Basic equations: effect of ph. Analyzing the ph dependence of enzymatic reactions may be useful: To understand the enzyme s function in the organism

Transcription

1 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 Stomach pepsin Liver Glucose-6-phosphatase

2 Basic equations: effect of ph The questions: The protonated enzyme is fully active We call it E Which equation should we use to fit the experimental data? 2. What repreents the «pka»? 80 Vi The de-protonated enzyme is inactive We call it EH ph

3 ph E + S ES No reaction H + H+ K a1 k 1 K a2 EH + S EHS E + products k -1 k 2 Vi ph How to derive the Michaelis equation? Usual hypothesis initial rates mass conservation (with [S] >>[E], so [S] total = [S] free ) [E] total = sum of all forms of E Steady-state [ES]=constant NOTE THAT ph=-log of FREE H+]

4 E + S H + H+ K a1 ph ES No reaction K a2 k 1 EH+ + S EHS+ E + products k -1 k 2 [E] total = sum of all forms of E [E] total = [E] + [EH + ] + [ES] + [ESH + ] [H + ] [E] Ka1= [EH + ] [H + ] [ES] Ka2= [ESH + ] Ka1 [E] = [EH + ] [H + ] Ka2 [ES] = [ESH + ] [H + ]

5 ph [E] total = [E] + [EH + ] + [ES] + [ESH + ] [H + ] [E] Ka1= [EH + ] Ka1 [E] = [EH + ] [H + ] [H + ] [ES] Ka2= [ESH + ] Ka2 [ES] = [ESH + ] [H + ] Ka1 Ka2 [E] total = [EH + ] [EH + ] + [ESH + ] [ESH + ] [H + ] [H + ] Ka1 Ka2 [E] total = [EH + ] ( )+ [ESH + ] ( ) [H + ] [H + ]

6 ph Ka1 Ka2 [E] total = [EH + ] ( )+ [ESH + ] ( ) [H + ] [H + ] X1 [E] total = [EH + ] X1 + [ESH + ] X2 Next step: steady-state E + S X2 ES No reaction H + H+ K a1 K a2 k 1 EH + S EHS E + products k 1 [EH] [S] = (k 1 k -1 k 2 + k 2 ) [EHS] [EH] = (k 1 + k 2 )/ k 1 [EHS]/[S]

7 ph [E] total = [EH + ] X1 + [ESH + ] X2 [EH] = (k 1 + k 2 )/ k 1 [EHS]/[S] (k 1 + k 2 )/ k 1 = Km [E] total = [ESH + ] Km/[S] X1 + [ESH + ] X2 V = k 2 [EHS] k 2 [E] total V = Km/[S] X1 + X2 V = V max [S]/X2 Km X1/X2 + /[S]

8 ph V max [S]/X2 V = Km X1/X2 + /[S] V app max [S] V = K app m + /[S] 1 V app max = V max Ka [H + ] Ka K app [H m = K m ] Ka [H + ] V max app V max = Ka1 K m [H + ] K m app V max app is a function of the Ka of the FREE enzyme (it can be K app m measured directly)

9 ph V app max V max = Ka1 K m [H + ] K m app 1 Ka [H + ] K app m = K m Ka [H + ] 1 V app max = V max Ka [H + ] Last step: verify that the equation describes our experiment: In acid medium [H+]>>Ka2 V max app = V max In alkaline medium, [H+]<<Ka2 V max app = 0 OK! ALLWAYS VERIFY THAT YOUR FINAL EQUATION IS CORRECT

10 ph In this reaction scheme, H + is an mixed-type activator (because it binds both to the free enzyme and to the ES comples) Practical hint: the «kinetic» pka may be obtained from the log-log plot: Vi log Vi ph ph

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

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

13 Suppose that the enzyme is not protonated/deprotonated, but the substrate is. O NH 2 O P N N O P O O O O N N O X TDP X = OH AZT-DP X = N 3 3 -NH 2 -TDP X = NH 2 3 -NH 3+ -TDP is not a substrate

