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. 2014 Jul;10(7):1824-32.
doi: 10.1039/c4mb00022f.

Dimerization-based Control of Cooperativity

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Free PMC article

Dimerization-based Control of Cooperativity

Mehdi Bouhaddou et al. Mol Biosyst. .
Free PMC article

Abstract

Cooperativity of ligand-receptor binding influences the input-output behavior of a biochemical system and thus is an important determinant of its physiological function. Canonically, such cooperativity is understood in terms of ligand-receptor binding affinity, where an initial binding event changes the affinity for subsequent binding events. Here, we demonstrate that dimerization-a simple yet pervasive signaling motif across biology-can have significant control over cooperativity and even dominate over the canonical mechanism. Through an exhaustive parameter sensitivity analysis of a general kinetic model for signal-mediated dimerization, we show that quantitative modulation of dimerization processes can reinforce, eliminate, and even reverse cooperativity imposed by the canonical allosteric ligand-receptor binding affinity mechanism. The favored accumulation of stoichiometrically asymmetric dimers (those with ligand-receptor stoichiometry of 1 : 2) is a major determinant of dimerization-based cooperativity control. However, simulations demonstrate that favoring accumulation of such stoichiometrically asymmetric dimers can either increase or decrease cooperativity, and thus the quantitative relationship between stoichiometrically asymmetric dimers and cooperativity is highly dependent on the parameter values of the particular system of interest. These results suggest that the dimerization motif provides a novel mechanism for both generating and quantitatively tuning cooperativity that, due to the ubiquity of dimerization motifs in biochemical systems, may play a major role in a host of biological functions. Thus, the canonical, allosteric view of cooperativity is incomplete without considering dimerization effects, which is of particular importance as dimerization is often a necessary feature of the allosteric mechanism.

Figures

Figure 1
Figure 1. The cooperativity behavior resulting from different dimerization schemes
Figure 1 depicts a kinetic scheme, dose-response curves, and a Scatchard plot (left-to-right, respectively) for the full model and various model subsets when all rate constant parameters are set to unity. (A) Complete model schematic depicting all possible species resulting from the binding and dimerization interactions between a signal, S, a downstream protein, P, and the complex SP. This results in no cooperativity. (B) A schematic of S binding P, followed by the dimerization of SP with an additional P, resulting in the stoichiometrically asymmetric dimer, SPP. This results in negative cooperativity. (C) A schematic of S binding P, followed by the dimerization between two SP molecules, resulting in the stoichiometrically symmetric dimer, SPSP. This results in positive cooperativity.
Figure 2
Figure 2. The effect of dimerization affinity on cooperativity behavior
(A) Graphical description of each horizontal bar (in B and C). Each horizontal bar corresponds to 729 (36) simulations and spans the range of Hill coefficients attainable by altering dimerization rate constants while keeping signal-binding rate constants fixed. The dark blue section of each bar denotes Hill coefficients between the 5th and 95th percentiles and the light blue tips span the remaining 5% on either side. Each bar contains a single red dot, indicating the “baseline” Hill coefficient when all dimerization rate constants are set to unity. (B) Results for Scatchard Hill coefficients (ns). (C) Results for functional Hill coefficients (nf). In B and C, the dashed line divides negative cooperativity values on the left (n<1) from positive cooperativity values on the right (n>1).
Figure 3
Figure 3. Examples of dimerization rate constants reversing and reinforcing cooperativity behavior
In all Panels, dimerization rate constants are modulated and signal-binding rate constants are held constant. The Scatchard analyses are on the left and the functional analyses are on the right. Solid black lines refer to the baseline case, when all dimerization parameters are set to unity, the red and blue dashed lines denote the dose-response curves possessing the maximum and minimum hill coefficients, respectively, induced by changing dimerization rate constants. (A) Example simulation when the baseline n<1. The signal-binding rate constants are: k1,k7,k8=0.1, k10=1, and k2,k9=10. The dose-response curves for max Scatchard (k3,k6,k11=0.1, k4,k5,k12=10), min Scatchard (k4,k5,k11=0.1, k3,k6,k12=10), max functional (k3,k6=0.1, k4,k5,k11,k12=10), and min functional (k4,k6,k11,k12=0.1, k3,k5=10) are displayed alongside their respective hill coefficients. (B) Example simulation when the baseline n>1. The signal-binding rate constants are: k8,k9,k10=0.1, k7=1, and k1,k2=10. The dose-response curves for max Scatchard (k3,k6,k11,k12=0.1, k4=1, k5=10), min Scatchard (k4,k5,k12=0.1, k3,k6,k11=10), max functional (k3,k6=0.1, k4,k12=1, k5,k11=10), and min functional (k4,k5=0.1, k3=1, k6,k11,k12=10) are displayed alongside their respective hill coefficients. (C) Example simulation when the baseline n~1. The signal-binding rate constants are: k2,k7,k9=0.1, k8,k10=1, and k1=10. The dose-response curves for max Scatchard (k3,k11,k12=0.1, k4,k5,k6=10), min Scatchard (k3,k4,k5,k6,k12=0.1, k11=10), max functional (k3,k11,k12=0.1, k4,k5,k6=10), and min functional (k4,k5,k6=0.1, k12=1, k3,k11=10) are displayed alongside their respective hill coefficients.
Figure 4
Figure 4. Stoichiometrically asymmetric dimer accumulation is a major determinant of cooperativity
(A) An example of how “SPP area” (shaded region) is calculated. (B) Scatterplot showing the correlation between Scatchard Hill coefficients (ns) and their corresponding SPP areas for each of the 312 (531,441) simulations. The correlation is highly significant (ρ=−0.48, p<0.001). (C) Scatterplot showing the correlation between functional Hill coefficients (nf) and their corresponding SPP areas for each of the 312 simulations. The correlation is significant (ρ=−0.23, p<0.001).
Figure 5
Figure 5. Effect of changes in dimerization affinity on asymmetric dimer accumulation
(A) Each plot represents one example set, in which dimerization parameters are altered (to be either 0.1, 1, or 10 s−1 or nM−1s−1) but signal binding parameters are held constant (36 total simulations per plot), and individual simulations are colored according to that simulations’ Scatchard hill coefficient. Dark red and dark blue represent the maximum and minimum hill coefficient, respectively, for that set. Sets’ cooperativity behavior is sometimes positively correlated (top panel) and sometimes negatively correlated (bottom panel) with SPP area. (B) Bar plot showing the mean of the Pearson’s r correlation coefficients, which capture the correlation between cooperativity and SPP area, for sets with a baseline greater than 2 (left) or less than 0.6 (right). The two groups are strongly statistically different (p<10−102). Error bars depict the standard deviation. (C) Boxplots show the relationship between Pearson’s r correlation coefficients and the ratio between the dissociation constants Kd9,10 and Kd7,8 ((k9/k10)/(k7/k8).

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