Drivers of structural features in gene regulatory networks: From biophysical constraints to biological function

Stability of Pattern Formation in Systems with Dynamic Source Regions

We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with a step-function production term, we identify the phase transition between low-precision indeterminate patterning and the phase in which a traveling, well-defined contact zone between two domains is formed. Our model analytically explains single- and two-gene domain dynamics and provides pattern stability conditions for all possible two-gene regulatory network motifs.

Scaling of intrinsic noise in an autocratic reaction network

Biochemical reactions in living cells often produce stochastic trajectories due to the fluctuations of the finite number of the macromolecular species present inside the cell. A significant number of computational and theoretical studies have previously investigated stochasticity in small regulatory networks to understand its origin and regulation. At the systems level regulatory networks have been determined to be hierarchical resembling social networks. In order to determine the stochasticity in networks with hierarchical architecture, here we computationally investigated intrinsic noise in an autocratic reaction network in which only the upstream regulators regulate the downstream regulators. We studied the effects of the qualitative and quantitative nature of regulatory interactions on the stochasticity in the network. We established an unconventional scaling of noise with average abundance in which the noise passes through a minimum indicating that the network can be noisy both in the low and high abundance regimes. We determined that the bursty kinetics of the trajectories are responsible for such scaling. The scaling of noise remains intact for a mixed network that includes democratic subnetworks within the autocratic network.

Gene Regulatory Network Inference: Connecting Plant Biology and Mathematical Modeling

Plant responses to environmental and intrinsic signals are tightly controlled by multiple transcription factors (TFs). These TFs and their regulatory connections form gene regulatory networks (GRNs), which provide a blueprint of the transcriptional regulations underlying plant development and environmental responses. This review provides examples of experimental methodologies commonly used to identify regulatory interactions and generate GRNs. Additionally, this review describes network inference techniques that leverage gene expression data to predict regulatory interactions. These computational and experimental methodologies yield complex networks that can identify new regulatory interactions, driving novel hypotheses. Biological properties that contribute to the complexity of GRNs are also described in this review. These include network topology, network size, transient binding of TFs to DNA, and competition between multiple upstream regulators. Finally, this review highlights the potential of machine learning approaches to leverage gene expression data to predict phenotypic outputs.

Qualitative and quantitative nature of mutual interactions dictate chemical noise in a democratic reaction network

The functions of a living cell rely on a complex network of biochemical reactions that allow it to respond against various internal and external cues. The outcomes of these chemical reactions are often stochastic due to intrinsic and extrinsic noise leading to population heterogeneity. The majority of calculations of stochasticity in reaction networks have focused on small regulatory networks addressing the role of timescales, feedback regulations, and network topology in propagation of noise. Here we computationally investigated chemical noise in a network with democratic architecture where each node is regulated by all other nodes in the network. We studied the effects of the qualitative and quantitative nature of mutual interactions on the propagation of both intrinsic and extrinsic noise in the network. We show that an increased number of inhibitory signals lead to ultrasensitive switching of average and that leads to sharp transition of intrinsic noise. The intrinsic noise exhibits a biphasic power-law scaling with the average, and the scaling coefficients strongly correlate with the strength of inhibitory signal. The noise strength critically depends on the strength of the interactions, where negative interactions attenuate both intrinsic and extrinsic noise.

