Download presentation

Presentation is loading. Please wait.

Published byTrinity Compton Modified over 2 years ago

1
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Edda Klipp Systems biology 2 – Reaction kinetics Sommmersemester 2010 Humboldt-Universität zu Berlin Institut für Biologie Theoretische Biophysik

2
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Enzymes -Proteins, often complexed with cofactors -Anorganic cofactors: metall ions -Organic cofactors (coenzymes): vitamin-derived complex groups - remain unchanged after reaction as catalyst - have a catalytical centre - are in general highly specific - are often pH- and temperature dependent Turnover number : 1000 /sec (100 /sec million /sec) Acceleration (compared to non-catalyzed reaction) by 10 6 to fold Thermodynamics: Enzymes reduce the necessary activation energy for the reaction

3
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Classification of enzymatic reactions irreversible - reversible S P S P

4
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Classification of enzymatic reactions Number of substrates (and products) S P S 1 +S 2 P S 1 +S 2 +S 3 P 1 S 2 large (0.5) S 2 small (0) uni bi ter

5
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Classification of enzymatic reactions Type of kinetics v = k S Linear Mass action Hyperbolic Michaelis-Menten Sigmoidal Hill kinetics, Monod, Koshland. v Hyperbolic and Sigmoidal show saturation, Linear involves unlimited reaction rates.

6
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Deterministic kinetic modeling of biochemical reactions Basic quantities: Concentration S : number of molecules per unit of volume Reaction rate v : concentration change per unit time Postulat: The reaction rate v at point r in space at time t can be expressed as a unique function of the concentrations of all substances at point r at time t : Simplifying assumptions: - spatial homogeneity (well-stirred) - autonomous systemes (not directly dependent on time) Kinetics of Enzymatic Reactions v(r,t) = v(S(r,t),t) v(t) = v(S(t))

7
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin The reaction rate is proportional to the probability of collision of reactants, This is in turn proportional to the concentration of reactants to the power of their molecularity. (Guldberg and Waage, 19. century) A+B2 C Reaction rate Rate constants Equilibrium constant The Mass Action Law

8
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Brown (1902): Mechanism for Invertase reaction (with sucrose), Which holds for one-substrate-systemes with backward reaction of effectors: E – catalyst S – substrate P – product k i – kinetic constant complex formation reversible Michaelis, Menten (1913): rate equation under the assumption That second reaction will not influence the first equilibrium (Hypothesis of quasi-equilibrium) Briggs, Haldane (1925): more general derivation of Rate law under the assumption of a steady state for the enzyme-substrate-complex (where ) Michaelis-Menten Kinetics complex degradation irreversible

9
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Non-linear ordinary differential equation system - The rate of product formation is equal to the reaction rate (1) (2) (3) (4) - The sum of equations (2) and (3) is a conservation relation for the enzyme - The whole set of equations cannot be solved analytically. Using quasi-steady state assumption Michaelis-Menten Kinetics: derivation of rate law

10
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Reaction rate Maximal velocity Michaelis constant Michaelis-Menten- Rate expression S v V max Michaelis-Menten-Kinetics: The rate equation

11
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Integrated Form of MM rate law Reaction rate = Product increase or substrate decrease per unit time Integration from t 0, S 0 to t, S results in and for This is a function or. One can record a progress curve and estimate the kinetic constants using non-linear regression. Henri-Michaelis- Menten-equation

12
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Estimation of Parameters V max and K m 1. Measurement of initial rates Measure initial rates for different initial concentrations, i.e. measure initial change of S. 2. Interpretation Plot measurement results in (S,V)-Diagram; Compare with Michaelis-Menten rate law; Estimate parameters by non-lineare regression, for example least-squares methode

13
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Linearizations of the MM rate law Lineweaver-Burk-Plot Eadie-Plot Hanes-Plot

14
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Additional aspects Relation to thermodynamics V max is related to turnover number, k cat Condition: completely saturated enzymes, maximal rate: [1/(mol*s)] Dissoziation constante K S of the enzyme-substrate-complex: [mol]

15
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Here: the enzyme as target of effectors Regulation of Enzyme Activity - Regulation of enzyme amount (Gene expression / proteine degradation) - Action of effectors (inhibitors, activators) - Composition of mediums (pH, ions) - Regulation of protein activity by kinases / phosphatases / methylases.... Important mechanism for the regulation of cellular processes upon the adaptation to internal and external changes.

