Understanding the Control of Metabolism

by David Fell

Portland Press, London

1997

ISBN 1 85578 047 X

301 pp

Outlined with Review Comments

by Franklin R. Leach

for Bioch 5853

2

Preface

Fell claims not much action in current research on metabolic subjects. I disagree. Justlook at the table of contents of a recent JBC. There are many applications of molecularbiology techniques to problems that are related to metabolism. There is currently a greateremphasis on metabolism. The reason is that there are newly developed techniques thatallow examination of questions that were not possible a few years ago.

Even 20 years ago, a group of researchers became convinced that there were fundamentalflaws in the explanations of regulation and control of metabolism. “Together, these criticscreated Metabolic Control Analysis. What about the work of Michael Savageau onBiochemical Systems Analysis? Fell ignores the real beginning.

“However, their criticism and reworkings of traditional biochemical explanations are stillnot widely known and have, as yet, had little influence on the contents of the standardbiochemistry textbooks, which still cling to the rejected concepts, usually without evenmentioning the doubts and problems.” I recognized the importance of BiochemicalSystems Analysis in the 1970s and incorporated the information into my course onBiochemical Regulation. A key problem that Fell recognizes is “one factor that hasundeniably worked against the wide acceptance of Metabolic Control Analysis is that itinevitably involves more mathematical concepts and numerical computations than is usual inmetabolic biochemistry.” I started in the 1970s discussing the quantitative aspect ofmetabolic regulation using the biochemical systems approach of Savageau for mybiochemical regulation class.

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Chapter 1

Introduction: Regulation and Control

1.1 Regulation and control

Knowledge of the compounds and their interconnection does not reveal what determinesbulk flow and how balance is maintained.

Why study?1. To understand what controls metabolism under both normal and abnormal

conditions.2. To understand the action of chemical substances on metabolism.3. To help in designing of modifying agents (drugs).4. To enhance biotechnological uses of metabolism.

Regulation

Fellregulation is when a system maintains a variable constant

it is linked to homeostasis

from American Heritage Dictionary n. Abbr. reg.

1. The act of regulating or the state of being regulated.2. A principle, rule, or law designed to control or govern conduct.3. A governmental order having the force of law. Also called executive order.4. Embryology. The capacity of an embryo to continue normal development

following injury to or alteration of a structure.Noun: A code or set of codes governing action, procedure, etc. rule, dictate,

prescript.

Noun: A principle governing the affairs of man within or among political units.law, rule, institute, ordinance, canon, decree, prescription, precept, edict.

Webster Definition for "regulation"

Regulation \Reg`u*la"tion\ (-l?"sh?n), n. 1. The act of regulating, or the state of beingregulated.

The temper and regulation of our own minds. --Macaulay.

2. A rule or order prescribed for management or government; prescription; a regulatingprinciple; a governing direction; precept; law;as, the regulations of a society or a school.

Regulation sword, cap, uniform, etc. (Mil.), a sword, cap, uniform, etc., of the kind or qualityprescribed by the official regulations.

Syn: Law; rule; method; principle; order; precept. See Law.

4

Control

Felladjusting the output of a systemto start, stop, direct, or adjustmetabolic control is the power to change the state of metabolism in response to an

external signal

Noun: The act of exercising controlling power or the condition of being socontrolled. rule, command, domination, dominance, mastery, dominion, sway.

Noun: The continuous exercise of authority over a political unit. government,administration, direction, rule, governance.

Noun: The keeping of one's thoughts and emotions to oneself. reserve, restraint,self-control, self-restraint, reticence, taciturnity.

Noun: The right and power to command, decide, rule, or judge. power, authority,command, jurisdiction, domination, might, mastery, dominion, sway, prerogative.

Verb: To bring one's emotions under control. contain, collect, cool, compose.

Verb: To exercise authority or influence over. direct, rule, govern, dominate.

Verb: To keep the mechanical operation of (a device) within proper parameters.govern, regulate.

1. To exercise authoritative or dominating influence over; direct.2. To hold in restraint; check.3.a. To verify or regulate (a scientific experiment) by conducting a parallel experiment

or by comparing with another standard.b. To verify (an account, for example) by using a duplicate register for

comparison.

n.1. Authority or ability to manage or direct.2. Abbr. cont., contr. a. One that controls; a controlling agent, device, or

organization. b. Often controls. An instrument or set of instruments used to operate,regulate, or guide a machine or vehicle.

3. A restraining device, measure, or limit; a curb.4.a. A standard of comparison for checking or verifying the results of an

experiment.b. An individual or group used as a standard of comparison in a control

experiment.5. An intelligence agent who supervises or instructs another agent.6. A spirit presumed to speak or act through a medium.

Webster Definition for "control"

Control \Con*trol"\, n. [F. contr[^o]le a counter register, contr. fr. contr-r[^o]le; contre (L.contra) + r[^o]le roll, catalogue. SeeCounter and Roll, and cf. Counterroll.] 1. A duplicate book, register, or account, kept tocorrect or check another account or register; acounter register. [Obs.] --Johnson.

