Ultrasensitive response motifs: basic amplifiers in molecular signalling networks

Beyond homogeneity: Assessing the validity of the Michaelis-Menten rate law in spatially heterogeneous environments

The Michaelis-Menten (MM) rate law has been a fundamental tool in describing enzyme-catalyzed reactions for over a century. When substrates and enzymes are homogeneously distributed, the validity of the MM rate law can be easily assessed based on relative concentrations: the substrate is in large excess over the enzyme-substrate complex. However, the applicability of this conventional criterion remains unclear when species exhibit spatial heterogeneity, a prevailing scenario in biological systems. Here, we explore the MM rate law's applicability under spatial heterogeneity by using partial differential equations. In this study, molecules diffuse very slowly, allowing them to locally reach quasi-steady states. We find that the conventional criterion for the validity of the MM rate law cannot be readily extended to heterogeneous environments solely through spatial averages of molecular concentrations. That is, even when the conventional criterion for the spatial averages is satisfied, the MM rate law fails to capture the enzyme catalytic rate under spatial heterogeneity. In contrast, a slightly modified form of the MM rate law, based on the total quasi-steady state approximation (tQSSA), is accurate. Specifically, the tQSSA-based modified form, but not the original MM rate law, accurately predicts the drug clearance via cytochrome P450 enzymes and the ultrasensitive phosphorylation in heterogeneous environments. Our findings shed light on how to simplify spatiotemporal models for enzyme-catalyzed reactions in the right context, ensuring accurate conclusions and avoiding misinterpretations in in silico simulations.

Bounds on the Ultrasensitivity of Biochemical Reaction Cascades

The ultrasensitivity of a dose response function can be quantifiably defined using the generalized Hill coefficient of the function. We examined an upper bound for the Hill coefficient of the composition of two functions, namely the product of their individual Hill coefficients. We proved that this upper bound holds for compositions of Hill functions, and that there are instances of counterexamples that exist for more general sigmoidal functions. Additionally, we tested computationally other types of sigmoidal functions, such as the logistic and inverse trigonometric functions, and we provided computational evidence that in these cases the inequality also holds. We show that in large generality there is a limit to how ultrasensitive the composition of two functions can be, which has applications to understanding signaling cascades in biochemical reactions.

A robust ultrasensitive transcriptional switch in noisy cellular environments

Ultrasensitive transcriptional switches enable sharp transitions between transcriptional on and off states and are essential for cells to respond to environmental cues with high fidelity. However, conventional switches, which rely on direct repressor-DNA binding, are extremely noise-sensitive, leading to unintended changes in gene expression. Here, through model simulations and analysis, we discovered that an alternative design combining three indirect transcriptional repression mechanisms, sequestration, blocking, and displacement, can generate a noise-resilient ultrasensitive switch. Although sequestration alone can generate an ultrasensitive switch, it remains sensitive to noise because the unintended transcriptional state induced by noise persists for long periods. However, by jointly utilizing blocking and displacement, these noise-induced transitions can be rapidly restored to the original transcriptional state. Because this transcriptional switch is effective in noisy cellular contexts, it goes beyond previous synthetic transcriptional switches, making it particularly valuable for robust synthetic system design. Our findings also provide insights into the evolution of robust ultrasensitive switches in cells. Specifically, the concurrent use of seemingly redundant indirect repression mechanisms in diverse biological systems appears to be a strategy to achieve noise-resilience of ultrasensitive switches.

Phototriggered Equilibrated and Transient Orthogonally Operating Constitutional Dynamic Networks Guiding Biocatalytic Cascades

The photochemical deprotection of structurally engineered o-nitrobenzylphosphate-caged hairpin nucleic acids is introduced as a versatile method to evolve constitutional dynamic networks, CDNs. The photogenerated CDNs, in the presence of fuel strands, interact with auxiliary CDNs, resulting in their dynamically equilibrated reconfiguration. By modification of the constituents associated with the auxiliary CDNs with glucose oxidase (GOx)/horseradish peroxidase (HRP) or the lactate dehydrogenase (LDH)/nicotinamide adenine dinucleotide (NAD+) cofactor, the photogenerated CDN drives the orthogonal operation upregulated/downregulated operation of the GOx/HRP and LDH/NAD+ biocatalytic cascade in the conjugate mixture of auxiliary CDNs. Also, the photogenerated CDN was applied to control the reconfiguration of coupled CDNs, leading to upregulated/downregulated formation of the antithrombin aptamer units, resulting in the dictated inhibition of thrombin activity (fibrinogen coagulation). Moreover, a reaction module consisting of GOx/HRP-modified o-nitrobenzyl phosphate-caged DNA hairpins, photoresponsive caged auxiliary duplexes, and nickase leads upon irradiation to the emergence of a transient, dissipative CDN activating in the presence of two alternate auxiliary triggers, achieving transient operation of up- and downregulated GOx/HRP biocatalytic cascades.

Activation of Thoeris antiviral system via SIR2 effector filament assembly

To survive bacteriophage (phage) infections, bacteria developed numerous anti-phage defence systems1-7. Some of them (for example, type III CRISPR-Cas, CBASS, Pycsar and Thoeris) consist of two modules: a sensor responsible for infection recognition and an effector that stops viral replication by destroying key cellular components8-12. In the Thoeris system, a Toll/interleukin-1 receptor (TIR)-domain protein, ThsB, acts as a sensor that synthesizes an isomer of cyclic ADP ribose, 1''-3' glycocyclic ADP ribose (gcADPR), which is bound in the Smf/DprA-LOG (SLOG) domain of the ThsA effector and activates the silent information regulator 2 (SIR2)-domain-mediated hydrolysis of a key cell metabolite, NAD+ (refs. 12-14). Although the structure of ThsA has been solved15, the ThsA activation mechanism remained incompletely understood. Here we show that 1''-3' gcADPR, synthesized in vitro by the dimeric ThsB' protein, binds to the ThsA SLOG domain, thereby activating ThsA by triggering helical filament assembly of ThsA tetramers. The cryogenic electron microscopy (cryo-EM) structure of activated ThsA revealed that filament assembly stabilizes the active conformation of the ThsA SIR2 domain, enabling rapid NAD+ depletion. Furthermore, we demonstrate that filament formation enables a switch-like response of ThsA to the 1''-3' gcADPR signal.

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.

First-order ultrasensitivity in phosphorylation cycles

Cellular signal transduction takes place through a network of phosphorylation cycles. These pathways take the form of a multi-layered cascade of cycles. This work focuses on the sensitivity of single, double and n length cycles. Cycles that operate in the zero-order regime can become sensitive to changes in signal, resulting in zero-order ultrasensitivity (ZOU). Using frequency analysis, we confirm previous efforts that cascades can act as noise filters by computing the bandwidth. We show that n length cycles display what we term first-order ultrasensitivity which occurs even when the cycles are not operating in the zero-order regime. The magnitude of the sensitivity, however, has an upper bound equal to the number of cycles. It is known that ZOU can be significantly reduced in the presence of retroactivity. We show that the first-order ultrasensitivity is immune to retroactivity and that the ZOU and first-order ultrasensitivity can be blended to create systems with constant sensitivity over a wider range of signal. We show that the ZOU in a double cycle is only modestly higher compared with a single cycle. We therefore speculate that the double cycle has evolved to enable amplification even in the face of retroactivity.

