Uncovering the interleukin-12 pharmacokinetic desensitization mechanism and its consequences with mathematical modeling.

The cytokine interleukin-12 (IL-12) is a potential immunotherapy because of its ability to induce a Th1 immune response. However, success in the clinic has been limited due to a phenomenon called IL-12 desensitization - the trend where repeated exposure to IL-12 leads to reduced IL-12 concentrations (pharmacokinetics) and biological effects (pharmacodynamics). Here, we investigated IL-12 pharmacokinetic desensitization via a modeling approach to (i) validate proposed mechanisms in literature and (ii) develop a mathematical model capable of predicting IL-12 pharmacokinetic desensitization. Two potential causes of IL-12 pharmacokinetic desensitization were identified: increased clearance or reduced bioavailability of IL-12 following repeated doses. Increased IL-12 clearance was previously proposed to occur due to the upregulation of IL-12 receptor on T cells that causes increased receptor-mediated clearance in the serum. However, our model with this mechanism, the accelerated-clearance model, failed to capture trends in clinical trial data. Alternatively, our novel reduced-bioavailability model assumed that upregulation of IL-12 receptor on T cells in the lymphatic system leads to IL-12 sequestration, inhibiting the transport to the blood. This model accurately fits IL-12 pharmacokinetic data from three clinical trials, supporting its biological relevance. Using this model, we analyzed the model parameter space to illustrate that IL-12 desensitization occurs over a robust range of parameter values and to identify the conditions required for desensitization. We next simulated local, continuous IL-12 delivery and identified several methods to mitigate systemic IL-12 exposure. Ultimately, our results provide quantitative validation of our proposed mechanism and allow for accurate prediction of IL-12 pharmacokinetics over repeated doses.

Linear-Decoupling Enables Accurate Speed and Accuracy Predictions for Copolymerization Processes.

Biological processes exhibit remarkable accuracy and speed and can be theoretically explored through various approaches. The Markov-chain copolymerization theory, describing polymer growth kinetics as a Markov chain, provides an exact set of equations to solve for error and speed. Still, due to nonlinearity, these equations are hard to solve. Alternatively, the enzyme-kinetics approach, which formulates a set of linear equations, simplifies the biological processes as transitions between discrete chemical states, but generally, it might not be accurate. Here, we show that the enzyme-kinetic approach can lead to inaccurate fluxes, even for first-order polymerization processes. To address the problem, we propose a simplified linear-decoupling approximation for steady-state probabilities of higher-order copolymer chains under biologically relevant conditions. Our findings demonstrate that the stationary speed and error rate obtained from the linear-decoupling method align closely with exact values from the Markov-chain (nonlinear) approximation. Extending the technique to higher-order processes with proofreading and internal states shows that it works equally well to describe trade-offs between speed and accuracy for DNA replication and transcription elongation. Our work underscores the proposed linear-decoupling approximation's efficacy in addressing the nonlinear behavior of the Markov-chain approach and the enzyme-kinetic approach's limitations, ensuring accurate predictions for high-fidelity biological processes.

Breakdown of Boltzmann-type models for the alignment of self-propelled rods.

Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these kinetic models often relies on Boltzmann's "molecular chaos" hypothesis, which assumes that correlations between individuals are short-lived. While this assumption is often the simplest way to derive tractable models, it is often not valid in practice due to the high levels of cooperation and self-organization present in biological systems. In this work, we illustrated this point by considering a general Boltzmann-type kinetic model for the alignment of self-propelled rods where rod reorientation occurs upon binary collisions. We examine the accuracy of the kinetic model by comparing numerical solutions of the continuous equations to an agent-based model that implements the underlying rules governing microscopic alignment. Even for the simplest case considered, our comparison demonstrates that the kinetic model fails to replicate the discrete dynamics due to the formation of rod clusters that violate statistical independence. Additionally, we show that introducing noise to limit cluster formation helps improve the agreement between the analytical model and agent simulations but does not restore the agreement completely. These results highlight the need to both develop and disseminate improved moment-closure methods for modeling biological and active matter systems.

Insights into Error Control Mechanisms in Biological Processes: Copolymerization and Enzyme-Kinetics Revisited.

