Simplified models of biological networks

Metaplasticity and memory in multilevel recurrent feed-forward networks

Network systems can exhibit memory effects in which the interactions between different pairs of nodes adapt in time, leading to the emergence of preferred connections, patterns, and subnetworks. To a first approximation, this memory can be modeled through a "plastic" Hebbian or homophily mechanism, in which edges get reinforced proportionally to the amount of information flowing through them. However, recent studies on glia-neuron networks have highlighted how memory can evolve due to more complex dynamics, including multilevel network structures and "metaplastic" effects that modulate reinforcement. Inspired by those systems, here we develop a simple and general model for the dynamics of an adaptive network with an additional metaplastic mechanism that varies the rate of Hebbian strengthening of its edge connections. The metaplastic term acts on a second network level in which edges are grouped together, simulating local, longer timescale effects. Specifically, we consider a biased random walk on a cyclic feed-forward network. The random walk chooses its steps according to the weights of the network edges. The weights evolve through a Hebbian mechanism modulated by a metaplastic reinforcement, biasing the walker to prefer edges that have been already explored. We study the dynamical emergence (memorization) of preferred paths and their retrieval and identify three regimes: one dominated by the Hebbian term, one in which the metareinforcement drives memory formation, and a balanced one. We show that, in the latter two regimes, metareinforcement allows the retrieval of a previously stored path even after the weights have been reset to zero to erase Hebbian memory.

Model integration of circadian- and sleep-wake-driven contributions to rhythmic gene expression reveals distinct regulatory principles

Analyses of gene-expression dynamics in research on circadian rhythms and sleep homeostasis often describe these two processes using separate models. Rhythmically expressed genes are, however, likely to be influenced by both processes. We implemented a driven, damped harmonic oscillator model to estimate the contribution of circadian- and sleep-wake-driven influences on gene expression. The model reliably captured a wide range of dynamics in cortex, liver, and blood transcriptomes taken from mice and humans under various experimental conditions. Sleep-wake-driven factors outweighed circadian factors in driving gene expression in the cortex, whereas the opposite was observed in the liver and blood. Because of tissue- and gene-specific responses, sleep deprivation led to a long-lasting intra- and inter-tissue desynchronization. The model showed that recovery sleep contributed to these long-lasting changes. The results demonstrate that the analyses of the daily rhythms in gene expression must take the complex interactions between circadian and sleep-wake influences into account. A record of this paper's transparent peer review process is included in the supplemental information.

ChromNetMotif: a Python tool to extract chromatin-sate marked motifs in a chromatin interaction network

Motivation

Analysis of network motifs is crucial to studying the robustness, stability, and functions of complex networks. Genome organization can be viewed as a biological network that consists of interactions between different chromatin regions. These interacting regions are also marked by epigenetic or chromatin states which can contribute to the overall organization of the chromatin and proper genome function. Therefore, it is crucial to integrate the chromatin states of the nodes when performing motif analysis in chromatin interaction networks. Even though there has been increasing production of chromatin interaction and genome-wide epigenetic modification data, there is a lack of publicly available tools to extract chromatin state-marked motifs from genome organization data.

Results

We develop a Python tool, ChromNetMotif, offering an easy-to-use command line interface to extract chromatin-state-marked motifs from a chromatin interaction network. The tool can extract occurrences, frequencies, and statistical enrichment of the chromatin state-marked motifs. Visualization files are also generated which allow the user to interpret the motifs easily. ChromNetMotif also allows the user to leverage the features of a multicore processor environment to reduce computation time for larger networks. The output files generated can be used to perform further downstream analysis. ChromNetMotif aims to serve as an important tool to comprehend the interplay between epigenetics and genome organization.

Availability and implementation

ChromNetMotif is available at https://github.com/lncRNAAddict/ChromNetworkMotif.

Temperature Controls Onset and Period of NF-κB Oscillations and can Lead to Chaotic Dynamics

The transcription factor NF-κB plays a vital role in the control of the immune system, and following stimulation with TNF-α its nuclear concentration shows oscillatory behaviour. How environmental factors, in particular temperature, can control the oscillations and thereby affect gene stimulation is still remains to be resolved question. In this work, we reveal that the period of the oscillations decreases with increasing temperature. We investigate this using a mathematical model, and by applying results from statistical physics, we introduce temperature dependency to all rates, resulting in a remarkable correspondence between model and experiments. Our model predicts how temperature affects downstream protein production and find a crossover, where high affinity genes upregulates at high temperatures. Finally, we show how or that oscillatory temperatures can entrain NF-κB oscillations and lead to chaotic dynamics presenting a simple path to chaotic conditions in cellular biology.

Temporal control of the integrated stress response by a stochastic molecular switch

Stress granules (SGs) are formed in the cytosol as an acute response to environmental cues and activation of the integrated stress response (ISR), a central signaling pathway controlling protein synthesis. Using chronic virus infection as stress model, we previously uncovered a unique temporal control of the ISR resulting in recurrent phases of SG assembly and disassembly. Here, we elucidate the molecular network generating this fluctuating stress response by integrating quantitative experiments with mathematical modeling and find that the ISR operates as a stochastic switch. Key elements controlling this switch are the cooperative activation of the stress-sensing kinase PKR, the ultrasensitive response of SG formation to the phosphorylation of the translation initiation factor eIF2α, and negative feedback via GADD34, a stress-induced subunit of protein phosphatase 1. We identify GADD34 messenger RNA levels as the molecular memory of the ISR that plays a central role in cell adaptation to acute and chronic stress.

