Fractional Cooperativity of a Few-State System in the Environment
Keywords:irreversible kinetic processes, energy fluctuations, dissipating environment, cooperativity, Hill’s coefficient, ligand-receptor assembly
Cooperativity represents a type of the not well-defined quantities implemented in different fields ranging from physics to chemistry, biology, informatics, etc. In the present work, we define the cooperativity from the physical point of view by relating it to the stability of a few-state system with respect to the irreversibility. First, we reduce this system evolving in time to the pair of fluctuating energy levels of different dimensionalities with the initial population of one level, different probabilities of microscopically reversible transitions between the levels, and some probability of irreversible decay of another level. Then we make an average of the reduced system over the energy level fluctuations to provide between-level transition rates with the explicit impacts of external controls on levels’ positions and dimensionalities. Finally, we demonstrate the emergence of the cooperativity of a fractional degree ranging between 2/e and unity when normalized in this system and observe that, at the lower bound of such degree, the system becomes unstable, so that, to restore the stability, one needs either to decrease the irreversible decay rate or to make the reversible backward transitions faster.
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