Controlling cooperativity of a metastable open system coupled weakly to a noisy environment

The notion of cooperativity comprises a specific characteristic of a multipartite system concerning its ability to demonstrate a sigmoidal-type response of varying sensitivities to input stimuli in transitions between states under controlled conditions.From a statistical physics viewpoint,in this work we attempt to describe the cooperativity by the stability of a metastable open system with respect to irreversibility.To treat the evolution of a system weakly coupled to the environment in a kinetic framework,we consider two fluctuating energy levels of different dimensionalities,initial population of one level,reversible transitions of population between the levels,and irreversible depopulation of another level.An average is made over level fluctuations and environment vibrations so that an inter-level transition rate can be obtained accounting for the influences of external control on level position and dimensionality.It is found that the cooperativity of the two-level system is bounded approximately between 0.736 and unity,with the lower bound indicating worsening system stability.