Input output robustness in simple bacterial signaling systems

Enzyme-Responsive Supramolecular Self-Assembly in Small Amphiphiles

Enzyme-responsive molecular assemblies have recently made remarkable progress, owing to their widespread applications. As a class of catalysts with high specificity and efficiency, enzymes play a critical role in producing new molecules and maintaining metabolic stability in living organisms. Therefore, the study of enzyme-responsive assembly aids in understanding the origin of life and the physiological processes occurring within living bodies, contributing to further advancements across various disciplines. In this Review, we summarize three kinds of enzyme-responsive assembly systems in amphiphiles: enzyme-triggered assembly, disassembly, and structural transformation. Furthermore, motivated by the fact that biological macromolecules and complex structures all originated with small molecules, our focus lies on the small amphiphiles (e.g., peptides, surfactants, fluorescent molecules, and drug molecules). We also provide an outlook on the potential of enzyme-responsive assembly systems for biomimetic development and hope this Review will attract more attention to this emerging research branch at the intersection of assembly chemistry and biological science.

Design patterns of biological cells

Design patterns are generalized solutions to frequently recurring problems. They were initially developed by architects and computer scientists to create a higher level of abstraction for their designs. Here, we extend these concepts to cell biology to lend a new perspective on the evolved designs of cells' underlying reaction networks. We present a catalog of 21 design patterns divided into three categories: creational patterns describe processes that build the cell, structural patterns describe the layouts of reaction networks, and behavioral patterns describe reaction network function. Applying this pattern language to the E. coli central metabolic reaction network, the yeast pheromone response signaling network, and other examples lends new insights into these systems.

Bifunctional enzyme provides absolute concentration robustness in multisite covalent modification networks

Biochemical covalent modification networks exhibit a remarkable suite of steady state and dynamical properties such as multistationarity, oscillations, ultrasensitivity and absolute concentration robustness. This paper focuses on conditions required for a network of this type to have a species with absolute concentration robustness. We find that the robustness in a substrate is endowed by its interaction with a bifunctional enzyme, which is an enzyme that has different roles when isolated versus when bound as a substrate-enzyme complex. When isolated, the bifunctional enzyme promotes production of more molecules of the robust species while when bound, the same enzyme facilitates degradation of the robust species. These dual actions produce robustness in the large class of covalent modification networks. For each network of this type, we find the network conditions for the presence of robustness, the species that has robustness, and its robustness value. The unified approach of simultaneously analyzing a large class of networks for a single property, i.e. absolute concentration robustness, reveals the underlying mechanism of the action of bifunctional enzyme while simultaneously providing a precise mathematical description of bifunctionality.

Chemical Reaction Models in Synthetic Promoter Design in Bacteria

We discuss the formalism of chemical reaction networks (CRNs) as a computer-aided design interface for using formal methods in engineering living technologies. We set out by reviewing formal methods within a broader view of synthetic biology. Based on published results, we illustrate, step by step, how mathematical and computational techniques on CRNs can be used to study the structural and dynamic properties of the designed systems. As a case study, we use an E. coli two-component system that relays the external inorganic phosphate concentration signal to genetic components. We show how CRN models can scan and explore phenotypic regimes of synthetic promoters with varying detection thresholds, thereby providing a means for fine-tuning the promoter strength to match the specification.

The role of CenKR in the coordination of Rhodobacter sphaeroides cell elongation and division

Cell elongation and division are essential aspects of the bacterial life cycle that must be coordinated for viability and replication. The impact of misregulation of these processes is not well understood as these systems are often not amenable to traditional genetic manipulation. Recently, we reported on the CenKR two-component system (TCS) in the Gram-negative bacterium Rhodobacter sphaeroides that is genetically tractable, widely conserved in α-proteobacteria, and directly regulates the expression of components crucial for cell elongation and division, including genes encoding subunit of the Tol-Pal complex. In this work, we show that overexpression of cenK results in cell filamentation and chaining. Using cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET), we generated high-resolution two-dimensional (2D) images and three-dimensional (3D) volumes of the cell envelope and division septum of wild-type cells and a cenK overexpression strain finding that these morphological changes stem from defects in outer membrane (OM) and peptidoglycan (PG) constriction. By monitoring the localization of Pal, PG biosynthesis, and the bacterial cytoskeletal proteins MreB and FtsZ, we developed a model for how increased CenKR activity leads to changes in cell elongation and division. This model predicts that increased CenKR activity decreases the mobility of Pal, delaying OM constriction, and ultimately disrupting the midcell positioning of MreB and FtsZ and interfering with the spatial regulation of PG synthesis and remodeling. IMPORTANCE By coordinating cell elongation and division, bacteria maintain their shape, support critical envelope functions, and orchestrate division. Regulatory and assembly systems have been implicated in these processes in some well-studied Gram-negative bacteria. However, we lack information on these processes and their conservation across the bacterial phylogeny. In R. sphaeroides and other α-proteobacteria, CenKR is an essential two-component system (TCS) that regulates the expression of genes known or predicted to function in cell envelope biosynthesis, elongation, and/or division. Here, we leverage unique features of CenKR to understand how increasing its activity impacts cell elongation/division and use antibiotics to identify how modulating the activity of this TCS leads to changes in cell morphology. Our results provide new insight into how CenKR activity controls the structure and function of the bacterial envelope, the localization of cell elongation and division machinery, and cellular processes in organisms with importance in health, host-microbe interactions, and biotechnology.

Design principles of improving the dose-response alignment in coupled GTPase switches

"Dose-response alignment" (DoRA), where the downstream response of cellular signaling pathways closely matches the fraction of activated receptor, can improve the fidelity of dose information transmission. The negative feedback has been experimentally identified as a key component for DoRA, but numerical simulations indicate that negative feedback is not sufficient to achieve perfect DoRA, i.e., perfect match of downstream response and receptor activation level. Thus a natural question is whether there exist design principles for signaling motifs within only negative feedback loops to improve DoRA to near-perfect DoRA. Here, we investigated several model formulations of an experimentally validated circuit that couples two molecular switches-mGTPase (monomeric GTPase) and tGTPase (heterotrimeric GTPases) - with negative feedback loops. In the absence of feedback, the low and intermediate mGTPase activation levels benefit DoRA in mass action and Hill-function models, respectively. Adding negative feedback has versatile roles on DoRA: it may impair DoRA in the mass action model with low mGTPase activation level and Hill-function model with intermediate mGTPase activation level; in other cases, i.e., the mass action model with a high mGTPase activation level or the Hill-function model with a non-intermediate mGTPase activation level, it improves DoRA. Furthermore, we found that DoRA in a longer cascade (i.e., tGTPase) can be obtained using Hill-function kinetics under certain conditions. In summary, we show how ranges of activity of mGTPase, reaction kinetics, the negative feedback, and the cascade length affect DoRA. This work provides a framework for improving the DoRA performance in signaling motifs with negative feedback.

