Lecture 9

first order and second order kinetics

when [S] is low, Vo is proportional to [S] -first order when [S] is high, Vo becomes nearly constant (Vmax) and independent of [S] -zero order

Spontaneously =

without input doesn't tell you how fast it happens

how do enzymes catalyze these reactions? A catalytic cycle

* Enzymatically catalyzed reactions generally involve a series of successive transition states. Sometimes they can be trapped/observed, other times theorized Enzymes bind to a substrate, convert substrate through transition states to product, then release the product

why is this advantageous?

A: T state, takes a long time/ R state : overactive at low concentrations -when there's not a lot of substrate, we don't want the enzyme to be active, but as it increases the rate will increase (ramp up when substrate is low more quickly)

Reaction direction is determined by ΔG

All chemical reactions can proceed only if they are thermodynamically favored - that is, the free energy (G) of the products is lower than that of the reactants, so ΔG is negative. If the free energy of C + D is less than that of A + B, then the reaction spontaneously proceeds from left to right. This is true for all biochemical reactions, however complex: those that occur must be thermodynamically favored (i.e., free energy must be reduced by the reaction).

Enzymes only increase reaction rate

An enzyme cannot change the direction of the reaction, which depends solely on ΔG. If the reaction ran to equilibrium, the relative concentrations of reactants and products would be the same whether the reaction is catalyzed or not. Biochemical reactions as a rule do not run to equilibrium, because products are used as substrates in further reactions, or are excreted. In principle nothing ever reaches equilibrium, product of one rxn is the substrate of the next Enzymes work by lowering the activation energy, give substrates a transition state that is much lower

what are enzymes

As catalysts, enzymes participate in reactions without being consumed or permanently modified. Enzymes accelerate the rates of reactions that would occur more slowly in their absence (usually MUCH more slowly). Most enzymes catalyze reactions where reactants are converted to products. Other enzymes are required for moving molecules between cellular compartments (carriers) or for folding proteins (chaperones).

Why do we need isozymes? The special role of glucokinase among the hexokinases

Different isozymes can be expressed in different cell types The hexokinases phosphorylate simple sugars. There are 4 isozymes - hexokinase I, II, III, and IV Hexokinase IV usually is referred to as glucokinase. All hexokinases can phosphorylate glucose, but glucokinase has important differences from the others.

double displacement

Double Displacement reactions involve a covalent enzyme intermediate Aspartate amino transferase Enzyme is transferring amino group to OAA Aspartate is amino donor Enzyme becomes covalently modified The product becomes OAA which is released Alpha KG can bind, and glutamate product released -this reaction would not work in any other order

The key to MM is simplifying assumptions

Early in the reaction, there is little product, and there is negligible product binding back to the enzyme The enzyme reaction is at steady state The substrate is in great excess over the enzyme Enzyme present in nanomolar amounts, substrates in micromolar amounts for reaction

MM kinetics rely on steady state assumption

Early on the ES is increasing Then idea is that after early stage, all the enzyme is in equilibrium and reaches steady state look at figure

how does an enzyme reaction vary over time

Early time of enzyme is approx linear Bottom right -hyperbolic curve -goal is to come up with a model that gives you an equation fitting this data slide 27

Michaelis menten rate equation (IMPORTANT for enzyme kinetics)

Enzymatically catalyzed reactions showing the typical hyperbolic function are described by the Michaelis-Menten equation, named for the physician-scientists who developed it in 1913 (Leonor Michaelis and Maud Menten): Vo= Vmax [S]/ Km + [S] Km (the Michaelis constant) is the substrate concentration where V0 equals 50% of Vmax. slide 28

A reaction may be catalyzed by more than one enzyme

Enzymes A and B catalyze the same reaction, but with different Km's for the substrate and different Vmax's. Example: Ethanol at relatively low blood levels is metabolized to acetaldehyde by a high-affinity (low Km) enzyme, alcohol dehydrogenase. At higher concentrations, where alcohol dehydrogenase becomes saturated (zero-order kinetics), several low-affinity (high Km) enzymes significantly catalyze this reaction.

How do enzymes catalyze?

First, the enzyme binds its substrate in its active site. The active site lies in a groove or pocket of the enzyme. It typically includes residues from different segments of the polypeptide chain, and complements the substrate's shape, electrostatic properties, and hydrophilic/hydrophobic profile.

An example of induced-fit: glucose and glucokinase

Glucokinase has two domains joined by a hinge. It interconverts between open and closed conformations. -The open state predominates in the absence of glucose. -Glucose binding stabilizes the closed, active state.

