The segment polarity network is a robust developmental module

Developmental bias in horned dung beetles and its contributions to innovation, adaptation, and resilience

Developmental processes transduce diverse influences during phenotype formation, thereby biasing and structuring amount and type of phenotypic variation available for evolutionary processes to act on. The causes, extent, and consequences of this bias are subject to significant debate. Here we explore the role of developmental bias in contributing to organisms' ability to innovate, to adapt to novel or stressful conditions, and to generate well integrated, resilient phenotypes in the face of perturbations. We focus our inquiry on one taxon, the horned dung beetle genus Onthophagus, and review the role developmental bias might play across several levels of biological organization: (a) gene regulatory networks that pattern specific body regions; (b) plastic developmental mechanisms that coordinate body wide responses to changing environments and; (c) developmental symbioses and niche construction that enable organisms to build teams and to actively modify their own selective environments. We posit that across all these levels developmental bias shapes the way living systems innovate, adapt, and withstand stress, in ways that can alternately limit, bias, or facilitate developmental evolution. We conclude that the structuring contribution of developmental bias in evolution deserves further study to better understand why and how developmental evolution unfolds the way it does.

Bayesian model selection for the Drosophila gap gene network

Background

The gap gene system controls the early cascade of the segmentation pathway in Drosophila melanogaster as well as other insects. Owing to its tractability and key role in embryo patterning, this system has been the focus for both computational modelers and experimentalists. The gap gene expression dynamics can be considered strictly as a one-dimensional process and modeled as a system of reaction-diffusion equations. While substantial progress has been made in modeling this phenomenon, there still remains a deficit of approaches to evaluate competing hypotheses. Most of the model development has happened in isolation and there has been little attempt to compare candidate models.

Results

The Bayesian framework offers a means of doing formal model evaluation. Here, we demonstrate how this framework can be used to compare different models of gene expression. We focus on the Papatsenko-Levine formalism, which exploits a fractional occupancy based approach to incorporate activation of the gap genes by the maternal genes and cross-regulation by the gap genes themselves. The Bayesian approach provides insight about relationship between system parameters. In the regulatory pathway of segmentation, the parameters for number of binding sites and binding affinity have a negative correlation. The model selection analysis supports a stronger binding affinity for Bicoid compared to other regulatory edges, as shown by a larger posterior mean. The procedure doesn’t show support for activation of Kruppel by Bicoid.

Conclusions

We provide an efficient solver for the general representation of the Papatsenko-Levine model. We also demonstrate the utility of Bayes factor for evaluating candidate models for spatial pattering models. In addition, by using the parallel tempering sampler, the convergence of Markov chains can be remarkably improved and robust estimates of Bayes factors obtained.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2888-0) contains supplementary material, which is available to authorized users.

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

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

Transcriptome Analysis of Larval Segment Formation and Secondary Loss in the Echiuran Worm Urechis unicinctus

The larval segment formation and secondary loss in echiurans is a special phenomenon, which is considered to be one of the important characteristics in the evolutionary relationship between the Echiura and Annelida. To better understand the molecular mechanism of this phenomenon, we revealed the larval transcriptome profile of the echiuran worm Urechis unicinctus using RNA-Seq technology. Twelve cDNA libraries of U. unicinctus larvae, late-trochophore (LT), early-segmentation larva (ES), segmentation larva (SL), and worm-shaped larva (WL) were constructed. Totally 243,381 unigenes were assembled with an average length of 1125 bp and N50 of 1836 bp, and 149,488 unigenes (61.42%) were annotated. We obtained 70,517 differentially expressed genes (DEGs) by pairwise comparison of the larval transcriptome data at different developmental stages and clustered them into 20 gene expression profiles using STEM software. Based on the typical profiles during the larval segment formation and secondary loss, eight signaling pathways were enriched, and five of which, mTOR, PI3K-AKT, TGF-β, MAPK, and Dorso-ventral axis formation signaling pathway, were proposed for the first time to be involved in the segment formation. Furthermore, we identified 119 unigenes related to the segment formation of annelids, arthropods, and chordates, in which 101 genes were identified in Drosophila and annelids. The function of most segment polarity gene homologs (hedgehog, wingless, engrailed, etc.) was conserved in echiurans, annelids, and arthropods based on their expression profiles, while the gap and pair-rule gene homologs were not. Finally, we verified that strong positive signals of Hedgehog were indeed located on the boundary of larval segments using immunofluorescence. Data in this study provide molecular evidence for the understanding of larval segment development in echiurans and may serve as a blueprint for segmented ancestors in future research.

Beetles as Model Organisms in Physiological, Biomedical and Environmental Studies - A Review

Model organisms are often used in biological, medical and environmental research. Among insects, Drosophila melanogaster, Galleria mellonella, Apis mellifera, Bombyx mori, Periplaneta americana, and Locusta migratoria are often used. However, new model organisms still appear. In recent years, an increasing number of insect species has been suggested as model organisms in life sciences research due to their worldwide distribution and environmental significance, the possibility of extrapolating research studies to vertebrates and the relatively low cost of rearing. Beetles are the largest insect order, with their representative - Tribolium castaneum - being the first species with a completely sequenced genome, and seem to be emerging as new potential candidates for model organisms in various studies. Apart from T. castaneum, additional species representing various Coleoptera families, such as Nicrophorus vespilloides, Leptinotarsa decemlineata, Coccinella septempunctata, Poecilus cupreus, Tenebrio molitor and many others, have been used. They are increasingly often included in two major research aspects: biomedical and environmental studies. Biomedical studies focus mainly on unraveling mechanisms of basic life processes, such as feeding, neurotransmission or activity of the immune system, as well as on elucidating the mechanism of different diseases (neurodegenerative, cardiovascular, metabolic, or immunological) using beetles as models. Furthermore, pharmacological bioassays for testing novel biologically active substances in beetles have also been developed. It should be emphasized that beetles are a source of compounds with potential antimicrobial and anticancer activity. Environmental-based studies focus mainly on the development and testing of new potential pesticides of both chemical and natural origin. Additionally, beetles are used as food or for their valuable supplements. Different beetle families are also used as bioindicators. Another important research area using beetles as models is behavioral ecology studies, for instance, parental care. In this paper, we review the current knowledge regarding beetles as model organisms and their practical application in various fields of life science.

