Information

17: Inhibitor Kinetics (cont.), Sigmoidal kinetics, Enzyme Activation - Biology


Reading & Problems: LNC p. 210-213

I. Other effects on enzyme activity.

A. Temperature

increase in temperature speeds reaction, but high temperature will reduce enzyme stability. Most enzymes have a temperature optimum.

B. pH

can change state of catalytic groups or substrates accelerating or decelerating reaction. Usually a pH optimum that is characteristic of each enzyme.

C. Reversible covalent modification

phosphorylation most common. Occurs on specific Ser, Thr or Tyr residues. Can activate or inactivate depending on the particular enzyme. Addition of phosphate catalyzed by specific protein kinase (using ATP as donor), removal by specific protein phosphatase which releases free phosphate.

D. Proteolytic activation

enzyme synthesized as a pre-enzyme called "zymogen" that is cleaved by a protease to produce the active enzyme.

  1. Trypsin and chymotrypsin are produced this way and the zymogen precursors of these are called "trypsinogen" and "chymotrypsinogen".
  2. The formation of blood clots is activated by a series of proteolytic activation events that finally result in conversion of fibrinogen to fibrin and the formation of large fibrin polymers as the main components of the blood clots.


G&GIV Fig. 15.4 Every protein in the pathway, excepting the last protein, fibrinogen/fibrin, is a protease that cleaves and activates the next protein in the progressive activation pathway.

II Multi-substrate reactions - mechanism can be complex, but still amenable to kinetic analysis.

III. Solving enzyme kinetic problems - a few examples

Some take home information:

InhibitorBinds toConstant changed
CompetitiveEKm higher
NoncompetitiveES, EVmax lower
UncompetitiveESVmax lower, Km lower

If constant is Higher -> multiple by "the inhibitor factor" = 1+([I]/KI)
If constant is Lower -> divide by "the inhibitor factor" = 1+([I]/KI)

Formulas:

Contributors

  • Charles S. Gasser (Department of Molecular & Cellular Biology; UC Davis)


Interpreting enzyme and receptor kinetics: keeping it simple, but not too simple ☆

The hyperbolic parabola is commonly used to summarize kinetics for enzyme reactions and receptor binding kinetics. Depending on the experimental conditions, certain assumptions are valid but others might be violated so that the parameters used to fit this hyperbolic function, the maximum asymptote and the equilibrium constant, require different interpretations. The first topic of this review compares enzyme-induced transformations and receptor binding in terms of the appropriate assumptions. The second topic considers the complication of adding a competitive inhibitor as an enzyme substrate or a receptor ligand and the subtleties of inferring the equilibrium dissociation constant from the concentration of inhibitor (for example unlabeled drug) that leads to the midpoint, IC50, of an inhibition curve. Receptor binding may be measured directly by a concentration assay or as a pharmacodynamic response variable.


FAQs on Enzymes | Microbiology

Ans: Some enzymes require chemical groups other than their amino acid residues for activity. A cofactor may be either one or more inorganic ions like Fe 2+ , Mg 2+ , Mn 2+ , or Zn 2+ or a complex organic or metal organic molecule called a coenzyme. Some enzymes require both a coen­zyme and one or more metal ions for activity.

Q.2. What is a prosthetic group in an enzyme?

Ans: A coenzyme or metal ion which is covalently bound to an enzyme protein is called a pros­thetic group. A complete catalytically active enzyme along with its coenzyme and or metal ions is known as holoenzyme.

Q.3. What is meant by Apo enzyme or Apo protein?

Ans: The protein part in a holoenzyme is called Apo enzyme or Apo protein.

Q.4. Define specificity of enzymes.

Ans: It is the ability of an enzyme or a receptor to discriminate among competing substrates or ligands. The ligand is a small molecule which binds specifically to a larger one, e.g. a hormone is a ligand for its specific protein receptor.

Q.5. What do you mean by catalytic power of biocatalyst’s or enzymes?

Ans: The rate enhancement produced by enzymes or biocatalyst’s are often in the range of 7 to 14 orders of magnitude.

Q.6. Where does the energy come from to provide a dramatic lowering of the activation energies for specific reactions?

Ans: The specific groups of an enzyme as specific amino acid side chains, metal ions and coenzymes lower the activation energy and thereby accelerate the reaction by providing a lower energy reaction path. In the formation of each weak interaction the enzyme substrate or ES complex is accompanied by a small release of free energy which gives a degree of stability to the interaction. The energy derived from enzyme – substrate interaction is known as binding energy.

