Gene networks of fully connected triads with complete auto-activation enable multistability and stepwise stochastic transitions

MaxCal can infer models from coupled stochastic trajectories of gene expression and cell division

Gene expression is inherently noisy due to small numbers of proteins and nucleic acids inside a cell. Likewise, cell division is stochastic, particularly when tracking at the level of a single cell. The two can be coupled when gene expression affects the rate of cell division. Single-cell time-lapse experiments can measure both fluctuations by simultaneously recording protein levels inside a cell and its stochastic division. These information-rich noisy trajectory data sets can be harnessed to learn about the underlying molecular and cellular details that are often not known a priori. A critical question is: How can we infer a model given data where fluctuations at two levels-gene expression and cell division-are intricately convoluted? We show the principle of maximum caliber (MaxCal)-integrated within a Bayesian framework-can be used to infer several cellular and molecular details (division rates, protein production, and degradation rates) from these coupled stochastic trajectories (CSTs). We demonstrate this proof of concept using synthetic data generated from a known model. An additional challenge in data analysis is that trajectories are often not in protein numbers, but in noisy fluorescence that depends on protein number in a probabilistic manner. We again show that MaxCal can infer important molecular and cellular rates even when data are in fluorescence, another example of CST with three confounding factors-gene expression noise, cell division noise, and fluorescence distortion-all coupled. Our approach will provide guidance to build models in synthetic biology experiments as well as general biological systems where examples of CSTs are abundant.

Coupled Mutual Inhibition and Mutual Activation Motifs as Tools for Cell-Fate Control

Multistability is central to biological systems. It plays a crucial role in adaptation, evolvability, and differentiation. The presence of positive feedback loops can enable multistability. The simplest of such feedback loops are (a) a mutual inhibition (MI) loop, (b) a mutual activation (MA) loop, and (c) self-activation. While it is established that all three motifs can give rise to bistability, the characteristic differences in the bistability exhibited by each of these motifs is relatively less understood. Here, we use dynamical simulations across a large ensemble of parameter sets and initial conditions to study the bistability characteristics of these motifs. Furthermore, we investigate the utility of these motifs for achieving coordinated expression through cyclic and parallel coupling amongst them. Our analysis revealed that MI-based architectures offer discrete and robust control over gene expression, multistability, and coordinated expression among multiple genes, as compared to MA-based architectures. We then devised a combination of MI and MA architectures to improve coordination and multistability. Such designs help enhance our understanding of the control structures involved in robust cell-fate decisions and provide a way to achieve controlled decision-making in synthetic systems.

Functional Resilience of Mutually Repressing Motifs Embedded in Larger Networks

Elucidating the design principles of regulatory networks driving cellular decision-making has important implications for understanding cell differentiation and guiding the design of synthetic circuits. Mutually repressing feedback loops between 'master regulators' of cell fates can exhibit multistable dynamics enabling "single-positive" phenotypes: (high A, low B) and (low A, high B) for a toggle switch, and (high A, low B, low C), (low A, high B, low C) and (low A, low B, high C) for a toggle triad. However, the dynamics of these two motifs have been interrogated in isolation in silico, but in vitro and in vivo, they often operate while embedded in larger regulatory networks. Here, we embed these motifs in complex larger networks of varying sizes and connectivity to identify hallmarks under which these motifs maintain their canonical dynamical behavior. We show that an increased number of incoming edges onto a motif leads to a decay in their canonical stand-alone behaviors. We also show that this decay can be exacerbated by adding self-inhibition but not self-activation loops on the 'master regulators'. These observations offer insights into the design principles of biological networks containing these motifs and can help devise optimal strategies for the integration of these motifs into larger synthetic networks.

One cell, many fates

[Figure: see text].

