The segment polarity network is a robust developmental module

Quantitative nature of overexpression experiments

Overexpression experiments are sometimes considered as qualitative experiments designed to identify novel proteins and study their function. However, in order to draw conclusions regarding protein overexpression through association analyses using large-scale biological data sets, we need to recognize the quantitative nature of overexpression experiments. Here I discuss the quantitative features of two different types of overexpression experiment: absolute and relative. I also introduce the four primary mechanisms involved in growth defects caused by protein overexpression: resource overload, stoichiometric imbalance, promiscuous interactions, and pathway modulation associated with the degree of overexpression.

Robust Yet Fragile: Expression Noise, Protein Misfolding, and Gene Dosage in the Evolution of Genomes

The complex manner in which organisms respond to changes in their gene dosage has long fascinated geneticists. Oddly, although the existence of dominance implies that dosage reductions often have mild phenotypes, extra copies of whole chromosomes (aneuploidy) are generally strongly deleterious. Even more paradoxically, an extra copy of the genome is better tolerated than is aneuploidy. We review the resolution of this paradox, highlighting the roles of biochemistry, protein aggregation, and disruption of cellular microstructure in that explanation. Returning to life's curious combination of robustness and sensitivity to dosage changes, we argue that understanding how biological robustness evolved makes these observations less inexplicable. We propose that noise in gene expression and evolutionary strategies for its suppression play a role in generating dosage phenotypes. Finally, we outline an unappreciated mechanism for the preservation of duplicate genes, namely preservation to limit expression noise, arguing that it is particularly relevant in polyploid organisms.

Qualitative Dynamical Modelling Can Formally Explain Mesoderm Specification and Predict Novel Developmental Phenotypes

Given the complexity of developmental networks, it is often difficult to predict the effect of genetic perturbations, even within coding genes. Regulatory factors generally have pleiotropic effects, exhibit partially redundant roles, and regulate highly interconnected pathways with ample cross-talk. Here, we delineate a logical model encompassing 48 components and 82 regulatory interactions involved in mesoderm specification during Drosophila development, thereby providing a formal integration of all available genetic information from the literature. The four main tissues derived from mesoderm correspond to alternative stable states. We demonstrate that the model can predict known mutant phenotypes and use it to systematically predict the effects of over 300 new, often non-intuitive, loss- and gain-of-function mutations, and combinations thereof. We further validated several novel predictions experimentally, thereby demonstrating the robustness of model. Logical modelling can thus contribute to formally explain and predict regulatory outcomes underlying cell fate decisions.

Dynamical Robustness against Multiple Mutations in Signaling Networks

It has been known that the robust behavior of a cellular signaling network is strongly related to the structural characteristics of the network, such as connectivity, the number of feedback loops, and the number of feed-forward loops. Previous studies proved such relationships through dynamical simulations of various random network models. Most of them, however, focused on robustness against a single node mutation. Considering that complex diseases such as cancer are mostly caused by simultaneous dysfunction of multiple genes, it is needed to investigate the robustness of a network against multiple node mutations. In this paper, we investigated the robustness of a network against multiple node mutations through extensive simulations on the basis of Boolean network models. We found that the robustness against multiple mutations is, in most cases, weaker than the robustness against a single node mutation on average. Moreover, we found that the robustness against multiple mutations is strongly positively correlated with the robustness against single mutation. The difference between the multiple- and single-mutation robustness became larger as the number of mutated nodes increased or the number of nodes that are robust to single-mutation decreased. We further found that a node of relatively large connectivity or being involved with many feedback loops tends to be non-robust against multiple mutations. This finding is supported by the observation that poly-genic disease genes have high connectivity and are involved with a large number of feedback loops than mono-genic disease genes in a human signaling network. Together, our study shows that previous studies for a single node mutation can be extended to understand the network dynamics for multiple node mutations.

Odd-paired controls frequency doubling in Drosophila segmentation by altering the pair-rule gene regulatory network

The Drosophila embryo transiently exhibits a double-segment periodicity, defined by the expression of seven 'pair-rule' genes, each in a pattern of seven stripes. At gastrulation, interactions between the pair-rule genes lead to frequency doubling and the patterning of 14 parasegment boundaries. In contrast to earlier stages of Drosophila anteroposterior patterning, this transition is not well understood. By carefully analysing the spatiotemporal dynamics of pair-rule gene expression, we demonstrate that frequency-doubling is precipitated by multiple coordinated changes to the network of regulatory interactions between the pair-rule genes. We identify the broadly expressed but temporally patterned transcription factor, Odd-paired (Opa/Zic), as the cause of these changes, and show that the patterning of the even-numbered parasegment boundaries relies on Opa-dependent regulatory interactions. Our findings indicate that the pair-rule gene regulatory network has a temporally modulated topology, permitting the pair-rule genes to play stage-specific patterning roles.

