Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space

Number of Attractors in the Critical Kauffman Model Is Exponential

The Kauffman model is the archetypal model of genetic computation. It highlights the importance of criticality, at which many biological systems seem poised. In a series of advances, researchers have honed in on how the number of attractors in the critical regime grows with network size. But a definitive answer has remained elusive. We prove that, for the critical Kauffman model with connectivity one, the number of attractors grows at least, and at most, as (2/sqrt[e])^{N}. This is the first proof that the number of attractors in a critical Kauffman model grows exponentially.

Pervasive gene deregulation underlies adaptation and maladaptation in trimethoprim-resistant E. coli

IMPORTANCE

Bacteria employ a number of mechanisms to adapt to antibiotics. Mutations in transcriptional regulators alter the expression levels of genes that can change the susceptibility of bacteria to antibiotics. Two-component signaling proteins are a major class of signaling molecule used by bacteria to regulate transcription. In previous work, we found that mutations in MgrB, a feedback regulator of the PhoQP two-component system, conferred trimethoprim tolerance to Escherichia coli. Here, we elucidate how mutations in MgrB have a domino-like effect on the gene regulatory network of E. coli. As a result, pervasive perturbation of gene regulation ensues. Depending on the environmental context, this pervasive deregulation is either adaptive or maladaptive. Our study sheds light on how deregulation of gene expression can be beneficial for bacteria when challenged with antibiotics, and why regulators like MgrB may have evolved in the first place.

Theoretical investigation of functional responses of bio-molecular assembly networks

Cooperative protein-protein and protein-DNA interactions form programmable complex assemblies, often performing non-linear gene regulatory operations involved in signal transductions and cell fate determination. The apparent structure of those complex assemblies is very similar, but their functional response strongly depends on the topology of the protein-DNA interaction networks. Here, we demonstrate how the coordinated self-assembly creates gene regulatory network motifs that corroborate the existence of a precise functional response at the molecular level using thermodynamic and dynamic analyses. Our theoretical and Monte Carlo simulations show that a complex network of interactions can form a decision-making loop, such as feedback and feed-forward circuits, only by a few molecular mechanisms. We characterize each possible network of interactions by systematic variations of free energy parameters associated with the binding among biomolecules and DNA looping. We also find that the higher-order networks exhibit alternative steady states from the stochastic dynamics of each network. We capture this signature by calculating stochastic potentials and attributing their multi-stability features. We validate our findings against the Gal promoter system in yeast cells. Overall, we show that the network topology is vital in phenotype diversity in regulatory circuits.

Identification of Critical Molecular Factors and Side Effects Underlying the Response to Thalicthuberine in Prostate Cancer: A Systems Biology Approach

Background

Uncontrolled mitosis of cancer cells and resistance cells to chemotherapy drugs are the challenges of prostate cancer. Thalicthuberine causes a mitotic arrest and a reduction of the effects of drug resistance, resulting in cell death. In this study, we applied bioinformatics and computational biology methods to identify functional pathways and side effects in response to Thalicthuberine in prostate cancer patients.

Methods

Microarray data were retrieved from Gene Expression Omnibus (GEO), and protein-protein interactions and gene regulatory networks were constructed, using the Cytoscape software. The critical genes and molecular mechanisms in response to Thalicthuberine and its side effects were identified, using the Cytoscape software and WebGestalt server, respectively. Finally, GEPIA2 was used to predict the relationship between critical genes and prostate cancer.

Results

The POLQ, EGR1, CDKN1A, FOS, MDM2, CDC20, CCNB1, and CCNB2 were identified as critical genes in response to this drug. The functional mechanisms of Thalicthuberine include a response to oxygen levels, toxic substances and immobilization stress, cell cycle regulation, regeneration, the p53 signaling pathway, the action of the parathyroid hormone, and the FoxO signaling pathway. Besides, the drug has side effects including muscle cramping, abdominal pains, paresthesia, and metabolic diseases.

Conclusion

Our model suggested newly predicted crucial genes, molecular mechanisms, and possible side effects of this drug. However, further studies are required.

