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Quantitative properties of protein-protein interactions

Ed Evans, T-cell biology group


Why this lecture?

• Protein/protein interactions are fundamental to biology and therefore to medicine!

• In the past much of the focus has been on qualitative information.

a) What proteins interact?b) What is the function of the interaction?

• Now quantitative information is also considered increasingly important


An example: T-cell co-stimulationCD80

CD28 CTLA-4CD28 CTLA-4

CD86

Co-stimulation Inhibition

20M 4M 3M 0.2M

AffinityValencyStoichiometry

~10,000times

stronger


Why this lecture?

• Protein/protein interactions are fundamental to biology and therefore to medicine!

• In the past much of the focus has been on qualitative information.

a) What proteins interact?b) What is the function of the interaction?

• Now quantitative information is also considered increasingly important

a) Helps understand molecular mechanismsb) Essential for modelling complex processesc) Important for drug discovery


What we’ll cover (hopefully)

1. What binding properties are important?

2. How might we measure them? (introduction – more tomorrow!)

3. Comparison of interactions ‘in solution’ vs. at the cell surface


1. What binding properties are important?

One protein soluble:

Affinity Valency(Kinetics)(Thermodynamics)

Cell-cell interaction:

Mechanical Stress(unbinding force)

Real membranes:

Lateral diffusion rate

Inter-membrane distance (size)

Abundance => Avidity

A T O M I C S T R U C T U R E


Molecules involved … T-cell surface

CS1 CD11a*‡

TCR1* CD6* CD50*

CD48*

CD164

CD96* CD99 CD7*

CD244 CD97*NKp30*

CD147 CD46

CD162/R*

CD5*CDw210*

ESL-1

CD69*

??

CD71CD103‡ CD222

CD223

CD43

NTBA

CD100

CD107a

?

?

CD95

CD8 1*

Toso

CD120a

CD150

CD178

CD49a‡CD224

?

CD26

?

CD70CD86 RAGE

CD101CD160

CD168

?

CD201

CD226CD229

?

CD38

CD44

CD44R

CD49c‡ CD51‡ CD56

CD58 CD72 MAFA-LST2L

SRCLPorimin

CD146

CD45*

P

P

?

???

MDC-L

CD230

?

CD2*CD52*

Galectin-1

CD225*HM1.24

?

CD39 CD184*TIRC7* CD53*

CD122*

CD37*

Galectin-3

CD195* CD63

EDG4 CD47R CD183

CD132*CD25

Galectin-9

?

apoB48R

CCR1 CCR2

?

CD132*CD127

CXCR5 TRAILR2

CCR4

CRTH2Galectin-11

Galectin-13IL-11R

OAP-1

CD59

TR2

??

GPR68* FLJ23270*

CD247()*

CD3*TCR2* CD236R

2*

NKG2E/H*CD94

CD68

?

NKG2-F


Molecules involved … T-cell surfaceIncluding less well characterised / housekeeping molecules...


Background: binding models1. The majority of protein:protein interactions are

simple 1:1 associations: A + B ABThis is what we will focus on in this lecture.

2. The most common variation of this scheme is where one protein (e.g. B) has additional binding sites.

e.g. AB + A A2B or AB + C ABC

3. If these binding sites are independent then one simply treats each interaction as a 1:1 association and adds them together.

4. If the binding sites are not independent then one has positive or negative cooperativity (i.e. allosteric effects) and more complex modeling is required.


What binding properties are important?

