Cis-regulatory logic in the endo16 gene: switching from a specification to a differentiation mode of control

A digital twin reproducing gene regulatory network dynamics of early Ciona embryos indicates robust buffers in the network

How gene regulatory networks (GRNs) encode gene expression dynamics and how GRNs evolve are not well understood, although these problems have been studied extensively. We created a digital twin that accurately reproduces expression dynamics of 13 genes that initiate expression in 32-cell ascidian embryos. We first showed that gene expression patterns can be manipulated according to predictions by this digital model. Next, to simulate GRN rewiring, we changed regulatory functions that represented their regulatory mechanisms in the digital twin, and found that in 55 of 100 cases, removal of a single regulator from a conjunctive clause of Boolean functions did not theoretically alter qualitative expression patterns of these genes. In other words, we found that more than half the regulators gave theoretically redundant temporal or spatial information to target genes. We experimentally substantiated that the expression pattern of Nodal was maintained without one of these factors, Zfpm, by changing the upstream regulatory sequence of Nodal. Such robust buffers of regulatory mechanisms may provide a basis of enabling developmental system drift, or rewiring of GRNs without changing expression patterns of downstream genes, during evolution.

A single-cell RNA-seq analysis of Brachyury-expressing cell clusters suggests a morphogenesis-associated signal center of oral ectoderm in sea urchin embryos

Brachyury is a T-box family transcription factor and plays pivotal roles in morphogenesis. In sea urchin embryos, Brachyury, is expressed in the invaginating endoderm, and in the oral ectoderm of the invaginating mouth opening. The oral ectoderm is hypothesized to serve as a signaling center for oral (ventral)-aboral (dorsal) axis formation and to function as a ventral organizer. Our previous results of a single-cell RNA-seq (scRNA-seq) atlas of early Strongylocentrotus purpuratus embryos categorized the constituent cells into 22 clusters, in which the endoderm consists of three clusters and the oral ectoderm four clusters (Foster et al., 2020). Here we examined which clusters of cells expressed Brachyury in relation to the morphogenesis and the identity of the ventral organizer. Our results showed that cells of all three endoderm clusters expressed Brachyury in blastulae. Based on expression profiles of genes involved in the gene regulatory networks (GRNs) of sea urchin embryos, the three clusters are distinguishable, two likely derived from the Veg2 tier and one from the Veg1 tier. On the other hand, of the four oral-ectoderm clusters, cells of two clusters expressed Brachyury at the gastrula stage and genes that are responsible for the ventral organizer at the late blastula stage, but the other two clusters did not. At a single-cell level, most cells of the two oral-ectoderm clusters expressed organizer-related genes, nearly a half of which coincidently expressed Brachyury. This suggests that the ventral organizer contains Brachyury-positive cells which invaginate to form the stomodeum. This scRNA-seq study therefore highlights significant roles of Brachyury-expressing cells in body-plan formation of early sea urchin embryos, though cellular and molecular mechanisms for how Brachyury functions in these processes remain to be elucidated in future studies.

Fitting thermodynamic-based models: Incorporating parameter sensitivity improves the performance of an evolutionary algorithm

A detailed comprehension of transcriptional regulation is critical to understanding the genetic control of development and disease across many different organisms. To more fully investigate the complex molecular interactions controlling the precise expression of genes, many groups have constructed mathematical models to complement their experimental approaches. A critical step in such studies is choosing the most appropriate parameter estimation algorithm to enable detailed analysis of the parameters that contribute to the models. In this study, we develop a novel set of evolutionary algorithms that use a pseudo-random Sobol Set to construct the initial population and incorporate parameter sensitivities into the adaptation of mutation rates, using local, global, and hybrid strategies. Comparison of the performance of these new algorithms to a number of current state-of-the-art global parameter estimation algorithms on a range of continuous test functions, as well as synthetic biological data representing models of gene regulatory systems, reveals improved performance of the new algorithms in terms of runtime, error and reproducibility. In addition, by analyzing the ability of these algorithms to fit datasets of varying quality, we provide the experimentalist with a guide to how the algorithms perform across a range of noisy data. These results demonstrate the improved performance of the new set of parameter estimation algorithms and facilitate meaningful integration of model parameters and predictions in our understanding of the molecular mechanisms of gene regulation.

How haematopoiesis research became a fertile ground for regulatory network biology as pioneered by Eric Davidson

PURPOSE OF REVIEW

This historical perspective reviews how work of Eric H. Davidson was a catalyst and exemplar for explaining haematopoietic cell fate determination through gene regulation.

RECENT FINDINGS

Researchers studying blood and immune cells pioneered many of the early mechanistic investigations of mammalian gene regulatory processes. These efforts included the characterization of complex gene regulatory sequences exemplified by the globin and T-cell/B-cell receptor gene loci, as well as the identification of many key regulatory transcription factors through the fine mapping of chromosome translocation breakpoints in leukaemia patients. As the repertoire of known regulators expanded, assembly into gene regulatory network models became increasingly important, not only to account for the truism that regulatory genes do not function in isolation but also to devise new ways of extracting biologically meaningful insights from even more complex information. Here we explore how Eric H. Davidson's pioneering studies of gene regulatory network control in nonvertebrate model organisms have had an important and lasting impact on research into blood and immune cell development.

SUMMARY

The intellectual framework developed by Davidson continues to contribute to haematopoietic research, and his insistence on demonstrating logic and causality still challenges the frontier of research today.

Multiscale modeling of vertebrate limb development

We review the current state of mathematical modeling of cartilage pattern formation in vertebrate limbs. We place emphasis on several reaction-diffusion type models that have been proposed in the last few years. These models are grounded in more detailed knowledge of the relevant regulatory processes than previous ones but generally refer to different molecular aspects of these processes. Considering these models in light of comparative phylogenomics permits framing of hypotheses on the evolutionary order of appearance of the respective mechanisms and their roles in the fin-to-limb transition. This article is categorized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Mechanistic Models Developmental Biology > Developmental Processes in Health and Disease Analytical and Computational Methods > Analytical Methods.

