CHAPTER 1: ENZYME KINETICS AND APPLICATIONS

Transcription

1 CHAPTER 1: ENZYME KINETICS AND APPLICATIONS EM /13 ERT 317 BIOCHEMICAL ENGINEERING

2 Course details Credit hours/units : 4 Contact hours : 3 hr (L), 3 hr (P) and 1 hr (T) per week Evaluations Final Exam 50% Midterm Tests 20% Course works 30% Laboratories 15% Assignments 15% CARRY MARKS 50%

3 Course details Course Outcome (COs) will be covered: CO1 Ability to develop enzyme reactions based on its kinetics study and applied catalysis Course works (Overall evaluations) Assignments - 2 Quizzes -1 Midterm test 1 Class participations Max. of 3 points

4 Important reminder Attendance should not less than 80%, or else you will be barred from taking final examination. Plagiarism and copying other students work is strictly prohibited especially in doing assignments and lab reports, or else both parties will get zero. Cheating in quizzes and examinations is also prohibited, or else both parties will get zero. Therefore, study hard and smart. Take note of the important chapters or things that will be highlighted throughout lectures.

5 C1.1 Kinetics of Enzyme Catalyzed Reactions Week 1 (10-21 Sept 2012) Reading assignment: 1. Chapter 3, Bioprocess Engineering basic Concepts. Shuler and Kargi (Main)

6 Outline Introduction to enzymes Enzyme structure Enzyme function Enzyme kinetics Michaelis-Menten Kinetics The Rapid Equilibrium Assumption The Quasi-Steady-State Assumption

7 Enzymes Enzymes are usually proteins Typically high molecular weight (15kDa several million kda) Over 2000 enzymes have been identified Often named by adding the suffix ase to the name of substrate acted upon, or the reaction catalyzed such as urease, alcohol dehydrogenase Catalytic function very specific and effective The majority of cellular reactions are catalyzed by enzymes

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9 Enzyme Specificity Absolute specificity the enzyme will catalyze only one reaction Group specificity the enzyme will act only on molecules that have specific functional groups, such amino, phosphate or methyl groups Linkage specificity the enzyme will act on a particular type of chemical bond regardless of the rest of the molecular structure Stereochemical specificity the enzyme will act on a particular steric or optical isomer

10 Enzyme Structure Some enzymes require a non-protein group for their activity Co-factors: metal and other chemical ions, such as Mg2+, Zn 2+, Mn2+, Fe2+, Fe3+, Ca2+, K+ Co-enzymes: complex organic molecules such as NAD, FAD, CoA, or some vitamins Enzyme that contains a non-protein group is called holoenzyme, the protein part of the holoenzyme is called apoenyzme: Apoenzyme + Co-factor = Holoenzyme

11 Enzyme Function Enzymes lower the activation energy of reaction catalyzed They do this by binding to the substrate of the reaction, and forming an enzyme-substrate (ES) complex Substrate binds to a specific site on the enzyme called the active site Multi-substrate reactions possible Lock and key model

12 Lysozyme - Structure The first enzyme structure to solved by X-ray crystallography Monomer of 14.9kDa 5 helices and a 3 stranded antiparallel sheet Deep, long binding cleft, sufficient for hexasaccaride open at the ends Catalytic residue Glu35 & Asp52

13 X-Ray structure of HEW lysozyme. a) The polypeptide chain with a bound (NAG) 6 substrate (green). b) A ribbon diagram highlighting the protein s secondary structure.

14 Note: catalytic residue Glu35 (yellow) Asp52 (yellow) X-Ray structure of HEW lysozyme. A computer-generated model showing the protein s molecular envelope (purple) and C a backbone (blue).

