| 9-9:40 am |
Michael Brenner
Harvard University
Excitability constraints on voltage gated sodium channels
There are nine distinct mammalian genes encoding voltage gated sodium channels, many of which are more than 90% identical by sequence. This diversity could reflect redundancy or specialization. To distinguish between these possibilities we have collected functional data for various sodium channel properties from the literature. The data set uses 177 different sets of measurements from 41 distinct publications, including both wild type and mutant Na_v1.1-1.9, in human, mouse and rat, under a variety of different conditions. Analysis of the data set demonstrates strong quantitative distinctions between four independent groups of channels: (i) the channels (Na_v1.1,1.2,1.3,1.6,1.7), which are primarily expressed in nervous tissue; (ii) those expressed primarily in muscle (Na_v1.4,1.5); (iii) the channel Na_v1.8 and (iv) the channel Na_v1.9. Within each group there is a strong positive correlation between the voltage dependence of activation and that of inactivation. We present a theoretical analysis of the constraints on sodium channels arising from the requirements of excitability and the uniqueness of the resting potential. These constraints bound the allowed channel properties, in quantitative agreement with the dataset. Additionally they suggest potential explanations for the differences in the channel groupings: the difference between the channels expressed in nerve and muscle tissue suggests that the reversal potential for potassium ions in muscle is shifted by about -10mV compared to nervous tissue. The channel Na_v1.8 is distinguished by its potential for a substantially higher voltage threshold than the other channels. The channel Na_v1.9 can only produce action potentials in a narrow conductance range and even then has a maximum voltage threshold which is less than thermal fluctuations. The separation of the channels into functionally distinct groups suggests that they have evolved to perform specialized tasks.
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| 9:40-10:20 am |
Nancy Kopell
Boston University
Multiple Rhythms and Switches in the Nervous System
The nervous system produces dynamical activity at all times. This activity can be parsed into frequency ranges associated with different behavioral states. Two of the most important such ranges are the "theta" rhythm (4-12 Hz) and the "gamma" rhythm (30-90 Hz). This talk discusses the biophysical origins of the different rhythms, and their interaction. The two rhythms are shown to be based on different anatomical circuits with overlapping components. Dynamical systems ideas are used to show how the rhythms compete and coordinate.
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