5

2. That which serves to check, restrain, or hinder; restraint. ``Speak without control.'' --Dryden.

3. Power or authority to check or restrain; restraining or regulating influence;superintendence; government; as, children should beunder parental control.

The House of Commons should exercise a control over all the departments of the executiveadministration. --Macaulay.

Board of control. See under Board.

Control \Con*trol"\, v. t. [imp. & p. p. Controlled; p. pr. & vb. n. Controlling.] [F.contr[^o]ler, fr. contr[^o]le.] [Formerly writtencomptrol and controul.] 1. To check by a counter register or duplicate account; to prove bycounter statements; to confute. [Obs.]

This report was controlled to be false. --Fuller.

2. To exercise restraining or governing influence over; to check; to counteract; to restrain; toregulate; to govern; to overpower.

Give me a staff of honor for mine age, But not a scepter to control the world. --Shak.

I feel my virtue struggling in my soul: But stronger passion does its power control. --Dryden.

Syn: To restrain; rule; govern; manage; guide; regulate; hinder; direct; check; curb;counteract; subdue.

1.2 Approaches to metabolic regulation

System levelmethods of studyingmethods of identifying ‘rate-limiting’ stepsMetabolic control analysis

Flux rather than rate

The properties of a system are different from those of an isolated enzyme.Two different perspectives for studying; two groups of investigators.

ReductionistHoloistic

The two really don’t communicate.

1.2.1 Molecular or reductionist explanations

Humpty dumptyput it back together again

Break apart and simplifybut something is lost on breaking.

There are system properties.

6

To fully understand an enzyme such as glutamine synthase with 3 substrates, 3products, and 9 major effectors 415 or 109 measurements would be required (4concentrations). But the experiment needs to be replicated.

1.2.2 Qualitative systems approach

The information about the underlying molecular structure is used in general termsonly. This descriptive approach attempts to forge logical and clear simplifications.

1.2.3 Quantitative systems theory

A quantitative systems approach involves using information about the general featuresof the underlying molecular structure to build a formal (mathematical) description of thesystem properties. A metabolic system has system properties that are not revealed by astudy of the component parts. To quantitate our understanding a mathematical approachmust be used.

1.3 An overview of mechanisms of regulation and control

There is a wide range of time scales involved in the regulation of a metabolic system -subseconds to days.

(1) Long time scalesHours to days

Synthesis and degradation of enzymes(2) Medium time scales

Minutes to a few secondsPhosphorylation/dephosphorylation

(3) Short time scalesSeconds or less

Binding of compounds

1.4 Basic theory of metabolism

1.4.1 Metabolic steady state

Given the regulation that occurs within an organism there is usually very littlevariation in the amounts of metabolites. There is a dynamic equilibrium –– material andenergy are imported, used, and then eliminated.

An exact steady state is a mathematical abstraction. The environment is neverconstant. So what results is a quasi steady state.

1.4.2 Thermodynamics of metabolic pathways

Thermodynamics is the science of energy relationships. Classical thermodynamicdeals with closed systems and we have already seen that the living system is not closed.They are in a non-equilibrium stable state.

Where there is a net flow through a metabolic pathway, there must be a negative freeenergy change at each reaction step, every one of which must therefore be displaced fromequilibrium. Whereas successive reactions in an unbranched metabolic pathway must begoing at the same rate in the steady state, there is no requirement that they all have the samefree energy change, since this has no direct link with kinetics.

The simplest way that metabolite concentrations can be kept within reasonable boundsis for reactions with large negative standard free energy changes to be far from equilibrium,and for reaction with small standard free energy changes to be near equilibrium.

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1.4.3 Principles of regulation and control

Troublesome concept –– the rate-limiting step.A requirement of successive steps along a linear metabolic pathway is that they are

operating at the same rate in the steady state, so none of them could be termed the ‘slowest’step in the normal sense of the word.

More than one enzyme can affect the rate of a pathway; although it is possible toimagine conditions where only one step affects the rate of a pathway, experimental studiesshow that this is not the usual cased.

Metabolic Control Analysis introduces coefficients that measure the potential ofenzymes to fulfill an enzyme’s response to external signals.

1.5 Summary

(1) Regulation is homeostasis, or the maintenance of constant conditions in the face ofexternal perturbations.

(2) Control is the ability to make changes as necessary.(3) Regulation and control are properties of metabolic systems of great complexity and

the unsolved challenge is to link our knowledge of molecular details to system-levelexplanations in a convincing yet feasible manner.

(4) In metabolism, different mechanisms for regulation and control exist on differenttime scales

On long time scales, amounts of enzyme are changed by enzyme synthesis anddegradation.

On medium time scales, the activities of ready-formed enzymes are altered altered bycovalent modification.

On short time scales, the activities of enzymes are altered in response to changes incompound concentration.

(5) Metabolic pathways generally tend to a steady state, a dynamic equilibrium whererates of formation of intermediates equal their rates of breakdown and the concentrationsremain constant. Ideal reactions are displaced from chemical equilibrium, but reactions withsmall standard free energy changes tend to be close to equilibrium and reactions with largestandard free energy changes tend to be far from equilibrium.

