Thermodynamics and Kinetics in Biology

-Physical parameters in binding studies-principles, techniques and instrumentation-Methods to probe non-covalent macromolecular interaction (stopped-flow, BIAcore, and Microcalorimetry)

Lecturer: Po-Huang Liang 梁博煌 , Associate Research FellowInstitute of Biological Chemistry, Academia SinicaTel: 27855696 ext. 6070

Activation energy profile of a reaction.(a) Activation energy (Go╪), free energy change (Go)(b) A comparison of activation energy profilesfor catalyzed and uncatalyzed reactions.

Transition state theory of enzyme Catalysis

For a reaction A + B PRate = -A/t = -B/t = P/t= k+[A][B] – k-[P]k = (T/h) exp (-G ╪ /RT)=Boltzmann constant, h=Planck constantR: gas constant)Go = -RT lnKeq (Keq = [P]/[A][B])Keq = k+ / k- ( 一個反應的平衡常數 = 正向反應速率常數 / 逆向反應速率常數 )

Steady-state Enzyme Kinetics (simplified scheme)

E + S k1

k-1

ES E + P

k1[E][S] = k-1[ES] + k2 [ES] k1([E]T – [ES]) [S] = k-1[ES] + k2 [ES] ([E]T – [ES]) [S] / [ES] = (k-1 + k2) / k1 = KM

[E]T [S] – [ES] [S] = KM [ES] [E]T [S] = [ES] (KM + [S])[ES] = [E]T [S] / (KM + [S])V = [ES] k2 Vmax = [E]T k2

V = Vmax [S] / (KM + [S]) Michaelis-Menten equationwhen [S] = KM, V = ½ Vmax

Km = (k-1 + k2) / k1 , when k-1 >> k2 (rapid equilibrium), KM = KES = k-1/ k1

In the case of k-1 is comparable to k2 (Briggs-Haldane kinetics), KM = KES + k2 / k1

k2

If [S] >> [E], d[ES]/dt = 0Rate = k2[ES]d[ES]/dt =0 is called steady-state condition.d[ES]/dt = k1[E][S] –k-1[ES] + k2 [ES] = 0

Lineweaver-Burk double reciprocal plot

Vmax / [E]T = turnover number = kcat

kcat indicates catalytic efficiency (kcat is larger, reaction is faster)

KM indicates substrate binding affinity (KM is smaller,

binding is tighter)

Enzyme reaction is complicated

1. Calculation of net rate constant

A B C D E Fk1 k2 k3 k4 k5

k-1 k-2 k-3 k-4

The net rate constant for D -> E, k4’ = k4k5/(k-4 + k5)The net rate constant for C -> D, k3’ = k3k4’/(k-3 + k4’) …….etc

P A F The partitioning of A to F vs. P =k1’/kP

k1’kP

2. Use of transit times instead of rate constant

EP1 EP2 EP3 EP4 ….. EPn

k1 k2 k3 k4 kn-1

The total time from P1 to Pn, 1/k, is given by the sum of the transit times for each step1/k = 1/k1 + 1/k2 + 1/k3 + 1/k4 + …. + 1/kn-1

As an example E + A EA E + PThe binding step is reduced to k1[A]k2 / (k-1 + k2)[E]o/V = 1/k = (k-1 + k2) / k1[A]k2 + 1/k2 1/V = (k-1 + k2) / k1[A]Vmax + 1/Vmax

1/V = KM / [A] Vmax + 1/Vmax

Pre-steady-state kinetics vs steady-state kinetics 1. The order of binding of substrates and release of product serves to define the reactants present at the active site during catalysis: it does not establishthe kinetically preferred order of substrate addition and product release orallow conclusions pertaining to the events occurring between substrate bindingand product release.2. The value of kcat sets a lower limit on each of the first-order rate constantsgoverning the conversion of substrate to product following the initial collisionof substrate with enzyme. These include conformational changes in the enzyme-Substrate complex, chemical reactions (including the formation and breakdownof intermediates), and conformational changes that limit the rate of product release.3. The value of kcat/KM defines the apparent second-order rate constant for substrate binding and sets a lower limit on the second-order rate constant forsubstrate binding. The term kcat/KM is less than the true rate constant by a factor defined by the kinetic partitioning of the E-S to dissociate or go forward in the reaction.

