Conservation Law in Gene Regulatory Network modelling

Conservation Law in Gene Regulatory Network modelling

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I was going through the GRN modelling from Chemical and enzyme kinetics by D. Gonze & M. Kaufman (PDF). The gene has 2 sites for activator/repressor. It say the DNA $D_0$ combines with activator/repressor at one of the sites leading to $D_1$ and then $D_1$ combines with $X$ again leading to $D_2$. It says then then total DNA is conserved in the reaction leading to $D_{Total} = D_0 + 2D_1 + D_2$. I want to ask why is there "2" with $D_1$ shouldn't it be $D_{Total} = D_0 + D_1 + D_2$. What I am talking about is given on page 49 of the document. $$D_0 + X leftrightarrow D_1$$ $$D_1 + X leftrightarrow D_2$$ For first chemical reaction the rates are $k_1$ and $k_{-1}$. For the second reaction the chemical reaction rates are $alpha k_1$ and $k_{-1}$. Also, what will be the rate of the reaction for $D_2+X ightarrow D_3$ when the DNA has 3 sites instead of 2.

Developmental gene regulatory network evolution: insights from comparative studies in echinoderms

One of the central concerns of Evolutionary Developmental biology is to understand how the specification of cell types can change during evolution. In the last decade, developmental biology has progressed toward a systems level understanding of cell specification processes. In particular, the focus has been on determining the regulatory interactions of the repertoire of genes that make up gene regulatory networks (GRNs). Echinoderms provide an extraordinary model system for determining how GRNs evolve. This review highlights the comparative GRN analyses arising from the echinoderm system. This work shows that certain types of GRN subcircuits or motifs, i.e., those involving positive feedback, tend to be conserved and may provide a constraint on development. This conservation may be due to a required arrangement of transcription factor binding sites in cis regulatory modules. The review will also discuss ways in which novelty may arise, in particular through the co-option of regulatory genes and subcircuits. The development of the sea urchin larval skeleton, a novel feature that arose in echinoderms, has provided a model for study of co-option mechanisms. Finally, the types of GRNs that can permit the great diversity in the patterns of ciliary bands and their associated neurons found among these taxa are discussed. The availability of genomic resources is rapidly expanding for echinoderms, including genome sequences not only for multiple species of sea urchins but also a species of sea star, sea cucumber, and brittle star. This will enable echinoderms to become a particularly powerful system for understanding how developmental GRNs evolve.

Keywords: cell fate specification process early development process echinoderm evolution process invertebrate.

Benchmarking algorithms for gene regulatory network inference from single-cell transcriptomic data

We present a systematic evaluation of state-of-the-art algorithms for inferring gene regulatory networks from single-cell transcriptional data. As the ground truth for assessing accuracy, we use synthetic networks with predictable trajectories, literature-curated Boolean models and diverse transcriptional regulatory networks. We develop a strategy to simulate single-cell transcriptional data from synthetic and Boolean networks that avoids pitfalls of previously used methods. Furthermore, we collect networks from multiple experimental single-cell RNA-seq datasets. We develop an evaluation framework called BEELINE. We find that the area under the precision-recall curve and early precision of the algorithms are moderate. The methods are better in recovering interactions in synthetic networks than Boolean models. The algorithms with the best early precision values for Boolean models also perform well on experimental datasets. Techniques that do not require pseudotime-ordered cells are generally more accurate. Based on these results, we present recommendations to end users. BEELINE will aid the development of gene regulatory network inference algorithms.

Conflict of interest statement

The authors declare no competing interests.