• Affinity

– KA (affinity constant) or KD (dissociation constant)

– KD= 1/KA

• Kinetics

– kass or kon (association rate constant or on rate)

– kdiss or koff (dissociation rate constant or off rate)

• Thermodynamic properties H (enthalpy change on binding)

S (entropy change on binding)

C (heat capacity change on binding)


Affinity

1. Measures how favourable an interaction is 2. Best expressed as affinity constant: KA

3. For A + B AB

– Best thought of as the ratio of [products] vs. [reactants] at equilibrium

– Note the units (M-1)

– Higher affinity = higher KA

Deqeq

eqA KBA

ABK

1


Affinity

4. Also expressed as dissociation constant: KD

– The inverse of KA

– Usually thought of as concentration of A at which half of B is bound ([B]=[AB]) at equilibrium

– Units are M

– Higher affinity = lower KD

eq

eqeqD AB

BAK


Measuring the affinity constant

1. One could simply measure [A], [B] and [AB] at equilibrium and calculate KD

2. In practice this is difficult and the following approach is used.

3. Increasing fixed concentrations of one molecules A ([A]) are added to a fixed small amount of its ligand B and you measure the amount of bound A (Bound)

4. Plot the results and fit the 1:1 Langmuir equation to the data to determine KD and Boundmax

D

D

total

D

KA

BoundABound

KA

ABAAB

ABAB

ABBB

AB

BAK

max

max

max

or

][

getweg,rearranginand

)1(into)2(ofonsubstitutiBy

)2(

and

)1(

DERIVATION


Measuring affinity constant

DKA

BoundABound

max

Bou

nd

(arb

itra

ry u

nit

s)

[A], M

KD = 19 M

Boundmax=200

• Data are circles• Line is non-linear fit of the

equation performed by a computer (e.g. Origin, R)

• Gives the indicated values for KD and Boundmax

• If the fit is good it indicates that binding follows the simple 1:1 model

• Difficult to see if fit is poor in this plot


Scatchard plot

• A plot of

• Linear for a 1:1 interaction• If curved it indicates wrong

model and possible problem with the experiment

• Most commonly concave upUsually caused by

experimental error (often heterogeneity)

Sometimes due to negative cooperativity

• Far less common is to see concave downUsually caused by positive cooperativity

Bou

nd

/[A

]

Boundmax

versus AA

Bound

Slope = -1/Kd


**** **

T cell

bilayer

boundfree

Dustin et al. 1996 JCB 132, 465

Experimental set-up Data collection

Measuring 2D Kds


Comparing 2D and 3D affinities

110100 0.11000

3D Kd (M)

hCD2TCRCD28

CTLA-4KIR

CD8SLAM

CD4

2D Kd (mols/m2)47 1.1hCD2rCD2

rCD2

Kd > 2 M

“barely adequate” strong interaction


Thermodynamics of binding

1. Binding is favoured if it leads to a net increase in disorder or entropy.

2. This includes entropy of….a) the system (interacting molecules and solvent)

• represented as change in entropy or S b) the environment (everything else)

• as the system releases or absorbs heat it changes the entropy of the surroundings

• heat release is measure as change in enthalpy or H


Gibbs free energy change

1. The change in Gibbs free energy (G) is a measure of the net change in universal entropy - i.e. the extent to which binding is favoured.

G = H -T SIf G < 0 then binding is favoured.

2. G depends on concentration. At equilibrium G = 0

3. Go is the standard state G which assumes all components are at the standard state concentration of 1 M (mol.L-1)

4. It can be calculated from the affinity constant

Go = RTlnKD

R = Gas Constant (2 cal.mol-1.K-1) T = absolute temp. in Kelvin (oC+273.18) and KD is expressed in units M


Origins of enthalpy and entropy changes

Go = H -TSo

1. Change in enthalpy (H)a) Release of heat (H <0) favours bindingb) This happens when bonds are formed

• e.g. hydrogen bonds, salt bridges, van der Waals contactsc) However bonds are also broken upon binding

• displacement of water and ions (always)• conformational change (sometimes)

2. Change in entropy (TS)a) Increase in entropy (S >0) favours bindingb) Protein/protein interactions leads to decrease in entropy

• Stabilise conformation at the binding interface• Decreased rotation/translation of proteins

c) However displacement of water from the binding interface leads to an increase in entropy (the hydrophobic effect)


The key role of water

1. Water is present at very high concentrations (55 M) and interacts with protein surfaces

2. Thus, many water bonds need to be broken, which has an unfavourable enthalpic effect

3. Water can also act as glue filling in gaps between surfaces that lack surface shape complementarity

4. Water is believed to form an organised shell over hydrophobic surfaces. Ejection of water from these surfaces into free solution has favourable entropic effect. This is the ‘hydrophobic effect’.