The relation between crosstalk and gene regulation form revisited

Genes differ in the frequency at which they are expressed and in the form of regulation used to control their activity. In particular, positive or negative regulation can lead to activation of a gene in response to an external signal. Previous works proposed that the form of regulation of a gene correlates with its frequency of usage: positive regulation when the gene is frequently expressed and negative regulation when infrequently expressed. Such network design means that, in the absence of their regulators, the genes are found in their least required activity state, hence regulatory intervention is often necessary. Due to the multitude of genes and regulators, spurious binding and unbinding events, called “crosstalk”, could occur. To determine how the form of regulation affects the global crosstalk in the network, we used a mathematical model that includes multiple regulators and multiple target genes. We found that crosstalk depends non-monotonically on the availability of regulators. Our analysis showed that excess use of regulation entailed by the formerly suggested network design caused high crosstalk levels in a large part of the parameter space. We therefore considered the opposite ‘idle’ design, where the default unregulated state of genes is their frequently required activity state. We found, that ‘idle’ design minimized the use of regulation and thus minimized crosstalk. In addition, we estimated global crosstalk of S. cerevisiae using transcription factors binding data. We demonstrated that even partial network data could suffice to estimate its global crosstalk, suggesting its applicability to additional organisms. We found that S. cerevisiae estimated crosstalk is lower than that of a random network, suggesting that natural selection reduces crosstalk. In summary, our study highlights a new type of protein production cost which is typically overlooked: that of regulatory interference caused by the presence of excess regulators in the cell. It demonstrates the importance of whole-network descriptions, which could show effects missed by single-gene models.

Genes differ in the frequency at which they are expressed and in the form of regulation used to control their activity. The basic level of regulation is mediated by different types of DNA-binding proteins, where each type regulates particular gene(s). We distinguish between two basic forms of regulation: positive—if a gene is activated by the binding of its regulatory protein, and negative—if it is active unless bound by its regulatory protein. Due to the multitude of genes and regulators, spurious binding and unbinding events, called “crosstalk”, could occur. How does the form of regulation, positive or negative, affect the extent of regulatory crosstalk? To address this question, we used a mathematical model integrating many genes and many regulators. As intuition suggests, we found that in most of the parameter space, crosstalk increased with the availability of regulators. We propose, that crosstalk is usually reduced when networks are designed such that minimal regulation is needed, which we call the ‘idle’ design. In other words: a frequently needed gene will use negative regulation and conversely, a scarcely needed gene will employ positive regulation. In both cases, the requirement for the regulators is minimized. In addition, we demonstrate how crosstalk can be calculated from available datasets and discuss the technical challenges in such calculation, specifically data incompleteness.

Protein ensembles link genotype to phenotype

Classically, phenotype is what is observed, and genotype is the genetic makeup. Statistical studies aim to project phenotypic likelihoods of genotypic patterns. The traditional genotype-to-phenotype theory embraces the view that the encoded protein shape together with gene expression level largely determines the resulting phenotypic trait. Here, we point out that the molecular biology revolution at the turn of the century explained that the gene encodes not one but ensembles of conformations, which in turn spell all possible gene-associated phenotypes. The significance of a dynamic ensemble view is in understanding the linkage between genetic change and the gained observable physical or biochemical characteristics. Thus, despite the transformative shift in our understanding of the basis of protein structure and function, the literature still commonly relates to the classical genotype-phenotype paradigm. This is important because an ensemble view clarifies how even seemingly small genetic alterations can lead to pleiotropic traits in adaptive evolution and in disease, why cellular pathways can be modified in monogenic and polygenic traits, and how the environment may tweak protein function.

φ-evo: A program to evolve phenotypic models of biological networks

Molecular networks are at the core of most cellular decisions, but are often difficult to comprehend. Reverse engineering of network architecture from their functions has proved fruitful to classify and predict the structure and function of molecular networks, suggesting new experimental tests and biological predictions. We present φ-evo, an open-source program to evolve in silico phenotypic networks performing a given biological function. We include implementations for evolution of biochemical adaptation, adaptive sorting for immune recognition, metazoan development (somitogenesis, hox patterning), as well as Pareto evolution. We detail the program architecture based on C, Python 3, and a Jupyter interface for project configuration and network analysis. We illustrate the predictive power of φ-evo by first recovering the asymmetrical structure of the lac operon regulation from an objective function with symmetrical constraints. Second, we use the problem of hox-like embryonic patterning to show how a single effective fitness can emerge from multi-objective (Pareto) evolution. φ-evo provides an efficient approach and user-friendly interface for the phenotypic prediction of networks and the numerical study of evolution itself.