The Logic Backbone of a Transcription Network

Modelling gene regulatory networks not only requires a thorough understanding of the biological system depicted but also the ability to accurately represent this system from a mathematical perspective. Throughout this chapter, we aim to familiarise the reader with the biological processes and molecular factors at play in the process of gene expression regulation.We first describe the different interactions controlling each step of the expression process, from transcription to...

Central to the functioning of a living cell is its ability to control the readout or expression of information encoded in the genome. In many cases, a single transcription factor protein activates or represses the expression of many genes. As the concentration of the transcription factor varies, the target genes thus undergo correlated changes, and this redundancy limits the ability of the cell to transmit information about input signals. We explore how interactions among the...

Random Boolean networks have been used widely to explore aspects of gene regulatory networks. A modified form of the model through which to systematically explore the effects of increasing the number of gene states has previously been introduced. In this paper, these discrete dynamical networks are coevolved within coupled, rugged fitness landscapes to explore their behaviour. Results suggest the general properties of the Boolean model remain with higher valued logic regardle...

Biological phenomena differ significantly from physical phenomena. At the heart of this distinction is the fact that biological entities have computational abilities and thus they are inherently difficult to predict. This is the reason why simplified models that provide the minimal requirements for computation turn out to be very useful to study networks of many components. In this chapter, we briefly review the dynamical aspects of models of regulatory networks, discussing t...

We investigate the evolution of Boolean networks subject to a selective pressure which favors robustness against noise, as a model of evolved genetic regulatory systems. By mapping the evolutionary process into a statistical ensemble and minimizing its associated free energy, we find the structural properties which emerge as the selective pressure is increased and identify a phase transition from a random topology to a "segregated core" structure, where a smaller and more den...

In this paper, we propose a mean-field model which attempts to bridge the gap between random Boolean networks and more realistic stochastic modeling of genetic regulatory networks. The main idea of the model is to replace all regulatory interactions to any one gene with an average or effective interaction, which takes into account the repression and activation mechanisms. We find that depending on the set of regulatory parameters, the model exhibits rich nonlinear dynamics. T...

Due to the scarcity of quantitative details about biological phenomena, quantitative modeling in systems biology can be compromised, especially at the subcellular scale. One way to get around this is qualitative modeling because it requires few to no quantitative information. One of the most popular qualitative modeling approaches is the Boolean network formalism. However, Boolean models allow variables to take only two values, which can be too simplistic in some cases. The p...

The co-evolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of gene regulatory network. We find that a critical state emerges spontaneously resulting from interplay between topology and dynamics during the evolution. The final evolved state is shown to be independent of initial conditions. The network appears to be driven to a random Boolean network with uniform in-degree of two in the large network limit. Howev...

We show that logic computational circuits in gene regulatory networks arise from a fibration symmetry breaking in the network structure. From this idea we implement a constructive procedure that reveals a hierarchy of genetic circuits, ubiquitous across species, that are surprising analogues to the emblematic circuits of solid-state electronics: starting from the transistor and progressing to ring oscillators, current-mirror circuits to toggle switches and flip-flops. These c...

Interaction graphs provide an important qualitative modeling approach for System Biology. This paper presents a novel approach for construction of interaction graph with the help of Boolean function decomposition. Each decomposition part (Consisting of 2-bits) of the Boolean functions has some important significance. In the dynamics of a biological system, each variable or node is nothing but gene or protein. Their regulation has been explored in terms of interaction graphs w...