The special role of glucokinase among the hexokinases

Glucokinase is expressed in liver and has a much higher Km for glucose (5 mM) than the other hexokinases (0.1 mM). Its main role in these cells is to convert excess glucose to a storage form (glycogen). Fasting blood glucose normally is 4.5 - 6 mM In contrast, when glucose is low, the high Km of glucokinase assures that available glucose will be used by the hexokinases that are expressed in other tissues (e.g., brain) to maintain necessary metabolic processes (including the synthesis of the high-energy intermediate ATP). Thus, although these enzymes all catalyze the same reaction, their different kinetic characteristics and tissue distribution are suited to their different roles at the organismal level.

Steps in peptide bond hydrolysis by chymotrypsin Note the multiple transition states figure slide 19

In active site, substrate binding -it can orient a serine (has important acid/base properties) which is former activated by aspartate -normally a peptide bond is stable to water, but if you deprotenate a water its more reactive, form intermediate

induced fit

In the induced-fit model (Daniel Koshland, 1958), the unoccupied binding site has some affinity for the substrate, but binding induces a conformational change in the enzyme that brings reactive groups close to the substrate.

lock and key

In the lock-and-key model, the binding site is optimized for the substrate. Proposed by Emil Fischer (1894) to explain the remarkable specificity of some enzymes for their substrates. However, the behavior of most enzymes is better explained by the induced-fit model.

Effects of enzyme concentration on Vmax and Km

Increasing the amount of enzyme increases the maximum reaction rate (Vmax), but not the affinity of the substrate for the enzyme (Km). Units for Vmax: how much product over time this is dependent on how much enzyme you have

lineweaver-burk transformation slide 42

Inverse of velocity as linearly proportional to substrate concentrations In practice, Lineweaver-Burk plots are not used anymore for measuring Km and Vmax. However, they are still quite useful for inhibition. -Much more accurate to do nonlinear regression/hyperbolic curve

equilibrium constant

K

MM equation limitations

MM equation was established based on Purified invertase preparations Only one substrate available (sucrose) Well-mixed solution Is the MM approximation appropriate for other enzymes? Or enzymes in an intact cell? Multiple substrates with differing kinetics (substrate competition) Enzyme activity is regulated (population of enzymes working a substrate) Intracellular crowdedness

enzyme cofactors

Many enzymes require an additional small molecule (a cofactor). The cofactor may be covalently bound to the protein part of the enzyme, in which case the protein is called the apoenzyme and the full complex is the holoenzyme. The cofactor can be a metal ion, or it can be an organic molecule (a coenzyme), most of which are vitamins or derived from vitamins. Cofactors serve as intermediates in the transfer of active groups from one substrate to another, or in reduction-oxidation reactions. Metal ions can be catalytic or structural Enzymes are dependent on the 20 proteinogenic amino acids to perform their chemistries Cofactors enable enzymes to use different organic and organic chemical groups to catalyze more reactions. Some that are tightly bound are regenerated during the catalytic cycle (Can you think of any?) ex: heme/hemoglobin Cofactors that are loosely bound are often regenerated in another reaction and can be thought of as a cosubstrate. ex: NADH

Non MM kinetics

Many important enzymes display non-MM behavior A classic example is ATCase (aspartate transcarbamoylase) Curve is sigmoidal, not hyperbolic

The rate of reaction is reduced by energy barriers

Many thermodynamically favorable reactions proceed spontaneously but slowly, due to high-energy intermediates called transition states. Enzymes increase the rate of thermodynamically favorable reactions by lowering energy barriers imposed by transition states. A higher transition state will slow the reaction These are also dependent on temperature (in the lab you can heat up a reaction to ensure they have enough energy to reach the transition state)

Some rate enhancements produced by enzymes

Most enzymes increase the reaction rate by a factor of 106 to 1014. To illustrate a 1011 fold increase in rate: A reaction that would spontaneously occur only once a year would, when catalyzed by the enzyme, occur 30,000 times per second. Such a reaction effectively depends on enzyme activity - there is essentially no spontaneous reaction.

Catalysis involving multiple substrates

Multiple substrates are bought together and properly oriented with respect to each other, and to reactive sites of the enzyme. Greatly increases the probability of interactions that would occur very rarely in solution, and coordinates the steps of the reaction.

If breaking peptide bonds is so energetically favorable, how do we assemble amino acids to make proteins?

Need to use additional energy Amino acids are charged by ATP, activates them, gives a favorable reaction The reverse reaction is not the same, ex: phosphatase is no the reverse of a kinase (doesn't generate ATP back, it hydrolyzes a phosphate (?)

