Perfect and Near-Perfect Adaptation in Cell Signaling

Minimal motifs for habituating systems

Habituation-a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld-is universally observed in living systems from animals to unicellular organisms. Despite its prevalence, generic mechanisms for this fundamental form of learning remain poorly defined. Drawing inspiration from prior work on systems that respond adaptively to step inputs, we study habituation from a nonlinear dynamics perspective. This approach enables us to formalize classical hallmarks of habituation that have been experimentally identified in diverse organisms and stimulus scenarios. We use this framework to investigate distinct dynamical circuits capable of habituation. In particular, we show that driven linear dynamics of a memory variable with static nonlinearities acting at the input and output can implement numerous hallmarks in a mathematically interpretable manner. This work establishes a foundation for understanding the dynamical substrates of this primitive learning behavior and offers a blueprint for the identification of habituating circuits in biological systems.

Effects of growth feedback on adaptive gene circuits: A dynamical understanding

The successful integration of engineered gene circuits into host cells remains a significant challenge in synthetic biology due to circuit-host interactions, such as growth feedback, where the circuit influences cell growth and vice versa. Understanding the dynamics of circuit failures and identifying topologies resilient to growth feedback are crucial for both fundamental and applied research. Utilizing transcriptional regulation circuits with adaptation as a paradigm, we systematically study more than four hundred topological structures and uncover various categories of failures. Three dynamical mechanisms of circuit failures are identified: continuous deformation of the response curve, strengthened or induced oscillations, and sudden switching to coexisting attractors. Our extensive computations also uncover a scaling law between a circuit robustness measure and the strength of growth feedback. Despite the negative effects of growth feedback on the majority of circuit topologies, we identify several circuits that maintain optimal performance as designed, a feature important for applications.

Transient frequency preference responses in cell signaling systems

Ligand-receptor systems, covalent modification cycles, and transcriptional networks are the fundamental components of cell signaling and gene expression systems. While their behavior in reaching a steady-state regime under step-like stimulation is well understood, their response under repetitive stimulation, particularly at early time stages is poorly characterized. Yet, early-stage responses to external inputs are arguably as informative as late-stage ones. In simple systems, a periodic stimulation elicits an initial transient response, followed by periodic behavior. Transient responses are relevant when the stimulation has a limited time span, or when the stimulated component's timescale is slow as compared to the timescales of the downstream processes, in which case the latter processes may be capturing only those transients. In this study, we analyze the frequency response of simple motifs at different time stages. We use dose-conserved pulsatile input signals and consider different metrics versus frequency curves. We show that in ligand-receptor systems, there is a frequency preference response in some specific metrics during the transient stages, which is not present in the periodic regime. We suggest this is a general system-level mechanism that cells may use to filter input signals that have consequences for higher order circuits. In addition, we evaluate how the described behavior in isolated motifs is reflected in similar types of responses in cascades and pathways of which they are a part. Our studies suggest that transient frequency preferences are important dynamic features of cell signaling and gene expression systems, which have been overlooked.

Use of interactive mathematical simulations in Fundamentals of Biochemistry, a LibreText online educational resource, to promote understanding of dynamic reactions

Biology is perhaps the most complex of the sciences, given the incredible variety of chemical species that are interconnected in spatial and temporal pathways that are daunting to understand. Their interconnections lead to emergent properties such as memory, consciousness, and recognition of self and non-self. To understand how these interconnected reactions lead to cellular life characterized by activation, inhibition, regulation, homeostasis, and adaptation, computational analyses and simulations are essential, a fact recognized by the biological communities. At the same time, students struggle to understand and apply binding and kinetic analyses for the simplest reactions such as the irreversible first-order conversion of a single reactant to a product. This likely results from cognitive difficulties in combining structural, chemical, mathematical, and textual descriptions of binding and catalytic reactions. To help students better understand dynamic reactions and their analyses, we have introduced two kinds of interactive graphs and simulations into the online educational resource, Fundamentals of Biochemistry, a LibreText biochemistry book. One is available for simple binding and kinetic reactions. The other displays progress curves (concentrations vs. time) for simple reactions and complex metabolic and signal transduction pathways. Users can move sliders to change dissociation and kinetic constants as well as initial concentrations and see instantaneous changes in the graphs. They can also export data into a spreadsheet for further processing, such as producing derivative Lineweaver-Burk and traditional Michaelis-Menten graphs of initial velocity (v0) versus substrate concentration.

Signal Integration and Adaptive Sensory Diversity Tuning in Escherichia coli Chemotaxis

In uncertain environments, phenotypic diversity can be advantageous for survival. However, as the environmental uncertainty decreases, the relative advantage of having diverse phenotypes decreases. Here, we show how populations of E. coli integrate multiple chemical signals to adjust sensory diversity in response to changes in the prevalence of each ligand in the environment. Measuring kinase activity in single cells, we quantified the sensitivity distribution to various chemoattractants in different mixtures of background stimuli. We found that when ligands bind uncompetitively, the population tunes sensory diversity to each signal independently, decreasing diversity when the signal ambient concentration increases. However, amongst competitive ligands the population can only decrease sensory diversity one ligand at a time. Mathematical modeling suggests that sensory diversity tuning benefits E. coli populations by modulating how many cells are committed to tracking each signal proportionally as their prevalence changes.

Homeostasis in networks with multiple inputs

Homeostasis, also known as adaptation, refers to the ability of a system to counteract persistent external disturbances and tightly control the output of a key observable. Existing studies on homeostasis in network dynamics have mainly focused on 'perfect adaptation' in deterministic single-input single-output networks where the disturbances are scalar and affect the network dynamics via a pre-specified input node. In this paper we provide a full classification of all possible network topologies capable of generating infinitesimal homeostasis in arbitrarily large and complex multiple inputs networks. Working in the framework of 'infinitesimal homeostasis' allows us to make no assumption about how the components are interconnected and the functional form of the associated differential equations, apart from being compatible with the network architecture. Remarkably, we show that there are just three distinct 'mechanisms' that generate infinitesimal homeostasis. Each of these three mechanisms generates a rich class of well-defined network topologies-called homeostasis subnetworks. More importantly, we show that these classes of homeostasis subnetworks provides a topological basis for the classification of 'homeostasis types': the full set of all possible multiple inputs networks can be uniquely decomposed into these special homeostasis subnetworks. We illustrate our results with some simple abstract examples and a biologically realistic model for the co-regulation of calcium ( Ca ) and phosphate ( PO 4 ) in the rat. Furthermore, we identify a new phenomenon that occurs in the multiple input setting, that we call homeostasis mode interaction, in analogy with the well-known characteristic of multiparameter bifurcation theory.

