Information- and Communication Theory in Molecular Biology by Martin Bossert

Author:Martin Bossert
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Further, we showed that a small subset of input nodes determines the states of most other network parts. To identify these nodes, a notion that quantifies the determinative power of an input variable over state variables in the network is needed. We argue that the mutual information (MI) between a subset of the inputs of node i and the function associated with node i quantifies the determinative power of this subset of inputs over node i. To study the relation of determinative power to sensitivity to perturbations, we related the MI to measures of perturbations, such as the influence of a variable in terms of inequalities. This result shows that, maybe surprisingly, an input that has large influence does not necessarily have large determinative power.

The main tool for this analysis is the Fourier analysis of Boolean functions. Whether a function is sensitive to perturbations or not, and which are the determinative inputs, depends on which coefficients the Fourier weight is concentrated. We derived a relation between the influence and MI for unate functions.

The above-mentioned properties give hints to design principles of transcriptional networks. Further, a low average sensitivity increases the robustness of the network. Most mutations will have no effect in most situations. This allows a bacterial population to explore a large set of mutations without a decrease in fitness.

In the application for the first funding period we stated that we will not only consider networks with random inputs but Boolean networks with a random structure. However, the above results were very compromising and we do not expect many new findings leading to the overall project goal, when investigating above properties of random networks. Hence, we restricted ourselves on the original regulatory network.

Properties of Canalizing and Nested Canalizing Networks

In this phase, we performed general investigations of the adaptivity, evolvability, and robustness of networks consisting of canalizing (CF) and nested canalizing functions (NCF) as we showed that the Boolean model of the regulatory network of E. coli mainly contains such functions (Klotz et al. 2013b).

It has been shown that NCFs have a stabilizing effect on the network dynamics (robustness) (Kauffman et al. 2004) and it is well known that the average sensitivity plays a central role for the stability of (random) Boolean networks (Schober and Bossert 2007). In Li et al. (2013) it was conjectured by authors that the average sensitivity of NCFs is smaller than . In Klotz et al. (2013c) we proved this (tight) upper bound using Fourier analytical techniques and gave further results dependent of the number of relevant input variables. This shows that a large number of functions appearing in biological networks belong to a class that has low average sensitivity, which is even close to a tight lower bound, and hence, that they have a high robustness against small disturbances, such as mutation.

However, a high robustness may also imply that the network has poor information processing abilities (adaptivity), as can be for example seen at a network with only constant functions. Hence, we investigated the mutual information of CF.

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