16
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin 1.Competitive inhibition: substrate and inhibitor compete for the binding place at the enzyme Equilibrium for inhibitor binding Conservation relation for the enzyme Rate equation Enzyme Inhibition

17
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Examples Competitive Inhibition 2. Acetylcholin esterase has as substrate acetylcholin and is inhibited by Neostigmin. Note that obviously only the charged N(CH 3 ) 3 + -group is active. 3. Sulfonamide(antibiotica) block as competitive inhibitors the production of DNA, Since they are used by the enzyme instead of the vitamine precursor p-Aminobenzoesäure. 1. Succinic acid dehydrogenase has as substrate succinic acid and is inhibited by Malonic acid. Bernsteinsäuredehydrogenase

18
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin 2. Uncompetitive inhibition : Inhibitor binds only to the enzyme-substrate-complex 3. Non-competitive inhibition : Inhibitor binds to free and bound enzyme Enzyme Inhibition

19
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin 4. Irreversible inhibition : inhibitor binds the enzyme irreversibly, partial or complete loss of catalytic effectivity Example: Reaction of Iod acetate with –SH groups in cystein side chains of the reaction centre Enzyme Inhibition, 3 1. Di-isopropyl-fluorophosphate (DFP) and other alkylphosphates bind covalently to acetylcholinesterase. This enzyme is responsible for Transmission of nerve stimuli. The organsims die of paralysis (Lähmung) of organ function. (used in military gases and insektizids)

20
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Allosteric Inhibition : Inhibition by a molecule that does not bind to the reaction centre. conformation change of the enzyme, Change of reaction coordinate Enzyme Inhibition, 5 Product Inhibition : - Inhibition by the product due to allosteric inhibition (prevents excess production) - Reduction of the net reaction rate, due to an accumulation of product which is substrate of the backward reaction.

21
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Substrate Excess Inhibition Example: Succinic acid dehydrogenase Binding a further substrate molecule to ES-complex Enzyme-Substrate-Complex ESS, Which does not transforms to reaction products. Reversible inhibition, if one molecule dissociates. Equilibrium assumptions Enzyme conservation Reaction rate Optimum

22
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Activation Increase of the rate by - Change of substrate binding - Acceleration of product formation Enzyme Activation Example Substrate activation : Substrats S acts as activator A. Reaction rate = Product formation rate Enzyme conservation Quasi-equilibrium condition Reaction rate

23
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Activation and Inhibition for Mass Action Kinetics A PS + I PS - compulsoryadditional

24
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Ligand: compound that binds to enzyme / protein Here: Binding of ligands to monomeric und oligomeric proteins. several ligand binding sites at a protein: Possibility of interactions between these sites during binding This phenomenon is called cooperativity Positive/negative cooperativity: Binding of a ligand molecule increases/reduces the affinity of the protein for further ligands. Homotrope/heterotrope cooperativity : Binding of a ligand molecule affects binding of further molecules Of the same/ other ligands. Ligand Binding and Cooperativity

25
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Case of 1 binding site: Binding of S (Ligand) to E (Protein) Binding constante Definition: Fractional Saturation Fractional saturation for 1 subunit Plot of Y versus S is hyperbolic Fractional Saturation

26
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Positive, homotrope cooperativity Simplest case: dimeric protein - two similar ligand binding sites - Binding of first ligand increases affinity to second ligand Assumption: Binding of S increases affinity M 2 S reacts with S as soon as it is formed Fractional saturation: Complete cooperativity (each subunit is either empty or completey saturated) M = monomere Untereinheit, M 2 = Dimer Binding constante Hill-Kinetik Fractional saturation:

27
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin For complete homotrope cooperativity of a protein with n subunits holds: This is a form of the Hill equation Hemoglobin: sigmoid bindung curve of oxygen against oxygen partial pressure Hill (1909): Interaction between binding sites - positive cooperativity Known: hem binds oxygen molecules Unknown: number of subunits per protein Assumption: complete cooperativity - experimental Hill coefficient h=2.8 Four Binding sites per hemoglobin molecule No complete cooperativity High oxygen partial pressure in lungs: good binding of oxygen to Hb Low oxygen partial pressure in body – easy delivery of O 2 Y S Hill Kinetics

28
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Monod-Wyman-Changeux model for enzymes with sigmoidal kinetics Model assumptions (J.Mol.Biol.(1965),12,88) : i)Enzyme consists of several identical subunits (SU) ii) each SU can assume one of two conformations (active = R or inactive = T) iii)all SU of an enzyme have the same conformation Conformation change for all SU at the same time (concerted transition). R – Conc. active conformation R 0 – R- Conc. without bound substrate R 1 – R- Conc. with 1 bound substrate T – Conc. of inactive conformation T 0 – Conc. without bound substrates R - active T - inactive L Conformation equilibrium Allosteric constant

