Jürgen F. Fohlmeister, Principal Investigator

Modeling of Complex Systems

This researcher is involved in three projects using the modeling capabilities of the Basic Sciences Computing Laboratory. Two of these projects investigate aspects of neural excitation, and the third investigates the behavior of proto-continents.

The first project investigates the role of membrane capacitance in neural excitation. Although membrane capacitance (1 mF/cm2) was accurately measured about two decades prior to the first delineation of the ionic currents responsible for the nerve impulse (the Hodgkin-Huxley model), capacitance of the neural membrane has generally been regarded as an unavoidable and unimportant linear path in parallel with the critical sodium, calcium, and potassium currents (Na-, Ca-, and Kcurrents). More recently, however, it has become important to model impulse encoding in neurons of the central nervous system with non-uniform channel density distributions, for which the membrane capacitance can introduce unexpected excitation phenomena. This research project has shown that these phenomena are of two kinds, which are related to the charge-storage function of capacitance. In the space-clamped mode, capacitance can act as a battery; stimulus current can charge the membrane capacitance, which is capable of holding it voltage under certain circumstances. This occurs when regions of low channel density are present in the neural morphology; the local low charge leakage can control the dynamic range of impulse frequency generation. This is found specifically in retinal ganglion cells (as well as hippocampal neurons), where the distribution and density of channels on the dendrites becomes an important factor in impulse encoding, even when the dendrites themselves are incapable of supporting impulses on their membrane. Other specialized neural regions, specifically the impulse “trigger zone,” which operates with the highest electrically gated channel densities, also interact with their neighboring membranes to determine the rate of impulses on their membrane.

Another project involves neural excitation as a function of temperature in the squid axon membrane. Although the Hodgkin-Huxley model for the squid axon membrane is incapable of generating nerve impulses at mammalian temperatures, the mathematical structure of the Hodgkin- Huxley equations has nevertheless been the basis for their simulation throughout the last half-century at all physiological temperatures. This has been achieved by ad hoc adjustments to the equations. This research shows that the primary reason for the mammalian temperature failure of the Hodgkin-Huxley model lies in the magnitude of that model’s gating kinetic rate constants in the presence of membrane capacitance; in the absence of the capacitance, the model will generate impulses at all temperatures. Applying the Q10 factor of three to the temperature dependence of all rate constants narrows the impulse from 2.5 ms (6.3 °C) to 0.6 ms (38 °C) in the absence of the capacitative current; on the other hand, the impulse collapses for the same (and lesser) temperature shifts in the presence of capacitance. Phase space analysis shows that the repolarizing K-current overtakes the normally faster regenerative Nacurrent, because the rapid rate-of-rise of the Nacurrent is compromised by the necessarily accompanying large capacitative current, which is proportional to the rate-of-rise. The slower-recovering K-current is associated with a smaller time-rate of voltage change, and is therefore less affected by capacitative current. This research project has shown that phase space analysis offers the necessary adjustments to voltage-clamp data, which are typically contaminates by artifacts due to the difficulty of achieving the necessary space-clamp, effects that are most pronounced in simulations involving large time-rates of change.

The final project created a “sticky” model that simulates the primordial accreting process of continents and their associated tectonic plates. Buoyant “flakes” of hard materials are assumed to be persistently and randomly generated at isolated convective up-welling centers of the rocky Earth (mantle), and are driven horizontally and radially away from the up-welling centers (hotspots) on the upper surface of convection cells. These flakes accumulate and represent the growth of the continents and associated tectonic plates.