Molecular Noise and Cooperativity Drive Balanced Fate Decisions and Clonal Heterogeneity in Bistable Gene Circuits

Molecular Noise and Cooperativity Drive Balanced Fate Decisions and Clonal Heterogeneity in Bistable Gene Circuits | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Molecular Noise and Cooperativity Drive Balanced Fate Decisions and Clonal Heterogeneity in Bistable Gene Circuits Yathu Krishna, Y K This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7548630/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Genetically identical cell populations frequently exhibit remarkable phenotypic variation, a feature that is commonly ascribed to the interaction of molecular noise with nonlinear gene-regulatory networks. Here, we examine the traditional genetic toggle switch as a simple model for stochastic dynamics-based bistable cell-fate decisions. We used a dry-lab method to model clonal populations of 100 − 10,000 "cells" as autonomous realizations of noisy toggle-switch dynamics, taking into account noise throughout temporal evolution as well as initial condition heterogeneity. Cells deterministically resolve into one of two mutually exclusive states (A-dominant or B-dominant) when noise is absent. Clonal heterogeneity was recapitulated by adding molecular noise during dynamics, which significantly changed the results and produced balanced percentages of A- and B-dominant cells. The mean fractions of A-dominant cells stabilized around ~ 0.5 +/- 0.03 across replicates, indicating a shift from entirely deterministic outcomes (σ = 0) to noise-balanced destinies (σ ~ 0.15–0.6) according to a systematic sweep of noise amplitude (σ). This phenomenon was found to be consistent across several noise models (additive versus multiplicative), production strengths (α = 3–7), and Hill coefficients (n = 2–6), according to robustness analyses. Additionally, population-level fractions remained constant when scaling up to 10,000 cells, suggesting that the effect is not a result of a limited sample size. Collectively, our findings demonstrate that molecular noise can serve as a balancing mechanism that diversifies destiny in clonal populations rather than only upsetting bistability. This establishes a conceptual connection between microbial persistence, gene-circuit multistability, and differentiation processes in which genetically identical cells take on various phenotypes. Our results demonstrate how crucial stochastic modeling is for revealing broad rules of fate diversification in biological systems with noise. Systems Biology Computational Biology Bioinformatics genetic toggle switch bistability stochastic dynamics molecular noise cell fate decision clonal heterogeneity noise-induced diversification Hill coefficient robustness analysis population heterogeneity gene regulatory networks Introduction One of the biggest mysteries in developmental and systems biology is how genetically identical cells decide to have different fates. The idea of molecular noise—random variations in gene expression resulting from both internal and external sources—is essential to this issue [ 1 , 2 ]. While extrinsic noise includes environmental and cellular-level variability, such as unequal molecular partitioning, metabolic fluctuations, or organelle distributions, intrinsic noise is caused by the discrete and stochastic nature of molecular interactions, such as transcriptional bursting [ 3 , 4 ]. Biological precision has long been thought to be hampered by noise. Nevertheless, there is growing evidence that noise might serve a useful purpose by encouraging phenotypic variety in clonal populations. For instance, noise increases the population's potential for adaptation in B. subtilis by assisting cells in stochastically adopting competence states under stress [ 5 ]. Similar to this, noise in genetic circuits during development can produce spatial waves of differentiation or sharpen morphogen borders that deviate from deterministic predictions [ 6 ]. The genetic toggle switch, which is made up of two genes that are mutually repressive, is a crucial feature in representing binary fate decisions. Bipolarity, a system with two persistent expression states produced by this architecture, allows for switch-like reactions to graded signals and memory-like behavior [ 7 ]. The fundamentals of bistability were established by traditional theoretical investigations of toggle switches under deterministic dynamics [ 8 , 9 ]. Researchers have recently studied the effects of noise on these switches, finding that depending on whether the fluctuations are additive or multiplicative, intrinsic or extrinsic, noise can synchronize populations or alter switching dynamics in addition to inducing state-switching [ 10 , 11 ]. However, there are still unanswered questions about how noise type, noise amplitude, and circuit parameters interact to influence population-level results. In particular: What is the impact of noise on the population fractions that settle in each attractor? To what extent do these effects hold true for circuit factors