(6) Enzymes that catalyze reactions that are far from equilibrium are thought to be moreimportant in regulation and control than those whose reactions are near to equilibrium.

(7) In the past, analysis of regulation and control concentrated on identifying thesupposed rate-limiting enzymes for each pathway.

(8) Regulatory enzymes can function to regulate intermediate concentrations or to controlflux.

8

Chapter 2

Methods for studying metabolism and its regulation

2.1 Introduction

The aim of the book is to describe a new approach to the interpretation of control andregulation in metabolism. But it is at least 25 years old).

Four major issues1. choice of the experimental system2. problem of measuring metabolite concentrations3. measuring the activity of enzymes under physiological conditions4. deciding how to measure flux

2.2 Experimental systems

2.2.1 Whole multicellular organisms

A. Advantage - real systemB. Disadvantage

1. Interactions2. Permeability3. Biological variability

2.2.2 Isolated tissues or organs

A. Advantages1. Cut out other tissues2. Easier to control concentrations3. Tissue integrity retained

B. Disadvantages1. Supplying nutrients and removal of waste difficult2. Heterogeneous cells3. Permeability4. Biological variability

2.2.3 Tissue slices

A. Advantages1. Simpler2. More replicates

B. Disadvantages1. Cell damage2. Still permeability barrier

2.2.4 Isolated cells

A. Advantages1. Can supply nutrients2. Many replicates3. Fewer animals needed

B. Disadvantages1. Amount of material small

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2. Still permeability barrier

2.2.5 Permeabilized cells

A. Advantages1. Same as above + permeable

B. Disadvantages1. Dilution2. Potential damage to cells

2.2.6 Cell-free extracts

A. Advantages1. Simplicity2. Reproducibility3. No permeability problems

B. Disadvantages1. Loss of structure2. Dilution

2.2.7 Isolated organelles

A. Advantages1. Partial purification2. Like studying cells

B. Disadvantages1. Damage2. Artificial environment3. Membranes are permeability barrier

2.2.8 Isolated enzyme

Simple but structural constraints removed

2.3 Measurement of metabolites

2.3.1 Fixing

QuenchingpH changerapid freezingorganic solvent

2.3.2 Low concentrations in complex mixtures

A. EnzymaticSpectrophotometricFluorimetricLuminometric

B. ChromatographyC. ImmunoassayD. NMR

2.3.3 Compartmentation

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2.3.4 Free and bound metabolites

2.4 Measurement of enzyme activity

2.4.1 Assay conditions

2.4.2 What to measure

2.4.3 Control of other factors affecting in vivo activity

A. UnknownsB. Modification/demodificationC. Loss of structure

2.5 Measurement of metabolic fluxes

Blum’s group

2.6 Summary

(1) Methodologies exist to study metabolism in systems at all levels of organizationwhole multicellular organismsisolated tissues and organstissues slicesisolated cellspermeabilized cells cell-free systems

(2) Measurement of metabolite concentrations can be demanding because of the lowvalues and the complex mixtures that have to be analyzed. Even, then there are furtherproblems of experimental design and interpretation in order to ensure the results arerepresentative of in vivo concentrations at the site of interest. These include

the need to prevent changes in metabolite levels during preparation and analysis ofsamples

the need to relate the measured metabolites to known cellular and subcellularcompartments of known volumes

the difficulty of testing whether the metabolite exists mainly in the free state or not(3) The measurement of enzyme activities also raises difficult issues about relevance of

in vitro measurements to in vivo conditions(4) Measurement of overall metabolic fluxes is often a simple analytical problem of

measuring rates of change of input and output metabolites. Measuring internal fluxes,however, can require ingenious use of isotope tracer methodologies, using detection byradioactive, NMR or mass spectrometry.

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Chapter 3

Enzyme activity: the molecular basis for its regulation

3.1 Introduction

A description of metabolic regulation at the molecular level must include an account ofhow the rates of the enzyme-catalyzed reactions vary with the concentrations of metabolitesand effectors in the cell.

This chapter will considerA. The effects of a product on enzyme ratesB. The kinetics of enzymes with two substratesC. Binding of metabolites by enzymesD. The kinetics of enzymes whose rates are affected by metabolites

3.2 Michaelis-Menten kinetics

The Michaelis and Menten model of enzyme action was developed to describe how theinitial rate of reaction of an enzyme-catalyzed conversion of a single substrate to product(s)varied with substrate concentration.

But the majority of enzymes have more than one substrate.In a functioning system there is always a substantial concentration of product(s).

3.2.1 The measurement of Km and V

There is a discussion of these techniques.

3.2.2 Product inhibition

Most measurements of enzyme kinetics are based on initial rate measurements,where only substrate is originally present and the measurement is completed before muchproduct has accumulated. This is not the real life situation.

The enzyme is a catalyst and cannot change the equilibrium constant for theconversion of the substrate to product.

The product is probably closely enough related structurally to react with the active siteof the enzyme.

3.3 Two-substrate enzymes

Approximately 3/4 of all enzymes have two substrates, given that coenzymes such asNAD+ and ATP, count as substrate in the short term. The true substrate is MgATP forATP-requiring reactions.