The Cellular Abundance of Chemoreceptors, Chemosensory Signaling Proteins, Sensor Histidine Kinases, and Solute Binding Proteins of Pseudomonas aeruginosa Provides Insight into Sensory Preferences and Signaling Mechanisms

Chemosensory pathways and two-component systems are important bacterial signal transduction systems. In the human pathogen Pseudomonas aeruginosa, these systems control many virulence traits. Previous studies showed that inorganic phosphate (Pi) deficiency induces virulence. We report here the abundance of chemosensory and two-component signaling proteins of P. aeruginosa grown in Pi deficient and sufficient media. The cellular abundance of chemoreceptors differed greatly, since a 2400-fold difference between the most and least abundant receptors was observed. For many chemoreceptors, their amount varied with the growth condition. The amount of chemoreceptors did not correlate with the magnitude of chemotaxis to their cognate chemoeffectors. Of the four chemosensory pathways, proteins of the Che chemotaxis pathway were most abundant and showed little variation in different growth conditions. The abundance of chemoreceptors and solute binding proteins indicates a sensing preference for amino acids and polyamines. There was an excess of response regulators over sensor histidine kinases in two-component systems. In contrast, ratios of the response regulators CheY and CheB to the histidine kinase CheA of the Che pathway were all below 1, indicative of different signaling mechanisms. This study will serve as a reference for exploring sensing preferences and signaling mechanisms of other bacteria.

Synthetic bacteria for the detection and bioremediation of heavy metals

Toxic heavy metal accumulation is one of anthropogenic environmental pollutions, which poses risks to human health and ecological systems. Conventional heavy metal remediation approaches rely on expensive chemical and physical processes leading to the formation and release of other toxic waste products. Instead, microbial bioremediation has gained interest as a promising and cost-effective alternative to conventional methods, but the genetic complexity of microorganisms and the lack of appropriate genetic engineering technologies have impeded the development of bioremediating microorganisms. Recently, the emerging synthetic biology opened a new avenue for microbial bioremediation research and development by addressing the challenges and providing novel tools for constructing bacteria with enhanced capabilities: rapid detection and degradation of heavy metals while enhanced tolerance to toxic heavy metals. Moreover, synthetic biology also offers new technologies to meet biosafety regulations since genetically modified microorganisms may disrupt natural ecosystems. In this review, we introduce the use of microorganisms developed based on synthetic biology technologies for the detection and detoxification of heavy metals. Additionally, this review explores the technical strategies developed to overcome the biosafety requirements associated with the use of genetically modified microorganisms.

Foundations of static and dynamic absolute concentration robustness

Absolute Concentration Robustness (ACR) was introduced by Shinar and Feinberg (Science 327:1389-1391, 2010) as robustness of equilibrium species concentration in a mass action dynamical system. Their aim was to devise a mathematical condition that will ensure robustness in the function of the biological system being modeled. The robustness of function rests on what we refer to as empirical robustness-the concentration of a species remains unvarying, when measured in the long run, across arbitrary initial conditions. Even simple examples show that the ACR notion introduced in Shinar and Feinberg (Science 327:1389-1391, 2010) (here referred to as static ACR) is neither necessary nor sufficient for empirical robustness. To make a stronger connection with empirical robustness, we define dynamic ACR, a property related to long-term, global dynamics, rather than only to equilibrium behavior. We discuss general dynamical systems with dynamic ACR properties as well as parametrized families of dynamical systems related to reaction networks. We find necessary and sufficient conditions for dynamic ACR in complex balanced reaction networks, a class of networks that is central to the theory of reaction networks.

Spatial engineering of E. coli with addressable phase-separated RNAs

Biochemical processes often require spatial regulation and specific microenvironments. The general lack of organelles in bacteria limits the potential of bioengineering complex intracellular reactions. Here, we demonstrate synthetic membraneless organelles in Escherichia coli termed transcriptionally engineered addressable RNA solvent droplets (TEARS). TEARS are assembled from RNA-binding protein recruiting domains fused to poly-CAG repeats that spontaneously drive liquid-liquid phase separation from the bulk cytoplasm. Targeting TEARS with fluorescent proteins revealed multilayered structures with composition and reaction robustness governed by non-equilibrium dynamics. We show that TEARS provide organelle-like bioprocess isolation for sequestering biochemical pathways, controlling metabolic branch points, buffering mRNA translation rates, and scaffolding protein-protein interactions. We anticipate TEARS to be a simple and versatile tool for spatially controlling E. coli biochemistry. Particularly, the modular design of TEARS enables applications without expression fine-tuning, simplifying the design-build-test cycle of bioengineering.

Vertex results for the robust analysis of uncertain biochemical systems

We consider the problem of assessing the sensitivity of uncertain biochemical systems in the presence of input perturbations (either constant or periodic) around a stable steady state. In particular, we propose approaches for the robust sensitivity analysis of systems with uncertain parameters assumed to take values in a hyper-rectangle. We highlight vertex results, which allow us to check whether a property is satisfied for all parameter choices in the hyper-rectangle by simply checking whether it is satisfied for all parameter choices at the vertices of the hyper-rectangle. We show that, for a vast class of systems, including (bio)chemical reaction networks with mass-action kinetics, the system Jacobian has a totally multiaffine structure (namely, all minors of the Jacobian matrix are multiaffine functions of the uncertain parameters), which can be exploited to obtain several vertex results. We consider different problems: robust non-singularity; robust stability of the steady-state; robust steady-state sensitivity analysis, in the case of constant perturbations; robust frequency-response sensitivity analysis, in the presence of periodic perturbations; and robust adaptation analysis. The developed theory is then applied to gain insight into some examples of uncertain biochemical systems, including the incoherent feed-forward loop, the coherent feed-forward loop, the Brusselator oscillator and the Goldbeter oscillator.

Dynamics and Sensitivity of Signaling Pathways

Purpose of Review

Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs for treating diseases, such as cancer. An achievement that would facilitate the use of such models is their ability to identify controlling biochemical parameters in signaling pathways, such as molecular abundances and chemical reaction rates, because this would help determine effective points of attack by therapeutics.

Recent Findings

We summarize the current state of understanding the sensitivity of phosphorylation cycles with and without sequestration. We also describe some basic properties of regulatory motifs including feedback and feedforward regulation.

Summary

Although much recent work has focused on understanding the dynamics and particularly the sensitivity of signaling networks in eukaryotic systems, there is still an urgent need to build more scalable models of signaling networks that can appropriately represent their complexity across different cell types and tumors.

Phenotypic variability, not noise, accounts for most of the cell-to-cell heterogeneity in IFN-γ and oncostatin M signaling responses

Cellular signaling responses show substantial cell-to-cell heterogeneity, which is often ascribed to the inherent randomness of biochemical reactions, termed molecular noise, wherein high noise implies low signaling fidelity. Alternatively, heterogeneity could arise from differences in molecular content between cells, termed molecular phenotypic variability, which does not necessarily imply imprecise signaling. The contribution of these two processes to signaling heterogeneity is unclear. Here, we fused fibroblasts to produce binuclear syncytia to distinguish noise from phenotypic variability in the analysis of cytokine signaling. We reasoned that the responses of the two nuclei within one syncytium could approximate the signaling outcomes of two cells with the same molecular content, thereby disclosing noise contribution, whereas comparison of different syncytia should reveal contribution of phenotypic variability. We found that ~90% of the variance in the primary response (which was the abundance of phosphorylated, nuclear STAT) to stimulation with the cytokines interferon-γ and oncostatin M resulted from differences in the molecular content of individual cells. Thus, our data reveal that cytokine signaling in the system used here operates in a reproducible, high-fidelity manner.

