Models of Biological Transport in Ionic Channels

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Jerome 9704458 The investigator develops, analyzes, and computes with models of biological transport for ionic channels. Ionic channels are now known to mediate significant electrical activity through cellular membranes. The discovery of the patch clamp has made experimental verification of such electrical currents possible. Theoretical predictions proceed through a hierarchy of models. For the simpler models, categorization of possible behavior is sought, and the dynamics carefully studied. In particular, gating is analyzed in great detail; this includes both regular and anomalous behavior. An understanding of the relation of the channel to its ambient environment is achieved through the calculation of the heat exchange of the protein. In addition, a complex asymptotic procedure yields a high field model, particularly appropriate for channels, yet originally developed for semiconductors. This proposal benefits from the investigators' previous experience in semiconductor modeling. The common thread of electro-diffusion leads to mathematical models of surprising similarity. This analogy has facilitated some interesting studies, as well as some provocative conjectures. One of these deals with the role of temperature in channels. Another deals with so-called active transport, and the association with the molecule ATP. Ionic channels are protein molecules in cell membranes, and have been linked to such diverse applications as drug receptors on the one hand, and irregular gating in the brain and mental illness on the other hand. The investigator and colleagues in mathematics and biology model the electrical and energetic activity of channels. The project greatly benefits from the similarity in the mathematical models developed for both ionic channels and semiconductor devices. Whereas electrical currents are induced by ions in channels, a similar role is played by electrons and holes in semiconductors. Powerful electric fields coexist with int ense biological activity in the channel pore. The principal investigator and his colleagues study these analogies, as well as separate issues of biological import, including the possibility of explaining, in mathematical terms, the pulses associated with the opening and closing of channels and the energetics associated with active transport, including the action of various ion "pumps." The work aims to clarify details surrounding energy exchange, heating, and temperature variation. The project uses both mathematical analysis and extensive computer simulations.