Stochastic Dynamics

Noise in neurons is message-dependent

with M. Sigman, J-M. Alonso, L. Martinez, D. Chialvo and M. Magnasco

Go to the Neurobiology Page

Noise-induced memory in extended excitable media

with D. Chialvo and M. Magnasco

Go to the Neurobiology Page

We describe a form of memory exhibited by extended excitable systems driven by stochastic fluctuations. Under such conditions, the system self-organizes into a state characterized by power-law correlations thus retaining long-term memory of previous states. The exponents are robust and model-independent. We discuss novel implications of these results for the functioning of cortical neurons as well as for networks of neurons (Phys. Rev. E, 61(5), 5654-5658, May 2000).

(A): Hamming distance from initial sinusoidal pattern as a function of time. (B): Distance between two consecutives wavefronts as a function of noise.

Negative Resistance in Brownian Transport

with Marcelo Magnasco

We prove that negative incremental resistance cannot occur on 1D spaces like the circle or the line; we construct an explicit two-dimensional model on the cylinder, and its collapse into a branched 1D backbone. We derive an accurate numerical method for solving our 2D model, and discuss the relevance of the model to biological ion channels. Physical Review Letters 78 (11) 1968-1971 (1996).

Plot of particle current as a function of the applied force

For repints, go to Macelo's Page

Efficiency of DNA replication in the Polymerase Chain Reaction

with Gustavo Stolovitzky

We present a detailed kinetic model for the Polymerase Chain Reaction, and model the probability of replication in terms of the physical parameters of the problem. Applying the theory of branching processes, we show the existance of a new phenomenon affecting the probability distribution function of the number of replicants: for small number of initial molecules, the limiting behavior (with increasing number of cycles) of the pdf is represented by a multi-modal funtion. Proceedings of the National Academy of Sciences Volume 93, Number 23; Pages: 12947-12952, November 12, 1996.

Plot of the pdf of the number of molecules after 10 cycles for one initial molecule

Also, go to Gustavo's Page

A preprint is available.

Guillermo A. Cecchi
Center for Studies in Physics and Biology
The Rockefeller University
1230 York Avenue, Box 348
New York, NY10021