Evolution of miRNA binding sites and regulatory networks in cichlids

The divergence of regulatory regions and gene regulatory network (GRN) rewiring is a key driver of cichlid phenotypic diversity. However, the contribution of miRNA binding site turnover has yet to be linked to GRN evolution across cichlids. Here, we extend our previous studies by analysing the selective constraints driving evolution of miRNA and transcription factor (TF) binding sites of target genes, to infer instances of cichlid GRN rewiring associated with regulatory binding site turnover. Comparative analyses identified increased species-specific networks that are functionally associated to traits of cichlid phenotypic diversity. The evolutionary rewiring is associated with differential models of miRNA and TF binding site turnover, driven by a high proportion of fast-evolving polymorphic sites in adaptive trait genes compared to subsets of random genes. Positive selection acting upon discrete mutations in these regulatory regions is likely to be an important mechanism in rewiring GRNs in rapidly radiating cichlids. Regulatory variants of functionally associated miRNA and TF binding sites of visual opsin genes differentially segregate according to phylogeny and ecology of Lake Malawi species, identifying both rewired e.g. clade-specific and conserved network motifs of adaptive trait associated GRNs. Our approach revealed several novel candidate regulators, regulatory regions and three-node motifs across cichlid genomes with previously reported associations to known adaptive evolutionary traits.

A Motif-Based Network Analysis of Regulatory Patterns in Doxorubicin Effects on Treating Breast Cancer, a Systems Biology Study

Background

Breast cancer is the most common malignancy worldwide. Doxorubicin is an anthracycline used to treat breast cancer as the first treatment choice. Nevertheless, the molecular mechanisms underlying the response to Doxorubicin and its side effects are not comprehensively understood so far. We used systems biology and bioinformatics methods to identify essential genes and molecular mechanisms behind the body response to Doxorubicin and its side effects in breast cancer patients.

Methods

Omics data were extracted and analyzed to construct the protein-protein interaction and gene regulatory networks. Network analysis was performed to identify hubs, bottlenecks, clusters, and regulatory motifs to evaluate crucial genes and molecular mechanisms behind the body response to Doxorubicin and its side effects.

Results

Analyzing the constructed PPI and gene-TF-miRNA regulatory network showed that MCM3, MCM10, and TP53 are key hub-bottlenecks and seed proteins. Enrichment analysis also revealed cell cycle, TP53 signaling, Forkhead box O (FoxO) signaling, and viral carcinogenesis as essential pathways in response to this drug. Besides, SNARE interactions in vesicular transport and neurotrophin signaling were identified as pathways related to the side effects of Doxorubicin. The apoptosis induction, DNA repair, invasion inhibition, metastasis, and DNA replication are suggested as critical molecular mechanisms underlying Doxorubicin anti-cancer effect. SNARE interactions in vesicular transport and neurotrophin signaling and FoxO signaling pathways in glucose metabolism are probably the mechanisms responsible for side effects of Doxorubicin.

Conclusion

Following our model validation using the existing experimental data, we recommend our other newly predicted biomarkers and pathways as possible molecular mechanisms and side effects underlying the response to Doxorubicin in breast cancer requiring further investigations.

Generation of Realistic Gene Regulatory Networks by Enriching for Feed-Forward Loops

The regulatory relationships between genes and proteins in a cell form a gene regulatory network (GRN) that controls the cellular response to changes in the environment. A number of inference methods to reverse engineer the original GRN from large-scale expression data have recently been developed. However, the absence of ground-truth GRNs when evaluating the performance makes realistic simulations of GRNs necessary. One aspect of this is that local network motif analysis of real GRNs indicates that the feed-forward loop (FFL) is significantly enriched. To simulate this properly, we developed a novel motif-based preferential attachment algorithm, FFLatt, which outperformed the popular GeneNetWeaver network generation tool in reproducing the FFL motif occurrence observed in literature-based biological GRNs. It also preserves important topological properties such as scale-free topology, sparsity, and average in/out-degree per node. We conclude that FFLatt is well-suited as a network generation module for a benchmarking framework with the aim to provide fair and robust performance evaluation of GRN inference methods.

Testing biological network motif significance with exponential random graph models

Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions. However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over 10 years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s41109-021-00434-y.