such as cooperativity or production rate? Do various noise models (such as multiplicative versus additive) produce behavior that is qualitatively similar? We conducted a thorough dry-lab investigation to simulate stochastic gene-expression patterns in clonal populations of toggle switches in order to address these problems. We implemented stochastic (Euler–Maruyama) and deterministic simulations using a basic ODE framework with Hill-type repression. By comparing noise models and increasing cell population size to achieve statistical robustness, we examined the ways in which noise drives fate diversification by sweeping across noise amplitudes (σ), cooperativity values (Hill coefficients), and production strengths. To find parameter regimes where toggles produce stable 50:50 fate splits, determine whether noise only breaks bistability or if it can also serve as a balancing force that promotes robust heterogeneity, and test the generality of these phenomena across biologically relevant configurations were our goals. Materials and methods 2.1 Mathematical model of the toggle switch We modeled the canonical synthetic genetic toggle switch originally introduced by Gardner et al. [ 7 ] and further developed in theoretical treatments of bistability [ 8 – 10 ]. Proteins A and B, two transcriptional regulators that are mutually repressive, make up the toggle switch. Deterministic Hill-function kinetics were used to depict their dynamics, together with an extra baseline leak term to account for low-level constitutive expression. The following were the definitions of the governing ordinary differential equations (ODEs): where K is the repression threshold, n is the Hill coefficient that indicates cooperativity, α is the maximum production rate, and β is the degradation/dilution rate. In line with other modeling studies of toggle dynamics [17–20], parameter values were used. Unless otherwise noted, we investigated Hill coefficients between n = 2 and 6 and utilized α = 5.0, β = 1.0, K = 1.0, leak = 0.02. 2.2 Incorporation of stochasticity The Euler–Maruyama integration scheme [ 12 , 17 ] was used to incorporate stochastic variations in gene expression, which are known to be crucial in determining cell fate [ 1 , 4 , 13 , 14 ]. Two formulations of noise were taken into consideration: Extrinsic variations that are not influenced by the molecular copy number are represented by additive noise. The intrinsic oscillations that scale with protein quantity are represented by multiplicative noise [ 1 , 13 , 16 ]. In both cases, noise terms were Gaussian with zero mean and variance scaled by \(\:\:\sigma\:\sqrt{dt}\) , where σ denotes the noise amplitude and dt the integration timestep. Simulations were performed over t = 20–50 units with dt = 0.05–0.1. Each trajectory was initiated with symmetric concentrations (A = 1.0, B = 1.0 unless otherwise stated). 2.3 Single-cell simulations and population sweeps According to other single-cell modeling research [ 1 , 13 , 15 ], separate trajectories were simulated for each parameter set to resemble a population of cells. Depending on whether short or comprehensive parameter sweeps were carried out, we used N = 200–1000 simulated cells. We varied among these virtual populations in: Noise amplitude (σ): from 0.0 to 0.6, capturing regimes from deterministic bistability to noise-driven switching [ 12 , 16 ]. Hill coefficient (n): between 2 and 6, reflecting different levels of cooperativity in repression Noise models: additive vs multiplicative. Three categories—A-dominant, B-dominant, or Balanced (neither species surpassing threshold)—were created by recording the final state for each trajectory. In accordance with previous toggle analyses, classification criteria were established at concentrations greater than 2.0 [ 7 , 9 ]. 2.4 Quantification of outcomes We calculated the fraction of cells adopting A-dominant fates as a function of σ, n, and noise model in order to assess the robustness of toggling behavior. These data were combined into summary tables and displayed using heatmaps to show global patterns of robustness and line graphs to monitor trends across parameters. Furthermore, we ran prolonged simulations ( T = 50) with N = 500 cells at σ = 0.0 and σ = 0.6 to resolve distributions of single-cell outcomes under low vs. high noise conditions. In order to compare the variance and modality of fate distributions under various stochastic regimes, the final protein A concentrations were combined and displayed using violin plots. 