Experimental Evolution of Anticipatory Regulation in Escherichia coli

Environmental cues in an ecological niche are often temporal in nature. For instance, in temperate climates, temperature is higher in daytime compared to during night. In response to these temporal cues, bacteria have been known to exhibit anticipatory regulation, whereby triggering response to a yet to appear cue. Such an anticipatory response in known to enhance Darwinian fitness, and hence, is likely an important feature of regulatory networks in microorganisms. However, the conditions under which an anticipatory response evolves as an adaptive response are not known. In this work, we develop a quantitative model to study response of a population to two temporal environmental cues, and predict variables which are likely important for evolution of anticipatory regulatory response. We follow this with experimental evolution of Escherichia coli in alternating environments of rhamnose and paraquat for ∼850 generations. We demonstrate that growth in this cyclical environment leads to evolution of anticipatory regulation. As a result, pre-exposure to rhamnose leads to a greater fitness in paraquat environment. Genome sequencing reveals that this anticipatory regulation is encoded via mutations in global regulators. Overall, our study contributes to understanding of how environment shapes the topology of regulatory networks in an organism.

Complex small-world regulatory networks emerge from the 3D organisation of the human genome

The discovery that overexpressing one or a few critical transcription factors can switch cell state suggests that gene regulatory networks are relatively simple. In contrast, genome-wide association studies (GWAS) point to complex phenotypes being determined by hundreds of loci that rarely encode transcription factors and which individually have small effects. Here, we use computer simulations and a simple fitting-free polymer model of chromosomes to show that spatial correlations arising from 3D genome organisation naturally lead to stochastic and bursty transcription as well as complex small-world regulatory networks (where the transcriptional activity of each genomic region subtly affects almost all others). These effects require factors to be present at sub-saturating levels; increasing levels dramatically simplifies networks as more transcription units are pressed into use. Consequently, results from GWAS can be reconciled with those involving overexpression. We apply this pan-genomic model to predict patterns of transcriptional activity in whole human chromosomes, and, as an example, the effects of the deletion causing the diGeorge syndrome.

Picking the right metaphors for addressing microbial systems: economic theory helps understanding biological complexity

Any descriptive language is necessarily metaphoric and interpretative. Two somewhat overlapping-but not identical-languages have been thoroughly employed in the last decade to address the issue of regulatory complexity in biological systems: the terminology of network theory and the jargon of electric circuitry. These approaches have found many formal equivalences between the layout of extant genetic circuits and the architecture of man-made counterparts. However, these languages still fail to describe accurately key features of biological objects, in particular the diversity of signal-transfer molecules and the diffusion that is inherent to any biochemical system. Furthermore, current formalisms associated with networks and circuits can hardly face the problem of multi-scale regulatory complexity-from single molecules to entire ecosystems. We argue that the language of economic theory might be instrumental not only to portray accurately many features of regulatory networks, but also to unveil aspects of the biological complexity problem that remain opaque to other types of analyses. The main perspective opened by the economic metaphor when applied to control of microbiological activities is a focus on metabolism, not gene selfishness, as the necessary background to make sense of regulatory phenomena. As an example, we analyse and reinterpret the widespread phenomenon of catabolite repression with the formal frame of the consumer's choice theory.

SUMO mediated regulation of transcription factors as a mechanism for transducing environmental cues into cellular signaling in plants

Across all species, transcription factors (TFs) are the most frequent targets of SUMOylation. The effect of SUMO conjugation on the functions of transcription factors has been extensively studied in animal systems, with over 200 transcription factors being documented to be modulated by SUMOylation. This has resulted in the establishment of a number of paradigms that seek to explain the mechanisms by which SUMO regulates transcription factor functions. For instance, SUMO has been shown to modulate TF DNA binding activity; regulate both localization as well as the abundance of TFs and also influence the association of TFs with chromatin. With transcription factors being implicated as master regulators of the cellular signalling pathways that maintain phenotypic plasticity in all organisms, in this review, we will discuss how SUMO mediated regulation of transcription factor activity facilitates molecular pathways to mount an appropriate and coherent biological response to environmental cues.

Optimizing energetic cost of uncertainty in a driven system with and without feedback

Many biological functions require dynamics to be necessarily driven out of equilibrium. In contrast, in various contexts, a nonequilibrium dynamics at fast timescales can be described by an effective equilibrium dynamics at a slower timescale. In this work, we study two different aspects: (i) the energy-efficiency tradeoff for a specific nonequilibrium linear dynamics of two variables with feedback and (ii) the cost of effective parameters in a coarse-grained theory as given by the "hidden" dissipation and entropy production rate in the effective equilibrium limit of the dynamics. To meaningfully discuss the tradeoff between energy consumption and the efficiency of the desired function, a one-to-one mapping between function(s) and energy input is required. The function considered in this work is the variance of one of the variables. We get a one-to-one mapping by considering the minimum variance obtained for a fixed entropy production rate and vice versa. We find that this minimum achievable variance is a monotonically decreasing function of the given entropy production rate. When there is a timescale separation, in the effective equilibrium limit, the cost of the effective potential and temperature is the associated "hidden" entropy production rate.

Reverse engineering directed gene regulatory networks from transcriptomics and proteomics data of biomining bacterial communities with approximate Bayesian computation and steady-state signalling simulations

BACKGROUND

Network inference is an important aim of systems biology. It enables the transformation of OMICs datasets into biological knowledge. It consists of reverse engineering gene regulatory networks from OMICs data, such as RNAseq or mass spectrometry-based proteomics data, through computational methods. This approach allows to identify signalling pathways involved in specific biological functions. The ability to infer causality in gene regulatory networks, in addition to correlation, is crucial for several modelling approaches and allows targeted control in biotechnology applications.

METHODS

We performed simulations according to the approximate Bayesian computation method, where the core model consisted of a steady-state simulation algorithm used to study gene regulatory networks in systems for which a limited level of details is available. The simulations outcome was compared to experimentally measured transcriptomics and proteomics data through approximate Bayesian computation.

RESULTS

The structure of small gene regulatory networks responsible for the regulation of biological functions involved in biomining were inferred from multi OMICs data of mixed bacterial cultures. Several causal inter- and intraspecies interactions were inferred between genes coding for proteins involved in the biomining process, such as heavy metal transport, DNA damage, replication and repair, and membrane biogenesis. The method also provided indications for the role of several uncharacterized proteins by the inferred connection in their network context.

