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 with currents recorded with a T-step protocol 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;
• applying a fixed holding voltage uH followed by a successive test voltages UT , and measuring said successive test voltages and a test current, and wherein a plurality of test voltages are of a higher voltage than the fixed holding voltage;
• generating a cell physiologic state by setting said voltage uH to about a cell rest potential and the successive test voltage both of which define a voltage range RT of the T-step protocol, to generate a plurality of independent test currents;
• finding, through the Hodgkin Huxley inversion process, for each sample on the normalized test currents derivative J(t=tr) taken at time tr, tr a recording a time of a sample, couples of activating and inactivating gates (y0(tr)y1(tr)) to reproduce J(t =tr) within pre-specified experimental margin of error;
• evaluating, for each gating variable couple (y0(tr)y1(tr)) to reproduce J(t=tr), R=1/g to reproduce a sample on the test current I(t=tr) within a pre-specified experimental margin of error;
• adjusting uH and RT of a T-step voltage clamp stimulation protocol, in an iterative manner, such that the operator identifies a range for R to reproduce all T-step currents I(t) over the entire recording time interval within a pre-specified experimental margin of error;
• picking among gating variable couples (y0(tr)y1(tr)) where the Hodgkin Huxley formalism reproduces J(t=tr) with only couples that correspond to values of R within the range identified by the operator and that reproduces T-step currents I(t) over a recording time interval within a pre-specified experimental margin of error;
• evaluating for each gating variable couple (y0 (tr)y1(tr)) to reproduce J(t =tr) with an experimental margin of error restricted to couples permitting to reproduce all T-step currents I(t) over the recording time interval within a pre-specified margin of error, a time constant τi for each gating variable yj of each restricted couple;
• and
• extracting from an array of time constants evaluated through Hodgkin Huxley inversion, and that are consistent with values of R identified by the operator to reproduce I(t) over the entire recording time interval within a pre-specified margin of error, τi that are consistent with the Hodgkin Huxley formalism, where τi(u) is substantially the same for all samples of a test current, and changes wherein the voltage dependence of τi(u) does not exhibit a jump or discontinuities at any potential uT in the range RT of the T-step protocol.