Functional characteristics of a double positive feedback loop coupled with autorepression

We study the functional characteristics of a two-gene motif consisting of a double positive feedback loop and an autoregulatory negative feedback loop. The motif appears in the gene regulatory network controlling the functional activity of pancreatic $\beta$-cells. The model exhibits bistability and hysteresis in appropriate parameter regions. The two stable steady states correspond to low (OFF state) and high (ON state) protein levels respectively. Using a deterministic approach, we show that the region of bistability increases in extent when the copy number of one of the genes is reduced from two to one. The negative feedback loop has the effect of reducing the size of the bistable region. Loss of a gene copy, brought about by mutations, hampers the normal functioning of the $\beta$-cells giving rise to the genetic disorder, maturity-onset diabetes of the young (MODY). The diabetic phenotype makes its appearance when a sizable fraction of the $\beta$-cells is in the OFF state. Using stochastic simulation techniques, we show that, on reduction of the gene copy number, there is a transition from the monostable ON to the ON state in the bistable region of the parameter space. Fluctuations in the protein levels, arising due to the stochastic nature of gene expression, can give rise to transitions between the ON and OFF states. We show that as the strength of autorepression increases, the ON$\to$OFF state transitions become less probable whereas the reverse transitions are more probable. The implications of the results in the context of the occurrence of MODY are pointed out..

💡 Research Summary

The paper investigates a two‑gene regulatory motif that combines a double positive feedback loop with an autoregulatory negative feedback loop, a configuration found in the network governing pancreatic β‑cell activity. Using deterministic ordinary differential equations, the authors first identify the steady‑state structure of the system. They show that, depending on the strengths of the positive feedback (parameter α) and the negative autorepression (parameter κ), the circuit can exhibit either a single stable “ON” state (high protein concentration) or a bistable regime where a low “OFF” state and a high “ON” state coexist. Hysteresis is observed: the system’s trajectory depends on its history, a hallmark of memory in gene‑regulatory networks.

A key focus is the effect of gene copy number. When the copy number of one gene is reduced from two to one (mimicking a loss‑of‑function mutation), the deterministic analysis reveals an expansion of the bistable region. Although the total transcriptional output is halved, the nonlinear activation functions cause the system to become more susceptible to bistability, meaning a larger fraction of parameter space supports coexistence of ON and OFF states. This finding links gene dosage reduction to an increased likelihood that a substantial subset of β‑cells will reside in the OFF state, providing a mechanistic explanation for the onset of maturity‑onset diabetes of the young (MODY).

The negative autoregulatory loop has the opposite effect: increasing κ shrinks the bistable region and can eliminate bistability altogether, driving the system toward a single high‑expression state. This reflects the classic role of negative feedback in dampening fluctuations and enhancing robustness.

To capture stochastic effects inherent in gene expression, the authors perform Gillespie simulations of the full reaction network. In the two‑copy scenario, the system remains predominantly in the ON state, with rare spontaneous transitions to OFF. When the copy number is reduced to one, intrinsic noise dramatically raises the probability of OFF excursions even when deterministic parameters predict a monostable ON regime. The simulations quantify transition rates: as κ increases, OFF→ON transitions become more frequent while ON→OFF transitions become markedly less likely. Thus, stronger autorepression biases the system toward the high‑expression phenotype, reducing the chance that noise will push a cell into the dysfunctional OFF state.

Overall, the study integrates deterministic bifurcation analysis with stochastic simulation to dissect how gene dosage and feedback architecture shape the dynamical landscape of a biologically relevant circuit. The results suggest that loss of a gene copy sensitizes β‑cells to stochastic fluctuations, promoting phenotypic heterogeneity that can manifest as MODY. Conversely, enhancing negative autoregulation could be a potential strategy to stabilize the ON state and mitigate disease risk. The work underscores the importance of considering both deterministic and stochastic mechanisms when linking molecular network design to cellular phenotypes and disease.