2.5 Computational implementation Python 3.10 was used to implement all simulations, with Matplotlib/Seaborn being used for visualization, pandas for data collection, and NumPy for numerical computations. Using proprietary code that implemented the Euler–Maruyama approach, stochastic integration was carried out and verified against previous stochastic toggle investigations [ 9 , 10 , 12 , 17 ]. Results We first verified that, in the absence of stochasticity, the conventional toggle switch model is bistable. Trajectories converged to an A-high/B-low or A-low/B-high state, which is compatible with classical bistability, after beginning with unequal initial conditions (Gardner et al., 2000; Cherry and Adler, 2000). A metastable balanced state was instead produced with symmetric initial circumstances (A = 1.0, B = 1.0), with final protein concentrations close to A = 1.325, B = 1.325. This demonstrates that two dominant attractors, separated by a shallow unstable basin, are admitted into the deterministic system. The Euler-Maruyama system, which introduced stochasticity, demonstrated resilient fate diversification. The population solely accepted the B-dominant fate (fraction A-dominant = 0.0) in deterministic simulations (σ = 0.0). But even with low noise (σ = 0.075), results were almost symmetric (fraction A-dominant = 0.485), and this balance held true for noise levels ranging from 0.075 to 0.600, with fractions varying from 0.46 to 0.55 (Table 1 ). Therefore, in order to overcome deterministic bias and restore population-level symmetry in fate outcomes, stochasticity was both required and sufficient. Table 1. Fractions of A- vs. B-dominant fates across noise amplitudes. Next, we evaluated the robustness of these results to changes in sampling size and system settings. The same qualitative trend was replicated in large-scale simulations with N = 10,000 cells: fractions were balanced (A = 0.489, B = 0.511) under noise (σ = 0.3) but all cells selected B-dominant destinies under deterministic dynamics (σ = 0.0). At σ = 0.3, we changed α between 3.0, 5.0, and 7.0 to investigate sensitivity to production strength (N = 2000). Results were roughly balanced in each instance (fraction A-dominant = 0.496–0.512), suggesting that destiny distributions may withstand modest variations in the maximal expression rate. Qualitatively identical responses were found when comparing multiplicative and additive noise models. For instance, multiplicative noise under the identical conditions produced 0.000 at σ = 0.0 and gradually balanced fractions at higher σ, whereas additive noise at σ = 0.15 produced fraction A = 0.505 with Hill coefficient n = 2. These findings highlight that, while the balance of switching may rely on accurate noise scaling, both intrinsic and extrinsic noise are adequate to diversity toggling outcomes. The main conclusion is that noise flattens deterministic bias and restores fate symmetry in bistable toggle circuits under all conditions. Long-term simulations supported this, with violin plot distributions displaying unimodal, skewed results at σ = 0.0 and bimodal, balanced populations at σ = 0.6. This illustrates how in toggle-switch networks, stochasticity serves as a symmetry-restoring mechanism. Discussion Stochastic fluctuations significantly alter the functioning of the genetic toggle switch, as demonstrated by our simulations. The system showed a substantial bias toward the B-dominant attractor in the strictly deterministic domain, with symmetric beginning conditions convergent to an unstable, metastable balanced state. The intrinsic nature of bistable toggling dynamics, where shallow separatrices frequently tilt trajectories toward one attractor, is compatible with this asymmetry in fate result [ 7 – 9 ]. It was both necessary and sufficient to introduce stochasticity in order to restore population-level symmetry. Results were diversified by even extremely modest noise (σ = 0.075), resulting in almost equal shares of A- and B-dominant states. Throughout the entire range of noise amplitudes examined (σ = 0.075–0.600), this balance remained stable, with A-dominant fractions only varying between about 0.46 and 0.55. In line with previous theoretical predictions that noise might "rescue" hidden attractors or broaden destiny distributions [ 12 , 14 , 16 ], these findings highlight the function of noise as a symmetry-restoring mechanism in bistable gene circuits. Crucially, this equilibrium held up well when the system's parameters changed. Diversification was not eliminated by changes in production rate (α = 3.0–7.0), and the results from the multiplicative (intrinsic-like) and additive (extrinsic-like) noise models were qualitatively comparable. This implies that the impact represents a general characteristic of stochastic toggle dynamics rather than being reliant on fine-tuning. The concept that symmetry restoration by noise is an architectural element of the toggle switch rather than an artifact of particular parameter choices is further supported by the uniformity across Hill coefficients. Additional mechanistic understanding was obtained by long-term simulations. The unimodal, skewed distributions produced by deterministic trajectories demonstrated the supremacy of a single attractor. In contrast, violin plots revealed that outcome distributions became bimodal and balanced at high noise levels (σ = 0.6). This demonstrates how stochasticity changes the gene expression landscape, turning a biased deterministic system into one that produces balanced but diverse populations. All things considered, these results are consistent with more