A Time to Model and a Time to Experiment

The nature and role of models have been amply discussed by philosophers of science. They have emphasized the diversity of models and their functions. Biological sciences in general, and molecular and cellular biology in particular, are no exceptions. The nature and role of models in molecular and cellular biology are also a legacy of the different disciplines that contributed to its formation. Models can be a step toward abstraction, or the opposite, a step toward a material representation of an-to date-abstract phenomenon. Models can also help to collect information and knowledge. I will consider different models that played a highly important role in molecular and cellular biology, up to the Gene Regulatory Network model. There is a right time to model, and a right way to do it. I will try to understand why a model is well received (or not), and what kind of relationship it may or must have with experiments and experimental data.

Encounters across networks: Windows into principles of genomic regulation

Gene regulatory networks account for the ability of the genome to program development in complex multi-cellular organisms. Such networks are based on principles of gene regulation by combinations of transcription factors that bind to specific cis-regulatory DNA sites to activate transcription. These cis-regulatory regions mediate logic processing at each network node, enabling progressive increases in organismal complexity with development. Gene regulatory network explanations of development have been shown to account for patterning and cell type diversification in fly and sea urchin embryonic systems, where networks are characterized by fast coupling between transcriptional inputs and changes in target gene transcription rates, and crucial cis-regulatory elements are concentrated relatively close to the protein coding sequences of the target genes, thus facilitating their identification. Stem cell-based development in post-embryonic mammalian systems also depends on gene networks, but differs from the fly and sea urchin systems. First, the number of regulatory elements per gene and the distances between regulatory elements and the genes they control are considerably larger, forcing searches via genome-wide transcription factor binding surveys rather than functional assays. Second, the intrinsic timing of network state transitions can be slowed considerably by the need to undo stem-cell chromatin configurations, which presumably add stability to stem-cell states but retard responses to transcription factor changes during differentiation. The dispersed, partially redundant cis-regulatory systems controlling gene expression and the slow state transition kinetics in these systems already reveal new insights and opportunities to extend understanding of the repertoire of gene networks and regulatory system logic.

Developmental effector gene regulation: Multiplexed strategies for functional analysis

The staggering complexity of the genome controls for developmental processes is revealed through massively parallel cis-regulatory analysis using new methods of perturbation and readout. The choice of combinations of these new methods is tailored to the system, question and resources at hand. Our focus is on issues that include the necessity or sufficiency of given cis-regulatory modules, cis-regulatory function in the normal spatial genomic context, and easily accessible high throughput and multiplexed analysis methods. In the sea urchin embryonic model, recombineered BACs offer new opportunities for consecutive modes of cis-regulatory analyses that answer these requirements, as we here demonstrate on a diverse suite of previously unstudied sea urchin effector genes expressed in skeletogenic cells. Positively active cis-regulatory modules were located in single Nanostring experiments per BAC containing the gene of interest, by application of our previously reported "barcode" tag vectors of which> 100 can be analyzed at one time. Computational analysis of DNA sequences that drive expression, based on the known skeletogenic regulatory state, then permitted effective identification of functional target site clusters. Deletion of these sub-regions from the parent BACs revealed module necessity, as simultaneous tests of the same regions in short constructs revealed sufficiency. Predicted functional inputs were then confirmed by site mutations, all generated and tested in multiplex formats. There emerged the simple conclusion that each effector gene utilizes a small subset of inputs from the skeletogenic GRN. These inputs may function to only adjust expression levels or in some cases necessary for expression. Since we know the GRN architecture upstream of the effector genes, we could then conceptually isolate and compare the wiring of the effector gene driver sub-circuits and identify the inputs whose removal abolish expression.

An integrative method to decode regulatory logics in gene transcription

Modeling of transcriptional regulatory networks (TRNs) has been increasingly used to dissect the nature of gene regulation. Inference of regulatory relationships among transcription factors (TFs) and genes, especially among multiple TFs, is still challenging. In this study, we introduced an integrative method, LogicTRN, to decode TF–TF interactions that form TF logics in regulating target genes. By combining cis-regulatory logics and transcriptional kinetics into one single model framework, LogicTRN can naturally integrate dynamic gene expression data and TF-DNA-binding signals in order to identify the TF logics and to reconstruct the underlying TRNs. We evaluated the newly developed methodology using simulation, comparison and application studies, and the results not only show their consistence with existing knowledge, but also demonstrate its ability to accurately reconstruct TRNs in biological complex systems.

Existing transcriptional regulatory networks models fall short of deciphering the cooperation between multiple transcription factors on dynamic gene expression. Here the authors develop an integrative method that combines gene expression and transcription factor-DNA binding data to decode transcription regulatory logics.

Eric Davidson and deep time

Eric Davidson had a deep and abiding interest in the role developmental mechanisms played in generating evolutionary patterns documented in deep time, from the origin of the euechinoids to the processes responsible for the morphological architectures of major animal clades. Although not an evolutionary biologist, Davidson's interests long preceded the current excitement over comparative evolutionary developmental biology. Here I discuss three aspects at the intersection between his research and evolutionary patterns in deep time: First, understanding the mechanisms of body plan formation, particularly those associated with the early diversification of major metazoan clades. Second, a critique of early claims about ancestral metazoans based on the discoveries of highly conserved genes across bilaterian animals. Third, Davidson's own involvement in paleontology through a collaborative study of the fossil embryos from the Ediacaran Doushantuo Formation in south China.

