Theoretical Binding Models

Question 1

Single Site Binding Model

Answer 1

[M] = free protein
[L] = free ligand
[ML] = protein ligand complex

Question 2

Assumptions of Binding

Answer 2

• reversible
• ligand availability is limited only by diffusion
• measurements taken when thermodynamic eq. is reached
• assumptions supported with structural data about number of ligand binding sites / conformational changes on binding

Question 3

Rates of Binding

Answer 3

forward rate : kon [M][L]
forward rate : koff [ML]
- at equilibrium the rates are equal
Kon / Koff = Ka (association constant)
- Kd is Koff / Kon

Question 4

Association Constant

Answer 4

• high affinity binding: large Ka

- low affinity binding: small Ka

Question 5

Thermodynamics of Single Site Binding

Answer 5

• change in standard Gibbs free energy of association
• Gibbs free energy links free energy changes with binding constants
  G = -RTlnKa

Question 6

Fractional Saturation

Answer 6

• fraction of protein saturated with ligand
• 0-1
  Y = [ML] / [M][L]
• Y easily determined from quantity measured in the experiment
• but by rearranging we can express Y in terms of ligand concentration and not protein ligand complex concentration
  Y = [L] / Kd [L]

Question 7

Langmuir Isotherm

Answer 7

• hyperbolic binding curve
• [L] vs. Y
• Kd is the ligand concentration at which binding site is half saturated (Y = 0.5)

Question 8

Semi-log Plot

Answer 8

• plot binding curve on a semi-log plot

- changes in affinity shifts the curve to the right and Kd comparison is easier

Question 9

Experimental Errors

Answer 9

• systematic errors: incorrect binding model, aggregation, inactive protein, etc
• random errors: random experimental errors

Question 10

Scatchard Equation

Answer 10

The Scatchard equation is an equation used in molecular biology to calculate the affinity and number of binding sites of a receptor for a ligand
* see equation *

Question 11

Scatchard Plot

Answer 11

• Scatchard plot shows that the slope equals to -1/Kd while the x-intercept equals the number of ligand binding sites n.
• linearising the data by transforming the expression for Y
• plot Y/[L] vs Y
• higher affinity has a steeper gradient
• easier to see deviations from a straight line but transformation multiplies errors

Question 12

Scatchard Analysis

Answer 12

• mix solution of retinoic acid receptor and retinoic acid that is radiolabelled
• add charcoal pellets to bind free ligand and remove it
• then analyse the receptor and bound ligand

Question 13

Kd when receptor concentration is not known

Answer 13

** see notes

Question 14

Multiple Sites of equal affinity

Answer 14

• two binding constants (K)
• macroscopic eq. association constants for binding of the 1st and 2nd ligands respectively
• independent binding to multiple sites can be analyzed as for single site binding except Y replaced by v
• ** see notes!!!!!

Question 15

v

Answer 15

[M] of bound protein / total [M] of protein
- varies from 0 to n
v = 2[L] / Kd + [L]

Question 16

Plotting Multiple Binding Sites

Answer 16

• scatchard plot of v vs v/[L]
• intercept of n/Kd
• gradient of -1/Kd
• model is similar to normal Scatchard equation except Y is replaced by v

Question 17

Cooperative Binding

Answer 17

• binding of first ligand changes affinity for 2nd ligand
• positive cooperativity: binding enhances affinity
• shape goes in a N shape as low affinity goes to high affinity back to lower
• negative cooperativity: binding reduces affinity
• gives a parabolic Scatchard plot (N or U shape)

Question 18

Hill Plot

Answer 18

• quantitative analysis of cooperativity
  The Hill plot is the rearrangement of the Hill–Langmuir Equation into a straight line.
  A slope greater than one thus indicates positively cooperative binding between the receptor and the ligand, while a slope less than one indicates negatively cooperative binding.

Question 19

Calcuation and Fitting of Binding Data

Answer 19

** SEE NOTEs **