general ideas in synthetic biology and systems: stochasticity is an active promoter of robustness and adaptability rather than just a disruption [ 1 – 4 , 13 ]. Such noise-driven diversification may foster evolutionary flexibility and robustness in natural systems, and it may be used to create circuits that retain variability in synthetic settings. Conclusion In this work, we showed that the behavior of the synthetic genetic toggle switch is significantly changed by stochasticity. The addition of noise was both required and sufficient to restore balanced fate distributions, whereas deterministic simulations produced biased results dominated by a single attractor. This effect demonstrated its resilience as a general characteristic of toggle circuits, as it was consistent across noise amplitudes, repression cooperativity, production speeds, and noise models. These findings highlight how stochasticity in genetic networks can be advantageous. Noise can serve as a symmetry-restoring mechanism that increases variation at the population level rather than being a disruptive force. This has ramifications for synthetic biology, where noise might be used to create circuits with controllable heterogeneity, as well as natural systems, where adaptability is based on variety. References Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Stochastic gene expression in a single cell. Science 297(5584):1183–1186. 10.1126/science.1070919 Johnston RJ Jr, Desplan C (2010) Stochastic mechanisms of cell fate specification that yield random or robust outcomes. Annu Rev Cell Dev Biol 26:689–719. 10.1146/annurev-cellbio-100109-104113 Johnston IG (2019) Organelle variability and cell-to-cell heterogeneity in eukaryotic gene expression. J Cell Sci 132(5):jcs220491. 10.1242/jcs.220491 Paulsson J (2004) Summing up the noise in gene networks. Nature 427(6973):415–418. 10.1038/nature02257 Süel GM, Garcia-Ojalvo J, Liberman LM, Elowitz MB (2006) An excitable gene regulatory circuit induces transient cellular differentiation. Nature 440(7083):545–550. 10.1038/nature04588 Perez-Carrasco R, Guerrero P, Briscoe J, Page KM (2016) Intrinsic noise profoundly alters the dynamics and steady state of morphogen-controlled bistable genetic switches. PLoS Comput Biol 12(10):e1005154. 10.1371/journal.pcbi.1005154 Gardner TS, Cantor CR, Collins JJ (2000) Construction of a genetic toggle switch in Escherichia coli . Nature 403(6767):339–342. 10.1038/35002131 Cherry JL, Adler FR (2000) How to make a biological switch. J Theor Biol 203(2):117–133. 10.1006/jtbi.1999.1065 Tian T, Burrage K (2006) Stochastic models for regulatory networks of the genetic toggle switch. PNAS USA 103(22):8372–8377. 10.1073/pnas.0507818103 Roma DM, O’Flanagan RA, Ruckenstein AE, Sengupta AM, Mukhopadhyay R (2005) Optimal path to epigenetic switching. Phys Rev E 71(1):011902. 10.1103/PhysRevE.71.011902 Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361. 10.1021/j100540a008 Higham DJ (2001) An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev 43(3):525–546. 10.1137/S0036144500378302 Shahrezaei V, Swain PS (2008) Analytical distributions for stochastic gene expression. PNAS USA 105(45):17256–17261. 10.1073/pnas.0803850105 Kepler TB, Elston TC (2001) Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys J 81(6):3116–3136. 10.1016/S0006-3495(01)75949-8 Walczak AM, Mugler A, Wiggins CH (2012) Analytic methods for modeling stochastic regulatory networks. Methods Mol Biol 880:273–322. 10.1007/978-1-61779-833-7_14 Mehta P, Mukhopadhyay R, Wingreen NS (2008) Exponential sensitivity of noise-driven switching in genetic networks. Phys Biol 5(2):026005. 10.1088/1478-3975/5/2/026005 Kloeden PE, Platen E (1992) Numerical Solution of Stochastic Differential Equations. Springer, Berlin. 10.1007/978-3-662-12616-5 Additional Declarations The authors declare no competing interests. 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The idea of molecular noise\u0026mdash;random variations in gene expression resulting from both internal and external sources\u0026mdash;is essential to this issue [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. While extrinsic noise includes environmental and cellular-level variability, such as unequal molecular partitioning, metabolic fluctuations, or organelle distributions, intrinsic noise is caused by the discrete and stochastic nature of molecular interactions, such as transcriptional bursting [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Biological precision has long been thought to be hampered by noise. Nevertheless, there is growing evidence that noise might serve a useful purpose by encouraging phenotypic variety in clonal populations. For instance, noise increases the population's potential for adaptation in B. subtilis by assisting cells in stochastically adopting competence states under stress [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Similar to this, noise in genetic circuits during development can produce spatial waves of differentiation or sharpen morphogen borders that deviate from deterministic