# Binding Curves and Hill Plots psst, don’t overthink this shit it’s literally just L + ratios but with saturation and (non)cooperative binding (and thrown onto a graph in a dumb way) https://www.andrew.cmu.edu/course/03-231/DryLab/Coop/nonCoop.htm > [!important]+ Partial Pressure vs Equilibrium Constants > This note will try to > Partial pressure ($pO_2$) ## Binding Curves A ligand-binding curve plot can depict the Fractional Saturation ($Y$) Hill Coefficient: describes degree of cooperativity ![[Pasted image 20231119211311.png]] A hyperbolic curve illustrates non-cooperative binding while a sigmoidal curve indicates cooperativity. $K_d=[L]$ at which $Y_L=0.5$ $Y=$ The **fractional saturation** of the enzyme, defined as the ratio of bound substrate to total binding sites As the concentration of the ### Impact of Cooperative Binding ![[Pasted image 20231205141358.png|300]] Hemoglobin has four oxygen binding sites which ## Hill Plots The **Hill equation** is a mathematical representation used to quantify the *degree of cooperativity* between binding sites. $Y=\frac{[L]^n}{{K_a}^n+[L]^n}$ ![[Pasted image 20231119211259.png]] ### The Hill Equation > [[Logarithms]] **The Hill Equation:** $Y_{O_2}=\frac{(pO_2)^n}{(p_{50})^n + (pO_2)^n}$ --- Taking the log of both sides gives us a linear equation of the form: $y=mx+b$ $\log(\frac{1-Y}{Y}) = n \cdot \log ([L]) - n \cdot \log (K_d)$ The x-intercept = $\log(p_{50})$ The y-intercept = $n\cdot\log(p_{50})$ $K_d = p50 =$ **The Hill Constant** - $n > 1$ indicates positive cooperatively binding - $n<1$ indicates negatively cooperative binding - $n=1$ indicates noncooperative (completely independent) binding