Kota Ikeda

Generation of membrane potential beyond the conceptual range of Donnan theory and Goldman-Hodgkin-Katz equation

Donnan theory and Goldman-Hodgkin-Katz equation (GHK eq.) state that the nonzero membrane potential is generated by the asymmetric ion distribution between two solutions separated by a semipermeable membrane and/or by the continuous ion transport across the semipermeable membrane. However, there have been a number of reports of the membrane potential generation behaviors in conflict with those theories. The authors of this paper performed the experimental and theoretical investigation of membrane potential and found that (1) Donnan theory is valid only when the macroscopic electroneutrality is sufficed and (2) Potential behavior across a certain type of membrane appears to be inexplicable on the concept of GHK eq. Consequently, the authors derived a conclusion that the existing theories have some limitations for predicting the membrane potential behavior and we need to find a theory to overcome those limitations. The authors suggest that the ion adsorption theory named Ling’s adsorption theory, which attributes the membrane potential generation to the mobile ion adsorption onto the adsorption sites, could overcome those problems.

Bifurcation structure of a car-following model with nonlinear dependence on the relative velocity

ABSTRACT Understanding the stability of solutions of mathematical models of traffic flow is important for alleviating jams as these are considered stable inhomogeneous solutions of traffic models. Traffic jams can be alleviated by destabilizing these solutions. Solution stability can be studied with the aid of bifurcation analysis, which has been used to describe the global bifurcation structure of a car-following model that exhibits bistable behavior and loss of stability due to Hopf bifurcations. However, previous studies on bifurcation analysis for traffic models have not considered the relative velocity effect, which is important in real-world traffic scenarios. This study analytically derives linear stability conditions and numerically investigates the global bifurcation structure of a car-following model with nonlinear dependence on the relative velocity (the STNN model), which exhibits multistable states. Moreover, the relative velocity drastically changes the bifurcation structure. This supports implementation of (semi-)automatic driving systems as a means to alleviate traffic jams.

Another interpretation of the Goldman–Hodgkin–Katz equation based on Ling’s adsorption theory

According to standard membrane theory, the generation of membrane potential is attributed to transmembrane ion transport. However, there have been a number of reports of membrane behavior in conflict with the membrane theory of cellular potential. Putting aside the membrane theory, we scrutinized the generation mechanism of membrane potential from the view of the long-dismissed adsorption theory of Ling. Ling’s adsorption theory attributes the membrane potential generation to mobile ion adsorption. Although Ling’s adsorption theory conflicts with the broadly accepted membrane theory, we found that it well reproduces experimentally observed membrane potential behavior. Our theoretical analysis finds that the potential formula based on the GHK eq., which is a fundamental concept of membrane theory, coincides with the potential formula based on Ling’s adsorption theory. Reinterpreting the permeability coefficient in the GHK eq. as the association constant between the mobile ion and adsorption site, the GHK eq. turns into the potential formula from Ling’s adsorption theory. We conclude that the membrane potential is generated by ion adsorption as Ling’s adsorption theory states and that the membrane theory of cellular potential should be amended even if not discarded.

Ling’s Adsorption Theory as a Mechanism of Membrane Potential Generation Observed in Both Living and Nonliving Systems

The potential between two electrolytic solutions separated by a membrane impermeable to ions was measured and the generation mechanism of potential measured was investigated. From the physiological point of view, a nonzero membrane potential or action potential cannot be observed across the impermeable membrane. However, a nonzero membrane potential including action potential-like potential was clearly observed. Those observations gave rise to a doubt concerning the validity of currently accepted generation mechanism of membrane potential and action potential of cell. As an alternative theory, we found that the long-forgotten Ling’s adsorption theory was the most plausible theory. Ling’s adsorption theory suggests that the membrane potential and action potential of a living cell is due to the adsorption of mobile ions onto the adsorption site of cell, and this theory is applicable even to nonliving (or non-biological) system as well as living system. Through this paper, the authors emphasize that it is necessary to reconsider the validity of current membrane theory and also would like to urge the readers to pay keen attention to the Ling’s adsorption theory which has for long years been forgotten in the history of physiology.

Computer-Aided Bifurcation Analysis for a Novel Car-Following Model with Relative Velocity Effect

The global behaviour of mathematical models for traffic flow is important in order to understand their characteristics because of the bistable property observed in real traffic. This bi-stability can be discussed in a bifurcation analysis. In fact, bifurcation analysis of optimal velocity models in several studies has revealed the global bifurcation structure of the model, which shows a loss of stability due to the Hopf bifurcation and bistable property. Shamoto et al. proposed a novel car-following model with relative velocity effect (STNN model), which was not introduced into the optimal velocity model, but is important in real traffic scenarios. They discussed the linear stability of homogeneous traffic flow; however, they did not reveal the global bifurcation structure of the STNN model. In this paper, we numerically investigated the global bifurcation structure of the STNN model and observed that the strength of the relative velocity effect drastically changes the bifurcation structure. This result provides a possibility of implementing (semi-)automatic driving systems to alleviate traffic jams.