Digital logic circuits in yeast with CRISPR-dCas9 NOR gates

Natural genetic circuits enable cells to make sophisticated digital decisions. Building equally complex synthetic circuits in eukaryotes remains difficult, however, because commonly used components leak transcriptionally, do not arbitrarily interconnect or do not have digital responses. Here, we designed dCas9-Mxi1-based NOR gates in Saccharomyces cerevisiae that allow arbitrary connectivity and large genetic circuits. Because we used the chromatin remodeller Mxi1, our gates showed minimal leak and digital responses. We built a combinatorial library of NOR gates that directly convert guide RNA (gRNA) inputs into gRNA outputs, enabling the gates to be 'wired' together. We constructed logic circuits with up to seven gRNAs, including repression cascades with up to seven layers. Modelling predicted the NOR gates have effectively zero transcriptional leak explaining the limited signal degradation in the circuits. Our approach enabled the largest, eukaryotic gene circuits to date and will form the basis for large, synthetic, cellular decision-making systems.

Echinoderm development and evolution in the post-genomic era

The highly recognizable animals within the phylum Echinodermata encompass an enormous disparity of adult and larval body plans. The extensive knowledge of sea urchin development has culminated in the description of the exquisitely detailed gene regulatory network (GRN) that governs the specification of various embryonic territories. This information provides a unique opportunity for comparative studies in other echinoderm taxa to understand the evolution and developmental mechanisms underlying body plan change. This review focuses on recent work that has utilized new genomic resources and systems-level experiments to address questions of evolutionary developmental biology. In particular, we synthesize the results of several recent studies from various echinoderm classes that have explored the development and evolution of the larval skeleton, which is a major feature that distinguishes the two predominant larval subtypes within the Phylum. We specifically examine the ways in which GRNs can evolve, either through cis regulatory and/or protein-level changes in transcription factors. We also examine recent work comparing evolution across shorter time scales that occur within and between species of sea urchin, and highlight the kinds of questions that can be addressed by these comparisons. The advent of new genomic and transcriptomic datasets in additional species from all classes of echinoderm will continue to empower the use of these taxa for evolutionary developmental studies.

The Functionality and Evolution of Eukaryotic Transcriptional Enhancers

Enhancers regulate precise spatial and temporal patterns of gene expression in eukaryotes and, moreover, evolutionary changes in these modular cis-regulatory elements may represent the predominant genetic basis for phenotypic evolution. Here, we review approaches to identify and functionally analyze enhancers and their transcription factor binding sites, including assay for transposable-accessible chromatin-sequencing (ATAC-Seq) and clustered regularly interspaced short palindromic repeats (CRISPR)/Cas9, respectively. We also explore enhancer functionality, including how transcription factor binding sites combine to regulate transcription, as well as research on shadow and super enhancers, and how enhancers can act over great distances and even in trans. Finally, we discuss recent theoretical and empirical data on how transcription factor binding sites and enhancers evolve. This includes how the function of enhancers is maintained despite the turnover of transcription factor binding sites as well as reviewing studies where mutations in enhancers have been shown to underlie morphological change.

Integrated microfluidic approach for quantitative high-throughput measurements of transcription factor binding affinities

Protein binding to DNA is a fundamental process in gene regulation. Methodologies such as ChIP-Seq and mapping of DNase I hypersensitive sites provide global information on this regulation in vivo In vitro methodologies provide valuable complementary information on protein-DNA specificities. However, current methods still do not measure absolute binding affinities. There is a real need for large-scale quantitative protein-DNA affinity measurements. We developed QPID, a microfluidic application for measuring protein-DNA affinities. A single run is equivalent to 4096 gel-shift experiments. Using QPID, we characterized the different affinities of ATF1, c-Jun, c-Fos and AP-1 to the CRE consensus motif and CRE half-site in two different genomic sequences on a single device. We discovered that binding of ATF1, but not of AP-1, to the CRE half-site is highly affected by its genomic context. This effect was highly correlated with ATF1 ChIP-seq and PBM experiments. Next, we characterized the affinities of ATF1 and ATF3 to 128 genomic CRE and CRE half-site sequences. Our affinity measurements explained that in vivo binding differences between ATF1 and ATF3 to CRE and CRE half-sites are partially mediated by differences in the minor groove width. We believe that QPID would become a central tool for quantitative characterization of biophysical aspects affecting protein-DNA binding.

An enhancer composed of interlocking submodules controls transcriptional autoregulation of suppressor of hairless

Positive autoregulation is an effective mechanism for the long-term maintenance of a transcription factor's expression. This strategy is widely deployed in cell lineages, where the autoregulatory factor controls the activity of a battery of genes that constitute the differentiation program of a postmitotic cell type. In Drosophila, the Notch pathway transcription factor Suppressor of Hairless activates its own expression, specifically in the socket cell of external sensory organs, via an autoregulatory enhancer called the ASE. Here, we show that the ASE is composed of several enhancer submodules, each of which can independently initiate weak Su(H) autoregulation. Cross-activation by these submodules is critical to ensure that Su(H) rises above a threshold level necessary to activate a maintenance submodule, which then sustains long-term Su(H) autoregulation. Our study reveals the use of interlinked positive-feedback loops to control autoregulation dynamically and provides mechanistic insight into initiation, establishment, and maintenance of the autoregulatory state.

Discover context-specific combinatorial transcription factor interactions by integrating diverse ChIP-Seq data sets

Combinatorial interactions among transcription factors (TFs) are critical for integrating diverse intrinsic and extrinsic signals, fine-tuning regulatory output and increasing the robustness and plasticity of regulatory systems. Current knowledge about combinatorial regulation is rather limited due to the lack of suitable experimental technologies and bioinformatics tools. The rapid accumulation of ChIP-Seq data has provided genome-wide occupancy maps for a large number of TFs and chromatin modification marks for identifying enhancers without knowing individual TF binding sites. Integration of the two data types has not been researched extensively, resulting in underused data and missed opportunities. We describe a novel method for discovering frequent combinatorial occupancy patterns by multiple TFs at enhancers. Our method is based on probabilistic item set mining and takes into account uncertainty in both types of ChIP-Seq data. By joint analysis of 108 TFs in four human cell types, we found that cell–type-specific interactions among TFs are abundant and that the majority of enhancers have flexible architecture. We show that several families of transposable elements disproportionally overlap with enhancers with combinatorial patterns, suggesting that these transposable element families play an important role in the evolution of combinatorial regulation.

