Switch Gears to Enzymes

Transcription

1 Switch Gears to Enzymes Their energetic profiles What we measure and the information content (macro vs microscopic constants Structural contributions to catalysis

2 References Excellent reference for all aspects of enzyme kinetics including important elements of Metabolic Control Analysis of relevance to systems analysis of enzyme function and regulation: Fundamentals of Enzyme Kinetics 4 th Edition (2012) Athel Cornish-Bowden, Wiley-Blackwell, ISBN (great historical notes and excellent plot visuals as bonuses) Straightforward presentation of theory, methods, examples for enzyme kinetics, catalysis and folding: Structure and Mechanism in Protein Science (1999) A. Fersht, Freeman. Extensive descriptions of enzyme mechanisms with overall and active site structures of the enzymes: Enzymatic Reaction Mechanisms (2007) PA Frey & AD Hegeman, Oxford Univ. Press. In depth reference for biologically relevant kinetics Kinetics for the Life Sciences: Receptors, Transmitters, and Catalysts (1995) H. Gutfreund, Cambridge University Press Older encyclopedia of SS kinetics eqns for multiple substrates, all types of product and reversible inhibition Enzyme Kinetics (1975) I.H. Segel, Wiley & Sons.

3 Reaction Paths Breaking Bonds - Transition States ΔG values for uncatalyzed biological reactions are large Again, experimentally determined rate constants defined by difference in free energy of GS and TS, ΔG k 1 = k B T/h exp{ ΔG 1 /RT) k 1 = k B T/h exp{ ΔG 1 /RT)

4 Reaction Paths Breaking Bonds - Transition States Enzymes catalyze specific reactions by providing a lower energy path - increased rate: larger k 1 & k -1, lower ΔG 1 & ΔG -1 - while ΔG o remains unchanged noncatalyzed catalyzed Profile drawn for standard state [A] = [Q] = 1 M

5 Reaction Paths Breaking Bonds - Transition States How large are ΔΔG values for biological reactions (ΔG non - ΔG cat )? Enzyme k non (s -1 ) k cat (s -1 ) ΔG non (kcal/mol) ΔG cat (kcal/mol) Rate constants from A. Radzicka & R. Wolfenden 1995 Science Vol. 267 ΔΔG (kcal/mol) OMP decarboxylase 2.8 x Staphylococcal nuclease 1.7 x Adenosine deaminase 1.8 x AMP nucleosidase 1.0 x Cytidine deaminase 3.2 x Phosphotriesterase 7.5 x , Carboxypeptidase A 3.0 x Ketosteroid isomerase 1.7 x , Triosephosphate isomerase 4.3 x , Chorismate mutase 2.8 x Carbonic anhydrase 2.8 x x Cyclophilin 2.8 x ,

6 Reaction Paths Breaking Bonds - Transition States First note the differences in the free energy profiles Enzymes bind their substrates and products noncatalyzed catalyzed Profile drawn for standard state [A] = [Q] = 1 M

7 Reaction Paths Kinetics Binding changes environment but also adds kinetic barriers Profile drawn for standard state [A] = [Q] = 1 M Profile with TS bind & TS off [A] 1 M, [Q] = 0

8 Reaction Paths Kinetics 2 nd order 1st order Rates =? What/How do we measure? What is the behavior?

9 Constant flux or classic steady-state kinetics A enzyme as catalyst Q - set [E T ] << [A T ] and [Q init ] = 0 [A] [Q] v i time - measure initial velocity rate = v i = dq/dt = da/dt, where reaction remains ~ linear, i.e. < 10% reacted E T = E + EA + EQ Steady-state assumption: d[e] dt = d[ea] dt = d[eq] dt = 0

10 *Most common* behavior of v i vs [A T ] & [E T ] at const. [E T ] << [A T ] V max (M/s) k cat (s -1 ) [E T ] (M) Hyperbolic dependence on [A] indicates minimal 2-step mechanism just as in 2-step single turnover k 1 k 2 k cat E + A EA E + Q

11 Key Parameters at const. [E T ] << [A T ] v i = V max A T K M + A T = k 1 k 2 k cat E + A EA E + Q k cat E T A T K M + A T k obs = v i /E T = k cat A T K M + A T A T -> A T >> K M v i = V max - maximal velocity (or rate) V max = k cat E T k cat - macroscopic 1st order rate constant (s -1 ) A T -> 0 A T << K M v i = (V max /K M ) A T = (k cat /K M )E T A T V max /K M - pseudofirst order rate const k cat /K M - macroscopic 2nd order rate constant (M -1 s -1 ) A T = K M v i = V max /2 K M = Michaelis constant [E] = E T /2 Σ[E bound ] = E T /2

