Bistability in Gene Regulation: Simulating Positive Feedback and Toggle Circuits Using Python and Hill Functions

Krishna Y K, Y.

doi:10.1101/2025.08.05.668746

Home/Archive/bioRxiv

bioRxiv · 10.1101/2025.08.05.668746

Bistability in Gene Regulation: Simulating Positive Feedback and Toggle Circuits Using Python and Hill Functions

Krishna Y K, Y.

View original source ↗Export metadata ↓

Abstract

Cellular decision-making relies heavily on bistable gene regulatory networks, which allow systems to respond to internal or external stimuli by switching between several stable expression states. Processes like cell differentiation, epigenetic memory, and the creation of artificial biological switches all depend on these dynamics. In this work, we introduce a simple and reproducible Python framework for modeling bistability in genetic feedback systems by means of ordinary differential equations (ODEs) driven by Hill functions. We employ two fundamental motifs, both of which are recognized for their ability to generate bistable behavior: a two-gene mutual inhibition toggle switch and a single-gene positive feedback loop. We investigate the effects of different Hill coefficients, production rates, and initial expression levels on system dynamics by numerical integration using SciPy. Our simulations show phase-plane convergence to several attractors, map expression outcomes over a grid of beginning circumstances, and illustrate the onset of bistability above a key Hill threshold. The delicate reliance of final states on cooperativity and beginning values is further demonstrated by heatmaps and bifurcation-like graphs. For accessibility, all code is hosted at Google Colab and is written in open-source Python. This study promotes research and teaching in synthetic biology, systems biology, and computational modeling while providing a simple yet effective computational framework for investigating the fundamentals of gene circuit bistability.

Explore related subjects

synthetic biology Preprint

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Krishna Y K, Y.. 2025-08-05. Bistability in Gene Regulation: Simulating Positive Feedback and Toggle Circuits Using Python and Hill Functions. https://doi.org/10.1101/2025.08.05.668746

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

bioRxiv2026

Gene expression noise is reduced in communicating synthetic cell populations

A major goal in bottom-up synthetic biology is the construction of multicellular synthetic systems capable of coordinated and robust collective behaviours. However, robustness is often limited by noise and variability arising from increased molecular complexity. Whilst communication has been implemented in synthetic multi-cellular systems, the ability for communication to suppress cell free gene expression variability in populations of synthetic cells remain unexplored. To address this, we encapsulated the Lux and Las quorum sensing gene circuits in lipid vesicles under cell-free conditions to test the effect of communication on reducing cell-free gene expression variability across the population. Our results show that communication, limiting expression resources, and membrane surface effects can reduce gene expression variability. Resource limited Gillespie simulations for transcription and translation show that communication-mediated coupling reduces population-level expression noise under constrained and excess resource conditions. Together, our work provides simple strategies to reduce gene expression variability and thereby improve robustness in synthetic multicellular systems, an important criteria for the future applications of synthetic cells.

synthetic biology↗

bioRxiv2026

Boolean Logic-responsive FRET Biosensors via Genetically Encoded Autonomous Compilation

Forster resonance energy transfer (FRET) is commonly used to monitor protein-protein interactions in situ. The high spatiotemporal resolution and facile implementation inside complex molecular environments have spearheaded FRET's widespread adoption in biosensing. Despite these advantages, current FRET biosensors are largely restricted to the detection of the presence/absence of individual inputs and are thus unable to sense several multiplexable inputs simultaneously within complex milieu of biological environments. In this work, we introduce a generalizable strategy to construct genetically encoded protein-based FRET biosensors capable of recognizing multiple inputs following Boolean logic-type (YES/OR/AND) operations. These topologically specified FRET sensors powerfully expand the input capacity in sensing protein-protein interactions while providing a user-programmable platform for monitoring heterogeneous biological activities both in vitro and in living cells.

synthetic biology↗

bioRxiv2026

AI-Guided Multi-Objective Engineering of Glucoamylase Enables Acidification-Free Starch Saccharification

Glucoamylase is essential for industrial starch saccharification, but the limited thermostability and near-neutral pH tolerance of fungal glucoamylases necessitate cooling and acidification of liquefied starch. Here, we developed an artificial intelligence-guided strategy to simultaneously improve the thermostability, pH tolerance, and catalytic activity of glucoamylase from Penicillium oxalicum (PoGA). Two property-specific machine-learning models, CASPE-T and CASPE-A, identified substitutions associated with thermostability and pH tolerance, respectively. Experimental screening identified beneficial substitutions in 11 of 21 CASPE-T and 12 of 22 CASPE-A candidates. Folding-energy-guided recombination integrated the two traits while maintaining structural compatibility. The optimal variant, PoGA T513E/Q305N, exhibited 2.21-fold higher specific activity than the wild type, with half-life extended from 22.3 to 57.9 min at 60 degrees C and from 16.6 to 64.7 min at pH 8.0. Molecular dynamics simulations attributed these improvements to reinforcement of high-occupancy hydrogen-bonding networks, suppression of conformational fluctuations in the linker and carbohydrate-binding module, enhanced long-range dynamic coordination, and preservation of a compact catalytic architecture. At 60 degrees C and pH 6.5 without acidification, PoGA T513E/Q305N produced 219.9 g/L glucose and achieved 89.1% starch conversion, 31.4% higher than the wild type. This work provides an efficient framework for multi-objective enzyme engineering and sustainable starch biorefining.

synthetic biology↗