The high fidelity observed in biological information processing ranging from replication to translation has stimulated significant research efforts to clarify the underlying microscopic picture. Theoretically, several approaches to analyze the error rates have been proposed. The copolymerization theory describes the addition and removal of monomers at the growing tip of a copolymer, leading to a closed set of nonlinear equations. On the other hand, enzyme-kinetics approaches formulate linear equations of biochemical networks, describing transitions between discrete chemical states. However, it is still unclear whether the error values computed by the two approaches agree. Moreover, there are conflicting interpretations on whether the error is under thermodynamic or kinetic discrimination control. In this work, we examine the error rate in persistent copying biochemical processes by specifically analyzing both theoretical approaches. The initial disagreement of the results between the two theories motivated us to rederive the formula for the error rate in the kinetic model. The error computed with the new method resulted in excellent agreement between both theoretical approaches and with Monte Carlo simulations. Furthermore, our theoretical analysis shows that the kinetic discrimination controls the error, even when the energy difference between adding the right and wrong products is very small. Our theoretical investigation gives important insights into the physical-chemical properties of complex biological processes by providing the quantitative framework to evaluate them.

Beyond microtubules: The cellular environment at the endoplasmic reticulum attracts proteins to the nucleus, enabling nuclear transport.

All proteins are translated in the cytoplasm, yet many, including transcription factors, play vital roles in the nucleus. While previous research has concentrated on molecular motors for the transport of these proteins to the nucleus, recent observations reveal perinuclear accumulation even in the absence of an energy source, hinting at alternative mechanisms. Here, we propose that structural properties of the cellular environment, specifically the endoplasmic reticulum (ER), can promote molecular transport to the perinucleus without requiring additional energy expenditure. Specifically, physical interaction between proteins and the ER impedes their diffusion and leads to their accumulation near the nucleus. This result explains why larger proteins, more frequently interacting with the ER membrane, tend to accumulate at the perinucleus. Interestingly, such diffusion in a heterogeneous environment follows Chapman's law rather than the popular Fick's law. Our findings suggest a novel protein transport mechanism arising solely from characteristics of the intracellular environment.

Cell behaviors underlying Myxococcus xanthus aggregate dispersal.

IMPORTANCE: Understanding the processes behind bacterial biofilm formation, maintenance, and dispersal is essential for addressing their effects on health and ecology. Within these multicellular communities, various cues can trigger differentiation into distinct cell types, allowing cells to adapt to their specific local environment. The soil bacterium Myxococcus xanthus forms biofilms in response to starvation, marked by cells aggregating into mounds. Some aggregates persist as spore-filled fruiting bodies, while others disperse after initial formation for unknown reasons. Here, we use a combination of cell tracking analysis and computational simulations to identify behaviors at the cellular level that contribute to aggregate dispersal. Our results suggest that cells in aggregates actively determine whether to disperse or persist and undergo a transition to sporulation based on a self-produced cue related to the aggregate size. Identifying these cues is an important step in understanding and potentially manipulating bacterial cell-fate decisions.

Synergy among Pausing, Intrinsic Proofreading, and Accessory Proteins Results in Optimal Transcription Speed and Tolerable Accuracy.

Cleavage of dinucleotides after the misincorporational pauses serves as a proofreading mechanism that increases transcriptional elongation accuracy. The accuracy is further improved by accessory proteins such as GreA and TFIIS. However, it is not clear why RNAP pauses and why cleavage-factor-assisted proofreading is necessary despite transcriptional errors in vitro being of the same order as those in downstream translation. Here, we developed a chemical-kinetic model that incorporates most relevant features of transcriptional proofreading and uncovers how the balance between speed and accuracy is achieved. We found that long pauses are essential for high accuracy, whereas cleavage-factor-stimulated proofreading optimizes speed. Moreover, in comparison to the cleavage of a single nucleotide or three nucleotides, RNAP backtracking and dinucleotide cleavage improve both speed and accuracy. Our results thereby show how the molecular mechanism and the kinetic parameters of the transcriptional process were evolutionarily optimized to achieve maximal speed and tolerable accuracy.

The Slowdown of Growth Rate Controls the Single-Cell Distribution of Biofilm Matrix Production via an SinI-SinR-SlrR Network.

