Ortega et al., (2006). Bistability from double phosphorylation in signaltransduction. 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 biologyexhibit a switch-like behaviour, namely the capability to transform atemporary or a time-varying stimulus into an irreversible response, forexample in the case of stem cell differentiation , or cellular apoptosis .
Previous studies have shown that switch-like behaviour can be achieved either byultrasensitivity (i.e. a large variation of some system's variable in responseto a comparatively modest stimulus) or by bistability (i.e. the system canflip-flop between two stable states in response to opportune triggers, andpreserve its new state after the triggering stimulus has been removed) [1,2].
Some authors have described positive feedback loops or double negative feedbackloops as necessary (although not sufficient) conditions for bistability .However, other studies have pointed out that bistability can solely arise fromtwo-step protein modification cycle, if the modification steps are performed bythe same enzyme . Ortega and coworkers [4, BIOMD0000000258] were able to derive quantitatively theprecise kinetic conditions that such a system should satisfy in order to exhibitbistability. Moreover, from the results of their analysis, they identified thedouble phosphorylation cycle of MAPKK1 as exhibiting the kineticcharacteristics that make it a plausible candidate for a bistable switch.
Figure 1:Diagram of the double modification cycle (which can consist of phosphorylationsor other generic covalent modifications). The protein can exist in three formsWα, Wβ, Wγ. The two "forward" steps (1 and 3) arecatalysed by the same enzyme e1, and the two "backwards" steps (2 and 4)are catalysed by the same enzyme e2.Figure taken from .
The kinetic diagram for the double phosphorylation cycle considered in thearticle is given in Figure 1.A generic proteins W undergoes two covalent modifications (that are assumed tohappen in a mandatory sequence) on two residues, The resulting forms are theunmodified protein (Wα), modified on one residue (Wβ), andmodified on two residues (Wγ).
The two forward modification steps are catalysed by the same enzyme e1, whilstthe backward steps are catalysed by a demodifier enzyme e2. All fourmodifications are assumed to follow a Michaelis-Menten mechanism.
It is found that if the enzyme responsible for the first modification step issaturated by its substrate, and the ratio of the catalytic constants in themodification/demodification steps that form the first cycle is is lesser thanthe ratio for the second cycle, then the system has three possible steadystates,two of which are stable .
Interestingly, the authors also claim that in the case of multisitephosphorylation (Figure 2A), the system can still exhibit bistability (underopportune conditions) but not multistability, and bistability can appear ina much wider region of the parametric space, in comparison with the two-sitephosphorylation model.
However, in this latter case, analytical solutions were not available and theconclusions were drawn on the basis of numerical results, based on simulationswith a "broad set of parameters"[sic], but the results were not reported, andneither was the precise extent of the performed parametric scan. Therefore,on the basis of the published information, it would probably be more correct toavoidclaiming the absolute generality of the results for the multisitephosphorylation model, although their validity still holds for a wide range ofconditions.
The last part of the paper shows, instead that multistability can be achieved bya hierarchical arrangement of two double-modification cycles, where thedouble-modified protein of the first cycle is the modifier enzyme in the secondcycle (Figure 2B).
In summary, the most relevant finding in this paper is that bistability canarise in a double phosphorylation cycle without feedback loops. Moreover, amultiple phosphorylation cycle where forward and backward modification steps arecatalysed by only two enzymes, one modifier and one demodifier, results(usually) at most in bistability and not in multistability. Finally, thehierarchical arrangements of two double cycles can result in multistability ifboth cycles are simultaneously exhibiting bistability.
These findings are all the more relevant, given that the frequency with whichtwo-steps phosphorylation cycles are encountered in signaling networks. Theseresults can be used to single out elements of signaling cascades that arepotentially responsible for the generation of bistability. Moreover, theyprovide a theoretical bridge to explain the possibility of bistable/multistable behaviour in biochemical cascades where experiments had nothighlighted any feedback mechanism.
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 .
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