Principles of Bioenergetics and Catalysis Kinetics Substrate diffusion

Principles of Bioenergetics and Catalysis Kinetics

Substrate diffusion and catalyis • What are bacteria? The advantage of being small. • What do bacteria do? Catalyse exergonic redox reactions. • Substrate diffusion to the cell: Can we predict the random diffusion of a molecule? Not of one, but of many molecules. • What is the kinetics of substrate diffusion (1 st order kinetics, Fick’s law). • What is diffusion driven by? Order, Concentration gradient, • How come that many molecules seem to have a behaviour but an individual molecule does not? • What is the principle of catalysing redox reaction? The enzyme does not bind to the substrate.

What do bacteria do? • Catalyse exergonic redox reactions • Exergonic, (downhill) reactions loose Gibbs Free Energy. G (DG=negative) • Bacteria utilise a portion of the free energy released for growth processes and multiplication S ΔG P

What does ΔG (Gibbs Free Energy Change) mean? • Spontaneous reactions are downhill reactions • Energy of substrates is higher than of products • Products are more stable than Substrate (stable = low energy) • The driving force = hill height = G difference in G = Delta (Δ) G ΔG = G (prod. ) – G (substr. ) • The reaction is driven by the loss in G Change in G is a negative value (e. g. Δ G = -256 k. J/mol) S ΔG P

Does the Δ G allow to predict the reaction rate ? • No • But for Δ G = zero, reaction rate will be zero • For Δ G = positive, reaction would go backwards (P S) • The rate is determined by G the activation energy (AE) • In biological reactions the AE is largely determined by the presence of enzymes (lower AE) • Now how do they do that? S AE ΔG P

The ΔGo of redox reaction is related to the ΔEo of e- donor and acceptor • ΔEo is the difference in redox potential of the half reactions • Couple with lower Eo will become e- donor -Eo • If not reaction would reverse • ΔGo = n F Δ Eo • Microbes that use electron donors of a very low Eo (e. g. H 2 and an electron acceptor of a very high level e. g. O 2) have a lot of free energy available for growth edon. ΔE eacc.

What is an enzyme reaction ? A reaction catalysed by a protein. What are the consequences of enzyme catalysis? The rate of a spontaneous reaction is increased. G If the reaction is already spontaneous, why do we need an enzyme? Spontaneous = downhill = exergonic Enzymes can not catalyse uphill = endergonic reactions If catalysed uphill reactions proceed in the reverse direction (Products Substrates) G Reaction path 7

How do enzymes catalyze ? A. By lowering the activation energy barrier! B. By binding to the substrate like a lock to a key? ? ? This is the simplified textbook explanation, but how can we visualise it? How can an enzyme convert a substrate to product by binding to it? Binding means stabilising (lower Energy level) and hence slowing Example: Antibody binding to antigen. Antibody is a protein designed by the immune system to bind and “neutralise” a foreign substances (the antigen). 8

Why don’t antigens catalyze? P S Will an antibody against the substrate be able to catalyse the reaction? No What is the difference between an antigen and an enzyme. Both bind, one catalyses the other does not. Does the enzyme have perhaps a special mechanism (lever) that can break into the substrates? No 9

How do enzymes catalyse ? Example: Substrate = stick, Product = broken stick S For the stick to be broken it must go through a transition state (T) How does the enzyme (stickase, of course) catalyse by binding to the stick? T P Binding to the stick stabilises rather than activates the substrate not making reaction easier The simplified concept of the enzyme binding to the substrate does not make sense Let’s have a closer look at the energy diagram for clues. 10

How do enzymes catalyse ? High Energy= T Unlikely, reactive, activated S G P P needed to lower the activation energy level: a way to make the transition (T) state more likely Low Energy= Likely to exist, stable Reaction path Note T not an intermediate just a “deformed molecule” that makes forward and backward reaction equally likely 11

How do enzymes catalyse ? Example: Substrate = stick, Product = broken stick S For the stick to be broken it must go through a transition state (T) The enzyme (stickase, of course) binds to T T P stabilises T makes T more likely higher quantities of T available higher likelyhood for P to form (P cannot form when T is in ultra low concentration) Enzymes catalyse by binding to the transition state and making it more likely. 12

