Sequence-based model of gap gene regulatory network

Impact of Negative Feedbacks on De Novo Pyrimidines Biosynthesis in Escherichia coli

Earlier studies aimed at investigating the metabolism of endogenous nucleoside triphosphates in synchronous cultures of E. coli cells revealed an auto-oscillatory mode of functioning of the pyrimidine and purine nucleotide biosynthesis system, which the authors associated with the dynamics of cell division. Theoretically, this system has an intrinsic oscillatory potential, since the dynamics of its functioning are controlled through feedback mechanisms. The question of whether the nucleotide biosynthesis system has its own oscillatory circuit is still open. To address this issue, an integral mathematical model of pyrimidine biosynthesis was developed, taking into account all experimentally verified negative feedback in the regulation of enzymatic reactions, the data of which were obtained under in vitro conditions. Analysis of the dynamic modes of the model functioning has shown that in the pyrimidine biosynthesis system, both the steady-state and oscillatory functioning modes can be realized under certain sets of kinetic parameters that fit in the physiological boundaries of the investigated metabolic system. It has been demonstrated that the occurrence of the oscillatory nature of metabolite synthesis depended on the ratio of two parameters: the Hill coefficient, h_UMP1-the nonlinearity of the UMP effect on the activity of carbamoyl-phosphate synthetase, and the parameter r characterizing the contribution of the noncompetitive mechanism of UTP inhibition to the regulation of the enzymatic reaction of UMP phosphorylation. Thus, it has been theoretically shown that the E. coli pyrimidine biosynthesis system possesses its own oscillatory circuit whose oscillatory potential depends to a significant degree on the mechanism of regulation of UMP kinase activity.

Nonequilibrium model of short-range repression in gene transcription regulation

Transcription factors are proteins that regulate gene activity by activating or repressing gene transcription. A special class of transcriptional repressors operates via a short-range mechanism, making local DNA regions inaccessible to binding by activators, and thus providing an indirect repressive action on the target gene. This mechanism is commonly modeled assuming that repressors interact with DNA under thermodynamic equilibrium and neglecting some configurations of the gene regulatory region. We elaborate on a more general nonequilibrium model of short-range repression using the graph formalism for transitions between gene states, and we apply analytical calculations to compare it with the equilibrium model in terms of the repression strength and expression noise. In contrast to the equilibrium approach, the new model allows us to separate two basic mechanisms of short-range repression. The first mechanism is associated with the recruiting of factors that mediate chromatin condensation, and the second one concerns the blocking of factors that mediate chromatin loosening. The nonequilibrium model demonstrates better performance on previously published gene expression data obtained for transcription factors controlling Drosophila development, and furthermore it predicts that the first repression mechanism is the most favorable in this system. The presented approach can be scaled to larger gene networks and can be used to infer specific modes and parameters of transcriptional regulation from gene expression data.

Inferring Gene Regulatory Networks from Multiple Datasets

Gaussian process dynamical systems (GPDS) represent Bayesian nonparametric approaches to inference of nonlinear dynamical systems, and provide a principled framework for the learning of biological networks from multiple perturbed time series measurements of gene or protein expression. Such approaches are able to capture the full richness of complex ODE models, and can be scaled for inference in moderately large systems containing hundreds of genes. Related hierarchical approaches allow for inference from multiple datasets in which the underlying generative networks are assumed to have been rewired, either by context-dependent changes in network structure, evolutionary processes, or synthetic manipulation. These approaches can also be used to leverage experimentally determined network structures from one species into another where the network structure is unknown. Collectively, these methods provide a comprehensive and flexible platform for inference from a diverse range of data, with applications in systems and synthetic biology, as well as spatiotemporal modelling of embryo development. In this chapter we provide an overview of GPDS approaches and highlight their applications in the biological sciences, with accompanying tutorials available as a Jupyter notebook from https://github.com/cap76/GPDS .