15 Lysozyme - Function Lysozyme catalyzes the hydrolysis of the b (1->4) glycosidic bonds in bacterial cell wall peptidoglycans and chitin (fungal cell walls) Found in egg white, tears and mucus membranes, bacterial viruses Substrate Products

16 Enzyme-Substrate Complex

17 Activation Energy

18 Potential-energy curves for the reaction of substrate, S, to products, P.

19 Comparison of activation energies in the uncatalyzed and catalyzed decompositions of ozone.

20 Enzyme-Substrate Binding Proximity effect: In multi-substrate enzyme-catalyzed reactions, enzymes can hold substrates such that reactive regions of substrates are close to each other and to enzyme s active site Orientation effect: Enzymes may hold the substrates at certain positions or angles to improve the reaction rate Induced fit: In some cases, formation of the ES complex causes slight changes in the 3D shape of the enzyme May contribute to catalytic activity of the enzyme

21 LOCK-AND- KEY INDUCED FIT

22 The Conformational Change Induced in Hexokinase by the Binding of a substrate, D- Glucose BINDING CLEFT CLEFT CLOSES

23 Enzyme Kinetics Mathematical models of single-substrate, enzymecatalyzed reactions were first developed by Henri in 1902 and Michaelis & Menten in 1913 Simple enzyme kinetics are now commonly referred to as Michaelis-Menten or saturation kinetics At high substrate concentrations, all active sites on the enzyme are occupied by substrate enzyme is saturated Models are based on data from batch reactors with constant liquid volume in which the initial substrate, [S 0 ], and enzyme, [E 0 ], concentrations are known

24 Single-Substrate Enzyme Kinetics E It is assumed that: k1 k2 S ES E P k 1 (3.1) The ES complex is established very rapidly The rate of the reverse reaction of the second step is negligible (i.e k-2~0) Assumption 2 is typically only valid when product (P) accumulation is negligible, at the beginning of the reaction

25 Rate of Reaction as a Function of Substrate Concentration

26 Mechanistic Models for Simple Enzyme Kinetics The rate of product formation is: P d v k2 dt ES (3.2) Where v is the rate of product formation or substrate consumption in moles/l-s The rate constant k 2 is often denoted as k cat in biological literature

27 Mechanistic Models (cont d) The rate of variation of the ES complex is: d ES dt k E S k ES k ES 1 1 And since the enzyme is not consumed: E E ES 0 2 (3.3) (3.4) At this point, an assumption is required in order to achieve an analytical solution

28 The Rapid Equilibrium Assumption Assuming equilibrium in the first part of the reaction (E+S forms ES), we can use the equilibrium coefficient to express [ES] in terms of [S] The equilibrium constant is: Since E E ES 0 ES ES ' K m k k 1 1 E S ES if the enzyme is conserved E 0 S (3.6) k S k 1 1 E S 0 ' K S m (3.7) (3.5)

29 The Rapid Equilibrium Assumption Substitution Eq 3.7 into Eq 3.2 yields: dp E 0 S Vm S v k2 ' ' (3.8) dt K S K S m m Where V m k 2 E 0 and Vm is the maximum forward rate of the reaction V m changes with the addition of additional enzyme, but not additional substrate ' K m is called the Michaelis-Menten constant, and the prime( ) indicates that it was derived assuming rapid equilibrium A low value of ' K m suggests that the enzyme has a high affinity for the substrate ' K ' V m corresponds to the [S], such that m Km 2

30 The Quasi-Steady-State Assumption The assumption of rapid equilibrium is often not valid The QSSA assumes that if the initial substrate concentration greatly exceeds the initial enzyme concentration S, then 0E 0 des 0 dt Computer simulations show that the QSSA holds, in a closed system, after a brief transition period while the reaction is initiated and equilibrium achieved Applying the QSSA to Eq 3.3 gives us: ES k k 1 E S 1 k 2 (3.9)

31 Formation of [ES] and Initiation of Steady State

32 The Quasi-Steady-State Assumption Substituting the enzyme conservation Eq 3.4 into Eq 3.9 yields Solving Eq 3.10 for [ES] ES ES Substituting Eq 3.11 into Eq 3.2 v k 1 k P d dt E ES S 1 0 k 1 E0 k k 1 k k 2 S 2 S k2 1 k k 1 E S 2 S (3.10) (3.11) (3.12a)