How do enzymes catalyse ? Significant product formation depends on availability of T. T Non catalysed reactions are slow because [T] is low S G P P Reaction path By binding to T enzymes increase the chances of T to exist, hence speed up the reaction. Binding does not mean, holding on to T but releasing T rapidly, either as S or as P. 13

How do enzymes catalyse ? The enzyme substrate complex (ES) is not a transitional state but a true, existing, defined intermediate T S Intermediates are in a “valley” ES G P Transition states are on a “peak” P Reaction path 14

How far will the catalysed reacton go? With decreasing substrate concentration the energy content of the substrates sinks. Increasing product concentrations lift the energy content of the products. S The reaction continues until the difference in G (Delta G) is zero. ` G P Reaction path Then the energy level of substrate equals that of the product Reaction is at equilibrium Rate of backwards reaction equals that of forward reaction. The ratio [P]/[S] now represents the equilibrium constant keq. 15

The dynamic equilibrium The ratio [P]/[S] now represents the equilibrium constant keq. An original very exergonic reaction needs lots of P to accumulate until equilibrium is reached S ` G P at equilibrium [P]/[S] is very high (e. g. 10, 000) endergonic reactions have low keq (e. g. 0. 00001) Reaction path The enzyme does not affect the spontaneity or reversibility of reaction but the energetics does. Not surprisingly the reaction driving force 16 is related to keq ΔG =RT ln keq

Binding Energy Where does the energy come from to overcome activation energy? An enzyme/substrate to be more precise enzyme/T complex forms hydrogen bonds and hydrophobic interaction bonds. T The binding energy released is the energy source of lowering the activation energy (analogy of magnets in stickase) H bonds of T with H 2 O are replaced by bonds with E (dry bonding) 17

What is the effect of activation energy on reaction rate? The overal rate constant (k) of the reaction depends directly on the activation energy: k= (B/P*T)*e -DG(activ. )/RT B/P=Bolzman/Planck constant T E. g. lowering the activation energy by 5. 7 k. J will increase rate 10 fold 18

Part 2: Biological Reaction Kinetics The kinetic background of enzyme catalyzed reactions. Comparision of 2 biological reaction types with classical chemical reaction kinetics. Four reaction kinetics types: Zero order, First order, Michaelis Menten, exponential (multiplication of biocatalyst)

What is the effect of activation energy on reaction rate? After we have concluded: that the enzyme (E) catalyses the substrate (S) conversion by forming an Enzyme-substrate complex T Let us see how we can derive the kinetic behaviour of the enzyme reaction from first principles. The widely accepted enzyme kinetics model is the Michaelis Menten model. 20

Foundation of Michaelis-Menten Kinetics For the overall enzyme reaction a number of rate constants need to be considered: The rate of conversion of E and S to ES is k 1 E +S k 1 k-1 ES k 2 E+P k-1 is the rate constant for ES going back to E and S k 2 is the rate for conversion of ES to E and P In enzyme assays P is negligible (startup velocity of reaction) k-2 is not included. (Rate constants mean first order kinetics rate constants as explained below. ) 21

Foundation of Michaelis Menten kinetics E +S k 1 k-1 ES k 2 E+P Rate constant of first order reaction predicts that the rate is proportional to the substrate concentration The rate for ES to go to E +P is given by: ES (m. M) * k 2 (h-1) (m. M/h) 22

Foundation of Michaelis Menten kinetics E +S k 1 k-1 ES k 2 E+P At substrate saturation no free enzyme is available ([E]=0) overall rate is determined by k 2 ( kcat = k 2) (btw: kcat= vmax/(total enzyme concentration (Et, E+ES)) The ratio of ES formation over ES disintegration is km (formula? ) km = (k 2 + k-1)/k 1 enzyme with low km: ES formation faster than disintegration 23

