Kinetics of Protein-ProteinKinetics of Protein-ProteinInteractionsInteractions

November 2002November 2002

2

ContentContent

Preview – Basic kineticsPreview – Basic kinetics Protein-protein Kinetics – Basic viewProtein-protein Kinetics – Basic view Electrostatic steering – study reviewElectrostatic steering – study review

3

1.Preview – Basic kinetics1.Preview – Basic kinetics

Reaction Rate (V) – Change of concentration over timeReaction Rate (V) – Change of concentration over time

Basic Reaction Basic Reaction

A CA C

Rate slows asRate slows as concentration concentration of A decreasesof A decreases

Rate slows asRate slows as concentration concentration of A decreasesof A decreases

][

][

][

][

td

Cd

td

AdV ][

][

][

][

td

Cd

td

AdV

4

Reaction Rate constant Reaction Rate constant

A + B CA + B C

V = K [A] [B]V = K [A] [B]

Rate (at first Rate (at first stage stage

of reaction)of reaction)

Rate (at first Rate (at first stage stage

of reaction)of reaction)KineticKinetic

ConstantConstant

KineticKinetic ConstantConstant

Rate is dependant onRate is dependant on preliminary concentration of reactantspreliminary concentration of reactants

Rate is dependant onRate is dependant on preliminary concentration of reactantspreliminary concentration of reactants

Example 1: Example 1:

HH22 + F + F2 2 2HI 2HI

V = K [FV = K [F22] [H] [H22]]

(K1 – Slow)(K1 – Slow) F F22 + NO + NO2 2 NO NO22F + FF + F

Fast EquilibriumFast Equilibrium NO NO22 + F NO + F NO22FF

Would expectWould expect [NO[NO22][NO][NO22]]

Would expectWould expect [NO[NO22][NO][NO22]]

It appears things are not thatIt appears things are not thatsimple: simple: •MechanismMechanism•Different K’sDifferent K’s

It appears things are not thatIt appears things are not thatsimple: simple: •MechanismMechanism•Different K’sDifferent K’s

K1

Example 2:Example 2:

FF22 + 2NO + 2NO2 2 2NO 2NO22FF

V = K [FV = K [F22] [NO] [NO22]]

5

KT

Ea

AeK

Constant:Constant:•SizeSize•OrientationOrientation•SolventSolvent•electrostaticselectrostatics

Constant:Constant:•SizeSize•OrientationOrientation•SolventSolvent•electrostaticselectrostatics

Activation Energy –Activation Energy –Limiting BarrierLimiting Barrier

Activation Energy –Activation Energy –Limiting BarrierLimiting Barrier

ArrheniusArrhenius

Factors Influencing KFactors Influencing K

6

2.Protein-Protein Kinetics – Basic View2.Protein-Protein Kinetics – Basic View

Kd= Kdissociation / Kassociation (dissociation=off, association=on)Kd= Kdissociation / Kassociation (dissociation=off, association=on) ΔΔG = -RTln(Kd)G = -RTln(Kd)

ABKoff

KonBA

A B A B

Physiological conditions Physiological conditions Possible concentration of a unique Protein in a cell Possible concentration of a unique Protein in a cell

10^-6 – 10^-8 M 10^-6 – 10^-8 M Protein diameter 50 – 100 A (Protein surface ~8,000 Protein diameter 50 – 100 A (Protein surface ~8,000

A)A) Free Walk collision with interacting designated Free Walk collision with interacting designated

protein ~ 1000A – 2000A protein ~ 1000A – 2000A

A

1000 – 2000A

A

A

A

B

B

B

B

7

A more elaborate representationA more elaborate representation

Diffusion + PossibleSteering

Desolvation, VDW, Electrostatics

Intermediate

Transition-State

RandomDiffusion

ElectrostaticSteering

EncounterComplex

Final Complex

Transition

A

B

A

+ -

B+-

A

B

AB

AB

AB

Intermediate? ? ?√ √ √

8

Reaching the Encounter ComplexReaching the Encounter Complex

Random diffusion according to the Random diffusion according to the Smolochowski-Einstein equation - ~ Smolochowski-Einstein equation - ~ 10^9 - 10^10 1/MS10^9 - 10^10 1/MS

With geometrical constraints - ~ With geometrical constraints - ~ 10^5 – 10^6 1/MS10^5 – 10^6 1/MS