predictions [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. The genetic toggle switch, which is made up of two genes that are mutually repressive, is a crucial feature in representing binary fate decisions. Bipolarity, a system with two persistent expression states produced by this architecture, allows for switch-like reactions to graded signals and memory-like behavior [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. The fundamentals of bistability were established by traditional theoretical investigations of toggle switches under deterministic dynamics [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Researchers have recently studied the effects of noise on these switches, finding that depending on whether the fluctuations are additive or multiplicative, intrinsic or extrinsic, noise can synchronize populations or alter switching dynamics in addition to inducing state-switching [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eHowever, there are still unanswered questions about how noise type, noise amplitude, and circuit parameters interact to influence population-level results. In particular:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eWhat is the impact of noise on the population fractions that settle in each attractor?\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eTo what extent do these effects hold true for circuit factors such as cooperativity or production rate?\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eDo various noise models (such as multiplicative versus additive) produce behavior that is qualitatively similar?\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eWe conducted a thorough dry-lab investigation to simulate stochastic gene-expression patterns in clonal populations of toggle switches in order to address these problems. We implemented stochastic (Euler\u0026ndash;Maruyama) and deterministic simulations using a basic ODE framework with Hill-type repression. By comparing noise models and increasing cell population size to achieve statistical robustness, we examined the ways in which noise drives fate diversification by sweeping across noise amplitudes (σ), cooperativity values (Hill coefficients), and production strengths. To find parameter regimes where toggles produce stable 50:50 fate splits, determine whether noise only breaks bistability or if it can also serve as a balancing force that promotes robust heterogeneity, and test the generality of these phenomena across biologically relevant configurations were our goals.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1 Mathematical model of the toggle switch\u003c/h2\u003e\n \u003cp\u003eWe modeled the canonical synthetic genetic toggle switch originally introduced by Gardner et al. [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e] and further developed in theoretical treatments of bistability [\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e]. Proteins A and B, two transcriptional regulators that are mutually repressive, make up the toggle switch. Deterministic Hill-function kinetics were used to depict their dynamics, together with an extra baseline leak term to account for low-level constitutive expression. The following were the definitions of the governing ordinary differential equations (ODEs):\u003c/p\u003e\n \u003cp\u003e\u003cimg 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\" style=\"width: 274px; height: 108.099px;\" width=\"274\" height=\"108.099\"\u003e\u003c/p\u003e\n \u003cp\u003ewhere K is the repression threshold, n is the Hill coefficient that indicates cooperativity, \u0026alpha; is the maximum production rate, and \u0026beta; is the degradation/dilution rate. In line with other modeling studies of toggle dynamics [17\u0026ndash;20], parameter values were used. Unless otherwise noted, we investigated Hill coefficients between n\u0026thinsp;=\u0026thinsp;2 and 6 and utilized \u0026alpha;\u0026thinsp;=\u0026thinsp;5.0, \u0026beta;\u0026thinsp;=\u0026thinsp;1.0, K\u0026thinsp;=\u0026thinsp;1.0, leak\u0026thinsp;=\u0026thinsp;0.02.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2 Incorporation of stochasticity\u003c/h2\u003e\n \u003cp\u003eThe Euler\u0026ndash;Maruyama integration scheme [\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e] was used to incorporate stochastic variations in gene expression, which are known to be crucial in determining cell fate [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e]. Two formulations of noise were taken into consideration:\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eExtrinsic variations that are not influenced by the molecular copy number are represented by additive noise.