Intrinsic limits to gene regulation by global crosstalk

Gene regulation relies on the specificity of transcription factor (TF)–DNA interactions. Limited specificity may lead to crosstalk: a regulatory state in which a gene is either incorrectly activated due to noncognate TF–DNA interactions or remains erroneously inactive. As each TF can have numerous interactions with noncognate cis-regulatory elements, crosstalk is inherently a global problem, yet has previously not been studied as such. We construct a theoretical framework to analyse the effects of global crosstalk on gene regulation. We find that crosstalk presents a significant challenge for organisms with low-specificity TFs, such as metazoans. Crosstalk is not easily mitigated by known regulatory schemes acting at equilibrium, including variants of cooperativity and combinatorial regulation. Our results suggest that crosstalk imposes a previously unexplored global constraint on the functioning and evolution of regulatory networks, which is qualitatively distinct from the known constraints that act at the level of individual gene regulatory elements.

Limited specificity of transcription factor-DNA interactions leads to crosstalk in gene regulation. Here the authors consider global crosstalk in regulatory networks of growing size and complexity, and show that it imposes constraints on gene regulation and on the evolution of regulatory networks.

Multi-class and multi-scale models of complex biological phenomena

Computational modeling has significantly impacted our ability to analyze vast (and exponentially increasing) quantities of experimental data for a variety of applications, such as drug discovery and disease forecasting. Single-scale, single-class models persist as the most common group of models, but biological complexity often demands more sophisticated approaches. This review surveys modeling approaches that are multi-class (incorporating multiple model types) and/or multi-scale (accounting for multiple spatial or temporal scales) and describes how these models, and combinations thereof, should be used within the context of the problem statement. We end by highlighting agent-based models as an intuitive, modular, and flexible framework within which multi-scale and multi-class models can be implemented.

Convergent occurrence of the developmental hourglass in plant and animal embryogenesis?

BACKGROUND

The remarkable similarity of animal embryos at particular stages of development led to the proposal of a developmental hourglass. In this model, early events in development are less conserved across species but lead to a highly conserved 'phylotypic period'. Beyond this stage, the model suggests that development once again becomes less conserved, leading to the diversity of forms. Recent comparative studies of gene expression in animal groups have provided strong support for the hourglass model. How and why might such an hourglass pattern be generated? More importantly, how might early acting events in development evolve while still maintaining a later conserved stage?

SCOPE

The discovery that an hourglass pattern may also exist in the embryogenesis of plants provides comparative data that may help us explain this phenomenon. Whether the developmental hourglass occurs in plants, and what this means for our understanding of embryogenesis in plants and animals is discussed. Models by which conserved early-acting genes might change their functional role in the evolution of gene networks, how networks buffer these changes, and how that might constrain, or confer diversity, of the body plan are also discused.

CONCLUSIONS

Evidence of a morphological and molecular hourglass in plant and animal embryogenesis suggests convergent evolution. This convergence is likely due to developmental constraints imposed upon embryogenesis by the need to produce a viable embryo with an established body plan, controlled by the architecture of the underlying gene regulatory networks. As the body plan is largely laid down during the middle phases of embryo development in plants and animals, then it is perhaps not surprising this stage represents the narrow waist of the hourglass where the gene regulatory networks are the oldest and most robust and integrated, limiting species diversity and constraining morphological space.

The developmental genetics of biological robustness

BACKGROUND

Living organisms are continuously confronted with perturbations, such as environmental changes that include fluctuations in temperature and nutrient availability, or genetic changes such as mutations. While some developmental systems are affected by such challenges and display variation in phenotypic traits, others continue consistently to produce invariable phenotypes despite perturbation. This ability of a living system to maintain an invariable phenotype in the face of perturbations is termed developmental robustness. Biological robustness is a phenomenon observed across phyla, and studying its mechanisms is central to deciphering the genotype-phenotype relationship. Recent work in yeast, animals and plants has shown that robustness is genetically controlled and has started to reveal the underlying mechinisms behind it.

SCOPE AND CONCLUSIONS

Studying biological robustness involves focusing on an important property of developmental traits, which is the phenotypic distribution within a population. This is often neglected because the vast majority of developmental biology studies instead focus on population aggregates, such as trait averages. By drawing on findings in animals and yeast, this Viewpoint considers how studies on plant developmental robustness may benefit from strict definitions of what is the developmental system of choice and what is the relevant perturbation, and also from clear distinctions between gene effects on the trait mean and the trait variance. Recent advances in quantitative developmental biology and high-throughput phenotyping now allow the design of targeted genetic screens to identify genes that amplify or restrict developmental trait variance and to study how variation propagates across different phenotypic levels in biological systems. The molecular characterization of more quantitative trait loci affecting trait variance will provide further insights into the evolution of genes modulating developmental robustness. The study of robustness mechanisms in closely related species will address whether mechanisms of robustness are evolutionarily conserved.

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.

The spatiotemporal order of signaling events unveils the logic of development signaling

Motivation: Animals from worms and insects to birds and mammals show distinct body plans; however, the embryonic development of diverse body plans with tissues and organs within is controlled by a surprisingly few signaling pathways. It is well recognized that combinatorial use of and dynamic interactions among signaling pathways follow specific logic to control complex and accurate developmental signaling and patterning, but it remains elusive what such logic is, or even, what it looks like.

