Bistability from double phosphorylation in signal transduction

Abstract

Previous studies have suggested that positive feedback loops and ultrasensitivity are prerequisites for bistability in covalent modification cascades. However, it was recently shown that bistability and hysteresis can also arise solely from multisite phosphorylation. Here we analytically demonstrate that double phosphorylation of a protein (or other covalent modification) generates bistability only if: (a) the two phosphorylation (or the two dephosphorylation) reactions are catalyzed by the same enzyme; (b) the kinetics operate at least partly in the zero‐order region; and (c) the ratio of the catalytic constants of the phosphorylation and dephosphorylation steps in the first modification cycle is less than this ratio in the second cycle. We also show that multisite phosphorylation enlarges the region of kinetic parameter values in which bistability appears, but does not generate multistability. In addition, we conclude that a cascade of phosphorylation/dephosphorylation cycles generates multiple steady states in the absence of feedback or feedforward loops. Our results show that bistable behavior in covalent modification cascades relies not only on the structure and regulatory pattern of feedback/feedforward loops, but also on the kinetic characteristics of their component proteins.

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

“…In either case, the system under meaningful biological parameters shows convergence, not other dynamical properties such as periodic behavior or even chaotic behavior. Analytical studies done for the quasi-steady-state version of the model (slow dynamics), which is a monotone system, indicate that the reduced system is indeed monostable or bistable, see [31]. Thus, it is of great interest to show that, at least in certain parameter ranges (as required by singular perturbation theory), the full system inherits convergence properties from the reduced system, and this is what we do as an application of our results.…”

Bistability in the chemical master equation for dual phosphorylation cycles

“…Using definition (3) it is possible to explicitly compute a set of parameter values for the PdPC cycle, that satisfy the detailed balance condition (12) according to the relations…”

“…The PdPC with the nonspecific phosphatase controls the phosphorylation state of AMPA receptors that mediates induction of Long Term Potentiation (LTP) and Long Term Depression (LTD) in vitro and in vivo [2,3,20]. Recently, several authors have reported bistability in homogeneus pPdPC [6,12]) as well as those with a non-specific phosphatase and two different kinases [2]. The bistable behaviour of the homogeneous system is explained on the basis of a competition between the substrates for the enzymes.…”

“…A "natural" way to cope with this problem is the so-called Chemical Master Equation (CME) approach [18], that realizes in an exact way the proba-bilistic dynamics of a finite number of molecules, and recovers the chemical kinetics of the Law of Mass Action, which yields the continuous Michaelis-Menten equation in the thermodynamic limit (N → ∞,) using the mean field approximation. In this paper we study a stochastic formulation of enzymatic cycles that has been extensively considered by several authors ( [6,12]). The deterministic descriptions of these models characterize the stability of fixed points and give a geometrical interpretation of the observed steady states, as the intersection of conic curves( [12]).…”

“…In this paper we study a stochastic formulation of enzymatic cycles that has been extensively considered by several authors ( [6,12]). The deterministic descriptions of these models characterize the stability of fixed points and give a geometrical interpretation of the observed steady states, as the intersection of conic curves( [12]). The stochastic description can in fact provide further information on the relative stability of the different steady states in terms of a stationary distribution.…”