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eThe intrinsic oscillations that scale with protein quantity are represented by multiplicative noise [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003eIn both cases, noise terms were Gaussian with zero mean and variance scaled by\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\sigma\\:\\sqrt{dt}\\)\u003c/span\u003e\u003c/span\u003e, where \u0026sigma; denotes the noise amplitude and \u003cem\u003edt\u003c/em\u003e the integration timestep. Simulations were performed over \u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20\u0026ndash;50 units with dt\u0026thinsp;=\u0026thinsp;0.05\u0026ndash;0.1. Each trajectory was initiated with symmetric concentrations (A\u0026thinsp;=\u0026thinsp;1.0, B\u0026thinsp;=\u0026thinsp;1.0 unless otherwise stated).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3 Single-cell simulations and population sweeps\u003c/h2\u003e\n \u003cp\u003eAccording to other single-cell modeling research [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e], separate trajectories were simulated for each parameter set to resemble a population of cells. Depending on whether short or comprehensive parameter sweeps were carried out, we used \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;200\u0026ndash;1000 simulated cells. We varied among these virtual populations in:\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eNoise amplitude (\u0026sigma;): from 0.0 to 0.6, capturing regimes from deterministic bistability to noise-driven switching [\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eHill coefficient (n): between 2 and 6, reflecting different levels of cooperativity in repression\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eNoise models: additive vs multiplicative.\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n \u003cp\u003eThree categories\u0026mdash;A-dominant, B-dominant, or Balanced (neither species surpassing threshold)\u0026mdash;were created by recording the final state for each trajectory. In accordance with previous toggle analyses, classification criteria were established at concentrations greater than 2.0 [\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e2.4 Quantification of outcomes\u003c/h2\u003e\n \u003cp\u003eWe calculated the fraction of cells adopting A-dominant fates as a function of \u0026sigma;, n, and noise model in order to assess the robustness of toggling behavior. These data were combined into summary tables and displayed using heatmaps to show global patterns of robustness and line graphs to monitor trends across parameters. Furthermore, we ran prolonged simulations (\u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;50) with \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;500 cells at \u0026sigma;\u0026thinsp;=\u0026thinsp;0.0 and \u0026sigma;\u0026thinsp;=\u0026thinsp;0.6 to resolve distributions of single-cell outcomes under low vs. high noise conditions. In order to compare the variance and modality of fate distributions under various stochastic regimes, the final protein A concentrations were combined and displayed using violin plots.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n \u003ch2\u003e2.5 Computational implementation\u003c/h2\u003e\n \u003cp\u003ePython 3.10 was used to implement all simulations, with Matplotlib/Seaborn being used for visualization, pandas for data collection, and NumPy for numerical computations. Using proprietary code that implemented the Euler\u0026ndash;Maruyama approach, stochastic integration was carried out and verified against previous stochastic toggle investigations [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eWe first verified that, in the absence of stochasticity, the conventional toggle switch model is bistable. Trajectories converged to an A-high/B-low or A-low/B-high state, which is compatible with classical bistability, after beginning with unequal initial conditions (Gardner et al., 2000; Cherry and Adler, 2000). A metastable balanced state was instead produced with symmetric initial circumstances (A\u0026thinsp;=\u0026thinsp;1.0, B\u0026thinsp;=\u0026thinsp;1.0), with final protein concentrations close to A\u0026thinsp;=\u0026thinsp;1.325, B\u0026thinsp;=\u0026thinsp;1.325. This demonstrates that two dominant attractors, separated by a shallow unstable basin, are admitted into the deterministic system. The Euler-Maruyama system, which introduced stochasticity, demonstrated resilient fate diversification. The population solely accepted the B-dominant fate (fraction A-dominant\u0026thinsp;=\u0026thinsp;0.0) in deterministic simulations (\u0026sigma;\u0026thinsp;=\u0026thinsp;0.0). But even with low noise (\u0026sigma;\u0026thinsp;=\u0026thinsp;0.075), results were almost symmetric (fraction A-dominant\u0026thinsp;=\u0026thinsp;0.485), and this balance held true for noise levels ranging from 0.075 to 0.600, with fractions varying from 0.46 to 0.55 (Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Therefore, in order to overcome deterministic bias and restore population-level symmetry in fate outcomes, stochasticity was both required and sufficient.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1.\u003c/strong\u003e Fractions of A- vs. B-dominant fates across noise amplitudes.