SOX Transcription Factors as Important Regulators of Neuronal and Glial Differentiation During Nervous System Development and Adult Neurogenesis

The SOX proteins belong to the superfamily of transcription factors (TFs) that display properties of both classical TFs and architectural components of chromatin. Since the cloning of the Sox/SOX genes, remarkable progress has been made in illuminating their roles as key players in the regulation of multiple developmental and physiological processes. SOX TFs govern diverse cellular processes during development, such as maintaining the pluripotency of stem cells, cell proliferation, cell fate decisions/germ layer formation as well as terminal cell differentiation into tissues and organs. However, their roles are not limited to development since SOX proteins influence survival, regeneration, cell death and control homeostasis in adult tissues. This review summarized current knowledge of the roles of SOX proteins in control of central nervous system development. Some SOX TFs suspend neural progenitors in proliferative, stem-like state and prevent their differentiation. SOX proteins function as pioneer factors that occupy silenced target genes and keep them in a poised state for activation at subsequent stages of differentiation. At appropriate stage of development, SOX members that maintain stemness are down-regulated in cells that are competent to differentiate, while other SOX members take over their functions and govern the process of differentiation. Distinct SOX members determine down-stream processes of neuronal and glial differentiation. Thus, sequentially acting SOX TFs orchestrate neural lineage development defining neuronal and glial phenotypes. In line with their crucial roles in the nervous system development, deregulation of specific SOX proteins activities is associated with neurodevelopmental disorders (NDDs). The overview of the current knowledge about the link between SOX gene variants and NDDs is presented. We outline the roles of SOX TFs in adult neurogenesis and brain homeostasis and discuss whether impaired adult neurogenesis, detected in neurodegenerative diseases, could be associated with deregulation of SOX proteins activities. We present the current data regarding the interaction between SOX proteins and signaling pathways and microRNAs that play roles in nervous system development. Finally, future research directions that will improve the knowledge about distinct and various roles of SOX TFs in health and diseases are presented and discussed.

Critical Comparison of MaxCal and Other Stochastic Modeling Approaches in Analysis of Gene Networks

Learning the underlying details of a gene network with feedback is critical in designing new synthetic circuits. Yet, quantitative characterization of these circuits remains limited. This is due to the fact that experiments can only measure partial information from which the details of the circuit must be inferred. One potentially useful avenue is to harness hidden information from single-cell stochastic gene expression time trajectories measured for long periods of time—recorded at frequent intervals—over multiple cells. This raises the feasibility vs. accuracy dilemma while deciding between different models of mining these stochastic trajectories. We demonstrate that inference based on the Maximum Caliber (MaxCal) principle is the method of choice by critically evaluating its computational efficiency and accuracy against two other typical modeling approaches: (i) a detailed model (DM) with explicit consideration of multiple molecules including protein-promoter interaction, and (ii) a coarse-grain model (CGM) using Hill type functions to model feedback. MaxCal provides a reasonably accurate model while being significantly more computationally efficient than DM and CGM. Furthermore, MaxCal requires minimal assumptions since it is a top-down approach and allows systematic model improvement by including constraints of higher order, in contrast to traditional bottom-up approaches that require more parameters or ad hoc assumptions. Thus, based on efficiency, accuracy, and ability to build minimal models, we propose MaxCal as a superior alternative to traditional approaches (DM, CGM) when inferring underlying details of gene circuits with feedback from limited data.

Trajectory-based energy landscapes of gene regulatory networks

Multistability and natural biological variability can result in significant heterogeneity within a cell population, leading to challenges in understanding and modulating cell behavior. Energy landscapes can offer qualitatively intuitive visualizations of cell phenotype and facilitate a more quantitative understanding of cellular dynamics, but current methods for landscape generation are mathematically involved and often require specific system properties (e.g., ergodicity or independent gene/protein probability distributions) that do not always hold. Here, we present a simple kinetic Monte Carlo-based method for landscape generation from a system of ordinary differential equations using only simulation trajectories initialized throughout the phase space of interest. The resulting landscape produces three quantitative features relevant to understanding cell behavior: stability (reflected by the depth or potential of landscape valleys), velocity (representing average directional movement on the landscape), and variance in velocity (indicative of landscape positions with heterogeneous movements). We applied this method to a genetic toggle switch, a core decision-making network in binary cellular responses, to elucidate effects of biologically relevant intrinsic and extrinsic cues. Intrinsic noise, such as stochasticity in transcription-translation and differences in cell cycle position, manifests through changes in valley width and position, reflecting increased population heterogeneity and more probabilistic cell fate transitions. The landscapes also capture the effect of an external inducer, revealing a quantitative correlation between the rate of cell fate transition and the energy barrier above a threshold inducer concentration determined by the permissivity of the valley. Further, in tracking dynamically changing landscapes under time-varying external cues, we unexpectedly found that an oscillatory inducer input can modulate cell fate heterogeneity and lead to periodic cell fate transitions entrained to the input frequency, depending on the intrinsic degradation rate of the switch. The landscape generation approach outlined herein is generalizable to other network topologies and may provide new quantitative insights into their dynamics.