The goal of pre-steady-state kinetics to to establish the complete kinetic pathwayIncluding substrate binding, chemical reaction (substrate through intermediates to product), and product release.

E+ S ES EX EP E + Pk1

k2 k3 k4

k-1 k-2 k-3 k-4

Fast kinetics•Product release step is slow so the steady-state rate = product release rate

•To measure the rate of chemical step where the product release is much slower, a single-turnover condition needs to be employed.

•Under single-turnover condition where [E] >[S], product release needs not to be considered.

•Under multiple-turnover condition where [S] = 4 x [E], a burst kinetics (a fast phase followed by a steady-state phase of product formation) can be observed for a reaction with slower post-chemical step.

•A special tool Quench-Flow, needs to be used for single-turnover experiment in msec time scale.

•A Stopped-Flow instrument allows the measurements of

ligand interaction and chemical steps.

Rapid-Quench fast kinetics instrumentMeasure the real rate of chemical step (single turnover, [E]>[S])

Measure the product formation burst (multiple turnover, [S] = 4x[E])

UPPs (undeca-prenyl pyrophosphate synthase) reaction

UPPs catalyzes sequential addition of eight IPP to an FPP molecule, forming an undeca-prenyl pyrophosphate with 55 carbons and newlyformed cis double bonds.

UPPs synthesizes lipid carrier for bacterial cell wall assembly

Dolichyl pyrophosphate synthase catalyzes the lipid carrier for Glycoprotein syntehsis

kcat is 0.013 s-1 in the absence of triton and 190-fold higher (2.5 s-1) in the presence of triton. However, the rate 2.5 s-1 under enzyme single turnover is the same with or without triton

10 M E, 1 M FPP, 50 M [14C]IPP (With triton) (Without triton)

Enzyme single turnover rate is the same with or without triton

Pan et al., (2000) Biochemistry 10936-10942

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10 M UPPs, 1 M FPP, 50 M [14C]IPP Y axis represents the sum of [14C]IPP incorporated

The data represent the time courses of C20 (●), C25 (○), C30 (■), C35 (□), C40 (◆), C45 (◊), C50 (▲), and C55 (△).

UPPs single-turnover reaction time courses

The rate constants for IPP condensation determined from single-turnover

IPP

IPP

IPP

IPP

IPP

IPP

IPP

IPP

E + FPP E-FPPfast

30 s-1E-FPP-IPP E-C20

E-C20-IPPE-C25E-C25-IPPE-C30

E-C30-IPP E-C35 E-C35-IPP E-C40

E-C40-IPPE-C45E-C45-IPPE-C50

E-C50-IPP E-C55 E + C55

2.5 s-1

2 s-13.5 s-1

2.5 s-13 s-1

3.5 s-13.5 s-1

3 s-1 fast (with triton)

fast

2 M-1 s-1

UPPs multiple-turnover reaction

0.75 M enzyme, 6 M FPP and 50 M [14C]IPP without Triton

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The data indicate formation of C55 (△), C60 (●), C 65 (■), C70 (◆) and C75 (▲)

Product dissociation is partially rate limiting and protein conformational change is rate determining

IPP

IPP

IPP (without triton)

E-C55-IPP

E-C60

E-C60-IPP

0.4 s-1

E-C65

E-C65-IPP

0.4 s-1

E-C70

0.001 s-1

E* + C60

E* + C65

E + C70 + C75

E0.001 s-1

E0.001 s-1

E-C550.4 s-1

E* + C55E0.001 s-1

0.5 s-1

0.1 s-1

0.02 s-1

Substrate binding kinetics

E ESk1[S] Rate = d[E]/dt = -k1[S][E]

d[E]/[E] = -k1[S]dtln([E]t / [E]o) = -k1[S]t[E]t = [E]o exp (-k1[S]t)[ES] = [E]o-[E]t = [E]o(1-exp (-k1[S]t))kobs = k1 [S]

E ESk1[S]

kobs = k1[S] + k-1

The slope of kobs vs [S] gives kon and intercept gives koff

k-1

Stopped-flow for measurements of protein-protein and protein-small molecule interaction