CONCLUSIONS

The combination of fast algorithms with high-performance computing allowed the simulation of a multitude of gene regulatory networks and their comparison to experimentally measured OMICs data through approximate Bayesian computation, enabling the probabilistic inference of causality in gene regulatory networks of a multispecies bacterial system involved in biomining without need of single-cell or multiple perturbation experiments. This information can be used to influence biological functions and control specific processes in biotechnology applications.

The Physics of Cellular Decision Making During Epithelial-Mesenchymal Transition

The epithelial-mesenchymal transition (EMT) is a process by which cells lose epithelial traits, such as cell-cell adhesion and apico-basal polarity, and acquire migratory and invasive traits. EMT is crucial to embryonic development and wound healing. Misregulated EMT has been implicated in processes associated with cancer aggressiveness, including metastasis. Recent experimental advances such as single-cell analysis and temporal phenotypic characterization have established that EMT is a multistable process wherein cells exhibit and switch among multiple phenotypic states. This is in contrast to the classical perception of EMT as leading to a binary choice. Mathematical modeling has been at the forefront of this transformation for the field, not only providing a conceptual framework to integrate and analyze experimental data, but also making testable predictions. In this article, we review the key features and characteristics of EMT dynamics, with a focus on the mathematical modeling approaches that have been instrumental to obtaining various useful insights.

Cell Heterogeneity in Staphylococcal Communities

The human pathogen Staphylococcus aureus is a gram-positive bacterium that causes difficult-to-treat infections. One of the reasons why S. aureus is such as successful pathogen is due to the cell-to-cell physiological variability that exists within microbial communities. Many laboratories around the world study the genetic mechanisms involved in S. aureus cell heterogeneity to better understand infection mechanism of this bacterium. It was recently shown that the Agr quorum-sensing system, which antagonistically regulates biofilm-associated or acute bacteremia infections, is expressed in a subpopulation of specialized cells. In this review, we discuss the different genetic mechanism for bacterial cell differentiation and the physiological properties of the distinct cell types that are already described in S. aureus communities, as well as the role that these cell types play during an infection process.

Lane formation and critical coarsening in a model of bacterial competition

We study competition of two nonmotile bacterial strains in a three-dimensional channel numerically and analyze how their configuration evolves in space and time. We construct a lattice model that takes into account self-replication, mutation, and killing of bacteria. When mutation is not significant, the two strains segregate and form stripe patterns along the channel. The formed lanes are gradually rearranged, with increasing length scales in the two-dimensional cross-sectional plane. We characterize it in terms of coarsening and phase ordering in statistical physics. In particular, for the simple model without mutation and killing, we find logarithmically slow coarsening, which is characteristic of the two-dimensional voter model. With mutation and killing, we find a phase transition from a monopolistic phase, in which lanes are formed and coarsened until the system is eventually dominated by one of the two strains, to an equally mixed and disordered phase without lane structure. Critical behavior at the transition point is also studied and compared with the generalized voter class and the Ising class. These results are accounted for by continuum equations, obtained by applying a mean-field approximation along the channel axis. Our findings indicate relevance of critical coarsening of two-dimensional systems in the problem of bacterial competition within anisotropic three-dimensional geometry.

Birth and Resuscitation of (p)ppGpp Induced Antibiotic Tolerant Persister Cells

Transient antibiotic treatment typically eradicates most sensitive bacteria except a few survivors called persisters. The second messenger (p)ppGpp plays a key role in persister formation in Escherichia coli populations but the underlying mechanisms have remained elusive. In this study we induced (p)ppGpp synthesis by modulating tRNA charging and then directly observed the stochastic appearance, antibiotic tolerance, and resuscitation of persister cells using live microscopy. Different physiological parameters of persister cells as well as their regularly growing ancestors and sisters were continuously monitored using fluorescent reporters. Our results confirmed previous findings that high (p)ppGpp levels are critical for persister formation, but the phenomenon remained strikingly stochastic without any correlation between (p)ppGpp levels and antibiotic tolerance on the single-cell level. We could not confirm previous notions that persisters exhibit markedly low concentrations of intracellular ATP or were linked to post-transcriptional effects of (p)ppGpp through the activation of small genetic elements known as toxin-antitoxin (TA) modules. Instead, we suggest that persister cell formation under regular conditions is driven by the transcriptional response to increased (p)ppGpp levels.

Mathematical modeling of movement on fitness landscapes

Background

Movement of populations on fitness landscapes has been a problem of interest for a long time. While the subject has been extensively developed theoretically, reconciliation of the theoretical work with recent experimental data has not yet happened. In this work, we develop a computational framework and study evolution of the simplest transcription network between a single regulator, R and a single target protein, T.

Results

Through our simulations, we track evolution of this transcription network and comment on its dynamics and statistics of this movement. Significantly, we report that there exists a critical parameter which controls the ability of a network to reach the global fitness peak on the landscape. This parameter is the fraction of all permissible values of a biochemical parameter that can be accessed from its current value via a single mutation.

Conclusions

Overall, through this work, we aim to present a general framework for analysis of movement of populations (and particularly regulatory networks) on landscapes.

Electronic supplementary material

The online version of this article (10.1186/s12918-019-0704-0) contains supplementary material, which is available to authorized users.

On chaotic dynamics in transcription factors and the associated effects in differential gene regulation

The control of proteins by a transcription factor with periodically varying concentration exhibits intriguing dynamical behaviour. Even though it is accepted that transcription factors vary their dynamics in response to different situations, insight into how this affects downstream genes is lacking. Here, we investigate how oscillations and chaotic dynamics in the transcription factor NF-κB can affect downstream protein production. We describe how it is possible to control the effective dynamics of the transcription factor by stimulating it with an oscillating ligand. We find that chaotic dynamics modulates gene expression and up-regulates certain families of low-affinity genes, even in the presence of extrinsic and intrinsic noise. Furthermore, this leads to an increase in the production of protein complexes and the efficiency of their assembly. Finally, we show how chaotic dynamics creates a heterogeneous population of cell states, and describe how this can be beneficial in multi-toxic environments.

