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Cooperativity in Binding Processes: New Insights from Phenomenological Modeling.

Cattoni DI, Chara O, Kaufman SB, González Flecha FL - PLoS ONE (2015)

Bottom Line: Here we analyze the simplest phenomenological model that can account for cooperativity (i.e. ligand binding to a macromolecule with two binding sites) by generating equilibrium binding isotherms from deterministically simulated binding time courses.We show that the Hill coefficients determined for cooperative binding, provide a good measure of the Gibbs free energy of interaction among binding sites, and that their values are independent of the free energy of association for empty sites.We also conclude that although negative cooperativity and different classes of binding sites cannot be distinguished at equilibrium, they can be kinetically differentiated.

View Article: PubMed Central - PubMed

Affiliation: Laboratorio de Biofísica Molecular, Instituto de Química y Fisicoquímica Biológicas, Universidad de Buenos Aires - CONICET, Buenos Aires, Argentina.

ABSTRACT
Cooperative binding is one of the most interesting and not fully understood phenomena involved in control and regulation of biological processes. Here we analyze the simplest phenomenological model that can account for cooperativity (i.e. ligand binding to a macromolecule with two binding sites) by generating equilibrium binding isotherms from deterministically simulated binding time courses. We show that the Hill coefficients determined for cooperative binding, provide a good measure of the Gibbs free energy of interaction among binding sites, and that their values are independent of the free energy of association for empty sites. We also conclude that although negative cooperativity and different classes of binding sites cannot be distinguished at equilibrium, they can be kinetically differentiated. This feature highlights the usefulness of pre-equilibrium time-resolved strategies to explore binding models as a key complement of equilibrium experiments. Furthermore, our analysis shows that under conditions of strong negative cooperativity, the existence of some binding sites can be overlooked, and experiments at very high ligand concentrations can be a valuable tool to unmask such sites.

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Site occupation for a macromolecule showing positive cooperativity.Eqs 2 to 6 were numerically solved using the kinetic coefficients indicated in the main text for cooperative binding with ω = 10. (A) The average number of occupied sites (〈n〉t) was calculated using Eq 7 and represented as a function of time (in seconds). Arrow indicates increasing total ligand concentration. (B) The equilibrium values of 〈n〉 and [L] (μM) were obtained from each time course and plotted as a binding isotherm. (C) Wyman´s Hill plot of data from panel B. At both edges, the calculated data approaches to linear asymptotes with slope unity (dotted lines). The continuous red line represents a third order polynomial fitted to the data in the transition region with the best fitting parameters a3 = -0.016; a2 = 0.0807 a1 = 1.5085 and a0 = 2.718. From these values a Hill coefficient of 1.54 was obtained using Eq. B5 (S2 Appendix).
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pone.0146043.g003: Site occupation for a macromolecule showing positive cooperativity.Eqs 2 to 6 were numerically solved using the kinetic coefficients indicated in the main text for cooperative binding with ω = 10. (A) The average number of occupied sites (〈n〉t) was calculated using Eq 7 and represented as a function of time (in seconds). Arrow indicates increasing total ligand concentration. (B) The equilibrium values of 〈n〉 and [L] (μM) were obtained from each time course and plotted as a binding isotherm. (C) Wyman´s Hill plot of data from panel B. At both edges, the calculated data approaches to linear asymptotes with slope unity (dotted lines). The continuous red line represents a third order polynomial fitted to the data in the transition region with the best fitting parameters a3 = -0.016; a2 = 0.0807 a1 = 1.5085 and a0 = 2.718. From these values a Hill coefficient of 1.54 was obtained using Eq. B5 (S2 Appendix).

Mentions: Fig 3A shows the time course for the average number of binding sites of the macromolecule occupied by the ligand L (〈n〉t, denoting the time dependence of the binding density) simulated from the numerical solution of Eqs 2–6 associated to the reaction scheme depicted in Fig 2 with positive cooperativity. When the system reached the equilibrium, the values of 〈n〉 and [L] were represented as a binding isotherm (Fig 3B).