The binding energy is a major source of free energy used by enzymes to lower the activation energies of reactions. The binding energy, in this way provides specificity as well as catalysis. Also, the weak interactions are optimized in the reaction transition state. The enzyme active sites are complementary not to the substrates per se rather to transition states of the reactions they catalyze. Lock and key model (Fig.40.1) is one of the most common explanations for interaction of substrate and enzyme.

Q.7. What is an active site in an enzyme?

Ans: The region of an enzyme surface which binds the substrate molecule and catalytically trans­forms it is called active site or catalytic site. The fatty acid synthase complex is known to have 7 different active sites. The fatty acid synthase system in Escherichia coli consists of seven separate polypeptides which are tightly associated in a single, organized complex. The proteins act together to catalyze the formation of fatty acids from acetyl – CoA and malonyl – CoA.

The intermediates in this whole process remain attached covalently to one of the two thiol group of the complex. One of the point of attachment is the – SH group of a Cys residue in one of the seven proteins (P – ketoacyl – ACP synthase) while the other is – SH groups of acyl carrier protein with which the acyl intermedi­ates of fatty acid synthesis form a thioester.

Q.8. Give the requirements of active sites in enzymes.

Ans: The active site of an enzyme generally consists of a pocket on the enzyme surface lined with the amino acid side chains necessary to bind the substrate and catalyze its chemical transformation. For example in carboxypeptidase which leads to removal of carboxyl – terminal amino acid residues from its peptide substrates, comprises of a single chain of 307 amino acids. The two essential catalytic groups in the active site are furnished by Arg 145 and Glu 270 .

Q.9. How do enzymes work?

Ans: Most biological molecules are quite stable in the neutral pH, mild-temperature, aqueous environment found inside cells. The reactions required to digest food, send nerve signals or contract muscle simply do not occurs at a useful rate in absence of catalysis.

The enzyme – Catalyzed reaction occurs within the confines of a pocket on the enzyme known as active site. The molecule which is bound by the active site and is acted upon by the enzyme is known as substrate. The enzyme substrate complex is central to the action of enzymes and it is the starting point for mathematical treatments defining the kinetic behaviour of enzyme – catalyzed reactions and for theoretical descriptions of enzyme mechanisms. A simple enzymatic reaction may be given as below:

Here E, S and P represent enzyme, substrate and the product.

Q.10. When do enzymes typically exhibit maximum catalytic activity?

Ans: The enzymes typically show maximum catalytic activity at a characteristic pH known as opti­mum pH.

Fig 40.2. Optimum enzymatic activity of Lysozyme at pH 5.2

Q.11. How does uncontrolled diabetes of an individual turns fatal.

Ans: The pH of human blood plasma normally is 7.40. The pH regulating mechanisms fails when over production of metabolic acids causes’ acidosis. The pH of blood, so, may fall to 6.8 or below leading to irreparable cell damage and death. In other diseases the pH may rise to lethal levels. Therefore, biological control of pH of cells and body fluids is a matter of central impor­tance in all aspects of metabolism and cellular activities.

Q.12. Can the pH changes are used to measure acetylcholine levels?

Ans: Yes, the concentration of acetylcholine a neurotransmitter can be determined from the pH changes which accompany its hydrolysis. When incubated with a catalytic amount of the enzyme acetylcholinestrase, acetylcholine is quantitatively converted into choline and acetic acid which dissociates to yield acetate and hydrogen ion.

Ans: These are multiform of enzymes which catalyze the same reaction but differ from each other in their amino acid sequence, substrate affinity, Vmax and/or regulatory properties. These are also known as isoenzymes.

Q. 14. What is Cori cycle? Also discuss the isozymes (isoenzymes) associated with it.

Ans: The liver provides glucose to contracting skeletal muscle which derives ATP from the glyco­lytic conversion of glucose to lactate. The glucose is then synthesized from lactate by the liver. These conversions comprise the Cori cycle as shown in the figure below.

These conversions take place despite of differences in the catalytic properties of lactate dehy­drogenase enzymes in skeletal muscle and liver. The lactate dehydrogenise is a tetramer of 35 – kDa subunits. There are two types of polypeptide chains referred to as M and H which can form 5 types of tetramers, which are: M4, M3H, M2H2, M1H3 and H4.