It is becoming clear that the dynamics of transcription factors may be important for gene regulation. Here, the authors study the implications of oscillatory and chaotic dynamics of NF-κB and demonstrate that it allows a degree of control of gene expression and can generate phenotypic heterogeneity.

Optimal parameter values for the control of gene regulation

How does a transcription network arrive at the particular values of biochemical interactions defining it? These interactions define DNA-transcription factor interaction, degradation rates of proteins, promoter strengths, and communication of the environmental signal with the network. What is the structure of the fitness landscape that is defined by the space that these parameters can take on? To answer these questions, we simulate the simplest regulatory network: a transcription factor, R, and a target protein, T. We use a cost-benefit analysis to evolve the network and eventually arrive at values of parameters which maximize fitness. We show that for a given topology, multiple parameter sets exist which confer maximal fitness to the cell, and that pairwise correlations exist between parameters in optimal sets. In addition, our results indicate that in the parameter space defining the interactions in a topology, a highly rugged fitness landscape exists.

Models of life: epigenetics, diversity and cycles

This review emphasizes aspects of biology that can be understood through repeated applications of simple causal rules. The selected topics include perspectives on gene regulation, phage lambda development, epigenetics, microbial ecology, as well as model approaches to diversity and to punctuated equilibrium in evolution. Two outstanding features are repeatedly described. One is the minimal number of rules to sustain specific states of complex systems for a long time. The other is the collapse of such states and the subsequent dynamical cycle of situations that restitute the system to a potentially new metastable state.

Cell fate decisions emerge as phages cooperate or compete inside their host

The system of the bacterium Escherichia coli and its virus, bacteriophage lambda, is paradigmatic for gene regulation in cell-fate development, yet insight about its mechanisms and complexities are limited due to insufficient resolution of study. Here we develop a 4-colour fluorescence reporter system at the single-virus level, combined with computational models to unravel both the interactions between phages and how individual phages determine cellular fates. We find that phages cooperate during lysogenization, compete among each other during lysis, and that confusion between the two pathways occasionally occurs. Additionally, we observe that phage DNAs have fluctuating cellular arrival times and vie for resources to replicate, enabling the interplay during different developmental paths, where each phage genome may make an individual decision. These varied strategies could separate the selection for replication-optimizing beneficial mutations during lysis from sequence diversification during lysogeny, allowing rapid adaptation of phage populations for various environments.

Using Sub-Network Combinations to Scale Up an Enumeration Method for Determining the Network Structures of Biological Functions

Deduction of biological regulatory networks from their functions is one of the focus areas of systems biology. Among the different techniques used in this reverse-engineering task, one powerful method is to enumerate all candidate network structures to find suitable ones. However, this method is severely limited by calculation capability: due to the brute-force approach, it is infeasible for networks with large number of nodes to be studied using traditional enumeration method because of the combinatorial explosion. In this study, we propose a new reverse-engineering technique based on the enumerating method: sub-network combinations. First, a complex biological function is divided into several sub-functions. Next, the three-node-network enumerating method is applied to search for sub-networks that are able to realize each of the sub-functions. Finally, complex whole networks are constructed by enumerating all possible combinations of sub-networks. The optimal ones are selected and analyzed. To demonstrate the effectiveness of this new method, we used it to deduct the network structures of a Pavlovian-like function. The whole Pavlovian-like network was successfully constructed by combining robust sub-networks, and the results were analyzed. With sub-network combination, the complexity has been largely reduced. Our method also provides a functional modular view of biological systems.

Modulation of BMP signalling by integrins

The bone morphogenetic protein (BMP) pathway is a major conserved signalling pathway with diverse roles in development and homeostasis. Given that cells exist in three-dimensional environments, one important area is to understand how the BMP pathway operates within such complex cellular environments. The extracellular matrix contains information regarding tissue architecture and its mechanical properties that is transmitted to the cell via integrin receptors. In this review, I describe various examples of modulation of the BMP pathway by integrins. In the case of the Drosophila embryo and some cell line-based studies, integrins have been found to enhance BMP responses through different mechanisms, such as enhancement of BMP ligand–receptor binding and effects on Smad phosphorylation or stability. In these contexts, BMP-dependent activation of integrins is a common theme. However, I also discuss examples where integrins inhibit the BMP pathway, highlighting the context-dependent nature of integrin–BMP cross-talk.

Understanding transcriptional regulatory networks using computational models

Transcriptional regulatory networks (TRNs) encode instructions for animal development and physiological responses. Recent advances in genomic technologies and computational modeling have revolutionized our ability to construct models of TRNs. Here, we survey current computational methods for inferring TRN models using genome-scale data. We discuss their advantages and limitations. We summarize representative TRNs constructed using genome-scale data in both normal and disease development. We discuss lessons learned about the structure/function relationship of TRNs, based on examining various large-scale TRN models. Finally, we outline some open questions regarding TRNs, including how to improve model accuracy by integrating complementary data types, how to infer condition-specific TRNs, and how to compare TRNs across conditions and species in order to understand their structure/function relationship.

Revisiting demand rules for gene regulation

Starting with Savageau's pioneering work regarding demand rules for gene regulation from the 1970s, here, we choose the simplest transcription network and ask: how does the cell choose a particular regulatory topology from all available possibilities?