An overview of the BEELINE…

An overview of the BEELINE evaluation framework. We apply GRN inference algorithms to…

Summary of results for datasets…

Summary of results for datasets from synthetic networks. The first six columns display…

Visualization of t-SNE projections of…

Visualization of t-SNE projections of simulations reveals trajectories leading to steady states that…

Summary of results for 10…

Summary of results for 10 datasets without dropouts from curated models. Rows corresponds…

Summary of EPR results for…

Summary of EPR results for experimental single-cell RNA-seq datasets. The left half of…

Summary of properties of GRN…

Summary of properties of GRN inference algorithms and results obtained from BEELINE. Each…

Conservation and divergence of the p53 gene regulatory network between mice and humans

Understanding the p53 tumor suppressor pathway remains crucial for the design of anticancer strategies. Studies in human tumors and mouse models help to unravel the molecular mechanisms that underlie the p53 signaling pathway. Yet, the p53 gene regulatory network (GRN) is not the same in mice and humans. The comparison of the regulatory networks of p53 in mice and humans reveals that gene up- and down-regulation by p53 are distinctly affected during evolution. Importantly, gene up-regulation by p53 underwent more rapid evolution and gene down-regulation has been evolutionarily constrained. This difference stems from the two major mechanisms employed by p53 to regulate gene expression: up-regulation through direct p53 target gene binding and indirect down-regulation through the p53-p21-DREAM pathway. More than 1000 genes have been identified to differ in their p53-dependent expression between mice and humans. Analysis of p53 gene expression profiles and p53 binding data reveal that turnover of p53 binding sites is the major mechanism underlying extensive variation in p53-dependent gene up-regulation. Only a core set of high-confidence genes appears to be directly regulated by p53 in both species. In contrast to up-regulation, p53-induced down-regulation is well conserved between mice and humans and controls cell cycle genes. Here a curated data set is provided that extends the previously established web-atlas at to assess the p53 response of any human gene of interest and its mouse ortholog. Taken together, the analysis reveals a limited translation potential from mouse models to humans for the p53 GRN.

Conflict of interest statement

The author declares that he has no conflict of interest.


Meta-analysis of p53-dependent gene expression…

Meta-analysis of p53-dependent gene expression in the mouse genome. a The number of…

Gene down-regulation is more similar…

Gene down-regulation is more similar than up-regulation by p53 between mice and humans.…

Evolutionary variation in p53-dependent up-regulation…

Evolutionary variation in p53-dependent up-regulation relates to different p53 binding profiles and low…

Changes in p53 binding profiles…

Changes in p53 binding profiles relate to alterations in p53REs. Mouse and human…

Functions of common and species-specific…

Functions of common and species-specific direct p53 target genes. A flow chart displays…


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Associated Data


Hepatocellular carcinoma (HCC) is one of the most lethal cancers worldwide, and the mechanisms that lead to the disease are still relatively unclear. However, with the development of high-throughput technologies it is possible to gain a systematic view of biological systems to enhance the understanding of the roles of genes associated with HCC. Thus, analysis of the mechanism of molecule interactions in the context of gene regulatory networks can reveal specific sub-networks that lead to the development of HCC.


In this study, we aimed to identify the most important gene regulations that are dysfunctional in HCC generation. Our method for constructing gene regulatory network is based on predicted target interactions, experimentally-supported interactions, and co-expression model. Regulators in the network included both transcription factors and microRNAs to provide a complete view of gene regulation. Analysis of gene regulatory network revealed that gene regulation in HCC is highly modular, in which different sets of regulators take charge of specific biological processes. We found that microRNAs mainly control biological functions related to mitochondria and oxidative reduction, while transcription factors control immune responses, extracellular activity and the cell cycle. On the higher level of gene regulation, there exists a core network that organizes regulations between different modules and maintains the robustness of the whole network. There is direct experimental evidence for most of the regulators in the core gene regulatory network relating to HCC. We infer it is the central controller of gene regulation. Finally, we explored the influence of the core gene regulatory network on biological pathways.


Our analysis provides insights into the mechanism of transcriptional and post-transcriptional control in HCC. In particular, we highlight the importance of the core gene regulatory network we propose that it is highly related to HCC and we believe further experimental validation is worthwhile.

Comparative Analysis of Gene Regulatory Networks: From Network Reconstruction to Evolution

Regulation of gene expression is central to many biological processes. Although reconstruction of regulatory circuits from genomic data alone is therefore desirable, this remains a major computational challenge. Comparative approaches that examine the conservation and divergence of circuits and their components across strains and species can help reconstruct circuits as well as provide insights into the evolution of gene regulatory processes and their adaptive contribution. In recent years, advances in genomic and computational tools have led to a wealth of methods for such analysis at the sequence, expression, pathway, module, and entire network level. Here, we review computational methods developed to study transcriptional regulatory networks using comparative genomics, from sequence to functional data. We highlight how these methods use evolutionary conservation and divergence to reliably detect regulatory components as well as estimate the extent and rate of divergence. Finally, we discuss the promise and open challenges in linking regulatory divergence to phenotypic divergence and adaptation.

