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Critical molecular events that control conformational transitions in most allosteric proteins are ill-defined. The mannose-specific FimH protein of Escherichia coli is a prototypic bacterial adhesin that switches from an ‘inactive’ low-affinity state (LAS) to an ‘active’ high-affinity state (HAS) conformation allosterically upon mannose binding and mediates shear-dependent catch bond adhesion. Here we identify a novel type of antibody that acts as a kinetic trap and prevents the transition between conformations in both directions. Disruption of the allosteric transitions significantly slows FimH’s ability to associate with mannose and blocks bacterial adhesion under dynamic conditions. FimH residues critical for antibody binding form a compact epitope that is located away from the mannose-binding pocket and is structurally conserved in both states. A larger antibody-FimH contact area is identified by NMR and contains residues Leu-34 and Val-35 that move between core-buried and surface-exposed orientations in opposing directions during the transition. Replacement of Leu-34 with a charged glutamic acid stabilizes FimH in the LAS conformation and replacement of Val-35 with glutamic acid traps FimH in the HAS conformation. The antibody is unable to trap the conformations if Leu-34 and Val-35 are replaced with a less bulky alanine. We propose that these residues act as molecular toggle switches and that the bound antibody imposes a steric block to their reorientation in either direction, thereby restricting concerted repacking of side chains that must occur to enable the conformational transition. Residues homologous to the FimH toggle switches are highly conserved across a diverse family of fimbrial adhesins. Replacement of predicted switch residues reveals that another E. coli adhesin, galactose-specific FmlH, is allosteric and can shift from an inactive to an active state. Our study shows that allosteric transitions in bacterial adhesins depend on toggle switch residues and that an antibody that blocks the switch effectively disables adhesive protein function., Author summary To bind their ligands, allosteric proteins shift between ‘inactive’ and ‘active’ states, but molecular details of the conformational changes during the transition are often unclear. We describe a monoclonal antibody against the mannose-specific bacterial adhesin, FimH, that blocks the conformational transition in both directions. The antibody-trapped LAS and HAS conformations of FimH are unable to mediate bacterial adhesion under dynamic shear conditions. We propose that the conformational trapping involves a steric block of the core-to-surface switching of certain residues which is critical for the allosteric transitions. Furthermore, we demonstrate that the allosteric switches are structurally and functionally conserved across a broad spectrum of bacterial fimbrial adhesins.

Gene regulatory networks exhibiting Boolean behaviour, e.g. AND, OR or XOR, have been routinely designed for years. However, achieving more sophisticated functions, such as control or computation, usually requires sequential circuits or so-called state machines. For such a circuit, outputs depend both on inputs and the current state of the system. Although it is still possible to design such circuits by analogy with digital electronics, some particularities of biology make the task trickier. The impact of two of them, namely the stochasticity of biological processes and the inhomogeneity in the response of regulation mechanisms, are assessed in this paper. Numerical simulations performed in two use cases point out high risks of malfunctions even for designed GRNs functional from a theoretical point of view. Several solutions to improve reliability of such systems are also discussed.

The mechanisms and design principles of regulatory systems establishing stable polarized protein patterns within cells are well studied. However, cells can also dynamically control their cell polarity. Here, we ask how an upstream signaling system can switch the orientation of a polarized pattern. We use a mathematical model of a core polarity system based on three proteins as the basis to study different mechanisms of signal-induced polarity switching. The analysis of this model reveals four general classes of switching mechanisms with qualitatively distinct behaviors: the transient oscillator switch, the reset switch, the prime-release switch, and the push switch. Each of these regulatory mechanisms effectively implements the function of a spatial toggle switch, however with different characteristics in their nonlinear and stochastic dynamics. We identify these characteristics and also discuss experimental signatures of each type of switching mechanism., Author summary Cell polarity is key to processes such as cell growth, division, differentiation, and motility. Polarity arises from asymmetric distributions of proteins in the cell. How asymmetric patterns develop from uniform protein distributions, has been studied extensively. However, it is less clear how cells can switch such protein patterns in response to a signal. Here, we identify four qualitatively different mechanisms for how a polar protein pattern can be reversed. For each mechanism, we describe experimental signatures permitting their identification in natural systems. By providing possible regulatory circuits for these mechanisms, we also offer blueprints for synthetic implementations of switchable cell polarity, in artificial or engineered cells.