Band-pass processing in a GPCR signaling pathway selects for NFAT transcription factor activation

Many biological processes are rhythmic and proper timing is increasingly appreciated as being critical for development and maintenance of physiological functions. To understand how temporal modulation of an input signal influences downstream responses, we employ microfluidic pulsatile stimulation of a G-protein coupled receptor, the muscarinic M3 receptor, in single cells with simultaneous real-time imaging of both intracellular calcium and NFAT nuclear localization. Interestingly, we find that reduced stimulation with pulses of ligand can give more efficient transcription factor activation, if stimuli are timed appropriately. Our experiments and computational analyses show that M3 receptor-induced calcium oscillations form a low pass filter while calcium-induced NFAT translocation forms a high pass filter. The combination acts as a band-pass filter optimized for intermediate frequencies of stimulation. We demonstrate that receptor desensitization and NFAT translocation rates determine critical features of the band-pass filter and that the band-pass may be shifted for different receptors or NFAT dynamics. As an example, we show that the two NFAT isoforms (NFAT4 and NFAT1) have shifted band-pass windows for the same receptor. While we focus specifically on the M3 muscarinic receptor and NFAT translocation, band-pass processing is expected to be a general theme that applies to multiple signaling pathways.

The role of mRNA and protein stability in the function of coupled positive and negative feedback systems in eukaryotic cells

Oscillators and switches are important elements of regulation in biological systems. These are composed of coupling negative feedback loops, which cause oscillations when delayed, and positive feedback loops, which lead to memory formation. Here, we examine the behavior of a coupled feedback system, the Negative Autoregulated Frustrated bistability motif (NAF). This motif is a combination of two previously explored motifs, the frustrated bistability motif (FBM) and the negative auto regulation motif (NAR), which both can produce oscillations. The NAF motif was previously suggested to govern long term memory formation in animals, and was used as a synthetic oscillator in bacteria. We build a mathematical model to analyze the dynamics of the NAF motif. We show analytically that the NAF motif requires an asymmetry in the strengths of activation and repression links in order to produce oscillations. We show that the effect of time delays in eukaryotic cells, originating from mRNA export and protein import, are negligible in this system. Based on the reported protein and mRNA half-lives in eukaryotic cells, we find that even though the NAF motif possesses the ability for oscillations, it mostly promotes constant protein expression at the biologically relevant parameter regimes.

A Bone Anabolic Effect of RANKL in a Murine Model of Osteoporosis Mediated Through FoxP3+ CD8 T Cells

TNF-α and IL-17 secreted by proinflammatory T cells (T(EFF)) promote bone erosion by activating osteoclasts. We previously demonstrated that in addition to bone resorption, osteoclasts act as antigen-presenting cells to induce FoxP3 in CD8 T cells (Tc(REG)). The osteoclast-induced regulatory CD8 T cells limit bone resorption in ovariectomized mice (a murine model of postmenopausal osteoporosis). Here we show that although low-dose receptor activator of NF-κB ligand (RANKL) maximally induces Tc(REG) via Notch signaling pathway to limit bone resorption, high-dose RANKL promotes bone resorption. In vitro, both TNF-α and IL-17, cytokines that are abundant in ovariectomized animals, suppress Tc(REG) induction by osteoclasts by repressing Notch ligand expression in osteoclasts, but this effect can be counteracted by addition of RANKL. Ovariectomized mice treated with low-dose RANKL induced Tc(REG) that suppressed bone resorption, decreased T(EFF) levels, and increased bone formation. High-dose RANKL had the expected osteolytic effect. Low-dose RANKL administration in ovariectomized mice lacking CD8 T cells was also osteolytic, confirming that Tc(REG) mediate this bone anabolic effect. Our results show that although RANKL directly stimulates osteoclasts to resorb bone, it also controls the osteoclasts' ability to induce regulatory T cells, engaging an important negative feedback loop. In addition to the conceivable clinical relevance to treatment of osteoporosis, these observations have potential relevance to induction of tolerance and autoimmune diseases.

Effects of Four Different Regulatory Mechanisms on the Dynamics of Gene Regulatory Cascades

Gene regulatory cascades (GRCs) are common motifs in cellular molecular networks. A given logical function in these cascades, such as the repression of the activity of a transcription factor, can be implemented by a number of different regulatory mechanisms. The potential consequences for the dynamic performance of the GRC of choosing one mechanism over another have not been analysed systematically. Here, we report the construction of a synthetic GRC in Escherichia coli, which allows us for the first time to directly compare and contrast the dynamics of four different regulatory mechanisms, affecting the transcription, translation, stability, or activity of a transcriptional repressor. We developed a biologically motivated mathematical model which is sufficient to reproduce the response dynamics determined by experimental measurements. Using the model, we explored the potential response dynamics that the constructed GRC can perform. We conclude that dynamic differences between regulatory mechanisms at an individual step in a GRC are often concealed in the overall performance of the GRC, and suggest that the presence of a given regulatory mechanism in a certain network environment does not necessarily mean that it represents a single optimal evolutionary solution.

An Atlas of Network Topologies Reveals Design Principles for Caenorhabditis elegans Vulval Precursor Cell Fate Patterning

The vulval precursor cell (VPC) fate patterning in Caenorhabditis elegans is a classic model experimental system for cell fate determination and patterning in development. Despite its apparent simplicity (six neighboring cells arranged in one dimension) and many experimental and computational efforts, the patterning strategy and mechanism remain controversial due to incomplete knowledge of the complex biology. Here, we carry out a comprehensive computational analysis and obtain a reservoir of all possible network topologies that are capable of VPC fate patterning under the simulation of various biological environments and regulatory rules. We identify three patterning strategies: sequential induction, morphogen gradient and lateral antagonism, depending on the features of the signal secreted from the anchor cell. The strategy of lateral antagonism, which has not been reported in previous studies of VPC patterning, employs a mutual inhibition of the 2° cell fate in neighboring cells. Robust topologies are built upon minimal topologies with basic patterning strategies and have more flexible and redundant implementations of modular functions. By simulated mutation, we find that all three strategies can reproduce experimental error patterns of mutants. We show that the topology derived by mapping currently known biochemical pathways to our model matches one of our identified functional topologies. Furthermore, our robustness analysis predicts a possible missing link related to the lateral antagonism strategy. Overall, we provide a theoretical atlas of all possible functional networks in varying environments, which may guide novel discoveries of the biological interactions in vulval development of Caenorhabditis elegans and related species.