These species of enzymes are known as isozymes or isoenzymes. The M4 isozyme possesses a much higher affinity for pyruvate than the H, isozyme. The other isozymes have intermediate affinities. The principal isozyme in skeletal muscle and liver is M4 while the major one in the heart muscle is H4. Of course, these isozymes have been studied deeply but the reasons for the existence of their multiple forms yet remains unknown.

Q. 15. Which are two hallmarks of enzyme catalyzed reactions?

Ans: These are enormous activity and discriminating specificity. Crystallographic pictures of polypep­tide chains of enzymes show that they are coiled in intricate shapes or conformations which apparently impart specificity and activity.

Q. 16. What is enzyme kinetics?

Ans: Much information may be obtained concerning the mechanism of enzyme – catalyzed reaction by kinetic studies, which means studies of reaction rates under various conditions, e.g. the reversible reaction. Where S is the substrate, P the product and E the enzyme. Under constant and suitable conditions of temperature and pH. The rate of reaction depends on the concentration of substrate [S], the concentration of product [P] and concentration of enzyme [E], The reaction velocity in the absence of enzyme is negligible. The velocity of overall reactions may be obtained by determining the changes in [S] or [P] with time.

In the study of kinetics of forward reaction alone one usually determines the velocity over a short time interval at the beginning of the reaction where P is still negligibly small. This has the additional advantage minimizing the effect of enzyme inactivation during the experiment.

Q.17. What is Michaelis – Menten equations?

Ans: A theory explaining the changes which take place in enzymatic reactions was proposed by Leonor Michaelis and Maud Menten in 1913. They postulated that substrate combined reversibly with enzyme to form an enzyme substrate complex [ES] which in turn is decomposed to yield the product and the free enzyme. The latter could then react with more substrate and the cycle is repeated.

Hence Michaelis – Menten equation can be defined as the equation that describes the hyper­bolic dependence of the initial reaction velocity, Vo, on substrate concentration, [S], limited to early times in the course of the reaction. The biochemists Michaelis and Menten concerned themselves with the steady state rate and this type of analysis is called steady state kinetics.

Q.18. Define Michaelis – Menten constant (KJ.

Ans: It is the substrate concentration at which an enzyme – catalyzed reaction proceeds at one half its maximum velocity.

Q.19. Which characteristic of the enzymes makes them to follow Michaelis – Menten kinetics? Which enzymes are exceptions to it?

Ans: All enzymes which exhibit a hyperbolic dependence of Vo on [S] are said to follow Michaelis

– Menten kinetics. The regulatory enzymes and allosteric enzymes are exception to Michaelis

– Menten kinetics in many enzyme catalyzed reactions:

Q.20. What is Michaelis-Menten Kinetics?

Ans: A kinetic pattern in which the initial rate of an enzyme catalyzed reaction exhibits a hyperbolic dependence on substrate concentration.

Q.21. What is steady – state kinetics?

Ans: The enzyme while mixed first with a large excess of substrate there is an initial period called the pre-steady state during which the concentration of enzyme substrate complex increases or gets build up. Pre-steady state is usually too short to be easily observed.

The reaction soon achieves a steady state in which the ES and the concentration of any other intermediates is almost constant for some time. The measured V0 often reflects the steady state even though VQ is limited to early times in the course of the reaction.

Q.22. Name a best kinetic parameter used in comparison of catalytic efficiency.

Ans: The factor K cat /K m

Q.23. What is the usefulness of kinetic parameters Kcat and Km.

Ans: They are generally useful for the comparison and study of different enzymes to know whether their reaction mechanisms are simple or complex. Each enzyme possesses the optimum values of Kcat and Km which reflect the cellular environment.

Q.24. How can V mak and Km be determined or estimated?

Ans: They can be measured or determined by graphical methods.

Q.25. What are the multistep reactions? Discuss.

Ans: These reactions involve more than one step and are carried by multi enzyme complexes. The intermediates are channeled between glycolytic enzymes, which are a typical example. The enzymes of glycolysis usually described as soluble components of cytosol but there is grow­ing evidence that within the cell exists the multi enzymes complexes.

There exists kinetic evidence for the channeling of 1, 3 biphosphoglycerate from glyceraldehyde – 3- phosphate dehydrogenase to phosphoglycerate kinase without entering solution is corroborated by physi­cal evidence that the said two enzymes form stable complexes which are mono-covalent com­plexes.