12 Key Parameters are Macroscopic Constants de dea Applying the steady-state assumption: = = 0 dt dt to this minimal mechanism k 1 k 2 k cat E + A EA E + Q comparing v i /E T = where at face value k cat A T K M + A T = k cat A T k 2 + k cat + A T k 1 k cat appears to be a microscopic 1 st order rate constant (s -1 ) but both K M and k cat /K M are complex macroscopic constants k cat /K M = k 1 k cat k 2 + k cat K M = k 2 + k cat k 1 But further

13 the behavior of v i vs A T is macroscopic and consistent with many microscopic mechanisms, where k cat is also macroscopic, e.g. k 1 E + A EA EQ E + Q k 2 k 1 k 2 k 1 E + A EA EI EQ k 2 k cat /K M k 3 k 3 k 3 k 4 k cat E + A EA EQ k 4 k cat /K M k cat /K M k cat k 5 k 5 k cat k 5 k 6 E + Q k 7 E + Q The expressions for k cat and k cat /K M include microscopic constants for all steps within the brackets in each case. k cat /K M expressions include all steps from binding of A through the 1st irreversible step k cat expressions include all first order steps including chemistry, conformational changes, product dissociation k 2 k 3 k cat k 1 k 5 k 7 E + A EA E*Q E* + Q k cat /K M k 8 E K M expressions can be derived from ratio of k cat /(k cat /K M ) and are very complex

14 Reaction Paths Breaking Bonds - Transition States What barriers/processes do k cat, k cat /K M and K M reflect? A priori, we cannot predict which TS has the highest energy on a reaction path, i.e., ΔG rev and ΔG off may be <, =, or > ΔG 1

15 What processes do k cat /K M and K M reflect? k cat /K M = k 1 k 3 k 2 + k 3 K M = k 2 + k 3 k 1 k = k B T/h exp{-δg /RT}, i.e. ln(1/k) ΔG k 1 k 2 k 3 k cat = k 3 E + A EA E + Q k cat /K M TS 3 ΔG TS 1,2 ΔG ΔG E+A EA E+Q E+A EA E+Q E+A EA E+Q Rxn Rxn Rxn k 2 >> k 3 k 2 ~ k 3 k 2 << k 3 k cat /K M = K M = K D k 3 k 2 /k 1 = k 3 K D both k cat & k cat /K M limited by TS 3, i.e., chemistry k cat /K M = K M = k 2 + k 3 k 1 k 1 k 3 k 2 + k 3 = 2K D k cat /K M only partially limited by TS 3 (chemistry) K M = k cat /K M = k 1 k 3 k 1 = k cat k 1 > K D k cat /K M limited only by TS 1,2, i.e, diffusion

16 and what happens if EP accumulates? k cat Full expressions: k 1 k 3 k 5 k cat /K M = k 2 (k 4 + k 5 ) + k 3 k 5 k 1 k 2 k 3 E + A EA EQ k 4 k cat /K M k 5 E + Q k cat = k 3 k 5 K M = k 2 (k 4 + k 5 ) + k 3 k 5 k 3 + k 4 + k 5 k 1 (k 3 + k 4 + k 5 ) TS 3,4 TS 5 k 5 << k 3, k 4 k cat = ( ) k 3 k 3 + k 4 k 5 fraction of bound enzyme that accumulates as EQ k cat reflects TS 5, i.e., product dissoc. ΔG TS 1,2 k cat /K M ~ k 5 k 2 k 4 /k 1 k 3 EQ forms in equil with E & EA E+A EA EQ Rxn E+Q k cat /K M also reflects TS 5 for product dissoc. K M = ( ) k 2 (k 4 ) k 4 k 1 (k 3 + k 4 ) = K D k 3 + k 4 In this case, K M < K D

17 Summary of Steady-State Points k cat, k cat /K M and K M are all macroscopic constants k cat may be limited or partially limited by any 1st order process including chemistry, conformational changes, product dissociation - chemistry often not fully rate limiting k cat /K M may be limited by any step reversibly connected to substrate binding. Diffusion limited means chemistry is faster than substrate dissociation K M is a Kinetic constant = [A] that gives half maximal velocity. It may be equal to K D, the dissociation constant for A, but often is not and does not a priori reflect the binding affinity of A for E K M = Σ (net flux from EA to E: back + fwd) k on

18 Next up Structures how do they contribute to catalysis

19 Long standing concepts [TS ] in the TS Noncovalent binding interactions maximized at TS E+A obs ΔG bind A EA additional favorable ΔG bind felt here and Q EQ unfavorable ΔG destab felt only in GS E+Q Environmental changes that make A more reactive than in solution

