1
In the name of
GOD
2
Zeinab Mokhtari
10

Feb

2010
3
Isothermal titration calorimetry (ITC)
thermodynamics
of macromolecular
interactions in
biological
systems
direct measurement of heat exchange
extent of binding
a single experiment : binding constant, Gibbs free energy, enthalpy and entropy
Advantages
can be performed in a physiologically relevant buffer
the interacting species do not require immobilisation or chemical modification
an accurate determination of the stoichiometry (
independent of the binding affinity
)
Introduction
R=
1.98
cal mol

1
K

1
from the titration equivalence point
4
:
multiple binding events
analysis of systems involving
complexes
protein
formation of multi
binding of multivalent ligands
ligand
cooperativity
ITC for dissecting the thermodynamics of cooperativity
5
Selection of an Appropriate Binding Site Model
At the
beginning
of the experiment the calorimetric cell is
filled
with the
macromolecule
.
correction for displacement of liquid :
sensed calorimetrically
Normal
titration
6
nonlinear least squares curve fitting
necessary energy to maintain a constant temperature
(in microcalories per second)
each injection
binding
heat exchange
interaction
heat after each injection : the area under each peak
Heat
α
amount of binding
Saturation of macromolecule with the ligand
classical sigmoidal curve
decrease of the peaks magnitude until the peak
size reflects dilution and mechanical effects
7
model :
simplest
The
a single independent binding site
1
:
1
ligand/macromolecule
Wiseman isotherm
It is only in
c
value ranges of
approximately
1
to
1000
that
isotherms can be accurately
deconvoluted.
nonlinear least squares curve fitting
n
,
K
b
and ∆
H
8
Complex macromolecular interactions that display cooperativity
alternative binding models :
and the possible
multiple binding sites
between the binding sites
cooperativity
multiple
titration experiments :
The
contents
of the syringe and calorimetric cell are varied.
A
single
ITC experiment is often
insufficient
to sample
the shape of the binding isotherm and may not allow
derivation of the binding and cooperativity
parameters
.
9
Multiple Binding Sites
n
multiple ligand binding sites
two
different association constants:
the overall behaviour of the
n
sites (model dependent)
how binding occurs at each site (
model
dependent)
macroscopic
microscopic
1
:
1
interaction
only
one
association constant
determined by ITC
Overall binding constant
Stepwise binding constant
10
j
:any integer between
0
and
n
for ligation of the
j
th site:
ν :
the average number of ligand molecules bound per macromolecule
For multivalent macromolecules
11
Cooperativity
positive (synergistic)
negative (interfering)
α : a unitless term defined as the cooperativity constant
(
α <
1
)
(
α >
1
)
Noncooperative
(additive)
(
α =
1
)
Figure
1
.
Reaction scheme for the binding of heterogeneous ligands,
X
and
Y
, to a macromolecule,
M
, containing two binding sites.
12
binding sites
two
for a macromolecule with just
possible binding mechanisms
six
at least
The binding sites may be :
Identical
Independent (Neutral cooperativity (
α =
1
))
Negative cooperativity (
α <
1
)
Positive cooperativity (
α >
1
)
nonidentical
Independent (Neutral cooperativity (
α =
1
))
Negative cooperativity (
α <
1
)
Positive cooperativity (
α >
1
)
13
Cooperativity: Thermodynamics and Conformational Changes
conformational changes in macromolecular structure
large conformation changes
subtle changes
reinforcement of the interactions between the ligand and the receptor
Enthalpy
functional group interactions (ionic, hydrogen bonds, van der Waals interactions)
conformational changes
polarisation of the interacting groups
electrostatic complementarity
Entropy
a measure of disorder in a system
caused by changes in internal
loss of motion
Changes in the binding entropy reflect
of the molecules.
vibrations
and
rotations
upon complex formation
counterions
and the release of
Desolvation
entropy

enthalpy compensation
enthalpic chelate effect
structural tightening
classical entropic chelate effect
14
binding sites
dependent
two
binding to a macromolecule with
heterotropic
Gibbs
–
Helmholtz relationship
Vel
´
azquez

Campoy
15
entropy
: governed by
Type I
enthalpy
and
entropy
: governed by both
type II
enthalpic
: predominantly
type III
driven.

entropy
and

enthalpy
can be both
cooperativity
Positive
entropic cost of the
combined
cooperativity occurs when the
positive
Entropydriven
sequential binding events is
lower
than the
summation
of two independent events.
cooperative occurs when binding of the first ligand results
positive
driven

Enthalpy
in a
conformational
change
at the second binding site, rendering it
higher affinity
to
the ligand.
driven and occur when binding results in

entropy
cooperativity : mainly
Negative
a
loss of configurational entropy.
cooperativity : ligand binding leads to a conformational
negative
driven

Enthalpy
change that results in the
dissociation of a complex
.
homodimeric enzyme glycerol

