Ligand Binding
Most, if not all, biological processes/phenomina depend on
binding/interactions of molecules.
Antibody-antigen / Enzyme-sustrate / Receptor-hormone /
Protein-protein / Protein-lipid / Protein-carbohydrate / ProteinDNA / Protein-RNA /…etc, etc, etc…
Without binding, there is no biology!
2358 interactions for the 1548 proteins in the yeast proteome
Nat. Biotechnol. 18, 1257
What information do we need to get a full understanding
of ligand binding from biochemical perspective?
THERMODYNAMICS
Stoichimetry (n)
Affinity (Kd)
other thermodynamic properties (H, S, Cp)
KINETICS
rate constants for association (kon) and disociation (koff)
Reaction mechanism
STRUCTURE
Three-dimensional structure of the individual interacting
partners and their complex(es)
DYNAMICS
Molecular dynamics of individual interacting partners and their
complex(es)
P + L
k1
k2
PL
k1 is the association rate constant with units of M-1s-1, k2 is the
dissociation rate constant with uinits of s-1
The rate of formation of PL is k1[P][L]; the rate of breakdown of
PL is k2[PL]; at equilibrium, k1[P][L] = k2[PL]
Kd 
k2 [ P][ L] 1

 K ; Kd = dissociation constant
eq
k1
[ PL]
[P] = free protein concentration
[L] = free ligand concentration
[PL] = complex concentration = bound ligand concentration
r
[L]bound
[ PL]
([P][L]) Kd
[ L]



[P]total [P]  [PL] [ P]  ([P][L]) Kd Kd  [ L]
r = fraction of binding sites occupied
What happens when [L] << Kd?
What happens when [L] >> Kd?
Thermodynamic properties of a binding reaction
Binding constants provide an entry into thermodynamics
and viceversa
Keq
G = −RTlnKeq
∂lnKeq
∂T-1
H
∂H
∂T
 Cp
 G =  H − T S
G = Hr − TSr + Cp[(T − Tr) − Tln(T/Tr)]
What do G, H and S means for ligand binding?
G = binding affinity
H = change in the energy of the system, related to moleculasr
interactions such as electrostatics, van der Waals interactions
and hydrogend bonds
S = change in the degree of disorder or randomness in the
system, of which the most interesting parts are changes in
conformational dyanmics and hydrophobic interactions
WORKFLOW OF QUANTITATIVE CHARACTERISATION OF
BIOMOLECULAR BINDING INTERACTIONS
PRODUCTION
OF
REACTANTS
CHARACTERISATION
OF REACTANTS
IMPROVED
EXPERIMENTAL
DESIGN
SIMULATION
SELECTION
OF
METHOD(S)
BINDING
EXPERIMENT
INTERPRETATION
(BIOLOGICAL
SIGNIFICANCE)
Equilibrium MODEL
SELECTION and/or
CONSTRUCTION
RESULTS
DATA ANALYSIS
(FITTING &
STATISTICS)
BINDING
EQUATIONS
From Gonzalo Obal
Methods for measuring binding constants
Methods
Equilibrium
dialysis
Signal
radioactivity
Information
Kd
Advantage
large range
Fluorescence
spectroscopy
NMR
fluorescence
Kd (10-4-10-10 M)
fast
chemical shift
Kd (10-3-10-6 M)
ITC
heat of binding
Kd (10-4-10-9 M)
H, S, n
SPR
refractive index
Stopped-flow
fluorescence
Kd (10-3-10-8 M)
k1, k2
Kd (10-4-10-12 M)
k1, k2
Structural
information
No label needed,
complete binfing
parameters
small sample,
automated
fast
Disadvantages
usually for small
molecules; probe
needed
probe needed
large sample
large sample
surface coupled;
for large ligands
probe needed
Which ones are thermodynamic (equilibrium) methods?
Which ones are kinetic methods?
Spectroscopic Kd measurements
k1
P + L
PL
k2
ff 
[P]
[PL]
, fb 
, ff  1  fb
[Pt ]
[Pt ]
Sobs  Sf f f  Sb f b  Sf (1  f b )  Sb f b
 Sf  (Sb  Sf ) f b
 Sf  (Sb  Sf )[PL] / [Pt ]
Kd 
[P][L] ([Pt ]-[PL])([L t ]-[PL])

[PL]
[PL]
K d [PL]  [Pt ][L t ]  ([Pt ]  [L t ])[PL]  [PL]2
[PL]2  ([Pt ]  [L t ]  K d )[PL]  [Pt ][L t ]  0
[PL] 
[Pt ]  [L t ]  K d  ([Pt ]  [L t ]  K d ) 2  4[Pt ][L t ]
2
Sobs  Sf  ( Sb  Sf )
[P ]  [L ]  K
t
t
d

 ([Pt ]  [L t ]  K d ) 2  4[Pt ][L t ] [Pt ] / 2
Ff=100, Fb=30, [P]tot=1 M
Kd=0.01, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10 M
For best results, one designs a ligand-binding assay so that
[P]tot < 50  Kd, and [L]tot varies from 0 to >10  [P]tot
and >10  Kd
Isothermal titration calorimetry (ITC) – thermodynmic analysis
of binding
 Directly measure the energetics of ligand binding
 Universily applicable
 Label-free
Instrumentation
Before titration
From Stoyan Milev
GE Healthcare
Titration begins: first injection
Returns to baseline
From Stoyan Milev
GE Healthcare
Second injection, third injection, ……
End of titration
From Stoyan Milev
GE Healthcare
From Gonzalo Obal
From Gonzalo Obal
Surface plasma resonance (SPR) measurements – kinetic
analysis of binding
Schematic diagram of the setup of a surface plasmon resonance biosensor
Schematic graph showing surface plasmon resonance biosensor signal expected for a simple 1:1
interaction with binding kinetics of pseudo-first-order. Superposition of the expected signal for
different concentrations of mobile reactant. Association phase from 0-500 s, followed by a
dissociation phase from 500-1000 s.
k1
k2
PL
k1[L]
k2
PL
P+L
P
kapp  k1[L]
R (t )  R0  ( Req  R0 )(1  e  kobst )
kobs  k1[L]  k2
PL
k2
P+L
R (t )  R  ( Req  R )e  k2t
Thermodynamic analysis surface plasma resonance
measurements – self-consistency tests
[L]
Req (L)  R0  ( Rsat  R0 ) eq
K d  [L]
Consistency test 1.
K deq  K dkin 
k2
k1
Consistency test 2a.
kobs  k1[L]  k2
The value of k2 obtained from the analysis of the association
data should be approximately equal to that determined directly
from the dissociation data.
Consistency test 2b.
At the minimal level of consistency, the value of k2 obtained
from the analysis of the association data must be greater than
zero and kobs must be greater than k2 determined from the
dissociation data.
Rova, U. et al. (1995) Biochemistry 34, 4267-4275