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Abstract
Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity.
Highlights
Decision-making processes are essential to many biological functions
The local analysis is performed at a saddle point, an unstable equilibrium of the model, which is shown to be a key ruler of the decisionmaking process
The analysis is first applied to a small model of the apoptotic switch proposed by Eißing et al [3], to a larger model of the apoptotic switch by Schliemann et al [9] and to a model of long term potentiation proposed by Aslam et al [6]
Summary
They are commonly implemented through bistable dynamical switches where both stable steadystates correspond to a distinct decision. Example of bistable switches are found in biological processes including cell cycle progression [1,2], cell death signaling [3,4], developmental processes [5], memory formation (long-term potentiation) [6], or infectious diseases such as prion propagation [7]. The key observation is that the local analysis must not be performed around the stable steady-states of the model, which correspond to experimentally observed conditions. The local analysis is performed at a saddle point, an unstable equilibrium of the model, which is shown to be a key ruler of the (transient) decisionmaking process. Results are illustrated on three previously published models of bistable switches: two models of apoptosis, the programmed cell death [3,9] and a model of long-term potentiation [6]
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