14 Case 1. The protonated substrate is inactive Km

15 Case 2. The protonated substrate is active

16 Basic equations: effect of ph A MORE COMPLICATED SITUATION pka1 pka2

17 Basic equations: effect of ph A MORE COMPLICATED SITUATION 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. E - ES - K E1 K ES1 S + EH k1 K S EH-S k 2 EH + P k-1 K E2 K ES2 EH 2 EH 2 S ionizations in the free enzyme or free substrate ionizations in the enzymesubstrate complex

18 E - ES - K E1 K ES1 S + EH K S EH-S k 2 EH + P K E2 K ES2 EH 2 V V app max = max [H ] K ES2 [H + ] V max app K ES1 EH 2 S V max = K m [H ] K E2 [H + ] K m app K E1 [H ] K E2 K [H + K app m = K m E1 ] [H K ] ES2 [H + ] K ES1

19 ph

20 ph

21 Acid-base properties of amino acids side chains Attention! 1. Strong acids (HCl) and strong bases (NaOH) do not have pka (they are totally dissociated) 1. H + in solution is H 3 O + Same pka scale for acids and bases AH A - + H + -COOH COO - + H + BH + B + H + -NH 3+ NH 2 + H + Acide/base Eq de HENDERSON-HASSELBALCH ph = pka + log 10 [ A - ]/[ AH ]

22 Acid-base properties of amino acids side chains x 1,2 1 Data 1 Eq de Henderson-Hasselbalch x ph = pka + log 10 [ A - ]/[ AH ] [AH] x 0,8 0,6 0,4 0,2 Binding curve 1,2 1 Data [ H ] + x [AH] 0,8 0,6 Titration curve 0,4 0, ph

23 Acid-base properties of amino acids side chains tautomers Histidine is aromatic both protonated and unprotonated Histidine pka 6.5 Lysine pka 9.5 Arginine pka 12 H 2 N NH 2 N H

24 Acid-base properties of amino acids side chains Aspartate et Glutamate pka 4.4 COOH terminal pka 3.0 Cystéine pka 8.5 Tyrosine pka 10 NH2terminal pka 8.0

25 Acid-base properties of amino acids side chains O H C C NH C H 2 H N N + +1 H O H C C NH C H 2 H N N 0 [ BH ] + 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0, ph The slope is the same irrespective of the pka, UNLESS there is a cooperative proton binding

26 Macrocryptates Acid-base properties of amino acids side chains 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. SUPRAMOLECULAR CHEMISTRY - SCOPE AND PERSPECTIVES MOLECULES - SUPERMOLECULES - MOLECULAR DEVICES Nobel lecture, December 8, 1987 by JEAN-MARIE LEHN

27 Acid-base properties of amino acids side chains 1. L environnement apolaire des chaînes latérales favorise la forme non-ionisée pka augmente pour les COOH et diminue pour les NH2 2. La proximité d une chaîne latérale chargée modifie le pka ,9 0,8 His dans une protéine [ AH ] + 0,7 0,6 0,5 0, ,3 0,2 0, ph - - -

28 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 NH 2 -CH 2 -COOH NH 3+ -CH 2 -COOH NH 3+ -CH 2 -COO - NH 2 -CH 2 -COO - NH 3+ -CH 2 -CO-NH-CH 2 -COOH NH 3+ -CH 2 -CO-NH-CH 2 -COO - NH 2 -CH 2 -CO-NH-CH 2 -COO -

29 Acid-base properties of amino acids side chains Glycine pka of the NH2 group is 9.78, while in glycinamide is 8.2 NH 3+ -CH 2 -COO - NH 2 -CH 2 -COO - pka 9.78 NH 3+ -CH 2 -CO-NH2 NH 2 -CH 2 -CO-NH2 pka 8.2 From the pka we may calculate the free energy associate to the salt bridge

30 Acid-base properties of amino acids side chains NH 3+ -CH 2 -COO - NH 2 -CH 2 -COO - pka 9.78 NH 3+ -CH 2 -CO-NH2 NH 2 -CH 2 -CO-NH2 pka 8.2 From the pka we may calculate the free energy associate to the salt bridge