Density physics-informed neural networks reveal sources of cell heterogeneity in signal transduction

The transduction time between signal initiation and final response provides valuable information on the underlying signaling pathway, including its speed and precision. Furthermore, multi-modality in a transduction-time distribution indicates that the response is regulated by multiple pathways with different transduction speeds. Here, we developed a method called density physics-informed neural networks (Density-PINNs) to infer the transduction-time distribution from measurable final stress response time traces. We applied Density-PINNs to single-cell gene expression data from sixteen promoters regulated by unknown pathways in response to antibiotic stresses. We found that promoters with slower signaling initiation and transduction exhibit larger cell-to-cell heterogeneity in response intensity. However, this heterogeneity was greatly reduced when the response was regulated by slow and fast pathways together. This suggests a strategy for identifying effective signaling pathways for consistent cellular responses to disease treatments. Density-PINNs can also be applied to understand other time delay systems, including infectious diseases.

SHR and SCR coordinate root patterning and growth early in the cell cycle

Precise control of cell division is essential for proper patterning and growth during the development of multicellular organisms. Coordination of formative divisions that generate new tissue patterns with proliferative divisions that promote growth is poorly understood. SHORTROOT (SHR) and SCARECROW (SCR) are transcription factors that are required for formative divisions in the stem cell niche of Arabidopsis roots1,2. Here we show that levels of SHR and SCR early in the cell cycle determine the orientation of the division plane, resulting in either formative or proliferative cell division. We used 4D quantitative, long-term and frequent (every 15 min for up to 48 h) light sheet and confocal microscopy to probe the dynamics of SHR and SCR in tandem within single cells of living roots. Directly controlling their dynamics with an SHR induction system enabled us to challenge an existing bistable model3 of the SHR-SCR gene-regulatory network and to identify key features that are essential for rescue of formative divisions in shr mutants. SHR and SCR kinetics do not align with the expected behaviour of a bistable system, and only low transient levels, present early in the cell cycle, are required for formative divisions. These results reveal an uncharacterized mechanism by which developmental regulators directly coordinate patterning and growth.

Weak synchronization can alter circadian period length: implications for aging and disease conditions

The synchronization of multiple oscillators serves as the central mechanism for maintaining stable circadian rhythms in physiology and behavior. Aging and disease can disrupt synchronization, leading to changes in the periodicity of circadian activities. While our understanding of the circadian clock under synchronization has advanced significantly, less is known about its behavior outside synchronization, which can also fall within a predictable domain. These states not only impact the stability of the rhythms but also modulate the period length. In C57BL/6 mice, aging, diseases, and removal of peripheral circadian oscillators often result in lengthened behavioral circadian periods. Here, we show that these changes can be explained by a surprisingly simple mathematical relationship: the frequency is the reciprocal of the period, and its distribution becomes skewed when the period distribution is symmetric. The synchronized frequency of a population in the skewed distribution and the macroscopic frequency of combined oscillators differ, accounting for some of the atypical circadian period outputs observed in networks without synchronization. Building on this finding, we investigate the dynamics of circadian outputs in the context of aging and disease, where synchronization is weakened.

Ultrasensitive dose-response for asbestos cancer risk implied by new inflammation-mutation model

Alterations in complex cellular phenotype each typically involve multistep activation of an ultrasensitive molecular switch (e.g., to adaptively initiate an apoptosis, inflammasome, Nrf2-ARE anti-oxidant, or heat-shock activation pathway) that triggers expression of a suite of target genes while efficiently limiting false-positive switching from a baseline state. Such switches exhibit nonlinear signal-activation relationships. In contrast, a linear no-threshold (LNT) dose-response relationship is expected for damage that accumulates in proportion to dose, as hypothesized for increased risk of cancer in relation to genotoxic dose according to the multistage somatic mutation/clonal-expansion theory of cancer, e.g., as represented in the Moolgavkar-Venzon-Knudsen (MVK) cancer model by a doubly stochastic nonhomogeneous Poisson process. Mesothelioma and lung cancer induced by exposure to carcinogenic (e.g., certain asbestos) fibers in humans and experimental animals are thought to involve modes of action driven by mutations, cytotoxicity-associated inflammation, or both, rendering ambiguous expectations concerning the nature of model-implied shape of the low-dose response for above-background increase in risk of incurring these endpoints. A recent Inflammation Somatic Mutation (ISM) theory of cancer posits instead that tissue-damage-associated inflammation that epigenetically recruits, activates and orchestrates stem cells to engage in tissue repair does not merely promote cancer, but rather is a requisite co-initiator (acting together with as few as two somatic mutations) of the most efficient pathway to any type of cancer in any reparable tissue (Dose-Response 2019; 17(2):1-12). This theory is reviewed, implications of this theory are discussed in relation to mesothelioma and lung cancer associated with chronic asbestos inhalation, one of the two types of ISM-required mutations is here hypothesized to block or impede inflammation resolution (e.g., by doing so for GPCR-mediated signal transduction by one or more endogenous autacoid specialized pro-resolving mediators or SPMs), and supporting evidence for this hypothesis is discussed.

Phenotypic heterogeneity in human genetic diseases: ultrasensitivity-mediated threshold effects as a unifying molecular mechanism

Phenotypic heterogeneity is very common in genetic systems and in human diseases and has important consequences for disease diagnosis and treatment. In addition to the many genetic and non-genetic (e.g., epigenetic, environmental) factors reported to account for part of the heterogeneity, we stress the importance of stochastic fluctuation and regulatory network topology in contributing to phenotypic heterogeneity. We argue that a threshold effect is a unifying principle to explain the phenomenon; that ultrasensitivity is the molecular mechanism for this threshold effect; and discuss the three conditions for phenotypic heterogeneity to occur. We suggest that threshold effects occur not only at the cellular level, but also at the organ level. We stress the importance of context-dependence and its relationship to pleiotropy and edgetic mutations. Based on this model, we provide practical strategies to study human genetic diseases. By understanding the network mechanism for ultrasensitivity and identifying the critical factor, we may manipulate the weak spot to gently nudge the system from an ultrasensitive state to a stable non-disease state. Our analysis provides a new insight into the prevention and treatment of genetic diseases.

Improving cooperativity of transcription activators by oligomerization domains in mammalian cells

Cooperative activation is critical for the applications of synthetic biology in mammalian cells. In this study, we have developed cooperative transcription factor by fusing oligomerization domain in mammalian cells. Firstly, we demonstrated that two oligomerized domains (CI434 and CI) successfully improved transcription factor cooperativity in bacterial cells but failed to increase cooperativity in mammalian cells, possibly because the additional mammalian activation domain disrupted their oligomerization capability. Therefore, we chose a different type of oligomerized domain (CarHC), whose ability to oligomerize is not dependent on its C-terminal domains, to fuse with a transcription factor (RpaR) and activation domain (VTR3), forming a potential cooperative transcription activator RpaR-CarH-VTR3 for mammalian regulatory systems. Compared with RpaR-VTR3, the cooperativity of RpaR-CarH-VTR3 was significantly improved with higher Hill coefficient and a narrower input range in the inducible switch system in mammalian cells. Moreover, a mathematical model based on statistical mechanics model was developed and the simulation results supported the hypothesis that the tetramer of the CarH domain in mammalian cells was the reason for the cooperative capacity of RpaR-CarH-VTR3.