Developmental cis-regulatory analysis of the cyclin D gene in the sea urchin Strongylocentrotus purpuratus

Cyclin D genes regulate the cell cycle, growth and differentiation in response to intercellular signaling. While the promoters of vertebrate cyclin D genes have been analyzed, the cis-regulatory sequences across an entire cyclin D locus have not. Doing so would increase understanding of how cyclin D genes respond to the regulatory states established by developmental gene regulatory networks, linking cell cycle and growth control to the ontogenetic program. Therefore, we conducted a cis-regulatory analysis on the cyclin D gene, SpcycD, of the sea urchin, Strongylocentrotus purpuratus, during embryogenesis, identifying upstream and intronic sequences, located within six defined regions bearing one or more cis-regulatory modules each.

Global parameter estimation for thermodynamic models of transcriptional regulation

Deciphering the mechanisms involved in gene regulation holds the key to understanding the control of central biological processes, including human disease, population variation, and the evolution of morphological innovations. New experimental techniques including whole genome sequencing and transcriptome analysis have enabled comprehensive modeling approaches to study gene regulation. In many cases, it is useful to be able to assign biological significance to the inferred model parameters, but such interpretation should take into account features that affect these parameters, including model construction and sensitivity, the type of fitness calculation, and the effectiveness of parameter estimation. This last point is often neglected, as estimation methods are often selected for historical reasons or for computational ease. Here, we compare the performance of two parameter estimation techniques broadly representative of local and global approaches, namely, a quasi-Newton/Nelder-Mead simplex (QN/NMS) method and a covariance matrix adaptation-evolutionary strategy (CMA-ES) method. The estimation methods were applied to a set of thermodynamic models of gene transcription applied to regulatory elements active in the Drosophila embryo. Measuring overall fit, the global CMA-ES method performed significantly better than the local QN/NMS method on high quality data sets, but this difference was negligible on lower quality data sets with increased noise or on data sets simplified by stringent thresholding. Our results suggest that the choice of parameter estimation technique for evaluation of gene expression models depends both on quality of data, the nature of the models [again, remains to be established] and the aims of the modeling effort.

TWO-LAYER MATHEMATICAL MODELING OF GENE EXPRESSION: INCORPORATING DNA-LEVEL INFORMATION AND SYSTEM DYNAMICS

High-throughput genome sequencing and transcriptome analysis have provided researchers with a quantitative basis for detailed modeling of gene expression using a wide variety of mathematical models. Two of the most commonly employed approaches used to model eukaryotic gene regulation are systems of differential equations, which describe time-dependent interactions of gene networks, and thermodynamic equilibrium approaches that can explore DNA-level transcriptional regulation. To combine the strengths of these approaches, we have constructed a new two-layer mathematical model that provides a dynamical description of gene regulatory systems, using detailed DNA-based information, as well as spatial and temporal transcription factor concentration data. We also developed a semi-implicit numerical algorithm for solving the model equations and demonstrate here the efficiency of this algorithm through stability and convergence analyses. To test the model, we used it together with the semi-implicit algorithm to simulate a Drosophila gene regulatory circuit that drives development in the dorsal-ventral axis of the blastoderm-stage embryo, involving three genes. For model validation, we have done both mathematical and statistical comparisons between the experimental data and the model's simulated data. Where protein and cis-regulatory information is available, our two-layer model provides a method for recapitulating and predicting dynamic aspects of eukaryotic transcriptional systems that will greatly improve our understanding of gene regulation at a global level.

Pantropic retroviruses as a transduction tool for sea urchin embryos

Sea urchins are an important model for experiments at the intersection of development and systems biology, and technical innovations that enhance the utility of this model are of great value. This study explores pantropic retroviruses as a transduction tool for sea urchin embryos, and demonstrates that pantropic retroviruses infect sea urchin embryos with high efficiency and genomically integrate at a copy number of one per cell. We successfully used a self-inactivation strategy to both insert a sea urchin-specific enhancer and disrupt the endogenous viral enhancer. The resulting self-inactivating viruses drive global and persistent gene expression, consistent with genomic integration during the first cell cycle. Together, these data provide substantial proof of principle for transduction technology in sea urchin embryos.

A two-scale mathematical model for DNA transcription

Unlike the earlier description of regulation of DNA transcription as a biological switch which simply turns on and off, scientists now understand that DNA transcription is a much more complex process. It can depend on several transcription factors (proteins) and DNA regulatory elements (transcription factor binding sites). The combination of these two groups of different scaled factors determines the transcription outcome. In this paper, we propose a two-scale mathematical model for the DNA transcription processes, which integrates the characteristics of both transcription factors and DNA cis-regulatory elements. The model was tested on a well designed synthetic system during early development stage of Drosophila embryo. The system involves three transcription factors (two activators and one repressor) and a reporter gene. The predicted results using the model were compared with the real experimental data using both graphical methods and statistical methods. Parameter estimation will also be discussed in the paper.

