Cellular Biophysics and Membrane Models
Dynamic phenomena, characteristic times, compartmental models, equilibrium potentials, ionic currents, and scalar bifurcations.
Topics to Explore
- Exponential growth, decay, relaxation; exponential time constants; characteristic times.
- Classification of scalar ODEs; solution of simple ODE IVPs by separating variables and integrating; checking candidate solutions of ODE IVPs.
- Single compartment models of biochemical kinetics; conservation laws vs. constitutive relations; conservation laws expressed in terms of rate of change of concentration vs. number; physical dimensions and units of variables and parameters.
- Deriving ODE systems for chemical reactions using mass action kinetics; eliminating equations by identifying conserved quantities; conservation laws expressed in terms of concentration vs. number.
- Phase diagrams for scalar ODEs; classification of steady states using graphical and analytical techniques; the concept of bistability.
- Nernst equilibrium potential; relative sizes of conductances of resting membranes; relative sizes of physiological ion concentrations inside vs. outside cells; reversal potentials of physiologically important ions.
- Equivalent circuit view of the cell plasma membrane; current-voltage relations for membrane currents; effective reversal potentials for multiple passive currents.
- Vocabulary for describing ionic currents: depolarizing, hyperpolarizing, inward, outward, passive, voltage-gated, depolarization activated, hyperpolarization activated, regenerative, restorative, inward rectifying, outward rectifying, etc.
- Fundamental aspects of physiologically important ionic currents including the potassium leakage current, the L-type voltage-gated Ca2+ current, the hyperpolarization activated cation current known as Ih, also called Isag, and others.
- Goldman-Hodgkin-Katz current equation; GHK voltage equation; their assumptions; their relationship.
- Interpreting bifurcation diagrams summarizing the number and/or stability of steady states of an ODE model.