Differential roles of transcriptional and translational negative autoregulations in protein dynamics

Cells continuously respond to stimuli to function properly by employing a wide variety of regulatory mechanisms that often involve protein up or down regulations. This study focuses on dynamics of a protein with negative autoregulations in E. coli, and assumes that the input signal up-regulates the protein, and then the protein down-regulates its own production via 2 distinct types of mechanisms. The mathematical models describe the dynamics of mRNA and protein for 3 scenarios: (i) a simplistic model with no regulation, (ii) a model with transcriptional negative autoregulation, and (iii) a model with translational negative autoregulation. Our analysis shows that the negative autoregulation models produce faster responses and quicker return times to the input signals compared to the model with no regulation, while the transcriptional autoregulation model is the only model capable of producing oscillatory dynamics. The stochastic simulations predict that the transcriptional autoregulation model is the noisiest followed by the simplistic model, and the translational autoregulation model has the least noise. The noise level depends on the strength of inhibition. Furthermore, the transcriptional autoregulation model filters out the noise in the input signal for longer periods of time, and this time increases as the strength of the feedback gets stronger.

Automatic differentiation and the optimization of differential equation models in biology

A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters. Differentiation enhances the discovery of improved performance in large models, an achievement that was previously difficult or impossible. Recently, a second computational advance optimizes the temporal trajectories traced by differential equations. Optimization requires differentiating a measure of performance over a trajectory, such as the closeness of tracking the environment, with respect to the parameters of the differential equations. Because model trajectories are usually calculated numerically by multistep algorithms, such as Runge-Kutta, the automatic differentiation must be passed through the numerical algorithm. This article explains how such automatic differentiation of trajectories is achieved. It also discusses why such computational breakthroughs are likely to advance theoretical and statistical studies of biological problems, in which one can consider variables as dynamic paths over time and space. Many common problems arise between improving success in computational learning models over performance landscapes, improving evolutionary fitness over adaptive landscapes, and improving statistical fits to data over information landscapes.

The sequestration mechanism as a generalizable approach to improve the sensitivity of biosensors and bioassays

Biosensors and bioassays, both of which employ proteins and nucleic acids to detect specific molecular targets, have seen significant applications in both biomedical research and clinical practice. This success is largely due to the extraordinary versatility, affinity, and specificity of biomolecular recognition. Nevertheless, these receptors suffer from an inherent limitation: single, saturable binding sites exhibit a hyperbolic relationship (the "Langmuir isotherm") between target concentration and receptor occupancy, which in turn limits the sensitivity of these technologies to small variations in target concentration. To overcome this and generate more responsive biosensors and bioassays, here we have used the sequestration mechanism to improve the steepness of the input/output curves of several bioanalytical methods. As our test bed for this we employed sensors and assays against neutrophil gelatinase-associated lipocalin (NGAL), a kidney biomarker for which enhanced sensitivity will improve the monitoring of kidney injury. Specifically, by introducing sequestration we have improved the responsiveness of an electrochemical aptamer based (EAB) biosensor, and two bioassays, a paper-based "dipstick" assay and an enzyme-linked immunosorbent assay (ELISA). Doing so we have narrowed the dynamic range of these sensors and assays several-fold, thus enhancing their ability to measure small changes in target concentration. Given that introducing sequestration requires only the addition of the appropriate concentration of a high-affinity "depletant," the mechanism appears simple and easily adaptable to tuning the binding properties of the receptors employed in a wide range of biosensors and bioassays.

Identification of nonmonotonic concentration-responses in Tox21 high-throughput screening estrogen receptor assays

Environmental endocrine-disrupting chemicals (EDCs) interfere with the metabolism and actions of endogenous hormones. It has been well documented in numerous in vivo and in vitro studies that EDCs can exhibit nonmonotonic dose response (NMDR) behaviors. Not conforming to the conventional linear or linear-no-threshold response paradigm, these NMDR relationships pose practical challenges to the risk assessment of EDCs. In the meantime, the endocrine signaling pathways and biological mechanisms underpinning NMDR remain incompletely understood. The US Tox21 program has conducted in vitro cell-based high-throughput screening assays for estrogen receptors (ER), androgen receptors, and other nuclear receptors, and screened the 10 K-compound library for potential endocrine activities. Using 15 concentrations across several orders of magnitude of concentration range and run in both agonist and antagonist modes, these Tox21 assay datasets contain valuable quantitative information that can be explored to evaluate the nonlinear effects of EDCs and may infer potential mechanisms. In this study we analyzed the concentration-response curves (CRCs) in all 8 Tox21 ERα and ERβ assays by developing clustering and classification algorithms customized to the datasets to identify various shapes of CRCs. After excluding NMDR curves likely caused by cytotoxicity, luciferase inhibition, or autofluorescence, hundreds of compounds were identified to exhibit Bell or U-shaped CRCs. Bell-shaped CRCs are about 7 times more frequent than U-shaped ones in the Tox21 ER assays. Many compounds exhibit NMDR in at least one assay, and some EDCs well-known for their NMDRs in the literature were also identified, suggesting their nonmonotonic effects may originate at cellular levels involving transcriptional ER signaling. The developed computational methods for NMDR identification in ER assays can be adapted and applied to other high-throughput bioassays.

Dynamic Catalysis Guided by Nucleic Acid Networks and DNA Nanostructures

Nucleic acid networks conjugated to native enzymes and supramolecular DNA nanostructures modified with enzymes or DNAzymes act as functional reaction modules for guiding dynamic catalytic transformations. These systems are exemplified with the assembly of constitutional dynamic networks (CDNs) composed of nucleic acid-functionalized enzymes, as constituents, undergoing triggered structural reconfiguration, leading to dynamically switched biocatalytic cascades. By coupling two nucleic acid/enzyme networks, the intercommunicated feedback-driven dynamic biocatalytic operation of the system is demonstrated. In addition, the tailoring of a nucleic acid/enzyme reaction network driving a dissipative, transient, biocatalytic cascade is introduced as a model system for out-of-equilibrium dynamically modulated biocatalytic transformation in nature. Also, supramolecular nucleic acid machines or DNA nanostructures, modified with DNAzyme or enzyme constituents, act as functional reaction modules driving temporal dynamic catalysis. The design of dynamic supramolecular machines is exemplified with the introduction of an interlocked two-ring catenane device that is dynamically reversibly switched between two states operating two different DNAzymes, and with the tailoring of a DNA-tweezers device functionalized with enzyme/DNAzyme constituents that guides the dynamic ON/OFF operation of a biocatalytic cascade by opening and closing the molecular device. In addition, DNA origami nanostructures provide functional scaffolds for the programmed positioning of enzymes or DNAzyme for the switchable operation of catalytic transformations. This is introduced by the tailored functionalization of the edges of origami tiles with nucleic acids guiding the switchable formation of DNAzyme catalysts through the dimerization/separation of the tiles. In addition, the programmed deposition of two-enzyme/cofactor constituents on the origami raft allowed the dynamic photochemical activation of the cofactor-mediated biocatalytic cascade on the spatially biocatalytic assembly on the scaffold. Furthermore, photoinduced "mechanical" switchable and reversible unlocking and closing of nanoholes in the origami frameworks allow the "ON" and "OFF" operation of DNAzyme units in the nanoholes, confined environments. The future challenges and potential applications of dynamic nucleic acid/enzyme and DNAzyme conjugates are discussed in the conclusion paragraph.

