thermodynamics and kinetics in biology -physical parameters in binding studies-principles,...
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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
0
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0 2 4 6 8 10Time (sec)
Con
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n (u
M)
-0.2
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0.4
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1
1.2
0 1 2 3 4 5 6
Con
cent
rati
on (
uM)
Time (sec)
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
0
2
4
6
8
10
0 20 40 60 80 100 120 140 160Time (sec)
Con
cent
rati
on (
uM)
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 20 40 60 80 100 120 140 160Time (sec)
Con
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rati
on (
uM)
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
300 320 340 360 380 400 420 4400
500
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3500F
luo
resc
en
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a.u
.)
Wavelength (nm)
300 320 340 360 380 400 420 4400
500
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3500
Flu
ore
sce
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In
ten
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(a
.u.)
Wavelength (nm)
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Flu
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In
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.u.)
Wavelength (nm)
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
400 450 500 550 6000
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F
luor
esce
nce
Inte
nsity
(a.
u.)
Wavelength (nm)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
200
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700
Flu
ores
cenc
e In
tens
ity (
a.u.
)
Concentration ()
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.