User:J. C. Martinez-Garcia/Notebook/HMS Activities/2008/09/18
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Today I continued with the study concerning the modeling of the hysteretical behavior in term of the Dahl's dynamical friction model. The model no captures the essential behavior of the observed phenomenon (in qualitative terms), and can be then used in order to argue about the underlying nature of the dynamical behavior observed experimentally in the AKT reduced signaling pathway. However, since the Dahlmodel depends on the change of the variable representing the velocity of the the sliding mass, it is difficult to argue about the associated dominancy of the negative feedback loop when the sign of the velocity changes from positive to negative, since a negative sign of the velocity let to interpet the friction model as a positive feedback loop. I think that the model can be useful being careful when writing about the underlying nature of the hysteretical observed behavior. I also for differential equation used directly to model hysteresis and I found a very interesting paper: Ordinary Differential Systems Describing Hysteresis Effects and Numerical Simulations, by E. Minchev et al. (http://www.hindawi.com/GetArticle.aspx?doi=10.1155/S108533750220603X). This paper provides models which can present clockwise or counterclockwise hysteresis depending on the choice of some parameters and initial conditions. I think that I will review this paper only if necessary. I though also about the possibility to write a paper concerning only the hysteresis effect on biomolecular systems, and it such case a general mathematical framework could be useful.
When writing about rules-based modeling techniques (of molecular systems), I read something about stochastic simulation and the Gillespie algorithm. I would like to know if the algorithm used in kappa Factory is a discrete time implementation if this algorithm. I think the best thing to do is to ask to the people involved in the creation of Kappa Factory. Maybe Vincent Danos (I think his email is Vincent.Danos@pps.jussieu.fr).
A proposal for Walter Fontana
I think that I can propose something to Walter. maybe a small project on evolution (I must look for the lambda calculus) and also somthing about the appliaction of Kappa Factory to this kind of research problems. To be continued...