5. Note that there is a weak unfavourable enthalpic effect as well since the water molecules in the shell interact weakly

Hydrophilic patchin binding site

binding

binding

Hydrophobic patch


15

10

5

0

-5

-10

-15

-20

-25

Antibody/protein

(11)

Protein/protein

(30)

TCR/pep-MHC

(2)

kcal

/Mol

H

Go

-TSo

TCR and antibody binding have distinct thermodynamic properties

(Data from Willcox et al 1999 and Stites 1997)

Favourable

Unfavourable


Changes in conformation at a T cell receptor/peptide-MHC interface

TCR

pMHC

Garcia et al (1998)


Heat capacity change (C)

1. H and TS usually vary with temperature2. The extent of this variation is given by C3. This is a consequence of changes in water

with temperature

binding

Low temp – binding disrupts water ‘shell’ with unfavourable effects on H and favorable effects on S

Hydophobic patch

binding

High temp – water shell already ‘melted’ so both effects are lost

Hydophobic patch


Why measure heat capacity change? 1. S includes

contributions from changes in solvent entropy (hydrophobic effect) and protein entropy

2.The heat capacity change can be used to estimate solvent entropy change, enabling estimation of the protein entropy change.

DETAILED EXPLANATION(Spolar and Record (1994) Science 263:777)

• C correlates with non-polar surface area that is buried by binding (Anp) =>

• C can be used to estimate the contribution of the hydrophobic effect (She) to total entropy change (STotal)

• The change in rotational and translational entropy (Srt) can be calculated, and is same for all protein-protein interactions.

• Thus Sother can be calculated since

STotal = She + Srot/trans + Sother

• Main contribution to Sother is thought to be reductions in conformational flexibility accompanying binding i.e. it’s a measure of amount of conf. change


Measuring thermodynamic parameters

1. S can’t be measured directly2. G and H are measured and

G = H -TS 3. H can be measured in 2 ways

a)calorimetry (see later) or b)van’t Hoff analysis

Van’t Hoff analysis1. G is measured over a range of

temperature and plotted2. The non-linear van’t Hoff

equation* is fitted to the data to determine H, S and C

3. The slope represents H4. This plot is curved for

macromolecular interactions as H varies with temperature

5. The curvature represents C etemperatur reference abitrary an is where

ln)(

equationHofftvan'linearNon*

To

To

TCTToTCSTHG ToTo


Kinetics

Since biological systems are not at equilibrium,the rate of binding and dissociation is criticalFor a simple 1:1 interaction (A + B AB)…1. Rate of dissociation

a)d[AB]/dt = k diss[AB] b)where kdiss is the dissociation rate constant (koff)

2. Rate of association a) d[AB]/dt = kass[A][B]b)where kass is the association rate constant (kon)

3. At equilibrium the rate of association must equal the rate of dissociationkdiss[AB] = kass[A][B] =>kdiss/kass = [A][B]/[AB] = KD


Dissociation

• Any reaction of the form d[AB]/dt ∞ [AB] will be exponential so

a) i.e. [AB]t = [AB]oe-kdisst

b) kdiss determined directly by curve fitting

• The half life (t1/2) can be calculate as follows:

Since at t = t1/2

[AB]t/[AB]o=0.5=e-kdisst1/2

It follows that -kdisst1/2= ln(0.5) = 0.693

Thus t1/2 = 0.693/koff

Dissociation ofA from BSymbols are data, lines are fitted curves

t1/2


Association

• In most experimental system it is impossible to follow association alone in the absence of simultaneous dissociation