Algorithmic and Stochastic Representations of Gene Regulatory Networks and Protein-Protein Interactions

BACKGROUND

Latest studies reveal the importance of Protein-Protein interactions on physiologic functions and biological structures. Several stochastic and algorithmic methods have been published until now, for the modeling of the complex nature of the biological systems.

OBJECTIVE

Biological Networks computational modeling is still a challenging task. The formulation of the complex cellular interactions is a research field of great interest. In this review paper, several computational methods for the modeling of GRN and PPI are presented analytically.

METHODS

Several well-known GRN and PPI models are presented and discussed in this review study such as: Graphs representation, Boolean Networks, Generalized Logical Networks, Bayesian Networks, Relevance Networks, Graphical Gaussian models, Weight Matrices, Reverse Engineering Approach, Evolutionary Algorithms, Forward Modeling Approach, Deterministic models, Static models, Hybrid models, Stochastic models, Petri Nets, BioAmbients calculus and Differential Equations.

RESULTS

GRN and PPI methods have been already applied in various clinical processes with potential positive results, establishing promising diagnostic tools.

CONCLUSION

In literature many stochastic algorithms are focused in the simulation, analysis and visualization of the various biological networks and their dynamics interactions, which are referred and described in depth in this review paper.

Identifying (un)controllable dynamical behavior in complex networks

We present a technique applicable in any dynamical framework to identify control-robust subsets of an interacting system. These robust subsystems, which we call stable modules, are characterized by constraints on the variables that make up the subsystem. They are robust in the sense that if the defining constraints are satisfied at a given time, they remain satisfied for all later times, regardless of what happens in the rest of the system, and can only be broken if the constrained variables are externally manipulated. We identify stable modules as graph structures in an expanded network, which represents causal links between variable constraints. A stable module represents a system "decision point", or trap subspace. Using the expanded network, small stable modules can be composed sequentially to form larger stable modules that describe dynamics on the system level. Collections of large, mutually exclusive stable modules describe the system's repertoire of long-term behaviors. We implement this technique in a broad class of dynamical systems and illustrate its practical utility via examples and algorithmic analysis of two published biological network models. In the segment polarity gene network of Drosophila melanogaster, we obtain a state-space visualization that reproduces by novel means the four possible cell fates and predicts the outcome of cell transplant experiments. In the T-cell signaling network, we identify six signaling elements that determine the high-signal response and show that control of an element connected to them cannot disrupt this response.

Growth zone segmentation in the milkweed bug Oncopeltus fasciatus sheds light on the evolution of insect segmentation

Background

One of the best studied developmental processes is the Drosophila segmentation cascade. However, this cascade is generally considered to be highly derived and unusual, with segments being patterned simultaneously, rather than the ancestral sequential segmentation mode. We present a detailed analysis of the segmentation cascade of the milkweed bug Oncopletus fasciatus, an insect with a more primitive segmentation mode, as a comparison to Drosophila, with the aim of reconstructing the evolution of insect segmentation modes.

Results

We document the expression of 12 genes, representing different phases in the segmentation process. Using double staining we reconstruct the spatio-temporal relationships among these genes. We then show knock-down phenotypes of representative genes in order to uncover their roles and position in the cascade.

Conclusions

We conclude that sequential segmentation in the Oncopeltus germband includes three slightly overlapping phases: Primary pair-rule genes generate the first segmental gene expression in the anterior growth zone. This pattern is carried anteriorly by a series of secondary pair-rule genes, expressed in the transition between the growth zone and the segmented germband. Segment polarity genes are expressed in the segmented germband with conserved relationships. Unlike most holometabolous insects, this process generates a single-segment periodicity, and does not have a double-segment pattern at any stage. We suggest that the evolutionary transition to double-segment patterning lies in mutually exclusive expression patterns of secondary pair-rule genes. The fact that many aspects of the putative Oncopeltus segmentation network are similar to those of Drosophila, is consistent with a simple transition between sequential and simultaneous segmentation.

Electronic supplementary material

The online version of this article (10.1186/s12862-018-1293-z) contains supplementary material, which is available to authorized users.