Allostery and protein plasticity: the keystones for bacterial signaling and regulation

Bacteria sense intracellular and environmental signals using an array of proteins as antennas. The information is transmitted from such sensory modules to other protein domains that act as output effectors. Sensor and effector can be part of the same polypeptide or instead be separate diffusible proteins that interact specifically. The output effector modules regulate physiologic responses, allowing the cells to adapt to the varying conditions. These biological machineries are known as signal transduction systems (STSs). Despite the captivating architectural diversity exhibited by STS proteins, a universal feature is their allosteric regulation: signal binding at one site modifies the activity at a physically distant site. Allostery requires protein plasticity, precisely encoded within their 3D structures, and implicating programmed molecular motions. This review summarizes how STS proteins connect stimuli to specific responses by exploiting allostery and protein plasticity. Illustrative examples spanning a wide variety of protein folds will focus on one- and two-component systems (TCSs). The former encompass the entire transmission route within a single polypeptide, whereas TCSs have evolved as separate diffusible proteins that interact specifically, sometimes including additional intermediary proteins in the pathway. Irrespective of their structural diversity, STS proteins are able to modulate their own molecular motions, which can be relatively slow, rigid-body movements, all the way to fast fluctuations in the form of macromolecular flexibility, thus spanning a continuous protein dynamics spectrum. In sum, STSs rely on allostery to steer information transmission, going from simple two-state switching to rich multi-state conformational order/disorder transitions.

Bacterial two-component systems as sensors for synthetic biology applications

Two-component systems (TCSs) are a ubiquitous family of signal transduction pathways that enable bacteria to sense and respond to diverse physical, chemical, and biological stimuli outside and inside the cell. Synthetic biologists have begun to repurpose TCSs for applications in optogenetics, materials science, gut microbiome engineering, and soil nutrient biosensing, among others. New engineering methods including genetic refactoring, DNA-binding domain swapping, detection threshold tuning, and phosphorylation cross-talk insulation are being used to increase the reliability of TCS sensor performance and tailor TCS signaling properties to the requirements of specific applications. There is now potential to combine these methods with large-scale gene synthesis and laboratory screening to discover the inputs sensed by many uncharacterized TCSs and develop a large new family of genetically-encoded sensors that respond to an unrivaled breadth of stimuli.

Continuous variable responses and signal gating form kinetic bases for pulsatile insulin signaling and emergence of resistance

Evolutionarily conserved insulin signaling is central to nutrient sensing, storage, and utilization across tissues. Dysfunctional insulin signaling is associated with metabolic disorders, cancer, and aging. Hence, the pathway components have emerged as key targets for pharmacological interventions in addition to insulin administration itself. Despite this, activation–inactivation dynamics of individual components, which exert regulatory control in a physiological context, is poorly understood. Now, with our systems-based approach, we reveal kinetic parameters, which define the flow of information through both metabolic and growth-factor arms and thus determine signaling architecture. We also provide a kinetic basis for 1) the advantage of pulsatile-fasted insulin signaling that enables fed-insulin response and 2) the detrimental impact of repeat fed-insulin inputs that causes resistance.

Understanding kinetic control of biological processes is as important as identifying components that constitute pathways. Insulin signaling is central for almost all metazoans, and its perturbations are associated with various developmental disorders, metabolic diseases, and aging. While temporal phosphorylation changes and kinetic constants have provided some insights, constant or variable parameters that establish and maintain signal topology are poorly understood. Here, we report kinetic parameters that encode insulin concentration and nutrient-dependent flow of information using iterative experimental and mathematical simulation-based approaches. Our results illustrate how dynamics of distinct phosphorylation events collectively contribute to selective kinetic gating of signals and maximum connectivity of the signaling cascade under normo-insulinemic but not hyper-insulinemic states. In addition to identifying parameters that provide predictive value for maintaining the balance between metabolic and growth-factor arms, we posit a kinetic basis for the emergence of insulin resistance. Given that pulsatile insulin secretion during a fasted state precedes a fed response, our findings reveal rewiring of insulin signaling akin to memory and anticipation, which was hitherto unknown. Striking disparate temporal behavior of key phosphorylation events that destroy the topology under hyper-insulinemic states underscores the importance of unraveling regulatory components that act as bandwidth filters. In conclusion, besides providing fundamental insights, our study will help in identifying therapeutic strategies that conserve coupling between metabolic and growth-factor arms, which is lost in diseases and conditions of hyper-insulinemia.

The inverse correlation between robustness and sensitivity to autoregulation in two-component systems

Two-component systems (TCS) are signal transduction systems in bacteria and many other organisms that relay the sensory signal to genetic components. TCS consist of two proteins: a histidine kinase and a response regulator that the histidine kinase activates. This seemingly simple machinery can generate complex regulatory dynamics that enables the level of gene expression that matches the input signal: many TCS response regulators act on their own genes as transcription factors, resulting in a positive autoregulation mechanism. This regulation, in return, modulates the transcription factor activity as a function of the input signal. Positive autoregulation does not necessarily result in positive feedback. Sensitivity to autoregulation is quantified as the output level amplification resulting from the positive autoregulation mechanism. Another structural property of these systems is formally characterized as "robustness": in a robust TCS, the output of the system is solely a function of the input signal. Thus, a robust TCS remains insensitive to fluctuations in the concentrations of its protein components and, this way, maintains the precision in the output transcription factor activity in response to input stimulus. In this paper, we show with a formal model that TCS operate on a spectrum of inverse correlation between robustness and sensitivity to autoregulation. Our model predicts that the modulation by positive autoregulation is a function of loss in TCS robustness, for example, by spontaneous dephosphorylation of the histidine kinase. Consequently, the loss in robustness provides a proportional modulation by positive autoregulation to widen the response range with a scaled amplification of the output. At the other end of the spectrum, in the presence of a strictly robust TCS machinery, amplification of the transcription factor activity by autoregulation is diminished. We show that our results are in agreement with published experimental results. Our results suggest that these TCS evolve to converge at a trade-off between robustness and positive autoregulation.

Uncertainty propagation for deterministic models of biochemical networks using moment equations and the extended Kalman filter

Differential equation models of biochemical networks are frequently associated with a large degree of uncertainty in parameters and/or initial conditions. However, estimating the impact of this uncertainty on model predictions via Monte Carlo simulation is computationally demanding. A more efficient approach could be to track a system of low-order statistical moments of the state. Unfortunately, when the underlying model is nonlinear, the system of moment equations is infinite-dimensional and cannot be solved without a moment closure approximation which may introduce bias in the moment dynamics. Here, we present a new method to study the time evolution of the desired moments for nonlinear systems with polynomial rate laws. Our approach is based on solving a system of low-order moment equations by substituting the higher-order moments with Monte Carlo-based estimates from a small number of simulations, and using an extended Kalman filter to counteract Monte Carlo noise. Our algorithm provides more accurate and robust results compared to traditional Monte Carlo and moment closure techniques, and we expect that it will be widely useful for the quantification of uncertainty in biochemical model predictions.

Stochastic Simulations as a Tool for Assessing Signal Fidelity in Gene Expression in Synthetic Promoter Design

Simple Summary

Synthetic biology is an emerging discipline, offering new perspectives in many industrial fields, from pharma and row-material production to renewable energy. Developing synthetic biology applications is often a lengthy and expensive process with extensive and tedious trial-and-error runs. Computational models can direct the engineering of biological circuits in a computer-aided design setting. By providing a virtual lab environment, in silico models of synthetic circuits can contribute to a quantitative understanding of the underlying molecular pathways before a wet-lab implementation. Here, we illustrate this notion from the point of view of signal fidelity and noise relationship. Noise in gene expression can undermine signal fidelity with implications on the well-functioning of the engineered organisms. For our analysis, we use a specific biological circuit that regulates the gene expression in bacterial inorganic phosphate economy. Applications that use this circuit include those in pollutant detection and wastewater treatment. We provide computational models with different levels of molecular detail as virtual labs. We show that inherent fluctuations in the gene expression machinery can be predicted via stochastic simulations to introduce control in the synthetic promoter design process. Our analysis suggests that noise in the system can be alleviated by strong synthetic promoters with slow unbinding rates. Overall, we provide a recipe for the computer-aided design of synthetic promoter libraries with specific signal to noise characteristics.