Adding electrostatic steering could Adding electrostatic steering could enhance rate to 10^9 1/MS enhance rate to 10^9 1/MS

A

B

A

+ -

B+-

A

B

RandomDiffusion

ElectrostaticSteering

EncounterComplex

? ?√

Energetic factors:Energetic factors:

∆S

Electrostatic

AttractionAttraction AttractionAttraction SteeringSteeringSteeringSteering

9

An example of electrostatic steeringAn example of electrostatic steering

10

Barnase-Barstar Electrostatic potential LandscapeBarnase-Barstar Electrostatic potential Landscape

11

3.Evaluation of steering effect (Camacho, Vajda)3.Evaluation of steering effect (Camacho, Vajda)

A. Chymotrypsin with turkey ovomucoid third domain (1CHO); B. human leukocyte elastase with turkey ovomucoid third domain (1PPF), ionic strength 0.15 M and protein dielectric 4; C. kallikrein A and pancreatic trypsin inhibitor (2KAI), ionic strength 0.15 M and protein dielectric 4;D. barnase and barstar (1BGS); E. subtilisin and chymotrypsin inhibitor (2SNI); F. subtilisin and eglin-c (1CSE), ionic strength 0.15 M and protein dielectric 4;G. trypsin and bovine pancreatic trypsin inhibitor (2PTC).

A. Chymotrypsin with turkey ovomucoid third domain (1CHO); B. human leukocyte elastase with turkey ovomucoid third domain (1PPF), ionic strength 0.15 M and protein dielectric 4; C. kallikrein A and pancreatic trypsin inhibitor (2KAI), ionic strength 0.15 M and protein dielectric 4;D. barnase and barstar (1BGS); E. subtilisin and chymotrypsin inhibitor (2SNI); F. subtilisin and eglin-c (1CSE), ionic strength 0.15 M and protein dielectric 4;G. trypsin and bovine pancreatic trypsin inhibitor (2PTC).

Complex separation (5A) + XY rotationComplex separation (5A) + XY rotation

12

Evaluation of steering effect (Wade)Evaluation of steering effect (Wade)

ccp:cc - cytochrome c peroxidase:cytochrome cache:fas - acetylcholinesterase: fasciculin-2Bn:bs - Barnase-Barstarhyhel5:hel - HyHEL-5 antibody: hen egg white lysozyme;hyhel10:hel - HyHEL-10 antibody:hen egg white lysozyme

ccp:cc - cytochrome c peroxidase:cytochrome cache:fas - acetylcholinesterase: fasciculin-2Bn:bs - Barnase-Barstarhyhel5:hel - HyHEL-5 antibody: hen egg white lysozyme;hyhel10:hel - HyHEL-10 antibody:hen egg white lysozyme

13

Evaluation of steering effect (Wade)Evaluation of steering effect (Wade)

N

i

kTxEN

x1

12)/),(exp(

1)(

14

Evaluation of steering effect (Wade)Evaluation of steering effect (Wade)

15

Structure – Tem1 Structure – Tem1 ββ LactamaseLactamase

16

Structure – Tem1 Structure – Tem1 ββ Lactamase Lactamase

17

Structure – BLIP-Structure – BLIP-ΙΙΙΙ

18

Bound – Blip-Bound – Blip-ΙΙΙΙ & TEM1 & TEM1

19

Bound – Blip-Bound – Blip-ΙΙΙΙ & TEM1 & TEM1

20

Mutations on BLIP outside the active siteMutations on BLIP outside the active site

21

ResultsResults

22

ResultsResults

23

Possible Transition state orientationPossible Transition state orientation

Still water molecules awaiting extraction Still water molecules awaiting extraction Possibly a core of atoms in proximity with final orientation Possibly a core of atoms in proximity with final orientation

24

Encounter complex modelingEncounter complex modeling

Bound ModelBound Model Camacho/wade – Electrostatic minimaCamacho/wade – Electrostatic minima

Barnase - BarstarBarnase - Barstar

25

Encounter complex modelingEncounter complex modeling

Bound ModelBound Model Janin – 50% surface area + rotational Janin – 50% surface area + rotational limitlimit

Barnase - BarstarBarnase - Barstar

26

Encounter complex modelingEncounter complex modeling

Bound ModelBound Model Vijayakumar – solvent separation + (2 Vijayakumar – solvent separation + (2 angles – 3dg limit)angles – 3dg limit)

Barnase - BarstarBarnase - Barstar