A stochastic model for the sigmoidal behaviour of cooperative biological systems

A stochastic model for cooperative transitions in biological systems based on a Markov chain is proposed. This model requires only two parameters, the mean probability, p, and the coupling capacity, Deltap, which measure the probability of forming a new weak bond depending on the number of similar bonds already formed and it is also responsible for the transition. In this paper we show how the model works for a large number of identical molecules and how it can be useful for studying the noise around the centre of the transition where, increasing the degree of cooperativity, i.e. the number n in the well-known Hill equation, the width of the noise increases along with its fractal dimension. A simple relationship between the degree of cooperativity and the parameter Deltap is proposed, suggesting that the cooperativity of real biological transitions is related to the coupling capacity Deltap of the present model.