Conservation Law in Gene Regulatory Network modelling - Biology

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To understand the processes of development and evolution of living organisms, the “gene regulatory networks”, or GRNs have to be taken into account. The variability of such networks determines the diversity of organ forms and functions in plants and animals [1, 2]. Specialized trichome cells are useful as a model for studying the molecular processes of cell fate determination, cell cycle control and cellular morphogenesis [3]. In particular, this model was instrumental in dissecting the mechanisms of epidermal morphogenesis in the model plant Arabidopsis thaliana L [4]. The central role in determining the cellular fate of cells with trichomes is played by the assembly of the trichome initiation MBW complex - (GL3/EGL3-GL1-TTG1), which initiates the expression of the gene GLABRA2 (GL2) encoding a transcription factor to initiate the cell transition to differentiation into trichomes [5]. In addition to GL2, the MBW complex induces the expression of repressor genes (TRY/CPC), which can move between the cells and assemble into a complex (GL3/EGL3-CPC/TRY-TTG1) that is unable to initiate trichome formation. In Arabidopsis, seven R3-MYB proteins of inhibitors of the MBW complex were found: TRIPTYCHON (TRY) [6, 7], CAPRICE (CPC) [8], ENHANCER OF TRY and CPC 1, 2 и 3 (ETC1, ETC2 и ETC3) [9,10,11], and TRICHOMELESS 1 и 2 (TCL1 2 TCL2) [12, 13]. Different efficiency of the function between them was shown [11, 14]. TCL1 most likely acts as a negative regulator of GL1 expression [12] as well as trichome development, influencing both the expression of GL1 and competing with GL1 for binding to GL3 [15, 16]. It is to be noted that the pattern of trichome formation is described by the widespread mechanism of lateral inhibition, which is known to exist in various plant and animal organisms. In addition, it is responsible for the cyanobacterial heterocyst development [17, 18].

In addition to the MBW complex, a number of genes that increase the expression of the genes of the initiator complex, were found in leaves and flowers: GLABROUS INFLORESCENCE STEMS (GIS), [19] GIS2, ZINC FINGER PROTEIN 8 (ZFP8) [20, 21], ZFP5 [22, 23], и ZFP6 [24]. It was shown that GL1 and GL3, which are the key transcription factors in the MBW complex, function after being activated by GIS2 and ZFP8 [24].

A number of studies have shown that genes orthologous to the Arabidopsis trichome related genes are involved in the cotton hair formation [25,26,27,28,29]. However, it was earlier suggested that in more phylogenetically distant species trichomes can develop in a convergent way through other genetic mechanisms [30]. Also, certain data speak in favor of functional diversification of individual regulatory pathways of trichome development. It was shown that the ectopic expression of the rice R3 MYB transcription factor OsTCL1 in the Arabidopsis genome influences the trichome formation however, changes in OsTCL1 expression in rice do not lead to any trichome-related phenotypic changes [31]. In addition, the overexpression of the GL1 gene in tobacco has no effect on the development of trichomes. One explanation is that the gene network with the GL1 gene first appeared in Rosids. Besides, tobacco has five types of trichomes, which should reflect no differences in genetic mechanisms, either [30].

It should be noted that the MBW complex, together with its regulators, directly participates in inhibition of morphogenesis of root hairs [7, 9, 10, 32]. Thus, there is reason to suggest that variations of one gene network are responsible for formation of the trichome pattern of leaf epidermis and root hairs in A. thaliana [33]. Using RNA-seq data, Huang showed that the main set of genes responsible for root hairs is preserved at evolutionary distances up to 200 million years or more [34]. However, the patterns of expression of these genes can vary significantly between different species [35].

