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 comprises:

• 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 voltage clamp stimulation protocol and one or more processes including an inversion process of a set of underlying differential equations of a Hodgkin-Huxley formalism;
• providing a known voltage dependence of a steady state function of a set of gating variables from previously run H-step and C-step protocols;
• providing a known voltage dependence of the time constant of a set of gating variables in the range RT from a previously run T-step protocol. applying said voltage difference across said cell membrane according to a G-step voltage clamp stimulation protocol to generate a set of experimental data to quantify the time constants of said Hodgkin Huxley formalism with activating and inactivating gates in a voltage range RG, extending said voltage range RT from said previously run T-step protocol, applying a fixed holding voltage uH, followed by a conditioning voltage uC, of a time interval uC, followed by successive gap voltages uG of time interval vG, not generating the test pulse usually present in a G-step protocol, during clamping said gap voltage uG and measuring gap current, and wherein a plurality of gap voltages are of lower voltage than said conditioning voltage uC;
• generating a cell physiologic state by setting said voltage uH to about a cell rest potential and also either in the range RH or RC of previously run H-step and C-step protocols, and setting said conditioning voltage uC, in the range RT of a previously run T-step protocol, followed by successive gap voltages uG, where the parameters of the stimulation protocol are adjusted iteratively by the operator in a manner to generate independent gap currents;
• generating the global bound for R of the inverse solution of an Hodgkin Huxley formalism with activating and inactivating gates from gap currents of a G-step stimulation protocol;
• adjusting the G-step stimulation protocol parameters based on the global bound for R in a manner to reduce as much as possible the number of possible inverse solutions;
• inverting, for any Rk picked within the global bounds for R, the Hodgkin Huxley formalism with activating and inactivating gates for the time constant of each gating variable, in the process generating a tree-like structure spanning the range RG and associated to the voltage dependence of the time constant of each gating variable;
• and
• extracting, for each Rk and for each gating variable the roots of the tree-like structure traversing the range RG, where each root represents the time constant of the gating variables permitting the Hodgkin Huxley formalism to reproduce the gap currents.

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

• 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 voltage clamp stimulation protocol and one or more processes including an inversion process of a set of underlying differential equations of a Hodgkin-Huxley formalism;
• providing a known voltage dependence of a steady state function of a set of gating variables from previously run H-step and C-step protocols;
• providing a known voltage dependence of the time constant of a set of gating variables in the range RT from a previously run T-step protocol;
• applying said voltage difference across said cell membrane according to a G-step voltage clamp stimulation protocol to generate a set of experimental data to quantify the time constants of said Hodgkin Huxley formalism with activating and inactivating gates in a voltage range RG, extending said voltage range RT from said previously run T-step protocol, applying a fixed holding voltage uH, followed by a conditioning voltage uC, of a time interval uC, followed by successive gap voltages uG of time interval vG, followed by a test voltage uT, during which measuring said test voltage and a test current, and wherein a plurality of gap voltages are of lower voltage than both of said conditioning voltage uC, and said test voltage uT;
• generating a cell physiologic state by setting said voltage uH to about a cell rest potential and in the range of either RH or RG of previously run H-step and C-step protocols, and setting said conditioning voltage uC, and said test voltage uT in the range RT of a previously run T-step protocol, applying successive gap voltages uG of time interval vG, where the parameters of the G-step stimulation protocol are iteratively adjusted by the operator in a manner to generate independent gap and test currents;
• and
• evaluating yGi, the value of each gating variable at the end of the gap pulse by interpreting the test currents with an inversion the Hodgkin Huxley formalism for initial conditions prior to the application of the test pulse, evaluating τi (u), u∈RG from yGi, si(u), u∈RH or u∈RG, and τi(u), u∈RT.