Gibbs free energy and equilibrium Gibbs free energy and equilibrium constantconstant

Gibbs Free EnergyGibbs Free Energy, , GGIs Is the thermodynamic function that is most the thermodynamic function that is most useful for biochemistryuseful for biochemistry..

G is a function of G is a function of EnthalpyEnthalpy, , HH, a measure of the energy (heat , a measure of the energy (heat

content) of the system at constant pressure, content) of the system at constant pressure, and and

Entropy, S,Entropy, S, a measure of the randomness a measure of the randomness (disorder) of the system.(disorder) of the system.

The change in Gibbs free energyThe change in Gibbs free energy)) ΔΔG) G) for a reaction quantitatively measure for a reaction quantitatively measure the energy available to do useful work. the energy available to do useful work. It is related to the change in enthalpy It is related to the change in enthalpy and the change in entropyand the change in entropy::

ΔΔ G G = = ΔΔ H H - - T T ΔΔ S S

TheThe actualactual free energy changefree energy change)) ΔΔG) G) depends on 2 parametersdepends on 2 parameters::

the standard free energy change for that the standard free energy change for that reactionreaction)) ΔΔG°) (and thus to KeqG°) (and thus to Keq, , defining defining where equilibrium for this reaction lies), andwhere equilibrium for this reaction lies), and

the actual mass action ratio, reflecting the the actual mass action ratio, reflecting the actual starting conditions, the actual actual starting conditions, the actual concentrations of reactants and productsconcentrations of reactants and products actualactual ΔΔGG = = ΔΔG° + RTlnG° + RTln {actual mass action {actual mass action ratioratio}}

A + BA + B  <=>     <=>   C + DC + D

All reactions/processes proceed in direction All reactions/processes proceed in direction required to go TOWARD EQUILIBRIUMrequired to go TOWARD EQUILIBRIUM..

For this reaction, the mass action ratio is For this reaction, the mass action ratio is given by: [C] [D]/ [A] [B]given by: [C] [D]/ [A] [B] The mass action ratio atThe mass action ratio at equilibriumequilibrium is the is the equilibrium constant for the reactionequilibrium constant for the reaction

KeqKeq =[ C] [D] / [A] [B]=[ C] [D] / [A] [B]

TheThe standard free energy changestandard free energy change for a for a reactionreaction ) )ΔΔG°) is the change in free energy G°) is the change in free energy

under STANDARD CONDITIONS.   It is under STANDARD CONDITIONS.   It is related to the equilibrium constant by the related to the equilibrium constant by the

equationequation::

ΔΔG°G°-- = = RT ln Keq RT ln Keq

Where R : is the natural gas constant equal Where R : is the natural gas constant equal 8.315 joules or 1.987 Cal 8.315 joules or 1.987 Cal

T :is the absolute temperatureT :is the absolute temperature ln : natural logarithm. ln : natural logarithm.

Keq :Keq : equilibrium constant equilibrium constant

At equilibrium At equilibrium ΔΔG = 0 G = 0

and K eq = [C] [D]/ [A] [B]and K eq = [C] [D]/ [A] [B]

hencehence

0 = 0 = ΔΔG° + RT ln KeqG° + RT ln Keq

ΔΔG °= -RT ln KeqG °= -RT ln Keq

Continuation of life requires continuous Continuation of life requires continuous chemical reactionchemical reaction

Reactions that reach equilibrium have stopped, can't get out Reactions that reach equilibrium have stopped, can't get out of that state without external changeof that state without external change..

Consumption of foodConsumption of food provides a continued supply of provides a continued supply of substrates for reactions yielding net negativesubstrates for reactions yielding net negative ΔΔG.G. Net Net negativenegative ΔΔGG ensures that reactions proceed in the required ensures that reactions proceed in the required direction for continuation of lifedirection for continuation of life

. . Energy made available fromEnergy made available from breakdownbreakdown of some of some compounds, e.g. sugars, fats, amino acids, can be used to compounds, e.g. sugars, fats, amino acids, can be used to drive the synthesis of other molecules, e.gdrive the synthesis of other molecules, e.g. . structural structural componentscomponents of cells, or compounds such as of cells, or compounds such as polysaccharides thatpolysaccharides that store energy for future needsstore energy for future needs..

