Third-Order Memristive Morris–Lecar Model of Barnacle Muscle Fiber

This paper presents a detailed analysis of various oscillatory behaviors observed in relation to the calcium and potassium ions in the third-order Morris–Lecar model of giant barnacle muscle fiber. Since, both the calcium and potassium ions exhibit all of the characteristics of memristor fingerprints, we claim that the time-varying calcium and potassium ions in the third-order Morris–Lecar model are actually time-invariant calcium and potassium memristors in the third-order memristive Morris–Lecar model. We confirmed the existence of a small unstable limit cycle oscillation in both the second-order and the third-order Morris–Lecar model by numerically calculating the basin of attraction of the asymptotically stable equilibrium point associated with two subcritical Hopf bifurcation points. We also describe a comprehensive analysis of the generation of oscillations in third-order memristive Morris–Lecar model via small-signal circuit analysis and a subcritical Hopf bifurcation phenomenon.

Intracellular Cl− Dependence of Na-H Exchange in Barnacle Muscle Fibers under Normotonic and Hypertonic Conditions

We previously showed that shrinking a barnacle muscle fiber (BMF) in a hypertonic solution (1,600 mosM/kg) stimulates an amiloride-sensitive Na-H exchanger. This activation is mediated by a G protein and requires intracellular Cl−. The purpose of the present study was to determine (a) whether Cl− plays a role in the activation of Na-H exchange under normotonic conditions (975 mosM/kg), (b) the dose dependence of [Cl−]i for activation of the exchanger under both normo- and hypertonic conditions, and (c) the relative order of the Cl−- and G-protein-dependent steps. We acid loaded BMFs by internally dialyzing them with a pH-6.5 dialysis fluid containing no Na+ and 0–194 mM Cl−. The artificial seawater bathing the BMF initially contained no Na+. After dialysis was halted, adding 50 mM Na+ to the artificial seawater caused an amiloride-sensitive pHi increase under both normo- and hypertonic conditions. The computed Na-H exchange flux (JNa-H) increased with increasing [Cl−]i under both normo- and hypertonic conditions, with similar apparent Km values (∼120 mM). However, the maximal JNa-H increased by nearly 90% under hypertonic conditions. Thus, activation of Na-H exchange at low pHi requires Cl− under both normo- and hypertonic conditions, but at any given [Cl−]i, JNa-H is greater under hyper- than normotonic conditions. We conclude that an increase in [Cl−]i is not the primary shrinkage signal, but may act as an auxiliary shrinkage signal. To determine whether the Cl−-dependent step is after the G-protein-dependent step, we predialyzed BMFs to a Cl−-free state, and then attempted to stimulate Na-H exchange by activating a G protein. We found that, even in the absence of Cl−, dialyzing with GTPγS or AlF3, or injecting cholera toxin, stimulates Na-H exchange. Because Na-H exchange activity was absent in control Cl−-depleted fibers, the Cl−-dependent step is at or before the G protein in the shrinkage signal-transduction pathway. The stimulation by AlF3 indicates that the G protein is a heterotrimeric G protein.

Effect of isosmotic removal of extracellular Na+ on cell volume and membrane potential in muscle cells

Isosmotic removal of extracellular Na+ (Nao) is a frequently performed manipulation. With the use of isolated voltage-clamped barnacle muscle cells, the effect of this manipulation on isosmotic cell volume was studied. Replacement of Nao by tris(hydroxymethyl)aminomethane produced membrane depolarization (approximately 20 mV) and cell volume loss (approximately 14%). The membrane depolarization was verapamil insensitive but depended on extracellular Ca2+ (Cao) and was probably due to activation of intracellular Ca2+ (Cai)-dependent nonselective cation channels. The cell volume loss did not require membrane depolarization but depended on Cao. This was probably due to an increase in Cai, mediated by activation of Ca2+ influx via Na+/Ca2+ exchange. Nao replacement by Li+ also promoted membrane depolarization (approximately 20 mV) and cell volume loss (20%). Both effects were reduced (approximately 73%) but were not abolished by Cao removal. Under this condition, the remaining membrane depolarization was probably due to a higher membrane permeability of Li+ over Na+. The remaining cell volume loss was due to membrane depolarization, which probably induced Ca2+ release from intracellular stores.