X-Message-Number: 26125 From: Date: Tue, 3 May 2005 07:45:12 EDT Subject: Uploading technology (2.i.1) How many currents? Uploading technology (2.i.1) How many currents? In the Hodgkin-Huxley (HH) model, based on the action potential propagation in the squid giant axon, there was three currents: One capacitive in the membrane and two ionic in the axon core, one produced by the Na+ ions and the other by the potassium K+ ion species. The Rose-Hindmarsh use only two coupled differential equations, and not 4 as the HH case. A better fit is produced with an extended model using 3 equations. The problem is with the number of currents the model must take into account. For example, Ca++ ions have no great electric effects, they are not very numerous, but they have a very large chemical action at many level. So they must be taken into account. Even for a single ion, for example K+, there are different channels, each with its own permeability, response time, closing property and so on. That produce different currents with some non-trivial aspects. For example, a neural network, having a short and a long duration currents in a single post synaptic dendrite spine head, may generate a very complex patern of oscillations with cyclic behaviors. (1) Studies of the bullfrog sympathetic ganglion cells have revealed 7 currents: 1- A fast sodium current, 2- A fast calcium current, 3- A transient outward potassium one, 4-A non-inactivating muscarinic potassium one, 5- A delayed rectifying pottassium one, 6- A non-inactivating calcium dependent pottassium one, and: 7- A voltage dependent, calcium dependent, potassium current. (2) When Rose and Hindmarsh studied the thalamic neuron, they started with their 3 dimensional model, but then was forced to extend it to seven dimensions: That is, one "dimension" or independent differential equation for each of the above current (3). This is not even the limit, mammalian neuron have at least 10 well defined currents. In the past years, there has been an explosion in the current number. The question is: Have they any information value? each variation in a protein receptor or channel gate can produce a new different current. May be these variant proteins do no harm and have been produced by random mutation without any constrain to eliminate them. So they remain, even if they are not useful. Another case is provided by mutated channels with different sensibility to pathogen toxins. A toxin could be evolved to block a definite channel, but it could not do it for many related protein channels. This would be interesting as a way to resist some pathogens. It is clear that such biological adaptation have no interest in the frame field of uploading electronics circuits. The really useful neuron currents are in the 10 - 12 range, this is a rather large number. There is then a need for as much coupled differential equations. As seen before, a first way to reduce the computing load is to broke them into two classes: the fast and the slow. The fast bolck being worked out in FPGAs and the slow one in a computer. Some currents, particularly those omplying Ca++ have mostly a chemical action, they can be handled at the programming level. For example if they trigger a chemical change implied in memory (creation of more fiber at presynaptic terminal, production or activation of dendrite spines), the effect may be taken into account by doing the adaptation job without current simulation. This is a difference between research simulation to understand the neuron working processes and the uploading aimed simulation. The useful currents seem to split nearly evenly between fast and slow, so there would be 5 - 6 currents in both, the FPGA and the computer. Most "software taken into account" currents are on the slow side, so the computer could have only 3 - 4 currents to simulate. For fast ones, many are rather simple as the membrane capacitive one and can be worked out from a memory table: They are computed one time to fill the table and then when used only the table result are looked after, the retrived value is then compounded with a probability fuction before use. (1) Kleinfeld, D., Sompolinsky, H., (1989) in: Methods in Neuronal Modeling, ch.7. Koch C., Segev I. ed. MIT Press. (2) Yamada, W., et al, (1988) in Soc. Neurosci. Abst. vol.14: p. 118.119. (3) Rose, R. M., and Hindmarsh, J. L. (1989) in : Proc. R. Soc. London Ser. B vol. 237, p. 267 to 334 (3 papers) Yvan Bozzonetti. Content-Type: text/html; charset="US-ASCII" [ AUTOMATICALLY SKIPPING HTML ENCODING! ] Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=26125