Computational Modeling and Reverse Engineering to Reveal Dominant Regulatory Interactions Controlling Osteochondral Differentiation: Potential for Regenerative Medicine

The specialization of cartilage cells, or chondrogenic differentiation, is an intricate and meticulously regulated process that plays a vital role in both bone formation and cartilage regeneration. Understanding the molecular regulation of this process might help to identify key regulatory factors that can serve as potential therapeutic targets, or that might improve the development of qualitative and robust skeletal tissue engineering approaches. However, each gene involved in this process is influenced by a myriad of feedback mechanisms that keep its expression in a desirable range, making the prediction of what will happen if one of these genes defaults or is targeted with drugs, challenging. Computer modeling provides a tool to simulate this intricate interplay from a network perspective. This paper aims to give an overview of the current methodologies employed to analyze cell differentiation in the context of skeletal tissue engineering in general and osteochondral differentiation in particular. In network modeling, a network can either be derived from mechanisms and pathways that have been reported in the literature (knowledge-based approach) or it can be inferred directly from the data (data-driven approach). Combinatory approaches allow further optimization of the network. Once a network is established, several modeling technologies are available to interpret dynamically the relationships that have been put forward in the network graph (implication of the activation or inhibition of certain pathways on the evolution of the system over time) and to simulate the possible outcomes of the established network such as a given cell state. This review provides for each of the aforementioned steps (building, optimizing, and modeling the network) a brief theoretical perspective, followed by a concise overview of published works, focusing solely on applications related to cell fate decisions, cartilage differentiation and growth plate biology. Particular attention is paid to an in-house developed example of gene regulatory network modeling of growth plate chondrocyte differentiation as all the aforementioned steps can be illustrated. In summary, this paper discusses and explores a series of tools that form a first step toward a rigorous and systems-level modeling of osteochondral differentiation in the context of regenerative medicine.

Development and Evolutionary Constraints in Animals

We review the evolutionary importance of developmental mechanisms in constraining evolutionary changes in animals—in other words, developmental constraints. We focus on hard constraints that can act on macroevolutionary timescales. In particular, we discuss the causes and evolutionary consequences of the ancient metazoan constraint that differentiated cells cannot divide and constraints against changes of phylotypic stages in vertebrates and other higher taxa. We conclude that in all cases these constraints are caused by complex and highly controlled global interactivity of development, the disturbance of which has grave consequences. Mutations that affect such global interactivity almost unavoidably have many deleterious pleiotropic effects, which will be strongly selected against and will lead to long-term evolutionary stasis. The discussed developmental constraints have pervasive consequences for evolution and critically restrict regeneration capacity and body plan evolution.

The Thermodynamics of Development in Bioartificial Tissue Design

The fabrication of bioartificial tissues with authentic structures that could assure their clinical efficacy remains a challenging problem. A new paradigm has emerged that designs bioartificial tissues as intermediate in development tissue forms, which can inherently progress autonomously on developmental pathways, self-organizing their cells into tissue structures as in their in vivo development. Biological processes involved in energy exchange between co-developing tissues are responsible for cell organization into the thermodynamically robust cellular patterns of tissue structures. Bioartificial tissue design rules that aim towards in vitro recapitulation of these processes can ensure the thermodynamic operation of developing tissues, leading to formation of the cellular patterns of tissue structures.

Developmental Bias and Evolution: A Regulatory Network Perspective

Phenotypic variation is generated by the processes of development, with some variants arising more readily than others-a phenomenon known as "developmental bias." Developmental bias and natural selection have often been portrayed as alternative explanations, but this is a false dichotomy: developmental bias can evolve through natural selection, and bias and selection jointly influence phenotypic evolution. Here, we briefly review the evidence for developmental bias and illustrate how it is studied empirically. We describe recent theory on regulatory networks that explains why the influence of genetic and environmental perturbation on phenotypes is typically not uniform, and may even be biased toward adaptive phenotypic variation. We show how bias produced by developmental processes constitutes an evolving property able to impose direction on adaptive evolution and influence patterns of taxonomic and phenotypic diversity. Taking these considerations together, we argue that it is not sufficient to accommodate developmental bias into evolutionary theory merely as a constraint on evolutionary adaptation. The influence of natural selection in shaping developmental bias, and conversely, the influence of developmental bias in shaping subsequent opportunities for adaptation, requires mechanistic models of development to be expanded and incorporated into evolutionary theory. A regulatory network perspective on phenotypic evolution thus helps to integrate the generation of phenotypic variation with natural selection, leaving evolutionary biology better placed to explain how organisms adapt and diversify.

Ankyrin domain encoding genes from an ancient horizontal transfer are functionally integrated into Nasonia developmental gene regulatory networks

BACKGROUND

How regulatory networks incorporate additional components and how novel genes are functionally integrated into well-established developmental processes are two important and intertwined questions whose answers have major implications for understanding the evolution of development. We recently discovered a set of lineage-restricted genes with strong and specific expression patterns along the dorsal-ventral (DV) axis of the embryo of the wasp Nasonia that may serve as a powerful system for addressing these questions. We sought to both understand the evolutionary history of these genes and to determine their functions in the Nasonia DV patterning system.

RESULTS

We have found that the novel DV genes are part of a large family of rapidly duplicating and diverging ankyrin domain-encoding genes that originated most likely by horizontal transfer from a prokaryote in a common ancestor of the wasp superfamily Chalcidoidea. We tested the function of those ankyrin-encoding genes expressed along the DV axis and found that they participate in early embryonic DV patterning. We also developed a new wasp model system (Melittobia) and found that some functional integration of ankyrin genes have been preserved for over 90 million years.

CONCLUSIONS

Our results indicate that regulatory networks can incorporate novel genes that then become necessary for stable and repeatable outputs. Even a modest role in developmental networks may be enough to allow novel or duplicate genes to be maintained in the genome and become fully integrated network components.

Self-sustaining positive feedback loops in discrete and continuous systems

We consider a dynamic framework frequently used to model gene regulatory and signal transduction networks: monotonic ODEs that are composed of Hill functions. We derive conditions under which activity or inactivity in one system variable induces and sustains activity or inactivity in another. Cycles of such influences correspond to positive feedback loops that are self-sustaining and control-robust, in the sense that these feedback loops "trap" the system in a region of state space from which it cannot exit, even if the other system variables are externally controlled. To demonstrate the utility of this result, we consider prototypical examples of bistability and hysteresis in gene regulatory networks, and analyze a T-cell signal transduction ODE model from the literature.