Signal amplification in the KEAP1-NRF2-ARE antioxidant response pathway

The KEAP1-NRF2-ARE signaling pathway plays a central role in mediating the adaptive cellular stress response to oxidative and electrophilic chemicals. This canonical pathway has been extensively studied and reviewed in the past two decades, but rarely was it looked at from a quantitative signaling perspective. Signal amplification, i.e., ultrasensitivity, is crucially important for robust induction of antioxidant genes to appropriate levels that can adequately counteract the stresses. In this review article, we examined a number of well-known molecular events in the KEAP1-NRF2-ARE pathway from a quantitative perspective with a focus on how signal amplification can be achieved. We illustrated, by using a series of mathematical models, that redox-regulated protein sequestration, stabilization, translation, nuclear trafficking, DNA promoter binding, and transcriptional induction - which are embedded in the molecular network comprising KEAP1, NRF2, sMaf, p62, and BACH1 - may generate highly ultrasensitive NRF2 activation and antioxidant gene induction. The emergence and degree of ultrasensitivity depend on the strengths of protein-protein and protein-DNA interaction and protein abundances. A unique, quantitative understanding of signal amplification in the KEAP1-NRF2-ARE pathway will help to identify sensitive targets for the prevention and therapeutics of oxidative stress-related diseases and develop quantitative adverse outcome pathway models to facilitate the health risk assessment of oxidative chemicals.

Elucidating multi-input processing 3-node gene regulatory network topologies capable of generating striped gene expression patterns

A central problem in developmental and synthetic biology is understanding the mechanisms by which cells in a tissue or a Petri dish process external cues and transform such information into a coherent response, e.g., a terminal differentiation state. It was long believed that this type of positional information could be entirely attributed to a gradient of concentration of a specific signaling molecule (i.e., a morphogen). However, advances in experimental methodologies and computer modeling have demonstrated the crucial role of the dynamics of a cell’s gene regulatory network (GRN) in decoding the information carried by the morphogen, which is eventually translated into a spatial pattern. This morphogen interpretation mechanism has gained much attention in systems biology as a tractable system to investigate the emergent properties of complex genotype-phenotype maps. In this study, we apply a Markov chain Monte Carlo (MCMC)-like algorithm to probe the design space of three-node GRNs with the ability to generate a band-like expression pattern (target phenotype) in the middle of an arrangement of 30 cells, which resemble a simple (1-D) morphogenetic field in a developing embryo. Unlike most modeling studies published so far, here we explore the space of GRN topologies with nodes having the potential to perceive the same input signal differently. This allows for a lot more flexibility during the search space process, and thus enables us to identify a larger set of potentially interesting and realizable morphogen interpretation mechanisms. Out of 2061 GRNs selected using the search space algorithm, we found 714 classes of network topologies that could correctly interpret the morphogen. Notably, the main network motif that generated the target phenotype in response to the input signal was the type 3 Incoherent Feed-Forward Loop (I3-FFL), which agrees with previous theoretical expectations and experimental observations. Particularly, compared to a previously reported pattern forming GRN topologies, we have uncovered a great variety of novel network designs, some of which might be worth inquiring through synthetic biology methodologies to test for the ability of network design with minimal regulatory complexity to interpret a developmental cue robustly.

Systems biology is a fast growing field largely powered by advances in high-performance computing and sophisticated mathematical modeling of biological systems. Based on these advances, we are now in a position to mechanistically understand and accurately predict the behavior of complex biological processes, including cell differentiation and spatial pattern formation during embryogenesis. In this article, we use an in silico approach to probe the design space of multi-input, three-node Gene Regulatory Networks (GRNs) capable of generating a striped gene expression pattern in the context of a simplified 1-D morphogenetic field.

Teaching computational systems biology with an eye on quantitative systems pharmacology at the undergraduate level: Why do it, who would take it, and what should we teach?

Computational systems biology (CSB) is a field that emerged primarily as the product of research activities. As such, it grew in several directions in a distributed and uncoordinated manner making the area appealing and fascinating. The idea of not having to follow a specific path but instead creating one fueled innovation. As the field matured, several interdisciplinary graduate programs emerged attempting to educate future generations of computational systems biologists. These educational initiatives coordinated the dissemination of information across student populations that had already decided to specialize in this field. However, we are now entering an era where CSB, having established itself as a valuable research discipline, is attempting the next major step: Entering undergraduate curricula. As interesting as this endeavor may sound, it has several difficulties, mainly because the field is not uniformly defined. In this manuscript, we argue that this diversity is a significant advantage and that several incarnations of an undergraduate-level CSB biology course could, and should, be developed tailored to programmatic needs. In this manuscript, we share our experiences creating a course as part of a Biomedical Engineering program.

Weak selection helps cheap but harms expensive cooperation in spatial threshold dilemmas

Public Goods Games (PGGs) are n-person games with dependence of individual fitness benefits on the collective investment by the players. We have studied a simple PGG scenario played out by cooperating (C) and defecting (D) agents, applying the highly nonlinear threshold benefit function in an individual-based lattice model. A semi-analytical approximation of the lattice model has been developed and shown to describe the dynamics fairly well in the vicinity of the steady state. Besides the expected outcomes (i.e., the negative effect on cooperator persistence of higher cooperation costs and/or more intensive mixing of the population) we have found a surprising, counter-intuitive effect of the strength of selection on the steady state of the model. The effect is different at low and high cooperation costs, and it shows up only in the lattice model, suggesting that stochastic effects and higher order spatial correlations due to the emergent spatial clustering of cooperators (not taken into account in the semi-analytical approximation) must be responsible for the unexpected results for which we propose an intuitive explanation, present a tentative demonstration, and shortly discuss their biological relevance.

Harnessing Thorpe-Ingold Dialkylation to Access High-Hill-Percentage pH Probes

Sensitivity is an important parameter for a molecular probe. Hill-type pH probes exhibit improved detection sensitivity compared to the traditional pH probes following the Henderson-Hasselbalch equation. Exploiting positive cooperativity, we recently devised a novel molecular scaffold (PHX) to offer such an unconventional Hill-type pH titration profile. We previously confirmed that PHX is not a pure Hill-type probe yet. Only 64% of its absorbance/fluorescence turn-on is the result of a Hill-type pathway. The remaining 36% is from an undesired Henderson-Hasselbalch-type pathway (HH pathway). In this work, the Thorpe-Ingold dialkylation was harnessed to further suppress the percent contribution of the HH pathway down to 16%. We also propose that PHX is a viable molecular model for assessing the efficacy of the steric compressing effect induced by different Thorpe-Ingold dialkylations.

