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ENZYME MECHANISM

ENZYME MECHANISM. specific activity is the amount of product formed by an enzyme in a given amount of time under given conditions per milligram of enzyme . The rate of a reaction is the concentration of substrate disappearing (or product produced) per unit time ( mol L − 1 s − 1)

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ENZYME MECHANISM

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  1. ENZYMEMECHANISM

  2. specific activity is the amount of product formed by an enzyme in a given amount of time under given conditions per milligram of enzyme. • The rate of a reaction is the concentration of substrate disappearing (or product produced) per unit time (molL − 1s − 1) • The enzyme activity is the moles converted per unit time (rate × reaction volume). Enzyme activity is a measure of quantity of enzyme present. The SI unit is the katal, 1 katal = 1 mol s-1, but this is an excessively large unit. A more practical value is 1 enzyme unit (EU) = 1 μmol min-1 (μ = micro, x 10-6). • The specific activity is the moles converted per unit time per unit mass of enzyme (enzyme activity / actual mass of enzyme present). The SI units are katal kg-1, but more practical units are μmol mg-1 min-1. Specific activity is a measure of enzyme efficiency, usually constant for a pure enzyme. • If the specific activity of 100% pure enzyme is known, then an impure sample will have a lower specific activity, allowing purity to be calculated. • The % purity is 100% × (specific activity of enzyme sample / specific activity of pure enzyme). The impure sample has lower specific activity because some of the mass is not actually enzyme.

  3. Enzyme Action • Each enzyme has a unique three-dimensional shape that binds and recognizes a group of reacting molecules called substrates. • The active site of the enzyme is a small pocket to which the substrate directly binds. • Some enzymes are specific only to one substrate; others can bind more than one substrate.

  4. Enzyme-Substrate Binding

  5. Models of Enzyme Action • Early theory: lock-and-key model. Active site (lock) had the same shape as the substrate (key). Only the right shape key could bind. • Current theory: induced fit model. Active site closely resembles but does not exactly bind the substrate. • Allows for more flexibility in type of substrate • Also explains how the reaction itself occurs. As the substrate flexes to fit the active site, bonds in the substrate are flexed and stressed -- this causes changes/conversion to product.

  6. Molecular Recognition How does an enzyme bind a substrate, reduce the activation barrier, and produce a product? Lock & Key Hypothesis Induced Fit Hypothesis vs.

  7. C. Factors Affecting Enzyme Activity • Enzyme activity is defined as how fast an enzyme catalyzes its reaction. • Many factors affect enzyme activity: • Temperature: most have an optimum temp around 37oC • pH: most cellular enzymes are optimal around physiological pH, but enzymes in the stomach have a lower optimum pH • Concentration of enzyme and substrate: have all of the enzyme molecules been used up, even though substrate is still available?

  8. Energy of activation: ΔG‡ Effect of catalysis ΔG‡ ΔGcat‡ A → B Effect of temp ΔGT1‡ ΔGT2‡ (T1 > T2) A → B

  9. Rate acceleration: mechanisms EX‡ E + S ES E + P Stabilization of the transition state: covalent bonds, metals, acid-base, and proximity. Destabilization of ES: strain, charge, electrostatics Reduced entropy in ES formation.

  10. Rate acceleration: mechanisms hydrolysis of a β-glycosidic bond yielding a unit of α-glucose

  11. Major factors: pH, ions, & temp At pH ~ 7 amino acids exist as zwitterions. The R group determines pH. aspartic acid [pKa = 4.0] arginine [pKa = 12.5]

  12. Major factors: pH, ions, & temp • pH • ionic strength • temperature barley α-amylase activity plotted as a function of pH

  13. Major factors: pH, ions, & temp • pH • ionic strength • temperature Having the correct ions is important. Why? barley α-amylase isozyme 1 [crystallized with Ca2+ (green)]

  14. Major factors: pH, ions, & temp • pH • ionic strength • temperature barley α-amylase with CaCl2 barley α-amylase w/o CaCl2

