4 Обмен энергией (1160073), страница 4
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Heterotrophic cells acquire free energy from nutrient molecules,and photosynthetic cells acquire it from absorbed solar radiation. Bothkinds of cells transform this free energy into ATP and other energyrich compounds, capable of providing energy for biological work at constant temperature.Standard Free-Energy Change Is Directly Relatedto the Equilibrium ConstantThe composition of a reacting system (a mixture of chemical reactantsand products) will tend to continue changing until equilibrium isreached. At the equilibrium concentration of reactants and products,the rates of the forward and reverse reactions are exactly equal and nofurther net change occurs in the system. The concentrations of reactants and products at equilibrium define the equilibrium constant(p.
90). In the general reaction aA + 6B ^=± cC 4- dD, where a, 6, c,and d are the number of molecules of A, B, C, and D participating, theequilibrium constant is given bywhere [A], [B], [C], and [D] are the molar concentrations of the reactioncomponents at the point of equilibrium.When a reacting system is not at equilibrium, the tendency tomove toward equilibrium represents a driving force, the magnitude ofwhich can be expressed as the free-energy change for the reaction, AG.Under standard conditions (298 K (25 °C)), when reactants and products are initially present at 1 M concentrations or, for gases, at partialpressures of 101.3 kPa (1 atm), the force driving the system towardequilibrium is defined as the standard free-energy change, AG°.
By thisdefinition, the standard state for reactions that involve hydrogen ionsis [H + ] = 1 M, or pH is 0. Most biochemical reactions occur in wellbuffered aqueous solutions near pH 7; both the pH and the concentration of water (55.5 M) are essentially constant. For convenience of calculations, biochemists therefore define a slightly different standardstate, in which the concentration of H + is 10~7 M (pH is 7) and that ofwater is 55.5 M. Physical constants based on this biochemical standardstate are written with a prime (e.g., AG°' and K'eq) to distinguish themfrom the constants used by chemists and physicists.
Under this convention, when H2O or H + are reactants or products, their concentrations are not included in equations such as Equation 13—2, but areinstead incorporated into the constants AG°' and K'eq.Just as K'eq is a physical constant characteristic for each reaction,so too is AG°' a constant. As we noted in Chapter 8 (p. 204), there is asimple relationship between K'eq and AG°':AG°' = -RT In K'eqChapter 13 Principles of BioenergeticsThe standard free-energy change of a chemical reaction is simply analternative mathematical way of expressing its equilibrium constant.Table 13-2 shows the relationship between AG°' a n d ^ q . If the equilibrium constant for a given chemical reaction is 1.0, the standard freeenergy change of that reaction is 0.0 (the natural logarithm of 1.0 iszero).
If K'eq of a reaction is greater than 1.0, its AG°' is negative. If Kfeqis less than 1.0, AG°' is positive. Because the relationship between AG°'and K'eq is exponential, relatively small changes in AG°' correspond tolarge changes in K'eq.It may be helpful to think of the standard free-energy change inanother way. AG°' is the difference between the free-energy content ofthe products and the free-energy content of the reactants under standard conditions.
When AG°' is negative, the products contain less freeenergy than the reactants. The reaction will therefore proceed spontaneously to form the products under standard conditions, because allchemical reactions tend to go in the direction that results in a decreasein the free energy of the system. A positive value of AG°' means thatthe products of the reaction contain more free energy than the reactants. The reaction will therefore tend to go in the reverse direction ifwe start with 1.0 M concentrations of all components. Table 13-3 summarizes these points.Table 13-3 Relationships among K'e<v AG°\ and the direction ofchemical reactions under standard conditionsWhen K'eq is>1.01.0AGO/ isStarting with 1 M components the reactionNegativeZeroPositiveProceeds forwardIs at equilibriumProceeds in reverseAs an example, let us make a simple calculation of the standardfree-energy change of the reaction catalyzed by the enzyme phosphoglucomutase:Glucose-1-phosphateglucose-6-phosphateChemical analysis shows that whether we start with, say, 20 mM glucose-1-phosphate (but no glucose-6-phosphate) in the presence of phosphoglucomutase, or with 20 mM glucose-6-phosphate, the final equilibrium mixture in either case will contain 1 mM glucose-1-phosphate and19 mM glucose-6-phosphate at 25 °C and pH 7.0.
