Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.
Deep Dive into Bridging Time Scales in Cellular Decision Making with a Stochastic Bistable Switch.
Cellular transformations which involve a significant phenotypical change of the cell’s state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism’s lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the conside
The dynamics of biological systems span a wide range of temporal and spatial scales. The interactions among dynamical properties on different scales govern the overall behavior of the biological system, and thus form an important area of computational research in biology [18]. A particularly interesting question in this context is how the behavior on a slow time scale emerges mechanistically from the dynamics on fast time scales. For example, how do cell population dynamics in tissues, which may evolve on a time scale of months, years or even decades, originate from the dynamics of the underlying gene regulatory networks, with a time scale of just minutes to hours?
In this work, we aim at bridging the time scale from gene regulation to cellular transformation processes on the tissue or cell population level. We specifically consider cellular transformation processes based on a bistable biochemical switch. Such switches have two distinct stable stationary states, and the cell initiates a transformation when the switch changes from one stable state to the other one. Bistable switches have previously been used to model a large number of cellular transformation events, such as progression through cell cycle arrest in the maturation of Xenopus oocytes [11,10] or initiation of programmed cell death [6] and cellular differentiation [4] in higher organisms. Most models for these systems are constructed as deterministic models, and thus an external stimulus is required to induce changes in the switch’s state.
Here, we consider transformation processes which apparently do not require any external stimulus to be initiated, and which still follow reliable temporal characteristics. Reliable thereby means that in a large population of cells, the number of cells that have already initiated the transformation can be described deterministically with high accuracy. We propose a generic transformation process, where a phenotypical change in the state of a cell is initiated as soon as a bistable biochemical switch changes its internal state. In previous studies, random switching caused by internal fluctuations is usually attributed to pathological events [15]. In the mechanism proposed here, random switching has a regular physiological function.
A striking example for the kind of transformation processes we aim to describe is involved in mammalian oocyte maturation. In mammalian females, all or almost all of the oocytes that will ovulate through the organism’s life-span are already present at birth or shortly thereafter as a population of so-called primordial follicles. Throughout the organism’s reproductive life, follicles undergo the primordial to primary transition, which marks the start of a development process that will eventually lead to either ovulation or removal of the oocyte through atresia [12,26]. In this way, there is a steady supply of mature follicles for ovulation, while the pool of primordial follicles is gradually depleted. The mechanisms through which the follicle transition is initiated are largely unknown, although a number of ovarian factors that may be relevant have been identified experimentally [23,2,21]. Importantly, the transition seems to be regulated locally in the ovary, and not through the endocrine system [1]. An astonishing observation in this process is that in one follicle, the transition may occur already a few months after generation of the primordial follicle pool, while another follicle may stay several decades (for organisms with a sufficiently long lifespan) in the resting stage before growth is initiated. From the medical side, a misregulation of this process is implicated in premature ovarian failure due to follicle depletion, which is a major reason for infertility in human females.
By way of a case study, we apply the proposed transformation mechanism to the problem of growth initiation in ovarian follicles. Including also cell-cell interactions supported by experimental evidence, we obtain a physiologically plausible model for this process, showing very good agreement with human clinical data on a scale of several decades.
The model of a bistable switch that we use is based on a positive feedback loop between two components. Consider a biochemical reaction network involving the two molecular species X and Y. Mathematically, the temporal evolution of the amounts of the two species is described with the ordinary differential equation
where x and y denote the amounts of X and Y, respectively. The vector (x, y) T will be referred to as the microstate of the biochemical reaction system. Ultrasensitivity, which is required to achieve bistability [11], is generated by the Hill-type production rates v 2 and v 4 .
In the sequel, we will assume that the molecular species X and Y represent gene transcripts, and the amounts x and y indicate the respective transcript copy number. The nominal parameter values that we use are given in Table 1. For simplicity, we assume that the parameters
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