In Bacillus subtilis, master regulator Spo0A controls several cell-differentiation pathways. Under moderate starvation, phosphorylated Spo0A (Spo0A~P) induces biofilm formation by indirectly activating genes controlling matrix production in a subpopulation of cells via an SinI-SinR-SlrR network. Under severe starvation, Spo0A~P induces sporulation by directly and indirectly regulating sporulation gene expression. However, what determines the heterogeneity of individual cell fates is not fully understood. In particular, it is still unclear why, despite being controlled by a single master regulator, biofilm matrix production and sporulation seem mutually exclusive on a single-cell level. In this work, with mathematical modeling, we showed that the fluctuations in the growth rate and the intrinsic noise amplified by the bistability in the SinI-SinR-SlrR network could explain the single-cell distribution of matrix production. Moreover, we predicted an incoherent feed-forward loop; the decrease in the cellular growth rate first activates matrix production by increasing in Spo0A phosphorylation level but then represses it via changing the relative concentrations of SinR and SlrR. Experimental data provide evidence to support model predictions. In particular, we demonstrate how the degree to which matrix production and sporulation appear mutually exclusive is affected by genetic perturbations. IMPORTANCE The mechanisms of cell-fate decisions are fundamental to our understanding of multicellular organisms and bacterial communities. However, even for the best-studied model systems we still lack a complete picture of how phenotypic heterogeneity of genetically identical cells is controlled. Here, using B. subtilis as a model system, we employ a combination of mathematical modeling and experiments to explain the population-level dynamics and single-cell level heterogeneity of matrix gene expression. The results demonstrate how the two cell fates, biofilm matrix production and sporulation, can appear mutually exclusive without explicitly inhibiting one another. Such a mechanism could be used in a wide range of other biological systems.

Mean-field model for nematic alignment of self-propelled rods.

Self-propelled rods are a facet of the field of active matter relevant to many physical systems ranging in scale from shaken granular media and bacterial alignment to the flocking dynamics of animals. In this paper we develop a model for nematic alignment of self-propelled rods interacting through binary collisions. We avoid phenomenological descriptions of rod interaction in favor of rigorously using a set of microscopic-level rules. Under the assumption that each collision results in a small change to a rod's orientation, we derive the Fokker-Planck equation for the evolution of the kinetic density function. Using analytical and numerical methods, we study the emergence of the nematic order from a homogeneous, uniform steady state of the mean-field equation. We compare the level of orientational noise needed to destabilize this nematic order and compare our results to an existing phenomenological model that does not explicitly account for the physical collisions of rods. We show the presence of an additional geometric factor in our equations reflecting a reduced collision rate between nearly aligned rods that reduces the level of noise at which nematic order is destroyed, suggesting that alignment that depends on purely physical collisions is less robust.

Clinically translatable cytokine delivery platform for eradication of intraperitoneal tumors.

Proinflammatory cytokines have been approved by the Food and Drug Administration for the treatment of metastatic melanoma and renal carcinoma. However, effective cytokine therapy requires high-dose infusions that can result in antidrug antibodies and/or systemic side effects that limit long-term benefits. To overcome these limitations, we developed a clinically translatable cytokine delivery platform composed of polymer-encapsulated human ARPE-19 (RPE) cells that produce natural cytokines. Tumor-adjacent administration of these capsules demonstrated predictable dose modulation with spatial and temporal control and enabled peritoneal cancer immunotherapy without systemic toxicities. Interleukin-2 (IL2)-producing cytokine factory treatment eradicated peritoneal tumors in ovarian and colorectal mouse models. Furthermore, computational pharmacokinetic modeling predicts clinical translatability to humans. Notably, this platform elicited T cell responses in NHPs, consistent with reported biomarkers of treatment efficacy without toxicity. Combined, our findings demonstrate the safety and efficacy of IL2 cytokine factories in preclinical animal models and provide rationale for future clinical testing in humans.

The energy cost and optimal design of networks for biological discrimination.

Many biological processes discriminate between correct and incorrect substrates through the kinetic proofreading mechanism that enables lower error at the cost of higher energy dissipation. Elucidating physico-chemical constraints for global minimization of dissipation and error is important for understanding enzyme evolution. Here, we identify theoretically a fundamental error-cost bound that tightly constrains the performance of proofreading networks under any parameter variations preserving the rate discrimination between substrates. The bound is kinetically controlled, i.e. completely determined by the difference between the transition state energies on the underlying free energy landscape. The importance of the bound is analysed for three biological processes. DNA replication by T7 DNA polymerase is shown to be nearly optimized, i.e. its kinetic parameters place it in the immediate proximity of the error-cost bound. The isoleucyl-tRNA synthetase (IleRS) of E. coli also operates close to the bound, but further optimization is prevented by the need for reaction speed. In contrast, E. coli ribosome operates in a high-dissipation regime, potentially in order to speed up protein production. Together, these findings establish a fundamental error-dissipation relation in biological proofreading networks and provide a theoretical framework for studying error-dissipation trade-off in other systems with biological discrimination.

Bacillus subtilis Histidine Kinase KinC Activates Biofilm Formation by Controlling Heterogeneity of Single-Cell Responses.