Stochastic analysis of genetic feedback controllers to reprogram a pluripotency gene regulatory network

Cellular reprogramming is traditionally accomplished through an open loop (OL) control approach, wherein key transcription factors (TFs) are injected in cells to steer the state of the pluripotency (PL) gene regulatory network (GRN), as encoded by TFs concentrations, to the pluripotent state. Due to the OL nature of this approach, the concentration of TFs cannot be accurately controlled. Recently, a closed loop (CL) feedback control strategy was proposed to overcome this problem with promising theoretical results. However, previous analyses of the controller were based on deterministic models. It is well known that cellular systems are characterized by substantial stochasticity, especially when molecules are in low copy number as it is the case in reprogramming problems wherein the gene copy number is usually one or two. Hence, in this paper, we analyze the Chemical Master Equation (CME) for the reaction model of the PL GRN with and without the feedback controller. We computationally and analytically investigate the performance of the controller in biologically relevant parameter regimes where stochastic effects dictate system dynamics. Our results indicate that the feedback control approach still ensures reprogramming even when both the PL GRN and the controller are stochastic.

Intracellular Noise Level Determines Ratio Control Strategy Confined by Speed-Accuracy Trade-off

Robust and precise ratio control of heterogeneous phenotypes within an isogenic population is an essential task, especially in the development and differentiation of a large number of cells such as bacteria, sensory receptors, and blood cells. However, the mechanisms of such ratio control are poorly understood. Here, we employ experimental and mathematical techniques to understand the combined effects of signal induction and gene expression stochasticity on phenotypic multimodality. We identify two strategies to control phenotypic ratios from an initially homogeneous population, suitable roughly to high-noise and low-noise intracellular environments, and we show that both can be used to generate precise fractional differentiation. In noisy gene expression contexts, such as those found in bacteria, induction within the circuit's bistable region is enough to cause noise-induced bimodality within a feasible time frame. However, in less noisy contexts, such as tightly controlled eukaryotic systems, spontaneous state transitions are rare and hence bimodality needs to be induced with a controlled pulse of induction that falls outside the bistable region. Finally, we show that noise levels, system response time, and ratio tuning accuracy impose trade-offs and limitations on both ratio control strategies, which guide the selection of strategy alternatives.

Modeling Gene Networks to Understand Multistability in Stem Cells

Stem cells are unique in their ability to differentiate into diverse phenotypes capable of displaying radically different, yet stable, gene expression profiles. Understanding this multistable behavior is key to rationally influencing stem cell differentiation for both research and therapeutic purposes. To this end, mathematical paradigms have been adopted to simulate and explain the dynamics of complex gene networks. In this chapter, we introduce strategies for building deterministic and stochastic mathematical models of gene expression and demonstrate how analysis of these models can benefit our understanding of complex observed behaviors. Developing a mathematical understanding of biological processes is of utmost importance in understanding and controlling stem cell behavior.

Maximum Caliber Can Characterize Genetic Switches with Multiple Hidden Species

Gene networks with feedback often involve interactions between multiple species of biomolecules, much more than experiments can actually monitor. Coupled with this is the challenge that experiments often measure gene expression in noisy fluorescence instead of protein numbers. How do we infer biophysical information and characterize the underlying circuits from this limited and convoluted data? We address this by building stochastic models using the principle of Maximum Caliber (MaxCal). MaxCal uses the basic information on synthesis, degradation, and feedback-without invoking any other auxiliary species and ad hoc reactions-to generate stochastic trajectories similar to those typically measured in experiments. MaxCal in conjunction with Maximum Likelihood (ML) can infer parameters of the model using fluctuating trajectories of protein expression over time. We demonstrate the success of the MaxCal + ML methodology using synthetic data generated from known circuits of different genetic switches: (i) a single-gene autoactivating circuit involving five species (including mRNA), (ii) a mutually repressing two-gene circuit (toggle switch) with seven species (including mRNA) considering stochastic time traces of two proteins, and (iii) the same toggle switch circuit considering stochastic time traces of only one of the two proteins. To further challenge the MaxCal + ML inference scheme, we repeat our analysis for the second and third scenario with traces expressed in noisy fluorescence instead of protein number to closely mimic typical experiments. We show that, for all of these models with increasing complexity and obfuscation, the minimal model of MaxCal is still able to capture the fluctuations of the trajectory and infer basic underlying rate parameters when benchmarked against the known values used to generate the synthetic data. Importantly, the model also yields an effective feedback parameter that can be used to quantify interactions within these circuits. These applications show the promise of MaxCal's ability to characterize circuits with limited data, and its utility to better understand evolution and advance design strategies for specific functions.

