A novel equation for cooperativity of the allosteric state function

Area of Science:

• Biochemistry
• Molecular Biology
• Biophysics

Background:

• The Monod-Wyman-Changeux (MWC) allosteric model describes protein conformational changes.
• It postulates two states: T (tense, low affinity) and R (relaxed, high affinity).
• Cooperativity is a key feature of allosteric proteins.

Purpose of the Study:

• To investigate the distinct properties of fractional binding site occupation (Y¯) and fractional R state molecules (R¯) in the MWC model.
• To clarify the determinants of cooperativity in allosteric systems.
• To derive a new equation for cooperativity based on R¯.

Main Methods:

• Theoretical analysis of the MWC allosteric model.
• Derivation of a new equation relating the Hill coefficient to R¯.
• Mathematical modeling of allosteric transitions.

Main Results:

• Cooperativity exhibits markedly different behaviors for Y¯ and R¯.
• For R¯, cooperativity is solely dependent on the relative affinities of the T and R states.
• The relative intrinsic stabilities of the states do not influence cooperativity when considering R¯.

Conclusions:

• The fraction of molecules in the R state (R¯) is a critical determinant of allosteric cooperativity.
• Cooperativity in the MWC model is primarily governed by ligand-binding affinities, independent of state stability.
• A simplified equation elucidates the relationship between the Hill coefficient and R¯.