Correlation function, response function and effective temperature of gene networks

For general Markov chains, especially non-equilibrium biological systems, we proposed a new formalism for response functions, as well as new algebraic equations for power spectra of correlation functions, response functions and effective temperatures. An analytical expression of a constant effective temperature in high frequency limit is given. We applied the formalism to self-regulators. In the non-adiabatic limit, the time scale of the response function is very different to that of the correlation function. It is also shown that the self-regulators with high (low) binding/unbinding rate can transfer more energy to high (low) frequency environmental fluctuating modes coupled to the system.