  15. k1 k2 (k-1+k2) Vmax [S] E + S ↔ ES → E + P Km = ν = k-1 k1 Km + [S] Michaelis-Menten Kinetics Assumptions: [1] Steady-state of the intermediate complex ES [2] Neglect back rxn from product (k-2; not shown) [3] Conservation of mass ([ET] = [E] + [ES]) Vmax = k2[ET] where:

  16. Michaelis-Menten Kinetics

  17. Michaelis-Menten Kinetics Many types of inhibition can be included in the MM model as well as multiple substrates and steps: Inhibition: competitive (rev) noncompetitive (rev) mixed (rev) irreversible Reaction Schemes: single substrate multiple substrate single displacement double disp (ping-pong)

  18. Reaction Rate vs. Enzyme and Substrate Conc.

  19. Control of Enzyme Activity • We don’t always need high levels of products of enzyme-catalyzed reactions around. What kind of control system is used to regulate amounts of enzyme and products? • Two main methods: zymogens, and feedback control.

  20. Zymogens • Many enzymes are active as soon as they’re made. • However, some are made in an inactive form and stored. This inactive form is called a zymogen or proenzyme. • To become active, the body needs only to cleave off a small peptide fragment.

  21. Feedback Control • Some enzymes (allosteric enzymes) bind molecules called regulators (different from the substrate) that can affect the enzyme either positively or negatively • Positive regulator: speeds up the reaction by changing the shape of the active site -- substrate binds more effectively • Negative regulator: slows down reaction by preventing proper substrate binding, again, by changing enzyme shape • Feedback control: the end product acts as a negative regulator. If there is enough of the end product, it will slow down the first enzyme in a pathway.

  22. The kinetics of enzyme catalysis: Steady state kinetics

  23. A hyperbolic curve between V0 and [S] was revealed by in vitro studies using purified enzymes • It was the initial velocity (rate), V0, that was measured, so the change of [S] could be ignored. • The catalysis was assumed to occur as: • The enzyme will become saturated at high [S]: theV0 will not be affected by [S] at high [S].

  24. Vmax is extrapolated from the plot: V0 approaches but never quite reaches Vmax. The effect on V0 of varying [S] is measured when the enzyme concentration is held constant. Hyperbolic relationship between V0 and [S]

  25. A mathematical relationship between V0 and [S] was established (Michaelis and Menten, 1913; Briggs and Haldane, 1925) • E + S ES E + P • Formation of ES is fast and reversible. • The reverse reaction from PS (k-2 step) was assumed to be negligible. • The breakdown of ES to product and free enzyme is the rate limiting step for the overall reaction. • ES was assumed to be at a steady state: its concentration remains constant over time. • Thus V0 = k2[ES] k 1 k 2 ( )

  26. k1 k2 k -1 • Steady-state assumption: • Rate of ES formation=rate of ES breakdown • k1([Et]-[ES])[S]=k-1[ES] + k2[ES] ([Et] is the total enzyme concentration.) • Solve the equation for [ES]: Km is called the Michaelis constant. V0 = k2[ES]

  27. The maximum velocity is achieved when all the enzyme is saturated by substrate, i.e., when [ES] =[Et]. Thus Vmax =k2[Et] The Michaelis-Menten Equation

  28. When [S] >> Km When [S] << Km The Michaelis-Menten Equation nicely describes the experimental observations. The substrate concentration at which V0 is half maximal isKm

  29. The Vmax and Km values of a certain enzyme can be measured by the double reciprocal plot (i.e., the Lineweaver-Burk plot).

  30. The double reciprocal plot: 1/V0 vs 1/[S]

  31. The Michaelis-Menten equation, but not their approximated mechanism applies to a great many enzymes • Most enzymes (except the regulatory enzymes) have been found to follow the Michaelis-Menten kinetics, but their actual mechanisms are usually more complicated (by having more intermediate steps) than the one assumed by Michaelis and Menten. • The values of Vmax and Km alone provide little information about the number, rates, or chemical nature of discrete steps in the reaction.