Towards synthetic gene circuits with enhancers: biology's multi-input integrators

One of the greatest challenges facing synthetic biology is to develop a technology that allows gene regulatory circuits in microbes to integrate multiple inputs or stimuli using a small DNA sequence "foot-print", and which will generate precise and reproducible outcomes. Achieving this goal is hindered by the routine utilization of the commonplace σ(70) promoters in gene-regulatory circuits. These promoters typically are not capable of integrating binding of more than two or three transcription factors in natural examples, which has limited the field to developing integrated circuits made of two-input biological "logic" gates. In natural examples the regulatory elements, which integrate multiple inputs are called enhancers. These regulatory elements are ubiquitous in all organisms in the tree of life, and interestingly metazoan and bacterial enhancers are significantly more similar in terms of both Transcription Factor binding site arrangement and biological function than previously thought. These similarities imply that there may be underlying enhancer design principles or grammar rules by which one can engineer novel gene regulatory circuits. However, at present our current understanding of enhancer structure-function relationship in all organisms is limited, thus preventing us from using these objects routinely in synthetic biology application. In order to alleviate this problem, in this book chapter, I will review our current view of bacterial enhancers, allowing us to first highlight the potential of enhancers to be a game-changing tool in synthetic biology application, and subsequently to draw a road-map for developing the necessary quantitative understanding to reach this goal.

MODELING AND SIMULATION OF MOLECULAR BIOLOGY SYSTEMS USING PETRI NETS: MODELING GOALS OF VARIOUS APPROACHES

Petri nets are a discrete event simulation approach developed for system representation, in particular for their concurrency and synchronization properties. Various extensions to the original theory of Petri nets have been used for modeling molecular biology systems and metabolic networks. These extensions are stochastic, colored, hybrid and functional. This paper carries out an initial review of the various modeling approaches based on Petri net found in the literature, and of the biological systems that have been successfully modeled with these approaches. Moreover, the modeling goals and possibilities of qualitative analysis and system simulation of each approach are discussed.

Stochastic modeling of the relationship between copy number and gene expression based on transcriptional logic

DNA copy number alterations (CNAs) can cause genetic diseases, and studies have revealed a relationship between CNAs and gene expression; however, the manner in which CNAs relate to gene expression and what regulatory mechanisms underlying the relationship remain unclear. In many instances, real data have revealed a nonlinear relationship between copy number and gene expression. In this paper, queueing theory is used to model this relationship, with the basic structural parameters involving transcription factor (TF) arrival and departure rates. A key finding is that the ratio of TF arrival rate to TF departure rate is critical: small and large ratios corresponding to nonlinear and linear relationships, respectively. Indeed, copy number amplifications do not necessarily lead to expression increases: when one of the regulatory TFs exists in a small amount, copy number gains can cause a down regulation. Using the concept of mutual information, we show that the TF with minimum activation probability can have maximum dependence in regulation: a TF in small amount could result in a nonlinear copy-number-gene-expression relationship and play a major role in regulation. The expectation-maximization algorithm is used to estimate the ratio of TF arrival rate to TF departure rate. The theoretical results are illustrated via simulations.

Evolutionary crossroads in developmental biology: sea urchins

Embryos of the echinoderms, especially those of sea urchins and sea stars, have been studied as model organisms for over 100 years. The simplicity of their early development, and the ease of experimentally perturbing this development, provides an excellent platform for mechanistic studies of cell specification and morphogenesis. As a result, echinoderms have contributed significantly to our understanding of many developmental mechanisms, including those that govern the structure and design of gene regulatory networks, those that direct cell lineage specification, and those that regulate the dynamic morphogenetic events that shape the early embryo.

Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance

In quantitative genetics, the degree of resemblance between parents and offspring is described in terms of the additive variance (V(A)) relative to genetic (V(G)) and phenotypic (V(P)) variance. For populations with extreme allele frequencies, high V(A)/V(G) can be explained without considering properties of the genotype-phenotype (GP) map. We show that randomly generated GP maps in populations with intermediate allele frequencies generate far lower V(A)/V(G) values than empirically observed. The main reason is that order-breaking behaviour is ubiquitous in random GP maps. Rearrangement of genotypic values to introduce order-preservation for one or more loci causes a dramatic increase in V(A)/V(G). This suggests the existence of order-preserving design principles in the regulatory machinery underlying GP maps. We illustrate this feature by showing how the ubiquitously observed monotonicity of dose-response relationships gives much higher V(A)/V(G) values than a unimodal dose-response relationship in simple gene network models.

Mathematical modeling of gene expression: a guide for the perplexed biologist

The detailed analysis of transcriptional networks holds a key for understanding central biological processes, and interest in this field has exploded due to new large-scale data acquisition techniques. Mathematical modeling can provide essential insights, but the diversity of modeling approaches can be a daunting prospect to investigators new to this area. For those interested in beginning a transcriptional mathematical modeling project, we provide here an overview of major types of models and their applications to transcriptional networks. In this discussion of recent literature on thermodynamic, Boolean, and differential equation models, we focus on considerations critical for choosing and validating a modeling approach that will be useful for quantitative understanding of biological systems.

Impulse control: temporal dynamics in gene transcription

Regulatory circuits controlling gene expression constantly rewire to adapt to environmental stimuli, differentiation cues, and disease. We review our current understanding of the temporal dynamics of gene expression in eukaryotes and prokaryotes and the molecular mechanisms that shape them. We delineate several prototypical temporal patterns, including "impulse" (or single-pulse) patterns in response to transient environmental stimuli, sustained (or state-transitioning) patterns in response to developmental cues, and oscillating patterns. We focus on impulse responses and their higher-order temporal organization in regulons and cascades and describe how core protein circuits and cis-regulatory sequences in promoters integrate with chromatin architecture to generate these responses.

Experimentally based sea urchin gene regulatory network and the causal explanation of developmental phenomenology

Gene regulatory networks for development underlie cell fate specification and differentiation. Network topology, logic and dynamics can be obtained by thorough experimental analysis. Our understanding of the gene regulatory network controlling endomesoderm specification in the sea urchin embryo has attained an advanced level such that it explains developmental phenomenology. Here we review how the network explains the mechanisms utilized in development to control the formation of dynamic expression patterns of transcription factors and signaling molecules. The network represents the genomic program controlling timely activation of specification and differentiation genes in the correct embryonic lineages. It can also be used to study evolution of body plans. We demonstrate how comparing the sea urchin gene regulatory network to that of the sea star and to that of later developmental stages in the sea urchin, reveals mechanisms underlying the origin of evolutionary novelty. The experimentally based gene regulatory network for endomesoderm specification in the sea urchin embryo provides unique insights into the system level properties of cell fate specification and its evolution.