Energy profile for a biochemical reaction in the absence of the enzyme that normally catalyzes it

Take Spontaneous cleavage of peptide bonds at a site normally catalyzed by the enzyme chymotrypsin. Favorable, but slow (900 years) The energy required to reach the transition state is called the activation energy, symbolized as G‡. Peptide bond is incredibly stable (but we need to break it down constantly)

Chymotrypsin uses several of these strategies

Oxyanion hole: part of enzyme can bind tetrahedral intermediate -enzymes help stabilize transition state, lower energy of highest point Can attack with water to break it off and form intermediate

Allostery/Cooperativity is common for metabolic enzymes

Sigmoidal curve is property of enzymes that act in multimeric units For complexes there are two states, (Tense state/relaxed state) Once you bind one monomer, drives protein to adopt more active R state

Effects of different substrates on Vmax and Km

The affinity of a substrate for its enzyme is inversely related to its Km. High Km means low affinity. Here, two substrates have different affinities for the binding site, but once bound each undergoes reaction at about the same rate (Vmax). Km is dependent on the substrate as well as the enzyme Chymotrypsin: protein substrates all have diff Km, will react on diff substrates with diff rates

Chymotrypsin lowers the activation energy (G‡)

The energy profile for the reaction, as catalyzed by chymotrypsin the energy barrier is lowered by the enzyme interacting with the transition state

Law of Mass Action and equilibrium

The rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants. It implies that for a reversible chemical reaction the reaction reaches an equilibrium in which the rate of product formation and reactant formation is identical. In other words, the ratio between the concentration of reactants and products is constant.

Thermodynamics vs. Kinetics

Thermodynamics tells us the relative stability of reactants vs. products, and therefore the direction of the reaction Kinetics tells us the rate at which the reaction occurs

two most important properties of enzyme function:

Vmax Km

Graphing V0 as a hyperbolic function of [S] originally limitations for visualizing enzyme kinetics

Vmax is an asymptote that is not reached at finite substrate concentrations, and one needs to know the true value of Vmax to calculate Km. It is difficult to compare the behavior of different enzymes, or the effect of inhibitors on enzyme behavior, since Km can vary over orders of magnitude.

you can plot transitions between energy states during a reaction

We don't know the free energy at each stage, this is just a visual Thermodynamics determined entirely by free energy of the substrate and the products

Chymotrypsin has pockets for stabilization and selectivity

We know what these look like (x ray crystallography) Specificity pocket in proteases-trypsin, elastase are very conserved, amino acids give it specificity pocket Elastase/trypsin hydrophobic pockets

covalent catalysis

a nucleophile (electron-rich group with a strong tendency to donate electrons to an electron-deficient nucleus) on the enzyme displaces a leaving group on the substrate the enzyme-substrate bind is then hydrolyzed to form product and free enzyme Enzyme covalently bonds the substrate -water would not hydrolyze it but you can activate a nucleophile to do it

isozymes

a real world example of Km Many biochemical reactions can be catalyzed by more than one enzyme. Enzymes that catalyze the same reaction are called isozymes. Isozymes can differ from one another in their Km or Vmax for the reaction. They can be subject to different forms of modulation. For example, one isoform might be subject to end-product inhibition, while another is not. Often, isozymes are expressed in a tissue-selective manner. The expression of distinct sets of isozymes is essential for preserving tissue-specific functions. As an example, in the next slide we consider the multiple kinases that phosphorylate D-glucose. Note that these enzymes are not protein kinases, which phosphorylate proteins.

proximity

an enzyme may bind two reactants and in doing so increase their proximity reaction rate is related to the number of collisions of correct orientation when an enzyme binds its substrates it insures that their orientation is precisely that required for reactivity Just having binding site increases the effective molarity (?) of the two molecules

mechanisms of how an enzyme can introduce alternative reaction pathways

covalent catalysis acid base catalysis proximity molecular distortion overall mechanism: stabilize the transition state

acid base catalysis

ex: lysozyme cleaves the glycosidic bond between C1 of n-acetylmuramic acid and C4 of N-acetylglucosamine of bacterial cell wall polysaccharides

Kcat

independent of the amount of enzyme present -tells you how fast a single molecule of enzyme can convert a single molecule of substrate to product

rate constant -

k

two models of enzyme substrate binding

lock and key induced fit

for the most part bimolecular reactions are...

second order reactions

Q: what are the units for rate constants?

second order- concentration/time first order-per time

Enzymes have a reaction order/kinetic mechanism enzymes with multiple substrates operate with three mechanisms:

sequential ordered sequential random ping-pong (double displacement) mechanism

How can we model enzyme reactions?

slide 26

enzyme kinetics

study of enzymatically catalyzed reactions provides a quantitative framework for analyzing enzyme behavior

Km

the concentration of substrate that enables the enzyme to run at 50% of its max rate inversely related to the enzyme's affinity for the substrate

molecular distortion

the enzyme active site undergoes a conformational change upon binding substrate distorting the substrate into a conformation resembling the transition state species Can twist the substrate: this will destabilize the substrate and lower the activation energy =If you need to break a stable bond, you can force the molecule into a conformation where it is no longer as stable

Vmax

the maximum rate (velocity) at which the enzyme can catalyze ar reaction, when given sufficient substrate to act on