Hybrid models of genetic networks: Mathematical challenges and biological relevance

We review results concerning dynamics in a class of hybrid ordinary differential equations which incorporates logical control to yield piecewise linear equations. These equations relate qualitative features of the structure of networks to qualitative properties of the dynamics. Because of their simple structure, they have been studied using techniques from discrete mathematics and nonlinear dynamics. Initially developed as a qualitataive description of gene regulatory networks, many generalizations of the basic approach have been developed. In particular, we show how this qualitative approach may be adapted to switching biochemical systems without degradation, illustrated by an example of a motif in which two branches of a pathway may be regulated differently when the thresholds for the two pathways are separated.

Coupling of DNA Replication and Negative Feedback Controls Gene Expression for Cell-Fate Decisions

Cellular decision-making arises from the expression of genes along a regulatory cascade, which leads to a choice between distinct phenotypic states. DNA dosage variations, often introduced by replication, can significantly affect gene expression to ultimately bias decision outcomes. The bacteriophage lambda system has long served as a paradigm for cell-fate determination, yet the effect of DNA replication remains largely unknown. Here, through single-cell studies and mathematical modeling we show that DNA replication drastically boosts cI expression to allow lysogenic commitment by providing more templates. Conversely, expression of CII, the upstream regulator of cI, is surprisingly robust to DNA replication due to the negative autoregulation of the Cro repressor. Our study exemplifies how living organisms can not only utilize DNA replication for gene expression control but also implement mechanisms such as negative feedback to allow the expression of certain genes to be robust to dosage changes resulting from DNA replication.

Robustness of a Reconstituted Escherichia coli Protein Translation System Analyzed by Computational Modeling

Robustness against environmental changes is one of the major features of biological systems, but its origin is not well understood. We recently constructed a large-scale computational model of an Escherichia coli-based reconstituted in vitro translation system that enumerates all protein synthesis processes in detail. Our model synthesizes a formyl-Met-Gly-Gly tripeptide (MGG peptide) from 27 initial molecular components through 968 biochemical reactions. Among the 968 kinetic parameters, 483 are nonzero parameters, and the simulator was used to determine how perturbations of 483 individual reactions affect the complex reaction network. We found that even when the kinetic parameter was changed from 100- to 0.01-fold, 94% of the changes hardly affected the two indicators of reaction dynamics in MGG peptide synthesis, which represent the yield of the MGG peptide and the initial lag-time of the peptide synthesis. Moreover, none of the indicators increased proportionally to these changes: e.g., a 100-fold increase in the kinetic parameter increased the yield by only 2.2-fold at most, indicating the insensitivity of the reaction network to perturbation. Robustness and insensitivity are likely to be a common feature of large-scale biological reaction networks.

Medical Systems Biology

The aim of this volume is to encourage the use of systems-level methodologies to contribute to the improvement of human-health . We intend to motivate biomedical researchers to complement their current theoretical and empirical practice with up-to-date systems biology conceptual approaches. Our perspective is based on the deep understanding of the key biomolecular regulatory mechanisms that underlie health, as well as the emergence and progression of human-disease . We strongly believe that the contemporary systems biology perspective opens the door to the effective development of novel methodologies to the improvement of prevention . This requires a deeper and integrative understanding of the involved underlying systems-level mechanisms. In order to explain our proposal in a simple way, in this chapter we privilege the conceptual exposition of our chosen framework over formal considerations. The formal exposition of our proposal will be expanded and discussed later in the next chapters.

Simulation of the Dynamics of Primary Immunodeficiencies in B Cells

Primary immunodeficiencies (PIDs) are a group of over 300 hereditary, heterogeneous, and mainly rare disorders that affect the immune system. Various aspects of immune system and PID proteins and genes have been investigated and facilitate systems biological studies of effects of PIDs on B cell physiology and response. We reconstructed a B cell network model based on data for the core B cell receptor activation and response processes and performed semi-quantitative dynamic simulations for normal and B cell PID failure modes. The results for several knockout simulations correspond to previously reported molecular studies and reveal novel mechanisms for PIDs. The simulations for CD21, CD40, LYN, MS4A1, ORAI1, PLCG2, PTPRC, and STIM1 indicated profound changes to major transcription factor signaling and to the network. Significant effects were observed also in the BCL10, BLNK, BTK, loss-of-function CARD11, IKKB, MALT1, and NEMO, simulations whereas only minor effects were detected for PIDs that are caused by constitutively active proteins (PI3K, gain-of-function CARD11, KRAS, and NFKBIA). This study revealed the underlying dynamics of PID diseases, confirms previous observations, and identifies novel candidates for PID diagnostics and therapy.

DSGRN: Examining the Dynamics of Families of Logical Models

We present a computational tool DSGRN for exploring the dynamics of a network by computing summaries of the dynamics of switching models compatible with the network across all parameters. The network can arise directly from a biological problem, or indirectly as the interaction graph of a Boolean model. This tool computes a finite decomposition of parameter space such that for each region, the state transition graph that describes the coarse dynamical behavior of a network is the same. Each of these parameter regions corresponds to a different logical description of the network dynamics. The comparison of dynamics across parameters with experimental data allows the rejection of parameter regimes or entire networks as viable models for representing the underlying regulatory mechanisms. This in turn allows a search through the space of perturbations of a given network for networks that robustly fit the data. These are the first steps toward discovering a network that optimally matches the observed dynamics by searching through the space of networks.

