X-Message-Number: 26855 From: Date: Sat, 20 Aug 2005 15:04:19 EDT Subject: Uploading technology (1.iii.1) The presynaptic simulation. Uploading technology (1.iii.1) The presynaptic simulation. The branching axon end into un number of presynaptic buttons. Here, the action potential is translated into one or more neurotransmitters. In most case, there is only one "classical" transmitter for excitatory synapses and two or more for inhibitory ones. The general working is that the action potential produce a membrane depolarization at the button level, this open up some ion channels producing an influx of Ca++ ions. These activate a chain of protein conformational change ending into the fusion with the cell membrane of vesicles loaded with something as 3,000 neuromediator molecules. On the presynaptic button, there are a number of Vesicle Release Site : VRS. At most it seems there are 7 VRS. For inhibitory presynaptic buttons, there are two vesicle kinds : The small and large ones. The small ones contain only the main neuromediator and are released by "ordinary" action potentials. The large ones are loaded with a mix of the main neuromediator and another one, in most case a polypeptide. This second messenger is a modulator of the action of the first.. Large vesicle are released by long action potential or repetitive neuron firing. At each vesicle fusion site, the action potential acts in a probabilistic way. There may be for example a 7% probability release at each site, giving a global propability of 56% for at least one vesicle release if there are 7 sites. This global probability is defined as P. Depending on the number and kind of ion channel activated, there may be some catalytic effect on the outcome of an action potential comming after one or more in a given time. It would be very difficult to simulate these ionic currents in an electronics device. The global effects can be reproduced by six exponential functions acting on the probability P : 1/ F1 : The facilitation 1 boost the probability with a decay time near 50 ms. That is, if an action potential produce a x 2 advantage for the next after 0 second (100% increase), this will be reduced, if that second AP comes after 50 milliseconds, to 1/e or near 36%. 2/ F2 : There is another facilitation with a decay time near 300 ms. 3/ A : after that, there is an augmentation with decay time in the 7 - 10 seconds range. 4/ Pot : Finally, there is the potentiation with decay time in the tens of minutes. 5/ Ds : These can be counteracted by the short time depression with seconds to minutes time constant. 6/ Dl : Or the long time depression with a time constant similar to the potentiation one. For each function three parameters must be provided : 1/ The increment after each action potential. 2/ The decay time constant. 3/ A multiplicative parameter of the decay exponential. Not all neurons display these six functions, so there must be a mask giving the active ones for a given neuron. The action potential is received as a two bits "word". 00 for no AP. 01 for "ordinary" (short) AP. 10 and 11 long APs. The long APs produce an instantaneous and punctual probability amplification. Depending on the AP, a compressed train of 01, a 10 or a 11 AP, there will be different amplification values mult-P with release of a second messenger for 10 and 11 in inhibitory synapses. The probability P may be seen as a product : P = P0 x (P1 + P2 + ... + P6). P0 is the basic probability of neurotransmitter release when there is an action potential of the 01 kind. P1,...,P6 are the added probability linked to facilitations, amplification, and so on. Now, not all release sites may start with the same P0, There may be two or three values, for example : 10%, 2% and 0%. The 10% ones would handle most of the 01 AP, when there is a high frequency firing, mult-P would act mostly on the 2% batch and the 0% lot would be activated only if there is a 10 or 11 AP. If the P value remains well above or under P0 for a long time, long, as counted in units of F1,F2,... decay, then P0 may be readjusted. There must be a computing parameter L, an adjust constant Alpha and a threshold T for each of the F1, F2,...,Dl. This may be a form of long term potentiation, even if most LTP effects come from the dendritic level. When a neuron fire an action potential, a part of it may back propagate in a subsample of the dendritic tree. There is a possible effect from the postsynaptic back potential to the presynaptic potential. An AP may then be amplified by the back potential comming at the same time. This cooperative effect would be an implementation of the Ebbian rule : Neurons that fire toghether get stronger links. Here, the back propagation facilitated 01 AP could look and work as a 10 or 11 AP, driving P well above its normal value. After some time, that would produce a P0 readjustment. Here I add two reflexions : First, in preceeding messages of the "2" kind, I have described the basic mathematical tools used to simulate neurons. There detailled simulations at the currents or molecular level give a model such the exponential decay of facilitation or the multiplicative consequence of long action potential. The full mathematical setting is no more used on the practical electronics neuron when there is such a model. Second, even the simplified result to be implemented in electronics is far more complexe and versatile than the first neuron idea from McCulloch and W.Pitts. One neuron is not a simple logic gate, it is a full microprocessor, even if its "technology" is far from the present day microprocessors powering a personnal computer. Yvan Bozzonetti. 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