Building Predictive Models of Genetic Circuits Using the Principle of Maximum Caliber

Learning the underlying details of a gene network is a major challenge in cellular and synthetic biology. We address this challenge by building a chemical kinetic model that utilizes information encoded in the stochastic protein expression trajectories typically measured in experiments. The applicability of the proposed method is demonstrated in an auto-activating genetic circuit, a common motif in natural and synthetic gene networks. Our approach is based on the principle of maximum caliber (MaxCal)-a dynamical analog of the principle of maximum entropy-and builds a minimal model using only three constraints: 1) protein synthesis, 2) protein degradation, and 3) positive feedback. The MaxCal-generated model (described with four parameters) was benchmarked against synthetic data generated using a Gillespie algorithm on a known reaction network (with seven parameters). MaxCal accurately predicts underlying rate parameters of protein synthesis and degradation as well as experimental observables such as protein number and dwell-time distributions. Furthermore, MaxCal yields an effective feedback parameter that can be useful for circuit design. We also extend our methodology and demonstrate how to analyze trajectories that are not in protein numbers but in arbitrary fluorescence units, a more typical condition in experiments. This "top-down" methodology based on minimal information-in contrast to traditional "bottom-up" approaches that require ad hoc knowledge of circuit details-provides a powerful tool to accurately infer underlying details of feedback circuits that are not otherwise visible in experiments and to help guide circuit design.

'Molecular habituation' as a potential mechanism of gradual homeostatic loss with age

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Constitutive signals indicate homeostatic dysregulation but their effect on signal transduction remains largely unexplored.

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A theoretical approach is undertaken to examine how oxidative stress may affect redox signal transduction.

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Constitutive signals can result in a ‘molecular habituation’ effect that interferes with information transmission.

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The robustness of such a theoretical observation to the underlying methodology hints at the generality of this principle.

The ability of reactive oxygen species (ROS) to cause molecular damage has meant that chronic oxidative stress has been mostly studied from the point of view of being a source of toxicity to the cell. However, the known duality of ROS molecules as both damaging agents and cellular redox signals implies another perspective in the study of sustained oxidative stress. This is a perspective of studying oxidative stress as a constitutive signal within the cell. In this work, we adopt a theoretical perspective as an exploratory and explanatory approach to examine how chronic oxidative stress can interfere with signal processing by redox signalling pathways in the cell. We report that constitutive signals can give rise to a ‘molecular habituation’ effect that can prime for a gradual loss of biological function. This is because a constitutive signal in the environment has the potential to reduce the responsiveness of a signalling pathway through the prolonged activation of negative regulators. Additionally, we demonstrate how this phenomenon is likely to occur in different signalling pathways exposed to persistent signals and furthermore at different levels of biological organisation.

SCL/TAL1: a multifaceted regulator from blood development to disease

SCL/TAL1 (stem cell leukemia/T-cell acute lymphoblastic leukemia [T-ALL] 1) is an essential transcription factor in normal and malignant hematopoiesis. It is required for specification of the blood program during development, adult hematopoietic stem cell survival and quiescence, and terminal maturation of select blood lineages. Following ectopic expression, SCL contributes to oncogenesis in T-ALL. Remarkably, SCL’s activities are all mediated through nucleation of a core quaternary protein complex (SCL:E-protein:LMO1/2 [LIM domain only 1 or 2]:LDB1 [LIM domain-binding protein 1]) and dynamic recruitment of conserved combinatorial associations of additional regulators in a lineage- and stage-specific context. The finely tuned control of SCL’s regulatory functions (lineage priming, activation, and repression of gene expression programs) provides insight into fundamental developmental and transcriptional mechanisms, and highlights mechanistic parallels between normal and oncogenic processes. Importantly, recent discoveries are paving the way to the development of innovative therapeutic opportunities in SCL+ T-ALL.