Heterogeneity and Robustness in Plant Morphogenesis: From Cells to Organs

Development is remarkably reproducible, producing organs with the same size, shape, and function repeatedly from individual to individual. For example, every flower on the Antirrhinum stalk has the same snapping dragon mouth. This reproducibility has allowed taxonomists to classify plants and animals according to their morphology. Yet these reproducible organs are composed of highly variable cells. For example, neighboring cells grow at different rates in Arabidopsis leaves, sepals, and shoot apical meristems. This cellular variability occurs in normal, wild-type organisms, indicating that cellular heterogeneity (or diversity in a characteristic such as growth rate) is either actively maintained or, at a minimum, not entirely suppressed. In fact, cellular heterogeneity can contribute to producing invariant organs. Here, we focus on how plant organs are reproducibly created during development from these highly variable cells.

The Evolution of Gene Regulatory Networks that Define Arthropod Body Plans

Our understanding of the genetics of arthropod body plan development originally stems from work on Drosophila melanogaster from the late 1970s and onward. In Drosophila, there is a relatively detailed model for the network of gene interactions that proceeds in a sequential-hierarchical fashion to define the main features of the body plan. Over the years, we have a growing understanding of the networks involved in defining the body plan in an increasing number of arthropod species. It is now becoming possible to tease out the conserved aspects of these networks and to try to reconstruct their evolution. In this contribution, we focus on several key nodes of these networks, starting from early patterning in which the main axes are determined and the broad morphological domains of the embryo are defined, and on to later stage wherein the growth zone network is active in sequential addition of posterior segments. The pattern of conservation of networks is very patchy, with some key aspects being highly conserved in all arthropods and others being very labile. Many aspects of early axis patterning are highly conserved, as are some aspects of sequential segment generation. In contrast, regional patterning varies among different taxa, and some networks, such as the terminal patterning network, are only found in a limited range of taxa. The growth zone segmentation network is ancient and is probably plesiomorphic to all arthropods. In some insects, it has undergone significant modification to give rise to a more hardwired network that generates individual segments separately. In other insects and in most arthropods, the sequential segmentation network has undergone a significant amount of systems drift, wherein many of the genes have changed. However, it maintains a conserved underlying logic and function.

Method for identification of sensitive nodes in Boolean models of biological networks

Biological systems are often represented as Boolean networks and analysed to identify sensitive nodes which on perturbation disproportionately change a predefined output. There exist different kinds of perturbation methods: perturbation of function, perturbation of state and perturbation in update scheme. Nodes may have defects in interpretation of the inputs from other nodes and calculation of the node output. To simulate these defects and systematically assess their effect on the system output, two new function perturbations, referred to as ‘not of function’ and ‘function of not’, are introduced. In the former, the inputs are assumed to be correctly interpreted but the output of the update rule is perturbed; and in the latter, each input is perturbed but the correct update rule is applied. These and previously used perturbation methods were applied to two existing Boolean models, namely the human melanogenesis signalling network and the fly segment polarity network. Through mathematical simulations, it was found that these methods successfully identified nodes earlier found to be sensitive using other methods, and were also able to identify sensitive nodes which were previously unreported.

Perspectives on theory at the interface of physics and biology

Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie evidence that theory, in the sense that physicists use the word, is impossible in a biological context. For others, this contrast serves to highlight a grand challenge. I am an optimist, and believe (along with many colleagues) that the time is ripe for the emergence of a more unified theoretical physics of biological systems, building on successes in thinking about particular phenomena. In this essay I try to explain the reasons for my optimism, through a combination of historical and modern examples.

Identifying the dynamic gene regulatory network during latent HIV-1 reactivation using high-dimensional ordinary differential equations

Reactivation of latently infected cells has emerged as an important strategy for eradication of HIV. However, genetic mechanisms of regulation after reactivation remain unclear. We describe a five-step pipeline to study the dynamics of the gene regulatory network following a viral reactivation using high-dimensional ordinary differential equations. Our pipeline implements a combination of five different methods, by detecting temporally differentially expressed genes (step 1), clustering genes with similar temporal expression patterns into a small number of response modules (step2), performing a functional enrichment analysis within each gene response module (step 3), identifying a network structure based on the gene response modules using ordinary differential equations (ODE) and a high-dimensional variable selection technique (step 4), and obtaining a gene regulatory model based on refined parameter estimates using nonlinear least squares (step 5). We applied our pipeline to a time course gene expression data of latently infected T-cells following a latency-reversion.

Robustness, Accuracy, and Cell State Heterogeneity in Biological Systems

The robustness of biological systems is often depicted as a key system-level emergent property that allows uniform phenotypes in fluctuating environments. Yet, analysis of single-cell signaling responses identified multiple examples of cellular responses with high degrees of heterogeneity. Here we discuss the implications of the observed lack of response accuracy in the context of new observations coming from single-cell approaches. Single-cell approaches provide a new way to measure the abundance of thousands of molecular species in a single-cell. Repeatedly, analysis of cell distributions identifies clusters within these distributions where cells can be grouped into specific cell states. If cells in a population occupy distinct cell states, the observed variable response could in fact be accurate for each cell conditioned on its own internal state. In this view, the observed lack of accuracy, i.e. response heterogeneity, could in fact be beneficial and a potentially regulated feature of cell state variability. Therefore, to truly determine whether the observed response heterogeneity is a desired property or a physical limitation, future analysis of signaling heterogeneity must take into account the internal states of cells in the population.