Regulatory modules function in a non-autonomous manner to control transcription of the mbp gene

Multiple regulatory modules contribute to the complex expression programs realized by many loci. Although long thought of as isolated components, recent studies demonstrate that such regulatory sequences can physically associate with promoters and with each other and may localize to specific sub-nuclear transcription factories. These associations provide a substrate for putative interactions and have led to the suggested existence of a transcriptional interactome. Here, using a controlled strategy of transgenesis, we analyzed the functional consequences of regulatory sequence interaction within the myelin basic protein (mbp) locus. Interactions were revealed through comparisons of the qualitative and quantitative expression programs conferred by an allelic series of 11 different enhancer/inter-enhancer combinations ligated to a common promoter/reporter gene. In a developmentally contextual manner, the regulatory output of all modules changed markedly in the presence of other sequences. Predicted by transgene expression programs, deletion of one such module from the endogenous locus reduced oligodendrocyte expression levels but unexpectedly, also attenuated expression of the overlapping golli transcriptional unit. These observations support a regulatory architecture that extends beyond a combinatorial model to include frequent interactions capable of significantly modulating the functions conferred through regulatory modules in isolation.

Thermodynamic modeling of transcription: sensitivity analysis differentiates biological mechanism from mathematical model-induced effects

Background

Quantitative models of gene expression generate parameter values that can shed light on biological features such as transcription factor activity, cooperativity, and local effects of repressors. An important element in such investigations is sensitivity analysis, which determines how strongly a model's output reacts to variations in parameter values. Parameters of low sensitivity may not be accurately estimated, leading to unwarranted conclusions. Low sensitivity may reflect the nature of the biological data, or it may be a result of the model structure. Here, we focus on the analysis of thermodynamic models, which have been used extensively to analyze gene transcription. Extracted parameter values have been interpreted biologically, but until now little attention has been given to parameter sensitivity in this context.

Results

We apply local and global sensitivity analyses to two recent transcriptional models to determine the sensitivity of individual parameters. We show that in one case, values for repressor efficiencies are very sensitive, while values for protein cooperativities are not, and provide insights on why these differential sensitivities stem from both biological effects and the structure of the applied models. In a second case, we demonstrate that parameters that were thought to prove the system's dependence on activator-activator cooperativity are relatively insensitive. We show that there are numerous parameter sets that do not satisfy the relationships proferred as the optimal solutions, indicating that structural differences between the two types of transcriptional enhancers analyzed may not be as simple as altered activator cooperativity.

Conclusions

Our results emphasize the need for sensitivity analysis to examine model construction and forms of biological data used for modeling transcriptional processes, in order to determine the significance of estimated parameter values for thermodynamic models. Knowledge of parameter sensitivities can provide the necessary context to determine how modeling results should be interpreted in biological systems.

De novo identification and biophysical characterization of transcription-factor binding sites with microfluidic affinity analysis

Gene expression is regulated in part by protein transcription factors (TFs) that bind target regulatory DNA sequences. Predicting DNA binding sites and affinities from transcription factor sequence or structure is difficult; therefore, experimental data are required to link TFs to target sequences. We present a microfluidics-based approach for de novo discovery and quantitative biophysical characterization of DNA target sequences. We validated our technique by measuring sequence preferences for 28 S. cerevisiae TFs with a variety of DNA binding domains, including several that have proven difficult to study via other techniques. For each TF, we measured relative binding affinities to oligonucleotides covering all possible 8-bp DNA sequences to create a comprehensive map of sequence preferences; for 4 TFs, we also determined absolute affinities. We anticipate that these data and future use of this technique will provide information essential for understanding TF specificity, improving identification of regulatory sites, and reconstructing regulatory interactions.

TATA is a modular component of synthetic promoters

The expression of most genes is regulated by multiple transcription factors. The interactions between transcription factors produce complex patterns of gene expression that are not always obvious from the arrangement of cis-regulatory elements in a promoter. One critical element of promoters is the TATA box, the docking site for the RNA polymerase holoenzyme. Using a synthetic promoter system coupled to a thermodynamic model of combinatorial regulation, we analyze the effects of different strength TATA boxes on various aspects of combinatorial cis-regulation. The thermodynamic model explains 75% of the variance in gene expression in synthetic promoter libraries with different strength TATA boxes, suggesting that many of the salient aspects of cis-regulation are captured by the model. Our results demonstrate that the effect of changing the TATA box on gene expression is the same for all synthetic promoters regardless of the arrangement of cis-regulatory sites we studied. Our analysis also showed that in our synthetic system the strength of the RNA polymerase-TATA interaction does not alter the combinatorial interactions between transcription factors, or between transcription factors and RNA polymerase. Finally, we show that although stronger TATA boxes increase expression in a predictable fashion, stronger TATA boxes have very little effect on noise in our synthetic promoters, regardless of the arrangement of cis-regulatory sites. Our results support a modular model of promoter function, where cis-regulatory elements can be mixed and matched (programmed) with outcomes on expression that are predictable based on the rules of simple protein-protein and protein-DNA interactions.

Perturbation analysis analyzed--athematical modeling of intact and perturbed gene regulatory circuits for animal development

Gene regulatory networks for animal development are the underlying mechanisms controlling cell fate specification and differentiation. The architecture of gene regulatory circuits determines their information processing properties and their developmental function. It is a major task to derive realistic network models from exceedingly advanced high throughput experimental data. Here we use mathematical modeling to study the dynamics of gene regulatory circuits to advance the ability to infer regulatory connections and logic function from experimental data. This study is guided by experimental methodologies that are commonly used to study gene regulatory networks that control cell fate specification. We study the effect of a perturbation of an input on the level of its downstream genes and compare between the cis-regulatory execution of OR and AND logics. Circuits that initiate gene activation and circuits that lock on the expression of genes are analyzed. The model improves our ability to analyze experimental data and construct from it the network topology. The model also illuminates information processing properties of gene regulatory circuits for animal development.

