Bistability to Quad-stability: Emergence of Hybrid Phenotypes & Enhanced Spatio-temporal Plasticity in Presence of Host-Circuit Coupling

TL;DR

This paper investigates how growth-induced resource competition interacts with diffusion to produce multistability and spatiotemporal cellular plasticity in cancer-like gene circuits. Using a mutual inhibitory loop between $U$ and $V$ with nonlinear dilution from host growth ($K_{GR}$) and resource coupling, the authors perform bifurcation analysis and extend the model to a 2D reaction-diffusion system with $D_U$ and $D_V$. Results show a progression from bistability to tristability to quad-stability as growth feedback strengthens, revealing two intermediate hybrid EMT states (hybrid I and II) that transiently stabilize before diffusion drives the system toward epithelial or mesenchymal extremes. The work highlights how diffusion rate, symmetry of diffusion, and resource limitation jointly shape spatiotemporal EMT-like phenotypic landscapes, offering mechanistic insight into cancer metastasis and potential avenues for targeting state transitions in therapy.

Abstract

In the context of multistability driven diseases, like cancer, spatiotemporal plasticity plays a significant role to achieve a spectrum of phenotypic variations. The interplay between gene regulatory networks and environmental factors, such as resource competition and spatial diffusion, plays a crucial role in determining cellular behaviour and phenotypic heterogeneity. Though reaction diffusion frameworks have been widely applied in developmental biology, less attention has been paid to the simultaneous effects of resource competition and growth feedback on spatial organization. In this paper, we observed that a bistable genetic circuit under high resource competition due to growth feedback gives rise to multiple emergent phenotypes, as observed in cancer systems. Furthermore, we observed how spatial diffusion coupled with intrinsic nonlinearity can drive the emergence of distinct spatial dynamics over time. The observed spatiotemporal plasticity can also be driven by the comparative stability of the fixed points, diffusivity, and asymmetry of diffusion. Our findings highlight that growth-induced resource competition combined with diffusion can provide deeper insights into metastasis and cancer progression.

Figures (9)

• Figure 1: (a) Schematic representation of the mutual inhibitory loop between the bistable genetic switch and cellular growth. Proteins $U$ and $V$ mutually repress each other, forming a bistable genetic circuit, which is further coupled to growth feedback through metabolic burden and dilution effects, thereby establishing a mutual inhibitory loop. (b) Schematic nullcline diagram for $U$ (blue) and $V$ (red). Their intersections correspond to the system’s steady states, yielding a total of seven fixed points. Filled circles denote stable fixed points, while hollow circles indicate unstable fixed points.
• Figure 2: (a)-(c) Bifurcation diagram of concentration of protein $U$ (in log scale) with variation of $K_{1u}$ (in log scale) for different growth rates: (a) $K_{GR}=5$ (b) $K_{GR}=8.65$ (c) $K_{GR}=9.25$; Corresponding parameters are: $K_{0u}=K_{0v}=0.005,\; K_{1v}=0.4,\; K_u=K_v=0.09,\; d_{0u}=d_{0v}=0.9,\; K_c=1.6,\; n=2,\; m=2.$ (d) Bifurcation diagram of concentration of protein $U$ (in log scale) with variation of $K_{GR}$ for a fixed protein synthesis rate ($K_{1u}\,=0.4$). Other parameters are: $K_{0u}=K_{0v}=0.005,\; K_{1v}=0.4,\; K_u=K_v=0.09,\; d_{0u}=d_{0v}=0.9,\; K_c=1.8,\; n=2,\; m=2.$ Blue lines and red lines indicate the stable and unstable states, respectively, and yellow circles represent the bifurcation points.
• Figure 3: Spatio-temporal pattern formation (in the presence of diffusion) for protein $U$. Corresponding parameters are: $K_{0u}=K_{0v}=0.005, K_{1u}=K_{1v}=0.4, K_u=K_v=0.09, d_{0u}=d_{0v}=0.9, K_c=1.6,K_{GR}=9.25, n=2, m=2,\; \epsilon_1=\epsilon_2=3$ Diffusion coefficients are $D_U$=$D_V=0.04$. Snapshots are taken after time: (a)$10$ (b)$100$ (c)$500$ (d)$800$ (e)$1000$ (f)$2000$. The colors of associated colorbars indicate different concentrations of protein U.
• Figure 4: Bistability vs. Quad-stability in spatio-temporal dynamics for protein $U$. (a) The value of $K_{GR}\,=5$ results in bistability as observed in the classical genetic switch. (b) Increasing $K_{GR}\,=9.25$ leads to multistability in the system. Snapshots are taken after time $500$; The parameters are same as Fig. \ref{['pattern']} .
• Figure 5: Gaussian stacked distributions illustrating the temporal evolution of protein $U$ concentration. (a) Probability distributions of protein $U$ at different time points ($t= 0,\, 100,\, 500,\, 2000$). The x-axis and y-axis represent the concentration of protein $U$ and the probability of cells at that specific concentration, respectively. (b) Temporal evolution of Gaussian distributions corresponding to the four phenotypic states: epithelial, hybrid-I, hybrid-II, and mesenchymal. Parameter values are taken as: $K_{0u}=K_{0v}=0.005,\; K_{1u}=K_{1v}=0.4,\; K_u=K_v=0.09,\; d_{0u}=d_{0v}=0.9,\; K_c=1.6,\;K_{GR}=9.25,\; n=m=2,\; D_U=D_V=0.04$.