29
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Monod-Wyman-Changeux model n = 4 subunits Binding constante for substrate S to one SU: K R or K T (Assumption: Binding only to active form, S + KRKR For each enzyme there are the following possible bound states: R 0 - Concentration of R without substrate binding, R 1 - Conc. of R with 1 bound molecule of S R 2 - Conc. of R with 2 bound molecules of S R 3 - Conc. of R with 3 bound molecules of S R 4 - Conc. of R with 4 bound molecules of S 1 possibility 4 possibilities 6 possibilities. 4 possibilities 1 possibility General: Possibilities of substrate binding for R i

30
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Monod-Wyman-Changeux model It holds: General: Sum of all active states: with binomic Formula: Fractional saturation Replacement of R and R i T exists only as T 0

31
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Monod-Wyman-Changeux model It follows Reaction rate Michaelis-Menten- Term "Regulatory Term"

32
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Monod-Wyman-Changeux model activation inhibition S v For S : Monod-Kinetics approaches Michaelis-Menten-Kinetics small S: regulatory term important depending on L L = 0: MM-Kinetics L >> 0: sigmoidal curve, shifted to right. Explanation of the action of activators and inhibitors: - Activators bind to active conformation - Inhibitors bind to inactive conformation -Shift of equilibrium to R or T Bindungskonstanten

33
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Monod-Wyman-Changeux model Example: Phosphofructokinase: experimentaly well studied system Activators: Inhibitors: DPG, ATP Typical value for

34
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Derivation of rate equation for steady state Relation between equilibrium constant q and kinetic constants of elementary steps Reaction rate Kinetics of Reversible Reactions

35
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Relation to phenomenological quantities S very high, P=0 P very high, S=0 Half-maximal forward rate Half-maximal backward rate For S and P very small holds This resembles Mass action kinetics (Also called linear kinetics). Kinetics of Reversible Reactions

36
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Several activated complexes

37
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Methode of King and Altman Empirical methode to derive steady-state rate equations for reactions, Which are catalyzed by an enzyme (no interaction between enzymes!) 1. Conservation of total enzyme amount: 2. Relative concentration of each enzyme species is equal to ratio of two sums of terms, where every term T ij is the product of n-1 rate constants and the related concentrations. 3. Every term T ij contains the rate constants (times substrate conc.), which are associated with the steps leading individually or sequentially to EX i. The sum of all possible combinations (j) are the numerator, the sum of all numerators for all EX i is the denominator. EX i - freies Enzym 4. The reaction is:

38
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin King-Altman for 3-Step reaction mechanism EES EP Sk 1 k -1 k -2 k2k2 k3k3 Pk Conservation of total enzyme amount: : 2., 3. Listing of all possibilities of n-1 = 2 lines leading to each enzyme species: For E k -1 k3k3 k -2 k3k3 k2k2 For ES Sk 1 k3k3 k -2 Pk -3 k -2 For EP Sk 1 k2k2 Pk -3 k2k2 k -1 Pk Reaction rate:

39
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Ordered bi-bi-Mechanismus (Example: Kreatinkinase) Further typical Mechanisms

40
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Ordered bi-bi-Mechanism (Example: Kreatinkinase) Ping-Pong-Mechanism (Example : Transaminase, Nukleosid-Diphosphokinase) Random bi-uni-Mechanism (Example : an Aldolase-Type) Further typical Mechanisms

41
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Unbranched Reaction Chain EX n EX 1 EX 2 EX n-1 Apparent rate constants Apparent equilibrium constants General rate law Holds for all sequential reaction mechanisms

42
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Example

43
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Convenience Kinetics (actually a generalized random kinetics….) Convenience Kinetics Ordered Kinetics r=0.946r=0.975 r=0.983 Ordered Kinetics Ping-pong Kinetics Convenience Kinetics Ping-pong Kinetics

44
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Other types of kinetics: S-Systems Introduced by M. Savageau, 1976 (synergistic systems) For i = 1...n n independent variables m dependent variables Steady state: XiXi X j2 X j3 X j4 X j5 X j1 Vi+Vi+ Vi-Vi- g, h – positive or negative, usually no integers

45
Humboldt- Universität Zu Berlin Edda Klipp, Humboldt-Universität zu Berlin Other types of kinetics: Lin-Log Kinetics Sef Heijnen and others

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google