These reactions involve one of the following a three-body collisiona compulsory-ordered mechanisma random-ordered mechanisma double-displacement mechanisms

The site may not be completely formed until one substrate binds – Koshland’ inducedfit model.

There is no mention of the Cleland analysis which I believe is the definitive evaluation ofthese questions.

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3.3.1 Experimental investigation

Since the way in which the velocity of a two substrate enzyme varies with onesubstrate is likely to depend on the concentration of the other, the experimental design mustinvolve simultaneous variation of the two substrates.

3.3.2 Compulsory-order mechanism

A defined order of interaction.

3.3.3 Random-order mechanism

Either substrate can bind to the enzyme.

3.3.4 Double-displacement mechanism

A clear distinguishable type of behavior.

3.4 Binding characteristics of enzyme sites

The binding of substances (ligands) by enzymes is like the other binding reactions inbiochemistry (substrate for transport, hormones to receptors, etc.) except there may be aninsuing chemical reaction involving the bound component.

3.4.1 Identical independent binding sites.

3.4.2 Non-identical independent binding sites

3.4.3 Identical interacting sites

3.5 Allosteric enzymes

Umbarger and Yates and Pardee first described.Generalizations by Monod, Changeux, and Jacob

(1) The enzymes have multiple numbers of subunits.(2) The feedback effector binds at a site distinctive from the active site.(3) Both activation and inhibition can occur.(4) Sigmoidal kinetics.

3.5.1 The concerted model

3.5.2 The sequential model

3.5.3 Specific examples

3.5.3.1 Hemoglobin

3.5.3.2 ATCase

3.5.3.3 Glyceraldehyde-3-phosphate dehydrogenase

Half of the sites reactivity

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3.6 Summary

(1) The well-known Michaelis-Menten equation is not a complete description of thebehavior of single-substrate enzymes in vivo because of product inhibition and reversibility.

(2) The majority of enzymes in metabolism have two substrates (and products) andcatalysis can involve one of three basic mechanisms:

compulsory orderrandom orderdouble displacement

(3) Generally, for two-substrate enzymes, the apparent Km for one substrate will varywith the concentration of the other, so prediction of the rate as any particular set of substrateconcentrations requires knowledge of the parameters of the appropriate rate equation.

(4) Many enzymes are composed of subunits. If the binding of a ligand, such as asubstrate, one subunit affects the affinity of another subunit for the same ligand, the bindingis said to be cooperative and to involve homotropic interaction.

(5) Allosteric enzymes are a class of multisubunit (or multimeric) enzymes that have sitesfor effectors as well as the active site. As well as homotropic interactions, heterotropicinteractions occur, whereby the effectors can cause activation or inhibition of the enzyme byaffecting the substrate binding via conformational changes.

(6) Theories for the mechanisms of allosteric enzymes, such as the concerted andsequential models, center around linkages between ligand binding and the conformationalstate of multimeric enzymes.

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Chapter 4

Traditional approaches to metabolic regulation

To understand the operation of a metabolic system one must understand both the individualparts and the system as a whole.

4.1 The teleological approach

Teleological arguments assume that the system has the properties necessary to fulfill itsfunction – the design is appropriate to the purpose.

The first committed step in a pathway has been assumed to be the regulated one, butthere are pathways where this is not the case.

4.2 Non-equilibrium enzymes

The presumed important ones.Measurements of the disequilibrium ratio can pose a number of difficulties. It depends

upon measurements of metabolite concentration – a problem. The equilibrium constantmust be known from in vitro experiments, but that is not obtained under physiologicalconditions. Equilibrium constants of biochemical reactions vary with pH, temperature, andionic conditions.

4.3 Isotopic measurement of flux

For near-equilibrium reactions the forward and reverse fluxes are larger than the pathwayflux.

For non-equilibrium reactions the forward flux is comparable to the pathway flux

4.4 Maximal enzyme activities

The maximal catalytic activities of enzymes are often much greater than the rate ofmetabolic flux.

4.5 Addition of intermediates

When added below the controlling point greater flux would result.

4.6 The cross-over theorem

A cross-over from increased substrate to decreased substrate concentration when thepathway flux had decreased indicating the site of an inhibition.

Works for simple linear pathways, but is not reliable for metabolic pathways in general.

4.7 Enzyme properties

A non-equilibrium enzyme might be considered regulatory ifkinetic studies reveal that the enzyme is inhibited or activated by pathway metabolites

other than the substrate.the enzyme is subject to reversible activity changes by modification reactions.

4.8 Metabolic mutants

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4.9 ConclusionNone of the lines of evidence described above has a single unambiguous meaning. In

the search for regulatory enzymes and ‘rate limiting steps’, it was usual to seekcorroboration from several different approaches. Unfortunately, that did not always lead toa single uncontested answer, and there were many cases where different laboratory groupsfound incompatible theories about the regulation of a particular pathway.

4.10 Summary

(1) For most of the second half of the 20th century, the main aim in the study ofmetabolic control was to find the ‘rate-limiting’ enzyme of a pathway. Candidate enzymesshould show one or more of the following characteristics.