It is also known that outgrowths of epidermal cells are widespread and are extremely ancient formations. Simple outgrowths are found in algae - Chara (Charophytales) and Spirogyra (Zygnematales) [36]. Risoids in mosses have a characteristic pattern and perform the functions of fixation in the substrate involved in absorption of water and nutrients [37]. It was revealed that Physcomitrella patens genes PpRSL1 and PpRSL2 affect the number of rhizoids on a plant [38, 39]. Mutants of Arabidopsis devoid of the function of RHD6 (one of the key genes of hair development) develop root hairs if they are transformed by the genes PpRSL1 from Physcomitrella. This indicates that the function of the RSL family proteins has not been lost for 420 million years of the species divergence [38].

Thus, to understand the processes of development and evolution of trichome morphogenesis of GRN, we need to combine data on proteins and their functions into the GRN topologies related to each major plant taxa divergence, and after we need to associate the changes in the GRN topologies with the changes in the GRN components (individual proteins).

Functions of any protein are a direct consequence of its chemical and physical properties, which in turn are defined by sterical and physico-chemical requirements for native folding in three-dimensional space into the protein globule. Therefore, it is anticipated that the change of residue interacting with other amino acids in a protein globule, is closely related to changes in the context of epistatic interactions of residues in a globule. In other words, protein evolution is rugged, and unevenness is driven by abrupt changes in the optimal three-dimensional protein space topology (e.g. Gibbs energy), which in turn leads to rugged selection in protein space and evolutionary time. Computational studies of protein evolution detected several well-known major epistasis signatures. These are (1) variability in amino acid states that cause protein malfunctions (or diseases) in various lineages [40] (2) mutation tolerability switching along protein evolution, or, in other words, deleterious mutations at one evolutionary time becoming non-deleterious or vice versa [41] (3) pervasive signatures of covariation in any proteins and any lineages [42,43,44]. In addition, gradual emergence of restrictive epistatic interactions was demonstrated to take place in the course of protein evolution [45, 46]. These interactions in turn makes the ancestral state deleterious or irreversible [45] or ‘Stokes shifts’ in protein evolution [46]. Despite these facts, until now the vast majority of currently available reconstruction procedures of ancestral sequences [47, 48] are based on reversibility of a single empirical amino acid substitution matrix (that is applied to all protein sites. Thus, the novel ancestral protein reconstruction software tools (e.g. ProtASR) [49] that adapt the protein structure and the folding stability should be most suitable. However, there is still a lack of experimentally solved 3D protein structures, notably in the plant science. Another way to account for protein epistasis in the standard ancestral protein reconstruction is construction of ancestral libraries to address the sequence uncertainty as a result of ancestral sequence reconstruction imperfection [50]. This approach takes into consideration a well-known pitfall that there is no guarantee that the ancestral sequences are correct biologically functional proteins and most useful in studying deep evolutionary events. The recent experimental study of mRFP1 protein artificial evolution shows that the ancestral sequences obtained by the maximum likelihood approach is most closely related to natural ancestral mRFP1 proteins, while the best proteins reconstructed by using the phylogenetic-tree-aware Bayesian method are not so similar to native ancestors [51]. However, only one best ancestral protein can be reconstructed using this approach that cannot be used in ancestral libraries generation. In order to make ancestral libraries generation sufficiently accurate, it was recently suggested using the ‘AltAll’ reconstruction approach. This approach combines all plausible alternative states introduced into a single protein and then functionally characterizes this protein by the set of these states [52, 53]. It was shown that this approach significantly corrects imperfection of ancestral sequences generated by Bayesian posterior probability exploration. Thus, the best we could do in the case of the lack of 3D protein structures was to use the ‘AltAll’ derived approach to construct ancestral libraries for subsequent evolutionary studies and to make evolutionary protein function inferences.

