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In genetic networks, information of relevance to the organism is represented by the concentrations of transcription factor molecules. In order to extract this information the cell must effectively measure these concentrations, but there are physical limits to the precision of these measurements. We explore this trading between bits of precision in measuring concentration and bits of relevant information that can be extracted, using the gap gene network in the early fly embryo as an example. We argue that cells in the embryo can extract all the available information about their position, but only if the concentration measurements approach the physical limits to information capacity. These limits necessitate the observed proliferation of enhancer elements with sensitivities to combinations of transcription factors, but fine tuning of the parameters of these multiple enhancers is not required.
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Gene expression levels carry information about signals that have functional significance for the organism. Using the gap gene network in the fruit fly embryo as an example, we show how this information can be decoded, building a dictionary that translates expression levels into a map of implied positions. The optimal decoder makes use of graded variations in absolute expression level, resulting in positional estimates that are precise to ~1% of the embryos length. We test this optimal decoder by analyzing gap gene expression in embryos lacking some of the primary maternal inputs to the network. The resulting maps are distorted, and these distortions predict, with no free parameters, the positions of expression stripes for the pair-rule genes in the mutant embryos.
The genetic regulatory network (GRN) plays a key role in controlling the response of the cell to changes in the environment. Although the structure of GRNs has been the subject of many studies, their large scale structure in the light of feedbacks from the metabolic network (MN) has received relatively little attention. Here we study the causal structure of the GRNs, namely the chain of influence of one component on the other, taking into account feedback from the MN. First we consider the GRNs of E. coli and B. subtilis without feedback from MN and illustrate their causal structure. Next we augment the GRNs with feedback from their respective MNs by including (a) links from genes coding for enzymes to metabolites produced or consumed in reactions catalyzed by those enzymes and (b) links from metabolites to genes coding for transcription factors whose transcriptional activity the metabolites alter by binding to them. We find that the inclusion of feedback from MN into GRN significantly affects its causal structure, in particular the number of levels and relative positions of nodes in the hierarchy, and the number and size of the strongly connected components (SCCs). We then study the functional significance of the SCCs. For this we identify condition specific feedbacks from the MN into the GRN by retaining only those enzymes that are essential for growth in specific environmental conditions simulated via the technique of flux balance analysis (FBA). We find that the SCCs of the GRN augmented by these feedbacks can be ascribed specific functional roles in the organism. Our algorithmic approach thus reveals relatively autonomous subsystems with specific functionality, or regulatory modules in the organism. This automated approach could be useful in identifying biologically relevant modules in other organisms for which network data is available, but whose biology is less well studied.
The phenotype of any organism on earth is, in large part, the consequence of interplay between numerous gene products encoded in the genome, and such interplay between gene products affects the evolutionary fate of the genome itself through the resulting phenotype. In this regard, contemporary genomes can be used as molecular records that reveal associations of various genes working in their natural lifestyles. By analyzing thousands of orthologs across ~600 bacterial species, we constructed a map of gene-gene co-occurrence across much of the sequenced biome. If genes preferentially co-occur in the same organisms, they were called herein correlogs; in the opposite case, called anti-correlogs. To quantify correlogy and anti-correlogy, we alleviated the contribution of indirect correlations between genes by adapting ideas developed for reverse engineering of transcriptional regulatory networks. Resultant correlogous associations are highly enriched for physically interacting proteins and for co-expressed transcripts, clearly differentiating a subgroup of functionally-obligatory protein interactions from conditional or transient interactions. Other biochemical and phylogenetic properties were also found to be reflected in correlogous and anti-correlogous relationships. Additionally, our study elucidates the global organization of the gene association map, in which various modules of correlogous genes are strikingly interconnected by anti-correlogous crosstalk between the modules. We then demonstrate the effectiveness of such associations along different domains of life and environmental microbial communities. These phylogenetic profiling approaches infer functional coupling of genes regardless of mechanistic details, and may be useful to guide exogenous gene import in synthetic biology.
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new links, allowing for the possibility that input and output links from a newly created node may have different probabilities of survival. We find some counterintuitive trends as parameters are varied, including the broadening of indegree distribution when the probability for retaining input links is decreased. We also find that both the scaling of transcription factors with genome size and the measured degree distributions for genes in yeast can be reproduced by the growth algorithm if and only if a special seed is used to initiate the process.
The evolution of the genome has led to very sophisticated and complex regulation. Because of the abundance of non-coding RNA (ncRNA) in the cell, different species will promiscuously associate with each other, suggesting collective dynamics similar to artificial neural networks. Here we present a simple mechanism allowing ncRNA to perform computations equivalent to neural network algorithms such as Boltzmann machines and the Hopfield model. The quantities analogous to the neural couplings are the equilibrium constants between different RNA species. The relatively rapid equilibration of RNA binding and unbinding is regulated by a slower process that degrades and creates new RNA. The model requires that the creation rate for each species be an increasing function of the ratio of total to unbound RNA. Similar mechanisms have already been found to exist experimentally for ncRNA regulation. With the overall concentration of RNA regulated, equilibrium constants can be chosen to store many different patterns, or many different input-output relations. The network is also quite insensitive to random mutations in equilibrium constants. Therefore one expects that this kind of mechanism will have a much higher mutation rate than ones typically regarded as being under evolutionary constraint.
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