Feed-forward loops and diamond motifs lead to tunable transmission of information in the frequency domain.

Using a Gaussian model, we study the transmission of time-varying biochemical signals through feed-forward motifs and diamond motifs. To this end, we compute the frequency dependence of the gain, the noise, as well as their ratio, the gain-to-noise ratio, which measures how reliably a network transmits signals at different frequencies. We find that both coherent and incoherent feed-forward motifs can either act as low-pass or high-pass filters for information: The frequency dependence of the gain-to-noise ratio increases or decreases with increasing frequency, respectively. Our analysis of diamond motifs reveals that cooperative activation of the output component can increase the gain-to-noise ratio. This means that from the perspective of information transmission, it can be beneficial to split the input signal in two and recombine the two propagated signals at the output. Cooperative activation can be implemented via the formation of homo- or heteromultimers that then bind and activate the output component or via the binding of individual molecules of the intermediate species to the output component.

Mesoscopic statistical properties of multistep enzyme-mediated reactions.

Enzyme-mediated reactions may proceed through multiple intermediate conformational states before creating a final product molecule, and one often wishes to identify such intermediate structures from observations of the product creation. In this study, the authors address this problem by solving the chemical master equations for various enzymatic reactions. A perturbation theory analogous to that used in quantum mechanics allows the determination of the first (n) and the second (σ2) cumulants of the distribution of created product molecules as a function of the substrate concentration and the kinetic rates of the intermediate processes. The mean product flux V=d(n)/dt (or 'dose-response' curve) and the Fano factor F= σ2/(n) are both realistically measurable quantities, and whereas the mean flux can often appear the same for different reaction types, the Fano factor can be quite different. This suggests both qualitative and quantitative ways to discriminate between different reaction schemes, and the authors explore this possibility in the context of four sample multistep enzymatic reactions. Measuring both the mean flux and the Fano factor can not only discriminate between reaction types, but can also provide some detailed information about the internal, unobserved kinetic rates, and this can be done without measuring single-molecule transition events.