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" width=\"584\" height=\"552\"\u003e\u003c/p\u003e\n\u003cp\u003eNext, we evaluated the robustness of these results to changes in sampling size and system settings. The same qualitative trend was replicated in large-scale simulations with N\u0026thinsp;=\u0026thinsp;10,000 cells: fractions were balanced (A\u0026thinsp;=\u0026thinsp;0.489, B\u0026thinsp;=\u0026thinsp;0.511) under noise (\u0026sigma;\u0026thinsp;=\u0026thinsp;0.3) but all cells selected B-dominant destinies under deterministic dynamics (\u0026sigma;\u0026thinsp;=\u0026thinsp;0.0). At \u0026sigma;\u0026thinsp;=\u0026thinsp;0.3, we changed \u0026alpha; between 3.0, 5.0, and 7.0 to investigate sensitivity to production strength (N\u0026thinsp;=\u0026thinsp;2000). Results were roughly balanced in each instance (fraction A-dominant\u0026thinsp;=\u0026thinsp;0.496\u0026ndash;0.512), suggesting that destiny distributions may withstand modest variations in the maximal expression rate. Qualitatively identical responses were found when comparing multiplicative and additive noise models. For instance, multiplicative noise under the identical conditions produced 0.000 at \u0026sigma;\u0026thinsp;=\u0026thinsp;0.0 and gradually balanced fractions at higher \u0026sigma;, whereas additive noise at \u0026sigma;\u0026thinsp;=\u0026thinsp;0.15 produced fraction A\u0026thinsp;=\u0026thinsp;0.505 with Hill coefficient n\u0026thinsp;=\u0026thinsp;2. These findings highlight that, while the balance of switching may rely on accurate noise scaling, both intrinsic and extrinsic noise are adequate to diversity toggling outcomes. The main conclusion is that noise flattens deterministic bias and restores fate symmetry in bistable toggle circuits under all conditions. Long-term simulations supported this, with violin plot distributions displaying unimodal, skewed results at \u0026sigma;\u0026thinsp;=\u0026thinsp;0.0 and bimodal, balanced populations at \u0026sigma;\u0026thinsp;=\u0026thinsp;0.6. This illustrates how in toggle-switch networks, stochasticity serves as a symmetry-restoring mechanism.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eStochastic fluctuations significantly alter the functioning of the genetic toggle switch, as demonstrated by our simulations. The system showed a substantial bias toward the B-dominant attractor in the strictly deterministic domain, with symmetric beginning conditions convergent to an unstable, metastable balanced state. The intrinsic nature of bistable toggling dynamics, where shallow separatrices frequently tilt trajectories toward one attractor, is compatible with this asymmetry in fate result [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. It was both necessary and sufficient to introduce stochasticity in order to restore population-level symmetry. Results were diversified by even extremely modest noise (σ\u0026thinsp;=\u0026thinsp;0.075), resulting in almost equal shares of A- and B-dominant states. Throughout the entire range of noise amplitudes examined (σ\u0026thinsp;=\u0026thinsp;0.075\u0026ndash;0.600), this balance remained stable, with A-dominant fractions only varying between about 0.46 and 0.55. In line with previous theoretical predictions that noise might \"rescue\" hidden attractors or broaden destiny distributions [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], these findings highlight the function of noise as a symmetry-restoring mechanism in bistable gene circuits. Crucially, this equilibrium held up well when the system's parameters changed. Diversification was not eliminated by changes in production rate (α\u0026thinsp;=\u0026thinsp;3.0\u0026ndash;7.0), and the results from the multiplicative (intrinsic-like) and additive (extrinsic-like) noise models were qualitatively comparable. This implies that the impact represents a general characteristic of stochastic toggle dynamics rather than being reliant on fine-tuning. The concept that symmetry restoration by noise is an architectural element of the toggle switch rather than an artifact of particular parameter choices is further supported by the uniformity across Hill coefficients. Additional mechanistic understanding was obtained by long-term simulations. The unimodal, skewed distributions produced by deterministic trajectories demonstrated the supremacy of a single attractor. In contrast, violin plots revealed that outcome distributions became bimodal and balanced at high noise levels (σ\u0026thinsp;=\u0026thinsp;0.6). This demonstrates how stochasticity changes the gene expression landscape, turning a biased deterministic system into one that produces balanced but diverse populations. All things considered, these results are consistent with more general ideas in synthetic biology and systems: stochasticity is an active promoter of robustness and adaptability rather than just a disruption [\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Such noise-driven diversification may foster evolutionary flexibility and robustness in natural systems, and it may be used to create circuits that retain variability in synthetic settings.