In Bacillus subtilis, biofilm and sporulation pathways are both controlled by a master regulator, Spo0A, which is activated by phosphorylation via a phosphorelay-a cascade of phosphotransfer reactions commencing with autophosphorylation of histidine kinases KinA, KinB, KinC, KinD, and KinE. However, it is unclear how the kinases, despite acting via the same regulator, Spo0A, differentially regulate downstream pathways, i.e., how KinA mainly activates sporulation genes and KinC mainly activates biofilm genes. In this work, we found that KinC also downregulates sporulation genes, suggesting that KinC has a negative effect on Spo0A activity. To explain this effect, with a mathematical model of the phosphorelay, we revealed that unlike KinA, which always activates Spo0A, KinC has distinct effects on Spo0A at different growth stages: during fast growth, KinC acts as a phosphate source and activates Spo0A, whereas during slow growth, KinC becomes a phosphate sink and contributes to decreasing Spo0A activity. However, under these conditions, KinC can still increase the population-mean biofilm matrix production activity. In a population, individual cells grow at different rates, and KinC would increase the Spo0A activity in the fast-growing cells but reduce the Spo0A activity in the slow-growing cells. This mechanism reduces single-cell heterogeneity of Spo0A activity, thereby increasing the fraction of cells that activate biofilm matrix production. Thus, KinC activates biofilm formation by controlling the fraction of cells activating biofilm gene expression. IMPORTANCE In many bacterial and eukaryotic systems, multiple cell fate decisions are activated by a single master regulator. Typically, the activities of the regulators are controlled posttranslationally in response to different environmental stimuli. The mechanisms underlying the ability of these regulators to control multiple outcomes are not understood in many systems. By investigating the regulation of Bacillus subtilis master regulator Spo0A, we show that sensor kinases can use a novel mechanism to control cell fate decisions. By acting as a phosphate source or sink, kinases can interact with one another and provide accurate regulation of the phosphorylation level. Moreover, this mechanism affects the cell-to-cell heterogeneity of the transcription factor activity and eventually determines the fraction of different cell types in the population. These results demonstrate the importance of intercellular heterogeneity for understanding the effects of genetic perturbations on cell fate decisions. Such effects can be applicable to a wide range of cellular systems.

Bacteriophage self-counting in the presence of viral replication.

When host cells are in low abundance, temperate bacteriophages opt for dormant (lysogenic) infection. Phage lambda implements this strategy by increasing the frequency of lysogeny at higher multiplicity of infection (MOI). However, it remains unclear how the phage reliably counts infecting viral genomes even as their intracellular number increases because of replication. By combining theoretical modeling with single-cell measurements of viral copy number and gene expression, we find that instead of hindering lambda's decision, replication facilitates it. In a nonreplicating mutant, viral gene expression simply scales with MOI rather than diverging into lytic (virulent) and lysogenic trajectories. A similar pattern is followed during early infection by wild-type phage. However, later in the infection, the modulation of viral replication by the decision genes amplifies the initially modest gene expression differences into divergent trajectories. Replication thus ensures the optimal decision-lysis upon single-phage infection and lysogeny at higher MOI.

Emergent Myxobacterial Behaviors Arise from Reversal Suppression Induced by Kin Contacts.

A wide range of biological systems, from microbial swarms to bird flocks, display emergent behaviors driven by coordinated movement of individuals. To this end, individual organisms interact by recognizing their kin and adjusting their motility based on others around them. However, even in the best-studied systems, the mechanistic basis of the interplay between kin recognition and motility coordination is not understood. Here, using a combination of experiments and mathematical modeling, we uncover the mechanism of an emergent social behavior in Myxococcus xanthus. By overexpressing the cell surface adhesins TraA and TraB, which are involved in kin recognition, large numbers of cells adhere to one another and form organized macroscopic circular aggregates that spin clockwise or counterclockwise. Mechanistically, TraAB adhesion results in sustained cell-cell contacts that trigger cells to suppress cell reversals, and circular aggregates form as the result of cells' ability to follow their own cellular slime trails. Furthermore, our in silico simulations demonstrate a remarkable ability to predict self-organization patterns when phenotypically distinct strains are mixed. For example, defying naive expectations, both models and experiments found that strains engineered to overexpress different and incompatible TraAB adhesins nevertheless form mixed circular aggregates. Therefore, this work provides key mechanistic insights into M. xanthus social interactions and demonstrates how local cell contacts induce emergent collective behaviors by millions of cells. IMPORTANCE In many species, large populations exhibit emergent behaviors whereby all related individuals move in unison. For example, fish in schools can all dart in one direction simultaneously to avoid a predator. Currently, it is impossible to explain how such animals recognize kin through brain cognition and elicit such behaviors at a molecular level. However, microbes also recognize kin and exhibit emergent collective behaviors that are experimentally tractable. Here, using a model social bacterium, we engineer dispersed individuals to organize into synchronized collectives that create emergent patterns. With experimental and mathematical approaches, we explain how this occurs at both molecular and population levels. The results demonstrate how the combination of local physical interactions triggers intracellular signaling, which in turn leads to emergent behaviors on a population scale.