Abstract

The design and development of synthetic biology applications in a workflow often involve connecting modular components. Whereas computer-aided design tools are picking up in synthetic biology as in other areas of engineering, the methods for verifying the correct functioning of living technologies are still in their infancy. Especially, fine-tuning for the right promoter strength to match the design specifications is often a lengthy and expensive experimental process. In particular, the relationship between signal fidelity and noise in synthetic promoter design can be a key parameter that can affect the healthy functioning of the engineered organism. To this end, based on our previous work on synthetic promoters for the E. coli PhoBR two-component system, we make a case for using chemical reaction network models for computational verification of various promoter designs before a lab implementation. We provide an analysis of this system with extensive stochastic simulations at a single-cell level to assess the signal fidelity and noise relationship. We then show how quasi-steady-state analysis via ordinary differential equations can be used to navigate between models with different levels of detail. We compare stochastic simulations with our full and reduced models by using various metrics for assessing noise. Our analysis suggests that strong promoters with low unbinding rates can act as control tools for filtering out intrinsic noise in the PhoBR context. Our results confirm that even simpler models can be used to determine promoters with specific signal to noise characteristics.

Molecular switch architecture determines response properties of signaling pathways

Many intracellular signaling pathways are composed of molecular switches, proteins that transition between two states-on and off Typically, signaling is initiated when an external stimulus activates its cognate receptor that, in turn, causes downstream switches to transition from off to on using one of the following mechanisms: activation, in which the transition rate from the off state to the on state increases; derepression, in which the transition rate from the on state to the off state decreases; and concerted, in which activation and derepression operate simultaneously. We use mathematical modeling to compare these signaling mechanisms in terms of their dose-response curves, response times, and abilities to process upstream fluctuations. Our analysis elucidates several operating principles for molecular switches. First, activation increases the sensitivity of the pathway, whereas derepression decreases sensitivity. Second, activation generates response times that decrease with signal strength, whereas derepression causes response times to increase with signal strength. These opposing features allow the concerted mechanism to not only show dose-response alignment, but also to decouple the response time from stimulus strength. However, these potentially beneficial properties come at the expense of increased susceptibility to upstream fluctuations. We demonstrate that these operating principles also hold when the models are extended to include additional features, such as receptor removal, kinetic proofreading, and cascades of switches. In total, we show how the architecture of molecular switches govern their response properties. We also discuss the biological implications of our findings.

Chaperone-Mediated Stress Sensing in Mycobacterium tuberculosis Enables Fast Activation and Sustained Response

Dynamical properties of gene regulatory networks are tuned to ensure bacterial survival. In mycobacteria, the MprAB-σ^E network responds to the presence of stressors, such as surfactants that cause surface stress. Positive feedback loops in this network were previously predicted to cause hysteresis, i.e., different responses to identical stressor levels for prestressed and unstressed cells. Here, we show that hysteresis does not occur in nonpathogenic Mycobacterium smegmatis but does occur in Mycobacterium tuberculosis However, the observed rapid temporal response in M. tuberculosis is inconsistent with the model predictions. To reconcile these observations, we implement a recently proposed mechanism for stress sensing, namely, the release of MprB from the inhibitory complex with the chaperone DnaK upon the stress exposure. Using modeling and parameter fitting, we demonstrate that this mechanism can accurately describe the experimental observations. Furthermore, we predict perturbations in DnaK expression that can strongly affect dynamical properties. Experiments with these perturbations agree with model predictions, confirming the role of DnaK in fast and sustained response.IMPORTANCE Gene regulatory networks controlling stress response in mycobacterial species have been linked to persistence switches that enable bacterial dormancy within a host. However, the mechanistic basis of switching and stress sensing is not fully understood. In this paper, combining quantitative experiments and mathematical modeling, we uncover how interactions between two master regulators of stress response-the MprAB two-component system (TCS) and the alternative sigma factor σ^E-shape the dynamical properties of the surface stress network. The result show hysteresis (history dependence) in the response of the pathogenic bacterium M. tuberculosis to surface stress and lack of hysteresis in nonpathogenic M. smegmatis Furthermore, to resolve the apparent contradiction between the existence of hysteresis and fast activation of the response, we utilize a recently proposed role of chaperone DnaK in stress sensing. These result leads to a novel system-level understanding of bacterial stress response dynamics.

Overlaid positive and negative feedback loops shape dynamical properties of PhoPQ two-component system

Bacteria use two-component systems (TCSs) to sense environmental conditions and change gene expression in response to those conditions. To amplify cellular responses, many bacterial TCSs are under positive feedback control, i.e. increase their expression when activated. Escherichia coli Mg²⁺ -sensing TCS, PhoPQ, in addition to the positive feedback, includes a negative feedback loop via the upregulation of the MgrB protein that inhibits PhoQ. How the interplay of these feedback loops shapes steady-state and dynamical responses of PhoPQ TCS to change in Mg²⁺ remains poorly understood. In particular, how the presence of MgrB feedback affects the robustness of PhoPQ response to overexpression of TCS is unclear. It is also unclear why the steady-state response to decreasing Mg²⁺ is biphasic, i.e. plateaus over a range of Mg²⁺ concentrations, and then increases again at growth-limiting Mg²⁺. In this study, we use mathematical modeling to identify potential mechanisms behind these experimentally observed dynamical properties. The results make experimentally testable predictions for the regime with response robustness and propose a novel explanation of biphasic response constraining the mechanisms for modulation of PhoQ activity by Mg²⁺ and MgrB. Finally, we show how the interplay of positive and negative feedback loops affects the network’s steady-state sensitivity and response dynamics. In the absence of MgrB feedback, the model predicts oscillations thereby suggesting a general mechanism of oscillatory or pulsatile dynamics in autoregulated TCSs. These results improve the understanding of TCS signaling and other networks with overlaid positive and negative feedback.

Feedback loops are commonly observed in bacterial gene-regulatory networks to enable proper dynamical responses to stimuli. Positive feedback loops often amplify the response to stimulus, whereas negative feedback loops are known to speed-up the response and increase robustness. Here we demonstrate how combination of positive and negative feedback in network sensing extracellular ion concentrations affects its steady-state and dynamic responses. We utilize published experimental data to calibrate mathematical models of the gene regulatory network. The resulting model quantitatively matches experimentally observed behavior and can make predictions on the mechanism of negative feedback control. Our results show the advantages of such a combination of feedback loops. We also predict the effect of their perturbation on the steady-state and dynamic responses. This study improves our understanding of how feedback loops shape dynamical properties of signaling networks.

A hidden integral structure endows absolute concentration robust systems with resilience to dynamical concentration disturbances

Biochemical systems that express certain chemical species of interest at the same level at any positive steady state are called 'absolute concentration robust' (ACR). These species behave in a stable, predictable way, in the sense that their expression is robust with respect to sudden changes in the species concentration, provided that the system reaches a (potentially new) positive steady state. Such a property has been proven to be of importance in certain gene regulatory networks and signaling systems. In the present paper, we mathematically prove that a well-known class of ACR systems studied by Shinar and Feinberg in 2010 hides an internal integral structure. This structure confers these systems with a higher degree of robustness than was previously known. In particular, disturbances much more general than sudden changes in the species concentrations can be rejected, and robust perfect adaptation is achieved. Significantly, we show that these properties are maintained when the system is interconnected with other chemical reaction networks. This key feature enables the design of insulator devices that are able to buffer the loading effect from downstream systems-a crucial requirement for modular circuit design in synthetic biology. We further note that while the best performance of the insulators are achieved when these act at a faster timescale than the upstream module (as typically required), it is not necessary for them to act on a faster timescale than the downstream module in our construction.