Diverse role of decoys on emergence and precision of oscillations in a biomolecular clock

Biomolecular clocks are key drivers of oscillatory dynamics in diverse biological processes including cell-cycle regulation, circadian rhythms, and pattern formation during development. A minimal clock implementation is based on the classical Goodwin oscillator, in which a repressor protein inhibits its own synthesis via time-delayed negative feedback. Clock motifs, however, do not exist in isolation; its components are open to interacting with the complex environment inside cells. For example, there are ubiquitous high-affinity binding sites along the genome, known as decoys, where transcription factors such as repressor proteins can potentially interact. This binding affects the availability of transcription factors and has often been ignored in theoretical studies. How does such genomic decoy binding impact the clock's robustness and precision? To address this question, we systematically analyze deterministic and stochastic models of the Goodwin oscillator in the presence of reversible binding of the repressor to a finite number of decoy sites. Our analysis reveals that the relative stability of decoy-bound repressors compared to the free repressor plays distinct roles on the emergence and precision of oscillations. Interestingly, active degradation of the bound repressor can induce sustained oscillations that are otherwise absent without decoys. In contrast, decoy abundances can kill oscillation dynamics if the bound repressor is protected from degradation. Taking into account low copy-number fluctuations in clock components, we show that the degradation of the bound repressors enhances precision by attenuating noise in both the amplitude and period of oscillations. Overall, these results highlight the versatile role of otherwise hidden decoys in shaping the stochastic dynamics of biological clocks and emphasize the importance of synthetic decoys in designing robust clocks.

Emergence and Enhancement of Ultrasensitivity through Posttranslational Modulation of Protein Stability

Signal amplification in biomolecular networks converts a linear input to a steeply sigmoid output and is central to a number of cellular functions including proliferation, differentiation, homeostasis, adaptation, and biological rhythms. One canonical signal amplifying motif is zero-order ultrasensitivity that is mediated through the posttranslational modification (PTM) cycle of signaling proteins. The functionality of this signaling motif has been examined conventionally by supposing that the total amount of the protein substrates remains constant, as by the classical Koshland-Goldbeter model. However, covalent modification of signaling proteins often results in changes in their stability, which affects the abundance of the protein substrates. Here, we use mathematical models to explore the signal amplification properties in such scenarios and report some novel aspects. Our analyses indicate that PTM-induced protein stabilization brings the enzymes closer to saturation. As a result, ultrasensitivity may emerge or is greatly enhanced, with a steeper sigmoidal response, higher magnitude, and generally longer response time. In cases where PTM destabilizes the protein, ultrasensitivity can be regained through changes in the activities of the involved enzymes or from increased protein synthesis. Importantly, ultrasensitivity is not limited to modified or unmodified protein substrates-when protein turnover is considered, the total free protein substrate can also exhibit ultrasensitivity under several conditions. When full enzymatic reactions are used instead of Michaelis-Menten kinetics for the modeling, the total free protein substrate can even exhibit nonmonotonic dose-response patterns. It is conceivable that cells use inducible protein stabilization as a strategy in the signaling network to boost signal amplification while saving energy by keeping the protein substrate levels low at basal conditions.

A computational model of mutual antagonism in the mechano-signaling network of RhoA and nitric oxide

BACKGROUND

RhoA is a master regulator of cytoskeletal contractility, while nitric oxide (NO) is a master regulator of relaxation, e.g., vasodilation. There are multiple forms of cross-talk between the RhoA/ROCK pathway and the eNOS/NO/cGMP pathway, but previous work has not studied their interplay at a systems level. Literature review suggests that the majority of their cross-talk interactions are antagonistic, which motivates us to ask whether the RhoA and NO pathways exhibit mutual antagonism in vitro, and if so, to seek the theoretical implications of their mutual antagonism.

RESULTS

Experiments found mutual antagonism between RhoA and NO in epithelial cells. Since mutual antagonism is a common motif for bistability, we sought to explore through theoretical simulations whether the RhoA-NO network is capable of bistability. Qualitative modeling showed that there are parameters that can cause bistable switching in the RhoA-NO network, and that the robustness of the bistability would be increased by positive feedback between RhoA and mechanical tension.

CONCLUSIONS

We conclude that the RhoA-NO bistability is robust enough in silico to warrant the investment of further experimental testing. Tension-dependent bistability has the potential to create sharp concentration gradients, which could contribute to the localization and self-organization of signaling domains during cytoskeletal remodeling and cell migration.

Mathematical modeling reveals quantitative properties of KEAP1-NRF2 signaling

Under oxidative and electrophilic stresses, cells launch an NRF2-mediated transcriptional antioxidant program. The activation of NRF2 depends on a redox sensor, KEAP1, which promotes the ubiquitination and degradation of NRF2. While a great deal has been learned about this duo, its quantitative signaling properties are largely unexplored. Here we examined these properties, including half-life, maximal activation, and response steepness (ultrasensitivity) of NRF2, through mathematical modeling. The models describe the binding of KEAP1 and NRF2 via ETGE and DLG motifs, NRF2 production, KEAP1-dependent and independent NRF2 degradation, and perturbations by different classes of NRF2 activators. Simulations revealed at the basal condition, NRF2 is sequestered by KEAP1 and the KEAP1-NRF2 complex is distributed comparably in an ETGE-bound (open) state and an ETGE and DLG dual-bound (closed) state. When two-step ETGE binding is considered, class I–V, electrophilic NRF2 activators shift the balance to a closed state incompetent to degrade NRF2, while the open and closed KEAP1-NRF2 complexes transition from operating in cycle mode to equilibrium mode. Ultrasensitive NRF2 activation (a steep rise of free NRF2) can occur when NRF2 nearly saturates KEAP1. The ultrasensitivity results from zero-order degradation through DLG binding and protein sequestration through ETGE binding. Optimal abundances of cytosolic and nuclear KEAP1 exist to maximize ultrasensitivity. These response characteristics do not require disruption of DLG binding as suggested by the hinge-latch hypothesis. In comparison, class VI NRF2 activators cause a shift to the open KEAP1-NRF2 complex and ultimately its complete dissociation, resulting in a fast release of NRF2 followed by stabilization. However, ultrasensitivity is lost due to decreasing free KEAP1 abundance. In summary, by simulating the dual role of KEAP1, i.e., sequestering and promoting degradation of NRF2, our modeling provides novel quantitative insights into NRF2 activation, which may help design novel NRF2 modulators and understand the oxidative actions of environmental stressors.

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Steep (ultrasensitive) NRF2 activation can occur when it rises to saturate KEAP1.

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Ultrasensitivity results from zero-order degradation and protein sequestration.

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Optimal cytosolic and nuclear KEAP1 abundances exist for maximal ultrasensitivity.

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Open and closed KEAP1-NRF2 complexes transition in cycle and equilibrium mode.

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NRF2 activation by KEAP1-NRF2 interaction inhibitors is more gradual.

