# CHAPTER 5 - BINDING

## B:  MATHEMATICAL ANALYES OF BINDING GRAPHS

Last Updated: 3/25/16

 Learning Goals/Objectives for Chapter 5B:  After class and this reading, students will be able to derive equations  from the equation for fractional saturation  Y = ([ML]/[M0] = [L]/(KD+ [L])  equations for 1/Y as a function of 1/[L] (double reciprocal plot), Y/[L] vs Y (bound/free vs bound or the Scatchard Plot) and draw a plot of Y vs log [L] (semilog plot) draw error bars on the plots of Y vs L, 1/Y vs I/L, Y/L vs Y and Y vs log L. explain from these derivative equations and graphs how to calculate determine Kd describe appropriate methods to fit the data from these equations with special attention given to the effect of error bars in the experimental value of Y

# B2.  Binding of Two Identical Ligands

Explore the interactive graphs below to see how binding of identical ligands to two independent sites with different affinity changes the nature of the binding graphs. The subtle changes in the graphs should make it clear that binding analyses should be done with a rigorous mathematical analysis fitting of data to the simplest hyperbolic model before moving on to more complex models.

Hyperbolic Graph for Two Independent Binding Sites

Wolfram Mathematica CDF Player - Fractional Saturation of Sites (0-1)for Binding of L to 2 Independet Sites - Hyperbolic Plot (free plugin required)

Interactive SageMath Graph: Fractional Saturation of Sites for binding of L to 2 Independent sites

Double Reciprocal Graph for Two Binding Sites

Wolfram Mathematica CDF Player - Fraction Saturation of Sites (0-1) for Binding of L to 2 Sities - Double Reciprocal Plot.  (Note that 1/Y max is 1 at the y intercept)

Scatchard Graph for Two Binding Sites

TBA

Wolfram Mathematica CDF Player - Semilog Plot for binding of ligand to 2 independent sites

Interactive SageMath Graph: Semilog Plot for binding of ligand to 2 independent sites