Please visit the new BioModels platform to access the latest content. This website is no longer updated and will be retired on 20 July 2020.
BioModels Database logo

BioModels Database


Ortega et al., (2006). Bistability from double phosphorylation in signal transduction. Kinetic and structural requirements.

December 2010, model of the month by Massimo Lai
Original model: BIOMD0000000258

Cellular signaling is largely based on reactions that are, in themselves, reversible. Nevertheless, many biochemical pathways in cellular biology exhibit a switch-like behaviour, namely the capability to transform a temporary or a time-varying stimulus into an irreversible response, for example in the case of stem cell differentiation , or cellular apoptosis [1].

Previous studies have shown that switch-like behaviour can be achieved either by ultrasensitivity (i.e. a large variation of some system's variable in response to a comparatively modest stimulus) or by bistability (i.e. the system can flip-flop between two stable states in response to opportune triggers, and preserve its new state after the triggering stimulus has been removed) [1,2].

Some authors have described positive feedback loops or double negative feedback loops as necessary (although not sufficient) conditions for bistability [2]. However, other studies have pointed out that bistability can solely arise from two-step protein modification cycle, if the modification steps are performed by the same enzyme [3]. Ortega and coworkers [4, BIOMD0000000258] were able to derive quantitatively the precise kinetic conditions that such a system should satisfy in order to exhibit bistability. Moreover, from the results of their analysis, they identified the double phosphorylation cycle of MAPKK1 as exhibiting the kinetic characteristics that make it a plausible candidate for a bistable switch.

Figure 1

Figure 1: Diagram of the double modification cycle (which can consist of phosphorylations or other generic covalent modifications). The protein can exist in three forms Wα, Wβ, Wγ. The two "forward" steps (1 and 3) are catalysed by the same enzyme e1, and the two "backwards" steps (2 and 4) are catalysed by the same enzyme e2. Figure taken from [1].

The kinetic diagram for the double phosphorylation cycle considered in the article is given in Figure 1. A generic proteins W undergoes two covalent modifications (that are assumed to happen in a mandatory sequence) on two residues, The resulting forms are the unmodified protein (Wα), modified on one residue (Wβ), and modified on two residues (Wγ).

The two forward modification steps are catalysed by the same enzyme e1, whilst the backward steps are catalysed by a demodifier enzyme e2. All four modifications are assumed to follow a Michaelis-Menten mechanism.

It is found that if the enzyme responsible for the first modification step is saturated by its substrate, and the ratio of the catalytic constants in the modification/demodification steps that form the first cycle is is lesser than the ratio for the second cycle, then the system has three possible steady states, two of which are stable [1].

Interestingly, the authors also claim that in the case of multisite phosphorylation (Figure 2A), the system can still exhibit bistability (under opportune conditions) but not multistability, and bistability can appear in a much wider region of the parametric space, in comparison with the two-site phosphorylation model.

However, in this latter case, analytical solutions were not available and the conclusions were drawn on the basis of numerical results, based on simulations with a "broad set of parameters"[sic], but the results were not reported, and neither was the precise extent of the performed parametric scan. Therefore, on the basis of the published information, it would probably be more correct to avoid claiming the absolute generality of the results for the multisite phosphorylation model, although their validity still holds for a wide range of conditions.

The last part of the paper shows, instead that multistability can be achieved by a hierarchical arrangement of two double-modification cycles, where the double-modified protein of the first cycle is the modifier enzyme in the second cycle (Figure 2B).

In summary, the most relevant finding in this paper is that bistability can arise in a double phosphorylation cycle without feedback loops. Moreover, a multiple phosphorylation cycle where forward and backward modification steps are catalysed by only two enzymes, one modifier and one demodifier, results (usually) at most in bistability and not in multistability. Finally, the hierarchical arrangements of two double cycles can result in multistability if both cycles are simultaneously exhibiting bistability.

These findings are all the more relevant, given that the frequency with which two-steps phosphorylation cycles are encountered in signaling networks. These results can be used to single out elements of signaling cascades that are potentially responsible for the generation of bistability. Moreover, they provide a theoretical bridge to explain the possibility of bistable/multistable behaviour in biochemical cascades where experiments had not highlighted any feedback mechanism.

Figure 2

Figure 2: (A) Diagram for the multisite covalent modification (4 possible forms for the same protein W); three forward conversion steps are catalysed by one enzyme e1 (1, 3, and 5), and 3 backward conversion steps are catalysed by one enzyme e2 (2, 4, and 6). (B) Hierarchical arrangement of two double modification cycles for proteins W and Z, where the double modified form of protein W is the enzyme responsible for the catalysis of the "forward" conversion steps for protein Z. Figure taken from [1].

Bibliographic References

  1. Ferrell JE Jr & Xiong W. Bistability in cell signaling: How to make continuous processes discontinuous, and reversible processes irreversible. Chaos , 11(1):227-236, 2001. [CiteXplore]
  2. Ferrell JE Jr. Self perpetuating states in signal transduction: positive feedback, double negative feedback and bistability. Curr Opin Chem Biol. , 6:140-148, 2002. [CiteXplore]
  3. Markevich NI, Hoek JB & Kholodenko BN. Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. J Cell Biol, 164(3):353-9, 2004. [CiteXplore]
  4. Ortega F, Garcés JL, Mas F, Kholodenko BN & Cascante M. FEBS Journal, 273(17):3915–3926, 2006. [CiteXplore]