Hill Equation

HILL EQUATION : -

🐣Developed by = Archibald Hill in 1910.

🐣Quantitatively describing Cooperative ligand binding to multisubmit proteins.

🐣1 Hb binds = 4 O2 molecules, so

Fractional saturation of Hb would be = 

🐣Replacement of exponent 4 by n, we can write -

🐣This is known as Hill equation.

🐣Describe = degree of saturation of Hb as as a function of PO2 & 

🐣Hill coefficient = measure of the cooperativity of O2 binding.

🐣It measures = degree of cooperativity in ligand (O2) binding.

🐣If n = 1 = reaction is said to be non - cooperative, for ex.  Mb -O2 binding,  & show hyperbolic curve. 

🐣If n < 1 = negative cooperativity, & binding of a legend, decreases affinity of other site for legend binding.

🐣If n > 1 = positive cooperativity & binding of ligand to one site increases affinity of other site for ligand binding, for ex. Hb -O2 binding.

🐣Hill plot for Mb -O2 binding = linear with slop of 1 &

🐣Hill plot for Hb -O2 = completely linear since binding is cooperative, in center with a slope of 2.8. 

🐣For normal human Hb = Hill cofficient is 2.8 to 3.0 that is Hb -O2 binding is highly cooperative.

FUNCTIONAL DIFFERENCE BETWEEN Mb & Hb : -

🐣Hb = allosteric protein.

🐣4 ligand binding sites. 

🐣Legend (O2) binds one site & this site affects the binding properties of another site on the same (Hb) protein. (not in Mb) 

🐣O2 - dissociation curve of Hb = sigmodial,

🐣For Mb = rectangular hyperbolic curve.

🐣Mb has = higher affinity for O2 than Hb.

🐣Hb -O2 affinity depends on pH. 

🐣Mb -O2 affinity independent of pH. 

🐣In Hb = degree of cooperativity expressed by = Hill coefficient (n).

🐣Hill coefficient (n) for Hb = 2.8 & for Mb = 1.0.

FACTORS AFFECTING THE AFFINITY OF Hb & O2 :-

🐣pO2 = Partial Oxygen Pressure & it determine - percent oxygen saturation of Hb. 

🐣Other factors influence & shift to entire curve = either to the left (higher affinity)  or to the right (lower affinity).

1. pH

🐣Low pH of blood = more acidic = affinity of Hb-O2 decrease.

🐣Effect of pH on Hb -O2 affinity = Bohr effect.

🐣Under low pH = more H+ ions (high acidic) & due to more H+ ions = side chain of Histidine on beta146 - becomes protonated &

🐣Quaternary structure of deoxyhemoglobin is stabilized due to formation of ionic interaction (Salt bridge).

🐣At high pH = His146 not protonated so no significant changes take place. 

🐣Conversation of deoxy-Hb to oxy-Hb requires  = disruption of ionic interactions.

2. Concentration of 2,3 - bisphosphoglycerate (BPG) 

🐣BPG = present in RBCs of human & other species. 

🐣Highly charged anion (-)

🐣One molecule binds in the central cavity of Hb &

🐣Form salt bridge with terminal NH2 group of both beta - chains.

🐣BPG stabilize deoxy-Hb (T - state) by = forming additional salt bridge therefore reduce Hb -O2 affinity.

🐣When we are in high altitude  = increases  BPG concentration in RBCs & cause decrease Hb -O2 affinity therefore our  breathing increases, to availability of O2 to tissue.

CARBON - DIOXIDE TRANSPORTED BY Hb :-

🐣CO2 binds with Hb & form = carbaminohemoglobin.

🐣Carbaminohemoglobin = binds with NH2 group of N terminal amino acids of alpha - & beta chains. 

🐣Hb transport = 23% CO2 &

🐣70% CO2 transported through blood plasma as bicarbonate ions.

🐥Next I'll post brief notes on SICKLE CELL HEMOGLOBIN (Hbs). &

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