Programmable DNA Framework Sensors for In Situ Cell-Surface pH Analysis

The availability of strategies for developing sensors with a defined responsiveness as well as the ability to working in a biological environment is critical to the fields of bioanalysis, nanomedicine, and nanorobotics. Herein, we developed programmable pH sensors by employing a tetrahedral DNA framework (TDF) as a robust structural skeleton for the sensors in biological working scenes and DNA i-motif structures as proton-recognition probes. The sensors' response midpoint and dynamic range can be fine-tuned by deliberately altering the i-motif's sequence composition or by combining different sensors, affording pH response windows that are consecutively distributed in the biologically relevant pH range of 5.0-7.5. This controllable tunability was successfully employed for in situ cell-surface pH analysis after anchoring the i-motif-TDF nanosensor on the cell surface via a two-step anchoring strategy, providing a useful platform for the diagnostics of diseases associated with extracellular pH variations.

Programming ultrasensitive threshold response through chemomechanical instability

The ultrasensitive threshold response is ubiquitous in biochemical systems. In contrast, achieving ultrasensitivity in synthetic molecular structures in a controllable way is challenging. Here, we propose a chemomechanical approach inspired by Michell's instability to realize it. A sudden reconfiguration of topologically constrained rings results when the torsional stress inside reaches a critical value. We use DNA origami to construct molecular rings and then DNA intercalators to induce torsional stress. Michell's instability is achieved successfully when the critical concentration of intercalators is applied. Both the critical point and sensitivity of this ultrasensitive threshold reconfiguration can be controlled by rationally designing the cross-sectional shape and mechanical properties of DNA rings.

Ultrasensitivity and bistability in covalent-modification cycles with positive autoregulation

Switch-like behaviours in biochemical networks are of fundamental significance in biological signal processing, and exist as two distinct types: ultra-sensitivity and bistability. Here we propose two new models of a reversible covalent-modification cycle with positive autoregulation (PAR), a motif structure that is thought to be capable of both ultrasensitivity and bistability in different parameter regimes. These new models appeal to a modelling framework that we call complex-complete, which accounts fully for the molecular complexities of the underlying signalling mechanisms. Each of the two new models encodes a specific molecular mechanism for PAR. We demonstrate that the modelling simplifications for PAR models that have been used in previous work, which rely on Michaelian approximations, are unable to accurately recapitulate the qualitative signalling responses supported by our detailed models. Strikingly, we show that complex-complete PAR models are capable of new qualitative responses such as one-way switches and a 'prozone' effect, depending on the specific PAR-encoding mechanism, which are not supported by Michaelian simplifications. Our results highlight the critical importance of accurately representing the molecular details of biochemical signalling mechanisms, and strongly suggest that the Michaelian approximation is inadequate for predictive models of enzyme-mediated chemical reactions with added regulations such as PAR.

Collapse of Intra-Tumor Cooperation Induced by Engineered Defector Cells

Anti-cancer therapies promote clonal selection of resistant cells that evade treatment. Effective therapy must be stable against the evolution of resistance. A potential strategy based on concepts from evolutionary game theory is to impair intra-tumor cooperation using genetically modified cells in which genes coding for essential growth factors have been knocked out. Such engineered cells would spread by clonal selection, driving the collapse of intra-tumor cooperation and a consequent reduction in tumor growth. Here, I test this idea in vitro in four cancer types (neuroendocrine pancreatic cancer, mesothelioma, lung adenocarcinoma and multiple myeloma). A reduction, or even complete eradication, of the producer clone and the consequent reduction in cell proliferation, is achieved in some but not all cases by introducing a small fraction of non-producer cells in the population. I show that the collapse of intra-tumor cooperation depends on the cost/benefit ratio of growth factor production. When stable cooperation among producer and non-producer cells occurs, its collapse can be induced by increasing the number of growth factors available to the cells. Considerations on nonlinear dynamics in the framework of evolutionary game theory explain this as the result of perturbation of the equilibrium of a system that resembles a public goods game, in which the production of growth factors is a cooperative phenotype. Inducing collapse of intra-tumor cooperation by engineering cancer cells will require the identification of growth factors that are essential for the tumor and that have a high cost of production for the cell.

Positive Cooperative Protonation of a Metal-Organic Framework: pH-Responsive Fluorescence and Proton Conduction

Positive cooperative binding, a phenomenon prevalent in biological processes, holds great appeal for the design of highly sensitive responsive molecules and materials. It has been demonstrated that metal-organic frameworks (MOFs) can show positive cooperative adsorption to the benefit of gas separation, but potential binding cooperativity is largely ignored in the study of sensory MOFs. Here, we report the first demonstration of positive cooperative protonation of a MOF and the relevant pH response in fluorescence and proton conduction. The MOF is built of Zr-O clusters and bipyridyl-based tetracarboxylate linkers and has excellent hydrolytic stability. It shows a unique pH response that features two synchronous abrupt turn-off and turn-on fluorescent transitions. The abrupt transitions, which afford high sensitivity to small pH fluctuations, are due to cooperative protonation of the pyridyl sites with a Hill coefficient of 1.6. The synchronous dual-emission response, which leads to visual color change, is ascribable to proton-triggered switching between (n, π*) and (π, π*) emissions. The latter emission can be quenched by electron donating anion-dependent through photoinduced electron transfer and ground-state charge transfer. Associated with cooperative protonation, the proton conductivity of the MOF is abruptly enhanced at low pH by two orders, but overhigh acid concentration is adverse because excessive anions can interrupt the conducting networks. Our work shows new perspectives of binding cooperativity in MOFs and should shed new light on the development of responsive fluorescent MOFs and proton conductive materials.

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.

Dosage Sensing, Threshold Responses, and Epigenetic Memory: A Systems Biology Perspective on Random X-Chromosome Inactivation

X-chromosome inactivation ensures dosage compensation between the sexes in mammals by randomly choosing one out of the two X chromosomes in females for inactivation. This process imposes a plethora of questions: How do cells count their X chromosome number and ensure that exactly one stays active? How do they randomly choose one of two identical X chromosomes for inactivation? And how do they stably maintain this state of monoallelic expression? Here, different regulatory concepts and their plausibility are evaluated in the context of theoretical studies that have investigated threshold behavior, ultrasensitivity, and bistability through mathematical modeling. It is discussed how a twofold difference between a single and a double dose of X-linked genes might be converted to an all-or-nothing response and how mutually exclusive expression can be initiated and maintained. Finally, candidate factors that might mediate the proposed regulatory principles are reviewed.

Programming folding cooperativity of the dimeric i-motif with DNA frameworks for sensing small pH variations

The response sensitivity of a molecular sensor is determined by the folding cooperativity of its responsive module. Using an H⁺-responsive dimeric DNA i-motif as a model, we demonstrate the enhancement of its folding cooperativity through preorganization by a DNA framework, and with it we fabricate robust intracellular pH sensors with high response sensitivity.