Other examples are pyruvate dehydrogenase complex which requires 5 coenzymes succinyl-CoA synthetase also called succinic thiokinase reaction fatty acid synthase from bacteria and plants is a complex of 7 different polypeptides construction of purine ring of insinuate (IMP) syntheses, synthesis of AMP and GMP from IMP, biosynthesis of pyrimidine nucleotides UTP (uridine – 5 – triphosphate) and CTP (cytidine – 5′ – triphosphate via orotidylate, and other biological oxidation reduction reactions.

Q.26. What do you mean by rate – limiting step?

Ans: A reaction consists of a number of steps out of which one or more steps are slowest (i.e., have lowest rate of reaction). These steps have highest activation energy. These steps are called rate limiting steps.Considering a simple case the rate limiting step is the highest energy point in the curve or diagrams that are often made for inter conversion of S and P, while S and P reaction (or S P) is catalyzed by an enzyme.

The ES and EP complexes are intermediates. These intermediates occupy valleys while reaction coordinate diagrams are drawn. In the citric acid cycle there are 3 strongly exergonic steps in the cycle which are catalyzed by enzymes citrate synthase, isocitrate dehydrogenase and a ketoglutarate dehydrogenase each of these enzymes can become a rate – limiting step under certain circumstances. The avail­ability of substrates for citrate synthase (acetyl – CoA and oxaloacetate) varies with the meta­bolic circumstances sometimes limits the rate of citrate formation.

To conclude the rate-limiting step may be:

(1) Generally the step in an enzymatic reaction with the greatest activation energy or the transition state of highest free energy.

(2)It is the Slowest step in a metabolic pathway.

Q.27. What are suicide inhibitors?

Ans: The suicide inhibitors are a special class of irreversible inhibitors which are comparatively unreactive until they bind to the active site of enzyme. A suicide inhibitor is designed to carry out few chemical steps of the normal enzyme. But it instead of forming a normal product, the inhibitor is converted to a very reactive compound which combines irreversibly with the enzyme. Therefore, these have also been referred as mechanism based in-activators since they utilize the normal enzyme reaction mechanism to inactivate the enzyme. This sort of inhibitors find application in therapeutics by finding new pharmaceutical agents, a process known as rational drug design.

Q.28. Write a short note on allosterism?

Ans: Many enzymes have sites referred to as allosteric sites, which are quite different from the substrate binding sites. The legends that bind at the allosteric site are called allosteric effec­tors or modulators. Binding of an allosteric effector causes a conformational change of the enzyme, so that the affinity for the substrate or the ligand also changes. These effectors can bind reversibly and non-covalently to all allosteric sites and they affect the rate of reaction.

Positive (+) allosteric effectors increase the enzyme affinity for the substrate or other ligand. The reverse is true for negative (-) allosteric effector. This is a type of regulation known as allosterism and the enzyme regulated this way is referred to as an allosteric enzyme. The allosteric site to which the positive effector bind is referred to as an activator site the negative effector binds at an inhibitory site.

Allosterism is an effective mechanism by which the enzymatic activities can be controlled to ensure that biological processes remain coordinated all times to meet the immediate metabolic requirement of a cell.

Q.29. What is an allosteric enzyme? Define.

Ans: It is a regulatory enzyme with catalytic activity modulated by non-covalent binding of a spe­cific metabolite at a site other than the active site. The term allosteric has been coined from Greek allows = other, and stereos = solid or shape. Therefore, allosteric enzymes are those enzymes that possess “other shapes” or conformation induced by the binding of modulators. The activity of regulatory enzymes is modulated by means of various signal molecules which are generally small metabolites or cofactors.

Q.30. How are allosteric enzymes regulated?

Allosteric enzymes are regulated by non-covalent binding of modulators. The modulator or modulators are metabolites which when bound to the allosteric site of an enzyme alter its kinetic characteristics.

Q.31. Give the principles of allosteric regulation.

Ans: Allosteric enzymes do not follow Michaelis – Menten kinetics. The allosteric enzymes do not obey Michaelis – Menten display sigmoidal plots of the reaction velocity substrate concentration [S] rather than the hyperbolic plots predicted by the Michaels equation. Here, an important similarity lies that oxygen binding curve myoglobin is whereas that of haemoglobin is sigmoidal. Thus this example is analogous to enzymes two models have been proposed regarding the allosteric interactions.

1. The concerted model for allosteric interactions.

2. Sequential model for allosteric interactions.

Q.32. Which are the two models that explain the kinetic behaviour of allosteric enzymes? Explain.