A B

Flow Cell

Light

Stop SyringeFluorescence Signal

Absorbance Signal

Substrate binding kinetics

E ESk1[S] Rate = d[E]/dt = -k1[S][E]

d[E]/[E] = -k1[S]dtln([E]t / [E]o) = -k1[S]t[E]t = [E]o exp (-k1[S]t)[ES] = [E]o-[E]t = [E]o(1-exp (-k1[S]t))kobs = k1 [S]

E ESk1[S]

kobs = k1[S] + k-1

The slope of kobs vs [S] gives kon and intercept gives koff

k-1

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FPP binding induces conformational change on 3 helix

wild-type W31F has less quench

W91F has almost no quench Chen et al., (2002) J. Biol. Chem. 7369-7376

Change of 3 from open to closed form makes L85, L88, andF89 close to bound FPP; W91 has altered fluorescence upon FPP binding

Synthesize FsPP to Probe UPPs Conformational Change

P

O

MeO OMeOMe

1 equiv Bu4NOHP

O

MeO O-

OMe

P

O

MeO OOMe

POMe

S

OMe

5.64 equiv TMSI

24 h, 94%100 oC Acetonitrile

-35 oC, 30 min

1 equiv (OMe)2P(S)Cl

-35 oC rtover 6 h

30~35%

P

O

TMSO OOTMS

PSTMS

O

OTMS

P

O

-O OO-

PS-

O

O-

Bu4NOH/H2O

P

O

-O OO-

PS

O

O-

0.45 equiv farnesyl chloride

Acetonitrile25 oC

6 h, 70%

3 NH4+

FsPP

Ki of FsPP as an inhibitor = 0.2 M kcat of FsPP as an alternative substrate = 3 x 10-7 s-1

Chen et al.(2002) J. Biol. Chem. 277, 7369-7376

Conformational change and substrate bindingObserved by Stopped-Flow

UPPs-FPP + IPP

UPPs-FsPP + IPP

Binding rates vs. [IPP] gives IPP kon = 2 M-1 s-1

3 phases in 10 sec

2 phases in 0.2 sec

1 phase in 0.2 sec

Fluorescent probe for ligand interaction and inhibitor binding using stopped-flow

OPP

PPOPPO

Inhibitor

OOPP

OO OPP

CF3

Chen et al., (2002) J. Am. Chem. Soc. 124, 15217-15224

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Characterization of the fluorescent probe

(A) Fluorescence is quenched by UPPs and recovered by replacement with FPP(B) Probe binds to UPPs with 1:1 stoichiometry

(A) (B)

(C) (D)

(C ) Probe binds to UPPs with a kon = 75 M-1 s-1

(D) Probe releases from UPPs (chased by FPP) with a koff = 31 s-1

Substrate and product release rate

FPP is released at 30 s-1 UPP is released at 0.5 s-1

Can this method apply to drug-targeted prenyltransferases to find non-competitive inhibitor?

IPPE + FPP E-FPP

fast

30 s-1E-FPP-IPP E-C20

E-C25 E-C30 E-C35 E-C40

E-C45 E-C50 E-C55 E + C55

2.5 s-1 2 s-1

3.5 s-1 2.5 s-1 3 s-1 3.5 s-1

3 s-13.5 s-1 0.5 s-1

2 M-1 s-1

BIACORE (Biosensor)

Sensor chip and couplingCM5: couple ligand covalently

NTA: bind His-tagged lignadSA: capture biotinylated biomolecules

HPA: anchor membrane bound ligand

SPR: surface plasmon resonance

Objects of the experiments

•Yes/No binding, ligand fishing•Kinetic rate analysis ka, kd

•Equilibrium analysis, KA, KD

•Concentration analysis, active concentration, solution equilibrium, inhibition

Control of flow rate (l/min) and immobilized level (RU)for different experiments

Definition

•Association rate constant: ka (M-1 s-1)---Range: 103 to 107

---called kon, k1

•Dissociation rate constant: kd (s-1)---Range: 10-5 to 10-2

---called koff, k-1

•Equilibrium constant: KA (M-1), KD (M)---KA = ka/kd = [AB]/[A][B]---KD = kd/ka = [A][B]/[AB]---range: pm to uM

A + B ABka

kd

Association and dissociation rate constant measurements

A + B ABka

kd

In solution at any time t : [A]t = [A]o – [AB]; [B]t = [B]o – [AB]d[AB]/dt = ka[A]t[B]t – kd[AB]tIn BIAcore at any time t: [A]t = C; [AB] = R; [B]o = Rmax thus [B]t = Rmax – Rd[R]/dt = ka*C*(Rmax-Rt) – kd (R)