• For the simple interaction A + B AB

d[AB]/dt = kass[A][B] – kdiss[AB]

It follows that [AB]t=[AB]final (1-e-kobst)

where kobs = kass[A]+koff

Thus one needs to know koff and [A] as well as measuring [AB] to calculate the kon


Determination of binding kinetics

kobs = [A]kass+ kdiss kass

42000 M-1.s-1

kdiss 0.5 s-1

KD 1.2 x 10-5 M

Residuals plot (difference between data and fitted curve)

Association phase (kobs)

Dissociation phase (kdiss)


Factors affecting kinetics

1. The association rate constant does not vary that mucha) Association requires two proteins to collide in the correct

orientation and in the correct conformationb) Depends on diffusion so will be similar for most proteinsc) The basic rate is about 105 M-1.s-1

d) Can be accelerated by long range electrostatic forces • Increased rate of collision• Steer binding sites into correct orientation• E.g. barnase/barnstar interaction

2. The dissociation rate constant varies considerably and is responsible for most variation in affinity constants

a) It is determined by the number and strength of bonds in the contact interface

b) Depends on size of interface and the degree of surface-shape and electrostatic complementarity


Summary of average affinity and kinetic constants for biological interactions

Interaction kon (M-1s-1) koff (s-1) KD (M)

Cell-cell recognition molecules

105 1-1010-5 to

10-4

Antibody/antigen 105 10-3 10-8

Cytokine/receptor 105 10-4 10-9

Enzyme/inhibitor (eg barnase/barnstar)

108 10-3 10-11


Transition state theory(or activation complex theory)

1. Proposes that when two molecules interact they traverse a mountain-like energy ‘landscape’.

2. Highest energy point is the putative transition state (AB‡).

3. The height of this point determines rate constant

4. Transition state then ‘relaxes’ into the final complex (AB).

‡Gdiss

A+B

AB‡

Binding coordinate

Pote

nti

al en

erg

y (

kcal.

Mol-1

)

AB

‡Gass

G

‡Gdiss


•Assume reactants are in equilibrium with transition state => it is possible to apply thermodynamic principles

A + B↔AB‡ => ‡G = ‡H-T‡S‡G : calculate from kass

‡H : determine by measured temperature dependence of kass

=> T‡S can be calculated

•Analyse in the same way as described previously

•Application: to study the structure of the transition state complex (i.e. how binding occurs)

e.g. by examining the effect of mutations on these values one can determine which residues in the binding site interact in the transition state complex

•The same approach can be used for dissociationAB↔AB‡

Transition state theory


• Breaking a bond analogous to pulling a cart up a hillheight of hill = work required = bond energyslope of hill = force required = mechanical strength

• Force = work/distanceMechanical strength = bond energy/bond length

bond energy

bond length

long bond length

short bond length

slope = mechanical strength

The importance of bond length


The mechanical strength of a bond is only indirectly related to affinity

Mechanical strength = bond energy/bond length =>

1. The bond energy is likely to be more closely related to the enthalpy change (ΔH) than the affinity (ΔG) since ΔH measures net number of bonds broken

2. Since some bonds reform during dissociation mechanical strength is related to the number of bonds broken to reach the transition state of dissociation

3. This is given by the activation enthalpy of dissociation or Δ‡Hdiss


IMPLICATIONS:

• Mechanical strength should be measured directly if possible.

• This can be done using techniques such atomic force microscopy

The mechanical strength of a bond is only indirectly related to affinity


2. How can we measure them?

SPR(BIAcore)

AUC ITC(microcalorimetry)

Surface Plasmon

Resonance

AnalyticalUltracentrifugatio

n

IsothermalCalorimetry


Measuring key properties of protein-protein interactions

Property AUC BIAcore Calorimetry

Affinity + ++ +

Enthalpy no + ++

Entropy no + ++

Heat capacity no + ++

Kinetics no ++ no

Stochiometry + + ++

Size & Shape + no no



•For most interactions of soluble proteins, want strong, specific interactions

•But what about on the cell surface?• How can you get TRANSIENT adhesion?