  32. The actual meaning of Km depends on the reaction mechanism k 1 • For • If k2 is rate-limiting, k2<<k-1, Km = k-1/k 1 • Km equals to the dissociation constant (Kd) of the ES complex; • Km represent a measure of affinity of the enzyme for its substrate in the ES complex. k -1

  33. PLOT EADIE-HOFSTEE DAN HANES - WOOLF • Plot Lineweaver – Burk mempunyai sedikit kelemahan, yaitu • Sering kali pada saat mengekstrapolasi grafik untuk menentukan harga -1/Km ternyata akan memotong sumbu 1/[S] di luar grafik yang dibuat • Pada konsentrasi substrat yang terlalu rendah, maka akan diperoleh hasil yang kurang akurat • Awal dari kelinearannya sering kurang jelas dibanding dengan plot lain, terutama plot Eadie – Hofstee, padahal hal ini sangat penting pada penentuan mekanisme reaksi

  34. Plot Eadie-Hofstee dan Hanes diturunkan dari persamaan Lineweaver-Burk dengan mengalikan kedua sisi persamaan dengan faktor vo Vmax sehingga akan diperoleh persamaan garis lurus selanjutnya dipergunakan untuk menghitung Vmax dan Km

  35. Dengan cara penurunan yang mirip, Hanes-Woolf mengalikan perasamaan Lineweaver-Burk dengan [So] maka diperoleh: Plot Eadie – Hofstee dan Hanes banyak digunakan pada studi kinetik enzim, namun demikian studi enzim secara umum masih menggunakan plot Lineweaver – Burk.

  36. Lineweaver-Burk (double reciprocal plot) • Rewrite Michaelis-Menten rate expression • Plot 1/v versus 1/[S]. Slope is Km/Vmax, intercept is 1/Vmax

  37. intercepts Graphical Solution 1/ V Slope = Km/ Vmax 1/ Vmax 1/ [S] -1/ Km

  38. Example: Lineweaver-Burk

  39. Resulting Plot slope = Km/ Vmax= 0.5686 y intercept = 1/ Vmax= 2.8687

  40. Michaelis-Menten Kinetics

  41. Vmax = 1/2.8687 x 10-4 = 3.49 x 10-5 M/min Km= 0.5686 x Vm = 1.98 x 10-5 M

  42. Other Methods • Eadie-Hofstee plot • Hanes- Woolf

  43. Comparison of Methods • Lineweaver-Burk: supposedly gives good estimate for Vmax, error is not symmetric about data points, low [S] values get more weight • Eadie-Hofstee: less bias at low [S] • Hanes-Woolf: more accurate for Vmax. • When trying to fit whole cell data – I don’t have much luck with any of them!

  44. PERSAMAAN HALDAN UNTUK REAKSI REVERSIBEL • Reaksi enzimatis dalam sel sering berlangsung secara reversibel. • Reaksi substrat tunggal, S P, berlangsung melalui pembentukan satu kompleks intermediate, arah ke kanan dianggap sebagai kompleks ES dan sebaliknya kompleks EP E + S ES/EP P + E

  45. Persamaan MM arah kekanan pada [Eo] tetap dengan laju awal vf dan Vsmax • Persamaan MM ke arah sebaliknya pada [Eo] tetap dengan laju awal vb dan VPmax

  46. Perumusan Haldan hubungan antara konstanta laju dan kesetimbangan reaksi pada reaksi kesetimbangan adalah • Karena

  47. Maka: • Bila konstanta kesetimbangan diketahui, maka persamaan tersebut dapat digunakan untuk memvalidasi konstanta laju yang diperoleh • Secara umum Km dari arah reaksi metabolisme penting akan sedikit lebih kecil dari arah sebaliknya. Namun arah metabolisme dipengaruhi juga oleh [S] dan [P] dalam sel

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