Role of integrated noise in pathway-specific signal propagation in feed-forward loops

Cells impose optimal noise control mechanism in diverse situations to cope with distinct environmental cues. Sometimes, it is desirable for the cell to utilize fluctuations for noise-driven processes. In other cases, noise can be harmful to the cell to show optimal fitness. It is, therefore, important to unravel the noise propagation mechanism inside the cell. Such noise controlling mechanism is accomplished by using gene transcription regulatory networks. One such gene regulatory network is feed-forward loop, having three regulatory nodes S, X and Y. Here, we consider the most abundant type 1 of coherent and incoherent feed-forward loops with both OR and AND logic functions, forming four different architectures. In OR logic function, the functions representing S and X act additively for the regulation of Y, while in AND logic function, the same functions (S and X) act multiplicatively for the regulation of Y. Measurement of susceptibility of the signal at output Y is done using elasticity of each regulation in FFLs. Using susceptibility, we demonstrate the nature of pathway integration by which one-step and two-step pathways get overlapped. The integration type is competitive for motifs having OR gate, while it is noncompetitive for the same with AND gate. The pathway integration property explains the output noise behavior of the motifs properly but cannot infer about the mechanism by which the upstream noise propagates to output. To account this, the total output noise is decomposed, which results in integrated noise as an additional noise source along with pathway-specific noise components. The integrated noise is found to appear as a consequence of integration between the pathways and has different functional characteristics explaining noise amplification and noise attenuation property of coherent and incoherent feed-forward loops, respectively. The noise decomposition also quantifies the contribution of different noise sources toward total noise. Finally, the noise propagation is being tuned as a function of input signal noise and its time scale of fluctuations, which shows considerable intrinsic noise strength and relatively slow relaxation time scale causes a higher degree of noise propagation in FFLs.

T cell circuits that sense antigen density with an ultrasensitive threshold

Overexpressed tumor-associated antigens [for example, epidermal growth factor receptor (EGFR) and human epidermal growth factor receptor 2 (HER2)] are attractive targets for therapeutic T cells, but toxic "off-tumor" cross-reaction with normal tissues that express low levels of target antigen can occur with chimeric antigen receptor (CAR)-T cells. Inspired by natural ultrasensitive response circuits, we engineered a two-step positive-feedback circuit that allows human cytotoxic T cells to discriminate targets on the basis of a sigmoidal antigen-density threshold. In this circuit, a low-affinity synthetic Notch receptor for HER2 controls the expression of a high-affinity CAR for HER2. Increasing HER2 density thus has cooperative effects on T cells-it increases both CAR expression and activation-leading to a sigmoidal response. T cells with this circuit show sharp discrimination between target cells expressing normal amounts of HER2 and cancer cells expressing 100 times as much HER2, both in vitro and in vivo.

Ultrasensitive molecular controllers for quasi-integral feedback

Feedback control has enabled the success of automated technologies by mitigating the effects of variability, unknown disturbances, and noise. While it is known that biological feedback loops reduce the impact of noise and help shape kinetic responses, many questions remain about how to design molecular integral controllers. Here, we propose a modular strategy to build molecular quasi-integral feedback controllers, which involves following two design principles. The first principle is to utilize an ultrasensitive response, which determines the gain of the controller and influences the steady-state error. The second is to use a tunable threshold of the ultrasensitive response, which determines the equilibrium point of the system. We describe a reaction network, named brink controller, that satisfies these conditions by combining molecular sequestration and an activation/deactivation cycle. With computational models, we examine potential biological implementations of brink controllers, and we illustrate different example applications.

Model-guided design of mammalian genetic programs

Genetically engineering cells to perform customizable functions is an emerging frontier with numerous technological and translational applications. However, it remains challenging to systematically engineer mammalian cells to execute complex functions. To address this need, we developed a method enabling accurate genetic program design using high-performing genetic parts and predictive computational models. We built multifunctional proteins integrating both transcriptional and posttranslational control, validated models for describing these mechanisms, implemented digital and analog processing, and effectively linked genetic circuits with sensors for multi-input evaluations. The functional modularity and compositional versatility of these parts enable one to satisfy a given design objective via multiple synonymous programs. Our approach empowers bioengineers to predictively design mammalian cellular functions that perform as expected even at high levels of biological complexity.

Roles of four feedback loops in mitochondrial permeability transition pore opening induced by Ca^{2+} and reactive oxygen species

Transient or sustained permeability transition pore (PTP) opening is important in normal physiology or cell death, respectively. These are closely linked to Ca^{2+} and reactive oxygen species (ROS). The entry of Ca^{2+} into mitochondria regulates ROS production, and both Ca^{2+} and ROS trigger PTP opening. In addition to this feedforward loop, there exist four feedback loops in the Ca^{2+}-ROS-PTP system. ROS promotes Ca^{2+} entering (F1) and induces further ROS generation (F2), forming two positive feedback loops. PTP opening results in the efflux of Ca^{2+} (F3) and ROS (F4) from the mitochondria, forming two negative feedback loops. Owing to these complexities, we construct a mathematical model to dissect the roles of these feedback loops in the dynamics of PTP opening. The qualitative agreement between simulation results and recent experimental observations supports our hypothesis that under physiological conditions the PTP opens in an oscillatory state, while under pathological conditions it opens in a high steady state. We clarify that the negative feedback loops are responsible for producing oscillations, wherein F3 plays a more prominent role than F4; whereas the positive feedback loops are beneficial for maintaining oscillation robustness, wherein F1 has a more dominant role than F2. Furthermore, we manifest that the proper increase in negative feedback strength or decrease in positive feedback strength not only facilitates the occurrence of oscillations and thus protects the system against a high steady state, but also assists in lowering the oscillation peak. This study may provide potential therapeutic strategies in treating neurodegenerative diseases due to PTP dysfunction.

Mechanics of a molecular mousetrap-nucleation-limited innate immune signaling

Innate immune responses, such as cell death and inflammatory signaling, are typically switch-like in nature. They also involve "prion-like" self-templating polymerization of one or more signaling proteins into massive macromolecular assemblies known as signalosomes. Despite the wealth of atomic-resolution structural information on signalosomes, how the constituent polymers nucleate and whether the switch-like nature of that event at the molecular scale relates to the digital nature of innate immune signaling at the cellular scale remains unknown. In this perspective, we review current knowledge of innate immune signalosome assembly, with an emphasis on structural constraints that allow the proteins to accumulate in inactive soluble forms poised for abrupt polymerization. We propose that structurally encoded nucleation barriers to protein polymerization kinetically regulate the corresponding pathways, which allows for extremely sensitive, rapid, and decisive signaling upon pathogen detection. We discuss how nucleation barriers satisfy the rigorous on-demand functions of the innate immune system but also predispose the system to precocious activation that may contribute to progressive age-associated inflammation.

Crosstalk and ultrasensitivity in protein degradation pathways

Protein turnover is vital to cellular homeostasis. Many proteins are degraded efficiently only after they have been post-translationally “tagged” with a polyubiquitin chain. Ubiquitylation is a form of Post-Translational Modification (PTM): addition of a ubiquitin to the chain is catalyzed by E3 ligases, and removal of ubiquitin is catalyzed by a De-UBiquitylating enzyme (DUB). Nearly four decades ago, Goldbeter and Koshland discovered that reversible PTM cycles function like on-off switches when the substrates are at saturating concentrations. Although this finding has had profound implications for the understanding of switch-like behavior in biochemical networks, the general behavior of PTM cycles subject to synthesis and degradation has not been studied. Using a mathematical modeling approach, we found that simply introducing protein turnover to a standard modification cycle has profound effects, including significantly reducing the switch-like nature of the response. Our findings suggest that many classic results on PTM cycles may not hold in vivo where protein turnover is ubiquitous. We also found that proteins sharing an E3 ligase can have closely related changes in their expression levels. These results imply that it may be difficult to interpret experimental results obtained from either overexpressing or knocking down protein levels, since changes in protein expression can be coupled via E3 ligase crosstalk. Understanding crosstalk and competition for E3 ligases will be key in ultimately developing a global picture of protein homeostasis.