Robustness under functional constraint: the genetic network for temporal expression in Drosophila neurogenesis

Precise temporal coordination of gene expression is crucial for many developmental processes. One central question in developmental biology is how such coordinated expression patterns are robustly controlled. During embryonic development of the Drosophila central nervous system, neural stem cells called neuroblasts express a group of genes in a definite order, which leads to the diversity of cell types. We produced all possible regulatory networks of these genes and examined their expression dynamics numerically. From the analysis, we identified requisite regulations and predicted an unknown factor to reproduce known expression profiles caused by loss-of-function or overexpression of the genes in vivo, as well as in the wild type. Following this, we evaluated the stability of the actual Drosophila network for sequential expression. This network shows the highest robustness against parameter variations and gene expression fluctuations among the possible networks that reproduce the expression profiles. We propose a regulatory module composed of three types of regulations that is responsible for precise sequential expression. This study suggests that the Drosophila network for sequential expression has evolved to generate the robust temporal expression for neuronal specification.

Cell fate specification is of key importance in the development of multicellular organisms. To specify various cell fates correctly, genetic networks precisely coordinate spatial and temporal gene expression patterns during various developmental stages. One central question in developmental biology is to elucidate the relationship between the pattern formation and the network architecture. During embryonic development of the Drosophila central nervous system, the neural stem cells express a group of genes in a definite order, which is responsible for the diversity of neural cells. To elucidate the underlying mechanism of the process, we analyzed the structure and dynamics of the genetic network for the temporal changes occurring in the Drosophila neural stem cells. Searching all the possible regulatory networks of these genes using a computer program, we detected the requisite regulations that reproduce observed gene expression profiles. By comparing the stability of the dynamics among the functional networks, we uncovered the robust nature of the actual Drosophila network against environmental and intrinsic fluctuations. These results indicate that the genetic network for sequential expression has evolved to be robust under functional constraints. Our study proposes regulatory modules that are responsible for the precise sequential expressions, which might exist in genetic networks for other temporal patterning processes.

Combinatorial binding predicts spatio-temporal cis-regulatory activity

Development requires the establishment of precise patterns of gene expression, which are primarily controlled by transcription factors binding to cis-regulatory modules. Although transcription factor occupancy can now be identified at genome-wide scales, decoding this regulatory landscape remains a daunting challenge. Here we used a novel approach to predict spatio-temporal cis-regulatory activity based only on in vivo transcription factor binding and enhancer activity data. We generated a high-resolution atlas of cis-regulatory modules describing their temporal and combinatorial occupancy during Drosophila mesoderm development. The binding profiles of cis-regulatory modules with characterized expression were used to train support vector machines to predict five spatio-temporal expression patterns. In vivo transgenic reporter assays demonstrate the high accuracy of these predictions and reveal an unanticipated plasticity in transcription factor binding leading to similar expression. This data-driven approach does not require previous knowledge of transcription factor sequence affinity, function or expression, making it widely applicable.

A computational framework for qualitative simulation of nonlinear dynamical models of gene-regulatory networks

Background

Due to the huge amount of information at genomic level made recently available by high-throughput experimental technologies, networks of regulatory interactions between genes and gene products, the so-called gene-regulatory networks, can be uncovered. Most networks of interest are quite intricate because of both the high dimension of interacting elements and the complexity of the kinds of interactions between them. Then, mathematical and computational modeling frameworks are a must to predict the network behavior in response to environmental stimuli. A specific class of Ordinary Differential Equations (ODE) has shown to be adequate to describe the essential features of the dynamics of gene-regulatory networks. But, deriving quantitative predictions of the network dynamics through the numerical simulation of such models is mostly impracticable as they are currently characterized by incomplete knowledge of biochemical reactions underlying regulatory interactions, and of numeric values of kinetic parameters.

Results

This paper presents a computational framework for qualitative simulation of a class of ODE models, based on the assumption that gene regulation is threshold-dependent, i.e. only effective above or below a certain threshold. The simulation algorithm we propose assumes that threshold-dependent regulation mechanisms are modeled by continuous steep sigmoid functions, unlike other simulation tools that considerably simplifies the problem by approximating threshold-regulated response functions by step functions discontinuous in the thresholds. The algorithm results from the interplay between methods to deal with incomplete knowledge and to study phenomena that occur at different time-scales.

Conclusion

The work herein presented establishes the computational groundwork for a sound and a complete algorithm capable to capture the dynamical properties that depend only on the network structure and are invariant for ranges of values of kinetic parameters. At the current state of knowledge, the exploitation of such a tool is rather appropriate and useful to understand how specific activity patterns derive from given network structures, and what different types of dynamical behaviors are possible.

Building developmental gene regulatory networks

Animal development is an elaborate process programmed by genomic regulatory instructions. Regulatory genes encode transcription factors and signal molecules, and their expression is under the control of cis-regulatory modules that define the logic of transcriptional responses to the inputs of other regulatory genes. The functional linkages among regulatory genes constitute the gene regulatory networks (GRNs) that govern cell specification and patterning in development. Constructing such networks requires identification of the regulatory genes involved and characterization of their temporal and spatial expression patterns. Interactions (activation/repression) among transcription factors or signals can be investigated by large-scale perturbation analysis, in which the function of each gene is specifically blocked. Resultant expression changes are then integrated to identify direct linkages, and to reveal the structure of the GRN. Predicted GRN linkages can be tested and verified by cis-regulatory analysis. The explanatory power of the GRN was shown in the lineage specification of sea urchin endomesoderm. Acquiring such networks is essential for a systematic and mechanistic understanding of the developmental process.