Robustness of a biomolecular oscillator to pulse perturbations

Biomolecular oscillators can function robustly in the presence of environmental perturbations, which can either be static or dynamic. While the effect of different circuit parameters and mechanisms on the robustness to steady perturbations has been investigated, the scenario for dynamic perturbations is relatively unclear. To address this, the authors use a benchmark three protein oscillator design - the repressilator - and investigate its robustness to pulse perturbations, computationally as well as use analytical tools of Floquet theory. They found that the metric provided by direct computations of the time it takes for the oscillator to settle after pulse perturbation is applied, correlates well with the metric provided by Floquet theory. They investigated the parametric dependence of the Floquet metric, finding that the parameters that increase the effective delay enhance robustness to pulse perturbation. They found that the structural changes such as increasing the number of proteins in a ring oscillator as well as adding positive feedback, both of which increase effective delay, facilitates such robustness. These results highlight such design principles, especially the role of delay, for designing an oscillator that is robust to pulse perturbation.

Absolutely robust controllers for chemical reaction networks

In this work, we design a type of controller that consists of adding a specific set of reactions to an existing mass-action chemical reaction network in order to control a target species. This set of reactions is effective for both deterministic and stochastic networks, in the latter case controlling the mean as well as the variance of the target species. We employ a type of network property called absolute concentration robustness (ACR). We provide applications to the control of a multisite phosphorylation model as well as a receptor-ligand signalling system. For this framework, we use the so-called deficiency zero theorem from chemical reaction network theory as well as multiscaling model reduction methods. We show that the target species has approximately Poisson distribution with the desired mean. We further show that ACR controllers can bring robust perfect adaptation to a target species and are complementary to a recently introduced antithetic feedback controller used for stochastic chemical reactions.

The interplay of spatial organization and biochemistry in building blocks of cellular signalling pathways

Biochemical pathways and networks are central to cellular information processing. While a broad range of studies have dissected multiple aspects of information processing in biochemical pathways, the effect of spatial organization remains much less understood. It is clear that space is central to intracellular organization, plays important roles in cellular information processing and has been exploited in evolution; additionally, it is being increasingly exploited in synthetic biology through the development of artificial compartments, in a variety of ways. In this paper, we dissect different aspects of the interplay between spatial organization and biochemical pathways, by focusing on basic building blocks of these pathways: covalent modification cycles and two-component systems, with enzymes which may be monofunctional or bifunctional. Our analysis of spatial organization is performed by examining a range of 'spatial designs': patterns of localization or non-localization of enzymes/substrates, theoretically and computationally. Using these well-characterized in silico systems, we analyse the following. (i) The effect of different types of spatial organization on the overall kinetics of modification, and the role of distinct modification mechanisms therein. (ii) How different information processing characteristics seen experimentally and studied from the viewpoint of kinetics are perturbed, or generated. (iii) How the activity of enzymes (bifunctional enzymes in particular) may be spatially manipulated, and the relationship between localization and activity. (iv) How transitions in spatial organization (encountered either through evolution or through the lifetime of cells, as seen in multiple model organisms) impacts the kinetic module (and pathway) behaviour, and how transitions in chemistry may be impacted by prior spatial organization. The basic insights which emerge are central to understanding the role of spatial organization in biochemical pathways in both bacteria and eukaryotes, and are of direct relevance to engineering spatial organization of pathways in bottom-up synthetic biology in cellular and cell-free systems.

The Robustness of Outputs With Respect to Disturbances for Boolean Control Networks

In this brief, we investigate the robustness of outputs with respect to disturbances for Boolean control networks (BCNs) by semi-tensor product (STP) of matrices. First, BCNs are converted into the corresponding algebraic forms by STP, then two sufficient conditions for the robustness are derived. Moreover, the corresponding permutation system and permutation graph are constructed. It is proven that if there exist controllers such that the outputs of permutation systems are robust with respect to disturbances, then there must also exist controllers such that the outputs of the corresponding original systems achieve robustness with respect to disturbances. One effective method is proposed to construct controllers to achieve robustness. Examples are also provided to illustrate the correctness of the obtained results.

Trade-offs between effectiveness and cost in bifunctional enzyme circuit with concentration robustness

A fundamental trade-off in biological systems is whether they consume resources to perform biological functions or save resources. Bacteria need to reliably and rapidly respond to input signals by using limited cellular resources. However, excessive resource consumption will become a burden for bacteria growth. To investigate the relationship between functional effectiveness and resource cost, we study the ubiquitous bifunctional enzyme circuit, which is robust to fluctuations in protein concentration and responds quickly to signal changes. We show that trade-off relationships exist between functional effectiveness and protein cost. Expressing more proteins of the circuit increases concentration robustness and response speed but affects bacterial growth. In particular, our study reveals a general relationship between free-energy dissipation rate, response speed, and concentration robustness. The dissipation of free energy plays an important role in the concentration robustness and response speed. High robustness can only be achieved with a large amount of free-energy consumption and protein cost. In addition, the noise of the output increases with increasing protein cost, while the noise of the response time decreases with increasing protein cost. We also calculate the trade-off relationships in the EnvZ-OmpR system and the nitrogen assimilation system, which both have the bifunctional enzyme. Similar results indicate that these relationships are mainly derived from the specific feature of the bifunctional enzyme circuits and are not relevant to the details of the models. According to the trade-off relationships, bacteria take a compromise solution that reliably performs biological functions at a reasonable cost.

Evidence of Robustness in a Two-Component System Using a Synthetic Circuit

Variation in the concentration of biological components is inescapable for any cell. Robustness in any biological circuit acts as a cushion against such variation and enables the cells to produce homogeneous output despite the fluctuation. The two-component system (TCS) with a bifunctional sensor kinase (that possesses both kinase and phosphatase activities) is proposed to be a robust circuit. Few theoretical models explain the robustness of a TCS, although the criteria and extent of robustness by these models differ. Here, we provide experimental evidence to validate the extent of the robustness of a TCS signaling pathway. We have designed a synthetic circuit in Escherichia coli using a representative TCS of Mycobacterium tuberculosis, MprAB, and monitored the in vivo output signal by systematically varying the concentration of either of the components or both. We observed that the output of the TCS is robust if the concentration of MprA is above a threshold value. This observation is further substantiated by two in vitro assays, in which we estimated the phosphorylated MprA pool or MprA-dependent transcription yield by varying either of the components of the TCS. This synthetic circuit could be used as a model system to analyze the relationship among different components of gene regulatory networks.IMPORTANCE Robustness in essential biological circuits is an important feature of the living organism. A few pieces of evidence support the existence of robustness in vivo in the two-component system (TCS) with a bifunctional sensor kinase (SK). The assays were done under physiological conditions in which the SK was much lower than the response regulator (RR). Here, using a synthetic circuit, we varied the concentrations of the SK and RR of a representative TCS to monitor output robustness in vivo. In vitro assays were also performed under conditions where the concentration of the SK was greater than that of the RR. Our results demonstrate the extent of output robustness in the TCS signaling pathway with respect to the concentrations of the two components.

