![Hill equation
For a protein with n binding sites, the equilibrium of the
reversible binding of a protein (P) to a ligand(L)
Equation becomes………
P + nL PLn …………………………1
and the expression for the association constant
becomes
[PLn]
Ka =-------------………2
[P][L]n](https://image.slidesharecdn.com/hillequation-200211144640/75/Hill-equation-3-2048.jpg)
![Hill equation
The expression for θ is,,
[L]n where, binding sites
occupied
• θ = ---------- …………………………………3 θ=--------------------
--
[L]n + Kd total binding sites
Rearranging, then taking the log of both sides, yields
θ [L]n
---------= ----- …………………………………….4
1 – θ Kd
θ
log(---------) = n log[L] – logKa ……………………………………………5
1 – θ
Equation 5 is the Hill equation](https://image.slidesharecdn.com/hillequation-200211144640/75/Hill-equation-4-2048.jpg)
Uploaded byShaikh Shohidul Islam
Hill equation
The document discusses the Hill equation, which describes cooperative ligand binding to multisubunit proteins like hemoglobin. The Hill equation models how the binding of oxygen to one subunit of hemoglobin affects the binding of oxygen to other subunits. Archibald Hill first analyzed cooperative oxygen binding to hemoglobin in 1910. The Hill equation takes the form of an expression relating the fraction of binding sites occupied to the ligand concentration.
Hill equation
- 1. Hill equation Prepared by: ShaikhShohidul Islam Lecturer Biochemistry and molecular biology Gono Bishwabidyalay
- 2. Hill equation Cooperative bindingof a ligand to a multimeric protein is a form of allosteric binding often observed in multimeric proteins .such as we observe with the binding of O2 to hemoglobin, Cooperative binding of oxygen by hemoglobin was first analyzed by Archibald Hill in 1910. From this work came a general approach to the study of cooperative ligand binding to multisubunit proteins.
- 3. Hill equation For aprotein with n binding sites, the equilibrium of the reversible binding of a protein (P) to a ligand(L) Equation becomes……… P + nL PLn …………………………1 and the expression for the association constant becomes [PLn] Ka =-------------………2 [P][L]n
- 4. Hill equation The expressionfor θ is,, [L]n where, binding sites occupied • θ = ---------- …………………………………3 θ=-------------------- -- [L]n + Kd total binding sites Rearranging, then taking the log of both sides, yields θ [L]n ---------= ----- …………………………………….4 1 – θ Kd θ log(---------) = n log[L] – logKa ……………………………………………5 1 – θ Equation 5 is the Hill equation
- 5. Allosteric protein An allostericprotein is one in which the binding of a ligand to one site affects the binding properties of another site on the same protein. Such as hemoglobin, myoglobin etc. • Hemoglobin (Mr 64,500; abbreviated Hb) is roughly spherical, with a diameter of nearly 5.5 nm. It is a tetrameric protein containing four heme prosthetic groups, one associated with each polypeptide chain.