Free energy change is dependent on Free energy change is dependent on concentrationconcentration

ΔΔ G Actual free energy change under specified conditions, G Actual free energy change under specified conditions, including concentration of reactants and productsincluding concentration of reactants and products ..

ΔΔ G ° Standard Free energy change, all reactants and G ° Standard Free energy change, all reactants and products in their standard states, i.e. 1 mol / L products in their standard states, i.e. 1 mol / L concentrationconcentration..Unfortunately, if Unfortunately, if HH++ concentration isconcentration is 1 mol / 1 mol / LL,, pH = 0pH = 0, , which is not consistent with biochemical which is not consistent with biochemical processesprocesses. .

Standard Free Energy change Standard Free Energy change ΔΔ G°´ for theG°´ for the biochemical biochemical standard statestandard state, , all reactants and products at 1 mol / L all reactants and products at 1 mol / L exceptexcept [H[H++] = [OH] = [OH--] = 10 ] = 10 -7-7mol / L, which allowsmol / L, which allows pH = 7pH = 7..

phosphorylation of glucose to produce phosphorylation of glucose to produce glucose-6-phosphateglucose-6-phosphate

Very important reaction in the cell.Very important reaction in the cell.

first reaction in metabolism of glucose that enters a first reaction in metabolism of glucose that enters a

cell from the bloodcell from the blood .. Reaction 1:  condensation of glucose (alcohol) Reaction 1:  condensation of glucose (alcohol)

with inorganic phosphate ion (acid) to make with inorganic phosphate ion (acid) to make glucose-6-phosphate (an ester)glucose-6-phosphate (an ester)

Glucose + PiGlucose + Pi <=> <=> glucose-6-phosphateglucose-6-phosphate ++HH22OO

ΔΔG°= + 13.8 KJ/mole. Endergonic reactionG°= + 13.8 KJ/mole. Endergonic reaction

Reaction 2:  hydrolysis of ATP, a phosphoanhydride, to Reaction 2:  hydrolysis of ATP, a phosphoanhydride, to generate ADP and inorganic phosphate.generate ADP and inorganic phosphate.

ATP +HATP +H22O O <=> <=> ADP + PiADP + Pi

ΔΔG°= - 30.5 Kj/mole. Exergonic reactionG°= - 30.5 Kj/mole. Exergonic reaction

To couple the 2 reactions (which requires some To couple the 2 reactions (which requires some chemical mechanism, of course), chemical mechanism, of course),

add reactants on left, add products on right, and addadd reactants on left, add products on right, and add ΔΔGGoo' ' values to getvalues to get ΔΔ G Goo' ' for coupled reactionfor coupled reaction::

Glucose + ATPGlucose + ATP <=> <=>   glucose-6-phosphate + ADPglucose-6-phosphate + ADP ΔΔ G Goo - = - = 16.716.7 = = kJ/molkJ/mol

TheThe coupled reaction is exergonic,coupled reaction is exergonic, it will go it will go spontaneously (forward, left to right) in the cell, butspontaneously (forward, left to right) in the cell, but will it proceed at awill it proceed at a raterate consistent with cellular consistent with cellular

needsneeds؟؟

Most biological reactions would proceed at a very Most biological reactions would proceed at a very slow rate indeed if they're not catalyzed.  The slow rate indeed if they're not catalyzed.  The biological catalyst enabling the coupled reaction biological catalyst enabling the coupled reaction above to proceed on a biological timescale is an above to proceed on a biological timescale is an enzyme, hexokinase.enzyme, hexokinase.

Free energy coupling, with enzymes as catalysts, Free energy coupling, with enzymes as catalysts, is the strategy used in metabolic pathways.is the strategy used in metabolic pathways.