Multisite phosphorylation drives phenotypic variation in (p)ppGpp synthetase-dependent antibiotic tolerance

Isogenic populations of cells exhibit phenotypic variability that has specific physiological consequences. Individual bacteria within a population can differ in antibiotic tolerance, but whether this variability can be regulated or is generally an unavoidable consequence of stochastic fluctuations is unclear. Here we report that a gene encoding a bacterial (p)ppGpp synthetase in Bacillus subtilis, sasA, exhibits high levels of extrinsic noise in expression. We find that sasA is regulated by multisite phosphorylation of the transcription factor WalR, mediated by a Ser/Thr kinase-phosphatase pair PrkC/PrpC, and a Histidine kinase WalK of a two-component system. This regulatory intersection is crucial for controlling the appearance of outliers; rare cells with unusually high levels of sasA expression, having increased antibiotic tolerance. We create a predictive model demonstrating that the probability of a given cell surviving antibiotic treatment increases with sasA expression. Therefore, multisite phosphorylation can be used to strongly regulate variability in antibiotic tolerance.

Hard Limits and Performance Tradeoffs in a Class of Antithetic Integral Feedback Networks

Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism called antithetic integral feedback, which can be implemented using the binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of antithetic integral feedback and contribute to a more general theory of biological control systems.

Electrically induced bacterial membrane-potential dynamics correspond to cellular proliferation capacity

Membrane-potential dynamics mediate bacterial electrical signaling at both intra- and intercellular levels. Membrane potential is also central to cellular proliferation. It is unclear whether the cellular response to external electrical stimuli is influenced by the cellular proliferative capacity. A new strategy enabling electrical stimulation of bacteria with simultaneous monitoring of single-cell membrane-potential dynamics would allow bridging this knowledge gap and further extend electrophysiological studies into the field of microbiology. Here we report that an identical electrical stimulus can cause opposite polarization dynamics depending on cellular proliferation capacity. This was demonstrated using two model organisms, namely Bacillus subtilis and Escherichia coli, and by developing an apparatus enabling exogenous electrical stimulation and single-cell time-lapse microscopy. Using this bespoke apparatus, we show that a 2.5-second electrical stimulation causes hyperpolarization in unperturbed cells. Measurements of intracellular K+ and the deletion of the K+ channel suggested that the hyperpolarization response is caused by the K+ efflux through the channel. When cells are preexposed to 400 ± 8 nm wavelength light, the same electrical stimulation depolarizes cells instead of causing hyperpolarization. A mathematical model extended from the FitzHugh-Nagumo neuron model suggested that the opposite response dynamics are due to the shift in resting membrane potential. As predicted by the model, electrical stimulation only induced depolarization when cells are treated with antibiotics, protonophore, or alcohol. Therefore, electrically induced membrane-potential dynamics offer a reliable approach for rapid detection of proliferative bacteria and determination of their sensitivity to antimicrobial agents at the single-cell level.

Adaptive information processing of network modules to dynamic and spatial stimuli

BACKGROUND

Adaptation and homeostasis are basic features of information processing in cells and seen in a broad range of contexts. Much of the current understanding of adaptation in network modules/motifs is based on their response to simple stimuli. Recently, there have also been studies of adaptation in dynamic stimuli. However a broader synthesis of how different circuits of adaptation function, and which circuits enable a broader adaptive behaviour in classes of more complex and spatial stimuli is largely missing.

RESULTS

We study the response of a variety of adaptive circuits to time-varying stimuli such as ramps, periodic stimuli and static and dynamic spatial stimuli. We find that a variety of responses can be seen in ramp stimuli, making this a basis for discriminating between even similar circuits. We also find that a number of circuits adapt exactly to ramp stimuli, and dissect these circuits to pinpoint what characteristics (architecture, feedback, biochemical aspects, information processing ingredients) allow for this. These circuits include incoherent feedforward motifs, inflow-outflow motifs and transcritical circuits. We find that changes in location in such circuits where a signal acts can result in non-adaptive behaviour in ramps, even though the location was associated with exact adaptation in step stimuli. We also demonstrate that certain augmentations of basic inflow-outflow motifs can alter the behaviour of the circuit from exact adaptation to non-adaptive behaviour. When subject to periodic stimuli, some circuits (inflow-outflow motifs and transcritical circuits) are able to maintain an average output independent of the characteristics of the input. We build on this to examine the response of adaptive circuits to static and dynamic spatial stimuli. We demonstrate how certain circuits can exhibit a graded response in spatial static stimuli with an exact maintenance of the spatial mean-value. Distinct features which emerge from the consideration of dynamic spatial stimuli are also discussed. Finally, we also build on these results to show how different circuits which show any combination of presence or absence of exact adaptation in ramps, exact mainenance of time average output in periodic stimuli and exact maintenance of spatial average of output in static spatial stimuli may be realized.

CONCLUSIONS

By studying a range of network circuits/motifs on one hand and a range of stimuli on the other, we isolate characteristics of these circuits (structural) which enable different degrees of exact adaptive and homeostatic behaviour in such stimuli, how they may be combined, and also identify cases associated with non-homeostatic behaviour. We also reveal constraints associated with locations where signals may act to enable homeostatic behaviour and constraints associated with augmentations of circuits. This consideration of multiple experimentally/naturally relevant stimuli along with circuits of adaptation of relevance in natural and engineered biology, provides a platform for deepening our understanding of adaptive and homeostatic behaviour in natural systems, bridging the gap between models of adaptation and experiments and in engineering homeostatic synthetic circuits.

Quantifying dynamic mechanisms of auto-regulation in Escherichia coli with synthetic promoter in response to varying external phosphate levels

Escherichia coli have developed one of the most efficient regulatory response mechanisms to phosphate starvation. The machinery involves a cascade with a two-component system (TCS) that relays the external signal to the genetic circuit, resulting in a feedback response. Achieving a quantitative understanding of this system has implications in synthetic biology and biotechnology, for example, in applications for wastewater treatment. To this aim, we present a computational model and experimental results with a detailed description of the TCS, consisting of PhoR and PhoB, together with the mechanisms of gene expression. The model is parameterised within the feasible range, and fitted to the dynamic response of our experimental data on PhoB as well as PhoA, the product of this network that is used in alkaline phosphatase production. Deterministic and stochastic simulations with our model predict the regulation dynamics in higher external phosphate concentrations while reproducing the experimental observations. In a cycle of simulations and experimental verification, our model predicts and explores phenotypes with various synthetic promoter designs that can optimise the inorganic phosphate intake in E. coli. Sensitivity analysis demonstrates that the Pho-controlled genes have a significant influence over the phosphate response. Together with experimental findings, our model should thus provide insights for the investigations on engineering new sensors and regulators for living technologies.

Event-Triggered Control for the Disturbance Decoupling Problem of Boolean Control Networks

This paper investigates the disturbance decoupling problem (DDP) of Boolean control networks (BCNs) by event-triggered control. Using the semi-tensor product of matrices, algebraic forms of BCNs can be achieved, based on which, event-triggered controllers are designed to solve the DDP of BCNs. In addition, the DDP of Boolean partial control networks is also derived by event-triggered control. Finally, two illustrative examples demonstrate the effectiveness of proposed methods.

Network Translation and Steady-State Properties of Chemical Reaction Systems

Network translation has recently been used to establish steady-state properties of mass action systems by corresponding the given system to a generalized one which is either dynamically or steady-state equivalent. In this work, we further use network translation to identify network structures which give rise to the well-studied property of absolute concentration robustness in the corresponding mass action systems. In addition to establishing the capacity for absolute concentration robustness, we show that network translation can often provide a method for deriving the steady-state value of the robust species. We furthermore present a MILP algorithm for the identification of translated chemical reaction networks that improves on previous approaches, allowing for easier application of the theory.