Influence of parameter values on the oscillation sensitivities of two p53-Mdm2 models

Biomolecular networks that present oscillatory behavior are ubiquitous in nature. While some design principles for robust oscillations have been identified, it is not well understood how these oscillations are affected when the kinetic parameters are constantly changing or are not precisely known, as often occurs in cellular environments. Many models of diverse complexity level, for systems such as circadian rhythms, cell cycle or the p53 network, have been proposed. Here we assess the influence of hundreds of different parameter sets on the sensitivities of two configurations of a well-known oscillatory system, the p53 core network. We show that, for both models and all parameter sets, the parameter related to the p53 positive feedback, i.e. self-promotion, is the only one that presents sizeable sensitivities on extrema, periods and delay. Moreover, varying the parameter set values to change the dynamical characteristics of the response is more restricted in the simple model, whereas the complex model shows greater tunability. These results highlight the importance of the presence of specific network patterns, in addition to the role of parameter values, when we want to characterize oscillatory biochemical systems.

Coupled positive and negative feedbacks produce diverse gene expression patterns in colonies

Formation of patterns is a common feature in the development of multicellular organism as well as of microbial communities. To investigate the formation of gene expression patterns in colonies, we build a mathematical model of two-dimensional colony growth, where cells carry a coupled positive-and-negative-feedback circuit. We demonstrate that the model can produce sectored, target (concentric), uniform, and scattered expression patterns of regulators, depending on gene expression dynamics and nutrient diffusion. We reconstructed the same regulatory structure in Escherichia coli cells and found gene expression patterns on the surface of colonies similar to the ones produced by the computer simulations. By comparing computer simulations and experimental results, we observed that very simple rules of gene expression can yield a spectrum of well-defined patterns in a growing colony. Our results suggest that variations of the protein content among cells lead to a high level of heterogeneity in colonies.

Importance Formation of patterns is a common feature in the development of microbial communities. In this work, we show that a simple genetic circuit composed of a positive-feedback loop and a negative-feedback loop can produce diverse expression patterns in colonies. We obtained similar sets of gene expression patterns in the simulations and in the experiments. Because the combination of positive feedback and negative feedback is common in intracellular molecular networks, our results suggest that the protein content of cells is highly diversified in colonies.

Formation of patterns is a common feature in the development of microbial communities. In this work, we show that a simple genetic circuit composed of a positive-feedback loop and a negative-feedback loop can produce diverse expression patterns in colonies. We obtained similar sets of gene expression patterns in the simulations and in the experiments. Because the combination of positive feedback and negative feedback is common in intracellular molecular networks, our results suggest that the protein content of cells is highly diversified in colonies.

How long can bacteriophage λ change its mind?

A key event in the lifecycle of a temperate bacteriophage is the choice between lysis and lysogeny upon infection of a susceptible host cell. In a recent paper, we showed that a prolonged period exists after the decision to lysogenize, during which bacteriophage λ can abandon the initial decision, and instead develop lytically, as a response to the accumulation of the late lytic regulatory protein Q. Here, we present evidence that expression of Q does not induce replication of λ DNA, suggesting that the DNA to be packaged into the resulting phage progeny was already present at the time of the initial decision to lysogenize. We summarize our findings in a working model of the key determinants of the duration of the post-decision period during which it is possible for the infected cell to switch from the lysogeny decision to successful lytic development.

Homeostatic control of presynaptic neurotransmitter release

It is well established that the active properties of nerve and muscle cells are stabilized by homeostatic signaling systems. In organisms ranging from Drosophila to humans, neurons restore baseline function in the continued presence of destabilizing perturbations by rebalancing ion channel expression, modifying neurotransmitter receptor surface expression and trafficking, and modulating neurotransmitter release. This review focuses on the homeostatic modulation of presynaptic neurotransmitter release, termed presynaptic homeostasis. First, we highlight criteria that can be used to define a process as being under homeostatic control. Next, we review the remarkable conservation of presynaptic homeostasis at the Drosophila, mouse, and human neuromuscular junctions and emerging parallels at synaptic connections in the mammalian central nervous system. We then highlight recent progress identifying cellular and molecular mechanisms. We conclude by reviewing emerging parallels between the mechanisms of homeostatic signaling and genetic links to neurological disease.

Impact of upstream and downstream constraints on a signaling module's ultrasensitivity

Much work has been done on the study of the biochemical mechanisms that result in ultrasensitive behavior of simple biochemical modules. However, in a living cell, such modules are embedded in a bigger network that constrains the range of inputs that the module will receive as well as the range of the module's outputs that network will be able to detect. Here, we studied how the effective ultrasensitivity of a modular system is affected by these restrictions. We use a simple setup to explore to what extent the dynamic range spanned by upstream and downstream components of an ultrasensitive module impact on the effective sensitivity of the system. Interestingly, we found for some ultrasensitive motifs that dynamic range limitations imposed by downstream components can produce effective sensitivities much larger than that of the original module when considered in isolation.

A fluorimetric readout reporting the kinetics of nucleotide-induced human ribonucleotide reductase oligomerization

Human ribonucleotide reductase (hRNR) is a target of nucleotide chemotherapeutics in clinical use. The nucleotide-induced oligomeric regulation of hRNR subunit α is increasingly being recognized as an innate and drug-relevant mechanism for enzyme activity modulation. In the presence of negative feedback inhibitor dATP and leukemia drug clofarabine nucleotides, hRNR-α assembles into catalytically inert hexameric complexes, whereas nucleotide effectors that govern substrate specificity typically trigger α-dimerization. Currently, both knowledge of and tools to interrogate the oligomeric assembly pathway of RNR in any species in real time are lacking. We therefore developed a fluorimetric assay that reliably reports on oligomeric state changes of α with high sensitivity. The oligomerization-directed fluorescence quenching of hRNR-α, covalently labeled with two fluorophores, allows for direct readout of hRNR dimeric and hexameric states. We applied the newly developed platform to reveal the timescales of α self-assembly, driven by the feedback regulator dATP. This information is currently unavailable, despite the pharmaceutical relevance of hRNR oligomeric regulation.

