Controllability of excitable systems

Area of Science:

• Computational neuroscience
• Mathematical biology
• Biophysics

Background:

• Cell electrical activity is modeled using nonlinear systems, often viewed as filters.
• These models relate applied current (input) to membrane potential (output).
• A key question is whether the input current can be recovered from the output potential.

Purpose of the Study:

• To investigate if applied current can be deduced from membrane potential in cell electrical activity models.
• To develop a general method for solving this inverse problem for a broad class of models.
• To apply the method to specific models and experimental data for parameter estimation.

Main Methods:

• Embedding nonlinear models into higher-dimensional quasilinear systems.
• Developing a procedure to find the inverse of these quasilinear filters.
• Demonstrating the method on the FitzHugh-Nagumo model and the Sherman-Rinzel-Keizer model.
• Using the inverse problem to estimate model parameters from experimental data.

Main Results:

• A method was established to deduce applied current from membrane potential for many nonlinear models.
• The inverse problem was successfully solved for the FitzHugh-Nagumo and Sherman-Rinzel-Keizer models.
• Parameter values for the Sherman-Rinzel-Keizer model were estimated by matching model output to experimental data.
• The technique allows parameter estimation without needing experimental values for all model variables.

Conclusions:

• The inverse problem of determining applied current from membrane potential is solvable for a significant class of cell electrical activity models.
• This approach provides a powerful tool for analyzing and parameterizing biophysical models.
• The method offers advantages in parameter estimation, reducing the need for complete experimental data.