Ans: These are as follows:

1. Concerted model or symmetry model:

This model was proposed by Jacques Monod, Jeffries Wyman and Jean – Pierre Changeux in 1965. According to this model allosteric enzymes can exist in two conformations, active and inactive. All subunits are in active form or all are in interactive form.

The assumption of this model is based on the thinking that both subunits must be in the same conformational state so that symmetry of the dimer is conserved. Every substrate molecule which binds increases the probability of a transition from the inactive to the active form.

It was proposed by Koshland in 1966. There are two conformations but subunits can undergo the conformational change individually. According to this model there are more potential intermediate states in comparison to the symmetry model. However, a conformational change in one subunit makes a similar change in an adjacent subunit, enabling the binding of a second molecule more likely.


Enzyme structure and substrate binding

Amino acid-based enzymes are globular proteins that range in size from less than 100 to more than 2 000 amino acid residues. These amino acids can be arranged as one or more polypeptide chains that are folded and bent to form a specific three-dimensional structure, incorporating a small area known as the active site ( Figure 1 ), where the substrate actually binds. The active site may well involve only a small number (less than 10) of the constituent amino acids.

It is the shape and charge properties of the active site that enable it to bind to a single type of substrate molecule, so that the enzyme is able to demonstrate considerable specificity in its catalytic activity.

The hypothesis that enzyme specificity results from the complementary nature of the substrate and its active site was first proposed by the German chemist Emil Fischer in 1894, and became known as Fischer's ‘lock and key hypothesis’, whereby only a key of the correct size and shape (the substrate) fits into the keyhole (the active site) of the lock (the enzyme). It is astounding that this theory was proposed at a time when it was not even established that enzymes were proteins. As more was learned about enzyme structure through techniques such as X-ray crystallography, it became clear that enzymes are not rigid structures, but are in fact quite flexible in shape. In the light of this finding, in 1958 Daniel Koshland extended Fischer's ideas and presented the ‘induced-fit model’ of substrate and enzyme binding, in which the enzyme molecule changes its shape slightly to accommodate the binding of the substrate. The analogy that is commonly used is the ‘hand-in-glove model’, where the hand and glove are broadly complementary in shape, but the glove is moulded around the hand as it is inserted in order to provide a perfect match.

Since it is the active site alone that binds to the substrate, it is logical to ask what is the role of the rest of the protein molecule. The simple answer is that it acts to stabilize the active site and provide an appropriate environment for interaction of the site with the substrate molecule. Therefore the active site cannot be separated out from the rest of the protein without loss of catalytic activity, although laboratory-based directed (or forced) evolution studies have shown that it is sometimes possible to generate smaller enzymes that do retain activity.

It should be noted that although a large number of enzymes consist solely of protein, many also contain a non-protein component, known as a cofactor, that is necessary for the enzyme's catalytic activity. A cofactor may be another organic molecule, in which case it is called a coenzyme, or it may be an inorganic molecule, typically a metal ion such as iron, manganese, cobalt, copper or zinc. A coenzyme that binds tightly and permanently to the protein is generally referred to as the prosthetic group of the enzyme.

When an enzyme requires a cofactor for its activity, the inactive protein component is generally referred to as an apoenzyme, and the apoenzyme plus the cofactor (i.e. the active enzyme) is called a holoenzyme ( Figure 2 ).

The need for minerals and vitamins in the human diet is partly attributable to their roles within metabolism as cofactors and coenzymes.

Enzymes and reaction equilibrium

How do enzymes work? The broad answer to this question is that they do not alter the equilibrium (i.e. the thermodynamics) of a reaction. This is because enzymes do not fundamentally change the structure and energetics of the products and reagents, but rather they simply allow the reaction equilibrium to be attained more rapidly. Let us therefore begin by clarifying the concept of chemical equilibrium.

In many cases the equilibrium of a reaction is far ‘to the right’—that is, virtually all of the substrate (S) is converted into product (P). For this reason, reactions are often written as follows:

This is a simplification, as in all cases it is more correct to write this reaction as follows:

This indicates the presence of an equilibrium. To understand this concept it is perhaps most helpful to look at a reaction where the equilibrium point is quite central.

