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• Articles by L. Goldman

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• Modifications of sodium channel gating in Myxicola giant axo...

  Modifications of sodium channel gating in Myxicola giant axons by deuterium oxide, temperature, and internal cations Biophysical Journal, Volume 27, Issue 2, 1 August 1979, Pages 193-208 C.L. Schauf and J.O. Bullock Abstract In dialyzed Myxicola axons substitution of heavy water (D2O) externally and internally slows both sodium and potassium kinetics and decreases the maximum conductances. Furthermore, this effect is strongly temperature dependent, the magnitude of the slowing produced by D2O substitution decreasing with increasing temperature over the range 3–14 degrees C with a Q10 of approximately 0.71. The relatively small magnitude of the D2O effect, combined with its strong temperature dependence, suggests that the rate limiting process producing a conducting channel involves appreciable local changes in solvent structure. Maximum conductances in the presence of D2O were decreased by approximately 30%, while the voltage dependences of both gNa and gK were not appreciably changed. In contrast to the effects of heavy water substitution on the ionic currents, membrane asymmetry currents were not altered by D2O, suggesting that gating charge movement may preceed by several steps the final transformation of the Na+ channel to a conducting state. In Myxicola axons the effect of temperature alone on asymmetry current kinetics can be well described via a simple temporal expansion equivalent to a Q10 of 2.2, which is somewhat less than the Q10 of GNa activation. The integral of membrane asymmetry current, representing maximum charge movement, is however not appreciably altered by temperature. Abstract | PDF (1073 kb)

• Exponentiated exponential model (Gompertz kinetics) of Na+ a...

  Exponentiated exponential model (Gompertz kinetics) of Na+ and K+ conductance changes in squid giant axon Biophysical Journal, Volume 22, Issue 1, 1 April 1978, Pages 15-28 D.M. Easton Abstract The conductance changes, gK(t) and gNa(t), of squid giant axon under voltage clamp (Hodgkin and Huxley, 1952) may be modeled by exponentiated exponential functions (Gompertz kinetics) from any holding potential VO to any membrane clamp potential V. The equation constants are set by the membrane potential V, and include, for any voltage step in the case of gK, the initial conductance, gO, the asymptote conductance g, and rate constant k: gK = g exp(-be-kt) where b = 1n g/gO. Equations of similar form relate g and k to the voltage V, and govern the corresponding parameters of the gNa system. For the gNa, the fast phase y = y exp (-be-kt) is cut down in proportion to a slow process p = (1 - p)e-k't + p, and thus gNa = py. The expo-exponential functions involve fewer constants than the Hodgkin-Huxley model. In particular, the role of the n, m, h parameters appears to be filled largely by 1n (g/gO) in the case of gK and by 1n (y/yO) in the case of gNa. Membrane action potentials during current clamp may be computed from the conductances generated by use of the appropriate differential forms of the equations; diverse other membrane behaviors may be predicted. Abstract | PDF (702 kb)

• On Mutations that Uncouple Sodium Channel Activation from In...

  On Mutations that Uncouple Sodium Channel Activation from Inactivation Biophysical Journal, Volume 76, Issue 5, 1 May 1999, Pages 2553-2559 L. Goldman Abstract Computations on sodium channel gating were conducted using a closed–open-inactivated coupled kinetic scheme. The time constant of inactivation () derives a voltage dependency from coupling to voltage-dependent activation even when rate constants between inactivated and other states are strictly voltage independent. The derived voltage dependency does not require any physical, molecular link between the structures responsible for inactivation and the charges producing voltage-dependent activation. The only requirement is that the closed to inactivated rate constant () differs from the open to inactivated (), consistent with experimental results. A number of mutations and other treatments uncouple sodium channel activation and inactivation in that the voltage dependency of is substantially reduced while voltage-dependent activation persists. However, a clear basis for uncoupling has not been described. A variety of experimental results are accounted for just by changes in the difference between and . In wild type channels, > and inactivation develops with a delay whose time constant is just that for channel opening. Mutations that reduce the − difference reduce the amplitude of the delay process and the derived voltage dependency of . If =, inactivation develops as a single exponential (no matter what the number of closed states), activation and inactivation become independent, parallel processes, and any voltage dependency of is then entirely intrinsic to inactivation. If <, inactivation develops as the sum of exponentials, at negative potentials speeds and then slows with more positive potentials. These predicted < effects have all been seen experimentally (O’Leary, M.E., L.-Q. Chen, R.G. Kallen, and R. Horn. 1995. . 106: 641–658). An open to closed rate constant of zero also removes the derived voltage dependency of , but activation and inactivation are still coupled and the inactivation delay remains. Abstract | Full Text | PDF (109 kb)

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Abstract

A variety of experimental observations in Myxicola and other preparations indicate that the sodium conductance, gNa, has properties quite different from those described by the m and h variables of Hodgkin and Huxley. A new quantitative description of the gNa is presented in which the gNa is assumed to be proportional to the fifth power of a generalized second-order variable, i.e., gNa = g'Na times v to the fifth, v = -Kav + K2U = K3, U = K4U + K5v + K6. This model is shown to be able to quantitatively simulate all of the experimentally observed behavior of the gNa. A view of the sodium gate consistent with these kinetics is to imagine it to be composed of five independent subunits, each of the type A eq. B eq. C eq. A where A represents the resting state, B the conducting state, and C the inactivated state. A model in which the subunit is of the type A eq. B eq. C could not simulate the experimental observations. It was concluded that two processes are sufficient to account for all of the behavior of the gNa.