September 26, 2021
Networks of gene regulation govern morphogenesis, determine cell identity and regulate cell function. But we have little understanding, at the local level, of which logics are biologically preferred or even permitted. To solve this puzzle, we studied the consequences of a fundamental aspect of gene regulatory networks: genes and transcription factors talk to each other but not themselves. Remarkably, this bipartite structure severely restricts the number of logical dependencies that a gene can have on other genes. We developed a theory for the number of permitted logics for different regulatory building blocks of genes and transcription factors. We tested our predictions against a simulation of the 19 simplest building blocks, and found complete agreement. The restricted range of biological logics is a key insight into how information is processed at the genetic level. It constraints global network function and makes it easier to reverse engineer regulatory networks from observed behavior.
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Developing and maintaining life requires a lot of computation. This is done by gene regulatory networks. But we have little understanding of how this computation is organized. I show that there is a direct correspondence between the structural and functional building blocks of regulatory networks, which I call regulatory motifs. I derive a simple bound on the range of function that these motifs can perform, in terms of the local network structure. I prove that this range is a...
Identity, response to external stimuli, and spatial architecture of a living system are central topics of molecular biology. Presently, they are largely seen as a result of the interplay between a gene repertoire and the regulatory machinery of the cell. At the transcriptional level, the cis-regulatory regions establish sets of interdependencies between transcription factors and genes, including other transcription factors. These ``transcription networks'' are too large to be...
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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...
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Gene Regulatory Networks (GRNs) consisting of combinations of transcription factors (TFs) and their cis promoters are assumed to be sufficient to direct the development of organisms. Mutations in GRNs are assumed to be the primary drivers for the evolution of multicellular life. Here it is proven that neither of these assumptions is correct. They are inconsistent with fundamental principles of combinatorics of bounded encoded networks. It is shown there are inherent complexit...
In this paper, we conduct theoretical analyses on inferring the structure of gene regulatory networks. Depending on the experimental method and data type, the inference problem is classified into 20 different scenarios. For each scenario, we discuss the problem that with enough data, under what assumptions, what can be inferred about the structure. For scenarios that have been covered in the literature, we provide a brief review. For scenarios that have not been covered in li...
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A great part of the effort in the study of coarse grained models of transcription networks is directed to the analysis of their dynamical features. In this letter, we consider the \emph{equilibrium} properties of such systems, showing that the logic backbone underlying all dynamic descriptions has the structure of a computational optimization problem. It involves variables, which correspond to gene expression levels, and constraints, which describe the effect of \emph{cis-}re...
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Gene regulatory networks are powerful abstractions of biological systems. Since the advent of high-throughput measurement technologies in biology in the late 90s, reconstructing the structure of such networks has been a central computational problem in systems biology. While the problem is certainly not solved in its entirety, considerable progress has been made in the last two decades, with mature tools now available. This chapter aims to provide an introduction to the basic...
Genetic regulatory networks enable cells to respond to the changes in internal and external conditions by dynamically coordinating their gene expression profiles. Our ability to make quantitative measurements in these biochemical circuits has deepened our understanding of what kinds of computations genetic regulatory networks can perform and with what reliability. These advances have motivated researchers to look for connections between the architecture and function of geneti...
Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions -- lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to expe...
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