Engineering of a synthetic quadrastable gene network to approach Waddington landscape and cell fate determination

The process of cell fate determination has been depicted intuitively as cells travelling and resting on a rugged landscape, which has been probed by various theoretical studies. However, few studies have experimentally demonstrated how underlying gene regulatory networks shape the landscape and hence orchestrate cellular decision-making in the presence of both signal and noise. Here we tested different topologies and verified a synthetic gene circuit with mutual inhibition and auto-activations to be quadrastable, which enables direct study of quadruple cell fate determination on an engineered landscape. We show that cells indeed gravitate towards local minima and signal inductions dictate cell fates through modulating the shape of the multistable landscape. Experiments, guided by model predictions, reveal that sequential inductions generate distinct cell fates by changing landscape in sequence and hence navigating cells to different final states. This work provides a synthetic biology framework to approach cell fate determination and suggests a landscape-based explanation of fixed induction sequences for targeted differentiation.

DOI:http://dx.doi.org/10.7554/eLife.23702.001

Cells in animals use a process called differentiation to specialize into specific cell types such as skin cells and liver cells. Proteins called transcription factors drive particular steps in differentiation by controlling the activity of specific genes. Many transcription factors interact with each other to form complex networks that regulate gene activity to determine the fate of a cell and control the whole differentiation process. Some individual gene networks can program cells to become any one of several different cell fates, a feature known as multistability.

In the 1950s, a scientist called Conrad Waddington proposed the concept of an “epigenetic landscape” to describe how the fate of a cell is decided as an animal develops. The cell, depicted as a ball, rolls down a rugged landscape and has the option of taking several different routes. Each route will eventually lead to a distinct cell fate. As the ball moves down the hill, the choice of routes and final destinations becomes more limited. Theoretical approaches have been used to understand how gene regulatory networks shape the epigenetic landscape of an animal. However, few studies have experimentally tested the findings of the theoretical approaches and it is not clear how environmental inputs help to determine which path a cell will take.

Although bacteria cells do not generally specialize into particular cell types, bacteria cells can use multistability in transcription factor networks to switch between different behaviors or “states” in response to cues from the environment. Wu et al. used a bacterium called E. coli as a model to investigate how a gene network called MINPA from mammals, which is involved in differentiation and is believed to show multistability, can guide cells to adopt different states. The work combined experimental and mathematical approaches to design, construct and test an artificial version of the MINPA gene network in E. coli.

The experiments showed that MINPA could direct the cells to adopt four different stable states in which the cells produced fluorescent proteins of different colors. With the help of mathematical modeling, Wu et al. charted how the landscape of cell states changed when external chemical cues were applied. Exposing the cells to several cues in particular orders guided the cells to different final states.

The findings of Wu et al. shed new light on how the fate of a cell is determined and provide a theoretical framework for understanding the complex networks that control cell differentiation. This could help develop new ways of directing cell fate that could ultimately be used to generate cells to treat human diseases.

DOI:http://dx.doi.org/10.7554/eLife.23702.002

A Blueprint for a Synthetic Genetic Feedback Controller to Reprogram Cell Fate

To artificially reprogram cell fate, experimentalists manipulate the gene regulatory networks (GRNs) that maintain a cell's phenotype. In practice, reprogramming is often performed by constant overexpression of specific transcription factors (TFs). This process can be unreliable and inefficient. Here, we address this problem by introducing a new approach to reprogramming based on mathematical analysis. We demonstrate that reprogramming GRNs using constant overexpression may not succeed in general. Instead, we propose an alternative reprogramming strategy: a synthetic genetic feedback controller that dynamically steers the concentration of a GRN's key TFs to any desired value. The controller works by adjusting TF expression based on the discrepancy between desired and actual TF concentrations. Theory predicts that this reprogramming strategy is guaranteed to succeed, and its performance is independent of the GRN's structure and parameters, provided that feedback gain is sufficiently high. As a case study, we apply the controller to a model of induced pluripotency in stem cells.

