Kotaro Shirane

Synergetic effects of Ca2+ and Cu2+ on phase transition in phosphatidylserine membranes

Abstract In complexes of divalent metals with large exchange rate constant ( K H 2 O ) of the coordinated H 2 O, such as Ca 2+ and Cu 2+ , the cubic structure in the ligand field is usually unstable and conformation changes are easily induced. We observed the molecular motion of phosphatidylserine (PS) in an amphipathic solvent (water / methanol / chloroform) by 1 H-NMR and ESR using Ca 2+ and / or Cu 2+ , which has a similar K H 2 O to that of Ca 2+ . We found that Ca 2+ did not hinder the molecular movements of PS. However, Cu 2+ reduced the movements of both headgroups and the double bonds in the fatty acids of PS. By addition of both Ca 2+ and Cu 2+ , phase transition to a soft solid phase in the PS membrane was observed at room temperature. The results indicate that the headgroups are clustered in two-dimensional network with each ligand field displaced from the aqueous phase to the water / oil interface. The structure changes of the polar headgroups after the binding of divalent cations are considered to trigger the phase transition of this acidic phospholipid membrane.

Ferroelectric diffused electrical bilayer model for membrane excitation

The gating mechanism of localized ion-conducting pores or channels in excitable membranes is discussed based on the ferroelectric model hypothesized by Leuchtag, and excitation is analyzed by a diffused electrical bilayer model. By the application of a self-organized chemical model to such membranes, which have ferroelectric transmembrane units, the membrane potential in ionic circumstances of aqueous electrolytic media is described by a nonlinear equation derived from a phenomenological function for a parameter that characterizes a phase transition of the membranes. The excitation appears with a jump in the potential at one of the points on the bifurcation sets at which the discriminant of the equation equals zero; the point represents the reaction threshold. Because the membrane potential is controlled by two variables (control parameters) in the nonlinear state equation, the jump is cusp catastrophic. The potential of a few types of membranes has been calculated by assuming suitable functions for these...

Dynamic approach to self-organization or a phase transition

Abstract Self-organization or a non-equilibrium phase transition emerges through a quasi-equilibrium state which arises by the coupling of a primary and a partial system acting as an internal force. Such phenomena are studied by an equation of motion of molecules using an overdamped approximation which relates a cause (an internal force produced by an external force) and its effect on the molecular system. In a quasi-equilibrium state a force constant K 1 , which is called a transition parameter, is near zero and the potential bifurcates at the critical point ( K 1 = 0) where K 1 changes from positive to negative. The temperature dependence of K 1 may be represented by an average of the elastic constants between molecules. As a simple example, an ion flux change on membrane excitation is discussed by this dynamic theory.

A self-organized chemical model and reaction cascade

Some reaction cascades in biological systems are analyzed by a self-organized chemical model, an autocatalytic reaction. This model is described by the coupling of a primary system which stabilizes the initial stage of the reaction rapidly and a partial system which controls the primary system slowly. By the internal force caused by a trigger above the threshold, the coupled system in near-equilibrium is broken and changed into a new state. From the rate equation for the coupled system, a dimensionless nonlinear state equation, n = -n3 - un - v, is derived, where n is the concentration of intermediate, and u, v are dynamic variables of the system. This equation is similar to a nonequilibrium tri-molecular reaction. By using this chemical network theory, fibrin polymerization. F + F----fm----fp + X, where F is a fibrinogen molecule, fm is a fibrin monomer, fp is fibrin polymer, and X is small peptides released from fibrinogen, is discussed as an excellent example of the enzyme reaction cascade.

Ferroelectric diffused electrical bilayer model for membrane excitation. II: Voltage clamped responses

Abstract The opening and closing mechanism of Na+ channels in excitable membranes has been discussed by applying our chemical self-organized theory to the ferroelectric diffused electrical bilayer model modified from Leuchtags ferroelectric hypothesis for the channel gating. A state equation for membrane potential η is described by η3 + Aη + B = 0, where A and B are the control variables related to dipole-dipole and dipole-ion interactions, respectively. By a stimulus above the threshold, A and B move along the equilibrium space of the above equation and membrane excitation occurs with a cusp catastrophe at a point on the bifurcation sets when A < 0; T < T c. The Na± current or -conductance in the voltage clamp method is analyzed by use of the functions for Ȧ and [Bdot] modified from Zeemans formulas and the experimental results have been explained successfully by this model.

