For the second model of this series, I will break my own rule limiting the topic to “systems-biology-like” models, i.e. models that are simulated with a computer to predict the behaviours of systems. However, a fair number of MWC models resulted in the instantiation of kinetics simulations, so I do not feel too bad about this breach. The reason to include the MWC model here is mainly because I think the work is one of the early examples where a model shed light on biochemical processes and led to a mechanism, rather than merely fit the results.
The model itself is described in a highly cited paper (5776 times according to Google Scholar on March 14th 2013):
Monod J, Wyman J, Changeux JP. On the nature of allosteric transitions: A plausible model. J Mol Biol 1965, 12: 88-118. http://identifiers.org/pubmed/14343300
Contrarily to the Hodgkin-Huxley model, described earlier in this post, the main body of the work is located in a single page, the fourth of the paper. The rest of the paper is certainly interesting, and several thesis (or even careers) have been devoted to the analysis of a formula or a figure found in the other pages (several papers were even focused on the various footnotes, the discussions still going on after 50 years). However, the magic is entirely contained in this fourth page.
Cooperativity of binding had been known for a long time, ever since the work of Christian Bohr (the father of Niels Bohr, the quantum physicist) on binding of oxygen to hemoglobin. For an historical account see this article, to be published in PLoS computational biology and then on Wikipedia. Around the year 1960, it was discovered that enzymes also exhibited this kind of ultrasensitive behaviour. In particular the multimeric “allosteric” enzymes, where regulators bind to sites sterically distinct from the substrate, displayed positive cooperativity for the regulation. At that time, the explanations of the cooperativity relied on the Adair-Klotz paradigm, that postulated a progressive increase of affinity as the ligand bound more sites, or the Pauling one, based on only one microscopic affinity and an energy component coming from subunit interactions. In both cases, the mechanisms are inductionist, the ligand “instructing” the protein to change its binding site affinities or its inter-subunit interactions. In addition, the state function (the fraction of active proteins) and the binding function (the fraction of protein bound to the ligand) were identical (more exactly there was not even the notion that two different functions existed), something that was shown to be wrong for the enzymes.
The model developed by Monod and Changeux (Jeffrey Wyman always referred to the paper as “the Monod and Changeux paper”) relied on brutally simple and physically based assumptions:
- thermodynamic equilibrium: the proteins which activities are regulated by the binding of ligands exist in different interconvertible conformations, in thermodynamic equilibrium, even in the absence of ligand. This assumption is opposed to the induced-fit mechanism whereby the protein always exists in a conformation in the absence of ligand, and is always in the other conformation when bound to the ligand.
- different affinities for the two states: the two conformations display different affinities for the ligand. Consequently, the ligand will shift the equilibrium towards the state with the highest affinity (that is the lowest free energy). This is a selectionist mechanism rather than instructionist. The binding of a ligand no longer provoke the switch of conformation. Proteins flicker, with or without the ligand bound. However, the time spent in any given conformation depends on the presence of ligand (or the probability to be in a given conformation).
- all monomers of a multimer are in the same conformation: this assumption was, and still is, the most controversial. It is opposed to the notion of sequential transitions, whereby the monomers switch conformation progressively, as the ligands binds to them.
The rest followed from simple thermodynamics, explained by the two figures below.
The MWC model has been successfully used to explain the behaviour of many proteins, such as hemoglobin or allosteric enzymes, as mentioned above, but also neurotransmitter receptors, transcription factors, intracellular signalling mediators or scaffolding proteins. For an example of how MWC thinking help to understand signalling cascades, see our work on calcium signalling in synaptic function (Stefan et al. PNAS 2008, 105: 10768-10773; Stefan et al. PLoS ONE 2012, 7(1): e29406; Li et al. PLoS ONE (2012), 7(9): e43810).
As for every useful theory, the MWC framework has since been refined and extended, for instance to encompass the interactions between several regulators, lattices of monomers etc. I’ll finish by a little advertisement for a conference to celebrate the 50th anniversary of the allosteric regulation