33 The Quasi-Steady-State Assumption Therefore: Where: v K V m m V K k m 2 m k S S 0 1 Eq 3.12b is the classic Michaelis-Menten equation for single-substrate enzyme kinetics 1 2, and E k k (3.12b)

34 Outline Simple enzyme kinetics Complex enzyme kinetics Allosteric enzymes Inhibited enzyme kinetics Competitive Noncompetitive Uncompetitive

35 Course details Course Outcome (COs) will be covered: CO1 Ability to develop enzyme reactions based on its kinetics study and applied catalysis Course works (Overall evaluations) Assignments 1 (Due Wed, 19/09) Quizzes 1 (Wed, 19/09) Midterm test 1 Class participations Max. of 3 points

36 Experimental Determination of Michaelis-Menten Parameters Determination of values for K m and V m with high precision can be difficult Experimental data are typically obtained from initialrate experiments Batch reactor charged with a known amount of substrate [S 0 ] and enzyme [E 0 ] Product and/or substrate concentration plotted against time Create many plots at different [S 0 ] and enzyme [E 0 ] and use to generate a plot as Figure 3.1 Cumbersome method of determining K m and V m, therefore after methods have been developed

37 Lineweaver-Burk Plot Eq 3.12b can be linearized in double-reciprocal form v 1 v V K m 1 V m m S S K V m m S A plot of 1/v versus 1/[S] yields a line with a slope of K m /V m and a y-intercept of 1/V m Give good estmates of V m but not necessarily K m Data points at low substrate concentrations influence the slope and intercept more than data points at high [S] 1 (3.12b) (3.13)

38 Lineweaver-Burk Plot

39 Lineweaver-Burk Plot with Actual Experimental Data Sets

40 Eadie-Hofstee Plot Eq 3.12b can be arranged as: v v S (3.14) V K m m A plot of v versus v/[s] results in a line with slope K m, and a y-intercept of V m Eadie-Hofstee plots can be subjected to large errors, since both coordinates contain v, but there is less bias on points at low [S] than with Lineweaver-Burk plots

41 Eadie-Hofstee Plot

42 Eadie-Hofstee Plot with Actual Experimental Data Sets

43 Hanes-Woolf Plot Rearrangement of Eq 3.12b yields: S v K 1 m V V m S A plot of [S]/v versus [S] results in a line of slope 1/V m with a y-intercept of K m /V m This plot is used to determine V m more accurately than the previous two plots m (3.15)

44 Hanes-Woolf Plot

45 Hanes-Woolf Plot with Actual Experimental Data Sets

46 Batch Kinetics The time course of variation of [S] in a batch enzymatic reaction can be determined by integrating equation 3.12b to yield: V V m m t S 0 S0 S Km ln S S S K S 0 m 0 ln t t S (3.16) (3.17) A plot 1/t (ln[s 0 ]/[S]) versus {[S 0 ]-[S]}/t results in a line of slope -1/K m with a y-intercept of V m /K m

47 Complex Enzyme Kinetics: Allosteric Enzymes Allosteric enzymes: Some enzymes posses more than one substrate binding site The binding of one substrate molecule to the enzyme facilitates binding of other substrate molecules This is known as allostery or cooperative binding Often seen in regulatory enzymes

48 Allosteric Enzymes Allos -other, steros shape The rate expression for allosteric enzymes is: n ds VmS v " n (3.18) dt Km S Where n = cooperativity coefficient and n>1 indicates positive cooperativity (=activator; n<1=inhibitor) The cooperativity coefficient can be determined by rearranging 3.18: v " ln nln S ln K (3.19) m Vm v And by plotting ln v/(vm-v) versus ln [S]

49 Allosteric Enzymes

50 Graphical Determination of the Cooperativity Coefficient, n