Gene regulatory networks (GRNs) are complex systems in which many genes regulate mutually to adapt the cell state to environmental conditions. In addition to function, the GRNs possess several kinds of robustness. This robustness means that systems do not lose their functionality when exposed to disturbances such as mutations or noise, and is widely observed at many levels in living systems. Both function and robustness have been acquired through evolution. In this respect, GRNs utilized in living systems are rare among all possible GRNs. In this study, we explored the fitness landscape of GRNs and investigated how robustness emerged in highly-fit GRNs. We considered a toy model of GRNs with one input gene and one output gene. The difference in the expression level of the output gene between two input states, “on” and “off”, was considered as fitness. Thus, the determination of the fitness of a GRN was based on how sensitively it responded to the input. We employed the multicanonical Monte Carlo method, which can sample GRNs randomly in a wide range of fitness levels, and classified the GRNs according to their fitness. As a result, the following properties were found: (1) Highly-fit GRNs exhibited bistability for intermediate input between “on” and “off”. This means that such GRNs responded to two input states by using different fixed points of dynamics. This bistability emerges necessarily as fitness increases. (2) These highly-fit GRNs were robust against noise because of their bistability. In other words, noise robustness is a byproduct of high fitness. (3) GRNs that were robust against mutations were not extremely rare among the highly-fit GRNs. This implies that mutational robustness is readily acquired through the evolutionary process. These properties are universal irrespective of the evolutionary pathway, because the results do not rely on evolutionary simulation., Author summary Living systems have developed through a long history of Darwinian evolution. They acquired characteristic properties distinct from other physical systems; one is biological function. Another important property, which is overlooked by non-experts, is robustness to noise and mutation. Here, robustness means that a system does not lose its functionality when exposed to disturbances. Then, how do they relate to each other? In this paper, we explored this question using a toy model of gene regulatory networks (GRNs). While evolutionary simulations are usually used for such purposes, we instead generated GRNs randomly and classified them according to functionality. By requiring sensitive responses to environmental change as a function, we found that bistability emerges as a common property of highly-functional GRNs. Since this property does not depend on a particular evolutionary pathway, if the evolution was rewound and repeated over and over again, phenotypes with the same property would always evolve. At the same time, such bistable GRNs were robust to noise. We also found that GRNs robust to mutation were not extremely rare among the highly-functional GRNs. This implies that mutational robustness would be readily acquired through evolution.

We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they are inter-connected. We use Maximum Caliber as an inference principle. The combinatorial challenge of high-dimensional data is handled using two different approximations to the pairwise couplings. We show two proofs of principle: in a nonlinear genetic toggle switch circuit, and in a toy neural network., Author summary Of major scientific interest are networks—the internet, commercial supply chains, social media, traffic, biochemical reactions inside cells, the neurons in the brain, and many others. Often, the challenge is to measure a few rates at a limited number of nodes of the network, and to try to infer more information about a complex network and its flow patterns under different conditions. Here we devise a mathematical method to infer the dynamics of such networks, given only limited experimental information. The tool best suited for this purpose is the Principle of Maximum Caliber, but it also requires that we handle the challenge of the high-dimensionality of real-world nets. We give two levels of approximation that reduce this to the simpler problem of inferring the dynamics of each node individually. We show that these approximations provide novel insights and accurate inferences and are promising for drawing inferences about large-scale biophysical and other networks.

The earliest models for how morphogen gradients guide embryonic patterning failed to account for experimental observations of temporal refinement in gene expression domains. Following theoretical and experimental work in this area, dynamic positional information has emerged as a conceptual framework to discuss how cells process spatiotemporal inputs into downstream patterns. Here, we show that diffusion determines the mathematical means by which bistable gene expression boundaries shift over time, and therefore how cells interpret positional information conferred from morphogen concentration. First, we introduce a metric for assessing reproducibility in boundary placement or precision in systems where gene products do not diffuse, but where morphogen concentrations are permitted to change in time. We show that the dynamics of the gradient affect the sensitivity of the final pattern to variation in initial conditions, with slower gradients reducing the sensitivity. Second, we allow gene products to diffuse and consider gene expression boundaries as propagating wavefronts with velocity modulated by local morphogen concentration. We harness this perspective to approximate a PDE model as an ODE that captures the position of the boundary in time, and demonstrate the approach with a preexisting model for Hunchback patterning in fruit fly embryos. We then propose a design that employs antiparallel morphogen gradients to achieve accurate boundary placement that is robust to scaling. Throughout our work we draw attention to tradeoffs among initial conditions, boundary positioning, and the relative timescales of network and gradient evolution. We conclude by suggesting that mathematical theory should serve to clarify not just our quantitative, but also our intuitive understanding of patterning processes., Author Summary In many developmental systems, cells interpret spatial gradients of chemical morphogens to produce gene expression boundaries in exact positions. The simplest mathematical models for positional information rely on threshold detection, but such models are not robust to variations in the morphogen gradient or initial protein concentrations. Furthermore, these models fail to account for experimental results showing dynamic shifts in boundary placement and increased boundary precision over time. Here, we argue that dynamic positional information is interpreted differently by a bistable patterning system depending upon whether gene expression products diffuse. We explore two mathematical methods to analyze pattern refinement with and without diffusion, and discuss design tradeoffs among precision, placement, accuracy, and timescale. We suggest that future research into dynamic positional information would benefit from perspectives that link local (cellular) and global (patterning) behaviors, as well as from mathematical theory that builds our intuitive understanding alongside more data-driven approaches.

