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(For a substrate concentration tenfoldIower, the number of collisions drops to 50,000 per second, and so on.) A random encounter between the surface of an enzyme and the matching surface ofits substrate molecule often leads immediately to the formation of anenzyme-substrate complex that is ready to react. A reaction in which a covalentbond is broken or formed can now occur extremely rapidly. \dhen one appreciates how quickly molecules move and react, the observed rates of enzymaticcatalysisdo not seem so amazing.Once an enzyrne and substrate have collided and snuggled together properlyat the active site, they form multiple weak bonds with each other that persist untilrandom thermal motion causesthe molecules to dissociateagain. In general,thestronger the binding of the enzyme and substrate,the slower their rate of dissociation.
However, when two colliding molecules have poorly matching surfaces,they form few noncovalent bonds and their total energy is negligible comparedwith that of thermal motion. In this case the two molecules dissociate as rapidlyas they come together, preventing incorrect and unwanted associations betvveenmismatched molecules, such as between an enzyme and the wrong substrate.oo-.orstancetraveledFigure2-48 A random walk. <GGTA>Moleculesin solutionmovein a randomfashionasa resultof the continualwithbuffetingthey receivein collisionsThismovementallowsother molecules.smallmoleculesto diffuserapidlyfromone part ofthe cellto another,asdescribedin the text.TheFree-EnergyChangefor a ReactionWhetherltDeterminesCanOccurWe must now digress briefly to introduce some fundamental chemistry.
Cells arechemical systems that must obey all chemical and physical laws. Althoughenzyrnes speed up reactions, they cannot by themselves force energetically unfavorable reactions to occur. In terms of a water analogy, enzymes by themselvescannot make water run uphill. Cells, however, must do just that in order to growand divide: they must build highly ordered and energy-rich molecules from smalland simple ones.We shall see that this is done through enzl'rnes that directly couple energetically favorable reactions, which release energy and produce heat, toenergetically unfavorable reactions, which produce biological order.Before examining how such coupling is achieved, we must consider morecarefully the term "energetically favorable." According to the second law of thermodynamics, a chemical reaction can proceed spontaneously only if it results ina net increase in the disorder of the universe (seeFigure 2-38). The criterion foran increase in disorder of the universe can be expressedmost conveniently interms of a quantity called the free energy, G of a system.
The value of G is ofinterest only when a system undergoes a change,and the change in G denotedAG (delta G), is critical, Supposethat the system being considered is a collectionof molecules. As explained in Panel 2-7 (pp. I18-tt9), free energy has beendefined such that AG directly measures the amount of disorder created in theuniverse when a reaction takes place that involves these molecules. Energeticallyfauorable reactions, by definition, are those that decrease free energy; in otherwords, they have a negatiue L,Gand disorder the universe (Figure 2-50).An example of an energetically favorable reaction on a macroscopic scale isthe "reaction" by which a compressed spring relaxes to an expanded state,releasing its stored elastic energy as heat to its surroundings; an example on amicroscopic scale is salt dissolving in water.
Conversely, energetically unfauorable reactions,with a positiue AG-such as the ioining of two amino acids to1 0 0n mFigure2-49 The structure of thecytoplasm.Thedrawingis approximatelythe crowdinginto scaleand emphasizesOnlythe macromoleculesthe cytoplasm.are shown:RNAsare shown in b/ue.ribosomesin green,and proteinsin red.diffuseEnzymesand other macromoleculesin partrelativelyslowlyin the cytoplasm,becausethey interactwith many otherbysmallmolecules,macromolecules;contrast,diffusenearlyas rapidlyasthey doin water.(Adaptedfrom D.S.Goodsell,TrendsBiochem.Sci.16:203-206,1991.Withpermissionfrom Elsevier.)76Chapter2: CellChemistryand BiosynthesisThe free energy of Yform a peptide bond-by themselves create order in the universe. Therefore,these reactions can take place only if they are coupled to a second reaction witha negative AG so large that the AG of the entire process is negative (Figure 2-5L).TheConcentrationof ReactantsInfluencesthe Free-EnergyChangeand a Reaction'sDirectionAs we have just described, a reaction Y = X will go in the direction Y -+ X whenthe associatedfree-energy change, AG, is negative,just as a tensed spring left toitself will relax and lose its stored energy to its surroundings as heat.
For a chemical reaction, however, AG depends not only on the energy stored in each individual molecule, but also on the concentrations of the molecules in the reactionmixture. Remember that AG reflects the degree to which a reaction creates amore disordered-in other words, a more probable-state of the universe.Recalling our coin analogy, it is very likely that a coin will flip from a head to atail orientation if a jiggling box contains 90 heads and 10 tails, but this is a lessprobable event if the box has l0 heads and 90 tails.The same is true for a chemical reaction. For a reversible reaction Y = X, alarge excessof Y over X will tend to drive the reaction in the direction Y -+ X; thatis, there will be a tendency for there to be more molecules making the transitionY -+ X than there are molecules making the transition X -->Y. If the ratio of Y toX increases,the AG becomes more negative for the transition Y -+ X (and morepositive for the transition X -+ Y).How much of a concentration difference is needed to compensate for agiven decreasein chemical bond energy (and accompanying heat release)?Theanswer is not intuitively obvious, but it can be determined from a thermodynamic analysis that makes it possible to separatethe concentration-dependentand the concentration-independent parts of the free-energy change.The AG fora given reaction can thereby be written as the sum of two parts: the first, calledIhe standard free-energychange,AGo,depends on the intrinsic charactersof thereacting molecules; the second depends on their concentrations.