Engineering Diagnostic and Therapeutic Gut Bacteria

Genetically engineered bacteria have the potential to diagnose and treat a wide range of diseases linked to the gastrointestinal tract, or gut. Such engineered microbes will be less expensive and invasive than current diagnostics and more effective and safe than current therapeutics. Recent advances in synthetic biology have dramatically improved the reliability with which bacteria can be engineered with the sensors, genetic circuits, and output (actuator) genes necessary for diagnostic and therapeutic functions. However, to deploy such bacteria in vivo, researchers must identify appropriate gut-adapted strains and consider performance metrics such as sensor detection thresholds, circuit computation speed, growth rate effects, and the evolutionary stability of engineered genetic systems. Other recent reviews have focused on engineering bacteria to target cancer or genetically modifying the endogenous gut microbiota in situ. Here, we develop a standard approach for engineering "smart probiotics," which both diagnose and treat disease, as well as "diagnostic gut bacteria" and "drug factory probiotics," which perform only the former and latter function, respectively. We focus on the use of cutting-edge synthetic biology tools, gut-specific design considerations, and current and future engineering challenges.

Ceramide-transfer protein-mediated ceramide transfer is a structurally tunable flow-inducing mechanism with structural feed-forward loops

This paper considers two models of ceramide-transfer protein (CERT)-mediated ceramide transfer at the trans-Golgi network proposed in the literature, short distance shuttle and neck swinging, and seeks structural (parameter-free) features of the two models, which rely exclusively on the peculiar interaction network and not on specific parameter values. In particular, it is shown that both models can be seen as flow-inducing systems, where the flows between pairs of species are tuned by the concentrations of other species, and suitable external inputs can structurally regulate ceramide transfer. In the short distance shuttle model, the amount of transferred ceramide is structurally tuned by active protein kinase D (PKD), both directly and indirectly, in a coherent feed-forward loop motif. In the neck-swinging model, the amount of transferred ceramide is structurally tuned by active PI4KIIIβ, while active PKD has an ambivalent effect, due to the presence of an incoherent feed-forward loop motif that directly inhibits ceramide transfer and indirectly promotes it; the structural role of active PKD is to favour CERT mobility in the cytosol. It is also shown that the influences among key variables often have structurally determined steady-state signs, which can help falsify the models against experimental traces.

Analysis of network motifs in cellular regulation: Structural similarities, input-output relations and signal integration

Much of the complexity of regulatory networks derives from the necessity to integrate multiple signals and to avoid malfunction due to cross-talk or harmful perturbations. Hence, one may expect that the input-output behavior of larger networks is not necessarily more complex than that of smaller network motifs which suggests that both can, under certain conditions, be described by similar equations. In this review, we illustrate this approach by discussing the similarities that exist in the steady state descriptions of a simple bimolecular reaction, covalent modification cycles and bacterial two-component systems. Interestingly, in all three systems fundamental input-output characteristics such as thresholds, ultrasensitivity or concentration robustness are described by structurally similar equations. Depending on the system the meaning of the parameters can differ ranging from protein concentrations and affinity constants to complex parameter combinations which allows for a quantitative understanding of signal integration in these systems. We argue that this approach may also be extended to larger regulatory networks.

Transient absolute robustness in stochastic biochemical networks

Absolute robustness allows biochemical networks to sustain a consistent steady-state output in the face of protein concentration variability from cell to cell. This property is structural and can be determined from the topology of the network alone regardless of rate parameters. An important question regarding these systems is the effect of discrete biochemical noise in the dynamical behaviour. In this paper, a variable freezing technique is developed to show that under mild hypotheses the corresponding stochastic system has a transiently robust behaviour. Specifically, after finite time the distribution of the output approximates a Poisson distribution, centred around the deterministic mean. The approximation becomes increasingly accurate, and it holds for increasingly long finite times, as the total protein concentrations grow to infinity. In particular, the stochastic system retains a transient, absolutely robust behaviour corresponding to the deterministic case. This result contrasts with the long-term dynamics of the stochastic system, which eventually must undergo an extinction event that eliminates robustness and is completely different from the deterministic dynamics. The transiently robust behaviour may be sufficient to carry out many forms of robust signal transduction and cellular decision-making in cellular organisms.

Operating regimes of covalent modification cycles at high enzyme concentrations

The Goldbeter-Koshland model has been a paradigm for ultrasensitivity in biological networks for more than 30 years. Despite its simplicity the validity of this model is restricted to conditions when the substrate is in excess over the converter enzymes - a condition that is easy to satisfy in vitro, but which is rarely satisfied in vivo. Here, we analyze the Goldbeter-Koshland model by means of the total quasi-steady state approximation which yields a comprehensive classification of the steady state operating regimes under conditions when the enzyme concentrations are comparable to or larger than that of the substrate. Where possible we derive simple expressions characterizing the input-output behavior of the system. Our analysis suggests that enhanced sensitivity occurs if the concentration of at least one of the converter enzymes is smaller (but not necessarily much smaller) than that of the substrate and if that enzyme is saturated. Conversely, if both enzymes are saturated and at least one of the enzyme concentrations exceeds that of the substrate the system exhibits concentration robustness with respect to changes in that enzyme concentration. Also, depending on the enzyme's saturation degrees and the ratio between their maximal reaction rates the total fraction of phosphorylated substrate may increase, decrease or change nonmonotonically as a function of the total substrate concentration. The latter finding may aid the interpretation of experiments involving genetic perturbations of enzyme and substrate abundances.

Dynamics robustness of cascading systems

A most important property of biochemical systems is robustness. Static robustness, e.g., homeostasis, is the insensitivity of a state against perturbations, whereas dynamics robustness, e.g., homeorhesis, is the insensitivity of a dynamic process. In contrast to the extensively studied static robustness, dynamics robustness, i.e., how a system creates an invariant temporal profile against perturbations, is little explored despite transient dynamics being crucial for cellular fates and are reported to be robust experimentally. For example, the duration of a stimulus elicits different phenotypic responses, and signaling networks process and encode temporal information. Hence, robustness in time courses will be necessary for functional biochemical networks. Based on dynamical systems theory, we uncovered a general mechanism to achieve dynamics robustness. Using a three-stage linear signaling cascade as an example, we found that the temporal profiles and response duration post-stimulus is robust to perturbations against certain parameters. Then analyzing the linearized model, we elucidated the criteria of when signaling cascades will display dynamics robustness. We found that changes in the upstream modules are masked in the cascade, and that the response duration is mainly controlled by the rate-limiting module and organization of the cascade’s kinetics. Specifically, we found two necessary conditions for dynamics robustness in signaling cascades: 1) Constraint on the rate-limiting process: The phosphatase activity in the perturbed module is not the slowest. 2) Constraints on the initial conditions: The kinase activity needs to be fast enough such that each module is saturated even with fast phosphatase activity and upstream changes are attenuated. We discussed the relevance of such robustness to several biological examples and the validity of the above conditions therein. Given the applicability of dynamics robustness to a variety of systems, it will provide a general basis for how biological systems function dynamically.

Cells use signaling pathways to transmit information received on its membrane to DNA, and many important cellular processes are tied to signaling networks. Past experiments have shown that cells’ internal signaling networks are sophisticated enough to process and encode temporal information such as the length of time a ligand is bound to a receptor. However, little research has been done to verify whether information encoded onto temporal profiles can be made robust. We examined mathematical models of linear signaling networks and found that the relaxation of the response to a transient stimuli can be made robust to certain parameter fluctuations. Robustness is a key concept in biological systems—it would be disastrous if a cell could not operate if there was a slight change in its environment or physiology. Our research shows that such dynamics robustness is a property of linear signaling cascades, and we outline the design principles needed to generate such robustness. We discovered that two conditions regarding the speed of the internal chemical reactions and concentration levels are needed to generate dynamics robustness.