Robustness versus evolvability analysis for regulatory feed-forward loops

From the definition, it appears that phenotypic robustness and evolvability of an organism are inversely related to each other. However, a number of studies exploring this question have found conflicting evidences in this regard. This question motivated the current work where we explore the relationship between robustness and evolvability. As a model system, we pick the Feed Forward Loops (FFLs), and develop a framework to characterize their performance in terms of their ability to resist changes to steady state expression (robustness), and their ability to evolve towards novel phenotypes (evolvability). We demonstrate that robustness and evolvability are positively correlated in some FFL topologies. We compare this against other small regulatory topologies, and show that the same trend does not hold among them. We postulate that the ability to positively link robustness and evolvability could be an additional reason for over-representation of FFLs in living organisms, as compared to other regulatory topologies.

Underlying Principles of Natural Selection in Network Evolution: Systems Biology Approach

Systems biology is a rapidly expanding field that integrates diverse areas of science such as physics, engineering, computer science, mathematics, and biology toward the goal of elucidating the underlying principles of hierarchical metabolic and regulatory systems in the cell, and ultimately leading to predictive understanding of cellular response to perturbations. Because post-genomics research is taking place throughout the tree of life, comparative approaches offer a way for combining data from many organisms to shed light on the evolution and function of biological networks from the gene to the organismal level. Therefore, systems biology can build on decades of theoretical work in evolutionary biology, and at the same time evolutionary biology can use the systems biology approach to go in new uncharted directions. In this study, we present a review of how the post-genomics era is adopting comparative approaches and dynamic system methods to understand the underlying design principles of network evolution and to shape the nascent field of evolutionary systems biology. Finally, the application of evolutionary systems biology to robust biological network designs is also discussed from the synthetic biology perspective.

Modeling the Sex Differences and Interindividual Variability in the Activity of the Hypothalamic-Pituitary-Adrenal Axis

Significant sex differences exist in the activity of the hypothalamic-pituitary-adrenal (HPA) axis. These differences are thought to contribute to the disparity in the prevalence of various autoimmune and infectious diseases between males and females. We used a mathematical model of the HPA axis to evaluate the hypothesis that differential sensitivity and negative feedback of the HPA axis network are causal factors for the observed sex differences in its activity. In doing so, we implicitly accounted for the differential influence of gonadal hormones on the HPA axis. Furthermore, we determined whether the putative mechanisms responsible for differences in basal HPA axis activity might also contribute to the observed differences in its stimulus-driven response. Model simulations predicted that the female HPA axis has greater adrenal sensitivity and weaker negative feedback. We identified two distinct sex-specific parameter spaces that generate corticosterone profiles in qualitative agreement with experimental results. We propose that these parameter subspaces indicate the interindividual variability in the regulatory mechanisms of the HPA axis. Furthermore, the model predicts that the maintenance of homeostatic rhythms in response to chronic stress requires specific regulatory adaptations resulting in a phenotype of allostatically driven chronic stress-sensitization. We propose that these adaptations indicate a physiological cost of adaptation to chronic stress. Model simulations suggest that individuals with high adrenal sensitivity are more vulnerable to chronic stress sensitization and might be more susceptible to the development of neuropsychiatric disorders. These results contribute to the study of sex differences in physiological feedback systems within a quantitative framework.

Redundant and incoherent regulations of multiple phenotypes suggest microRNAs' role in stability control

Each microRNA (miRNA) represses a web of target genes and, through them, controls multiple phenotypes. The difficulties inherent in such controls cast doubt on how effective miRNAs are in driving phenotypic changes. A "simple regulation" model posits "one target-one phenotype" control under which most targeting is nonfunctional. In an alternative "coordinate regulation" model, multiple targets are assumed to control the same phenotypes coherently, and most targeting is functional. Both models have some empirical support but pose different conceptual challenges. Here, we concurrently analyze multiple targets and phenotypes associated with the miRNA-310 family (miR310s) of Drosophila Phenotypic rescue in the mir310s knockout background is achieved by promoter-directed RNA interference that restores wild-type expression. For one phenotype (eggshell morphology), we observed redundant regulation, hence rejecting "simple regulation" in favor of the "coordinate regulation" model. For other phenotypes (egg-hatching and male fertility), however, one gene shows full rescue, but three other rescues aggravate the phenotype. Overall, phenotypic controls by miR310s do not support either model. Like a thermostat that controls both heating and cooling elements to regulate temperature, redundancy and incoherence in regulation generally suggest some capacity in stability control. Our results therefore support the published view that miRNAs play a role in the canalization of transcriptome and, hence, phenotypes.

The logic of the floral transition: Reverse-engineering the switch controlling the identity of lateral organs

Much laboratory work has been carried out to determine the gene regulatory network (GRN) that results in plant cells becoming flowers instead of leaves. However, this also involves the spatial distribution of different cell types, and poses the question of whether alternative networks could produce the same set of observed results. This issue has been addressed here through a survey of the published intercellular distribution of expressed regulatory genes and techniques both developed and applied to Boolean network models. This has uncovered a large number of models which are compatible with the currently available data. An exhaustive exploration had some success but proved to be unfeasible due to the massive number of alternative models, so genetic programming algorithms have also been employed. This approach allows exploration on the basis of both data-fitting criteria and parsimony of the regulatory processes, ruling out biologically unrealistic mechanisms. One of the conclusions is that, despite the multiplicity of acceptable models, an overall structure dominates, with differences mostly in alternative fine-grained regulatory interactions. The overall structure confirms the known interactions, including some that were not present in the training set, showing that current data are sufficient to determine the overall structure of the GRN. The model stresses the importance of relative spatial location, through explicit references to this aspect. This approach also provides a quantitative indication of how likely some regulatory interactions might be, and can be applied to the study of other developmental transitions.