31 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 NH 2 -CH 2 -COOH NH 3+ -CH 2 -COOH NH 3+ -CH 2 -COO - pka 2.35 NH 3+ -CH 2 -CO-NH-CH 2 -COOH NH 3+ -CH 2 -CO-NH-CH 2 -COO - pka 3.12 The ionic interaction decreases the pka, more for glycine since charges are closer

32 Acid-base properties of amino acids side chains 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 NH 2 -CH 2 -COOH NH 3+ -CH 2 -COO - NH 2 -CH 2 -COO - pka 9.78 NH 3+ -CH 2 -CO-NH-CH 2 -COO - pka 8.17 NH 2 -CH 2 -CO-NH-CH 2 -COO - The loss of the stabilizing interaction is more important for glycine since charges are closer

33 How to measure side chains pka in proteins? Why are pks important? Protein structure, stability and solubility depends on the charge on ionizable residues 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))

34 Typical pk a values in enzymes α-cooh Tyr-OH Cys-SH Ionizable Group Asp-COOH pk a in model peptides Glu-COOH 4.5 His-NH usual range observed in proteins α-nh ~ 8 Lys-NH ~ 10 Arg-N(H)C(NH 2 )NH

35 1. Propriétés acido-basiques pk values for the ionizable residues in folded RNase Sa Residue (N & T) Measured pk C-term(3.8) 2.42 Asp 01 (4.0) 3.44 Asp Asp Asp Asp Asp Asp Glul4(4.4) 5.02 Glu Glu Glu Glu His 53 (6.3) 8.27 His N-term (7.5) 9.14 Tyr 30 (9.6) 11.3 Tyr Tyr 51, 52, 55 > , 81, 86

36 Highly perturbed pk a values in enzymes COOH In a low polarity environment ionization is disfavoured pk a COO H 3 N ionization is stabilized via salt bridge pk a of carboxyl function pk a of amino function NH 2 In a low polarity environment charged group is disfavoured pk a Examples of perturbed pk a values: lysozyme Glu-35 (pk a = 6.5) acetoacetate decarboxylase Lys-NH 3+ (pk a = 5.9) papain His-159 (pk a 3.4) the environment surrounding an ionizable group can greatly influence its ionization

37 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 pka How? General method: NMR (but the protein should be small <200 aa) Specific methods Example: HisH + decreases the fluorescence intensity of a neighbouring Tryptophane

38 How to measure side chains pka in proteins? C-H stable 13 C H N H N H C-H stable Signals typical for protéine native N-H rapidly exchange in D 2 O and therefore the signal is lost 1 H-RMN Histidines are identified by sitedirected mutagenesis Aromatic protons

39 How to measure side chains pka in proteins? Example 1, phospholipase C of Bacilus cereus Phospholipase C This bond is hydrolyzed (nucleophilic atak on phosphorous Mécanisme similaire à celui e la RNaseA

40 Comment MESURER le pka des chaînes latérales dans les protéines? ex2 Tible 2. The pk, values of the histidines of B. cereus Pl-PLC Histidine Position pka dans des peptides: 6.5 H Site actif H Site actif H61 Enfuie H81 _ Enfuie H Surface de la protéine H Surface de la protéine

41 How to measure side chains pka in proteins? Example 1, phospholipase C of Bacilus cereus Determination of pka values of the histidine side chains of phosphatidylinositol-specific phospholipase C from Bacillus cereus by NMR spectroscopy and site-directed mutagenesis. Protein Sci Sep;6(9): 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 phosphatidylinositolspecific 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 Five of the six histidines have been individually substituted 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. The active 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 and His81 do not titrate over the ph range studied. These values are consistent with the crystal structure 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.

42 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

43 How to measure side chains pka in proteins? Example 3, the perturbation by charged ressidues Long-range surface charge-charge interactions in proteins. Comparison of experimental results with calculations from a theoretical method. J Mol Biol. 1993, 232, Loewenthal R, Sancho J, Reinikainen T, Fersht AR. MRC Unit for Protein Function and Design, Cambridge, England. PDB 1SBT Asp36 His A Lys136

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