Fig 1.
Allosteric interaction between tracer X and allosteric modulator A at receptor R. KX is the equilibrium dissociation constant of tracer X in the absence of A, KA is the equilibrium dissociation constant of allosteric modulator A in the absence of X and α is the factor of binding cooperativity between tracer and allosteric modulator.
Fig 2.
Two allosteric modulators binding to the same site.
Allosteric interaction between tracer X and allosteric modulators A and B at receptor R, assuming that the two allosteric modulators compete for the same allosteric site. Beside parameters in Fig 1, KB is the equilibrium dissociation constant of allosteric modulator B at the vacant receptor and β is the factor of binding cooperativity between tracer and allosteric modulator B.
Fig 3.
Two allosteric modulators each binding to its own site.
Allosteric interaction between tracer X and allosteric modulators A and B at receptor R. Each allosteric modulator binds to its own site, with cooperative interaction between the two sites. Besides parameters listed in Figs 1 and 2, γ is the factor of binding cooperativity between modulator A and modulator B and δ is the change in factor cooperativity γ caused by tracer binding.
Fig 4.
Concentration dependence of the interaction of two allosteric modulators that compete for the same allosteric site.
Upper row, simulation of tracer binding (ordinate) in the presence of two allosteric modulators A and B competing for the same allosteric site, where α is either less than one (left) or greater than one (right) and B is negative allosteric modulator. Binding of the tracer is expressed as the ratio to the binding in the absence of allosteric modulators. Abscissa, concentration of allosteric modulator A expressed as logarithm of molar concentration. Logarithm of concentration of allosteric modulator B is shown in the graph legend. Simulation parameters: KX = 0.1 nM, [X] = 0.1 nM, KA = 100 nM, KB = 1 μM, β = 10. Lower row, dependence of the apparent equilibrium dissociation constant of modulator A (K’A) on concentration of modulator B.
Fig 5.
Concentration dependence of the interaction of two allosteric modulators binding each to its own allosteric site.
Upper row, simulation of tracer binding (ordinate) in the presence two allosteric modulators A and B each binding to its own site, where A is either positive (left) or negative (right) and B is negative allosteric modulator. Binding of the tracer is expressed as the ratio to the binding in the absence of allosteric modulators. Abscissa, concentration of allosteric modulator A expressed as logarithm of molar concentration. Logarithm of concentration of allosteric modulator B is shown in the graph legend. Simulation parameters: KX = 0.1 nM, [X] = 0.1 nM, KA = 100 nM, KB = 1 μM, β = 10, γ = 1, δ = 1. Lower row, dependence of the apparent equilibrium dissociation constant of modulator A (K’A) on concentration of modulator B.
Fig 6.
Effect of cooperativity factor γ on the interaction of two allosteric modulators binding each to its own allosteric site.
Upper row, simulation of tracer binding (ordinate) in the presence two allosteric modulators A and B each binding to its own site, where A is either positive (left) or negative (right) and B is negative allosteric modulator. Binding of the tracer is expressed as the ratio to the binding in the absence of allosteric modulators. Abscissa, concentration of allosteric modulator A expressed as logarithm of molar concentration. Value of cooperativity factor γ is shown in the graph legend. Simulation parameters: KX = 0.1 nM, [X] = 0.1 nM, KA = 100 nM, KB = 1 μM, β = 10, log[B] = -5.5, δ = 1. Lower row, dependence of the apparent equilibrium dissociation constant of modulator A (K’A) on concentration of modulator B for various values of cooperativity factor γ.
Fig 7.
Effect of cooperativity factor δ on the interaction of two allosteric modulators binding each to its own allosteric site.
Upper row, simulation of tracer binding (ordinate) in the presence two allosteric modulators A and B each binding to its own site, where A is either positive (left) or negative (right) and B is negative allosteric modulator. Binding of the tracer is expressed as the ratio to the binding in the absence of allosteric modulators. Abscissa, concentration of allosteric modulator A expressed as logarithm of molar concentration. Value of cooperativity factor δ is shown in the graph legend. Simulation parameters: KX = 0.1 nM, [X] = 0.1 nM, KA = 100 nM, KB = 1 μM, β = 10, log[B] = -5.5, γ = 1. Lower row, dependence of the apparent equilibrium dissociation constant of modulator A (K’A) on concentration of modulator B for various values of cooperativity factor δ.
Fig 8.
Comparison of competition and allosteric interaction between modulators A and B. Simulation of tracer binding (ordinate) in the presence two allosteric modulators A and B each binding to its own allosteric site (yellow line) or competing for the same allosteric site (red line), where A is either positive (left) or negative (right) and B is negative allosteric modulator. Black curve, tracer binding in the absence of modulator B. Binding of the tracer is expressed as fold over control binding in the absence of allosteric modulators. Abscissa, concentration of allosteric modulator A expressed as logarithm of molar concentration. Simulation parameters: KX = 1 nM, [X] = 1 nM, KA = 100 nM, KB = 1 μM, β = 10, log[B] = -5.5.
Fig 9.
Concentration dependence of binding of allosteric modulator to two allosteric sites.
Simulation of tracer binding (ordinate) in the presence an allosteric modulator binding to two allosteric sites for various combinations of positive and negative cooperativity with the tracer indicated at headings of individual plots. Binding of the tracer is expressed as fold over control binding in the absence of allosteric modulator. Abscissa, concentration of allosteric modulator expressed as logarithm of molar concentration. Logarithm of concentration of tracer X is shown in the graph legend. Simulation parameters: KX = 0.1 nM, KA1 = 10 nM, KA2 = 1 μM, γ = 1, δ = 1.
Fig 10.
Effect of γ value on binding of allosteric modulator to two allosteric sites.
Simulation of tracer binding (ordinate) in the presence an allosteric modulator binding to two allosteric sites for various combinations of positive and negative cooperativity with the tracer indicated at headings of individual plots. Binding of the tracer is expressed as fold over control binding in the absence of allosteric modulator. Abscissa, concentration of allosteric modulator expressed as logarithm of molar concentration. Value of cooperativity factor γ is shown in the graph legend. Simulation parameters: KX = 0.1 nM, [X] = 0.1 nM KA1 = 100 nM, KA2 = 1 μM, δ = 1.
Fig 11.
Effect of δ value on binding of allosteric modulator to two allosteric sites.
Simulation of tracer binding (ordinate) in the presence an allosteric modulator binding to two allosteric sites for various combinations of positive and negative cooperativity with the tracer indicated at headings of individual plots. Binding of the tracer is expressed as fold over control binding in the absence of allosteric modulator. Abscissa, concentration of allosteric modulator expressed as logarithm of molar concentration. Value of cooperativity factor δ is shown in the graph legend. Simulation parameters: KX = 0.1 nM, [X] = 0.1 nM KA1 = 10 nM, KA2 = 1 μM, γ = 1.