A multiscale sensorimotor model of experience-dependent behavior in a minimal organism

To survive in ever-changing environments, living organisms need to continuously combine the ongoing external inputs they receive, representing present conditions, with their dynamical internal state, which includes influences of past experiences. It is still unclear in general, however 1) how this happens at the molecular and cellular levels and 2) how the corresponding molecular and cellular processes are integrated with the behavioral responses of the organism. Here, we address these issues by modeling mathematically a particular behavioral paradigm in a minimal model organism, namely chemotaxis in the nematode C. elegans. Specifically, we use a long-standing collection of elegant experiments on salt chemotaxis in this animal, in which the migration direction varies depending on its previous experience. Our model integrates the molecular, cellular, and organismal levels to reproduce the experimentally observed experience-dependent behavior. The model proposes specific molecular mechanisms for the encoding of current conditions and past experiences in key neurons associated with this response, predicting the behavior of various mutants associated with those molecular circuits.

A phenotypic screening approach to target p60AmotL2-expressing invasive cancer cells

BACKGROUND

Tumor cells have the ability to invade and form small clusters that protrude into adjacent tissues, a phenomenon that is frequently observed at the periphery of a tumor as it expands into healthy tissues. The presence of these clusters is linked to poor prognosis and has proven challenging to treat using conventional therapies. We previously reported that p60AmotL2 expression is localized to invasive colon and breast cancer cells. In vitro, p60AmotL2 promotes epithelial cell invasion by negatively impacting E-cadherin/AmotL2-related mechanotransduction.

METHODS

Using epithelial cells transfected with inducible p60AmotL2, we employed a phenotypic drug screening approach to find compounds that specifically target invasive cells. The phenotypic screen was performed by treating cells for 72 h with a library of compounds with known antitumor activities in a dose-dependent manner. After assessing cell viability using CellTiter-Glo, drug sensitivity scores for each compound were calculated. Candidate hit compounds with a higher drug sensitivity score for p60AmotL2-expressing cells were then validated on lung and colon cell models, both in 2D and in 3D, and on colon cancer patient-derived organoids. Nascent RNA sequencing was performed after BET inhibition to analyse BET-dependent pathways in p60AmotL2-expressing cells.

RESULTS

We identified 60 compounds that selectively targeted p60AmotL2-expressing cells. Intriguingly, these compounds were classified into two major categories: Epidermal Growth Factor Receptor (EGFR) inhibitors and Bromodomain and Extra-Terminal motif (BET) inhibitors. The latter consistently demonstrated antitumor activity in human cancer cell models, as well as in organoids derived from colon cancer patients. BET inhibition led to a shift towards the upregulation of pro-apoptotic pathways specifically in p60AmotL2-expressing cells.

CONCLUSIONS

BET inhibitors specifically target p60AmotL2-expressing invasive cancer cells, likely by exploiting differences in chromatin accessibility, leading to cell death. Additionally, our findings support the use of this phenotypic strategy to discover novel compounds that can exploit vulnerabilities and specifically target invasive cancer cells.

Enhancing circuit stability under growth feedback with supplementary repressive regulation

The field of synthetic biology and biosystems engineering increasingly acknowledges the need for a holistic design approach that incorporates circuit-host interactions into the design process. Engineered circuits are not isolated entities but inherently entwined with the dynamic host environment. One such circuit-host interaction, 'growth feedback', results when modifications in host growth patterns influence the operation of gene circuits. The growth-mediated effects can range from growth-dependent elevation in protein/mRNA dilution rate to changes in resource reallocation within the cell, which can lead to complete functional collapse in complex circuits. To achieve robust circuit performance, synthetic biologists employ a variety of control mechanisms to stabilize and insulate circuit behavior against growth changes. Here we propose a simple strategy by incorporating one repressive edge in a growth-sensitive bistable circuit. Through both simulation and in vitro experimentation, we demonstrate how this additional repressive node stabilizes protein levels and increases the robustness of a bistable circuit in response to growth feedback. We propose the incorporation of repressive links in gene circuits as a control strategy for desensitizing gene circuits against growth fluctuations.

On biochemical constructors and synthetic cells

Is it possible to build life? More specifically, is it possible to create a living synthetic cell from inanimate building blocks? This question precipitated into one of the most significant grand challenges in biochemistry and synthetic biology, with several large research consortia forming around this endeavour in Europe (European Synthetic Cell Initiative), the USA (Build-a-Cell Initiative) and Japan (Japanese Society for Cell Synthesis Research). The mature field of biochemistry, the advent of synthetic biology in the early 2000s, and the burgeoning field of cell-free synthetic biology made it feasible to tackle this grand challenge.

Robust homeostasis of cellular cholesterol is a consequence of endogenous antithetic integral control

Although cholesterol is essential for cellular viability and proliferation, it is highly toxic in excess. The concentration of cellular cholesterol must therefore be maintained within tight tolerances, and is thought to be subject to a stringent form of homeostasis known as Robust Perfect Adaptation (RPA). While much is known about the cellular signalling interactions involved in cholesterol regulation, the specific chemical reaction network structures that might be responsible for the robust homeostatic regulation of cellular cholesterol have been entirely unclear until now. In particular, the molecular mechanisms responsible for sensing excess whole-cell cholesterol levels have not been identified previously, and no mathematical models to date have been able to capture an integral control implementation that could impose RPA on cellular cholesterol. Here we provide a detailed mathematical description of cholesterol regulation pathways in terms of biochemical reactions, based on an extensive review of experimental and clinical literature. We are able to decompose the associated chemical reaction network structures into several independent subnetworks, one of which is responsible for conferring RPA on several intracellular forms of cholesterol. Remarkably, our analysis reveals that RPA in the cholesterol concentration in the endoplasmic reticulum (ER) is almost certainly due to a well-characterised control strategy known as antithetic integral control which, in this case, involves the high-affinity binding of a multi-molecular transcription factor complex with cholesterol molecules that are excluded from the ER membrane. Our model provides a detailed framework for exploring the necessary biochemical conditions for robust homeostatic control of essential and tightly regulated cellular molecules such as cholesterol.

Timed Pulses in DNA Strand Displacement Reactions

Inspired by naturally occurring regulatory mechanisms that allow complex temporal pulse features with programmable delays, we demonstrate here a strategy to achieve temporally programmed pulse output signals in DNA-based strand displacement reactions (SDRs). To achieve this, we rationally designed input strands that, once bound to their target duplex, can be gradually degraded, resulting in a pulse output signal. We also designed blocker strands that suppress strand displacement and determine the time at which the pulse reaction is generated. We show that by controlling the degradation rate of blocker and input strands, we can finely control the delayed pulse output over a range of 10 h. We also prove that it is possible to orthogonally delay two different pulse reactions in the same solution by taking advantage of the specificity of the degradation reactions for the input and blocker strands. Finally, we show here two possible applications of such delayed pulse SDRs: the time-programmed pulse decoration of DNA nanostructures and the sequentially appearing and self-erasing formation of DNA-based patterns.