(Remember that enzymes do not affect the point of equilibrium of a reaction; they merelyhasten its attainment.) From these data we can calculate the equilibrium constant:eq_ fglucose-6-phosphate][glucose-1-phosphate]19 mM= 191 mMFrom this value of K'eq we can calculate the standard free-energychange:AG0' =-RT\nK'eq= -(8.315 J/mol • KX298 K)(ln 19)= -7,296 J/mol = - 7 . 3 kJ/molBecause the standard free-energy change is negative, when the reaction starts with 1.0 M glucose-1-phosphate and 1.0 M glucoses-phosphate, the conversion of glucose-1-phosphate into glucose-6-phosphateTable 13-2 Relationship betweenthe equilibrium constants ofchemical reactions and theirstandardfree-energychangesAGO/ (kJ/mol)0.0010.010.11.010.0100.01,000.017.111.45.70.0-5.7-11.4-17.1370Part III Bioenergetics and Metabolismproceeds with a loss (release) of free energy.
For the reverse reaction(the conversion of glucose-6-phosphate to glucose-1-phosphate), AG°'has the same magnitude but the opposite sign.Table 13-4 gives the standard free-energy changes for several representative chemical reactions. Note that hydrolysis of simple esters,amides, peptides, and glycosides, as well as rearrangements and eliminations, proceed with relatively small standard free-energy changes,whereas hydrolysis of acid anhydrides occurs with relatively large decreases in standard free energy. The oxidation of organic compounds toCO2 and H2O proceeds with especially large decreases in standard freeenergy.
However, standard free-energy changes such as those in Table13-4 tell how much free energy is available from a reaction understandard conditions. To describe the energy released under the conditions that exist within cells, an expression for the actual free-energychange is essential.Table 13—4 Standard free-energy changes of some chemical reactionsat pH 7.0 and 25 °C (298 K)AGO)Reaction typeHydrolysis reactionsAcid anhydridesAcetic anhydride + H2O> 2 acetateATP + H2O> ADP + PiEstersEthyl acetate + H2O> ethanol + acetateGlucose-6-phosphate + H2O> glucose + PjAmides and peptidesGlutamine + H2O> glutamate + NH^Glycylglycine + H2O> 2 glycineGlycosidesMaltose + H2O> 2 glucoseLactose + H2O> glucose + galactoseRearrangementsGlucose-1-phosphate> glucose-6-phosphateFructose-6-phosphate> glucose-6-phosphateElimination of waterMalate> fumarate + H2OOxidations with molecular oxygenGlucose + 6O2> 6CO2 + 6H2OPalmitic acid + 23O2> 16CO2 + 16H2O(kJ/mol)(kcal/mol)*-91.1-30.5-21.8-7.3-19.6-13.8-4.7-3.3-14.2-9.2-3.4-2.2-15.5-15.9-3.7-3.8-7.3-1.7-1.74-0.403.10.75-2,840-9,770-686-2,338* Although joules and kilojoules are the standard units of energy and are used throughout thistext, biochemists sometimes express AG0' values in kilocalories per mole.
We have therefore included values in both kilojoules and kilocalories in this table and in Table 13-5. To convert kilojoules to kilocalories, divide the number of kilojoules by 4.184.The Actual Free-Energy Change Depends on theReactant and Product ConcentrationsWe must be careful to distinguish between two different quantities, thefree-energy change, AG, and the standard free-energy change, AG0'.Each chemical reaction has a characteristic standard free-energyChapter 13 Principles of Bioenergeticschange, which may be positive, negative, or zero, depending on theequilibrium constant of the reaction. The standard free-energy changetells us in which direction and how far a given reaction will go to reachequilibrium when the initial concentration of each component is 1.0 M,the pH is 7.0, and the temperature is 25 °C.
Thus AG°' is a constant: ithas a characteristic, unchanging value for a given reaction. But theactual free-energy change, AG, of a given chemical reaction is a function of the concentrations and of the temperature actually prevailingduring the reaction, which are not necessarily the standard conditionsas defined above. Moreover, the AG of any reaction proceeding spontaneously toward its equilibrium is always negative, becomes less negative as the reaction proceeds, and is zero at the point of equilibrium,indicating that no more work can be done by the reaction.AG and AGO/ for any reaction A + B ^—' C + D are related by theequationAG = AG°' + RT In -[^—1(13_3)in which the terms in red are those actually prevailing in the systemunder observation.
The concentration terms in this equation expressthe effects commonly called mass action. As an example, let us supposethat the reaction A + B ^=± C + D is taking place at the standardconditions of temperature (25 °C) and pressure (101.3 kPa) but that theconcentrations of A, B, C, and D are not equal and that none of them ispresent at the standard concentration of 1.0 M. TO determine the actualfree-energy change, AG, that will occur under these nonstandard conditions of concentration as the reaction proceeds from left to right, wesimply put in the actual concentrations of A, B, C, and D; the values ofR, T, and AG°' are the standard values.
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