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, Delta p, 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 Delta p is proposed, suggesting that the cooperativity of real biological transitions is related to the coupling capacity Delta p of the present model.