Results: We have developed a computational model for Drosophila eye development with innovated methods to reveal how interactions among multiple pathways control the dynamically generated hexagonal array of R8 cells. We obtained two novel findings. First, the coupling between the long-range inductive signals produced by the proneural Hh signaling and the short-range restrictive signals produced by the antineural Notch and EGFR signaling is essential for generating accurately spaced R8s. Second, the spatiotemporal orders of key signaling events reveal a robust pattern of lateral inhibition conducted by Ato-coordinated Notch and EGFR signaling to collectively determine R8 patterning. This pattern, stipulating the orders of signaling and comparable to the protocols of communication, may help decipher the well-appreciated but poorly defined logic of developmental signaling.

Availability and implementation: The model is available upon request.

Contact:hao.zhu@ymail.com

Supplementary information:Supplementary data are available at Bioinformatics online.

The Density and Length of Root Hairs Are Enhanced in Response to Cadmium and Arsenic by Modulating Gene Expressions Involved in Fate Determination and Morphogenesis of Root Hairs in Arabidopsis

Root hairs are tubular outgrowths that originate from epidermal cells. Exposure of Arabidopsis to cadmium (Cd) and arsenic [arsenite, As(III)] increases root hair density and length. To examine the underlying mechanism, we measured the expression of genes involved in fate determination and morphogenesis of root hairs. Cd and As(III) downregulated TTG1 and GL2 (negative regulators of fate determination) and upregulated GEM (positive regulator), suggesting that root hair fate determination is stimulated by Cd and As(III). Cd and As(III) increased the transcript levels of genes involved in root hair initiation (RHD6 and AXR2) and root hair elongation (AUX1, AXR1, ETR1, and EIN2) except CTR1. DR5::GUS transgenic Arabidopsis showed a higher DR5 expression in the root tip, suggesting that Cd and As(III) increased the auxin content in the root tip. Knockdown of TTG1 in Arabidopsis resulted in increased root hair density and decreased root hair length compared with the control (Col-0) on 1/2 MS media. This phenotype may be attributed to the downregulation of GL2 and CTR1 and upregulation of RHD6. By contrast, gem mutant plants displayed a decrease in root hair density and length with reduced expression of RHD6, AXR2, AUX1, AXR1, ETR1, CTR1, and EIN2. Taken together, our results indicate that fate determination, initiation, and elongation of root hairs are stimulated in response to Cd and As(III) through the modulation of the expression of genes involved in these processes in Arabidopsis.

Evolution-development congruence in pattern formation dynamics: Bifurcations in gene expression and regulation of networks structures

Search for possible relationships between phylogeny and ontogeny is important in evolutionary-developmental biology. Here we uncover such relationships by numerical evolution and unveil their origin in terms of dynamical systems theory. By representing developmental dynamics of spatially located cells with gene expression dynamics with cell-to-cell interaction under external morphogen gradient, gene regulation networks are evolved under mutation and selection with the fitness to approach a prescribed spatial pattern of expressed genes. For most numerical evolution experiments, evolution of pattern over generations and development of pattern by an evolved network exhibit remarkable congruence. Both in the evolution and development pattern changes consist of several epochs where stripes are formed in a short time, while for other temporal regimes, pattern hardly changes. In evolution, these quasi-stationary regimes are generations needed to hit relevant mutations, while in development, they are due to some gene expression that varies slowly and controls the pattern change. The morphogenesis is regulated by combinations of feedback or feedforward regulations, where the upstream feedforward network reads the external morphogen gradient, and generates a pattern used as a boundary condition for the later patterns. The ordering from up to downstream is common in evolution and development, while the successive epochal changes in development and evolution are represented as common bifurcations in dynamical-systems theory, which lead to the evolution-development congruence. Mechanism of exceptional violation of the congruence is also unveiled. Our results provide a new look on developmental stages, punctuated equilibrium, developmental bottlenecks, and evolutionary acquisition of novelty in morphogenesis.

A Systematic Ensemble Approach to Thermodynamic Modeling of Gene Expression from Sequence Data

To understand the relationship between an enhancer DNA sequence and quantitative gene expression, thermodynamics-driven mathematical models of transcription are often employed. These "sequence-to-expression" models can describe an incomplete or even incorrect set of regulatory relationships if the parameter space is not searched systematically. Here, we focus on an enhancer of the Drosophila gene ind and demonstrate how a systematic search of parameter space can reveal a more comprehensive picture of a gene's regulatory mechanisms, resolve outstanding ambiguities, and suggest testable hypotheses. We describe an approach that generates an ensemble of ind models; all of these models are technically acceptable solutions to the sequence-to-expression problem in light of wild-type data, and some represent mechanistically distinct hypotheses about the regulation of ind. This ensemble can be restricted to biologically plausible models using requirements gleaned from in vivo perturbation experiments. Biologically plausible models make unique predictions about how specific ind enhancer sequences affect ind expression; we validate these predictions in vivo through site mutagenesis in transgenic Drosophila embryos.