Monte Carlo analysis of an ODE Model of the Sea Urchin Endomesoderm Network

BACKGROUND

Gene Regulatory Networks (GRNs) control the differentiation, specification and function of cells at the genomic level. The levels of interactions within large GRNs are of enormous depth and complexity. Details about many GRNs are emerging, but in most cases it is unknown to what extent they control a given process, i.e. the grade of completeness is uncertain. This uncertainty stems from limited experimental data, which is the main bottleneck for creating detailed dynamical models of cellular processes. Parameter estimation for each node is often infeasible for very large GRNs. We propose a method, based on random parameter estimations through Monte-Carlo simulations to measure completeness grades of GRNs.

RESULTS

We developed a heuristic to assess the completeness of large GRNs, using ODE simulations under different conditions and randomly sampled parameter sets to detect parameter-invariant effects of perturbations. To test this heuristic, we constructed the first ODE model of the whole sea urchin endomesoderm GRN, one of the best studied large GRNs. We find that nearly 48% of the parameter-invariant effects correspond with experimental data, which is 65% of the expected optimal agreement obtained from a submodel for which kinetic parameters were estimated and used for simulations. Randomized versions of the model reproduce only 23.5% of the experimental data.

CONCLUSION

The method described in this paper enables an evaluation of network topologies of GRNs without requiring any parameter values. The benefit of this method is exemplified in the first mathematical analysis of the complete Endomesoderm Network Model. The predictions we provide deliver candidate nodes in the network that are likely to be erroneous or miss unknown connections, which may need additional experiments to improve the network topology. This mathematical model can serve as a scaffold for detailed and more realistic models. We propose that our method can be used to assess a completeness grade of any GRN. This could be especially useful for GRNs involved in human diseases, where often the amount of connectivity is unknown and/or many genes/interactions are missing.

Characterization of the bovine pregnancy-associated glycoprotein gene family--analysis of gene sequences, regulatory regions within the promoter and expression of selected genes

BACKGROUND

The Pregnancy-associated glycoproteins (PAGs) belong to a large family of aspartic peptidases expressed exclusively in the placenta of species in the Artiodactyla order. In cattle, the PAG gene family is comprised of at least 22 transcribed genes, as well as some variants. Phylogenetic analyses have shown that the PAG family segregates into 'ancient' and 'modern' groupings. Along with sequence differences between family members, there are clear distinctions in their spatio-temporal distribution and in their relative level of expression. In this report, 1) we performed an in silico analysis of the bovine genome to further characterize the PAG gene family, 2) we scrutinized proximal promoter sequences of the PAG genes to evaluate the evolution pressures operating on them and to identify putative regulatory regions, 3) we determined relative transcript abundance of selected PAGs during pregnancy and, 4) we performed preliminary characterization of the putative regulatory elements for one of the candidate PAGs, bovine (bo) PAG-2.

RESULTS

From our analysis of the bovine genome, we identified 18 distinct PAG genes and 14 pseudogenes. We observed that the first 500 base pairs upstream of the translational start site contained multiple regions that are conserved among all boPAGs. However, a preponderance of conserved regions, that harbor recognition sites for putative transcriptional factors (TFs), were found to be unique to the modern boPAG grouping, but not the ancient boPAGs. We gathered evidence by means of Q-PCR and screening of EST databases to show that boPAG-2 is the most abundant of all boPAG transcripts. Finally, we provided preliminary evidence for the role of ETS- and DDVL-related TFs in the regulation of the boPAG-2 gene.

CONCLUSION

PAGs represent a relatively large gene family in the bovine genome. The proximal promoter regions of these genes display differences in putative TF binding sites, likely contributing to observed differences in spatial and temporal expression. We also discovered that boPAG-2 is the most abundant of all boPAG transcripts and provided evidence for the role of ETS and DDVL TFs in its regulation. These experiments mark the crucial first step in discerning the complex transcriptional regulation operating within the boPAG gene family.

Evolution of gene regulatory network architectures: examples of subcircuit conservation and plasticity between classes of echinoderms

Developmental gene regulatory networks (GRNs) explain how regulatory states are established in particular cells during development and how these states then determine the final form of the embryo. Evolutionary changes to the sequence of the genome will direct reorganization of GRN architectures, which in turn will lead to the alteration of developmental programs. A comparison of GRN architectures must consequently reveal the molecular basis for the evolution of developmental programs among different organisms. This review highlights some of the important findings that have emerged from the most extensive direct comparison of GRN architectures to date. Comparison of the orthologous GRNs for endomesodermal specification in the sea urchin and sea star, provides examples of several discrete, functional GRN subcircuits and shows that they are subject to diverse selective pressures. This demonstrates that different regulatory linkages may be more or less amenable to evolutionary change. One of the more surprising findings from this comparison is that GRN-level functions may be maintained while the factors performing the functions have changed, suggesting that GRNs have a high capacity for compensatory changes involving transcription factor binding to cis regulatory modules.

Modeling the dynamics of transcriptional gene regulatory networks for animal development

The dynamic process of cell fate specification is regulated by networks of regulatory genes. The architecture of the network defines the temporal order of specification events. To understand the dynamic control of the developmental process, the kinetics of mRNA and protein synthesis and the response of the cis-regulatory modules to transcription factor concentration must be considered. Here we review mathematical models for mRNA and protein synthesis kinetics which are based on experimental measurements of the rates of the relevant processes. The model comprises the response functions of cis-regulatory modules to their transcription factor inputs, by incorporating binding site occupancy and its dependence on biologically measurable quantities. We use this model to simulate gene expression, to distinguish between cis-regulatory execution of "AND" and "OR" logic functions, rationalize the oscillatory behavior of certain transcriptional auto-repressors and to show how linked subcircuits can be dealt with. Model simulations display the effects of mutation of binding sites, or perturbation of upstream gene expression. The model is a generally useful tool for understanding gene regulation and the dynamics of cell fate specification.