Local negative feedback of Rac activity at the leading edge underlies a pilot pseudopod-like program for amoeboid cell guidance

To migrate efficiently, neutrophils must polarize their cytoskeletal regulators along a single axis of motion. This polarization process is thought to be mediated through local positive feedback that amplifies leading edge signals and global negative feedback that enables sites of positive feedback to compete for dominance. Though this two-component model efficiently establishes cell polarity, it has potential limitations, including a tendency to "lock" onto a particular direction, limiting the ability of cells to reorient. We use spatially defined optogenetic control of a leading edge organizer (PI3K) to probe how neutrophil-like HL-60 cells balance "decisiveness" needed to polarize in a single direction with the flexibility needed to respond to new cues. Underlying this balancing act is a local Rac inhibition process that destabilizes the leading edge to promote exploration. We show that this local inhibition enables cells to process input signal dynamics, linking front stability and orientation to local temporal increases in input signals.

Evolutionary Stability of Small Molecular Regulatory Networks That Exhibit Near-Perfect Adaptation

Large-scale protein regulatory networks, such as signal transduction systems, contain small-scale modules ('motifs') that carry out specific dynamical functions. Systematic characterization of the properties of small network motifs is therefore of great interest to molecular systems biologists. We simulate a generic model of three-node motifs in search of near-perfect adaptation, the property that a system responds transiently to a change in an environmental signal and then returns near-perfectly to its pre-signal state (even in the continued presence of the signal). Using an evolutionary algorithm, we search the parameter space of these generic motifs for network topologies that score well on a pre-defined measure of near-perfect adaptation. We find many high-scoring parameter sets across a variety of three-node topologies. Of all possibilities, the highest scoring topologies contain incoherent feed-forward loops (IFFLs), and these topologies are evolutionarily stable in the sense that, under 'macro-mutations' that alter the topology of a network, the IFFL motif is consistently maintained. Topologies that rely on negative feedback loops with buffering (NFLBs) are also high-scoring; however, they are not evolutionarily stable in the sense that, under macro-mutations, they tend to evolve an IFFL motif and may-or may not-lose the NFLB motif.

A plausible identifiable model of the canonical NF-κB signaling pathway

An overwhelming majority of mathematical models of regulatory pathways, including the intensively studied NF-κB pathway, remains non-identifiable, meaning that their parameters may not be determined by existing data. The existing NF-κB models that are capable of reproducing experimental data contain non-identifiable parameters, whereas simplified models with a smaller number of parameters exhibit dynamics that differs from that observed in experiments. Here, we reduced an existing model of the canonical NF-κB pathway by decreasing the number of equations from 15 to 6. The reduced model retains two negative feedback loops mediated by IκBα and A20, and in response to both tonic and pulsatile TNF stimulation exhibits dynamics that closely follow that of the original model. We carried out the sensitivity-based linear analysis and Monte Carlo-based analysis to demonstrate that the resulting model is both structurally and practically identifiable given measurements of 5 model variables from a simple TNF stimulation protocol. The reduced model is capable of reproducing different types of responses that are characteristic to regulatory motifs controlled by negative feedback loops: nearly-perfect adaptation as well as damped and sustained oscillations. It can serve as a building block of more comprehensive models of the immune response and cancer, where NF-κB plays a decisive role. Our approach, although may not be automatically generalized, suggests that models of other regulatory pathways can be transformed to identifiable, while retaining their dynamical features.

Universal structures for adaptation in biochemical reaction networks

At the molecular level, the evolution of life is driven by the generation and diversification of adaptation mechanisms. A universal description of adaptation-capable chemical reaction network (CRN) structures has remained elusive until now, since currently-known criteria for adaptation apply only to a tiny subset of possible CRNs. Here we identify the definitive structural requirements that characterize all adaptation-capable collections of interacting molecules, however large or complex. We show that these network structures implement a form of integral control in which multiple independent integrals can collaborate to confer the capacity for adaptation on specific molecules. Using an algebraic algorithm informed by these findings, we demonstrate the existence of embedded integrals in a variety of biologically important CRNs that have eluded previous methods, and for which adaptation has been observed experimentally. This definitive picture of biological adaptation at the level of intermolecular interactions represents a blueprint for adaptation-capable signaling networks across all domains of life, and for the design of synthetic biosystems.

On biological networks capable of robust adaptation in the presence of uncertainties: A linear systems-theoretic approach

Biological adaptation, the tendency of every living organism to regulate its essential activities in environmental fluctuations, is a well-studied functionality in systems and synthetic biology. In this work, we present a generic methodology inspired by systems theory to discover the design principles for robust adaptation, perfect and imperfect, in two different contexts: (1) in the presence of deterministic external and parametric disturbances and (2) in a stochastic setting. In all the cases, firstly, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as design requirements for the underlying networks. Thus, contrary to the existing approaches, the proposed methodologies provide an exhaustive set of admissible network structures without resorting to computationally burdensome brute-force techniques. Further, the proposed frameworks do not assume prior knowledge about the particular rate kinetics, thereby validating the conclusions for a large class of biological networks. In the deterministic setting, we show that unlike the incoherent feed-forward network structures (IFFLP or opposer modules), the modules containing negative feedback with buffer action (NFBLB or balancer modules) are robust to parametric fluctuations when a specific part of the network is assumed to remain unaffected. To this end, we propose a sufficient condition for imperfect adaptation and show that adding negative feedback in an IFFLP topology improves the robustness concerning parametric fluctuations. Further, we propose a stricter set of necessary conditions for imperfect adaptation. Turning to the stochastic scenario, we adopt a Wiener-Kolmogorov filter strategy to tune the parameters of a given network structure towards minimum output variance. We show that both NFBLB and IFFLP can be used as a reduced-order W-K filter. Further, we define the notion of nearest neighboring motifs to compare the output variances across different network structures. We argue that the NFBLB achieves adaptation at the cost of a variance higher than its nearest neighboring motifs whereas the IFFLP topology produces locally minimum variance while compared with its nearest neighboring motifs. We present numerical simulations to support the theoretical results. Overall, our results present a generic, systematic, and robust framework for advancing the understanding of complex biological networks.