Thus, two general objectives are highly relevant to our study: (1) to fill the gaps in understanding of evolutionary dynamics of the trichome morphogenesis GRN topology, we need to combine taxa-specific GRN and analyze their differences and (2) to fill the gaps in understanding the molecular basis of protein interactions into the taxa-specific GRN and the molecular basis on differences between the taxa-specific GRN, the evolution of structure and function of GRN proteins should be analyzed. In this work, we combine the qualitative information on the topology of GRN related to trichome morphogenesis with in-detail phylogenetic analysis of its components. The raw phylogenetic analysis allowed us to find a simple answer when the origination point of the core gene subnetwork is formed. Additionally, using detailed information about protein sequence structural classes/features, we studied the evolutionary variation of protein globules related to various speciation or duplication points and potential protein-protein interactions. This allows to hypothesize divergence and/or specialization in the GRN function associated with origination of plant taxa. Information about the structural targets of the protein evolution in the GRN also plays a predictive role for future discriminations of evolutionary switching points in the functioning of gene networks.


In order to understand cell functioning as a whole, it is necessary to describe, at the molecular level, how gene products interact with each other. This could help to identify new target genes and to design new drugs for treatment of several diseases [1–3]. Due to the high number of genes involved in these networks, activating or suppressing feedback loops, the dynamics of their interactions is very complex and difficult to infer.

With the development of high-throughput technologies, such as DNA microarrays, it is possible to simultaneously analyze the expression of up to thousands of genes and to construct gene networks based on inferences over gene expression data.

Several methods to model genetic networks were proposed in the last few years, such as the Bayesian networks [4–8], Structural Equation Models [9], Probabilistic Boolean Networks [10–12], Graphical Gaussian Models [13], Fuzzy controls [14], and Differential Equations [15].

Although these methods allow modeling several regulatory networks for which biological information is available, it is difficult to determine the flow of information when there is no a priori knowledge.

In addition, all of these methods face the same problem, i.e., the number of samples (microarrays) is very small, when compared to the high number of variables (genes) (ill posed problems, related to the "curse of dimensionality") [16]. Therefore, it is difficult to infer large scale networks using traditional statistical methods, limiting this inference to only a few genes. As a consequence, modeling and simulating large networks becomes a field of intensive and challenging research. At this point, it is important to define what is considered a "large" network. We consider as "large" a network in which the number of genes is larger than the number of microarrays experiments, implying in a large number of parameters to be estimated.

Some methods have been developed to overcome this problem. For example, Barrera et al. use mutual information for dimension reduction [17], with mutual information between genes being computed and then, the highest mutual informations selected. However, this approach is not founded on a statistical test, rendering it very difficult to interpret and identify the actual edges of the network. Therefore, the choice of the threshold parameter to determine whether there is or not a connection, becomes quite subjective. An alternative to model the large number of genes is to construct modules (clusters), where each module is composed by several genes, and then, to construct the module-module networks [18–20]. A limitation of these methods is that they still are not a gene-gene network, therefore, interpretation of the meaning of each module is difficult, varying with each cluster.

Here we present the Sparse Vector Autoregressive model to approach these problems. This method was first applied, with success, in neurosciences, to estimate functional connectivity between several brain areas [21]. Here, we present the Sparse Vector Autoregressive model based on LASSO penalized regression for variable selection to reduce the dimensionality on large gene networks.

In cases of multiple time series, a first approach to infer connectivity would be to apply techniques such as multivariate autoregressive modeling (VAR), which allows identification of connectivity by combining graphical modeling methods with the concept of Granger causality [22]. This is an attractive approach since it does not require a priori network information. Unfortunately, the current time series methods can only be applied only for cases in which the length of the time-series T is much larger than n, the number of genes, which is exactly the reverse of the situation commonly found in microarray experiments, for which relatively short time-series are measured over tens of thousands of genes. The Sparse Vector AutoRegressive model (SVAR), on the other hand, estimates the network in a two-stage process involving (i) penalized regression with LASSO regression [23] and (ii) pruning of unlikely connections by means of the False Discovery Rate (FDR) developed by [24]. Extensive simulations were performed with artificial gene networks having scale-free like topologies [25] and stable dynamics. These simulations show that the detection efficiency of connections of the proposed procedure is quite high. An application of the method to actual HeLa cell line data was illustrated by the identification of well known transcription factor targets and circuitries involving important genes in cancer development.