Independent control of mean and noise by convolution of gene expression distributions.

Gene expression noise can reduce cellular fitness or facilitate processes such as alternative metabolism, antibiotic resistance, and differentiation. Unfortunately, efforts to study the impacts of noise have been hampered by a scaling relationship between noise and expression level from individual promoters. Here, we use theory to demonstrate that mean and noise can be controlled independently by expressing two copies of a gene from separate inducible promoters in the same cell. We engineer low and high noise inducible promoters to validate this result in Escherichia coli, and develop a model that predicts the experimental distributions. Finally, we use our method to reveal that the response of a promoter to a repressor is less sensitive with higher repressor noise and explain this result using a law from probability theory. Our approach can be applied to investigate the effects of noise on diverse biological pathways or program cellular heterogeneity for synthetic biology applications.

Quantification of Myxococcus xanthus Aggregation and Rippling Behaviors: Deep-Learning Transformation of Phase-Contrast into Fluorescence Microscopy Images.

Myxococcus xanthus bacteria are a model system for understanding pattern formation and collective cell behaviors. When starving, cells aggregate into fruiting bodies to form metabolically inert spores. During predation, cells self-organize into traveling cell-density waves termed ripples. Both phase-contrast and fluorescence microscopy are used to observe these patterns but each has its limitations. Phase-contrast images have higher contrast, but the resulting image intensities lose their correlation with cell density. The intensities of fluorescence microscopy images, on the other hand, are well-correlated with cell density, enabling better segmentation of aggregates and better visualization of streaming patterns in between aggregates; however, fluorescence microscopy requires the engineering of cells to express fluorescent proteins and can be phototoxic to cells. To combine the advantages of both imaging methodologies, we develop a generative adversarial network that converts phase-contrast into synthesized fluorescent images. By including an additional histogram-equalized output to the state-of-the-art pix2pixHD algorithm, our model generates accurate images of aggregates and streams, enabling the estimation of aggregate positions and sizes, but with small shifts of their boundaries. Further training on ripple patterns enables accurate estimation of the rippling wavelength. Our methods are thus applicable for many other phenotypic behaviors and pattern formation studies.

A synthetic circuit for buffering gene dosage variation between individual mammalian cells.

Precise control of gene expression is critical for biological research and biotechnology. However, transient plasmid transfections in mammalian cells produce a wide distribution of copy numbers per cell, and consequently, high expression heterogeneity. Here, we report plasmid-based synthetic circuits - Equalizers - that buffer copy-number variation at the single-cell level. Equalizers couple a transcriptional negative feedback loop with post-transcriptional incoherent feedforward control. Computational modeling suggests that the combination of these two topologies enables Equalizers to operate over a wide range of plasmid copy numbers. We demonstrate experimentally that Equalizers outperform other gene dosage compensation topologies and produce as low cell-to-cell variation as chromosomally integrated genes. We also show that episome-encoded Equalizers enable the rapid generation of extrachromosomal cell lines with stable and uniform expression. Overall, Equalizers are simple and versatile devices for homogeneous gene expression and can facilitate the engineering of synthetic circuits that function reliably in every cell.

Theoretical Analysis Reveals the Cost and Benefit of Proofreading in Coronavirus Genome Replication.

Severe acute respiratory syndrome coronaviruses have unusually large RNA genomes replicated by a multiprotein complex containing an RNA-dependent RNA polymerase (RdRp). Exonuclease activity enables the RdRp complex to remove wrongly incorporated bases via proofreading, a process not utilized by other RNA viruses. However, it is unclear why the RdRp complex needs proofreading and what the associated trade-offs are. Here we investigate the interplay among the accuracy, speed, and energetic cost of proofreading in the RdRp complex using a kinetic model and bioinformatics analysis. We find that proofreading nearly optimizes the rate of functional virus production. However, we find that further optimization would lead to a significant increase in the proofreading cost. Unexpected importance of the cost minimization is further supported by other global analyses. We speculate that cost optimization could help avoid cell defense responses. Thus, proofreading is essential for the production of functional viruses, but its rate is limited by energy costs.

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

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

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

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