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn this work, we showed that the behavior of the synthetic genetic toggle switch is significantly changed by stochasticity. The addition of noise was both required and sufficient to restore balanced fate distributions, whereas deterministic simulations produced biased results dominated by a single attractor. This effect demonstrated its resilience as a general characteristic of toggle circuits, as it was consistent across noise amplitudes, repression cooperativity, production speeds, and noise models. These findings highlight how stochasticity in genetic networks can be advantageous. Noise can serve as a symmetry-restoring mechanism that increases variation at the population level rather than being a disruptive force. This has ramifications for synthetic biology, where noise might be used to create circuits with controllable heterogeneity, as well as natural systems, where adaptability is based on variety.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eElowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Stochastic gene expression in a single cell. Science 297(5584):1183\u0026ndash;1186. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1126/science.1070919\u003c/span\u003e\u003cspan address=\"10.1126/science.1070919\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJohnston RJ Jr, Desplan C (2010) Stochastic mechanisms of cell fate specification that yield random or robust outcomes. 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Springer, Berlin. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/978-3-662-12616-5\u003c/span\u003e\u003cspan address=\"10.1007/978-3-662-12616-5\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"genetic toggle switch, bistability, stochastic dynamics, molecular noise, cell fate decision, clonal heterogeneity, noise-induced diversification, Hill coefficient, robustness analysis, population heterogeneity, gene regulatory networks","lastPublishedDoi":"10.21203/rs.3.rs-7548630/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7548630/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGenetically identical cell populations frequently exhibit remarkable phenotypic variation, a feature that is commonly ascribed to the interaction of molecular noise with nonlinear gene-regulatory networks. Here, we examine the traditional genetic toggle switch as a simple model for stochastic dynamics-based bistable cell-fate decisions. We used a dry-lab method to model clonal populations of 100\u0026thinsp;\u0026minus;\u0026thinsp;10,000 \"cells\" as autonomous realizations of noisy toggle-switch dynamics, taking into account noise throughout temporal evolution as well as initial condition heterogeneity. Cells deterministically resolve into one of two mutually exclusive states (A-dominant or B-dominant) when noise is absent. Clonal heterogeneity was recapitulated by adding molecular noise during dynamics, which significantly changed the results and produced balanced percentages of A- and B-dominant cells. The mean fractions of A-dominant cells stabilized around ~\u0026thinsp;0.5 +/- 0.03 across replicates, indicating a shift from entirely deterministic outcomes (σ\u0026thinsp;=\u0026thinsp;0) to noise-balanced destinies (σ\u0026thinsp;~\u0026thinsp;0.15\u0026ndash;0.6) according to a systematic sweep of noise amplitude (σ). This phenomenon was found to be consistent across several noise models (additive versus multiplicative), production strengths (α\u0026thinsp;=\u0026thinsp;3\u0026ndash;7), and Hill coefficients (n\u0026thinsp;=\u0026thinsp;2\u0026ndash;6), according to robustness analyses. Additionally, population-level fractions remained constant when scaling up to 10,000 cells, suggesting that the effect is not a result of a limited sample size. Collectively, our findings demonstrate that molecular noise can serve as a balancing mechanism that diversifies destiny in clonal populations rather than only upsetting bistability. This establishes a conceptual connection between microbial persistence, gene-circuit multistability, and differentiation processes in which genetically identical cells take on various phenotypes. Our results demonstrate how crucial stochastic modeling is for revealing broad rules of fate diversification in biological systems with noise.\u003c/p\u003e","manuscriptTitle":"Molecular Noise and Cooperativity Drive Balanced Fate Decisions and Clonal Heterogeneity in Bistable Gene Circuits","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-09 06:55:28","doi":"10.21203/rs.3.rs-7548630/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"34560ef6-8af1-4919-8b71-fdb8bc850648","owner":[],"postedDate":"September 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":54290016,"name":"Systems Biology"},{"id":54290017,"name":"Computational Biology"},{"id":54290018,"name":"Bioinformatics"}],"tags":[],"updatedAt":"2025-09-09T06:55:28+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-09 06:55:28","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7548630","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7548630","identity":"rs-7548630","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}