Systems biology derived source-sink mechanism of BMP gradient formation

A morphogen gradient of Bone Morphogenetic Protein (BMP) signaling patterns the dorsoventral embryonic axis of vertebrates and invertebrates. The prevailing view in vertebrates for BMP gradient formation is through a counter-gradient of BMP antagonists, often along with ligand shuttling to generate peak signaling levels. To delineate the mechanism in zebrafish, we precisely quantified the BMP activity gradient in wild-type and mutant embryos and combined these data with a mathematical model-based computational screen to test hypotheses for gradient formation. Our analysis ruled out a BMP shuttling mechanism and a bmp transcriptionally-informed gradient mechanism. Surprisingly, rather than supporting a counter-gradient mechanism, our analyses support a fourth model, a source-sink mechanism, which relies on a restricted BMP antagonist distribution acting as a sink that drives BMP flux dorsally and gradient formation. We measured Bmp2 diffusion and found that it supports the source-sink model, suggesting a new mechanism to shape BMP gradients during development.

Before an animal is born, a protein called BMP plays a key role in establishing the difference between the front and the back of the animal. Cells nearer the front of the embryo contain higher amounts of the BMP protein, whilst cells nearer the back have progressively lower levels of BMP. This gradient of BMP ‘concentration’ affects the identity of the cells, with the level of BMP in each cell dictating what parts of the body are made where.

The prevailing view among scientists is that the BMP gradient is created by an opposing gradient of another protein called Chordin, which is found at high levels at the back of the embryo and lower levels near the front. Chordin inhibits BMP and the interaction between the two proteins establishes the gradients that create order across the embryo.

Zinski et al. used computer models to investigate how the BMP gradient is created. Several possibilities were considered, including the effect of Chordin. Comparing the models to precise experimental measurements of BMP activity in zebrafish embryos suggested that a different mechanism known as a source-sink model, rather than the opposing Chordin gradient, may be responsible for the pattern of BMP found in the embryo. In this model, the BMP is produced at the front of the embryo and moves towards the back end by diffusion. At the back of the embryo, BMP is mopped up by Chordin, resulting in a constant gradient of BMP along the embryo.

Many other processes that control how animals grow and develop rely on the formation of similar protein gradients, so these findings may also apply to other aspects of animal development. Understanding how animals grow and develop may help researchers to develop strategies to regrow tissues and organs in human patients.

L p -Adaptation: Simultaneous Design Centering and Robustness Estimation of Electronic and Biological Systems

The design of systems or models that work robustly under uncertainty and environmental fluctuations is a key challenge in both engineering and science. This is formalized in the design-centering problem, which is defined as finding a design that fulfills given specifications and has a high probability of still doing so if the system parameters or the specifications fluctuate randomly. Design centering is often accompanied by the problem of quantifying the robustness of a system. Here we present a novel adaptive statistical method to simultaneously address both problems. Our method, L_p-Adaptation, is inspired by the evolution of robustness in biological systems and by randomized schemes for convex volume computation. It is able to address both problems in the general, non-convex case and at low computational cost. We describe the concept and the algorithm, test it on known benchmarks, and demonstrate its real-world applicability in electronic and biological systems. In all cases, the present method outperforms the previous state of the art. This enables re-formulating optimization problems in engineering and biology as design centering problems, taking global system robustness into account.

Structure-based control of complex networks with nonlinear dynamics

What can we learn about controlling a system solely from its underlying network structure? Here we adapt a recently developed framework for control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This feedback-based framework provides realizable node overrides that steer a system toward any of its natural long-term dynamic behaviors, regardless of the specific functional forms and system parameters. We use this framework on several real networks, identify the topological characteristics that underlie the predicted node overrides, and compare its predictions to those of structural controllability in control theory. Finally, we demonstrate this framework's applicability in dynamic models of gene regulatory networks and identify nodes whose override is necessary for control in the general case but not in specific model instances.

A review of active learning approaches to experimental design for uncovering biological networks

Various types of biological knowledge describe networks of interactions among elementary entities. For example, transcriptional regulatory networks consist of interactions among proteins and genes. Current knowledge about the exact structure of such networks is highly incomplete, and laboratory experiments that manipulate the entities involved are conducted to test hypotheses about these networks. In recent years, various automated approaches to experiment selection have been proposed. Many of these approaches can be characterized as active machine learning algorithms. Active learning is an iterative process in which a model is learned from data, hypotheses are generated from the model to propose informative experiments, and the experiments yield new data that is used to update the model. This review describes the various models, experiment selection strategies, validation techniques, and successful applications described in the literature; highlights common themes and notable distinctions among methods; and identifies likely directions of future research and open problems in the area.

Decoding early myelopoiesis from dynamics of core endogenous network

A decade ago mainstream molecular biologists regarded it impossible or biologically ill-motivated to understand the dynamics of complex biological phenomena, such as cancer genesis and progression, from a network perspective. Indeed, there are numerical difficulties even for those who were determined to explore along this direction. Undeterred, seven years ago a group of Chinese scientists started a program aiming to obtain quantitative connections between tumors and network dynamics. Many interesting results have been obtained. In this paper we wish to test such idea from a different angle: the connection between a normal biological process and the network dynamics. We have taken early myelopoiesis as our biological model. A standard roadmap for the cell-fate diversification during hematopoiesis has already been well established experimentally, yet little was known for its underpinning dynamical mechanisms. Compounding this difficulty there were additional experimental challenges, such as the seemingly conflicting hematopoietic roadmaps and the cell-fate inter-conversion events. With early myeloid cell-fate determination in mind, we constructed a core molecular endogenous network from well-documented gene regulation and signal transduction knowledge. Turning the network into a set of dynamical equations, we found computationally several structurally robust states. Those states nicely correspond to known cell phenotypes. We also found the states connecting those stable states. They reveal the developmental routes-how one stable state would most likely turn into another stable state. Such interconnected network among stable states enabled a natural organization of cell-fates into a multi-stable state landscape. Accordingly, both the myeloid cell phenotypes and the standard roadmap were explained mechanistically in a straightforward manner. Furthermore, recent challenging observations were also explained naturally. Moreover, the landscape visually enables a prediction of a pool of additional cell states and developmental routes, including the non-sequential and cross-branch transitions, which are testable by future experiments. In summary, the endogenous network dynamics provide an integrated quantitative framework to understand the heterogeneity and lineage commitment in myeloid progenitors.

