02d basic equations effect of ph - freelascu.free.fr/enzymology/02d basic equations effect of...
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Basic equations: effect of pH
Analyzing the pH dependence of enzymatic reactions may be useful:
To understand the mechanism
To understand the enzyme’s function in the organism
Stomachpepsin
LiverGlucose-6-phosphatase
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Vi
pH
Basic equations: effect of pH
The de-protonated enzyme is inactive
The protonated enzyme is fully active
We call it EH
We call it E
1. Which equation should we use to fit the experimental data?
2. What repreents the « pKa »?
The questions:
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pH
E + S ES No reaction
EH + S EHS E + products
H+ H+
Ka1Ka2
k1
k-1
k2
How to derive the Michaelis equation?Usual hypothesis
initial ratesmass conservation (with [S] >>[E], so [S]total = [S]free)[E]total = sum of all forms of ESteady-state [ES]=constantNOTE THAT pH=-log of FREE |H+]
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pH
E + S ES No reaction
EH+ + S EHS+ E + products
H+ H+
Ka1Ka2
k1
k-1
k2
[E]total = sum of all forms of E
[E]total = [E] + [EH+] + [ES] + [ESH+]
Ka1= ------------[H+] [E]
[EH+]
Ka2= ------------[H+] [ES]
[ESH+]
[E] = [EH+] ------------[H+]
Ka1
[ES] = [ESH+] ------[H+]
Ka2
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pH
[E]total = [E] + [EH+] + [ES] + [ESH+]
Ka1= ------------[H+] [E]
[EH+]
Ka2= ------------[H+] [ES]
[ESH+]
[E] = [EH+] ------------[H+]
Ka1
[ES] = [ESH+] ------[H+]
Ka2
[E]total = [EH+] -------- + [EH+] + [ESH+] ------ + [ESH+] Ka2
[H+]
Ka1
[H+]
[E]total = [EH+] (-------- + 1)+ [ESH+] (------ + 1) Ka2
[H+]
Ka1
[H+]
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pH
[E]total = [EH+] (1+ -------)+ [ESH+] (1+ ------) Ka2
[H+]
Ka1
[H+]
X1 X2
Next step: steady-state E + S ES No reaction
EH + S EHS E + products
H+ H+
Ka1Ka2
k1
k-1
k2
k1 [EH] [S] = (k –1 + k 2) [EHS]
[EH] = (k –1 + k 2)/ k1 [EHS]/[S]
[E]total = [EH+] X1 + [ESH+] X2
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pH
[EH] = (k –1 + k 2)/ k1 [EHS]/[S]
[E]total = [EH+] X1 + [ESH+] X2
[E]total = [ESH+] Km/[S] X1 + [ESH+] X2
(k –1 + k 2)/ k1 = Km
V = k2 [EHS]
V = ---------------------------k2 [E]total
Km/[S] X1 + X2
V = ---------------------------Vmax [S]/X2
Km X1/X2 + /[S]
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pH
V = ---------------------------Vmax [S]/X2
Km X1/X2 + /[S] V = -----------------
Vmaxapp [S]
Kmapp + /[S]
Vmaxapp = Vmax ----------------
Kmapp = Km-----------------
Ka2[H+]
1 + ------
1
Ka2[H+]
1 + ------
Ka1[H+]
1 + ----------- = ------- ------------
Vmaxapp
Kmapp
Vmax
KmKa1[H+]
1 + ------
1
Vmaxapp
Kmapp
------------ is a function of the Ka of the FREE enzyme (it can be measured directly)
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pH
Vmaxapp = Vmax ----------------
Ka2[H+]
1 + ------
1
Kmapp = Km-----------------
Ka2
[H+]1 + ------
Ka1
[H+]1 + ------
----- = ------- ------------
Vmaxapp
Kmapp
Vmax
Km
Ka1
[H+]1 + ------
1
Last step: verify that the equation describes our experiment:In acid medium [H+]>>Ka2 Vmax
app = VmaxIn alkaline medium, [H+]<<Ka2 Vmax
app = 0 OK !
