INTRODUCTION TO ENZYME KINETICS

Transcription

1 Bilgy 00; Lecture 0 INTRODUCTION TO ENZYME INETICS enzye actie (catalytic) sites. stabilize substrate binding with sae cllectin f nn-calent interactins which theseles stabilize enzye 3-D cnfratins H-bnds, inic bnds, an der Waals interactins. again, ES interactins ust exclude water peratinally, this frequently eans the enzye is uch, uch larger than just thse residues fring the actie site als, actie sites ust be buried 3. nuber f actie (catalytic) sites per enzye hler is sall, frequently Q: where did this nuber ce fr? A: fr kinetic easureents f reactin elcity s. [substrate] In liing cells: enzye: substrate ratis are in the range :,000 t :50,000 cnsider a typical enzye-substrate partnership, hexkinase and glucse lier cell steady-state hexkinase (enzye) leel = 0 6 lecules / cell lier cell steady-state [glucse] = 5x0-3 M = (6x0 3 lecules/le)(5x0-3 le/liter)(5x0 - liter/cell) =.5x0 0 lecules/cell If we add trace enzye t a test-tube assay ixture cntaining buffer and substrate reactin elcity is nt cnstant starts ff fast and slws dwn fr reactin: S P easure [P] ersus tie by spectrphtetry (draw graph n bard) elcity is axiu at tie = zer because there is n back reactin t cntend with therefre, we extraplate elcity at tie = zer and call this alue Fr a trace aunt f enzye in buffer slutin ptiized fr actiity, if we plt (les/sec) ersus [, we get a saturatin cure Obseratins: at lw [, is prprtinal t [ at high [, is essentially independent f [ T explain this kinetic data, (Lenr) Michaelis and (Maud) Menten prpsed a siple kinetic del: a specific enzye-substrate cplex ES is a necessary interediate rate f prduct fratin is thus dependent nly n ES at lw [, S aailability liits rates f ES and P fratin at high [, ES is saturated, and P fratin is prprtinal t ES

2 Bilgy 00; Lecture 0 Michaelis-Menten ffered the siplest kinetic del (fewest assuptins) which accunts fr the data (Occa's razr): k k E + S ES E + P k Such siple kinetic dels then inle three kinetic cnstants, k, k -, and k This del des nt allw reersibility i.e., n reerse reactin with prduct Indeed, any tested enzyes d nt shw appreciable rates f the reerse reactin Iprtant: enzyes ften catalyze frward and reerse reactins at rates differing by rders f agnitude! Why? (a) Because they ay differentially bind substrate and prduct (b) Because ΔG alues fr frward and reerse reactin crdinates ay be different Nte: se enzyes DO quickly cheically equilibrate reactants and prducts Other enzyes DO NOT depends n hw enzyes perate in erall etablic cntext Thus, we ust nte a secnd, iprtant cnstraint n actie site cnfratins. ust stabilize transitin state interediates. yet, ust ften differentiate ang reactants and prducts Fr siple, Michaelis-Menten (neglecting back-reactin) enzyes: rate f ES fratin = k [E] [ rate f ES breakdwn = k [E + k - [E = (k + k - ) [E In real tie, any enzyes quickly reach a catalytic steady-state where, rate f ES fratin = rate f ES breakdwn Thus, k [E] [ = (k + k - ) [E Or, k [ E][ [ E k k We ay siplify this steady-state equatin, by cbining the three kinetic cnstants, such that: where [ E][ [ E r k k k [ E][ [ E

3 Bilgy 00; Lecture 0 Nw cnsider the free enzye, E : [E] = [E T ] - [E Substituting this alue fr [E] int the preius equatin: ([ ET ] [ E )[ [ E And sling fr ES : [ E [ E T [ ]( ) [ At the catalytic steady-state, fr the initial rate f prduct fratin (with n back-reactin): = k [E cbining these tw equatins: k[ E T ]( [ ) [ Nw, the axiu rate, = ax, is btained when substrate leels are s high as t saturate the reactin Under this cnditin, [ >> [ and, liit (S saturating) [ Thus, ax = k [E T ] Fr M-M enzyes bsering steady-state kinetics, k is the turner nuber fr the enzye, i.e., a easure f the ability f the substrate-saturated enzye t fr prduct, per unit tie And, [ () ax [ 3

4 Bilgy 00; Lecture 0 Equatin () explains the siple kinetic del f Michaelis-Menten: First, at r: [ <<, [ ax [ at [ >>, ax r, is independent f [ Secndly, fr equatin (), the eaning f is nw clear: when [ = then, ax Fr enzyes bsering siple Michaelis-Menten catalysis; and ax can be readily deried fr kinetic easureents f ersus [ first, siply inert equatin (): [ [ [ [ [ ax ax ax [ ( )( ) ax ax This equatin is f the fr: y = x + b S, plt f: slpe = ax ersus [ and Y-intercept = ax will yield a straight line, where ; X-intercept = This duble-reciprcal graph is called a Lineweaer-Burk plt 4

5 Bilgy 00; Lecture 0 The alues f any enzyes are in the icrlar range Althugh se enzyes hae uch higher alues As preiusly discussed, turner nubers ary any rders f agnitude: O, s k 3 is the turner nuber. What abut the ther kinetic cnstants? In siple M-M del, k alues are liited by ezye, substrate diffusin rates in i, k alues cannt exceed le - sec - One, ther, kinetic cnstant ay be deried: a easure f the fractin f successful enzye-substrate cllisins which g n t yield prduct se enzyes hae alues fr this cnstant in the range le - sec - therefre, these enzyes hae reached kinetic perfectin! eery interactin with substrate is prductie 5