In this reaction, if we start with a solution of 1 mol l 𢄡 glucose and add the enzyme, then upon completion we will have a mixture of approximately 0.5 mol l 𢄡 glucose and 0.5 mol l 𢄡 fructose. This is the equilibrium point of this particular reaction, and although it may only take a couple of seconds to reach this end point with the enzyme present, we would in fact come to the same point if we put glucose into solution and waited many months for the reaction to occur in the absence of the enzyme. Interestingly, we could also have started this reaction with a 1 mol l 𢄡 fructose solution, and it would have proceeded in the opposite direction until the same equilibrium point had been reached.

The equilibrium point for this reaction is expressed by the equilibrium constant Keq as follows:

Thus for a reaction with central equilibrium, Keq = 1, for an equilibrium ‘to the right’ Keq is ϡ, and for an equilibrium ‘to the left’ Keq is ρ.

Therefore if a reaction has a Keq value of 10 6 , the equilibrium is very far to the right and can be simplified by denoting it as a single arrow. We may often describe this type of reaction as ‘going to completion’. Conversely, if a reaction has a Keq value of 10 𢄦 , the equilibrium is very far to the left, and for all practical purposes it would not really be considered to proceed at all.

It should be noted that although the concentration of reactants has no effect on the equilibrium point, environmental factors such as pH and temperature can and do affect the position of the equilibrium.

It should also be noted that any biochemical reaction which occurs in vivo in a living system does not occur in isolation, but as part of a metabolic pathway, which makes it more difficult to conceptualize the relationship between reactants and reactions. In vivo reactions are not allowed to proceed to their equilibrium position. If they did, the reaction would essentially stop (i.e. the forward and reverse reactions would balance each other), and there would be no net flux through the pathway. However, in many complex biochemical pathways some of the individual reaction steps are close to equilibrium, whereas others are far from equilibrium, the latter (catalysed by regulatory enzymes) having the greatest capacity to control the overall flux of materials through the pathway.

Enzymes form complexes with their substrates

We often describe an enzyme-catalysed reaction as proceeding through three stages as follows:

The ES complex represents a position where the substrate (S) is bound to the enzyme (E) such that the reaction (whatever it might be) is made more favourable. As soon as the reaction has occurred, the product molecule (P) dissociates from the enzyme, which is then free to bind to another substrate molecule. At some point during this process the substrate is converted into an intermediate form (often called the transition state) and then into the product.

The exact mechanism whereby the enzyme acts to increase the rate of the reaction differs from one system to another. However, the general principle is that by binding of the substrate to the enzyme, the reaction involving the substrate is made more favourable by lowering the activation energy of the reaction.

In terms of energetics, reactions can be either exergonic (releasing energy) or endergonic (consuming energy). However, even in an exergonic reaction a small amount of energy, termed the activation energy, is needed to give the reaction a ‘kick start.’ A good analogy is that of a match, the head of which contains a mixture of energy-rich chemicals (phosphorus sesquisulfide and potassium chlorate). When a match burns it releases substantial amounts of light and heat energy (exergonically reacting with O2 in the air). However, and perhaps fortunately, a match will not spontaneously ignite, but rather a small input of energy in the form of heat generated through friction (i.e. striking of the match) is needed to initiate the reaction. Of course once the match has been struck the amount of energy released is considerable, and greatly exceeds the small energy input during the striking process.

As shown in Figure 3 , enzymes are considered to lower the activation energy of a system by making it energetically easier for the transition state to form. In the presence of an enzyme catalyst, the formation of the transition state is energetically more favourable (i.e. it requires less energy for the ‘kick start’), thereby accelerating the rate at which the reaction will proceed, but not fundamentally changing the energy levels of either the reactant or the product.


The integration and control of metabolism

Acetyl-CoA carboxylase

This is an allosteric enzyme which catalyses the primary regulating step in the synthesis of fatty acids ( page 256 ). It can exist in monomeric and polymeric forms, the latter being more active. Citrate activates the enzyme probably by favouring the polymeric configuration. Thus, citrate serves not only to transfer acetyl groups from the mitochondria to the cytoplasm ( page 255 ) but also to activate the initial enzyme on the path of fatty acid biosynthesis which uses the acetyl groups. Acetyl-CoA carboxylase is also regulated through covalent modification ( page 344 ).