Differential Masking of Natural Genetic Variation by miR-9a in Drosophila

Genetic variation is prevalent among individuals of the same species and yet the potential effects of genetic variation on developmental outcomes are frequently suppressed. Understanding the mechanisms that are responsible for this suppression is an important goal. Previously, we found that the microRNA miR-9a mitigates the impact of natural genetic variants that promote the development of scutellar bristles in adult Drosophila. Here we find that miR-9a does not affect the impact of genetic variants that inhibit the development of scutellar bristles. We show this using both directional and stabilizing selection in the laboratory. This specificity of action suggests that miR-9a does not interact with all functional classes of developmental genetic variants affecting sensory organ development. We also investigate the impact of miR-9a on a fitness trait, which is adult viability. At elevated physiological temperatures, miR-9a contributes to viability through masking genetic variants that hinder adult viability. We conclude that miR-9a activity in different developmental networks contributes to suppression of natural variants from perturbing development.

Synchronization of cells with activator-inhibitor pathways through adaptive environment-mediated coupling

In this paper, we report the synchronized dynamics of cells with activator-inhibitor pathways via an adaptive environment-mediated coupling scheme with feedbacks and control mechanisms. The adaptive character of the extracellular medium is modeled via its damping parameter as a physiological response aiming at annihilating the cellular differentiation existing between the chaotic biochemical pathways of the cells, in order to preserve homeostasis. We perform an investigation on the existence and stability of the synchronization manifold of the coupled system under the proposed coupling pattern. Both mathematical and computational tools suggest the accessibility of conducive prerequisites (conditions) for the emergence of a robust synchronous regime. The relevance of a phase-synchronized dynamics is appraised and several numerical indicators advocate for the prevalence of this fascinating phenomenon among the interacting cells in the phase space.

Designing a stochastic genetic switch by coupling chaos and bistability

In stem cell differentiation, a pluripotent stem cell becomes progressively specialized and generates specific cell types through a series of epigenetic processes. How cells can precisely determine their fate in a fluctuating environment is a currently unsolved problem. In this paper, we suggest an abstract gene regulatory network to describe mathematically the differentiation phenomenon featuring stochasticity, divergent cell fates, and robustness. The network consists of three functional motifs: an upstream chaotic motif, a buffering motif of incoherent feed forward loop capable of generating a pulse, and a downstream motif which is bistable. The dynamic behavior is typically a transient chaos with fractal basin boundaries. The trajectories take transiently chaotic journeys before divergently settling down to the bistable states. The ratio of the probability that the high state is achieved to the probability that the low state is reached can maintain a constant in a population of cells with varied molecular fluctuations. The ratio can be turned up or down when proper parameters are adjusted. The model suggests a possible mechanism for the robustness against fluctuations that is prominently featured in pluripotent cell differentiations and developmental phenomena.

Conditional robustness analysis for fragility discovery and target identification in biochemical networks and in cancer systems biology

Background

The study of cancer therapy is a key issue in the field of oncology research and the development of target therapies is one of the main problems currently under investigation. This is particularly relevant in different types of tumor where traditional chemotherapy approaches often fail, such as lung cancer.

Results

We started from the general definition of robustness introduced by Kitano and applied it to the analysis of dynamical biochemical networks, proposing a new algorithm based on moment independent analysis of input/output uncertainty. The framework utilizes novel computational methods which enable evaluating the model fragility with respect to quantitative performance measures and parameters such as reaction rate constants and initial conditions. The algorithm generates a small subset of parameters that can be used to act on complex networks and to obtain the desired behaviors. We have applied the proposed framework to the EGFR-IGF1R signal transduction network, a crucial pathway in lung cancer, as an example of Cancer Systems Biology application in drug discovery. Furthermore, we have tested our framework on a pulse generator network as an example of Synthetic Biology application, thus proving the suitability of our methodology to the characterization of the input/output synthetic circuits.

Conclusions

The achieved results are of immediate practical application in computational biology, and while we demonstrate their use in two specific examples, they can in fact be used to study a wider class of biological systems.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0216-5) contains supplementary material, which is available to authorized users.

Network-based discovery through mechanistic systems biology. Implications for applications--SMEs and drug discovery: where the action is

Phase II attrition remains the most important challenge for drug discovery. Tackling the problem requires improved understanding of the complexity of disease biology. Systems biology approaches to this problem can, in principle, deliver this. This article reviews the reports of the application of mechanistic systems models to drug discovery questions and discusses the added value. Although we are on the journey to the virtual human, the length, path and rate of learning from this remain an open question. Success will be dependent on the will to invest and make the most of the insight generated along the way.

The significance and scope of evolutionary developmental biology: a vision for the 21st century

Evolutionary developmental biology (evo-devo) has undergone dramatic transformations since its emergence as a distinct discipline. This paper aims to highlight the scope, power, and future promise of evo-devo to transform and unify diverse aspects of biology. We articulate key questions at the core of eleven biological disciplines-from Evolution, Development, Paleontology, and Neurobiology to Cellular and Molecular Biology, Quantitative Genetics, Human Diseases, Ecology, Agriculture and Science Education, and lastly, Evolutionary Developmental Biology itself-and discuss why evo-devo is uniquely situated to substantially improve our ability to find meaningful answers to these fundamental questions. We posit that the tools, concepts, and ways of thinking developed by evo-devo have profound potential to advance, integrate, and unify biological sciences as well as inform policy decisions and illuminate science education. We look to the next generation of evolutionary developmental biologists to help shape this process as we confront the scientific challenges of the 21st century.