It

It is easy to mis-interpret the data

Distinguish between fast bindingand bulk effect: use referenceor double reference

Two ways to overcome mass transfer limitation: 1.increase flow rate2. reduce ligand density

Example 2: Lackmann et al., (1996) Purification of a ligand for the EPH-like receptor

using a biosensor-based affinity detection approach. PNAS 93, 2523 (ligand fishing)

HEK affinity column

(A) Phenyl-Sepharose(B) Q-Sepharose

Ion-exchangeRP-HPLC

The ligand is Al-1, which is previous found as ligand for EPH-like RTK family

BIAcore analysis of bovine Insulin-like Growth Factor (IGF)-binding protein-2Identifies major IGF binding site determination in both the N- and C-terminal domainsJ. Biol. Chem. (2001) 276, 27120-27128.

IGFBPs contain Cys-rich N- and C-terminal and alinker domains. The truncated bIGFBP-2 weregenerated and their interaction with IGF werestudied.

Lane 2: 1-279 IGFBP-2HisLane 3: 1-132 IGFBP-2Lane 4: 1-185 IGFBP-2Lane 5: 96-279 IGFBP-2HisLane 6: 136-279 IGFBP-2His

MicroCalorimetry System Right: ITC (Isotheromal titration Calorimetry)

Inject “ligand” into “macromolecule”

A small constant power is applied to the reference To make T1 (Ts – Tr) negative. A cell feed-back(CFB) supplies power on a heater on the sample cell to drives the T1 back to zero.

Binding isotherms

Simulated isotherms for different c valuesc = K (binding constant) x macromoleculeconcentrationc should be between 1 and 1000Make 10-20 injections

can be used to obtain binding affinity or binding equilibrium constant (Keq),molecular ration or binding stoichiometry (n),And heat or enthalpy (H).

Signaling pathway of GPCR and RTK

Activation of Ras following binding of a hormone (e.g. EGF)to an RTK

GRB2 binds to a specific phosphotyrosine on the activated RTK and to Sos, which in turn reacts with inactive Ras-GDP. The GEF activity of Sos then promotes theformation of the active Ras-GTP.

Example: O’Brien et al., Alternative modes of binding of proteins with tandem SH2 domains (2000) Protein Sci. 9, 570-579

(A) pY110/112 bisphosphopeptide binds to ZAP70 showing a 1:1 complex

(B) Monophoshorylated pY740 binds to p85 with two binding events

(C) Binding of pY740/751 peptide intop85. The asymmetry of the isotherm shows two distinct binding eventsshowing that an initial 2:1 complex of protein to peptide is formed. As further peptide is titrated, a 1:1 complex is formed.

ITC data for the binding of peptides to ZAP70, p85, NiC, and isolated c-SH2 domain

KB1 and KB2 correspond to the equilibrium binding constants for the first and the second binding events.

Conformational change of two SH2 binding with phosphorylated peptide

(A) Primary sequence NiC(B) a. NiC; b.NiC + bisphosphorylated peptide (C ) a. N-terminal SH2 alone; b.N-terminal SH2 + pY751 peptide; c. C-terminal SH2; .d. C-terminal SH2 + pY751 peptide

Model for binding of bisphosphorylated peptide to the SH2 domain

(A) For AZP70, SH2 protein:peptide = 1:1(B) For p85 (or NiC), initial titration results in peptide: SH2 protein = 0.5:1, adding more peptide to reach 1:1 complex.

Interactions between SH2 domains and tyrosinephosphorylated PDGF – receptor sequences

(A) SH2 protein only binds to Phosphorylated Y751P peptide(B) The inclusion of competing peptide in the buffer yields first-orderdissociation

The N-terminal SH2 domain bound with high affinity to the Y751P peptide but not to the Y740P, whereas C-terminal SH2 interacts strongly with both

Panayotou et al., Molecular and Cellular Biology (1993) 13, 3567-3576

Thomas et al., (2001) Kinetic and thermodynamic analysis of the interactionsOf 23-residue peptide with endotoxin. J. Biol. Chem. 276, 35701-35706.