For the simplereactionY -+ X at 37'C,A G = A G + 0 . 6 1 6l n ] $ = A G + . r + 2 I o"e ElYllYlwhere AG is in kilocalories per mole, [Y] and [X] denote the concentrations of Yand X, ln is the natural logarithm, and the constant 0.616 is equal to R7: theproduct of the gas constant, R, and the absolute temperature, Z.Note that AG equals the value of AG when the molar concentrations of Yand X are equal (log I = 0).
As expected,AG becomes more negative as the ratioof X to Y decreases(the log of a number < I is negative).Inspection of the above equation reveals that the AG equals the value of AGwhen the concentrations of Y and X are equal. But as the favorable reactionY -+ Xproceeds,the concentration of the product X increasesand the concentration ofthe substrate Y decreases.This change in relative concentrations will cause ffi / [Y]to become increasingly large, making the initially favorable AG less and less negative. Eventually, when AG = 0, a chemical equilibrium will be attained; here theconcentration effect just balances the push given to the reaction by AG, and theratio of substrate to product reaches a constant value (Figure 2-52).How far will a reaction proceed before it stops at equilibrium? To addressthis question, we need to introduce the equilibrium constant, K The value of Kis different for different reactions, and it reflects the ratio ofproduct to substrateat equilibrium.
For the reactionY -+ X:IX]^=lfrThe equation that connects AG and the ratio tX / tYl allows us to connect AGdirectly to K Since AG = 0 at equilibrium, the concentrations of Y and X at thispoint are such that:tG =-r.421"cj+or,LG =-L4ZIogKthis reactioncan occurspontaneouslyENERGETICALLYUNFAVORABLEREACTIONlf the reactionX*Yo c c u r r e dA, Gw o u l dbe > 0, and theu n i v e r s ew o u l db e c o m em o r eoroereo.thisreactioncanoccuronlyifit iscoupledto a second,favorablereactionenergeticallyFigure2-50 The distinction betweenenergeticallyfavorableandenergeticallyunfavorablereactions.the energeticallyunfavorablereactionX*Y is driven by theenergeticallyfavorablereaction C*D, becausethe netfree-energychangefor thepair of coupled reactionsis lessthan zeroFigure 2-51 How reaction coupling isused to drive energetically unfavorablereactions.CLYSISANDTHEUSEOFENERGYBYCELLS77Figure2-52 Chemicalequilibrium.theWhena reactionreachesequilibrium,forwardand backwardfluxesof reactingareequaland opposite.moleculesTHEREACTIONTheformationof X isenergeticallyfavoredin thisexampleIn otherwords,theA6 of Y -+ X isnegativeandthe AGof X + Y ispositiveButbecauseof thermalbombardments,therewill alwaysbesomeX convertingto Y andviceversa.SUPPOSEWESTARTWITHAN EQUALNUMBEROFY ANDX MOLECULESthereforethe ratioof X to"moleculeswill increasey1Jh"transitionEVENTUALLYtherewill be a largeenoughexcessof X overY to justcompensatefor the slowrateof X -+ Y.EquilibriumwillthenbeattainedTable2-4 RelationshipBetweenthe StandardFreeEnergyChange,AG",and theEquilibriumConstantAT EQUILIBRIUMt h e n u m b e ro f Y m o l e c u l e sb e i n gc o n v e r t e dt o X m o l e c u l e se a c hs e c o n di s e x a c t l ye q u a lt o t h e n u m b e ro f X m o l e c u l e sb e i n gc o n v e r t e dt oY m o l e c u l e se a c hs e c o n ds.
o t h a t t h e r e i s n o n e t c h a n o ei n t h e r a t i o o f Y t o X .Using the last equation, we can see how the equilibrium ratio of X to Y(expressedas an equilibrium constant, K) depends on the intrinsic character ofthe molecules, as expressedin the value of AG (Ihble 2-4). Note that for every1.4 kcal/mole (5.9 kJ/mole) difference in free energy at 37"C, the equilibriumconstant changes by a factor of 10.\Alhen an enzyme (or any catalyst) lowers the activation energy for the reaction Y -+ X, it also lowers the activation energy for the reaction X -+ Y by exactlythe same amount (see Figure 2-44).The forward and backward reactions willtherefore be acceleratedby the same factor by an enzyme, and the equilibriumpoint for the reaction (and AG) is unchanged (Figure 2-53).ForSequentialReactions,AGoValuesAre AdditiveWe can predict quantitatively the course of most reactions.A large body of thermodlmamic data has been collected that makes it possible to calculate the standard change in free energy,AG, for most of the important metabolic reactionsof the cell.
The overall free-energy change for a metabolic pathway is then simply the sum of the free-energychangesin each of its component steps.Consider,for example, two sequential reactionsX-+Y and Y -+Zwhose AG values are +5 and -13 kcal/mole, respectively.(Recallthat a mole is 6x 1023molecules of a substance.)If these two reactions occur sequentially, theAG for the coupled reaction will be -8 kcal/mole. Thus, the unfavorable reactionX -+ Y which will not occur spontaneously, can be driven by the favorable reactionY -+ Z, provided that this second reaction follows the first.Cells can therefore cause the energetically unfavorable transition, X -+ Y tooccur if an enzyme catalyzing the X -+ Y reaction is supplemented by a secondenzyme that catalyzes the energetically fauorable reaction,Y -->Z.
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