(especially given number of molecules on a cell!)

•PROBLEM: how to reduce affinity without reducing specificity?• Reducing area of interaction will reduce both


3D Kd (M)110100 0.11000

hCD2TCRCD28

CTLA-4KIRCD8SLAM

CD4 rCD2 Ab:Ag

Inactive LFA-1 fully active LFA-1fully active Mac-1

Selectins

The range of affinities seen fortransient interactions at the cell surface


Best studied example: CD2:ligand interactions

CD48LFA-3

CD2

• CD2: cell adhesion molecule• enhances antigen recognition by T-cells

human: Kd = 15 M murine: Kd ~ 65 M

2B4CD2


Clues from the Rat sCD2 structure

T86

R87K43

E41

E33

structure elec. potential mutations


Charged residues & binding specificity

CD48:R31 to ? E44 to ?

CD2:E41A K43A


A new protein recognition paradigm?

CD2:LFA-3Kd = 15 mJ Bloggs

4351 6683 4798 1211

mAb:lysozymeKd = 1 nM


The value of electrostatic interactions

•Specificity is generated by electrostatic rather than surface/shape complementarity

•BUT this does not result in high affinity because salt bridges are approximately energy neutral.

•This is because binding energy from these interactions is counteracted by the need to disrupt the interactions between the charged residues and the solvent (i.e. water) before binding.


hydration of the charged residues in the unliganded

receptor

exclusion of water from the interface

The value of electrostatic interactions


Electrostatic complementarity predictsCD2:LFA-3 complex topology

Harvard complexWang et al.

Oxford predictionIkemizu et al.


But it’s not all like that... B7-1:CTLA-4 ~ High surface complementarity

Complementarity (S) = 0.75-0.76 (antibodies = 0.64-0.68; CD2 = 0.58; TCR = 0.45)


Thermodynamics of sB7-1/CTLA-4: some compensation?

0 1 2 3 4

-12

-8

-4

0

kcal/m

ole

of

inje

ctant

molar ratio

H = -11.6 G = -8.9 TS = -2.7 kcal/mol-1


Interactions are NOT uniform!

•All transient cell surface interactions are relatively weak but mechanism varies.

•Range of affinities/avidities is still large•Precise affinity/avidity and structural mechanisms used to determine it (and specificity) depend on FUNCTION.


Willcox et al. (1999) Immunity 10:357

TCR recognitionAnother reminder: TCR entropy barrier –

linked to function/nature of TCR?


Interactions are NOT uniform!

•All transient cell surface interactions are relatively weak but mechanism varies.

•Range of affinities/avidities is still large•Precise affinity/avidity and structural mechanisms used to determine it (and specificity) depend on FUNCTION.

•Oligomerisation state and valency are key factors in determining avidity (remember full e.g. at start)


• Interactions between two cell surface proteins are generally weak but remain highly specific

• Hierarchical affinities may determine the sequence of events in key processes such as T-cell activation

• Co-operative, avidity-driven interactions canprofoundly alter the strength of signalling

• In general, it is more important that these interactions are weak than how this is achieved – but there are other functional constraints.

• A variety of structural mechanisms underlie thise.g. Clustered charged residues allow weak specific recognition by CD2 and its ligands

Summary of the nature of recognition at the cell surface


What we’ve covered1. What binding properties are important?

a) Affinityb) Thermodynamicsc) Kineticsd) Stoichiometry, avidity etc.e) Mechanical binding strength

2. How might we measure them?a) SPR (BIAcore)b) ITC / microcalorimetryc) AUC


[email protected] quantitative properties of protein-protein interactions ed evans, t-cell...

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