Linking gene regulation to cell behaviors in the posterior growth zone of sequentially segmenting arthropods

Virtually all arthropods all arthropods add their body segments sequentially, one by one in an anterior to posterior progression. That process requires not only segment specification but typically growth and elongation. Here we review the functions of some of the key genes that regulate segmentation: Wnt, caudal, Notch pathway, and pair-rule genes, and discuss what can be inferred about their evolution. We focus on how these regulatory factors are integrated with growth and elongation and discuss the importance and challenges of baseline measures of growth and elongation. We emphasize a perspective that integrates the genetic regulation of segment patterning with the cellular mechanisms of growth and elongation.

Simulation of the dynamics of primary immunodeficiencies in CD4+ T-cells

Primary immunodeficiencies (PIDs) form a large and heterogeneous group of mainly rare disorders that affect the immune system. T-cell deficiencies account for about one-tenth of PIDs, most of them being monogenic. Apart from genetic and clinical information, lots of other data are available for PID proteins and genes, including functions and interactions. Thus, it is possible to perform systems biology studies on the effects of PIDs on T-cell physiology and response. To achieve this, we reconstructed a T-cell network model based on literature mining and TPPIN, a previously published core T-cell network, and performed semi-quantitative dynamic network simulations on both normal and T-cell PID failure modes. The results for several loss-of-function PID simulations correspond to results of previously reported molecular studies. The simulations for TCR PTPRC, LCK, ZAP70 and ITK indicate profound changes to numerous proteins in the network. Significant effects were observed also in the BCL10, CARD11, MALT1, NEMO, IKKB and MAP3K14 simulations. No major effects were observed for PIDs that are caused by constitutively active proteins. The T-cell model facilitates the understanding of the underlying dynamics of PID disease processes. The approach confirms previous knowledge about T-cell signaling network and indicates several new important proteins that may be of interest when developing novel diagnosis and therapies to treat immunological defects.

Ancient role of ten-m/odz in segmentation and the transition from sequential to syncytial segmentation

Background

Until recently, mechanisms of segmentation established for Drosophila served as a paradigm for arthropod segmentation. However, with the discovery of gene expression waves in vertebrate segmentation, another paradigm based on oscillations linked to axial growth was established. The Notch pathway and hairy delay oscillator are basic components of this mechanism, as is the wnt pathway. With the establishment of oscillations during segmentation of the beetle Tribolium, a common segmentation mechanism may have been present in the last common ancestor of vertebrates and arthropods. However, the Notch pathway is not involved in segmentation of the initial Drosophila embryo. In arthropods, the engrailed, wingless pair has a much more conserved function in segmentation than most of the hierarchy established for Drosophila.

Results

Here, we work backwards from this conserved pair by discussing possible mechanisms which could have taken over the role of the Notch pathway. We propose a pivotal role for the large transmembrane protein Ten-m/Odz. Ten-m/Odz may have had an ancient role in cell-cell communication, parallel to the Notch and wnt pathways. The Ten-m protein binds to the membrane with properties which resemble other membrane-based biochemical oscillators.

Conclusion

We propose that such a simple transition could have formed the initial scaffold, on top of which the hierarchy, observed in the syncytium of dipterans, could have evolved.

Collective Space-Sensing Coordinates Pattern Scaling in Engineered Bacteria

Scale invariance refers to the maintenance of a constant ratio of developing organ size to body size. Although common, its underlying mechanisms remain poorly understood. Here, we examined scaling in engineered Escherichia coli that can form self-organized core-ring patterns in colonies. We found that the ring width exhibits perfect scale invariance to the colony size. Our analysis revealed a collective space-sensing mechanism, which entails sequential actions of an integral feedback loop and an incoherent feedforward loop. The integral feedback is implemented by the accumulation of a diffusive chemical produced by a colony. This accumulation, combined with nutrient consumption, sets the timing for ring initiation. The incoherent feedforward is implemented by the opposing effects of the domain size on the rate and duration of ring maturation. This mechanism emphasizes a role of timing control in achieving robust pattern scaling and provides a new perspective in examining the phenomenon in natural systems.

Complexity of generic biochemical circuits: topology versus strength of interactions

The historical focus on network topology as a determinant of biological function is still largely maintained today, illustrated by the rise of structure-only approaches to network analysis. However, biochemical circuits and genetic regulatory networks are defined both by their topology and by a multitude of continuously adjustable parameters, such as the strength of interactions between nodes, also recognized as important. Here we present a class of simple perceptron-based Boolean models within which comparing the relative importance of topology versus interaction strengths becomes a quantitatively well-posed problem. We quantify the intuition that for generic networks, optimization of interaction strengths is a crucial ingredient of achieving high complexity, defined here as the number of fixed points the network can accommodate. We propose a new methodology for characterizing the relative role of parameter optimization for topologies of a given class.

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.