Self-Organized Bioelectricity via Collective Pump Alignment: Physical Origin of Chemiosmosis

TL;DR

A minimal model in which ion pump orientation and the intracellular electrochemical potential mutually reinforce each other is developed, which provides a self-organizing mechanism for the emergence of bioelectricity, with implications for the origin of life.

Abstract

Chemiosmosis maintains life in nonequilibrium through ion transport across membranes, yet the origin of this order remains unclear. We develop a minimal model in which ion pump orientation and the intracellular electrochemical potential mutually reinforce each other. This model shows that fluctuations can induce collective pump alignment and the formation of a membrane potential. The alignment undergoes a phase transition from disordered to ordered, analogous to the Ising model. Our results provide a self-organizing mechanism for the emergence of bioelectricity, with implications for the origin of life.

Figures (4)

• Figure 1: Pump-ion coupling model, consisting of three regions; internal, external, and membrane. Pumps, $P=\{P_i\}=\{P_1,P_2,...,P_{N_P}\}$, are embedded in a membrane and orient either inward ($P_i=+1$) or outward ($P_i=-1$). Ions are present in both the internal and external regions. Pumps and ions can interact with each other, resulting in ‘flip' of pumps and ‘transport' of ions. The direction of the arrows indicates the direction of ion transport; influx ($F^{\mathrm{in}}$) and outflux ($F^{\mathrm{out}}$).
• Figure 2: Distribution for three states of pumps for $2000$ samples (a) and their time series for one sample (b). Colors correspond to states: random (blue,$\alpha=0.01$), flipping (yellow,$\alpha=0.12$), and aligned (red,$\alpha=0.2$). Parameters $N_P=100,J=5.5,\gamma=1$. Frequency in (a) is calculated over $t=30$--$70$ and normalized so that the total amount is one.
• Figure 3: Phase diagram. (a) time-averaged ensemble mean of $|m|$ against $J$ and $\alpha$. (b) variance of $|m|$ multiplied by $N_P$ plotted against $J$ and $\alpha$. (c) time-averaged ensemble mean of $|m|$ (blue), $m$ at $t=70$ (blue in inset), and stable solutions of self-consistent equation (\ref{['selfconsistent']}) (red), against $\alpha$ at $J=5.5$. (d) variance of $|m|$ multiplied by $N_P$ plotted against $\alpha$ at $J=5.5$. (a),(b) transition lines $J=1/(2\alpha)+1/2$ (black). Parameters $N_P=100,\gamma=1$, and $200$ samples. The mean and variance are calculated from the samples at each time, then the time-averaged values are taken over $t=30$--$70$.
• Figure 4: $r_V$ dependence of pumps alignment. (a) time-averaged ensemble mean of $m$ against $r_V$ and $\alpha$. The black line shows bifurcation line $r_V=2\alpha(2J/\eta-1)-1$ (see End Matter). (b) $m$ at $t=100$ for $200$ samples (blue) and stable solutions of self-consistent equation (\ref{['general selfconsistent']}) (red), against $\alpha$ at $r_V=0.01$. Parameters $N_P=100,\gamma=1,J=5.5$, and $200$ samples. The mean is calculated from the samples at each time, then the time-averaged values are taken over $t = 0$--$100$.