3

phosphate:CTP transferase
multivalent carbohydrates to legume lectins
dissociation of the trimeric G

protein
cooperativity
Negative
three types of cooperativity
16
Reverse ITC Experiments
In order to fully resolve the binding and cooperative thermodynamics
to check the
stoichiometry
and the suitability of the binding
model
1
:
1
biomolecular reactions :
It is expected that the measured thermodynamic parameters are
invariant
when changing the
orientation
of the experiment.
BUT
One species may display greater aggregation when
concentrated
.
If normal and reverse titrations are insufficient to
fully describe the microscopic binding constants
Combination of the ITC data with other biophysical data that can
explore cooperativity, such as NMR and spectrofluorometry.
global fitting analysis
17
(
1
)
Selection of an appropriate model/binding polynomial
(
2
)
Calculation of the total macromolecule and ligand concentrations for each injections
(
3
)
Solvation of the the ligand conservation equation for each experimental point assuming
certain values
(
4
)
Calculation of the concentrations of each different complex or bound state
(
5
)
Calculation of the expected signal, assuming certain values for the binding enthalpies
(
6
)
Obtaining the optimal constants and enthalpies that reproduce the experimental data
using an iterative method,
i.e.
,
nonlinear least squares regression
General Analysis Procedure
mathematical methods for analysing cooperative ITC data
18
Analysis of Cooperativity Using the Binding Polynomial
Freire
et al.
major advantage : model independent
equilibrium conditions : the binding of ligand by a multivalent macromolecule may
be described by a
binding
polynomial
The number of binding sites should be known or fixed prior to analysis.
macroscopic association constants
and
enthalpy values
model specific constants
determining the correct model
starting point for data analysis in the absence of a validated binding model
19
partition function,
P
, of the system
summation of the different
concentrations of bound
species relative to the free
macromolecule concentration,
or
summation of the
concentration of free ligand in
terms of the macroscopic
association constant
fraction or population of each species
average number of ligand molecules bound per macromolecule
average excess molar enthalpy
average Gibbs free energy
model independent
20
three
states for a macromolecule with
two
binding sites
identical
binding polynomial for each
model
: summation of the terms in each
column
relative concentration of the
states
independent
general binding polynomial
21
ligand
homotropic
binding sites for a
two
a macromolecule with
example
Occupancy of the
binding sites
ligand concentration
association constants
cooperativity factor
event
heat
determined

nonlinear least squares regression analysis of the experimentally
22
accurate values for
β
j
and ∆
H
j
thermodynamic parameters
cooperativity factor
The value of the cooperativity parameter provides a very strong indication of the true binding model.
relate the macroscopic binding parameters to the microscopic binding parameters
23
Heterotropic Interactions
two different ligands
(
1
)
both ligands bind to the same binding site
(
2
)
both ligands bind to sites very close to one another, so that the ligands
themselves or binding site residues in the macromolecule interact
(
3
)
both ligands bind to binding sites distant to one another,
but are coupled
through a change in protein dynamics/conformation
Three mechanisms of
cooperativity
24
titration of ligand
X
into a calorimetric cell containing both
macromolecule, [
M
]
t
and ligand [
Y
]
t
assuming values of the
association
and
cooperativity constants
free concentrations of the reactants, [
M
], [
X
] and [
Y
]
concentrations of the complexes, [
MX
], [
MY
] and [
MXY
]
mass action law
solving the set of nonlinear equations numerically by the
Newton

Rhapson method
:
25
Only
one titration
experiment is required to determine the
interaction parameters instead of a series of experiments,
saving both
time
and
material
.
evaluating the heat effect,
q
i
,
associated with each
injection
by
nonlinear least squares fitting
26
Figure
2
.
Global and cooperative thermodynamic parameters associated
with the negatively cooperative binding of Fd to FNR

NADP+.
strong negative cooperativity
unfavourable
entropy
favourable
enthalpy
NADP+ complex with Fd

Titrations of FNR
α
=
0.17
Binding affinity is reduced by sixfold
when NADP+ is prebound to FNR.
27
Cooperativity of Long

Chain Macromolecules with Multiple Binding Sites
one

dimensional lattices
nucleic acids and carbohydrates
:
footprint
the minimal number of repeating units necessary to support binding (
l
)
characterisation of protein

lattice systems
affinity of the interaction
how the affinity varies with lattice heterogeneity
the binding site size (
l
)
whether ligand binding is cooperative
potential binding site overlap
cooperativity between neighbouring ligands
Ligands can bind to
lattices in three ways:
isolated binding
singly contiguous binding
doubly contiguous binding
intrinsic association constant
in the presence of neighbouring ligands
cooperativity factor,
α
28
homogenous lattice
actual number of free ligand binding sites on an unoccupied lattice
N

l
+
1
Figure
3
.
The three distinguishable types of ligand binding sites
29
Scatchard plot
a linear representation to facilitate data analysis
only linear when
l
=
1
and the binding sites are equivalent and independent
McGhee and von Hippel
any size of ligand footprint
cooperative interactions between contiguously bound ligands
infinite polymer
Extended by Tosodikov
et al. :
finite lattices
When
l >
1
, positive curvature reflecting the entropic resistance to saturation
30
Introduction of a cooperativity factor,
α
Scatchard plot is affected both by the entropic resistance
to saturation and the cooperativity parameter,
α
.
due to the entropic
negative cooperativity
Only linear if the apparent
.
positive cooperativity
resistance to saturation is compensated by real
the enthalpy associated with
the interaction between two
adjacent bound ligands
31
32
nature of the cooperativity
Change of the binding modes during the course of the titration
Non

