Cellular information dynamics through transmembrane flow of ions

Adding these gives14\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tau }_{i}=\frac{1}{{\alpha }_{i}+{\beta }_{i}},\,i=1,\ldots ,N.$$\end{document}τi=1αi+βi,i=1,…,N.This shows how the rates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha }_{{i}},{\beta }_{{i}}$$\end{document}αi,βi determine the rapidity of exponential change of ion rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{p}}_{{i}}({t})$$\end{document}pi(t) in Eqs (10).

These rates obviously play a similar role in our solution Eq. (10), supplemented by Eq. (14), to that of the activation energy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{E}}_{{a}}$$\end{document}Ea in the Arrhenius law13. They both govern the rapidity of an exponential falloff.

In summary, we propose the transmembrane ion gradients that permit neurons to form and propagate an action potential also play a critical role in the function and survival of non-neuronal cells. We propose this difference between extra- and intra-cellular ion concentrations produces initial conditions that allow reception, communication, processing and response to environmental information (Fig. 1). The information is detected by specialized gates within transmembrane ion channels that, by opening, allow transmission of the information into the cell in the form of an ion puff. By changing the structure of the proteins that form the gates, they can be made to be sensitive to a wide range of environmental factors. Furthermore, the information encoded in the flow of ions is received and processed in the cell through a local change of ion density and cation/anion concentrations around the channel. This may reduce (or increase) the mobile ion screening of negative charges in the inner leaf of the cell membrane and by increasing (or decreasing) the Debye length28,29, alter the attachment of peripheral membrane proteins (Fig. 1B). This can alter the structure of the membrane to respond to the perturbation. Furthermore, the function of a large number of enzymes is dependent on local is dependent of the local ion concentrations. For example, hexokinase30,31 is dependent on local Mg2+ concentrations and pyruvate kinase9 is dependent on K+ concentrations. In this way, the ion flux through K+ or Mg2+ 32 channels can promote or suppress reactions to rapidly respond to a perturbation.

Since the discovery of the structure and function of DNA, investigations of biological information dynamics have focused almost exclusively on gene replication and expression, and on translation. These include transgenerational transmission of information through chromosomes, epigenetic control and time dependent changes in transcription of genetic information in response to local environmental changes. However, in prior theoretical studies we have noted that the transmembrane ion gradients potentially may encode in excess of 1014 bits of Shannon information1,13,14. Further, the membrane ion protein pumps that generate these gradients can consume up to 40% of a cell’s energy budget33. Why does a cell invest such a large fraction of its resources to the formation of a transmembrane ion gradient? Indeed, at first glance, the large expenditure of energy to achieve the seemingly trivial task of replacing intracellular Na+ by K+ (or replacing Ca2+ with Mg2+), seems at best puzzling.

Here we propose a specific mechanism by which the transmembrane ion gradients, and their associated information dynamics, can detect, process and respond to environmental perturbations on a very rapid time scale without any direct input from the genes. That is, while the genome clearly contributes to these dynamics by encoding and translating the information in the associated proteins, the ion-based dynamics at the membrane can proceed locally and rapidly without additional input from the nucleus. As noted above, this model of information dynamics optimizes both speed and accuracy of information transmission. Thus, we propose that the large resource expenditure necessary for generation of the ion gradient is an indication of the critical role of these information dynamics in cell survival and function.

In general, our results support a more distributive model of biological information. Thus, information dynamics at the cell membrane are deeply linked with heritable information which contributes the molecular machinery that generates the gradients and permits detection, processing and response to environmental signals and perturbations. Similarly while we view the membrane information dynamics to occur independently on fast and local scales, we note that ion fluxes can generate molecular signals including lipid second messengers34 that communicate with the nucleus and other cellular organelles. Furthermore, ion flows may facilitate direct communication of cellular information to the nucleus. For example, ligand binding to EGFR is associated with gate opening in K+ channels5,35. This loss of K+ screening for the negative charges in the inner leaf of the membrane (Fig. 1A,B) may facilitate transmission of signal along the MAPK pathway by allowing coulomb interactions between positively charged Raf protein (pK of 9.3) or its associated scaffolding proteins to the GTP-activated Ras protein. Indeed, it is often stated that during MAPK signaling that Ras “recruits”7 Raf to the membrane. We note that the term “recruits” has no physical meaning but rather represent empirical observations that Raf moves very rapidly to the location to the membrane site containing an activated Ras. We propose the ion dynamics summarized in Fig. 1 could account for this rapid and specific movement.