Heritable epigenetic changes underlie the ability of cells to differentiate into distinct cell types. Here, we demonstrate that the fungal pathogen Candida tropicalis exhibits multipotency, undergoing stochastic and reversible switching between three cellular states. The three cell states exhibit unique cellular morphologies, growth rates, and global gene expression profiles. Genetic analysis identified six transcription factors that play key roles in regulating cell differentiation. In particular, we show that forced expression of Wor1 or Efg1 transcription factors can be used to manipulate transitions between all three cell states. A model for tristability is proposed in which Wor1 and Efg1 are self-activating but mutually antagonistic transcription factors, thereby forming a symmetrical self-activating toggle switch. We explicitly test this model and show that ectopic expression of WOR1 can induce white-to-hybrid-to-opaque switching, whereas ectopic expression of EFG1 drives switching in the opposite direction, from opaque-to-hybrid-to-white cell states. We also address the stability of induced cell states and demonstrate that stable differentiation events require ectopic gene expression in combination with chromatin-based cues. These studies therefore experimentally test a model of multistate stability and demonstrate that transcriptional circuits act synergistically with chromatin-based changes to drive cell state transitions. We also establish close mechanistic parallels between phenotypic switching in unicellular fungi and cell fate decisions during stem cell reprogramming., Author Summary Formation of different cell types accompanies development in multicellular organisms and increases population-level diversity in unicellular species. In both instances, binary cell fate decisions are often determined by toggle switches, in which two master regulators compete to define one of two possible cell states. However, much less is known about multistate transitions due to the lack of experimentally tractable systems. Here, we demonstrate that the fungal pathogen Candida tropicalis undergoes reversible and heritable transitions between three stable cell states. We propose that tristability is achieved by a symmetric self-activating toggle switch and test this model by ectopic expression of the two master transcription factors. Significantly, manipulating the expression of the two master regulators induced all six possible state-to-state transitions in the tristable system. Furthermore, we found that stable inheritance of transcriptionally induced states only occurred if combined with inhibition of a histone deacetylase activity. Together, these results define the genetic regulation of a tristable switch and demonstrate that synergistic genetic cues (one transcriptional and one chromatin-based) drive epigenetic inheritance in a unicellular species. We also discuss striking parallels between cell fate decisions in yeast and the regulation of cell differentiation events in higher eukaryotes.

Phenotypical variability in the absence of genetic variation often reflects complex energetic landscapes associated with underlying gene regulatory networks (GRNs). In this view, different phenotypes are associated with alternative states of complex nonlinear systems: stable attractors in deterministic models or modes of stationary distributions in stochastic descriptions. We provide theoretical and practical characterizations of these landscapes, specifically focusing on stochastic Slow Promoter Kinetics (SPK), a time scale relevant when transcription factor binding and unbinding are affected by epigenetic processes like DNA methylation and chromatin remodeling. In this case, largely unexplored except for numerical simulations, adiabatic approximations of promoter kinetics are not appropriate. In contrast to the existing literature, we provide rigorous analytic characterizations of multiple modes. A general formal approach gives insight into the influence of parameters and the prediction of how changes in GRN wiring, for example through mutations or artificial interventions, impact the possible number, location, and likelihood of alternative states. We adapt tools from the mathematical field of singular perturbation theory to represent stationary distributions of Chemical Master Equations for GRNs as mixtures of Poisson distributions and obtain explicit formulas for the locations and probabilities of metastable states as a function of the parameters describing the system. As illustrations, the theory is used to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, such as toggle switches in isolation or in communicating populations, a synthetic oscillator, and a trans-differentiation network., Author summary Regulatory mechanisms of slow gene activation and deactivation play a role in triggering and sustaining phenotypically heterogeneous, yet genetically identical (clonal), cellular populations in a wide variety of biological processes. These range from embryonic development and hematopoietic cell differentiation to the emergence of tumor heterogeneity and consequent resistance to therapy. In contrast to previously reported numerical simulations, we introduce in this paper a theoretical and computational approach to the characterization of the multi-attractor dynamic landscape of gene networks with slow promoter kinetics. We obtain precise formulas that are then illustrated through applications to several systems biology models including a trans-differentiation network and a communicating population of synthetic toggle switches.