Genome-Wide Transcriptome and Binding Sites Analyses Identify Early FOX Expressions for Enhancing Cardiomyogenesis Efficiency of hESC Cultures

The differentiation efficiency of human embryonic stem cells (hESCs) into heart muscle cells (cardiomyocytes) is highly sensitive to culture conditions. To elucidate the regulatory mechanisms involved, we investigated hESCs grown on three distinct culture platforms: feeder-free Matrigel, mouse embryonic fibroblast feeders, and Matrigel replated on feeders. At the outset, we profiled and quantified their differentiation efficiency, transcriptome, transcription factor binding sites and DNA-methylation. Subsequent genome-wide analyses allowed us to reconstruct the relevant interactome, thereby forming the regulatory basis for implicating the contrasting differentiation efficiency of the culture conditions. We hypothesized that the parental expressions of FOXC1, FOXD1 and FOXQ1 transcription factors (TFs) are correlative with eventual cardiomyogenic outcome. Through WNT induction of the FOX TFs, we observed the co-activation of WNT3 and EOMES which are potent inducers of mesoderm differentiation. The result strengthened our hypothesis on the regulatory role of the FOX TFs in enhancing mesoderm differentiation capacity of hESCs. Importantly, the final proportions of cells expressing cardiac markers were directly correlated to the strength of FOX inductions within 72 hours after initiation of differentiation across different cell lines and protocols. Thus, we affirmed the relationship between early FOX TF expressions and cardiomyogenesis efficiency.

Realization of tristability in a multiplicatively coupled dual-loop genetic network

Multistability is a crucial recurring theme in cell signaling. Multistability is attributed to the presence of positive feedback loops, but the general condition and essential mechanism for realizing multistability remain unclear. Here, we build a generic circuit model comprising two transcription factors and a microRNA, representing a kind of core architecture in gene regulatory networks. The circuit can be decomposed into two positive feedback loops (PFLs) or one PFL and one negative feedback loop (NFL), which are multiplicatively coupled. Bifurcation analyses of the model reveal that the circuit can achieve tristability through four kinds of bifurcation scenarios when parameter values are varied in a wide range. We formulate the general requirement for tristability in terms of logarithmic gain of the circuit. The parameter ranges for tristability and possible transition routes among steady states are determined by the combination of gain features of individual feedback loops. Coupling two PFLs with bistability or one NFL with a bistable PFL is most likely to generate tristability, but the underlying mechanisms are largely different. We also interpret published results and make testable predictions. This work sheds new light on interlinking feedback loops to realize tristability. The proposed theoretical framework can be of wide applicability.

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

BACKGROUND

Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level.

SCOPE OF REVIEW

We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies.

MAJOR CONCLUSIONS

Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies.

GENERAL SIGNIFICANCE

Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.

Finding Robust Adaptation Gene Regulatory Networks Using Multi-Objective Genetic Algorithm

Robust adaptation plays a key role in gene regulatory networks, and it is thought to be an important attribute for the organic or cells to survive in fluctuating conditions. In this paper, a simplified three-node enzyme network is modeled by the Michaelis-Menten rate equations for all possible topologies, and a family of topologies and the corresponding parameter sets of the network with satisfactory adaptation are obtained using the multi-objective genetic algorithm. The proposed approach improves the computation efficiency significantly as compared to the time consuming exhaustive searching method. This approach provides a systemic way for searching the feasible topologies and the corresponding parameter sets to make the gene regulatory networks have robust adaptation. The proposed methodology, owing to its universality and simplicity, can be used to address more complex issues in biological networks.

Build to understand: synthetic approaches to biology

In this review we discuss how synthetic biology facilitates the task of investigating genetic circuits that are observed in naturally occurring biological systems. Specifically, we give examples where experimentation with synthetic gene circuits has been used to understand four fundamental mechanisms intrinsic to development and disease: multistability, stochastic gene expression, oscillations, and cell-cell communication. Within each area, we also discuss how mathematical modeling has been employed as an essential tool to guide the design of novel gene circuits and as a theoretical basis for exploring circuit topologies exhibiting robust behaviors in the presence of noise.

A geometrical approach to control and controllability of nonlinear dynamical networks

In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.

Applications of synthetic gene networks

Synthetic gene networks have evolved from simple proof-of-concept circuits to complex therapy-oriented networks over the past 15 years. This advancement has greatly facilitated the expansion of the emerging field of synthetic biology. In this review, we highlight the main applications ofsynthetic gene networks in understanding biological design principles, developing biosensors for diagnosis, producing industrial and biomedical compounds, and treating human diseases. Finally, we outline current challenges and future prospects of synthetic gene networks for advancing practical applications.