A design principle underlying the paradoxical roles of E3 ubiquitin ligases

E3 ubiquitin ligases are important cellular components that determine the specificity of proteolysis in the ubiquitin-proteasome system. However, an increasing number of studies have indicated that E3 ubiquitin ligases also participate in transcription. Intrigued by the apparently paradoxical functions of E3 ubiquitin ligases in both proteolysis and transcriptional activation, we investigated the underlying design principles using mathematical modeling. We found that the antagonistic functions integrated in E3 ubiquitin ligases can prevent any undesirable sustained activation of downstream genes when E3 ubiquitin ligases are destabilized by unexpected perturbations. Interestingly, this design principle of the system is similar to the operational principle of a safety interlock device in engineering systems, which prevents a system from abnormal operation unless stability is guaranteed.

Efficient search, mapping, and optimization of multi-protein genetic systems in diverse bacteria

Developing predictive models of multi-protein genetic systems to understand and optimize their behavior remains a combinatorial challenge, particularly when measurement throughput is limited. We developed a computational approach to build predictive models and identify optimal sequences and expression levels, while circumventing combinatorial explosion. Maximally informative genetic system variants were first designed by the RBS Library Calculator, an algorithm to design sequences for efficiently searching a multi-protein expression space across a > 10,000-fold range with tailored search parameters and well-predicted translation rates. We validated the algorithm's predictions by characterizing 646 genetic system variants, encoded in plasmids and genomes, expressed in six gram-positive and gram-negative bacterial hosts. We then combined the search algorithm with system-level kinetic modeling, requiring the construction and characterization of 73 variants to build a sequence-expression-activity map (SEAMAP) for a biosynthesis pathway. Using model predictions, we designed and characterized 47 additional pathway variants to navigate its activity space, find optimal expression regions with desired activity response curves, and relieve rate-limiting steps in metabolism. Creating sequence-expression-activity maps accelerates the optimization of many protein systems and allows previous measurements to quantitatively inform future designs.

A mixed incoherent feed-forward loop allows conditional regulation of response dynamics

Expression of the SodA superoxide dismutase (MnSOD) in Escherichia coli is regulated by superoxide concentration through the SoxRS system and also by Fur (Ferric uptake regulator) through a mixed incoherent feed forward loop (FFL) containing the RyhB small regulatory RNA. In this work I theoretically analyze the function of this feed forward loop as part of the network controlling expression of the two cytoplasmic superoxide dismutases, SodA and SodB. I find that feed forward regulation allows faster response to superoxide stress at low intracellular iron levels compared to iron rich conditions. That is, it can conditionally modulate the response time of a superimposed transcriptional control mechanism.

Generic Properties of Random Gene Regulatory Networks

Modeling gene regulatory networks (GRNs) is an important topic in systems biology. Although there has been much work focusing on various specific systems, the generic behavior of GRNs with continuous variables is still elusive. In particular, it is not clear typically how attractors partition among the three types of orbits: steady state, periodic and chaotic, and how the dynamical properties change with network's topological characteristics. In this work, we first investigated these questions in random GRNs with different network sizes, connectivity, fraction of inhibitory links and transcription regulation rules. Then we searched for the core motifs that govern the dynamic behavior of large GRNs. We show that the stability of a random GRN is typically governed by a few embedding motifs of small sizes, and therefore can in general be understood in the context of these short motifs. Our results provide insights for the study and design of genetic networks.

FOUNDATIONS FOR MODELING THE DYNAMICS OF GENE REGULATORY NETWORKS: A MULTILEVEL-PERSPECTIVE REVIEW

A promising alternative for unraveling the principles under which the dynamic interactions among genes lead to cellular phenotypes relies on mathematical and computational models at different levels of abstraction, from the molecular level of protein-DNA interactions to the system level of functional relationships among genes. This review article presents, under a bottom–up perspective, a hierarchy of approaches to modeling gene regulatory network dynamics, from microscopic descriptions at the single-molecule level in the spatial context of an individual cell to macroscopic models providing phenomenological descriptions at the population-average level. The reviewed modeling approaches include Molecular Dynamics, Particle-Based Brownian Dynamics, the Master Equation approach, Ordinary Differential Equations, and the Boolean logic abstraction. Each of these frameworks is motivated by a particular biological context and the nature of the insight being pursued. The setting of gene network dynamic models from such frameworks involves assumptions and mathematical artifacts often ignored by the non-specialist. This article aims at providing an entry point for biologists new to the field and computer scientists not acquainted with some recent biophysically-inspired models of gene regulation. The connections promoting intuition between different abstraction levels and the role that approximations play in the modeling process are highlighted throughout the paper.

BioFNet: biological functional network database for analysis and synthesis of biological systems

In synthetic biology and systems biology, a bottom-up approach can be used to construct a complex, modular, hierarchical structure of biological networks. To analyze or design such networks, it is critical to understand the relationship between network structure and function, the mechanism through which biological parts or biomolecules are assembled into building blocks or functional networks. A functional network is defined as a subnetwork of biomolecules that performs a particular function. Understanding the mechanism of building functional networks would help develop a methodology for analyzing the structure of large-scale networks and design a robust biological circuit to perform a target function. We propose a biological functional network database, named BioFNet, which can cover the whole cell at the level of molecular interactions. The BioFNet takes an advantage in implementing the simulation program for the mathematical models of the functional networks, visualizing the simulated results. It presents a sound basis for rational design of biochemical networks and for understanding how functional networks are assembled to create complex high-level functions, which would reveal design principles underlying molecular architectures.