cooperative system
Isolated ligands will bind initially, followed by singly contiguous ligands
and finally doubly contiguous ligands with two nearest neighbours.
Positively cooperative system
The ligands will immediately cluster forming doubly contiguous ligands.
Negatively cooperative system
Isolated ligands would form initially, and only when ligand accumulated
would singly contiguous ligands be observed. Ligands with two
neighbours would only accumulate at very high ligand concentration.
Reverse titrations
to fully characterise the binding isotherms
the roles of the ligand and macromolecule reversed
33
An alternative method of implementing the
Non

cooperative McGhee
–
von Hippel model
Shriver
change in concentration of bound protein as the result of the
i
th injection
the heat of
dilution
observed with each injection after
saturation
of the binding sites at the
end of titration
can be solved for values of
k
and
l
34
Example:
Chromatin Protein Sac
7
d Binding to DNA
Binds
non

cooperatively
and
non

specifically
to the
minor groove
of duplex DNA
induces a significant
kink
(
66
°
) in the DNA structure
Titrations :
Sac
7
d
and
poly(dGdC)
non

cooperative McGhee
–
von Hippel model
ITC data
25
°
C
moderate intrinsic affinity (approximately
833
nM)
ligand footprint of
4.3
base pairs
entropy driven (
17.5
kcal mol
¡
1
)
unfavourable enthalpic contribution (
9.2
kcal mol
¡
1
)
polyelectrolyte
effect
energy needed to
distort DNA
and
unwinding
,
pair unstacking

base
is associated with
Kinking
as well the
widening of the minor groove
, which leads to
bending
release of water and counterions
(which would contribute to the
.
backbone charge redistribution
term) due to
entropy
favourable
35
Global Analysis
multiple titrations, such as normal and reverse titrations
increase the information and precision of the parameters as
long as unrecognised systematic errors are not introduced
temperature and pH dependence
floating parameter
n
:
Reaction stoichiometry and concentration errors
n
is often a non

integer
In global analysis
only integral values
reflecting the
stoichiometry
are permitted.
Therefore it is necessary to accurately determine the stoichiometry prior to
global analysis by
alternative biophysical techniques
.
multisite and cooperative binding
SEDPHAT
Houtman
et al.
global analysis of data from a variety of biophysical techniques
36
Figure
4
.
Thermodynamics of the binding event determined by application of the
non

cooperative McGhee
–
von Hippel model to ITC data
Favourable entropy
Unfavourable
enthalpy
energetic penalty of kinking DNA
37
Global analysis of ITC data
role of
cooperativity
in the assembly of a threecomponent multiprotein complex
Example:
LAT, Grb
2
and Sos
1
Ternary Complex Assembly
To reduce the complexity :
LAT
pY
191
can bind one Grb
2
molecule, which in turn can bind one Sos
1
NT molecule.
Two titrations were performed:
LAT
pY
191
into Grb
2
alone
and
LAT
pY
191
into a stoichiometrically mixed
1
:
1
Grb
2

Sos
1
NT solution
global model for the
ternary interaction
K
d
=
286
nM
∆
G
=

8
.
9
kcal mol

1
∆
H
=

3
.
9
kcal mol

1
In the presence
of Sos
1
NT:
α =
0.54
∆
g
=
0.37
kcal mol

1
∆
h
=

3
.
9
kcal mol

1
A model without permitting cooperativity was unable to account for systematic difference
in the initial heats of injection for LAT phosphopeptide to Grb
2
in the presence and
absence of Sos
1
NT and resulted in an almost threefold increase in the
χ
2
of the fit.
38
Combination of ITC and NMR to Study Cooperativity
NMR
spectroscopy
measuring the occupancies of individual binding sites
determining the
microscopic binding affinities
site

specific data
macroscopic binding data from ITC
Full characterisation of the microscopic and macroscopic binding affinities
(
2
D HSQC)
isotope

enriched two

dimensional heteronuclear single

quantum coherence experiment
(A method of determining
cooperativity
using
NMR
spectroscopy)
isotopically
labeled
ligands
(usually
1
H and
13
C or
15
N)
unenriched macromolecule
Isotherms are generated by plotting the peak volume integration against molar ratio.
site

specific binding models
39
Example:
Glycocholate Binding to I

BABP
Human ileal bile acid binding protein (
I

BABP
)
glycocholate
binding sites for
two
the physiologically most abundant bile salt
intrinsically
weak
affinity
extremely strong
positive
cooperativity
But
low ligand
–
protein ratios : a significant amount of glycocholate remains unbound
high ligand
–
protein ratios : more ligand is bound
ITC and heteronuclear
2
D HSQC NMR
sequential model
glycocholate was isotopically labeled
three
main resonance peaks :
unbound
glycocholate, glycocholate bound at
site
1
and glycocholate bound at
site
2
site

specific binding model
NMR : microscopic affinities , cooperativity constant
multiple sites
different ligands
40
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