Robust and precise morphogen-mediated patterning: trade-offs, constraints and mechanisms

The patterning of many developing tissues is organized by morphogens. Genetic and environmental perturbations of gene expression, protein synthesis and ligand binding are among the sources of unreliability that limit the accuracy and precision of morphogen-mediated patterning. While it has been found that the robustness of morphogen gradients to the perturbation of morphogen synthesis can be enhanced by particular mechanisms, how such mechanisms affect robustness to other perturbations, such as to receptor synthesis for the same morphogen, has been little explored. Here, we investigate the interplay between the robustness of patterning to the changes in receptor synthesis and morphogen synthesis and to the effects of cell-to-cell variability. Our analysis elucidates the trade-offs and constraints that arise as a result of achieving these three performance objectives simultaneously in the context of simple, steady-state morphogen gradients formed by diffusion and receptor-mediated uptake. Analysis of the interdependence between length scales of patterning and these performance objectives reveals several potential mechanisms for mitigating such trade-offs and constraints. One involves downregulation of receptor synthesis in the morphogen source, while another involves the presence of non-signalling cell-surface morphogen-binding molecules. Both of these mechanisms occur in Drosophila wing discs during their patterning. We computationally elucidate how these mechanisms improve the robustness and precision of morphogen-mediated patterning.

Inferring regulatory networks from experimental morphological phenotypes: a computational method reverse-engineers planarian regeneration

Transformative applications in biomedicine require the discovery of complex regulatory networks that explain the development and regeneration of anatomical structures, and reveal what external signals will trigger desired changes of large-scale pattern. Despite recent advances in bioinformatics, extracting mechanistic pathway models from experimental morphological data is a key open challenge that has resisted automation. The fundamental difficulty of manually predicting emergent behavior of even simple networks has limited the models invented by human scientists to pathway diagrams that show necessary subunit interactions but do not reveal the dynamics that are sufficient for complex, self-regulating pattern to emerge. To finally bridge the gap between high-resolution genetic data and the ability to understand and control patterning, it is critical to develop computational tools to efficiently extract regulatory pathways from the resultant experimental shape phenotypes. For example, planarian regeneration has been studied for over a century, but despite increasing insight into the pathways that control its stem cells, no constructive, mechanistic model has yet been found by human scientists that explains more than one or two key features of its remarkable ability to regenerate its correct anatomical pattern after drastic perturbations. We present a method to infer the molecular products, topology, and spatial and temporal non-linear dynamics of regulatory networks recapitulating in silico the rich dataset of morphological phenotypes resulting from genetic, surgical, and pharmacological experiments. We demonstrated our approach by inferring complete regulatory networks explaining the outcomes of the main functional regeneration experiments in the planarian literature; By analyzing all the datasets together, our system inferred the first systems-biology comprehensive dynamical model explaining patterning in planarian regeneration. This method provides an automated, highly generalizable framework for identifying the underlying control mechanisms responsible for the dynamic regulation of growth and form.

Developmental and regenerative biology experiments are producing a huge number of morphological phenotypes from functional perturbation experiments. However, existing pathway models do not generally explain the dynamic regulation of anatomical shape due to the difficulty of inferring and testing non-linear regulatory networks responsible for appropriate form, shape, and pattern. We present a method that automates the discovery and testing of regulatory networks explaining morphological outcomes directly from the resultant phenotypes, producing network models as testable hypotheses explaining regeneration data. Our system integrates a formalization of the published results in planarian regeneration, an in silico simulator in which the patterning properties of regulatory networks can be quantitatively tested in a regeneration assay, and a machine learning module that evolves networks whose behavior in this assay optimally matches the database of planarian results. We applied our method to explain the key experiments in planarian regeneration, and discovered the first comprehensive model of anterior-posterior patterning in planaria under surgical, pharmacological, and genetic manipulations. Beyond the planarian data, our approach is readily generalizable to facilitate the discovery of testable regulatory networks in developmental biology and biomedicine, and represents the first developmental model discovered de novo from morphological outcomes by an automated system.

STOCHASTIC MULTIRESONANCE INDUCED BY ADDITIVE AMPLITUDE MODULATION SIGNAL AND NOISE IN A GENE TRANSCRIPTIONAL REGULATORY MODEL

We investigate the stochastic resonance (SR) and stochastic multiresonance phenomena in a gene transcriptional regulatory system driven by additive amplitude modulation signal and cross-correlated noise. By using the general two-state approach, we obtained the analytic expression of signal-to-noise ratio (SNR) under the condition of adiabatic approximation. Our results show that the SR phenomenon can be observed and the peak of SR can be manipulated by the amplitude modulation deepness and the amplitude modulation frequency of the signal. More interestingly, stochastic multiresonance can be observed in the curve of SNR versus cross-correlation coefficient. Our results illustrate the potential to utilize the cross-correlation noise for controlling SNR under fixed noise intensity in the study of stochastic gene transcriptional regulatory process.