Derivation of MM kinetics from first principles E +S k 1 k-1 ES k 2 E+P k-1+ K 2 = km k 1 At steady state: rate of ES disintegration =rate of ES formation k-1*ES + K 2*ES = k 1*ES k-1 ES + K 2 ES = k 1(Et-ES)S k-1 ES + K 2 ES = k 1 E t S - k 1 E S S k-1 ES + K 2 ES + k 1 ESS = k 1 Et. S (Et=E+ES) multiply out right k 1 ESS bracket out ES (k-1+ K 2 + k 1 S ) = k 1 E t S ES = k 1 Et. S / (k-1+ K 2 + k 1 S ) ES = k 1 Et. S k-1+ K 2 + k 1 S solve for ES 24

E +S ES ES = = vo = k 2 vo = k 1 k-1 ES k 2 k 1 Et. S cancel k 1 k-1+ K 2 + k 1 S Et S km+S k-1+ K 2 = km k 1 E+P = E t. S k-1+ K 2 +S k 1 (as vo = k 2 *ES ES = vo/k 2 ) (as vmax =k 2*Et) k 2 Et S km+S vmax S km+S (k 2 is also called kcat) 25

The Michaelis Menten Model has been derived: (students don’t need to be able to derive it but to know the final equation) vo = vmax S km + S Vo = the initial velocity (no products present) S = [substrate] km = half saturation constant, also called k. S vmax = maximum velocity under substrate saturation when overall reaction only depends on k 2 26

Microbial Reaction Kinetics: The Michaelis Menten (MM) model is not only useful for enzymatic reactions but overall microbial reactions such as algal blooms or microbial growth in bioreactors. v =v S o seen maxwhere the most widely used After we have km + S biological kinetic mode comes from… let us compare 2 types of microbial kinetics (MM and exponential kinetics) with traditional chemical kinetics (zero and first order). 27

Zero Order kinetics • constant velocity • velocity independent of S • v = K (M/s) • Ex: limited access to S (O 2 diffusion to food) • water loss • enzyme reactions at high S S P V Time V S

First Order Kinetics • velocity decreases over time (parallel to [S]) • velocity is determined by and hence proportional to S • v = S * K (s-1) • K is the rate constant • Ex: Most chemical reactions • Radioactive decay (half time) P S V Time V S

Exponential Kinetics • velocity exponentially increasing over time • independent of S but related to P • Can give appearance of sudden increase in P • v ~ P * K (s-1) • a product must enhance reaction velocity (e. g. heat, chain reaction) Biological examples: • bacterial spoilage (e. g. milk) multiplication of catalyst • Auto-oxidation of fats (radicals propagation) S P V Time V P

Michaelis Menten Kinetics Phase 1 Phase 2 S P • • Two reaction phases: 1: zero order, [Enzyme] limiting 2: first order, [S] limiting Why do we get first and zero order if S or E is limiting? • [S] changes, [E] does not change! • v = vmax * S / (s + k. S) Examples: • Most biochemical reactions • Microbial reaction in the environment when S is low (pollution, groundwater, soil, ocean) V Time Phase 2 Phase 1 V S

Kinetics Summary • At least 4 different types of reaction can occur in biological environments • Development of reaction rate can increase, decrease or stay the same. • There are clear mechanistic reasons for reaction behaviour • Significance: When knowing the reaction kinetics the behaviour biological material (e. g. food, bioreactors, body) can be predicted • 2 nd order reaction (dependence on two substrates) is similar to 1 st order and neglected here S Time 1 Exp Enz V 0 S

Decide Order or Kinetics 1. Decide which order the reaction S kinetics is: • v constant, S decrease linear Zero order • v increasing exponential • v continuously slowing (1 st, 2 nd, 3 rd order) 1 • v constant , then slowing MM kinetics Time Enz Exp V 0 Time

Summary • Microbes catalyze downhill reactions by lowering the activation energy needed. • Spontaneity can be expressed as G • Catalysis is achieved by stabilizing the transitional state of the substrate not by binding to the substrate • Zero, first, second, MM and exponential are different reaction orders occuring in microbial reactions • Reaction order is essential for process modelling.