The spatial distribution of GPCR and Gβγ activity across a cell dictates PIP3 dynamics

Phosphatidylinositol (3,4,5) trisphosphate (PIP3) is a plasma membrane-bound signaling phospholipid involved in many cellular signaling pathways that control crucial cellular processes and behaviors, including cytoskeleton remodeling, metabolism, chemotaxis, and apoptosis. Therefore, defective PIP3 signaling is implicated in various diseases, including cancer, diabetes, obesity, and cardiovascular diseases. Upon activation by G protein-coupled receptors (GPCRs) or receptor tyrosine kinases (RTKs), phosphoinositide-3-kinases (PI3Ks) phosphorylate phosphatidylinositol (4,5) bisphosphate (PIP2), generating PIP3. Though the mechanisms are unclear, PIP3 produced upon GPCR activation attenuates within minutes, indicating a tight temporal regulation. Our data show that subcellular redistributions of G proteins govern this PIP3 attenuation when GPCRs are activated globally, while localized GPCR activation induces sustained subcellular PIP3. Interestingly the observed PIP3 attenuation was Gγ subtype-dependent. Considering distinct cell-tissue-specific Gγ expression profiles, our findings not only demonstrate how the GPCR-induced PIP3 response is regulated depending on the GPCR activity gradient across a cell, but also show how diversely cells respond to spatial and temporal variability of external stimuli.

Computing Arithmetic Functions Using Immobilised Enzymatic Reaction Networks

Living systems use enzymatic reaction networks to process biochemical information and make decisions in response to external or internal stimuli. Herein, we present a modular and reusable platform for molecular information processing using enzymes immobilised in hydrogel beads and compartmentalised in a continuous stirred tank reactor. We demonstrate how this setup allows us to perform simple arithmetic operations, such as addition, subtraction and multiplication, using various concentrations of substrates or inhibitors as inputs and the production of a fluorescent molecule as the readout.

Epigenetic inheritance of gene silencing is maintained by a self-tuning mechanism based on resource competition

Biological systems can maintain memories over long timescales, with examples including memories in the brain and immune system. It is unknown how functional properties of memory systems, such as memory persistence, can be established by biological circuits. To address this question, we focus on transgenerational epigenetic inheritance in Caenorhabditis elegans. In response to a trigger, worms silence a target gene for multiple generations, resisting strong dilution due to growth and reproduction. Silencing may also be maintained indefinitely upon selection according to silencing levels. We show that these properties imply the fine-tuning of biochemical rates in which the silencing system is positioned near the transition to bistability. We demonstrate that this behavior is consistent with a generic mechanism based on competition for synthesis resources, which leads to self-organization around a critical state with broad silencing timescales. The theory makes distinct predictions and offers insights into the design principles of long-term memory systems.

Protein-protein complexes can undermine ultrasensitivity-dependent biological adaptation

Robust perfect adaptation (RPA) is a ubiquitously observed signalling response across all scales of biological organization. A major class of network architectures that drive RPA in complex networks is the Opposer module-a feedback-regulated network into which specialized integral-computing 'opposer node(s)' are embedded. Although ultrasensitivity-generating chemical reactions have long been considered a possible mechanism for such adaptation-conferring opposer nodes, this hypothesis has relied on simplified Michaelian models, which neglect the presence of protein-protein complexes. Here we develop complex-complete models of interlinked covalent-modification cycles with embedded ultrasensitivity, explicitly capturing all molecular interactions and protein complexes. Strikingly, we demonstrate that the presence of protein-protein complexes thwarts the network's capacity for RPA in any 'free' active protein form, conferring RPA capacity instead on the concentration of a larger protein pool consisting of two distinct forms of a single protein. We further show that the presence of enzyme-substrate complexes, even at comparatively low concentrations, play a crucial and previously unrecognized role in controlling the RPA response-significantly reducing the range of network inputs for which RPA can obtain, and imposing greater parametric requirements on the RPA response. These surprising results raise fundamental new questions as to the biochemical requirements for adaptation-conferring Opposer modules within complex cellular networks.

Design Principles Underlying Robust Adaptation of Complex Biochemical Networks

Biochemical networks are often characterized by tremendous complexity-both in terms of the sheer number of interacting molecules ("nodes") and in terms of the varied and incompletely understood interactions among these molecules ("interconnections" or "edges"). Strikingly, the vast and intricate networks of interacting proteins that exist within each living cell have the capacity to perform remarkably robustly, and reproducibly, despite significant variations in concentrations of the interacting components from one cell to the next and despite mutability over time of biochemical parameters. Here we consider the ubiquitously observed and fundamentally important signalling response known as robust perfect adaptation (RPA). We have recently shown that all RPA-capable networks, even the most complex ones, must satisfy an extremely rigid set of design principles, and are modular, being decomposable into just two types of network building-blocks-opposer modules and balancer modules. Here we present an overview of the design principles that characterize all RPA-capable network topologies through a detailed examination of a collection of simple examples. We also introduce a diagrammatic method for studying the potential of a network to exhibit RPA, which may be applied without a detailed knowledge of the complex mathematical principles governing RPA.

Reconstructing gene regulatory networks of biological function using differential equations of multilayer perceptrons

BACKGROUND

Building biological networks with a certain function is a challenge in systems biology. For the functionality of small (less than ten nodes) biological networks, most methods are implemented by exhausting all possible network topological spaces. This exhaustive approach is difficult to scale to large-scale biological networks. And regulatory relationships are complex and often nonlinear or non-monotonic, which makes inference using linear models challenging.

RESULTS

In this paper, we propose a multi-layer perceptron-based differential equation method, which operates by training a fully connected neural network (NN) to simulate the transcription rate of genes in traditional differential equations. We verify whether the regulatory network constructed by the NN method can continue to achieve the expected biological function by verifying the degree of overlap between the regulatory network discovered by NN and the regulatory network constructed by the Hill function. And we validate our approach by adapting to noise signals, regulator knockout, and constructing large-scale gene regulatory networks using link-knockout techniques. We apply a real dataset (the mesoderm inducer Xenopus Brachyury expression) to construct the core topology of the gene regulatory network and find that Xbra is only strongly expressed at moderate levels of activin signaling.

CONCLUSION

We have demonstrated from the results that this method has the ability to identify the underlying network topology and functional mechanisms, and can also be applied to larger and more complex gene network topologies.