(2) The teleological argument is that there should be a rate-limiting enzyme at the firstunique step of a pathway.

(3) The rate–limiting step should be a non-equilibrium enzyme, since otherwise it couldnot have a significant role in metabolic control. Candidates should be identifiable bycomparing the mass action ratio with the equilibrium constant. Alternatively, isotopicmeasurements of forward and reverse fluxes should distinguish between near-equilibriumand non-equilibrium enzymes.

(4) A ‘rate-limiting’ enzyme is expected to have less capacity to work faster than otherenzymes, so should show a relatively low limiting rate value in assays.

(5) The pathway flux would be expected to be higher from intermediates added after therate-limiting step.

(6) A cross-over in relative metabolite levels between two metabolic states could indicatewhere a regulatory signal had acted on a rate-limiting enzyme to change the flux.

(7) Regulatory enzymes should slow changes in activity in response to metabolites otherthan their own substrates.

(8) Alteration of the activity or regulatory properties of a rate-limiting enzyme shoulddirectly after the metabolic flux.

(9) The results of such investigations are not always consistent. Conflicts can then arisethat cannot be readily resolved within the framework of the rate-limiting step.

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Chapter 5

Metabolic Control Analysis

5.1 The problem of traditional approaches

The assumption of only one rate limiting step.Need flux information

(1) There is one enzyme that is least able to go faster.(2) Rate constants - there is no theoretical basis for expecting that an unique rate-

limiting step inevitably exists.(3)Pathways can be affected by the activities of several of the steps/

Sensitivity analysis: This involves the assessment of how strongly a variable (such as apathway flux) responds to a change in any one of the factors that might conceivably affectit.

Biochemical Systems Theory and Metabolic Control Analysis are rather different inapproach, though they are basically compatible where they overlap. In BiochemicalSystems Theory, sensitivity analysis is just one part of a mathematical method for modelingand simulating of metabolic and physiological systems at a high level of generality.

Metabolic Control Analysis is not intended to be a complete approach to the modelingof metabolism; its principal concern is with sensitivity analyses and it maintains a closer linkto the individual underlying enzymatic reactions than does Biochemical Systems Theory.

Since this book is written by an investigator and disciple of Metabolic ControlAnalysis, it is biased toward MCA.

5.2 Flux control coefficients

Is this enzyme rate-limiting?Yes or no

How does the metabolic flux vary as the enzyme activity is changed?Not at all to greatly

How much does the flux vary?quantitatively

There is continuous variation of the response of the flux to the amount of enzymebetween these extremes.

5.2.1 Definition

Flux control coefficient

Cxase

Jydh =∂Jydh

∂E xase

⋅E xase

J ydh

=∂ ln J ydh

∂ lnE xase

= fluxcontrolcoefficient

Exase = amount of enzymeδJydh = small change in the fluxJ = fluxcatalyzed by ydh

5.2.2 Interpretation

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If the value of a flux control coefficient is known, approximate predictions can bemade about how the metabolic flux will change if the amount of enzyme is changed.

Power law formJ =aE C

5.2.3 The summation theorem

Addition of the control coefficient values of all the enzyme that influence the flux is 1.This is the summation theorem. This shows that the enzymes in a pathway can sharecontrol of the flux.

This shows that the flux control coefficient of an enzyme is a system property. It isnot a property of the enzyme, but is a property of the system. The flux control coefficientvalues apply to only one metabolic state and can be redistributed depending on conditions.

CiJ

i =1

n

∑ =1

5.1 ElasticitiesThere must of course be links between the enzyme’s kinetic properties and its potential

for flux control.

X0xase → Y ydh → Z zase → X1

Add extra ydh enzyme. The increased concentration will lower YThe lower Y will:

increase the rate of xase because of reduced product inhibitiondecrease the rate of ydh because of lower substrate concentration

The increase amount of ydh also tends to raise the concentration of Z. The increased Zwill:

decrease the rate of ydh because of increased product inhibitionincrease the rate of zase because of higher substrate concentration

In conclusion:the effects of the increased amount of ydh involve the relative sizes of the

responses of the enzymes to the pathway metabolitesthe effects on the metabolites could tend to counteract the change in the amount of

enzymethe effects on the metabolites could tend to change the rates of neighboring

enzymes to match the change in ydhThe flux coefficient of an enzyme is likely to be linked to its kinetic responses to

changed metabolite concentrations, as well as its ability to influence of concentrations ofmetabolites in the pathway. This measure is provided by the elasticity coefficient.

5.3.1 Definition and examplesElasticity are properties of individual enzymes and not the system. The elasticity of

an enzyme to a metabolite is related to the slope of the curve of the enzyme’s rate plottedagainst metabolite concentration.

The elasticity coefficient for the effect of metabolite S on the velocity v of enzymexase is the fractional change in rate of the isolated enzyme for a fractional change insubstrate S, with all other effectors of the enzyme held at the values that they have in themetabolic pathway.

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εSxase =

∂vxase

∂S⋅

S

v xase

=∂ ln vxase

∂ ln S

Elasticities have positive values for metabolites that stimulate the rate of a reaction(substrates, activators) and negative values for those (products, inhibitors) that slow thereaction.

