X-Message-Number: 26029
Date: Fri, 15 Apr 2005 14:12:31 EDT
Subject: Uploading (2.Vi.0) Markov

Uploading (2.Vi.0) Markov.
Here I explore a possibility with a stochastic model, namely the Markov 
chain. Assume we have a protein complex, may be able to bind one or more 

subassemblies or ion. The simplest case is one initial state A and one final 
state B. In 
each small time interval dT there is some probablity P(A,B) for a molecule in 
state A to  shift to B. In the same way, a molecule in state B may revert to 
A with a probability P (B,A). These probabilities rest on the nature of the 
molecule and the environment, nothing from an anterior state has any effect on 
them. For example, a molecule in state A could be there for tens of time 
intervals dT or just one, the probability to go to B would be the same. Such a 
system has no memory.
A simple ionic channel could have many intermediate states, may be half a 

dozen or more(1). The simplest interesting case is : A goes to B and B to either
C or D. C may goes back to B or link to D. To be sure, there are back 

probabilities from B to A for example. How is this process implemented on a 
Assume the probability A to B, P(A,B) is 30 percent or .3 in the time domain 
dT. Implicit in this statement is the probability P(A,A) = .7. P(A,A) is the 
probability that the system remains in state A. The sum of all probabilities 

must be 1, indeed here P(A,B) + P(A,A) = 1. In a simulation, the computer draw a
random number between 0 and 1, if this number is smaller or equal to .3 the 

state moves from A to B, if the number is larger than .3, P(A,A) is selected and
nothing happen.
If B can evolve back to A, stay the same or move to C or D, each probability 
will get a slice between 0 and 1 and their sum will be 1 as before. This 
system is computer intensive, because an array of states and probabilities is 
ascribed to each molecular complex.
This is one more tool in the mathematical modeling box, now assume we want to 
simulate a small unbranched dendrite section, what are the possibilities ?
The first possibility would be to use the cable theory, a differential class 
model. Depending on the boundaries limit conditions, one or another chunk of 
the cable equation will be used, this is a grammar model. Next is the Hodgkin 
and Huxley differential model or best an advanced simplified by-product: the 
Hindmarsh-Rose model. Next could be a simplified Markov model of the 20 to 40 

channels in the membrane as a stochastic supplement to the differential element,
we are here in the Langevin's domain. One step beyond, the full Markov model 
would be used. This is the stochastic domain, a taste of it can be found with 
StochSim at: http://www.anat.cam.ac.uk/~comp-cell//StochSim.html for 

downloading it see: ftp://ftp.cds.caltech.edu/pub/dbray/. Finally, everything 
could be 
modeled at the molecular dynamics scale. What to choose for uploading ? The 
surprising answer may be: All of them.
The molecular Dynamics could be used to validate the probability tables of 
the full Markov models. These would be used to find simplified but relevant 
models. Used with the Hindmarsh-Rose model, a set of generic dendrite segment 

could be computed. the same would be done with cable theory, so that a 
factor would be established. In a given neuron, a segment would be computed 
may be with the cable theory and then corrected by looking in a table to the 
nearest similar predefined segments.
There may be trillions of dendrite segments in a brain, but only some 

millions at most are different. This is not a new solution: There are billions 
people on Earth and only twenty shoe sizes or so.

(1)Sakmann, B., and Neher, E., (eds) (1995). Single-Channel Recording, 2nd 
ed. Plenum Press,New-York.

Yvan Bozzonetti.

 Content-Type: text/html; charset="US-ASCII"


Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=26029