A negative feedback loop in the GPCR pathway underlies efficient coding of external stimuli

Efficient navigation based on chemical cues is an essential feature shared by all animals. These cues may be encountered in complex spatiotemporal patterns and with orders of magnitude varying intensities. Nevertheless, sensory neurons accurately extract the relevant information from such perplexing signals. Here, we show how a single sensory neuron in Caenorhabditis elegans animals can cell-autonomously encode complex stimulus patterns composed of instantaneous sharp changes and of slowly changing continuous gradients. This encoding relies on a simple negative feedback in the G-protein-coupled receptor (GPCR) signaling pathway in which TAX-6/Calcineurin plays a key role in mediating the feedback inhibition. This negative feedback supports several important coding features that underlie an efficient navigation strategy, including exact adaptation and adaptation to the magnitude of the gradient's first derivative. A simple mathematical model explains the fine neural dynamics of both wild-type and tax-6 mutant animals, further highlighting how the calcium-dependent activity of TAX-6/Calcineurin dictates GPCR inhibition and response dynamics. As GPCRs are ubiquitously expressed in all sensory neurons, this mechanism may be a general solution for efficient cell-autonomous coding of external stimuli.

The dopamine circuit as a reward-taxis navigation system

Studying the brain circuits that control behavior is challenging, since in addition to their structural complexity there are continuous feedback interactions between actions and sensed inputs from the environment. It is therefore important to identify mathematical principles that can be used to develop testable hypotheses. In this study, we use ideas and concepts from systems biology to study the dopamine system, which controls learning, motivation, and movement. Using data from neuronal recordings in behavioral experiments, we developed a mathematical model for dopamine responses and the effect of dopamine on movement. We show that the dopamine system shares core functional analogies with bacterial chemotaxis. Just as chemotaxis robustly climbs chemical attractant gradients, the dopamine circuit performs ‘reward-taxis’ where the attractant is the expected value of reward. The reward-taxis mechanism provides a simple explanation for scale-invariant dopaminergic responses and for matching in free operant settings, and makes testable quantitative predictions. We propose that reward-taxis is a simple and robust navigation strategy that complements other, more goal-directed navigation mechanisms.

Synthetic nonlinear computation for genetic circuit design

Computation frameworks have been studied in synthetic biology to achieve biosignals integration and processing, for biosensing and therapeutics applications. Biological systems exhibit nonlinearity across scales from the molecular level, to biochemical network and intercellular systems. At the molecular level, cooperative bindings contribute to nonlinear molecular signal processing in a way similar to weight variables. At the intracellular network level, feedback and feedforward regulations result in cell behaviors such as multistability and adaptation. When biochemical networks are distributed in different cell groups, intercelluar networks can generate population dynamics. Here, we review works that highlight nonlinear computations in synthetic biology. We group the works according to the scale of implementations, from the cis-transcription level, to biochemical circuit level and cellular networks.

Stabilization of antithetic control via molecular buffering

A key goal in synthetic biology is the construction of molecular circuits that robustly adapt to perturbations. Although many natural systems display perfect adaptation, whereby stationary molecular concentrations are insensitive to perturbations, its de novo engineering has proven elusive. The discovery of the antithetic control motif was a significant step towards a universal mechanism for engineering perfect adaptation. Antithetic control provides perfect adaptation in a wide range of systems, but it can lead to oscillatory dynamics due to loss of stability; moreover, it can lose perfect adaptation in fast growing cultures. Here, we introduce an extended antithetic control motif that resolves these limitations. We show that molecular buffering, a widely conserved mechanism for homeostatic control in Nature, stabilizes oscillations and allows for near-perfect adaptation during rapid growth. We study multiple buffering topologies and compare their performance in terms of their stability and adaptation properties. We illustrate the benefits of our proposed strategy in exemplar models for biofuel production and growth rate control in bacterial cultures. Our results provide an improved circuit for robust control of biomolecular systems.

Temporal signaling, population control, and information processing through chromatin-mediated gene regulation

Chromatin regulation is a key pathway cells use to regulate gene expression in response to temporal stimuli, and is becoming widely used as a platform for synthetic biology applications. Here, we build a mathematical framework for analyzing the response of genetic circuits containing chromatin regulators to temporal signals in mammalian cell populations. Chromatin regulators can silence genes in an all-or-none fashion at the single-cell level, with individual cells stochastically transitioning between active, reversibly silent, and irreversibly silent gene states at constant rates over time. We integrate this mode of regulation with classical gene regulatory motifs, such as autoregulatory and incoherent feedforward loops, to determine the types of responses achievable with duration-dependent signaling. We demonstrate that repressive regulators without long-term epigenetic memory can filter out high frequency noise, and as part of an autoregulatory loop can precisely tune the fraction of cells in a population that expresses a gene of interest. Additionally, we find that repressive regulators with epigenetic memory can sum up and encode the total duration of their recruitment in the fraction of cells irreversibly silenced and, when included in a feed forward loop, enable perfect adaptation. Last, we use an information theoretic approach to show that all-or-none stochastic silencing can be used by populations to transmit information reliably and with high fidelity even in very simple genetic circuits. Altogether, we show that chromatin-mediated gene control enables a repertoire of complex cell population responses to temporal signals and can transmit higher information levels than previously measured in gene regulation.

Synthetic robust perfect adaptation achieved by negative feedback coupling with linear weak positive feedback

Unlike their natural counterparts, synthetic genetic circuits are usually fragile in the face of environmental perturbations and genetic mutations. Several theoretical robust genetic circuits have been designed, but their performance under real-world conditions has not yet been carefully evaluated. Here, we designed and synthesized a new robust perfect adaptation circuit composed of two-node negative feedback coupling with linear positive feedback on the buffer node. As a key feature, the linear positive feedback was fine-tuned to evaluate its necessity. We found that the desired function was robustly achieved when genetic parameters were varied by systematically perturbing all interacting parts within the topology, and the necessity of the completeness of the topological structures was evaluated by destroying key circuit features. Furthermore, different environmental perturbances were imposed onto the circuit by changing growth rates, carbon metabolic strategies and even chassis cells, and the designed perfect adaptation function was still achieved under all conditions. The successful design of a robust perfect adaptation circuit indicated that the top-down design strategy is capable of predictably guiding bottom-up engineering for robust genetic circuits. This robust adaptation circuit could be integrated as a motif into more complex circuits to robustly implement more sophisticated and critical biological functions.