Reshaping the epigenetic landscape during early flower development: induction of attractor transitions by relative differences in gene decay rates

BACKGROUND

Gene regulatory network (GRN) dynamical models are standard systems biology tools for the mechanistic understanding of developmental processes and are enabling the formalization of the epigenetic landscape (EL) model.

METHODS

In this work we propose a modeling framework which integrates standard mathematical analyses to extend the simple GRN Boolean model in order to address questions regarding the impact of gene specific perturbations in cell-fate decisions during development.

RESULTS

We systematically tested the propensity of individual genes to produce qualitative changes to the EL induced by modification of gene characteristic decay rates reflecting the temporal dynamics of differentiation stimuli. By applying this approach to the flower specification GRN (FOS-GRN) we uncovered differences in the functional (dynamical) role of their genes. The observed dynamical behavior correlates with biological observables. We found a relationship between the propensity of undergoing attractor transitions between attraction basins in the EL and the direction of differentiation during early flower development - being less likely to induce up-stream attractor transitions as the course of development progresses. Our model also uncovered a potential mechanism at play during the transition from EL basins defining inflorescence meristem to those associated to flower organs meristem. Additionally, our analysis provided a mechanistic interpretation of the homeotic property of the ABC genes, being more likely to produce both an induced inter-attractor transition and to specify a novel attractor. Finally, we found that there is a close relationship between a gene's topological features and its propensity to produce attractor transitions.

CONCLUSIONS

The study of how the state-space associated with a dynamical model of a GRN can be restructured by modulation of genes' characteristic expression times is an important aid for understanding underlying mechanisms occurring during development. Our contribution offers a simple framework to approach such problem, as exemplified here by the case of flower development. Different GRN models and the effect of diverse inductive signals can be explored within the same framework. We speculate that the dynamical role of specific genes within a GRN, as uncovered here, might give information about which genes are more likely to link a module to other regulatory circuits and signaling transduction pathways.

Elements of the cellular metabolic structure

A large number of studies have demonstrated the existence of metabolic covalent modifications in different molecular structures, which are able to store biochemical information that is not encoded by DNA. Some of these covalent mark patterns can be transmitted across generations (epigenetic changes). Recently, the emergence of Hopfield-like attractor dynamics has been observed in self-organized enzymatic networks, which have the capacity to store functional catalytic patterns that can be correctly recovered by specific input stimuli. Hopfield-like metabolic dynamics are stable and can be maintained as a long-term biochemical memory. In addition, specific molecular information can be transferred from the functional dynamics of the metabolic networks to the enzymatic activity involved in covalent post-translational modulation, so that determined functional memory can be embedded in multiple stable molecular marks. The metabolic dynamics governed by Hopfield-type attractors (functional processes), as well as the enzymatic covalent modifications of specific molecules (structural dynamic processes) seem to represent the two stages of the dynamical memory of cellular metabolism (metabolic memory). Epigenetic processes appear to be the structural manifestation of this cellular metabolic memory. Here, a new framework for molecular information storage in the cell is presented, which is characterized by two functionally and molecularly interrelated systems: a dynamic, flexible and adaptive system (metabolic memory) and an essentially conservative system (genetic memory). The molecular information of both systems seems to coordinate the physiological development of the whole cell.

Modeling the epigenetic attractors landscape: toward a post-genomic mechanistic understanding of development

Robust temporal and spatial patterns of cell types emerge in the course of normal development in multicellular organisms. The onset of degenerative diseases may result from altered cell fate decisions that give rise to pathological phenotypes. Complex networks of genetic and non-genetic components underlie such normal and altered morphogenetic patterns. Here we focus on the networks of regulatory interactions involved in cell-fate decisions. Such networks modeled as dynamical non-linear systems attain particular stable configurations on gene activity that have been interpreted as cell-fate states. The network structure also restricts the most probable transition patterns among such states. The so-called Epigenetic Landscape (EL), originally proposed by C. H. Waddington, was an early attempt to conceptually explain the emergence of developmental choices as the result of intrinsic constraints (regulatory interactions) shaped during evolution. Thanks to the wealth of molecular genetic and genomic studies, we are now able to postulate gene regulatory networks (GRN) grounded on experimental data, and to derive EL models for specific cases. This, in turn, has motivated several mathematical and computational modeling approaches inspired by the EL concept, that may be useful tools to understand and predict cell-fate decisions and emerging patterns. In order to distinguish between the classical metaphorical EL proposal of Waddington, we refer to the Epigenetic Attractors Landscape (EAL), a proposal that is formally framed in the context of GRNs and dynamical systems theory. In this review we discuss recent EAL modeling strategies, their conceptual basis and their application in studying the emergence of both normal and pathological developmental processes. In addition, we discuss how model predictions can shed light into rational strategies for cell fate regulation, and we point to challenges ahead.

