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

Abstract

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 canonical variants serve fundamental operations of synchronization and clocks (in their symmetric states) and memory storage (in their broken symmetry states). These conclusions introduce a theoretically principled strategy to search for computational building blocks in biological networks, and present a systematic route to design synthetic biological circuits.

Predicting synchronized gene coexpression patterns from fibration symmetries in gene regulatory networks in bacteria

“…Other solution with partial or no synchrony at all may exist and it's parameters of the system, activation function and initial conditions that determine which solutions can be realized. Numerical solutions of the dynamical evolution of the fibers studied here and performed in [22] indicate that for the particular type of interaction fibers found in genetic networks are stable and have a very big basin of attraction, therefore creating the dynamics basically indifferent to the initial conditions.…”

“…The fibers represent the functional set of synchronized genes in the TRN. For the TRNs of E. coli and B. subtilis and other species, we have previously organized the different types of observed fibers into a hierarchy, reflecting the different complexity of the topological features of their input trees [20,22]. This hierarchy identifies a broad range of fibers in E. coli (91 fibers) and B. subtilis (216 fibers).…”

“…In this paper, we first review the fibers found in the TRNs of E. coli and B. subtilis studied in [20,22] and then organize this rich set of fibers into a well-defined hierarchy. At the most simple and trivial level in this hierarchy, we find the known structures of operons and regulons that trivially lead to synchronization.…”

“…In a series of recent papers, we showed that symmetry principles applied to biology networks [20][21][22] can explain the synchronization in gene coexpression profiles. We have found structural symmetries in biological networks, described by the concept of symmetry fibrations [20], that provide a principled way to define building blocks of genetic networks supporting synchronized gene expression.…”

“…In the case of TRNs, fibration symmetries can reveal meaningful building blocks in regulatory networks [20,22]. In contrast to network motifs, which can only be found by their frequent occurrence, gene fibrations can find such circuits based on their symmetry properties even if these circuits are large and appear only once in the network.…”