arXiv subjects

S. R. Vaccaro

Publications and source records attributed to S. R. Vaccaro.

3 recordsLinked to original sources

arXiv2018

Reduction of a kinetic model for Na+ channel activation, and fast and slow inactivation within a neural or cardiac membrane

A fifteen state kinetic model for Na+ channel gating that describes the coupling between three activation sensors, a two-stage fast inactivation process and slow inactivated states, may be reduced to equations for a six state system by application of the method of multiple scales. By expressing the occupation probabilities for closed states and the open state in terms of activation and fast inactivation variables, and assuming that activation has a faster relaxation than inactivation and that the activation sensors are mutually independent, the kinetic equations may be further reduced to rate equations for activation, and coupled fast and slow inactivation that describe spike frequency adaptation, a repetitive bursting oscillation in the neural membrane, and a cardiac action potential with a plateau oscillation. The fast inactivation rate function is, in general, dependent on the activation variable m(t) but may be approximated by a voltage-dependent function, and the rate function for entry into the slow inactivated state is dependent on the fast inactivation variable.

physics.bio-ph↗

arXiv2017

Rate equations for a Na+ channel gating master equation during the action potential within a neural membrane

The action potential in a neural membrane is generated by Na+ and K+ channel ionic currents that may be calculated from a current equation and the rate equations for activation variables m and n, and the Na+ inactivation variable h. Assuming that a Na+ channel has three activation sensors, and activation and inactivation are cooperative processes, a twelve state master equation that describes channel gating may be reduced to kinetic equations for a five state system when the occupational probability of the first inactivated state is small, and the remaining inactivated states contribute to a total inactivated state. In the case of independent activation sensors, the inactivation rate is, in general, dependent on the activation variable m(t) as well as the forward inactivation transition rates. However, when m(t) has a faster time constant than h(t), the inactivation rate may be approximated by a voltage-dependent function, and therefore, the solution of the master equation during an action potential may be approximated by the solution of Hodgkin-Huxley rate equations for m and h.

physics.bio-ph↗

arXiv2016

Derivation of Hodgkin-Huxley equations for a Na+ channel from a master equation for coupled activation and inactivation

The Na+ current in nerve and muscle membranes may be described in terms of the activation variable m(t) and the inactivation variable h(t), which are dependent on the transitions of S4 sensors of each of the Na+ channel domains DI to DIV. The time-dependence of the Na+ current and the rate equations satisfied by m(t) and h(t) may be derived from the solution to a master equation which describes the coupling between two or three activation sensors regulating the Na+ channel conductance and a two stage inactivation process. If the inactivation rate from the closed or open states increases as the S4 sensors activate, a more general form for the Hodgkin-Huxley expression for the open state probability may be derived where m(t) is dependent on both activation and inactivation processes. The voltage dependence of the rate functions for inactivation and recovery from inactivation are consistent with the empirically determined expressions, and exhibit saturation for both depolarized and hyperpolarized clamp potentials.

physics.bio-ph↗