Boolean modeling: a logic-based dynamic approach for understanding signaling and regulatory networks and for making useful predictions

The biomolecules inside or near cells form a complex interacting system. Cellular phenotypes and behaviors arise from the totality of interactions among the components of this system. A fruitful way of modeling interacting biomolecular systems is by network-based dynamic models that characterize each component by a state variable, and describe the change in the state variables due to the interactions in the system. Dynamic models can capture the stable state patterns of this interacting system and can connect them to different cell fates or behaviors. A Boolean or logic model characterizes each biomolecule by a binary state variable that relates the abundance of that molecule to a threshold abundance necessary for downstream processes. The regulation of this state variable is described in a parameter free manner, making Boolean modeling a practical choice for systems whose kinetic parameters have not been determined. Boolean models integrate the body of knowledge regarding the components and interactions of biomolecular systems, and capture the system's dynamic repertoire, for example the existence of multiple cell fates. These models were used for a variety of systems and led to important insights and predictions. Boolean models serve as an efficient exploratory model, a guide for follow-up experiments, and as a foundation for more quantitative models.

Causal drift, robust signaling, and complex disease

The phenotype of many regulatory circuits in which mutations can cause complex, polygenic diseases is to some extent robust to DNA mutations that affect circuit components. Here I demonstrate how such mutational robustness can prevent the discovery of genetic disease determinants. To make my case, I use a mathematical model of the insulin signaling pathway implicated in type 2 diabetes, whose signaling output is governed by 15 genetically determined parameters. Using multiple complementary measures of a parameter's importance for this phenotype, I show that any one disease determinant that is crucial in one genetic background will be virtually irrelevant in other backgrounds. In an evolving population that drifts through the parameter space of this or other robust circuits through DNA mutations, the genetic changes that can cause disease will vary randomly over time. I call this phenomenon causal drift. It means that mutations causing disease in one (human or non-human) population may have no effect in another population, and vice versa. Causal drift casts doubt on our ability to infer the molecular mechanisms of complex diseases from non-human model organisms.

Quantitative and logic modelling of molecular and gene networks

Behaviours of complex biomolecular systems are often irreducible to the elementary properties of their individual components. Explanatory and predictive mathematical models are therefore useful for fully understanding and precisely engineering cellular functions. The development and analyses of these models require their adaptation to the problems that need to be solved and the type and amount of available genetic or molecular data. Quantitative and logic modelling are among the main methods currently used to model molecular and gene networks. Each approach comes with inherent advantages and weaknesses. Recent developments show that hybrid approaches will become essential for further progress in synthetic biology and in the development of virtual organisms.

Positional information, positional error, and readout precision in morphogenesis: a mathematical framework

The concept of positional information is central to our understanding of how cells determine their location in a multicellular structure and thereby their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns and examine the features of expression patterns that affect positional information quantitatively. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with nearly single-cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail.

Modeling the evolution of complex genetic systems: the gene network family tree

In 1994 and 1996, Andreas Wagner introduced a novel model in two papers addressing the evolution of genetic regulatory networks. This work, and a suite of papers that followed using similar models, helped integrate network thinking into biology and motivate research focused on the evolution of genetic networks. The Wagner network has its mathematical roots in the Ising model, a statistical physics model describing the activity of atoms on a lattice, and in neural networks. These models have given rise to two branches of applications, one in physics and biology and one in artificial intelligence and machine learning. Here, we review development along these branches, outline similarities and differences between biological models of genetic regulatory circuits and neural circuits models used in machine learning, and identify ways in which these models can provide novel insights into biological systems.

Systems biology. Accurate information transmission through dynamic biochemical signaling networks

Stochasticity inherent to biochemical reactions (intrinsic noise) and variability in cellular states (extrinsic noise) degrade information transmitted through signaling networks. We analyzed the ability of temporal signal modulation--that is, dynamics--to reduce noise-induced information loss. In the extracellular signal-regulated kinase (ERK), calcium (Ca(2+)), and nuclear factor kappa-B (NF-κB) pathways, response dynamics resulted in significantly greater information transmission capacities compared to nondynamic responses. Theoretical analysis demonstrated that signaling dynamics has a key role in overcoming extrinsic noise. Experimental measurements of information transmission in the ERK network under varying signal-to-noise levels confirmed our predictions and showed that signaling dynamics mitigate, and can potentially eliminate, extrinsic noise-induced information loss. By curbing the information-degrading effects of cell-to-cell variability, dynamic responses substantially increase the accuracy of biochemical signaling networks.

Dynamics of miRNA driven feed-forward loop depends upon miRNA action mechanisms

Background

We perform the theoretical analysis of a gene network sub-system, composed of a feed-forward loop, in which the upstream transcription factor regulates the target gene via two parallel pathways: directly, and via interaction with miRNA.

Results

As the molecular mechanisms of miRNA action are not clear so far, we elaborate three mathematical models, in which miRNA either represses translation of its target or promotes target mRNA degradation, or is not re-used, but degrades along with target mRNA. We examine the feed-forward loop dynamics quantitatively at the whole time interval of cell cycle. We rigorously proof the uniqueness of solutions to the models and obtain the exact solutions in one of them analytically.