A Stochastic Binary Model for the Regulation of Gene Expression to Investigate Responses to Gene Therapy

In this manuscript, we use an exactly solvable stochastic binary model for the regulation of gene expression to analyze the dynamics of response to a treatment aiming to modulate the number of transcripts of a master regulatory switching gene. The challenge is to combine multiple processes with different time scales to control the treatment response by a switching gene in an unavoidable noisy environment. To establish biologically relevant timescales for the parameters of the model, we select the RKIP gene and two non-specific drugs already known for changing RKIP levels in cancer cells. We demonstrate the usefulness of our method simulating three treatment scenarios aiming to reestablish RKIP gene expression dynamics toward a pre-cancerous state: (1) to increase the promoter's ON state duration; (2) to increase the mRNAs' synthesis rate; and (3) to increase both rates. We show that the pre-treatment kinetic rates of ON and OFF promoter switching speeds and mRNA synthesis and degradation will affect the heterogeneity and time for treatment response. Hence, we present a strategy for reaching increased average mRNA levels with diminished heterogeneity while reducing drug dosage by simultaneously targeting multiple kinetic rates that effectively represent the chemical processes underlying the regulation of gene expression. The decrease in heterogeneity of treatment response by a target gene helps to lower the chances of emergence of resistance. Our approach may be useful for inferring kinetic constants related to the expression of antimetastatic genes or oncogenes and for the design of multi-drug therapeutic strategies targeting the processes underpinning the expression of master regulatory genes.

Discovering adaptation-capable biological network structures using control-theoretic approaches

Constructing biological networks capable of performing specific biological functionalities has been of sustained interest in synthetic biology. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as ‘design requirements’ for the underlying networks. We go on to prove that a protein network with different input–output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of negative feedback or a feed-forward realization. We argue that presence of a particular class of negative feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This result explains how complex biological networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theoretical results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biological networks.

Biological systems display a remarkable diversity of functionalities, many of which can be conceived as the response of a large network composed of small interconnecting modules. Unravelling the connection pattern, i.e. design principles, behind important biological functionalities is one of the most challenging problems in systems biology. One such phenomenon is perfect adaptation, which merits special attention owing to its universal presence ranging from chemotaxis in bacterial cells to calcium homeostasis in mammalian cells. The present work focuses on finding the design principles for perfect adaptation in the presence of a stair-case type disturbance. To this end, the current work proposes a systems-theoretic approach to deduce precise mathematical (hence structural) conditions that comply with the key performance parameters for adaptation. The approach is agnostic to the particularities of the reaction kinetics, underlining the dominant role of the topological structure on the response of the network. Notably, the design principles obtained in this work serve as the most strict necessary structural conditions for a network of any size to provide perfect adaptation.

Differences in evolutionary accessibility determine which equally effective regulatory motif evolves to generate pulses

Transcriptional regulatory networks (TRNs) are enriched for certain "motifs." Motif usage is commonly interpreted in adaptationist terms, i.e., that the optimal motif evolves. But certain motifs can also evolve more easily than others. Here, we computationally evolved TRNs to produce a pulse of an effector protein. Two well-known motifs, type 1 incoherent feed-forward loops (I1FFLs) and negative feedback loops (NFBLs), evolved as the primary solutions. The relative rates at which these two motifs evolve depend on selection conditions, but under all conditions, either motif achieves similar performance. I1FFLs generally evolve more often than NFBLs. Selection for a tall pulse favors NFBLs, while selection for a fast response favors I1FFLs. I1FFLs are more evolutionarily accessible early on, before the effector protein evolves high expression; when NFBLs subsequently evolve, they tend to do so from a conjugated I1FFL-NFBL genotype. In the empirical S. cerevisiae TRN, output genes of NFBLs had higher expression levels than those of I1FFLs. These results suggest that evolutionary accessibility, and not relative functionality, shapes which motifs evolve in TRNs, and does so as a function of the expression levels of particular genes.

Quantal Ca2+ release mediated by very few IP3 receptors that rapidly inactivate allows graded responses to IP3

Inositol 1,4,5-trisphosphate receptors (IP₃Rs) are intracellular Ca²⁺ channels that link extracellular stimuli to Ca²⁺ signals. Ca²⁺ release from intracellular stores is "quantal": low IP₃ concentrations rapidly release a fraction of the stores. Ca²⁺ release then slows or terminates without compromising responses to further IP₃ additions. The mechanisms are unresolved. Here, we synthesize a high-affinity partial agonist of IP₃Rs and use it to demonstrate that quantal responses do not require heterogenous Ca²⁺ stores. IP₃Rs respond incrementally to IP₃ and close after the initial response to low IP₃ concentrations. Comparing functional responses with IP₃ binding shows that only a tiny fraction of a cell's IP₃Rs mediate incremental Ca²⁺ release; inactivation does not therefore affect most IP₃Rs. We conclude, and test by simulations, that Ca²⁺ signals evoked by IP₃ pulses arise from rapid activation and then inactivation of very few IP₃Rs. This allows IP₃Rs to behave as increment detectors mediating graded Ca²⁺ release.

Speed and Location Both Matter: Antigen Stimulus Dynamics Controls CAR-T Cell Response

Despite the success in B-cell malignancies, chimeric antigen receptor (CAR)-T cell therapies have not yet demonstrated consistent efficacy across all patients and tumor types, particularly against solid tumors. Higher rates of T cell exhaustion are associated with inferior clinical outcomes following CAR-T cell therapy, which is prevalent in solid tumors. T cell exhaustion may originate from persistent and chronic antigen stimulation by tumor cells that resist and/or evade T cell-mediated killing. We exploited CAR-T exhaustion with a classic negative feedback model (incoherent feedforward loop, IFFL) to investigate the balance between CAR-T cell activation and exhaustion under different antigen presentation dynamics. Built upon the experimental and clinical data, we hypothesize that the speed and anatomical location of antigenic stimulation are both crucial to CAR-T cell response. Chronic antigenic stimulation as well as the harsh tumor microenvironment present multiple barriers to CAR-T cell efficacy in solid tumors. Many therapeutic strategies are individually insufficient to improve of CAR-T responses against solid tumors, as they clear but one of the many barriers CAR-T cells face in solid tumors. A combination strategy targeting multiple barriers holds promise to improve CAR-T therapy in solid tumors.

Rapid prototyping and design of cybergenetic single-cell controllers

The design and implementation of synthetic circuits that operate robustly in the cellular context is fundamental for the advancement of synthetic biology. However, their practical implementation presents challenges due to low predictability of synthetic circuit design and time-intensive troubleshooting. Here, we present the Cyberloop, a testing framework to accelerate the design process and implementation of biomolecular controllers. Cellular fluorescence measurements are sent in real-time to a computer simulating candidate stochastic controllers, which in turn compute the control inputs and feed them back to the controlled cells via light stimulation. Applying this framework to yeast cells engineered with optogenetic tools, we examine and characterize different biomolecular controllers, test the impact of non-ideal circuit behaviors such as dilution on their operation, and qualitatively demonstrate improvements in controller function with certain network modifications. From this analysis, we derive conditions for desirable biomolecular controller performance, thereby avoiding pitfalls during its biological implementation.

