_0)/[X^+]_0$ in concentration of various ions $X^+$. $\gamma=1$ throughout. Environmental parameters taken from Table \ref{['tab:concentrations_neuron']}.
• Figure 5: Global probability current (a), subsystems' heat, internal energy, and information flow (b), and subsystems' efficiencies (c), when varying voltage in a range encompassing the neuronal action potential. Environmental parameters taken from Table \ref{['tab:concentrations_neuron']}.