Method and system to extend the conditions of application of an inversion of the Hodgkin-Huxley gating model

A method to quantify a time constant of each gate of a Hodgkin Huxley formalism with activating and inactivating gates, the method comprising:

• providing an electrophysiology apparatus configured to cause a voltage difference across a cell membrane of a cell and to measure a current through the cell membrane, and a computer configured to run a voltage clamp stimulation protocol and one or more processes comprising an inversion process of a set of underlying differential equations of the Hodgkin Huxley formalism;
• providing a known voltage dependence of a steady state function of a set of gating variables;
• providing a known voltage dependence of the time constant of a set of gating variables in a voltage range RT from a previously run T-step protocol;
• applying the voltage difference across the cell membrane according to a G-step voltage clamp stimulation protocol to generate a set of experimental data to quantify the time constants of the Hodgkin Huxley formalism with activating and inactivating gates in a voltage range RG, extending the voltage range RT from the previously run T-step protocol, applying a fixed holding voltage uH, followed by a conditioning voltage uC of a time interval vC, followed by applying successive gap voltages uG of a time interval vG, followed by applying a test voltage uT, during which a test current is measured, wherein the successive gap pulse voltages uG are of lower voltage than both the conditioning voltage uC and the test voltage uT;
• generating a cell physiologic state by setting the fixed holding voltage uH to about a cell rest potential and setting the conditioning voltage uC in a range of RH and/or RC of the previously run H-step and C-step protocols, voltage uC and the test voltage uT in the voltage range RT from the previously run T-step protocol, and applying the successive gap voltages uG of the time interval vG, wherein the parameters of the G-step voltage clamp stimulation protocol are adjusted to generate independent gap currents and test currents;
• and
• evaluating
• y
• G
• i
• representing a value of each gating variable i at the end of each successive gap pulse voltage uG tested in the G-step voltage clamp stimulation protocol by interpreting the test currents with an inversion of the Hodgkin Huxley formalism for initial conditions
• y
• G
• i
• just prior to the application of the test pulse voltage uT, from which the voltage dependence of the time constant
• τ
• G
• (
• i
• )
• of the gating variable i, for each gap voltage uG is deduced, and evaluating the voltage TG dependence of τi(u) for voltages u in the range RG.

A method to generate cell electrophysiology data to quantify a voltage dependence of a time constant of each gating variable of a Hodgkin Huxley gating model in a voltage range RG, wherein RG has an upper bound adjacent to a voltage range RT of a T-step voltage clamp stimulation protocol previously run to evaluate gating parameters of the Hodgkin Huxley gating model, comprising the steps of:

• providing an electrophysiology apparatus configured to cause a voltage difference across a cell membrane of a cell and to measure a current through said cell membrane, and a computer configured to run a voltage clamp stimulation protocol and one or more processes including an inversion process of the Hodgkin Huxley gating model;
• providing a voltage dependence of a steady state function si(u) of each gating variable i, i∈[0,1] of the Hodgkin Huxley gating model;
• providing a voltage dependence of a time constant τi(u) of each gating variable i, i∈[0,1] of the Hodgkin Huxley gating model to characterize in the voltage range RT of the T-step voltage clamp stimulation protocol from which that voltage dependence was obtained, and which fulfills conditions of an application of the inversion of the Hodgkin Huxley gating model;
• applying said voltage difference across the cell membrane according to a G-step voltage clamp protocol to generate cell electrophysiology data to quantify the voltage dependence of the time constant of each gating variable of an Hodgkin Huxley gating model in the voltage range RG, which is achieved by applying a fixed voltage uH in a vicinity of a cell rest potential for a duration long enough to reach a steady state followed by a conditioning voltage uc above uH of a duration vC, where a channel activates, followed by successive gap voltages ug of duration vg, where the channel inactivates, followed by a test voltage uT lasting long enough to observe the channel activate and then inactivate and during which the current is measured, wherein uC and uT are selected from voltage values where the voltage dependence of the steady state and the time constant of each gating variable are known, wherein a plurality of voltages uG span a voltage range extending RT, wherein durations vC and vg are adjusted based on inversion results to generate independent currents during the test pulse and to narrow the bound on R.