Conclusions

We have shown that different mechanisms of miRNA action lead to a variety of types of dynamical behavior of feed-forward loops. In particular, we found that the ability of feed-forward loop to dampen fluctuations introduced by transcription factor is the model and parameter dependent feature. We also discuss how our results could help a biologist to infer the mechanism of miRNA action.

Functional optimization of gene clusters by combinatorial design and assembly

Large microbial gene clusters encode useful functions, including energy utilization and natural product biosynthesis, but genetic manipulation of such systems is slow, difficult and complicated by complex regulation. We exploit the modularity of a refactored Klebsiella oxytoca nitrogen fixation (nif) gene cluster (16 genes, 103 parts) to build genetic permutations that could not be achieved by starting from the wild-type cluster. Constraint-based combinatorial design and DNA assembly are used to build libraries of radically different cluster architectures by varying part choice, gene order, gene orientation and operon occupancy. We construct 84 variants of the nifUSVWZM operon, 145 variants of the nifHDKY operon, 155 variants of the nifHDKYENJ operon and 122 variants of the complete 16-gene pathway. The performance and behavior of these variants are characterized by nitrogenase assay and strand-specific RNA sequencing (RNA-seq), and the results are incorporated into subsequent design cycles. We have produced a fully synthetic cluster that recovers 57% of wild-type activity. Our approach allows the performance of genetic parts to be quantified simultaneously in hundreds of genetic contexts. This parallelized design-build-test-learn cycle, which can access previously unattainable regions of genetic space, should provide a useful, fast tool for genetic optimization and hypothesis testing.

Natural selection canalizes expression variation of environmentally induced plasticity-enabling genes

Many organisms survive fluctuating and extreme environmental conditions by manifesting multiple distinct phenotypes during adulthood by means of developmental processes that enable phenotypic plasticity. We report on the discovery of putative plasticity-enabling genes that are involved in transforming the gill of the euryhaline teleost fish, Fundulus heteroclitus, from its freshwater to its seawater gill-type, a process that alters both morphology and function. Gene expression that normally enables osmotic plasticity is inhibited by arsenic. Gene sets defined by antagonistic interactions between arsenic and salinity show reduced transcriptional variation among individual fish, suggesting unusually accurate and precise regulatory control of these genes, consistent with the hypothesis that they participate in a canalized developmental response. We observe that natural selection acts to preserve canalized gene expression in populations of killifish that are most tolerant to abrupt salinity change and that these populations show the least variability in their transcription of genes enabling plasticity of the gill. We found that genes participating in this highly canalized and conserved plasticity-enabling response had significantly fewer and less complex associations with transcriptional regulators than genes that respond only to arsenic or salinity. Collectively these findings, which are drawn from the relationships between environmental challenge, plasticity, and canalization among populations, suggest that the selective processes that facilitate phenotypic plasticity do so by targeting the regulatory networks that gives rise to the response. These findings also provide a generalized, conceptual framework of how genes might interact with the environment and evolve toward the development of plastic traits.

On the Nature and Evolutionary Impact of Phenotypic Robustness Mechanisms

Biologists have long observed that physiological and developmental processes are insensitive, or robust, to many genetic and environmental perturbations. A complete understanding of the evolutionary causes and consequences of this robustness is lacking. Recent progress has been made in uncovering the regulatory mechanisms that underlie environmental robustness in particular. Less is known about robustness to the effects of mutations, and indeed the evolution of mutational robustness remains a controversial topic. The controversy has spread to related topics, in particular the evolutionary relevance of cryptic genetic variation. This review aims to synthesize current understanding of robustness mechanisms and to cut through the controversy by shedding light on what is and is not known about mutational robustness. Some studies have confused mutational robustness with non-additive interactions between mutations (epistasis). We conclude that a profitable way forward is to focus investigations (and rhetoric) less on mutational robustness and more on epistasis.

Systematic reverse engineering of network topologies: a case study of resettable bistable cellular responses

A focused theme in systems biology is to uncover design principles of biological networks, that is, how specific network structures yield specific systems properties. For this purpose, we have previously developed a reverse engineering procedure to identify network topologies with high likelihood in generating desired systems properties. Our method searches the continuous parameter space of an assembly of network topologies, without enumerating individual network topologies separately as traditionally done in other reverse engineering procedures. Here we tested this CPSS (continuous parameter space search) method on a previously studied problem: the resettable bistability of an Rb-E2F gene network in regulating the quiescence-to-proliferation transition of mammalian cells. From a simplified Rb-E2F gene network, we identified network topologies responsible for generating resettable bistability. The CPSS-identified topologies are consistent with those reported in the previous study based on individual topology search (ITS), demonstrating the effectiveness of the CPSS approach. Since the CPSS and ITS searches are based on different mathematical formulations and different algorithms, the consistency of the results also helps cross-validate both approaches. A unique advantage of the CPSS approach lies in its applicability to biological networks with large numbers of nodes. To aid the application of the CPSS approach to the study of other biological systems, we have developed a computer package that is available in Information S1.