Elasticities can be determined if:a complete kinetic equation is available that incorporates all the reactants and

effectors that occur in the cell and affect the enzymethe intracellular concentrations of all these metabolites in the compartment where

the enzyme is locatedall the kinetic parameters are known under intracellular conditions

5.3.2 Use and interpretationElasticities are a quantitative replacement for the vague concepts of responsiveness of

an enzyme to a metabolite that are used in qualitative explanations of metabolite regulation.5.3.3 The connectivity theorem

We have defined how metabolites affect the activity of enzymes, we can now return tothe question of how the flux control coefficients of enzymes can be related to the kineticproperties of the enzymes. This link is provided by the connectivity theorem.

CJ

ii =1

n

∑ ε si = 0

The summation theorem and the set of connectivity theorems for all the metabolites of alinear pathway provide exactly the number of simultaneous equations needed to solve forthe flux control coefficients of all the enzymes in terms of the elasticities.

Although the flux coefficients are system properties of the pathway, they arenevertheless explicable in terms of the kinetic properties of the constituent enzymes.

Pathways that have branches or are cyclic are solvable using branch-point andsubstrate cycle theorems.

5.4 Response coefficientsThere are many control mechanisms that operate on metabolic pathways, and some

operate on the catalytically active amount of an enzyme, others do not.Enzyme synthesis, enzyme activation or inactivation (covalent modification), allosteric

modification.

The response coefficient is RP

J ydh =∂Jydh

∂P⋅

P

Jydh

=Cxase

J ydh εPxase

The response of a pathway to an effector depends on two factors:the sensitivity of the pathway to the activity of the enzyme that is the target for the

effector (given by the enzyme’s flux control coefficient)strength of the effect of P on that enzyme (given by its elasticity)

It is necessary for both components to be non-zero for P to be able to affect the pathway.

If more than one enzyme is effected by P, the total response will be the sum of theindividual responses from each enzyme affected.

RP

J = ∑ CiJε P

i

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5.5 Control analysis and traditional approachesTwo special properties

displacement from equilibriumrelative limiting rates

5.5.1 Displacement from equilibrium

C1J : C2

J:C3J: K≡1 − p1 : p1 (1− p2 ): p1 p2(1− p3): K

Relative values of the disequilibrium ratios, pi, do not themselves show the relativecontributions of the enzymes to the control of flux, but the terms in the above equation do.

If any step I is a equilibrium (pi = 1) then its flux coefficient becomes 0.It is easy to create example where the step nearest to equilibrium is not the step with

the smallest flux control coefficientIt is also possible to create examples where the step furthest from equilibrium is not

the one with the largest flux control coefficientThere is a tendency for a linear pathway that the flux control coefficients to be largest

near the beginning of the pathway.5.5.2 Maximal enzyme activities

C1

J : C2J:C3

J: K≡Km,1

V1

:Km,2

V2 Keq,1

:Km ,3

V3 Keq,1Keq,2

K

5.6 Summary(1) The qualitative categories of ‘rate-limiting’ and ‘not rate-limiting’ are replaced in

Metabolic Control Analysis by a quantitative scale for the influence of an enzyme on ametabolic flux - the flux control coefficient

(2) The flux control coefficient of any enzyme is a system property of a metabolicpathway since its value can be affect by any or all of the other enzymes.

(3) The of metabolites on enzymes are measured in terms of the elasticity coefficients.These are related to kinetic properties of the enzymes, but are defined specifically for theconditions in the metabolic pathway at steady state.

(4) The connectivity theorem shows that the flux control coefficients of the enzymes in apathway have links to the elasticities, i.e., the system control properties can be related to theindividual kinetic characteristics of the enzymes.

(5) The action of external effectors on a pathway flux can be measured as a responsecoefficient, which can be shown to be the product of the flux control coefficient of theaffected enzyme and the elasticity of that enzyme with respect to the effector.

(6) Metabolic Control Analysis shows that neither the degree of displacement of areaction from equilibrium nor the relative value of the limiting rate of an enzyme is a reliableguide to the degree of control of an enzyme can exert on a flux, even though these factorshave been used for that purpose in the past.

flux control coefficients of MCA are equivalent to sensitivities of BSA

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Chapter 6Measuring control coefficients

IntroNeed to show

That Metabolic Control Analysis is not an abstract theory but can be applied tomeasurements on metabolism

when these measurements are made, they support the claims made earlier

6.1 Manipulation of enzyme activityA control coefficient expresses the effect of a change in the amount of active enzyme on

a system property such as metabolic flux or metabolite concentration. Must change theenzyme’s activity and observe the consequences. Make a series of graded changes andextrapolate.

