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

In gene regulatory circuits, resource competition plays a crucial role in understanding the dynamics of gene expression within the host cell [1][2][3][4]. Asymmetric utilization of significant cellular resources (such as ribosomes, RNA polymerase, proteases, etc.) can disrupt the cellular economy and affect genetic functions, impacting overall cellular homeostasis [5,6]. Many researchers demonstrated how growth feedback with circuit interaction results in unexpected outcomes [7][8][9][10]. If we consider the case of cancer specifically, then it should be noted that the uncontrolled growth of cancer cells demands increasing amounts of cellular resources, oxygen, nutrients, and growth factors [11,12]. Thus, the metabolic burden by growth exerts a diverse impact on gene circuits [7,13]. In tumor systems, competition can occur for cellular resources as well as for nutrients in the early stages [14,15], as diffusion allows only approximately 1 mm depth to reach from surrounding blood capillaries [16]. Thus, the primary site of cancer/tumor cells actually consists of some densely packed cells competing for scarce resources [17]. Metastasis, the migration of cells from their primary location to a secondary location [18,19], is also regulated by this resource scarcity in the primary location [20,21]. This motility does not always ensure cell fitness outside the primary location, as the majority of cells die rather than initiate a secondary tumor, but this migration effectively ensures the fitness of the primary tumor with a chance of secondary formation as well [22]. Further insights into the role of nutrient limitation in cancer evolvement have been established in [23], and resource heterogeneity in cancer systems have been pointed out [24]. Like many other diseases [25,26], cancer is also driven by inherent nonlinearity and multistable dynamics, which causes EMT (Epithelial-to-Mesenchymal Transition)driven cellular plasticity. Cellular plasticity refers to the ability of cells to reversibly transition between distinct phenotypic states in response to internal regulatory fluctuations or external environmental cues, without permanent genetic alterations. EMT is one of the most prominent manifestations of such plasticity, wherein stationary epithelial cells acquire mesenchymal characteristics. Classical bistable switch, the simplest depiction of multistable dynamics in genetic systems, is essentially a type of gene regulatory network consisting of two mutually inhibiting transcription factors (say U and V). This circuit is associated with binary cell fate decision i.e. existence of U-high/V-low and U-low/V-high state [27][28][29]. For example, in cancer, evidence shows that epithelial-mesenchymal transition (EMT) is regulated by mutually inhibitory miRNA-transcription factor (TF) circuits, such as the miR-200/ZEB and miR-34/SNAIL networks [30,31]. In these systems, high miRNA expression promotes epithelial traits, whereas high transcription-factor expression represses E-cadherin (a hallmark of the epithelial phenotype) and promotes mesenchymal traits. Recently, along with two extreme phenotypes, the existence of an intermediate hybrid E/M state (cluster cell migration) has been established [32]. In the hybrid state, cancer cells do not lose their epithelial property completely but gain the migratory trait [33,34]. This dual nature significantly enhances their malignant potential, enhancing their capacity for metastasis, and driving more aggressive cancer progression [31,35,36]. Recently it has also been explored that there are multiple hybrid states depending on the ratio of epithelial and mesenchymal traits the cells can exhibit [37,38]. The origin of these hybrid states have been modeled using the existence of strong autoregulations [31], multi-level boolean models [39], poor vascularization [40], hypoxic stress in the tumor microenvironment [41] etc. These observations highlight that EMT-associated phenotypic plasticity is not a static or purely binary process, but rather reflects the ability of cancer cells to reversibly transition among epithelial, mesenchymal, and intermediate hybrid states [31]. Such plasticity enables cells to dynamically adapt to fluctuating microenvironmental cues [42]. Importantly, this adaptive behavior manifests across both space and time within tumors: spatially due to gradients of nutrients, oxygen, and growth factors, and temporally due to dynamic reprogramming of gene regulatory networks and cell-cell interactions. This spatio-temporal plasticity is a key contributor to tumor heterogeneity, metastatic progression, and treatment resistance [43][44][45]. In this paper, our analysis suggests that a simple bistable genetic switch, operating under limited intracellular gene expression resources, can give rise to multiple intermediate phenotypes similar to those observed in the cancer system. Establishing the connection of resource limitation to the growth of the cell (which are fundament

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