Frequency-preference response in covalent modification cycles under substrate sequestration conditions

Covalent modification cycles (CMCs) are basic units of signaling systems and their properties are well understood. However, their behavior has been mostly characterized in situations where the substrate is in excess over the modifying enzymes. Experimental data on protein abundance suggest that the enzymes and their target proteins are present in comparable concentrations, leading to substrate sequestration by the enzymes. In this enzyme-in-excess regime, CMCs have been shown to exhibit signal termination, the ability of the product to return to a stationary value lower than its peak in response to constant stimulation, while this stimulation is still active, with possible implications for the ability of systems to adapt to environmental inputs. We characterize the conditions leading to signal termination in CMCs in the enzyme-in-excess regime. We also demonstrate that this behavior leads to a preferred frequency response (band-pass filters) when the cycle is subjected to periodic stimulation, whereas the literature reports that CMCs investigated so far behave as low-pass filters. We characterize the relationship between signal termination and the preferred frequency response to periodic inputs and we explore the dynamic mechanism underlying these phenomena. Finally, we describe how the behavior of CMCs is reflected in similar types of responses in the cascades of which they are part. Evidence of protein abundance in vivo shows that enzymes and substrates are present in comparable concentrations, thus suggesting that signal termination and frequency-preference response to periodic inputs are also important dynamic features of cell signaling systems, which have been overlooked.

Desensitisation of Notch signalling through dynamic adaptation in the nucleus

During embryonic development, signalling pathways orchestrate organogenesis by controlling tissue‐specific gene expression programmes and differentiation. Although the molecular components of many common developmental signalling systems are known, our current understanding of how signalling inputs are translated into gene expression outputs in real‐time is limited. Here we employ optogenetics to control the activation of Notch signalling during Drosophila embryogenesis with minute accuracy and follow target gene expression by quantitative live imaging. Light‐induced nuclear translocation of the Notch Intracellular Domain (NICD) causes a rapid activation of target mRNA expression. However, target gene transcription gradually decays over time despite continuous photo‐activation and nuclear NICD accumulation, indicating dynamic adaptation to the signalling input. Using mathematical modelling and molecular perturbations, we show that this adaptive transcriptional response fits to known motifs capable of generating near‐perfect adaptation and can be best explained by state‐dependent inactivation at the target cis‐regulatory region. Taken together, our results reveal dynamic nuclear adaptation as a novel mechanism controlling Notch signalling output during tissue differentiation.

A local regulatory T cell feedback circuit maintains immune homeostasis by pruning self-activated T cells

A fraction of mature T cells can be activated by peripheral self-antigens, potentially eliciting host autoimmunity. We investigated homeostatic control of self-activated T cells within unperturbed tissue environments by combining high-resolution multiplexed and volumetric imaging with computational modeling. In lymph nodes, self-activated T cells produced interleukin (IL)-2, which enhanced local regulatory T cell (Treg) proliferation and inhibitory functionality. The resulting micro-domains reciprocally constrained inputs required for damaging effector responses, including CD28 co-stimulation and IL-2 signaling, constituting a negative feedback circuit. Due to these local constraints, self-activated T cells underwent transient clonal expansion, followed by rapid death ("pruning"). Computational simulations and experimental manipulations revealed the feedback machinery's quantitative limits: modest reductions in Treg micro-domain density or functionality produced non-linear breakdowns in control, enabling self-activated T cells to subvert pruning. This fine-tuned, paracrine feedback process not only enforces immune homeostasis but also establishes a sharp boundary between autoimmune and host-protective T cell responses.

Context-aware synthetic biology by controller design: Engineering the mammalian cell

The rise of systems biology has ushered a new paradigm: the view of the cell as a system that processes environmental inputs to drive phenotypic outputs. Synthetic biology provides a complementary approach, allowing us to program cell behavior through the addition of synthetic genetic devices into the cellular processor. These devices, and the complex genetic circuits they compose, are engineered using a design-prototype-test cycle, allowing for predictable device performance to be achieved in a context-dependent manner. Within mammalian cells, context effects impact device performance at multiple scales, including the genetic, cellular, and extracellular levels. In order for synthetic genetic devices to achieve predictable behaviors, approaches to overcome context dependence are necessary. Here, we describe control systems approaches for achieving context-aware devices that are robust to context effects. We then consider cell fate programing as a case study to explore the potential impact of context-aware devices for regenerative medicine applications.

Perfect adaptation in biology

A distinctive feature of many biological systems is their ability to adapt to persistent stimuli or disturbances that would otherwise drive them away from a desirable steady state. The resulting stasis enables organisms to function reliably while being subjected to very different external environments. This perspective concerns a stringent type of biological adaptation, robust perfect adaptation (RPA), that is resilient to certain network and parameter perturbations. As in engineered control systems, RPA requires that the regulating network satisfy certain structural constraints that cannot be avoided. We elucidate these ideas using biological examples from systems and synthetic biology. We then argue that understanding the structural constraints underlying RPA allows us to look past implementation details and offers a compelling means to unravel regulatory biological complexity.

The structure of infinitesimal homeostasis in input-output networks

Homeostasis refers to a phenomenon whereby the output [Formula: see text] of a system is approximately constant on variation of an input [Formula: see text]. Homeostasis occurs frequently in biochemical networks and in other networks of interacting elements where mathematical models are based on differential equations associated to the network. These networks can be abstracted as digraphs [Formula: see text] with a distinguished input node [Formula: see text], a different distinguished output node o, and a number of regulatory nodes [Formula: see text]. In these models the input-output map [Formula: see text] is defined by a stable equilibrium [Formula: see text] at [Formula: see text]. Stability implies that there is a stable equilibrium [Formula: see text] for each [Formula: see text] near [Formula: see text] and infinitesimal homeostasis occurs at [Formula: see text] when [Formula: see text]. We show that there is an [Formula: see text] homeostasis matrix [Formula: see text] for which [Formula: see text] if and only if [Formula: see text]. We note that the entries in H are linearized couplings and [Formula: see text] is a homogeneous polynomial of degree [Formula: see text] in these entries. We use combinatorial matrix theory to factor the polynomial [Formula: see text] and thereby determine a menu of different types of possible homeostasis associated with each digraph [Formula: see text]. Specifically, we prove that each factor corresponds to a subnetwork of [Formula: see text]. The factors divide into two combinatorially defined classes: structural and appendage. Structural factors correspond to feedforward motifs and appendage factors correspond to feedback motifs. Finally, we discover an algorithm for determining the homeostasis subnetwork motif corresponding to each factor of [Formula: see text] without performing numerical simulations on model equations. The algorithm allows us to classify low degree factors of [Formula: see text]. There are two types of degree 1 homeostasis (negative feedback loops and kinetic or Haldane motifs) and there are two types of degree 2 homeostasis (feedforward loops and a degree two appendage motif).