Alter bygenetic meansinducers or dietadd purified enzymeadd specific inhibitors

6.1.1 Altering enzyme activity by genetic means6.1.1.1 Classical genetics: gene dosage6.1.1.2 Classical genetics: allozymes and heterozygotes6.1.1.3 Molecular genetics: gene dosage6.1.1.4 Molecular genetics: modulation of gene expression6.1.1.5 Molecular genetics: antisense RNA

6.1.2 Natural alteration of expressed activity6.1.3 Titration with purified enzyme

Add external enzyme6.1.4 Titration of enzymes by specific inhibitors

6.1.4.1 Theory6.1.4.2 Experimental application to oxidative phosphorylation6.1.4.3 Other experimental applications6.1.4.4 Problems

6.2 Control coefficients from computer modelsIt is impossible to look at the enzyme kinetic equations for the set of enzymes in a

pathway and guess how the system will behave, but for the past 30 years it has beenpossible to use computers to simulate numerically what will happen.

Garfinkel introduced.build a computer model

amount of experimental data needed with the kinetic equation for each enzyme ishard to obtain

weak, unknown interactions

6.3 Control coefficients from elasticitiesThree ways

(1) The connectivity theorem links the ratio of the control coefficients of adjacentenzymes to the inverse ratio of their elasticities to their common metabolite.

(2) The response of a flux to an external metabolite is a relatively easy measurementto make; the response is equal to the product of the flux control coefficient of the enzymeaffected by the external metabolite and the elasticity of that enzyme to the externalmetabolite.

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(3) The control coefficients of a pathway are expressible in terms of elasticities andthe relative fluxes and concentrations, by using summation, connectivity and, if necessary,branch point theorems. It is in principle possible to measure the elasticities and calculate allthe control coefficients of a pathway. This is the most informative.

Assumethat all of the relevant steps in the metabolic system have been identified, and

that all the significant influences of the metabolites on each steps have been recognized.that the theorems of control analysis apply to the system

6.3.1 An experimental example6.3.2 Experimental measurement in vivo by modulation

Double modulationa pair of equations

6.3.3 Experimental measurements in vivo: the ‘top-down’ approachThe difficulty with MCA is the amount of data required to completely described a

system.Martin Brand introduced a simplification called the top-down approach. Reactions

are grouped into blocks that are treated as individual. This simplifies the amount ofexperimental data required.

6.3.3.1 Experimental example: mitochondrial oxidative phosphorylationThe distribution of the control of flux varies according to the metabolic steady

state.6.3.3.2 Experimental example: hepatocyte energy metabolism6.3.3.3 Fatty acid metabolism

6.3.4 Calculation of elasticities6.3.4.1 Theory

Conclusions(1) the values of control coefficients are not equally sensitive to the values of all

the elasticities(2) the dependence of the value of any control coefficient on the value of an

elasticity follows a hyperbolic or inverse hyperbolic response(3) this applies particularly to elasticities of near equilibrium reactions, because

the elasticities are not only large in magnitude, but appear in substrate-product pairs whosecontributions tend to cancel, leading to the tendency of small control coefficients

(4) small feedback and product inhibition elasticities will tend to be particularlyimportant, in that small changes in their values will have the largest effects on the controlcoefficients

6.3.4.2 Applications6.3.4.3 Hybrid examples

6.4 Summary(1) There is now a large and growing body of experimental measurements of flux control

coefficients in a range of different pathways and organisms. Although the experimentsrequire a good degree of accuracy in order to obtain reasonably reliable values for fluxcontrol coefficients, they are based on familiar experimental techniques from genetics,molecular biology, and biochemistry.

(2) Direct methods of measuring flux coefficients involve measuring the change in fluxwhen the amount or activity of an enzyme is manipulated by some means. Indirect methods,including the top-down approach, involve calculation of the control coefficients frommeasured elasticity values.

(3) Values of flux control coefficients vary depending on the prevailing conditions.(4) There are only a few cases where a flux control coefficient is very close to 1.0, and in

some these, in extreme rather than physiologically normal conditions. Thus the control of apathway by a single, rate-limiting enzyme has been experimentally proved not to be thenorm.

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(5) As predicted by the theory, the control of flux is distributed, with more than one stepin a pathway having some measure of control. However, most flux control coefficients arefound to be relatively small or zero.

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Chapter 7Control structures in metabolism

IntroductionMCA started from a consideration of what an enzyme might do in the controlling of the

flux. But there is further organization in metabolism. BSA started with the whole, complexsystem. In this chapter the higher system properties are considered from the MCAviewpoint.

7.1 Supply and demandThe concentration of a metabolite needs to be regulated to insure sufficient material to

meet the demand for product without excess.Flux control coefficients show how effective the supply and demand pathways can be

at controlling the flux.

Csup plyJ =

εMdemand

ε Mdemand −εM

sup ply =1

1+ Q

CdemandJ =

−εMsup ply

εMdemand −εM

sup ply=

Q

1+Q

There are many instances where there is a large change in flux without a large change inmetabolite concentrations.

Advantages to metabolic homeostasis(1) If pathway intermediates are also participates in other metabolic pathways that

are not required to change in rate at the same time as the pathways being controlled, it isevidently better to minimize disturbances in the common intermediate concentrations.

(2) Having to make large changes in intermediate levels slows down the rate atwhich a pathway can respond to a control signal with a change in flux, so faster responsescan be made if metabolite concentrations are kept as near constant as possible.

(3) Avoiding large concentration changes during large flux changes minimize thepossibility of sudden adverse changes in cellular osmotic strength.