Network motif-based analysis of regulatory patterns in paralogous gene pairs

Current high-throughput experimental techniques make it feasible to infer gene regulatory interactions at the whole-genome level with reasonably good accuracy. Such experimentally inferred regulatory networks have become available for a number of simpler model organisms such as S. cerevisiae, and others. The availability of such networks provides an opportunity to compare gene regulatory processes at the whole genome level, and in particular, to assess similarity of regulatory interactions for homologous gene pairs either from the same or from different species. We present here a new technique for analyzing the regulatory interaction neighborhoods of paralogous gene pairs. Our central focus is the analysis of S. cerevisiae gene interaction graphs, which are of particular interest due to the ancestral whole-genome duplication (WGD) that allows to distinguish between paralogous transcription factors that are traceable to this duplication event and other paralogues. Similar analysis is also applied to E. coli and C. elegans networks. We compare paralogous gene pairs according to the presence and size of bi-fan arrays, classically associated in the literature with gene duplication, within other network motifs. We further extend this framework beyond transcription factor comparison to obtain topology-based similarity metrics based on the overlap of interaction neighborhoods applicable to most genes in a given organism. We observe that our network divergence metrics show considerably larger similarity between paralogues, especially those traceable to WGD. This is the case for both yeast and C. elegans, but not for E. coli regulatory network. While there is no obvious cross-species link between metrics, different classes of paralogues show notable differences in interaction overlap, with traceable duplications tending toward higher overlap compared to genes with shared protein families. Our findings indicate that divergence in paralogous interaction networks reflects a shared genetic origin, and that our approach may be useful for investigating structural similarity in the interaction networks of paralogous genes.

Cell-Free Characterization of Coherent Feed-Forward Loop-Based Synthetic Genetic Circuits

Regulatory pathways inside living cells employ feed-forward architectures to fulfill essential signal processing functions that aid in the interpretation of various types of inputs through noise-filtering, fold-change detection and adaptation. Although it has been demonstrated computationally that a coherent feed-forward loop (CFFL) can function as noise filter, a property essential to decoding complex temporal signals, this motif has not been extensively characterized experimentally or integrated into larger networks. Here we use post-transcriptional regulation to implement and characterize a synthetic CFFL in an Escherichia coli cell-free transcription-translation system and build larger composite feed-forward architectures. We employ microfluidic flow reactors to probe the response of the CFFL circuit using both persistent and short, noise-like inputs and analyze the influence of different circuit components on the steady-state and dynamics of the output. We demonstrate that our synthetic CFFL implementation can reliably repress background activity compared to a reference circuit, but displays low potential as a temporal filter, and validate these findings using a computational model. Our results offer practical insight into the putative noise-filtering behavior of CFFLs and show that this motif can be used to mitigate leakage and increase the fold-change of the output of synthetic genetic circuits.

Dynamical modules in metabolism, cell and developmental biology

Modularity is an essential feature of any adaptive complex system. Phenotypic traits are modules in the sense that they have a distinguishable structure or function, which can vary (quasi-)independently from its context. Since all phenotypic traits are the product of some underlying regulatory dynamics, the generative processes that constitute the genotype-phenotype map must also be functionally modular. Traditionally, modular processes have been identified as structural modules in regulatory networks. However, structure only constrains, but does not determine, the dynamics of a process. Here, we propose an alternative approach that decomposes the behaviour of a complex regulatory system into elementary activity-functions. Modular activities can occur in networks that show no structural modularity, making dynamical modularity more widely applicable than structural decomposition. Furthermore, the behaviour of a regulatory system closely mirrors its functional contribution to the outcome of a process, which makes dynamical modularity particularly suited for functional decomposition. We illustrate our approach with numerous examples from the study of metabolism, cellular processes, as well as development and pattern formation. We argue that dynamical modules provide a shared conceptual foundation for developmental and evolutionary biology, and serve as the foundation for a new account of process homology, which is presented in a separate contribution by DiFrisco and Jaeger to this focus issue.

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

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.

We show that the core functional logic of genetic circuits arises from a fundamental symmetry breaking of the interactions of the biological network. The idea can be put into a hierarchy of symmetric genetic circuits that reveals their logical functions. We do so through a constructive procedure that naturally reveals a series of building blocks, widely present across species. This hierarchy maps to a progression of fundamental units of electronics, starting with the transistor, progressing to ring oscillators and current-mirror circuits and then to synchronized clocks, switches and finally to memory devices such as latches and flip-flops.

Motifs enable communication efficiency and fault-tolerance in transcriptional networks

Analysis of the topology of transcriptional regulatory networks (TRNs) is an effective way to study the regulatory interactions between the transcription factors (TFs) and the target genes. TRNs are characterized by the abundance of motifs such as feed forward loops (FFLs), which contribute to their structural and functional properties. In this paper, we focus on the role of motifs (specifically, FFLs) in signal propagation in TRNs and the organization of the TRN topology with FFLs as building blocks. To this end, we classify nodes participating in FFLs (termed motif central nodes) into three distinct roles (namely, roles A, B and C), and contrast them with TRN nodes having high connectivity on the basis of their potential for information dissemination, using metrics such as network efficiency, path enumeration, epidemic models and standard graph centrality measures. We also present the notion of a three tier architecture and how it can help study the structural properties of TRN based on connectivity and clustering tendency of motif central nodes. Finally, we motivate the potential implication of the structural properties of motif centrality in design of efficient protocols of information routing in communication networks as well as their functional properties in global regulation and stress response to study specific disease conditions and identification of drug targets.