ALLWAYS VERIFY THAT YOUR FINAL EQUATION IS CORRECT
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pH
In this reaction scheme, H+ is an mixed-type activator (because it binds both to the free enzyme and to the ES comples)
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log
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pH
Practical hint: the « kinetic » pKa may be obtained from the log-log plot:
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pH
What happens if the enzyme is inactive while protonated? H+ isan mixed-type inhibitor. You may use directly the equation for mixed inhibition.
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What happens if the enzyme is active at alkaline, but not at acidic pH?
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Suppose that the enzyme is not protonated/deprotonated, but the substrate is.
O
N
N
N
N
O
P
O
O
O
P
O
OO
NH2
X
TDP X = OHAZT-DP X = N3
3’-NH2-TDP X = NH2
3’-NH3+-TDP is not a substrate
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Case 1. The protonated substrate is inactive
Km’
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Case 2. The protonated substrate is active
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Basic equations: effect of pHA MORE COMPLICATED SITUATION
pKa1 pKa2
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• The reversible effect of pH on an enzyme can be described in a scheme that is only slightly more complex than a classic inhibition scheme. Ionizations “inhibit” either the free enzyme or the enzyme-substrate complex.
S + EH
E-
EH2
KE1
KE2
EH-S
ES-
EH2S
KES1
KES2
k2EH + P
KS
ionizations in the free enzyme or free substrate
ionizations in the enzyme-substrate complex
Basic equations: effect of pHA MORE COMPLICATED SITUATION
k1
k-1
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S + EH
E-
EH2
KE1
KE2
EH-S
ES-
EH2S
KES1
KES2
k2EH + P
KS
Vmaxapp = ----------------
Vmax
[H+]------ + 1 + ------
KES2
KES1
[H+]Km
app = Km--------------------
[H+]------ + 1 + ------
KES2
KES1
[H+]
[H+]------ + 1 + ------
KE2
KE1
[H+]
----- = ------- ---------------Vmax
app
Kmapp
Vmax
Km
1
[H+]------ + 1 + ------
KE2
KE1
[H+]
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pH
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pH
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Acid-base properties of amino acids side chains
Same pKa scale for acids and bases
AH � A- + H+ -COOH � COO- + H+
BH+ � B + H+ -NH3+ � NH2 + H+
Acide/base Eq de HENDERSON-HASSELBALCH
pH = pKa + log10 [ A- ]/[ AH ]
Attention! 1. Strong acids (HCl) and strong
bases (NaOH) do not have pKa(they are totally dissociated)
1. H+ in solution is H3O+
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0
0,2
0,4
0,6
0,8
1
1,2
0 2 4 6 8 10
Data 1
x
x
pH
0
0,2
0,4
0,6
0,8
1
1,2
2 10-6 4 10-6 6 10-6 8 10-6 1 10-5
Data 1
x
x
[ H ]+
[AH]
[AH]
Eq de Henderson-Hasselbalch pH = pKa + log10 [ A- ]/[ AH ]
Binding curve
Titration curve
Acid-base properties of amino acids side chains
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Histidine pKa 6.5
Lysine pKa 9.5
Arginine pKa 12
tautomers
Histidine is aromatic both protonated and unprotonated
Acid-base properties of amino acids side chains
NH
NH2
NH2
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Aspartate etGlutamate pKa 4.4
COOH terminal pKa 3.0
Cystéine pKa 8.5
Tyrosine pKa 10
NH2terminal pKa 8.0
Acid-base properties of amino acids side chains
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0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
3 4 5 6 7 8 9 10 11pH
[ BH
]+
+1
N+
N
CH2
C
CO
NH
H
H
H
0
N
N
CH2
C
CO
NH
H
H
The slope is the same irrespective of the pKa,UNLESS there is a cooperative proton binding
Acid-base properties of amino acids side chains
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The facilitation of the second protonation of 10 represents a positive cooperativity, in which the first proton and the effector molecule water set the stage both structurally and energetically for the fixation of a second proton.
