Circuits with broken fibration symmetries perform core logic computations in biological networks

How intracellular and extracellular signals are integrated by transcription factors is essential for understanding complex cellular patterns at the population level. In this Letter, by using a synthetic genetic oscillator coupled to a quorum-sensing apparatus, we propose an experimentally feasible cis-regulatory module (CRM) which performs four possible logic operations (ANDN, ORN, NOR and NAND) of input signals. We show both numerically and theoretically that these different...

The effects of the finite size of the network on the evolutionary dynamics of a Boolean network are analyzed. In the model considered, Boolean networks evolve via a competition between nodes that punishes those in the majority. It is found that finite size networks evolve in a fundamentally different way than infinitely large networks do. The symmetry of the evolutionary dynamics of infinitely large networks that selects for canalizing Boolean functions is broken in the evolu...

It may be possible to discover much of the organization of synaptic connections in nervous systems by designing simple logic circuits that can perform a single, biologically advantageous function. This method has led to neuronal networks that can generate neural correlates of phenomena central to color vision, olfaction, short-term memory, and brain waves. One of the network designs is a family of general information processors that exhibit major features of cerebral cortex p...

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network th...

Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be determined. To understand these we investigate graph symmetries and search for such in the symmetrized versions of the forward and backward locomotive sub-networks of the Caenorhabditi elegans worm neuron network. The use of ordinarily differenti...

Structural and dynamical fingerprints of evolutionary optimization in biological networks are still unclear. We here analyze the dynamics of genetic regulatory networks responsible for the regulation of cell cycle and cell differentiation in three organisms or cell types each, and show that they obey a version of Hebb's rule which we term as coherence. More precisely, we find that simultaneously expressed genes with a common target are less likely to conflict at the attractor...

We quantify the influence of the topology of a transcriptional regulatory network on its ability to process environmental signals. By posing the problem in terms of information theory, we may do this without specifying the function performed by the network. Specifically, we study the maximum mutual information between the input (chemical) signal and the output (genetic) response attainable by the network in the context of an analytic model of particle number fluctuations. We ...

Current computers operate at enormous speeds of ~10^13 bits/s, but their principle of sequential logic operation has remained unchanged since the 1950s. Though our brain is much slower on a per-neuron base (~10^3 firings/s), it is capable of remarkable decision-making based on the collective operations of millions of neurons at a time in ever-evolving neural circuitry. Here we use molecular switches to build an assembly where each molecule communicates-like neurons-with many ...

Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's evolution. We, therefore, introduce a new modeling framework that describes the dynamics of networks composed of both oscillators and switches. Both oscillator synchronization and switch stability are preserved in these heterogeneous, couple...

Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behavior in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable, travelling-wave periodic solutions that are reachable, long-lived and robust to parameter changes. These solutions underlie ...