Quasi-robust control of biochemical reaction networks via stochastic morphing

One of the main objectives of synthetic biology is the development of molecular controllers that can manipulate the dynamics of a given biochemical network that is at most partially known. When integrated into smaller compartments, such as living or synthetic cells, controllers have to be calibrated to factor in the intrinsic noise. In this context, biochemical controllers put forward in the literature have focused on manipulating the mean (first moment) and reducing the variance (second moment) of the target molecular species. However, many critical biochemical processes are realized via higher-order moments, particularly the number and configuration of the probability distribution modes (maxima). To bridge the gap, we put forward the stochastic morpher controller that can, under suitable timescale separations, morph the probability distribution of the target molecular species into a predefined form. The morphing can be performed at a lower-resolution, allowing one to achieve desired multi-modality/multi-stability, and at a higher-resolution, allowing one to achieve arbitrary probability distributions. Properties of the controller, such as robustness and convergence, are rigorously established, and demonstrated on various examples. Also proposed is a blueprint for an experimental implementation of stochastic morpher.

Systems-Theoretic Approaches to Design Biological Networks with Desired Functionalities

The deduction of design principles for complex biological functionalities has been a source of constant interest in the fields of systems and synthetic biology. A number of approaches have been adopted, to identify the space of network structures or topologies that can demonstrate a specific desired functionality, ranging from brute force to systems theory-based methodologies. The former approach involves performing a search among all possible combinations of network structures, as well as the parameters underlying the rate kinetics for a given form of network. In contrast to the search-oriented approach in brute force studies, the present chapter introduces a generic approach inspired by systems theory to deduce the network structures for a particular biological functionality. As a first step, depending on the functionality and the type of network in consideration, a measure of goodness of attainment is deduced by defining performance parameters. These parameters are computed for the most ideal case to obtain the necessary condition for the given functionality. The necessary conditions are then mapped as specific requirements on the parameters of the dynamical system underlying the network. Following this, admissible minimal structures are deduced. The proposed methodology does not assume any particular rate kinetics in this case for deducing the admissible network structures notwithstanding a minimum set of assumptions on the rate kinetics. The problem of computing the ideal set of parameter/s or rate constants, unlike the problem of topology identification, depends on the particular rate kinetics assumed for the given network. In this case, instead of a computationally exhaustive brute force search of the parameter space, a topology-functionality specific optimization problem can be solved. The objective function along with the feasible region bounded by the motif specific constraints amounts to solving a non-convex optimization program leading to non-unique parameter sets. To exemplify our approach, we adopt the functionality of adaptation, and demonstrate how network topologies that can achieve adaptation can be identified using such a systems-theoretic approach. The outcomes, in this case, i.e., minimum network structures for adaptation, are in agreement with the brute force results and other studies in literature.

An opponent process for alcohol addiction based on changes in endocrine gland mass

Consuming addictive drugs is often initially pleasurable, but escalating drug intake eventually recruits physiological anti-reward systems called opponent processes that cause tolerance and withdrawal symptoms. Opponent processes are fundamental for the addiction process, but their physiological basis is not fully characterized. Here, we propose an opponent processes mechanism centered on the endocrine stress response, the hypothalamic-pituitary-adrenal (HPA) axis. We focus on alcohol addiction, where the HPA axis is activated and secretes β-endorphin, causing euphoria and analgesia. Using a mathematical model, we show that slow changes in the functional mass of HPA glands act as an opponent process for β-endorphin secretion. The model explains hormone dynamics in alcohol addiction and experiments on alcohol preference in rodents. The opponent process is based on fold-change detection (FCD) where β-endorphin responses are relative rather than absolute; FCD confers vulnerability to addiction but has adaptive roles for learning. Our model suggests gland mass changes as potential targets for intervention in addiction.

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Addiction involves tolerance and withdrawal over weeks

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Model of the HPA-axis and β-endorphins explains tolerance and withdrawal

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Effects due to changes in the functional mass of endocrine glands

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Fold-change detection makes circuit prone to addiction but boosts learning

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.

Biphasic regulation of transcriptional surge generated by the gene feedback loop in a two-component system

MOTIVATION

Transcriptional surges generated by two-component systems (TCSs) have been observed experimentally in various bacteria. Suppression of the transcriptional surge may reduce the activity, virulence, and drug resistance of bacteria. In order to investigate the general mechanisms, we use a PhoP/PhoQ TCS as a model system to derive a comprehensive mathematical modeling that governs the surge. PhoP is a response regulator, which serves as a transcription factor under a phosphorylation-dependent modulation by PhoQ, a histidine kinase.

RESULTS

Our model reveals two major signaling pathways to modulate the phosphorylated PhoP (P-PhoP) level, one of which promotes the generation of P-PhoP, while the other depresses the level of P-PhoP. The competition between the P-PhoP-promoting and the P-PhoP-depressing pathways determines the generation of the P-PhoP surge. Furthermore, besides PhoQ, PhoP is also a bifunctional modulator that contributes to the dynamic control of P-PhoP state, leading to a biphasic regulation of the surge by the gene feedback loop. In summary, the mechanisms derived from the PhoP/PhoQ system for the transcriptional surges provide a better understanding on such a sophisticated signal transduction system and aid to develop new antimicrobial strategies targeting TCSs.

AVAILABILITY

https://github.com/jianweishuai/TCS.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Adaptability of the ubiquitin-proteasome system to proteolytic and folding stressors

Aging, disease, and environmental stressors are associated with failures in the ubiquitin-proteasome system (UPS), yet a quantitative understanding of how stressors affect the proteome and how the UPS responds is lacking. Here we assessed UPS performance and adaptability in yeast under stressors using quantitative measurements of misfolded substrate stability and stress-dependent UPS regulation by the transcription factor Rpn4. We found that impairing degradation rates (proteolytic stress) and generating misfolded proteins (folding stress) elicited distinct effects on the proteome and on UPS adaptation. Folding stressors stabilized proteins via aggregation rather than overburdening the proteasome, as occurred under proteolytic stress. Still, the UPS productively adapted to both stressors using separate mechanisms: proteolytic stressors caused Rpn4 stabilization while folding stressors increased RPN4 transcription. In some cases, adaptation completely prevented loss of UPS substrate degradation. Our work reveals the distinct effects of proteotoxic stressors and the versatility of cells in adapting the UPS.