The effect of LacI autoregulation on the performance of the lactose utilization system in Escherichia coli

The lactose operon of Escherichia coli is a paradigm system for quantitative understanding of gene regulation in prokaryotes. Yet, none of the many mathematical models built so far to study the dynamics of this system considered the fact that the Lac repressor regulates its own transcription by forming a transcriptional roadblock at the O3 operator site. Here we study the effect of autoregulation on intracellular LacI levels and also show that cAMP-CRP binding does not affect the efficiency of autoregulation. We built a mathematical model to study the role of LacI autoregulation in the lactose utilization system. Previously, it has been argued that negative autoregulation can significantly reduce noise as well as increase the speed of response. We show that the particular molecular mechanism, a transcriptional roadblock, used to achieve self-repression in the lac system does neither. Instead, LacI autoregulation balances two opposing states, one that allows quicker response to smaller pulses of external lactose, and the other that minimizes production costs in the absence of lactose.

Ultrasensitive response motifs: basic amplifiers in molecular signalling networks

Multi-component signal transduction pathways and gene regulatory circuits underpin integrated cellular responses to perturbations. A recurring set of network motifs serve as the basic building blocks of these molecular signalling networks. This review focuses on ultrasensitive response motifs (URMs) that amplify small percentage changes in the input signal into larger percentage changes in the output response. URMs generally possess a sigmoid input–output relationship that is steeper than the Michaelis–Menten type of response and is often approximated by the Hill function. Six types of URMs can be commonly found in intracellular molecular networks and each has a distinct kinetic mechanism for signal amplification. These URMs are: (i) positive cooperative binding, (ii) homo-multimerization, (iii) multistep signalling, (iv) molecular titration, (v) zero-order covalent modification cycle and (vi) positive feedback. Multiple URMs can be combined to generate highly switch-like responses. Serving as basic signal amplifiers, these URMs are essential for molecular circuits to produce complex nonlinear dynamics, including multistability, robust adaptation and oscillation. These dynamic properties are in turn responsible for higher-level cellular behaviours, such as cell fate determination, homeostasis and biological rhythm.

Design principles of regulatory networks: searching for the molecular algorithms of the cell

A challenge in biology is to understand how complex molecular networks in the cell execute sophisticated regulatory functions. Here we explore the idea that there are common and general principles that link network structures to biological functions, principles that constrain the design solutions that evolution can converge upon for accomplishing a given cellular task. We describe approaches for classifying networks based on abstract architectures and functions, rather than on the specific molecular components of the networks. For any common regulatory task, can we define the space of all possible molecular solutions? Such inverse approaches might ultimately allow the assembly of a design table of core molecular algorithms that could serve as a guide for building synthetic networks and modulating disease networks.

Small-number effects: a third stable state in a genetic bistable toggle switch

A genetic toggle switch was studied experimentally and theoretically. We have found an additional kinetic stable state where all the genes express very lowly, which is predicted to be unstable by dynamical systems theory. It can also stably coexist with the other two known stable states, although this coexistence is forbidden in a deterministic dynamical system. We analyze that this nontrivial phenomenon results from the discrete and fluctuate nature in such a small system, by comparing experimental results with modeling results of exact stochastic simulations and differential equations.

Increasing signal specificity of the TOL network of Pseudomonas putida mt-2 by rewiring the connectivity of the master regulator XylR

Prokaryotic transcription factors (TFs) that bind small xenobiotic molecules (e.g., TFs that drive genes that respond to environmental pollutants) often display a promiscuous effector profile for analogs of the bona fide chemical signals. XylR, the master TF for expression of the m-xylene biodegradation operons encoded in the TOL plasmid pWW0 of Pseudomonas putida, responds not only to the aromatic compound but also, albeit to a lesser extent, to many other aromatic compounds, such as 3-methylbenzylalcohol (3MBA). We have examined whether such a relaxed regulatory scenario can be reshaped into a high-capacity/high-specificity regime by changing the connectivity of this effector-sensing TF within the rest of the circuit rather than modifying XylR structure itself. To this end, the natural negative feedback loop that operates on xylR transcription was modified with a translational attenuator that brings down the response to 3MBA while maintaining the transcriptional output induced by m-xylene (as measured with a luxCDABE reporter system). XylR expression was then subject to a positive feedback loop in which the TF was transcribed from its own target promoters, each known to hold different input/output transfer functions. In the first case (xylR under the strong promoter of the upper TOL operon, Pu), the reporter system displayed an increased transcriptional capacity in the resulting network for both the optimal and the suboptimal XylR effectors. In contrast, when xylR was expressed under the weaker Ps promoter, the resulting circuit unmistakably discriminated m-xylene from 3MBA. The non-natural connectivity engineered in the network resulted both in a higher promoter activity and also in a much-increased signal-to-background ratio. These results indicate that the working regimes of given genetic circuits can be dramatically altered through simple changes in the way upstream transcription factors are self-regulated by positive or negative feedback loops.

It is generally taken for granted that promoters regulated by transcriptional factors (TFs) that respond to small molecules control their specificity to given effectors by tightening or relaxing the intrinsic dual interaction between the TF and the particular inducer. One such promoter is Pu, which drives expression of an operon for the biodegradation of m-xylene by the soil bacterium P. putida mt-2. While XylR, the chief TF of this system, binds this substrate and activates Pu, the same regulator responds, to a lesser extent, to 3-methylbenzylalcohol and thus also activates the promoter. This work provides evidence that such natural effector promiscuity of the system can be altogether suppressed by replacing the naturally occurring negative autoregulation loop that governs XylR expression with an equivalent positive feedback loop. Based on this result, we argue that signal specificity of a given regulatory device depends not only on the TF involved but also on TF connectivity to upstream signals and downstream targets.