Abstract

The rate of product formation is an important measure of the speed of enzyme reactions. Classical studies of enzyme reactions have been conducted in dilute solutions and under conditions that justified the substrate abundance assumption. However, such assumption is well-known to break down in the context of cellular biochemistry. Instead, the concentration of available substrate can become rate limiting. Here we use the chemical master equation to obtain expressions for the instantaneous and time averaged rate of product formation without invoking the conventional substrate abundance assumption. The expressions are derived for a broad range of enzyme reaction mechanisms, including those that involve one or many enzyme molecules, require multiple substrates, and exhibit cooperativity and substrate inhibition. Novel results include: (i) the relationship between the average rate of product formation (calculated over the time it takes for the reaction to finish) and the substrate concentration, for a Michaelis–Menten (MM) reaction with one enzyme molecule, is approximately given by a logarithmically corrected MM form (ii) intrinsic noise decreases the sharpness of cooperative switches but enhances the filtering response of substrate inhibition (iii) the relationship between the initial average rate of product formation and the initial substrate concentration for a MM reaction with no reversible reaction and with any number of enzyme and substrate molecules is a sum of Michaelis–Menten equations.


Abstract

The rate of product formation is an important measure of the speed of enzyme reactions. Classical studies of enzyme reactions have been conducted in dilute solutions and under conditions that justified the substrate abundance assumption. However, such assumption is well-known to break down in the context of cellular biochemistry. Instead, the concentration of available substrate can become rate limiting. Here we use the chemical master equation to obtain expressions for the instantaneous and time averaged rate of product formation without invoking the conventional substrate abundance assumption. The expressions are derived for a broad range of enzyme reaction mechanisms, including those that involve one or many enzyme molecules, require multiple substrates, and exhibit cooperativity and substrate inhibition. Novel results include: (i) the relationship between the average rate of product formation (calculated over the time it takes for the reaction to finish) and the substrate concentration, for a Michaelis–Menten (MM) reaction with one enzyme molecule, is approximately given by a logarithmically corrected MM form (ii) intrinsic noise decreases the sharpness of cooperative switches but enhances the filtering response of substrate inhibition (iii) the relationship between the initial average rate of product formation and the initial substrate concentration for a MM reaction with no reversible reaction and with any number of enzyme and substrate molecules is a sum of Michaelis–Menten equations.


17: Inhibitor Kinetics (cont.), Sigmoidal kinetics, Enzyme Activation - Biology

a Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
E-mail: [email protected], [email protected]

b Laboratory of Macromolecular and Organic Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

c Schuit Institute for Catalysis, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

d Computational Biology, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Abstract

The adaptivity of biological reaction networks largely arises through non-covalent regulation of catalysts' activity. Such type of catalyst control is still nascent in synthetic chemical networks and thereby hampers their ability to display life-like behavior. Here, we report a bio-inspired system in which non-covalent interactions between two complementary phase-transfer catalysts are used to regulate reaction kinetics. While one catalyst gives bimolecular kinetics, the second displays autoinductive feedback, resulting in sigmoidal kinetics. When both catalysts are combined, the interactions between them allow rational control over the shape of the kinetic curves. Computational models are used to gain insight into the structure, interplay, and activity of each catalytic species, and the scope of the system is examined by optimizing the linearity of the kinetic curves. Combined, our findings highlight the effectiveness of regulating reaction kinetics using non-covalent catalyst interactions, but also emphasize the risk for unforeseen catalytic contributions in complex systems and the necessity to combine detailed experiments with kinetic modelling.


Abstract

The rate of product formation is an important measure of the speed of enzyme reactions. Classical studies of enzyme reactions have been conducted in dilute solutions and under conditions that justified the substrate abundance assumption. However, such assumption is well-known to break down in the context of cellular biochemistry. Instead, the concentration of available substrate can become rate limiting. Here we use the chemical master equation to obtain expressions for the instantaneous and time averaged rate of product formation without invoking the conventional substrate abundance assumption. The expressions are derived for a broad range of enzyme reaction mechanisms, including those that involve one or many enzyme molecules, require multiple substrates, and exhibit cooperativity and substrate inhibition. Novel results include: (i) the relationship between the average rate of product formation (calculated over the time it takes for the reaction to finish) and the substrate concentration, for a Michaelis–Menten (MM) reaction with one enzyme molecule, is approximately given by a logarithmically corrected MM form (ii) intrinsic noise decreases the sharpness of cooperative switches but enhances the filtering response of substrate inhibition (iii) the relationship between the initial average rate of product formation and the initial substrate concentration for a MM reaction with no reversible reaction and with any number of enzyme and substrate molecules is a sum of Michaelis–Menten equations.


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