Acid-base properties of amino acids side chains
Macrocryptates
SUPRAMOLECULAR CHEMISTRY - SCOPE AND PERSPECTIVES MOLECULES - SUPERMOLECULES -MOLECULAR DEVICESNobel lecture, December 8, 1987byJEAN-MARIE LEHN
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0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
3 4 5 6 7 8 9 10 11
[ AH
]+
pH
+
++
+
+
+
-
-
-
-
-
-
1. L’environnement apolaire des chaînes latérales favorise la forme non-ioniséepKa augmente pour les COOH et diminue pour les NH2
2. La proximité d’une chaîne latérale chargée modifie le pKa
His dans une protéine
Acid-base properties of amino acids side chains
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Glycine pKa are 2.35 and 9.78
The dipeptide glycylglycine pKa are 3.12 and 8.17
NH2-CH2-COOH
NH3+-CH2-COOH � NH3
+-CH2-COO- � NH2-CH2-COO-
NH3+-CH2-CO-NH-CH2 -COOH
NH3+-CH2-CO-NH-CH2 -COO-
NH2-CH2-CO-NH-CH2 -COO-
Acid-base properties of amino acids side chains
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Glycine pKa of the –NH2 group is 9.78, while in glycinamide is 8.2
Acid-base properties of amino acids side chains
NH3+-CH2-COO- � NH2-CH2-COO- pKa 9.78
NH3+-CH2-CO-NH2 � NH2-CH2-CO-NH2 pKa 8.2
From the pKa we may calculate the free energy associate to the salt bridge
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Acid-base properties of amino acids side chains
NH3+-CH2-COO- � NH2-CH2-COO- pKa 9.78
NH3+-CH2-CO-NH2 � NH2-CH2-CO-NH2 pKa 8.2
From the pKa we may calculate the free energy associate to the salt bridge
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NH3+-CH2-COOH � NH3
+-CH2-COO- pKa 2.35
NH3+-CH2-CO-NH-CH2 -COOH
NH3+-CH2-CO-NH-CH2 -COO- pKa 3.12
Acid-base properties of amino acids side chains
Glycine pKa are 2.35 and 9.78
The dipeptide glycylglycine pKa are 3.12 and 8.17
NH2-CH2-COOH
The ionic interaction decreases the pKa, more for glycine since charges are closer
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La glycine a des valeurs de pKa de 2.35 et 9.78
Le dipeptide glycylglycine a des valeurs de pKa de 3.12 et de 8.17 NH2-CH2-COOH
NH3+-CH2-COO- � NH2-CH2-COO- pKa 9.78
NH3+-CH2-CO-NH-CH2 -COO-
NH2-CH2-CO-NH-CH2 -COO-
pKa 8.17
Acid-base properties of amino acids side chains
The loss of the stabilizing interaction is more important for glycine since charges are closer
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Why are pKs important?
Protein structure, stability and solubility depends on the charge on ionizableresidues
Catalytic residues at enzyme active sites are 65% charged, 27% polar and 8% nonpolar
Catalytic residues at enzyme active sites are 18% His, 15% Asp, 11% Arg, and 11% Glu
(Barlett, Porter, Borkakoti, & Thornton, JMB, 324, 105 (2002))
How to measure side chains pKa in proteins?
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Typical pKa values in enzymes
2 – 5.5
3.6α-COOH
8 – 119.1Cys-SH
9 – 129.7Tyr-OH
12Arg-N(H)C(NH2)NH2
~ 1010.4Lys-NH2
~ 87.8α-NH3+
5 – 86.4His-NH+
4.5Glu-COOH
4.0Asp-COOH
usual range observed in
proteins
pKa in model peptides
Ionizable Group
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pK values for the ionizable residues in folded RNase SaResidue (N & T) Measured pKC-term(3.8) 2.42Asp 01 (4.0) 3.44Asp 17 3.72Asp 25 4.87Asp 33 2.39Asp 79 7.37Asp 84 3.01Asp 93 3.09Glul4(4.4) 5.02Glu41 4.14Glu54 3.42Glu74 3.53Glu78 3.17His 53 (6.3) 8.27His 85 6.24N-term (7.5) 9.14Tyr 30 (9.6) 11.3Tyr 49 10.6Tyr 51, 52, 55 > 11.580, 81, 86
1. Propriétés acido-basiques
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Highly perturbed pKa values in enzymes
• COOH In a low polarity environment– ionization is disfavoured ∴ ↑ pKa
• COO– - - - - +H3N– ionization is stabilized via salt bridge ∴ ↓ pKa of carboxyl function
↑ pKa of amino function
• NH2 In a low polarity environment– charged group is disfavoured ∴ ↓ pKa
Examples of perturbed pKa values:lysozyme Glu-35 (pKa = 6.5)acetoacetate decarboxylase Lys-NH3
+ (pKa = 5.9)papain His-159 (pKa 3.4)
∴ the environment surrounding an ionizable group can greatly influence its ionization
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How to measure side chains pKa in proteins?