Network formation in negative charged membranes by two divalent cations and the catastrophe

The ligands of Ca2+-Cu2+-phosphatidylserine (PS) complexes in membrane networks at the water-oil interface through the symmetry breaking instability and the head groups of PS molecules were changed into a solid-like state. A first step in this transition is described by the following scheme in one unit in which the molar ratio is Ca2+: Cu2+: PS = 1:2:4; [Oh]+2[Oh]*----3[Oh]*, where [Oh]* denotes a little distorted ligand structure [LnM2+...2H2O] from [LnM2+2H2O], where Ln is PS molecules (n = 2 to Cu2+ and 4 to Ca2+). All the ligands are changed to [D4h] by the unit-unit interaction due to the network formation; [Oh]*----[D4h]. The whole system is equivalent to Schlögls scheme and is given by a cubic state equation for suitable variables transformations: x = -x3 - ux - v, where x corresponds to the concentration of [Oh]*, and u and v are related to rate constants in the first and the second steps, and they also depend on the initial [Oh] and the final [D4h] concentrations. This system is transferred into a new state with a cusp catastrophe.

Self-Organized chemical model and approaches to membrane excitation

By applying our self-organized theory to the ferroelectric hypothesis for the channel gating mechanism by Leuchtag, we obtained a simple cubic state equation, z3 + Az + B = θ, for the behavior or instability of a dissipative structure like an excitable membrane, where — z corresponds to membrane potential and control variables A and B are assigned to dipole-dipole interaction between channel molecules and to dipole-ion interaction, respectively. This represents that, under the condition of A < 0 (T < βTc), membranes are excited with a cusp catastrophe on the bifurcation sets, 4A3 + 27B2 = 0, by the movement of A and B and that it returns to the initial metastable state, that is, the resting state. In the resting state Na+ channels are closed with the ferroelectricity and in the excited state they open with the paraelectricity. By using the functions for A˙ and B˙ which are modified from Zeemans formulas, we have calculated and analyzed some of membrane excitation; action potentials generally observed in ...

Self-organized chemical model and the application to membrane excitation

Abstract Self-organization in chemical or biological systems has been studied macroscopically with a self-organized chemical theory modeling an autocatalytic reaction. From a postulated formula for a transition parameter κ which represents an internal force of the coupling system between a primary and a partial system, a nonlinear state equation for a cusp catastrophe is derived and membrane excitation is treated with this model based on catastrophe theory.

Entrainment in nerve by a ferroelectric model: bifurcation and limit cycles

Abstract The excitation in nerve that is self-organized in a dissipative structure with the resting membrane potential (an equilibrium structure) occurs on an equilibrium space for the cusp catastrophe. The space is given by a nonlinear state equation η 3 + aη + b = 0 deduced from a chemical network model which is applied to Leuchtags ferroelectric hypothesis for Na channels, where −η corresponds to the membrane potential, a and b are control parameters related to the dipole-dipole and dipole-ion interactions, respectively. A phase transition of the membrane organized in a region, a T T c ), can be determined by a parameter which describes the difference from equilibrium. When the membrane in a self-oscillation is disturbed by a periodical Na current with the natural frequency of the membrane or near one, a stable limit cycle of the potential arises through an entrainment. With modified Zeemans formulas for the movements of a and b in the equation, the transitions are calculated to arise at two points (lowest s 1 and highest s h limits) discontinuously, so s h which is the subcritical point differs from the result by the modified Hodgkin-Huxley theory. This seems to show a characteristic of the catastrophe.

Method for separation of particles using a rotating tilted open column with steady flow (RSF). Calculation of power index n (RSF)

Abstract In the improvement of a rotating tilted liquid column (RTC) method (closed and open-bottom column systems), we have developed a method for rapid selective separation of particulate materials in a continuous or semi-continuous process: a rotating tilted open column with steady flow (RSF) method. The separation power of the RSF method is represented as (aj/ai)n(RSF), where ai and aj are radii of particles with the same density. The power index n(RSF) will increase with increase of the column rotation ω within the practical range of 1.3 ⩽ Aω/V0 ⩽ 7, where A is the radius of the column and V0 is the free falling velocity of the particle. From the relationship between particle loci and distribution of liquid flow speed, we derive an approximate equation to calculate n(RSF) practically and demonstrate the relationship 2 This method can be of use for the separation of fine particles, easily degenerated micro-organisms, etc.