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closeWhat exactly is new?
Posted by JWRMartini on 21 Mar 2016 at 13:20 GMT
To me it seems as if the main results presented here have already been well-known in scientific literature.
As the authors state in the abstract, they investigate binding time courses for a molecule with two binding sites for its ligand by deterministic simulations. In particular, they use this approach
1. to show that the Hill coefficient provides a measure of the free energy of interaction,
2. and to show that molecules with the same equilibrium binding properties but with
different interaction energy can be kinetically differentiated.
Considering the first point, I think it is well known that for systems consisting of only two binding sites, the interaction energy can be related to cooperativity and that for these small systems several different definitions of cooperativity coincide (see e.g. [1,2,3]). However, this correspondence is a special case. For a higher number of binding sites, the relation between different definitions of cooperativity is not obvious [4].
Considering the second point, the paper seems to be quite similar to what we did when we compared a stochastic model with a deterministic description of ligand binding kinetics (“Two binding sites and cooperativity” in [5]) . We have shown there that kinetics can be used to distinguish between different molecules with the same equilibrium distribution, based on a stochastic model as well as on a deterministic model. The only difference to the underlying equations used in [5], is that the concentration of the ligand is also modeled in the system in this work (by Eq.(6)). Thus, as the authors state, their modeling approach overcomes the limitation of pseudofirst order conditions. I understand this point, but I would like to ask whether this approach might not have conceptual problems. Modeling the ligand concentration L over time will only matter in situations in which the concentration of the ligand is not much higher than that of the target molecule. However, if the change in L is not close to zero, the measured Hill-coefficient will depend on the used concentration of M in the experiment. Does it make sense to define a quantity characterizing the binding behavior of a ligand to its target molecule in a way that depends on the number of molecules M used in the experiment?
[1] Onufriev, Alexey, and G. Matthias Ullmann. "Decomposing complex cooperative ligand binding into simple components: connections between microscopic and macroscopic models." The Journal of Physical Chemistry B 108.30 (2004): 11157-11169
[2] Martini, Johannes WR, and G. Matthias Ullmann. "A mathematical view on the decoupled sites representation." Journal of Mathematical Biology 66.3 (2013): 477-503.
[3] Martini, Johannes. Excursions in the theory of ligand binding. Diss. Universitätsbibliothek Mannheim, 2014.
[4] Martini, Johannes WR, Luis Diambra, and Michael Habeck. "Cooperative binding: a multiple personality." Journal of Mathematical Biology (2015): 1-28.
[5] Martini, Johannes WR, and Michael Habeck. "Comparison of the kinetics of different Markov models for ligand binding under varying conditions." The Journal of Chemical Physics 142.9 (2015): 094104.
About what is exactly new
DiegoCattoni replied to JWRMartini on 08 Aug 2016 at 09:44 GMT
This commentary follows up the comment posted by Dr. Johannes Martini regarding our article Cooperativity in Binding Processes: New Insights from Phenomenological Modeling (Cattoni et al, 2015).
The main ideas regarding cooperativity in binding processes were coined in the past century in a context strongly connecting theory and experiments. These ideas still are a matter of continuous investigation as it is reflected in several recent works. The papers referred by Dr. Martini in his comment are a sample of the large number of studies that are still being conducted regarding cooperativity in binding processes.
Although several cooperativity criteria have been proposed (including those proposed by Dr. Martini), we have chosen to perform our analysis by using the Hill coefficient, nH, because of its widespread use in experimental binding studies. The hypothesis linking the Hill coefficient (nH) with the free energy of interaction (∆Goint) was formulated by Wyman in his seminal article from the 60’s (Wyman, 1964), as it was explicitly acknowledged in our study.
Our results indicate that, for the binding between the macromolecule and two ligands, nH monotonically decreases with (∆Goint) following a quasi-linear regime in the parameter space area corresponding to the no-interaction case (Fig. 4 of Cattoni et al 2015). Additionally, we show that nH does not depend on the association free energy (∆Goint) upon fixing the cooperativity factor (w) (Fig 4 inset of Cattoni et al 2015). To our knowledge, these results have not been previously reported in the literature.
Regarding the second point, it is well known that the binding isotherm of a model involving a macromolecule with two identical sites displaying negative cooperativity cannot be distinguished from that of a model in which there are two distinct non-interacting sites. Two decades ago Wang & Pan (1996) proposed a kinetic method to distinguish between these two possible binding mechanisms from the closed-form solution of the differential equations obtained under two conditions: 1) irreversible binding, and 2) pseudofirst order for the ligand association step. Both conditions are very restrictive and it is unlikely that they will hold in most biological systems and experimental conditions. The kinetic analysis proposed in our work is not limited by such restrictions and thus constitute a useful tool to distinguish between negative cooperativity and different classes of sites without interactions in a real experimental context (e.g. Cattoni et al, 2009).
In the last part, we suppose Dr. Martini was addressing issues associated with the use of the Hill coefficient in the analysis of binding kinetic data. Certainly, we did not use the Hill coefficients in that way. Nevertheless, the question raised by Dr Martini should require additional research that to our knowledge has not yet been performed.
On behalf of the authors,
Dr. Luis Gonzalez Flecha and Dr. Osvaldo Chara
References
Cattoni DI, Chara O, Kaufman SB & González Flecha FL. 2015. Cooperativity in Binding Processes: New Insights from Phenomenological Modeling PLoS One. 10(12):e0146043.
Cattoni DI, Kaufman SB & González Flecha FL. 2009. Kinetics and thermodynamics of the interaction of 1-anilino-naphthalene-8-sulfonate with proteins Biochim Biophys Acta. 1794: 1700–1708.
Wang Z-X & Pan X-M. 1996. Kinetic differentiation between ligand-induced and pre-existent asymmetric models. FEBS Letters. 388: 73–75.
Wyman J.1964 Linked functions and reciprocal effects in hemoglobin: A second look. Adv Prot Chem. 1964; 19: 223–286.