02d basic equations effect of ph - freelascu.free.fr/enzymology/02d basic equations effect of...

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

20

40

60

80

100

3 4 5 6 7 8 9 10

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:

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+]

0

20

40

60

80

100

3 4 5 6 7 8 9 10

Vi

pH

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

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+]

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

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]

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)

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

pH

In this reaction scheme, H+ is an mixed-type activator (because it binds both to the free enzyme and to the ES comples)

20

40

60

80

100

3 4 5 6 7 8 9 10

Vi

pH

1

10

100

3 4 5 6 7 8 9 10

log

Vi

pH

Practical hint: the « kinetic » pKa may be obtained from the log-log plot:

pH

What happens if the enzyme is inactive while protonated? H+ isan mixed-type inhibitor. You may use directly the equation for mixed inhibition.

What happens if the enzyme is active at alkaline, but not at acidic pH?

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

Case 1. The protonated substrate is inactive

Km’

Case 2. The protonated substrate is active

Basic equations: effect of pHA MORE COMPLICATED SITUATION

pKa1 pKa2

• 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

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+]

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+

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


Histidine pKa 6.5

Lysine pKa 9.5

Arginine pKa 12

tautomers

Histidine is aromatic both protonated and unprotonated


NH

NH2

NH2

Aspartate etGlutamate pKa 4.4

COOH terminal pKa 3.0

Cystéine pKa 8.5

Tyrosine pKa 10

NH2terminal pKa 8.0


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


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.


Macrocryptates

SUPRAMOLECULAR CHEMISTRY - SCOPE AND PERSPECTIVES MOLECULES - SUPERMOLECULES -MOLECULAR DEVICESNobel lecture, December 8, 1987byJEAN-MARIE LEHN

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


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-


Glycine pKa of the –NH2 group is 9.78, while in glycinamide is 8.2


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



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

NH3+-CH2-COOH � NH3

+-CH2-COO- pKa 2.35

NH3+-CH2-CO-NH-CH2 -COOH

NH3+-CH2-CO-NH-CH2 -COO- pKa 3.12


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

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-CO-NH-CH2 -COO-

NH2-CH2-CO-NH-CH2 -COO-

pKa 8.17


The loss of the stabilizing interaction is more important for glycine since charges are closer

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?

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

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

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


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

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


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

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

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

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

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

How to measure side chains pKa in proteins? Example 3, the perturbation by charged ressidues

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