On the lowest level, cells have to be described by the theory of nonlinear biochemical reaction networks (for an introductory overview, see this talk).

We suspect that the fundamental mechanisms of adaptive selforganization, driven by fluctuations and varying growth rates, already apply at this molecular level (see following talk). As a first step in this direction, we are analyzing the statistical properties of fluctuations in typical reaction networks.

Such networks usually involve reversible covalent modification of signaling molecules, such as protein phosphorylation. Under conditions of small molecule numbers, as is frequently the case in living cells, mass action theory fails to describe the dynamics of such systems. Instead, the biochemical reactions must be treated as stochastic processes that intrinsically generate concentration fluctuations of the chemicals.

In a recent study we have investigated the stochastic reaction kinetics of covalent modification cycles (CMCs) by analytical modeling and numerically exact Monte-Carlo simulation of the temporally fluctuating concentration.

Depending on the parameter regime, we have found for the probability density of the concentration qualitatively distinct classes of distribution functions, including power law distributions with a fractional and tunable exponent.

Beside extremely broad probability distributions, the intrinsic concentration fluctuations in biochemical reaction networks may also give rise to long-time correlations. The fractional powerlaw correlations observed in the spoantaneous cytoskeletal fluctuations might then be explained by the underlying biochemical reaction processes. We have explored some of these possibilities in a recent diploma thesis (German). Parts of it have been publihed as a poster.