Fluctuations and noise in kinetic systems III. Cycling steady-state models

Abstract

The noise and fluctuations due to chemical reactions are considered for steady-state kinetic systems in which the Wegscheider relations are not obeyed (i.e. the systems are at a cycling steady state). We derive the noise power density spectrum in the quantity N = ∑ i = 0 x a i N i for an esemble of independent and equivalent systems each of which can exist in a set of discrete states i = 0, 1, 2, …, x. Ni is the number of systems of the ensemble in state i and ai's are constants. The transitions between two arbitrary states (i → j) are linear. The derived noise power spectrum is explicitly expressed as a function of the kinetic rate constants so that numerical calculations can easily be carried out for an arbitrary cycling steady-state model. This extends the derivations in two previous papers of this series in which only non-cycling models were discussed in detail. There are possible applications to optical pumping, photo adsorption-desorption reaction, active membrane transport, muscle contraction, etc. In each case, noise measurements would provide information about the kinetic scheme. Possible applications in biological systems in vivo are discussed in particular.