Translating natural genetic variation to gene expression in a computational model of the Drosophila gap gene regulatory network

Annotating the genotype-phenotype relationship, and developing a proper quantitative description of the relationship, requires understanding the impact of natural genomic variation on gene expression. We apply a sequence-level model of gap gene expression in the early development of Drosophila to analyze single nucleotide polymorphisms (SNPs) in a panel of natural sequenced D. melanogaster lines. Using a thermodynamic modeling framework, we provide both analytical and computational descriptions of how single-nucleotide variants affect gene expression. The analysis reveals that the sequence variants increase (decrease) gene expression if located within binding sites of repressors (activators). We show that the sign of SNP influence (activation or repression) may change in time and space and elucidate the origin of this change in specific examples. The thermodynamic modeling approach predicts non-local and non-linear effects arising from SNPs, and combinations of SNPs, in individual fly genotypes. Simulation of individual fly genotypes using our model reveals that this non-linearity reduces to almost additive inputs from multiple SNPs. Further, we see signatures of the action of purifying selection in the gap gene regulatory regions. To infer the specific targets of purifying selection, we analyze the patterns of polymorphism in the data at two phenotypic levels: the strengths of binding and expression. We find that combinations of SNPs show evidence of being under selective pressure, while individual SNPs do not. The model predicts that SNPs appear to accumulate in the genotypes of the natural population in a way biased towards small increases in activating action on the expression pattern. Taken together, these results provide a systems-level view of how genetic variation translates to the level of gene regulatory networks via combinatorial SNP effects.

In silico evolution of the Drosophila gap gene regulatory sequence under elevated mutational pressure

BACKGROUND

Cis-regulatory sequences are often composed of many low-affinity transcription factor binding sites (TFBSs). Determining the evolutionary and functional importance of regulatory sequence composition is impeded without a detailed knowledge of the genotype-phenotype map.

RESULTS

We simulate the evolution of regulatory sequences involved in Drosophila melanogaster embryo segmentation during early development. Natural selection evaluates gene expression dynamics produced by a computational model of the developmental network. We observe a dramatic decrease in the total number of transcription factor binding sites through the course of evolution. Despite a decrease in average sequence binding energies through time, the regulatory sequences tend towards organisations containing increased high affinity transcription factor binding sites. Additionally, the binding energies of separate sequence segments demonstrate ubiquitous mutual correlations through time. Fewer than 10% of initial TFBSs are maintained throughout the entire simulation, deemed 'core' sites. These sites have increased functional importance as assessed under wild-type conditions and their binding energy distributions are highly conserved. Furthermore, TFBSs within close proximity of core sites exhibit increased longevity, reflecting functional regulatory interactions with core sites.

CONCLUSION

In response to elevated mutational pressure, evolution tends to sample regulatory sequence organisations with fewer, albeit on average, stronger functional transcription factor binding sites. These organisations are also shaped by the regulatory interactions among core binding sites with sites in their local vicinity.

Analysis of functional importance of binding sites in the Drosophila gap gene network model

BACKGROUND

The statistical thermodynamics based approach provides a promising framework for construction of the genotype-phenotype map in many biological systems. Among important aspects of a good model connecting the DNA sequence information with that of a molecular phenotype (gene expression) is the selection of regulatory interactions and relevant transcription factor bindings sites. As the model may predict different levels of the functional importance of specific binding sites in different genomic and regulatory contexts, it is essential to formulate and study such models under different modeling assumptions.

RESULTS

We elaborate a two-layer model for the Drosophila gap gene network and include in the model a combined set of transcription factor binding sites and concentration dependent regulatory interaction between gap genes hunchback and Kruppel. We show that the new variants of the model are more consistent in terms of gene expression predictions for various genetic constructs in comparison to previous work. We quantify the functional importance of binding sites by calculating their impact on gene expression in the model and calculate how these impacts correlate across all sites under different modeling assumptions.

CONCLUSIONS

The assumption about the dual interaction between hb and Kr leads to the most consistent modeling results, but, on the other hand, may obscure existence of indirect interactions between binding sites in regulatory regions of distinct genes. The analysis confirms the previously formulated regulation concept of many weak binding sites working in concert. The model predicts a more or less uniform distribution of functionally important binding sites over the sets of experimentally characterized regulatory modules and other open chromatin domains.