Systems biology approaches to infer GRNs can provide a hypothesis for further experimental validation. Existing methods for bulk transcriptomics datasets are limited because they cannot capture the continuous cellular dynamics and/or require cell synchronization to avoid ‘average out’ expression. scRNAseq has emerged as an alternative because of its power to provide the transcriptomic snapshots of hundreds, thousands of cells on a massive scale, from same population. Subsequently, computational approaches used scRNAseq for GRN reconstruction ( 2, 12, 14, 15, 27–31, 46).

Many GRN reconstruction algorithms including TENET use the temporal gene expression changes, after ordering cells across pseudo-time. For example, GENIE3 ( 45) and GRNBOOST2 ( 46) were originally applied the ensembles of regression trees to temporal bulk expression data. LEAP ( 28) calculates possible maximum time-lagged correlations. SINCERITIES ( 29) and SCINGE ( 31) used Granger causality from pseudo-time ordered data. SCODE ( 27) uses a mechanistical model of ordinary differential equations on the pseudo-time aligned scRNAseq data. Compared with current methods, TENET makes use of the power of information theory by adopting TE on gene expression along the pseudo-time. Therefore, the performance of these predicted regulators could be dependent on the performance of the pseudo-time inference. However, we found that TENET is robust to the multiple pseudo-time inference approaches in comparison with other GRN reconstructors ( Supplementary Figure S6 ).

We showed that TE values of the known target genes were significantly higher than randomly selected genes (Figure 2B and Supplementary Figure S2 ). The target genes with higher TE values were more significantly perturbed by either overexpression or knockdown of the corresponding regulators (Figure 2C– F). We also performed comprehensive benchmarking of TENET and several GRN reconstructors using Beeline ( 52) and its automated pipeline. TENET was consistently one of the top performing GRN reconstructors in these tests.

The evaluation of the performances of GRN reconstructors by counting the number of true or false prediction does not fully reflect the importance of the inferred network. We observe that TENET consistently predicts and identifies key regulators. This is important because upstream regulators for a biological process are often of interest to explain the underlying mechanisms. It is still required to evaluate if the inferred networks reflect the key underlying biological processes. Applying TENET to a series of scRNAseq datasets including (i) mESC differentiation and (ii) reprogramming to cardiomyocytes, we find that TENET identified key factors as the top scoring hubs. For mESC differentiation, TENET ranked Nanog, Pou5f1, Esrrb and Tbx3 as the top 4 regulators, while existing methods failed to identify these key factors. In an additional test using GO terms, TENET identified gene relationships associated with pluripotency and neural differentiation (Figure 3B and C). Interestingly, existing methods including LEAP and SINCERITIES did not find any genes related to pluripotency in their networks ( Supplementary Figure S5b ). Analyzing the reprogramming to cardiomyocytes scRNAseq data, only TENET identified the reprogramming factors (Mef2c, Tbx5 and Gata4) ( 33 Figure 3D– F and Supplementary Figure S7 ). These results suggest that while other approaches successful in finding some regulatory rules, they cannot make networks focusing on the key biological process.

We further questioned if TENET is capable of identifying key regulators using BNs. While BNs may not be a perfect model of biological system, they can still provide a comprehensive systematic overview by visiting all potential states. In BN, the key nodes usually have small number of attractors as they drive the networks into more determined status. In our analysis using BNs, TENET-inferred networks were negatively correlated with the number of attractors ( Supplementary Figure S9 ), indicating the key ability to capture biological processes.

A number of studies showed distinct expression patterns in the pseudo-space ( 67, 68). Since pseudo-time inference can lead to multiple branched trajectories, we also applied TENET to individual branches. These expression changes for some genes may be attributed to association along the spatial axis. However, the associating potential causal relationships for them may not be relevant.

With the power to predict key regulators, we applied TENET to identify mESC culture-condition specific regulators. TENET predicted several TFs (Nanog, Esrrb and Nme2) as specific for 2iL compared to SL culture conditions ( Supplementary Figure S12 ). Although Nme2 is expressed both in 2iL and SL, perturbing Nme2 leads to more dramatic effects (reduced proliferation, AP staining and apoptosis) in the 2iL condition, consistent with our prediction. In sum, TENET is a useful approach to predict previously uncharacterized regulatory mechanisms from scRNAseq.

Watch the video: Simple Two-Gene Regulatory Network Simulation (June 2022).