Previous work has shown that substrates of Post-Translational Modification (PTM) cycles can have coupled responses if those substrates share enzymes. This implies that modifications leading to substrate degradation (e.g. ubiquitylation by an E3 ligase) could introduce coupling in concentrations of substrates sharing a ligase. Using mathematical models, we found adding protein turnover to a PTM cycle diminishes both sensitivity and ultrasensitivity, particularly in models admitting long ubiquitin chains. We also found that proteins sharing an E3 ligase can indeed have coupled changes in both expression and sensitivity to signals. These results imply that accounting for crosstalk in protein degradation networks is crucial for the interpretation of results from a wide variety of common experimental perturbations to living systems.

Dictated Emergence of Nucleic Acid-Based Constitutional Dynamic Networks by DNA Replication Machineries

The emergence of nucleic acid-based constitutional dynamic networks, CDNs, from a pool of nucleic acids is a key process for the understanding and modality of the evolution of biological networks. We present a versatile method that applies a library of nucleic acids coupled to biocatalytic DNA machineries as functional modules for the emergence of CDNs of diverse composition, complexity, and structural diversity. A set of four DNA template/blocker scaffolds coupled to the polymerase/dNTP replication machinery leads, in the presence of a primer, P₁, to the gated replication of the scaffolds and to the displacement of four components that reconfigure into a [2 × 2] CDN. Using six template/blocker scaffolds and the polymerase/dNTPs, the P₁-guided emergence of a [3 × 3] CDN is demonstrated. In addition, by further engineering the template/blocker scaffolds, the hierarchical control over the composition of the P₁-guided emergence of [3 × 3] CDNs is accomplished. Also, sequence-engineered template/blocker scaffolds, coupled to the polymerase/dNTP machinery, lead, in the presence of two primers P₁ and/or P₂, to the selective emergence of two different [2 × 2] CDNs or to a [3 × 3] CDN. Also, a set of six appropriately engineered template/blocker scaffolds, coupled to the polymerase/dNTP machinery, leads to the emergence of a CDN composed of four equilibrated DNA tetrahedra constituents. Finally, by further sequence engineering of the set of template/blocker scaffolds and their coupling to a nicking/polymerization/dNTP replication machinery, the amplified high-throughput emergence of CDNs is demonstrated.

Thermal tuning of arsenic selenide glass thin films and devices

We present a method of post-deposition tuning of the optical properties of thin film dielectric filters and mirrors containing chalcogenide glass (ChG) layers by thermally adjusting their refractive index. A common challenge associated with the use of ChG films in practical applications is that they suffer from slight run-to-run variations in optical properties resulting from hard-to-control changes in source material and deposition conditions. These variations lead to inconsistencies in optical constants, making the fabrication of devices with prescribed optical properties challenging. In this paper, we present new work that takes advantage of the large variation of a ChG films' refractive index as a function of annealing. We have carried out extensive characterization of the thermal index tuning and thickness change of arsenic selenide (As₂Se₃) ChG thin films and observed refractive index changes larger than 0.1 in some cases. We show results for refractive index as a function of annealing time and temperature and propose a model to describe this behavior based on bond rearrangement. We apply thermal refractive index tuning to permanently shift the resonance of a Fabry-Perot filter and the cutoff wavelength of a Bragg reflector. The Bragg reflector, consisting of alternating As₂Se₃ and CaF₂ layers, exhibits high reflectance across a ∼550 nm band with only five layers. Modeling results are compared with spectroscopic measurements, demonstrating good agreement.

A Shh/Gli-driven three-node timer motif controls temporal identity and fate of neural stem cells

How time is measured by neural stem cells during temporal neurogenesis has remained unresolved. By combining experiments and computational modeling, we define a Shh/Gli-driven three-node timer underlying the sequential generation of motor neurons (MNs) and serotonergic neurons in the brainstem. The timer is founded on temporal decline of Gli-activator and Gli-repressor activities established through down-regulation of Gli transcription. The circuitry conforms an incoherent feed-forward loop, whereby Gli proteins not only promote expression of Phox2b and thereby MN-fate but also account for a delayed activation of a self-promoting transforming growth factor-β (Tgfβ) node triggering a fate switch by repressing Phox2b. Hysteresis and spatial averaging by diffusion of Tgfβ counteract noise and increase temporal accuracy at the population level, providing a functional rationale for the intrinsically programmed activation of extrinsic switch signals in temporal patterning. Our study defines how time is reliably encoded during the sequential specification of neurons.

On the simultaneous activation of Agrobacterium tumefaciens ADP-glucose pyrophosphorylase by pyruvate and fructose 6-phosphate

Bacterial ADP-glucose pyrophosphorylases are allosterically regulated by metabolites that are key intermediates of central pathways in the respective microorganism. Pyruvate (Pyr) and fructose 6-phosphate (Fru6P) activate the enzyme from Agrobacterium tumefaciens by increasing V_max about 10- and 20-fold, respectively. Here, we studied the combined effect of both metabolites on the enzyme activation. Our results support a model in which there is a synergistic binding of these two activators to two distinct sites and that each activator leads the enzyme to distinct active forms with different properties. In presence of both activators, Pyr had a catalytically dominant effect over Fru6P determining the active conformational state. By mutagenesis we obtained enzyme variants still sensitive to Pyr activation, but in which the allosteric signal by Fru6P was disrupted. This indicated that the activation mechanism for each effector was not the same. The ability for this enzyme to have more than one allosteric activator site, active forms, and allosteric signaling mechanisms is critical to expand the evolvability of its regulation. These synergistic interactions between allosteric activators may represent a feature in other allosteric enzymes.

Multiplexed Profiling and Data Processing Methods to Identify Temperature-Regulated Primary Metabolites Using Gas Chromatography Coupled to Mass Spectrometry

This book chapter describes the analytical procedures required for the profiling of a metabolite fraction enriched for primary metabolites. The profiling is based on routine gas chromatography coupled to mass spectrometry (GC-MS). The generic profiling method is adapted to plant material, specifically to the analysis of plant material that was exposed to temperature stress. The method can be combined with stable isotope labeling and tracing experiments and is equally applicable to preparations of plant material and microbial photosynthetic organisms. The described methods are modular and can be multiplexed, that is, the same sample or a paired identical backup sample can be analyzed sequentially by more than one of the described procedures. The modules include rapid sampling and metabolic inactivation protocols for samples in a wide weight range, sample extraction procedures, chemical derivatization steps that are required to make the metabolite fraction amenable to gas chromatographic analysis, routine GC-MS methods, and procedures of data processing and data mining. A basic and extendable set of standardizations for metabolite recovery and retention index alignment of the resulting GC-MS chromatograms is included. The methods have two applications: (1) The rapid screening for changes of relative metabolite pools sizes under temperature stress and (2) the verification by exact quantification using GC-MS protocols that are extended by internal and external standardization.