20 Let s look under the hood Triosephosphate isomerase, A well-studied example

21 TIM Cellular Pathway J.R. Knowles & W.J. Albery (1977) Acc. Chem. Res GAPDH sn-glycerol-3-phosphate

22 TIM Reaction C-H are nonpolar and weakly acidic so hard to break polarization of C=O essential to lower pka B: essential Base J. R. Knowles 1970s, 80s, 90s, many others 90s - current

23 TIM Theory & Experiments Defining Free Energy Profile J.R. Knowles & W.J. Albery (1977) Acc. Chem. Res ) Kinetic isotope effects measure of hard C-H steps 2) Isotope exchange into substrate and product from solvent 3) Isotope exchange out of substrates to solvent (T=tritium, D=deuterium) 1) Albery & Knowles (1976) Biochemistry 15, 5588; 2) Herlihy, Maister, Albery & Knowles (1976) Biochemistry 15, 5601; 3) Maister, Pett, Albery & Knowles (1976) Biochemistry 15, 5607; 4) Fletcher, Herlihy, Albery & Knowles (1976) Biochemistry 15, 5612; 5) Leadlay, Albery & Knowles (1976) Biochemistry 15, 5617; 6) Fisher, Albery & Knowles (1976) Biochemistry 15, 5621; 7) Albery & Knowles (1976) Biochemistry 15, 5627; 8) Albery & Knowles (1976) Biochemistry 15, 5631.

24 TIM Free Energy Profile of a Perfect Enzyme J.R. Knowles & W.J. Albery (1977) Acc. Chem. Res k non = 6 x 10-7 s -1 k catg->d 2 x 10 3 s -1 ΔΔG 12.6 kcal/mol Why is this perfect? Physics! 1) Can t change ΔG 0 - thermo 2) TS for GAP dissociation is set by diffusion limit so k cat in DHAP -> GAP direction limited by that barrier no need to lower TS barrier for chemistry much below that 3) Need to keep GSs higher than free E + DHAP to maximize k cat.

25 TIM Key Structural Features Contributing to Catalysis a) Compact b) 3 Catalytic residues: Glu, His, Lys c) Loop closure (i) positions Glu (base) (ii) locks in substrate, (iii) dehydrates active site cavity with hydrophobics d) Pi substrate-assisted closure and specificity

26 How compact is TIM site? cyan helix magenta sheet pink loop DHAP yellow C PDB: 1NEY

27 TIM What s inside the box? Fig. from J. Richard, (2012) Biochemistry 21, Å structure from Jogl, et al (2003) PNAS 100, 50. Glu165 B: His95 polarizes C=O Lys12 binds P i and may help polarize DHAP C=O

28 TIM Motions within the box - a) Overlay of DHAP - cyan enediolate analog - magenta 1.2 Å structure from Jogl, et al (2003) PNAS 100, 50. d) Anisotropic motions of atoms in active site only in directions productive for catalysis

29 TIM but there s also a lid to the box that has many critical features! Loop 6 closure essential for proper placement of Glu165! Malabanan, et al (2010) Curr Opin Struct Biol 20, 702.

30 TIM but there s also a lid to the box that has many critical features! Several H-bonds form between Loop 6 backbone and side chains in other loops and Pi in substrate upon ligand binding and loop closure. Malabanan, et al (2010) Curr Opin Struct Biol 20, 702.

31 TIM but there s also a lid to the box that has many critical features! Loop hinge is rigid! - Hinge mutations cause enhanced nanosecond motions of loop - large loss of entropy on closure results in 2500-fold lower k cat. YE-PGG-AIGTG-GGG-TP Sun & Sampson (1998) Protein Sci 7, 1495.

32 TIM but there s also a lid to the box that has many critical features! Ile172 in Loop 6 pairs with Leu232 to form a hydrophobic cage around Glu165 restricts it to motions perpendicular to C1-C2 bond of substrate, and likely increases its pka so a better base catalyst to remove H + from C. Malabanan, et al (2010) Curr Opin Struct Biol 20, 702.

33 TIM one last bit Pi binding provides specificity, i.e., enhanced catalysis J.R. Knowles (1991) Phil. Trans. R. Soc. Lond. B 332, 115. Amyes, et al (2001) JACS 123, Comparing profiles with Glyceraldehyde (GA) vs GAP shows Pi provides ~ 4 kcal/mol binding energy at GS ~ 14 kcal/mol at TS!!

34 TIM Key Structural Features Contributing to Catalysis a) Compact b) 3 Catalytic residues: Glu, His, Lys c) Loop closure (i) positions Glu (base) (ii) locks in substrate, (iii) dehydrates active site cavity with hydrophobics d) Pi substrate-assisted closure and specificity

35 Background for Design Paper on Friday Privett et al 2012 PNAS 109, 3790