Cooperativity in Binding Processes: New Insights from Phenomenological Modeling.

Cattoni DI, Chara O, Kaufman SB, González Flecha FL - PLoS ONE (2015)

Site occupation for a macromolecule showing positive cooperativity.Eqs 2 to 6 were numerically solved using the kinetic coefficients indicated in the main text for cooperative binding with ω = 10. (A) The average number of occupied sites (〈n〉t) was calculated using Eq 7 and represented as a function of time (in seconds). Arrow indicates increasing total ligand concentration. (B) The equilibrium values of 〈n〉 and [L] (μM) were obtained from each time course and plotted as a binding isotherm. (C) Wyman´s Hill plot of data from panel B. At both edges, the calculated data approaches to linear asymptotes with slope unity (dotted lines). The continuous red line represents a third order polynomial fitted to the data in the transition region with the best fitting parameters a3 = -0.016; a2 = 0.0807 a1 = 1.5085 and a0 = 2.718. From these values a Hill coefficient of 1.54 was obtained using Eq. B5 (S2 Appendix).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4696654&req=5

pone.0146043.g003: Site occupation for a macromolecule showing positive cooperativity.Eqs 2 to 6 were numerically solved using the kinetic coefficients indicated in the main text for cooperative binding with ω = 10. (A) The average number of occupied sites (〈n〉t) was calculated using Eq 7 and represented as a function of time (in seconds). Arrow indicates increasing total ligand concentration. (B) The equilibrium values of 〈n〉 and [L] (μM) were obtained from each time course and plotted as a binding isotherm. (C) Wyman´s Hill plot of data from panel B. At both edges, the calculated data approaches to linear asymptotes with slope unity (dotted lines). The continuous red line represents a third order polynomial fitted to the data in the transition region with the best fitting parameters a3 = -0.016; a2 = 0.0807 a1 = 1.5085 and a0 = 2.718. From these values a Hill coefficient of 1.54 was obtained using Eq. B5 (S2 Appendix).
Mentions: Fig 3A shows the time course for the average number of binding sites of the macromolecule occupied by the ligand L (〈n〉t, denoting the time dependence of the binding density) simulated from the numerical solution of Eqs 2–6 associated to the reaction scheme depicted in Fig 2 with positive cooperativity. When the system reached the equilibrium, the values of 〈n〉 and [L] were represented as a binding isotherm (Fig 3B).

Bottom Line: Here we analyze the simplest phenomenological model that can account for cooperativity (i.e. ligand binding to a macromolecule with two binding sites) by generating equilibrium binding isotherms from deterministically simulated binding time courses.We show that the Hill coefficients determined for cooperative binding, provide a good measure of the Gibbs free energy of interaction among binding sites, and that their values are independent of the free energy of association for empty sites.We also conclude that although negative cooperativity and different classes of binding sites cannot be distinguished at equilibrium, they can be kinetically differentiated.

View Article: PubMed Central - PubMed

Affiliation: Laboratorio de Biofísica Molecular, Instituto de Química y Fisicoquímica Biológicas, Universidad de Buenos Aires - CONICET, Buenos Aires, Argentina.

ABSTRACT
Cooperative binding is one of the most interesting and not fully understood phenomena involved in control and regulation of biological processes. Here we analyze the simplest phenomenological model that can account for cooperativity (i.e. ligand binding to a macromolecule with two binding sites) by generating equilibrium binding isotherms from deterministically simulated binding time courses. We show that the Hill coefficients determined for cooperative binding, provide a good measure of the Gibbs free energy of interaction among binding sites, and that their values are independent of the free energy of association for empty sites. We also conclude that although negative cooperativity and different classes of binding sites cannot be distinguished at equilibrium, they can be kinetically differentiated. This feature highlights the usefulness of pre-equilibrium time-resolved strategies to explore binding models as a key complement of equilibrium experiments. Furthermore, our analysis shows that under conditions of strong negative cooperativity, the existence of some binding sites can be overlooked, and experiments at very high ligand concentrations can be a valuable tool to unmask such sites.

Show MeSH
Related in: MedlinePlus