Abstract
Biological systems are spatially organized. This microscopic heterogeneity has been shown to produce emergent complex behaviors such as bistability. Even though the connection between spatiality and dynamic response is essential to understand biological output, its robustness and extent has not been sufficiently explored. This work focuses on a previously described system which is composed of two monostable modules acting on different cellular compartments and sharing species through linear shuttling reactions. One of the two main purposes of this paper is to quantify the frequency of occurrence of bistability throughout the parameter space and to identify which parameters and in which value ranges control the emergence and the properties of bistability. We found that a very small fraction of the sampled parameter space produced a bistable response. Most importantly, shuttling parameters were among the most influential ones to control this property. The other goal of this paper is to simplify the same system as much as possible without losing compartment-induced bistability. This procedure provided a simplified model that still connects two monostable systems by a reduced set of linear shuttling reactions that circulates all the species around the two compartments. Bistable systems are one of the main building blocks of more complex behaviors such as oscillations, memory, and digitalization. Therefore, we expect that the proposed minimal system provides insight into how these behaviors can arise from compartmentalization.
Highlights
As a first building block we considered a single phosphorylation-dephosphorylation cycle modeled with Michaelis-Menten reactions, which has been shown to be monostable[3]: S
We studied the behavior of the system using the “going-up and coming-down” analysis with stimulus ranging from 10−3 to 103 over roughly 100,000 different randomly selected parameters sets sampled by Latin Hypercube Sampling (LHS)
Starting from a previously described system which is composed of two monostable modules acting on different cellular compartments and sharing species through shuttling reactions, we explored its vast parameter space in order to assess the robustness of the emergent bistability
Summary
This effect eventually feeds back generating a new increase in the concentration of the original species that, in turn, causes an even larger increase These motifs are common in networks governing cellular behaviors such as proliferation, differentiation, and apoptosis that exhibit all-or-none responses, in which cells commit—usually irreversibly—to one specific fate over a discrete set of possibilities. It has been shown that bistability can arise in a dual phosphorylation-dephosphorylation cycle with a non-processive, distributive mechanism for the enzymes This implies that a MAPK cascade formed by coupling these structures can exhibit bistable behavior, even in the absence of imposed positive feedback loops. From a mathematical point of view and describing the process in the simplest possible way, shuttling in and out of a compartment adds a linear term in the differential equations associated with the system and increases the dimensionality of both the system itself and its parameter space
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