We present a new modeling and computational tool that computes rigorous summaries of network dynamics over large sets of parameter values. These summaries, organized in a database, can be searched for observed dynamics, e.g., bistability and hysteresis, to discover parameter regimes over which they are supported. We illustrate our approach on several networks underlying the restriction point of the cell cycle in humans and yeast. We rank networks by how robustly they support hysteresis, which is the observed phenotype. We find that the best 6-node human network and the yeast network share similar topology and robustness of hysteresis, in spite of having no homology between the corresponding nodes of the network. Our approach provides a new tool linking network structure and dynamics., Author summary To summarize our understanding of how genes, their products and other cellular actors interact with each other, we often employ networks to describe their interactions. However, networks do not fully specify how the underlying biological system behaves in different conditions, nor how such response evolves in time. We present a new modeling and computational approach that allows us to compute and collect summaries of network dynamics for large sets of parameter values. We can then search these summaries for all observed behavior. We illustrate our approach on networks that govern entry to the cell cycle in humans and yeast. We rank networks based on how robustly they exhibit the experimentally observed behavior of hysteresis. We find similarities in network structure of the best ranked networks in yeast and humans, which are not explained by a common ancestry. Our approach provides a tool linking network structure and the behavior of the underlying system.

One of the most important roles of cells is performing their cellular tasks properly for survival. Cells usually achieve robust functionality, for example, cell-fate decision-making and signal transduction, through multiple layers of regulation involving many genes. Despite the combinatorial complexity of gene regulation, its quantitative behavior has been typically studied on the basis of experimentally verified core gene regulatory circuitry, composed of a small set of important elements. It is still unclear how such a core circuit operates in the presence of many other regulatory molecules and in a crowded and noisy cellular environment. Here we report a new computational method, named random circuit perturbation (RACIPE), for interrogating the robust dynamical behavior of a gene regulatory circuit even without accurate measurements of circuit kinetic parameters. RACIPE generates an ensemble of random kinetic models corresponding to a fixed circuit topology, and utilizes statistical tools to identify generic properties of the circuit. By applying RACIPE to simple toggle-switch-like motifs, we observed that the stable states of all models converge to experimentally observed gene state clusters even when the parameters are strongly perturbed. RACIPE was further applied to a proposed 22-gene network of the Epithelial-to-Mesenchymal Transition (EMT), from which we identified four experimentally observed gene states, including the states that are associated with two different types of hybrid Epithelial/Mesenchymal phenotypes. Our results suggest that dynamics of a gene circuit is mainly determined by its topology, not by detailed circuit parameters. Our work provides a theoretical foundation for circuit-based systems biology modeling. We anticipate RACIPE to be a powerful tool to predict and decode circuit design principles in an unbiased manner, and to quantitatively evaluate the robustness and heterogeneity of gene expression., Author summary Cells are able to robustly carry out their essential biological functions, possibly because of multiple layers of tight regulation via complex, yet well-designed, gene regulatory networks involving a substantial number of genes. State-of-the-art genomics technology has enabled the mapping of these large gene networks, yet it remains a tremendous challenge to elucidate their design principles and the regulatory mechanisms underlying their biological functions such as signal processing and decision-making. One of the key barriers is the absence of accurate kinetics for the regulatory interactions, especially from in vivo experiments. To this end, we have developed a new computational modeling method, Random Circuit Perturbation (RACIPE), to explore the dynamic behaviors of gene regulatory circuits without the requirement of detailed kinetic parameters. RACIPE takes a network topology as the input, and generates an unbiased ensemble of models with varying kinetic parameters. Each model is subjected to simulation, followed by statistical analysis for the ensemble. We tested RACIPE on several gene circuits, and found that the predicted gene expression patterns from all of the models converge to experimentally observed gene state clusters. We expect RACIPE to be a powerful method to identify the role of network topology in determining network operating principles.