It is of course more easy to calculate, but we want te MEASURE!
The proteins should be native (which exclude experiments <4 or >10
Most easy end interesting is the histidine pKaHow?� General method: NMR (but the protein should be small <200
aa)
� Specific methods Example: HisH+ decreases the fluorescence intensity of a
neighbouring Tryptophane
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N
N HH
H
N-H rapidly exchange in D2O and therefore the signal is lost
C-H stable
C-H stable
Aromatic protons
13C
Signals typical for protéine native
1H-RMN
Histidines are identified by site-directed mutagenesis
How to measure side chains pKa in proteins?
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Phospholipase C
Mécanisme similaire à celui e la RNaseA
This bond is hydrolyzed(nucleophilic atak on phosphorous
How to measure side chains pKa in proteins? Example 1, phospholipase C of Bacilus cereus
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Comment MESURER le pKa des chaînes latérales dans les protéines? ex2Tible 2. The pK, values of the histidines of B. cereus Pl-PLC
H32 7.6 Site actif
H82 6.9 Site actif
H61 — Enfuie
H81 _ Enfuie
H92 5.4 Surface de la protéine
Histidine Position
H227 6.9 Surface de la protéine
pKa dans des peptides: 6.5
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Determination of pKa values of the histidine side chains of phosphatidylinositol-specific phospholipase C fromBacillus cereus by NMR spectroscopy and site-directed mutagenesis. Protein Sci. 1997 Sep;6(9):1937-44.Liu T, Ryan M, Dahlquist FW, Griffith OH.
Institute of Molecular Biology, University of Oregon, Eugene 97403, USA.Two active site histidine residues have been implicated in the catalysis of phosphatidylinositol-specific phospholipase C (PI-PLC). In this report, we present the first study of the pKa values of histidines of a PI-PLC. All six histidines of Bacillus cereus PI-PLC were studied by 2D NMR spectroscopy and site-directed mutagenesis. The protein was selectively labeled with 13C epsilon 1-histidine. A series of 1H-13C HSQC NMR spectra were acquired over a pH range of 4.0-9.0. Fiveof the six histidines have been individually substit uted with alanine to aid the resonance assignments in the NMR spectra. Overall, the remaining histidines in the mutants show little chemical shift changes in the 1H-13C HSQC spectra, indicating that the alanine substitution has no effect on the tertiary structure of the protein. H32A and H82A mutants are inactive enzymes, while
H92A and H61A are fully active, and H81A retains about 15% of the wild-type activity. Theactive site histidines, His32 and His82, display pKa values of 7.6 and 6.9, respectively. His92 and His227 exhibit pKa values of 5.4 and 6.9. His61 andHis81 do not titrate over the pH range studied. These values are consistent with the crystalstructure data, which shows that His92 and His227 are on the surface of the protein, whereas His61 and His81 are buried. The pKa value of 6.9 corroborates the hypothesis of His82 acting as a general acid in the catalysis. His32 is essential to enzyme activity, but its putative role as the general base is in question due to its relatively high pKa.
How to measure side chains pKa in proteins? Example 1, phospholipase C of Bacilus cereus
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How to measure side chains pKa in proteins? Example 2, the Ribonuclease A
The pH titration curves of the six histidines in B. cereus PI-PLC. The pKa values were determined by non-linear regression fitting, using the Henderson-Hasselbalch equation
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Long-range surface charge-charge interactions in proteins. Comparison of experimental results with calculations from a theoretical method. J Mol Biol. 1993, 232, 574-83.Loewenthal R, Sancho J, Reinikainen T, Fersht AR. MRC Unit for Protein Function and Design, Cambridge, England.
PDB 1SBT
His64
Lys136
Asp36
24.5 A
How to measure side chains pKa in proteins? Example 3, the perturbation by charged ressidues
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How to measure side chains pKa in proteins? Example 3, the perturbation by charged ressidues