A high flux control coefficient and a low concentration control coefficient provides thebest regulation.

7.2 Feedback inhibition7.2.1 Discovery and relationship to allosteric enzymes

Umbarger and Yates and Pardee7.2.2 Feedback inhibition and control analysis

Feedback inhibition makes the flux control coefficient of the regulated enzymesmaller.

At this point mention is finally made of the contribution of BSA to understanding.Oscillations and instability are discussed.Feedback inhibition gives

(1) Feedback inhibition is applied to the tendency of reactions at the start of apathway to have the greater control of flux. It transfers control to the reactions using thefeedback metabolite from the enzyme it inhibits, which is probably the most rate-controllingenzyme in the supply of the metabolite, though this control is of lesser significance in thefull pathway.

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(2) Feedback inhibition improves homeostasis of the concentration of the feedbackmetabolite and increases the cooperatively of the inhibition specifically enhances this effect.

(3) Feedback inhibition improves the stability of pathways in that it speeds up thereturn to a steady state after some random perturbation or the rate of reaching a new steadystate when external conditions change.

7.2.3 Patterns of feedback inhibitionBranched pathways

NestedSequential

7.2.3.1 Theory of nested and sequential feedback7.2.3.2 Sequential feedback inhibition7.2.3.3 Nested feedback inhibition

7.2.3.3.1 Enzyme multiplicity7.2.3.3.2 Concerted feedback inhibition7.2.3.3.3 Cumulative feedback inhibition7.2.3.3.4 Synergistic feedback inhibition

7.3 Substrate or ‘futile’ cycles7.3.1 Definition

A circular reaction that occurs between two usually unidirectional reaction pathwayoccurring when all enzyme are simultaneously active. This can result in the dissipation ofenergy.

Glucose and glucose 6-phosphateFatty acids and triacyglycerolsfructose 6-phosphate and fructose 1,6-biphosphatase

Various topologies are shownThe substrate cycles exist when

the flux pattern in the network cannot be fully described as the combinationof the minimum number of linear pathways needed to account for the mass flow connectingthe inputs and outputs

one of the additional fluxes needed to compete the description is a feasible,internal cyclic route

there is one step of the cycle that can be deleted in principle and still leave anetwork capable of connecting the observed input fluxes to the observed output fluxes.

7.3.2 Evidence for substrate cyclingBlum’s group at Duke

7.3.3 Suggested functions(1) heat production in brown adipose tissue(2) more sensitive regulation of the net flux through the pathway by regulation of the

enzymes carrying the cyclic flux(3) control of the direction of flow at a branch point and in bidirectional pathways(4) buffering metabolite concentrations

7.3.4 ThermogenesisBumble bee

Fly at 10° C when other bees can’t7.3.5 Sensitivity of control

Newsome and colleagues at Oxford7.3.6 Switching the direction of flux7.3.7 Buffering metabolite concentrations

7.4 Regulation by covalent modification of enzymes7.4.1 Irreversible and cyclic cascades

post-translational modificationproteolytic cleavage

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ubiquitin marking7.4.2 Types of reversible modification

phosphorylation/dephosphorylationADP-ribosylaytion/de..Nucleotidylation/de...Methylation/de..Oxidation/reduction

7.4.3 Phosphorylation7.4.3.1 Kinases and their control signals

7.4.3.1.1 cAMP7.4.3.1.2 Ca2+ and calmodulin

10-8 M7.4..3.1.3 Diacylglycerols7.4.3.1.4 AMP (not a typo)

AEC7.4.3.2 Phosphatases7.4.3.3 Phosphorylation cycles

7.4.4 NuceotidylationAdenylationUrdylation

7.4.5 Properties of cyclic modification systems7.4.5.1 Catalytic amplification7.4.5.2 Signal amplification7.4.5.3 Sensitivity

Not the sensitivity of MCAa finite interval

7.4.5.5 Biological integration7.4.5.6 Multiple cyclic cascades7.4.5.7 Ultrasensitivity

Goldberger and Koshland7.4.5.8 Control analysis

(1) Must consider covalent modifications(2) MCA not as dependent on mechanism(3) Not applied to the system yet

7.5 Summary (1) Traditional theories of metabolic control assumed there were obvious advantages of

controlling the rate of a pathway near its start. Analysis of the control of supply anddemand for a metabolite shows that better homeostasis of metabolite concentration isachieved when the greater flux control is exerted by the demand reactions.

(2) Feedback inhibition loops are common regulatory structures in metabolic pathways.Analysis of their properties suggest their primary effect is homeostasis of metaboliteconcentrations rather than flux control, as previously believed. This is because feedbackloops transfer control to the demand reactions after the metabolite exerting feedback.

(3) In branched pathways, both sequential and nested pathways of feedback patterns offeedback inhibition are found.

(4) Cyclic pathways that dissipate energy potentially exist in metabolism, andmeasurements confirm that some of these cycles are indeed active. Such substrate cyclesfulfill a number of functions - thermogenesis, switching fluxes.

(5) Covalent modification cycles are common control mechanisms.

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Chapter 8

Summary

Will be reproduced completely and attached.