Populations of genetic circuits are unable to find the fittest solution in a multilevel genotype-phenotype map

The evolution of gene regulatory networks (GRNs) is of great relevance for both evolutionary and synthetic biology. Understanding the relationship between GRN structure and its function can allow us to understand the selective pressures that have shaped a given circuit. This is especially relevant when considering spatio-temporal expression patterns, where GRN models have been shown to be extremely robust and evolvable. However, previous models that studied GRN evolution did not include the evolution of protein and genetic elements that underlie GRN architecture. Here we use toyLIFE, a multilevel genotype-phenotype map, to show that not all GRNs are equally likely in genotype space and that evolution is biased to find the most common GRNs. toyLIFE rules create Boolean GRNs that, embedded in a one-dimensional tissue, develop a variety of spatio-temporal gene expression patterns. Populations of toyLIFE organisms choose the most common GRN out of a set of equally fit alternatives and, most importantly, fail to find a target pattern when it is very rare in genotype space. Indeed, we show that the probability of finding the fittest phenotype increases dramatically with its abundance in genotype space. This phenotypic bias represents a mechanism that can prevent the fixation in the population of the fittest phenotype, one that is inherent to the structure of genotype space and the genotype-phenotype map.

Modularity, criticality, and evolvability of a developmental gene regulatory network

The existence of discrete phenotypic traits suggests that the complex regulatory processes which produce them are functionally modular. These processes are usually represented by networks. Only modular networks can be partitioned into intelligible subcircuits able to evolve relatively independently. Traditionally, functional modularity is approximated by detection of modularity in network structure. However, the correlation between structure and function is loose. Many regulatory networks exhibit modular behaviour without structural modularity. Here we partition an experimentally tractable regulatory network—the gap gene system of dipteran insects—using an alternative approach. We show that this system, although not structurally modular, is composed of dynamical modules driving different aspects of whole-network behaviour. All these subcircuits share the same regulatory structure, but differ in components and sensitivity to regulatory interactions. Some subcircuits are in a state of criticality, while others are not, which explains the observed differential evolvability of the various expression features in the system.

Next Generation Networks: Featuring the Potential Role of Emerging Applications in Translational Oncology

Nowadays, networks are pervasively used as examples of models suitable to mathematically represent and visualize the complexity of systems associated with many diseases, including cancer. In the cancer context, the concept of network entropy has guided many studies focused on comparing equilibrium to disequilibrium (i.e., perturbed) conditions. Since these conditions reflect both structural and dynamic properties of network interaction maps, the derived topological characterizations offer precious support to conduct cancer inference. Recent innovative directions have emerged in network medicine addressing especially experimental omics approaches integrated with a variety of other data, from molecular to clinical and also electronic records, bioimaging etc. This work considers a few theoretically relevant concepts likely to impact the future of applications in personalized/precision/translational oncology. The focus goes to specific properties of networks that are still not commonly utilized or studied in the oncological domain, and they are: controllability, synchronization and symmetry. The examples here provided take inspiration from the consideration of metastatic processes, especially their progression through stages and their hallmark characteristics. Casting these processes into computational frameworks and identifying network states with specific modular configurations may be extremely useful to interpret or even understand dysregulation patterns underlying cancer, and associated events (onset, progression) and disease phenotypes.

A spectrum of modularity in multi-functional gene circuits

A major challenge in systems biology is to understand the relationship between a circuit's structure and its function, but how is this relationship affected if the circuit must perform multiple distinct functions within the same organism? In particular, to what extent do multi‐functional circuits contain modules which reflect the different functions? Here, we computationally survey a range of bi‐functional circuits which show no simple structural modularity: They can switch between two qualitatively distinct functions, while both functions depend on all genes of the circuit. Our analysis reveals two distinct classes: hybrid circuits which overlay two simpler mono‐functional sub‐circuits within their circuitry, and emergent circuits, which do not. In this second class, the bi‐functionality emerges from more complex designs which are not fully decomposable into distinct modules and are consequently less intuitive to predict or understand. These non‐intuitive emergent circuits are just as robust as their hybrid counterparts, and we therefore suggest that the common bias toward studying modular systems may hinder our understanding of real biological circuits.