An operational view of intercellular signaling pathways

Animal cells use a conserved repertoire of intercellular signaling pathways to communicate with one another. These pathways are well-studied from a molecular point of view. However, we often lack an "operational" understanding that would allow us to use these pathways to rationally control cellular behaviors. This requires knowing what dynamic input features each pathway perceives and how it processes those inputs to control downstream processes. To address these questions, researchers have begun to reconstitute signaling pathways in living cells, analyzing their dynamic responses to stimuli, and developing new functional representations of their behavior. Here we review important insights obtained through these new approaches, and discuss challenges and opportunities in understanding signaling pathways from an operational point of view.

Yeast GPCR signaling reflects the fraction of occupied receptors, not the number

According to receptor theory, the effect of a ligand depends on the amount of agonist-receptor complex. Therefore, changes in receptor abundance should have quantitative effects. However, the response to pheromone in Saccharomyces cerevisiae is robust (unaltered) to increases or reductions in the abundance of the G-protein-coupled receptor (GPCR), Ste2, responding instead to the fraction of occupied receptor. We found experimentally that this robustness originates during G-protein activation. We developed a complete mathematical model of this step, which suggested the ability to compute fractional occupancy depends on the physical interaction between the inhibitory regulator of G-protein signaling (RGS), Sst2, and the receptor. Accordingly, replacing Sst2 by the heterologous hsRGS4, incapable of interacting with the receptor, abolished robustness. Conversely, forcing hsRGS4:Ste2 interaction restored robustness. Taken together with other results of our work, we conclude that this GPCR pathway computes fractional occupancy because ligand-bound GPCR-RGS complexes stimulate signaling while unoccupied complexes actively inhibit it. In eukaryotes, many RGSs bind to specific GPCRs, suggesting these complexes with opposing activities also detect fraction occupancy by a ratiometric measurement. Such complexes operate as push-pull devices, which we have recently described.

Push-Pull and Feedback Mechanisms Can Align Signaling System Outputs with Inputs

Many cell signaling systems, including the yeast pheromone response system, exhibit "dose-response alignment" (DoRA), in which output of one or more downstream steps closely matches the fraction of occupied receptors. DoRA can improve the fidelity of transmitted dose information. Here, we searched systematically for biochemical network topologies that produced DoRA. Most networks, including many containing feedback and feedforward loops, could not produce DoRA. However, networks including "push-pull" mechanisms, in which the active form of a signaling species stimulates downstream activity and the nominally inactive form reduces downstream activity, enabled perfect DoRA. Networks containing feedbacks enabled DoRA, but only if they also compared feedback to input and adjusted output to match. Our results establish push-pull as a non-feedback mechanism to align output with variable input and maximize information transfer in signaling systems. They also suggest genetic approaches to determine whether particular signaling systems use feedback or push-pull control.

A network property necessary for concentration robustness

Maintenance of functionality of complex cellular networks and entire organisms exposed to environmental perturbations often depends on concentration robustness of the underlying components. Yet, the reasons and consequences of concentration robustness in large-scale cellular networks remain largely unknown. Here, we derive a necessary condition for concentration robustness based only on the structure of networks endowed with mass action kinetics. The structural condition can be used to design targeted experiments to study concentration robustness. We show that metabolites satisfying the necessary condition are present in metabolic networks from diverse species, suggesting prevalence of this property across kingdoms of life. We also demonstrate that our predictions about concentration robustness of energy-related metabolites are in line with experimental evidence from Escherichia coli. The necessary condition is applicable to mass action biological systems of arbitrary size, and will enable understanding the implications of concentration robustness in genetic engineering strategies and medical applications.

Absolute concentration robustness (ACR), independence of the steady-state concentration of a molecule from the environment, is difficult to predict. Here, the authors derive a network structure-based necessary condition for ACR, and suggest that metabolites satisfying the condition are prevalent.

Insights into the adaptive response of Arabidopsis thaliana to prolonged thermal stress by ribosomal profiling and RNA-Seq

BACKGROUND

Environmental stress puts organisms at risk and requires specific stress-tailored responses to maximize survival. Long-term exposure to stress necessitates a global reprogramming of the cellular activities at different levels of gene expression.

RESULTS

Here, we use ribosome profiling and RNA sequencing to globally profile the adaptive response of Arabidopsis thaliana to prolonged heat stress. To adapt to long heat exposure, the expression of many genes is modulated in a coordinated manner at a transcriptional and translational level. However, a significant group of genes opposes this trend and shows mainly translational regulation. Different secondary structure elements are likely candidates to play a role in regulating translation of those genes.

CONCLUSIONS

Our data also uncover on how the subunit stoichiometry of multimeric protein complexes in plastids is maintained upon heat exposure.

The Paradox of p53: What, How, and Why?

Unlike the rather stereotypic image by which it was portrayed until not too many years ago, p53 is now increasingly emerging as a multifaceted transcription factor that can sometimes exert opposing effects on biological processes. This includes pro-survival activities that seem to contradict p53's canonical proapoptotic features, as well as opposing effects on cell migration, metabolism, and differentiation. Such antagonistic bifunctionality (balancing both positive and negative signals) bestows p53 with an ideal attribute to govern homeostasis. The molecular mechanisms underpinning the paradoxical activities of p53 may be related to a protein conformational spectrum (from canonical wild-type to "pseudomutant"), diversity of DNA response elements, and/or higher-order chromatin configuration. Altogether, this functional flexibility positions p53 as a transcriptional "super hub" that dictates cell homeostasis, and ultimately cell fate, by governing a hierarchy of other functional hubs. Deciphering the mechanisms by which p53 determines which hubs to engage, and how one might modulate the preferences of p53, remains a major challenge for both basic science and translational cancer medicine.

A Comparison of Deterministic and Stochastic Modeling Approaches for Biochemical Reaction Systems: On Fixed Points, Means, and Modes

In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still expected to provide relevant indications on the underlying dynamics.

Survival of Phenotypic Information during Cellular Growth Transitions

Phenotypic memory can predispose cells to physiological outcomes, contribute to heterogeneity in cellular populations, and allow computation of environmental features, such as nutrient gradients. In bacteria and synthetic circuits in general, memory can often be set by protein concentrations: because of the relative stability of proteins, the degradation rate is often dominated by the growth rate, and inheritance is a significant factor. Cells can then be primed to respond to events that recur with frequencies faster than the time to eliminate proteins. Protein memory can be extended if cells reach extremely low growth rates or no growth. Here we characterize the necessary time scales for different quantities of protein memory, measured as relative entropy (Kullback–Leibler divergence), for a variety of cellular growth arrest transition dynamics. We identify a critical manifold in relative protein degradation/growth arrest time scales where information is, in principle, preserved indefinitely because proteins are trapped at a concentration determined by the competing time scales as long as nongrowth-mediated protein degradation is negligible. We next asked what characteristics of growth arrest dynamics and initial protein distributions best preserve or eliminate information about previous environments. We identified that sharp growth arrest transitions with skewed initial protein distributions optimize flexibility, with information preservation and minimal cost of residual protein. As a result, a nearly memoryless regime, corresponding to a form of bet-hedging, may be an optimal strategy for storage of information by protein concentrations in growth-arrested cells.