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.

Myoplasmic Impedance of the Barnacle Muscle Fiber

Myoplasmic impedance was measured on a barnacle (Balanus nubilus) single muscle fiber that was placed in a cylindrical cavity to limit the volume and prevent the hydration of the myoplasm. At both ends of the cavity, the myoplasm was in direct contact with an electrolyte solution. When equilibrium with the external medium was reached, the myoplasmic impedance was measured at 10 °C with an impedance bridge at 1000 Hz. The results indicated that the myoplasmic impedance of the muscle fiber is mainly resistive. Treating the myoplasm as a suspension of small conductive particles, we deduced the specific conductivity of the contractile filaments kf and their volume fraction ρ (kf = 2.78 × 10−3 Ω−1 cm−1, and ρ = 0.48). The experimental technique permits an estimate of the specific myoplasmic conductivity in vivo (6.27 × 10−3 Ω−1 cm−1). Finally, a decrease in the pH of the external solution from 10.1 to 4.0 lowered the myoplasmic conductivity by 16%. This may be considered as indirect evidence that the conductivity of the contractile filaments is associated with the protein counter-ions, since Hinke et al. (1973. Ann. N.Y. Acad. Sci. 204, 274–296.) reported evidence that a lowering of pH decreases the number of counter-ions.

Membrane Currents Carried by Ca, Sr, and Ba in Barnacle Muscle Fiber During Voltage Clamp

Membrane currents associated with voltage clamp of the giant muscle fibers of a barnacle, Balanus nubilus, were analyzed in terms of currents of the Ca and K channels. Although the activation of the K channel occurs more slowly than that of the Ca channel, both currents show a significant temporal overlap. The currents carried by Ca++, Sr++, or Ba++ through the Ca channel were compared under the conditions at which this overlap was the least. When only one divalent cation is present in the solution, Ba++ carries more current than Ca++ or Sr++ and the sequence of the current is Ba > Sr ≈ Ca. When the external solution contains a relatively high concentration of Co++, which is a blocking agent for the Ca channel, inversion of the sequence occurs, to Ca > Sr > Ba. This is due to the fact that the blocking effect differs depending on which ion carries current through the Ca channel. The Ba current is most sensitive and the Ca current is least affected. Ba suppresses the current of the K channel, independently of its current-carrying function through the Ca channel.

Temperature effects of the electrical characteristics of the barnacle muscle fiber

Page 240: J. Rothberg. "Temperature effects of the electrical characteristics of the barnacle muscle fiber." Page 240: the abstract, line 13, "rates up to 23 mV/°C" should read, "rates up to 2.3 mV/°C." Page 241: column 1, line 21 should read, "476 mM; K+, 8 mM; Ca++, 20 mM; Mg++, 12 mM; Cl–, 538 mM; and HCO3–, 10 mM ..."; line 26, "K+, 625 mM" should read, "K+, 652 mM."