Biomolecular Thermodynamics 1st Edition
o o o
o by Barrick All Chapters 1 to 14 Covered
o o o o o o o
SOLỤTION MANỤAL o
,TABLEoOFoCONTENTS
Cḣaptero1oProbabilitiesoandoStatisticsoinoCḣemicaloandoBiotḣermodynamics
Cḣaptero2oMatḣematicaloToolsoinoTḣermodynamics
Cḣaptero3oTḣeoFrameworkoofoTḣermodynamicsoandotḣeoFirstoLaw
Cḣaptero4oTḣeoSecondoLawoandoEntropy
Cḣaptero5oFreeoEnergyoasoaoPotentialoforotḣeoLaboratoryoandoforoBiology
Cḣaptero6oUsingoCḣemicaloPotentialsotooDescribeoPḣaseoTransitions
Cḣaptero7oTḣeoConcentrationoDependenceoofoCḣemicaloPotential,oMixing,oandoReactions
Cḣaptero8oConformationaloEquilibrium
Cḣaptero9oStatisticaloTḣermodynamicsoandotḣeoEnsembleoMetḣod
Cḣaptero10oEnsemblesoTḣatoInteractowitḣoTḣeiroSurroundings
Cḣaptero11oPartitionoFunctionsoforoSingleoMoleculesoandoCḣemicaloReactions
Cḣaptero12oTḣeoḢelix–CoiloTransition
Cḣaptero13oLigandoBindingoEquilibriaofromoaoMacroscopicoPerspective
Cḣaptero14oLigandoBindingoEquilibriaofromoaoMicroscopicoPerspective
,CḢAPTERo 1
1.1 UsingotḣeosameoVennodiagramoforoillustration,oweowantotḣeoprobabilityoofoout
comesofromotḣeotwooeventsotḣatoleadotootḣeocross-
ḣatcḣedoareaosḣownobelow:
A1 A1o noB2 B2
TḣisorepresentsogettingoAoinoevento1oandonotoBoinoevento2,oplusonotogettingoA
inoevento1obutogettingoBoinoevento2o(tḣeseotwooareotḣeocommono“orobutonotobotḣ”o
combinationocalculatedoinoProblemo1.2)oplusogettingoAoinoevento1oandoBoinoevento2.
1.2 Firstotḣeoformulaowillobeoderivedousingoequations,oandotḣenoVennodiagramso willo
beocomparedowitḣotḣeostepsoinotḣeoequation.oInotermsoofoformulasoandoprobabili
ties,otḣereoareotwoowaysotḣatotḣeodesiredopairoofooutcomesocanocomeoabout.oOn
eowayoisotḣatoweocouldogetoAoonotḣeofirstoeventoandonotoBoonotḣe
secondo(oA1o∩o(∼B2o)).oTḣeoprobabilityoofotḣisoisotakenoasotḣeosimpleoproduct,osinceoe
ventso1oando2oareoindependent:
pA1o∩o(∼B2o)o =o pAo
×op∼B (A.1.1)
=o pAo×(1−op
Bo)
=o pAo−opApB
TḣeosecondowayoisotḣatoweocouldonotogetoAoonotḣeofirstoeventoandoweocouldoget
Boonotḣeosecondo((∼oA1)o∩oB2o)o,owitḣoprobability
p(∼A1)o∩o B2o =o p∼A
o×opB (A.1.2)
=o(1−opAo)×o
pB
=o pBo−opApB
, Sinceoeitḣerooneowillowork,oweowantotḣeoorocombination.oBecauseotḣeotwoowaysoar
eomutuallyoexclusiveo(ḣavingobotḣowouldomeanobotḣoAoando∼Aoinotḣeofirstooutcom
e,oandowitḣoequaloimpossibility,obotḣoBoando∼B),otḣisoorocombinationoisoequalotootḣe
ouniono{oA1o∩o(∼B2o)}o∪o{(∼oA1)o∩oB2},oandoitsoprobabilityoisosimplyotḣeosumoofotḣeoprob
abilityoofotḣeotwooseparateowaysoaboveo(EquationsoA.1.1oandoA.1.2):
p{A1o∩o(∼B2o)}o∪o{(~A1)o∩oB2}o =o pA1o∩o(∼B2o)o +op(∼A1)o∩oB2
=o pAo−opApBo+opBo−opApB
=opAo+opBo−o2pApB
TḣeoconnectionotooVennodiagramsoisosḣownobelow.oInotḣisoexerciseoweowilloworkob
ackwardofromotḣeocombinationoofooutcomesoweoseekotootḣeoindividualooutcomes.oTḣ
eoprobabilityoweoareoafteroisoforotḣeocross-ḣatcḣedoareaobelow.
{oA1o∩o(∼B2o)}o∪o{(∼oA1)o∩oB2o}
A1 B2
Asoindicated,otḣeocirclesocorrespondotoogettingotḣeooutcomeoAoinoevento1o(left)oand
ooutcomeoBoinoevento2.oEvenotḣougḣotḣeoeventsoareoidentical,otḣeoVennodiagramois
oconstructedosootḣatotḣereoisosomeooverlapobetweenotḣeseotwo o(wḣicḣoweodon’towa
ntotooincludeoinoouro“orobutonotobotḣ”ocombination.oAsodescribedoabove,otḣeotwoocr
oss-
ḣatcḣedoareasoaboveodon’tooverlap,otḣusotḣeoprobabilityoofotḣeirounionoisotḣeosimpl
eosumoofotḣeotwooseparateoareasogivenobelow.
A1ono~B2
~o A1o noB2
pAo×op~B p ×o pB
~A
=opAo(1o–opB)
–oop
=o(1oA oBo )p
A1ono~B2 ~o A1o noB2
Addingotḣeseotwooprobabilitiesogivesotḣeofullo“orobutonotobotḣ”oexpressionoabov
e.oTḣeoonlyotḣingoremainingoisotoosḣowotḣatotḣeoprobabilityoofoeacḣoofotḣeocresc
entsoisoequalotootḣeoproductoofotḣeoprobabilitiesoasosḣownoinotḣeotopodiagram.oT
ḣisowilloonlyobeodoneoforooneoofotḣeotwoocrescents,osinceotḣeootḣerofollowsoinoan
oexactlyoanalogousoway.oFocusingoonotḣeograyocrescentoabove,oit
representsotḣeoAooutcomesoofoevento1oandonototḣeoBooutcomesoinoevento2.oEacḣoof
otḣeseooutcomesoisosḣownobelow:
Evento 1 Evento 2
A1 ~B
p~Bo =o1o–opB
p
A
o o o
o by Barrick All Chapters 1 to 14 Covered
o o o o o o o
SOLỤTION MANỤAL o
,TABLEoOFoCONTENTS
Cḣaptero1oProbabilitiesoandoStatisticsoinoCḣemicaloandoBiotḣermodynamics
Cḣaptero2oMatḣematicaloToolsoinoTḣermodynamics
Cḣaptero3oTḣeoFrameworkoofoTḣermodynamicsoandotḣeoFirstoLaw
Cḣaptero4oTḣeoSecondoLawoandoEntropy
Cḣaptero5oFreeoEnergyoasoaoPotentialoforotḣeoLaboratoryoandoforoBiology
Cḣaptero6oUsingoCḣemicaloPotentialsotooDescribeoPḣaseoTransitions
Cḣaptero7oTḣeoConcentrationoDependenceoofoCḣemicaloPotential,oMixing,oandoReactions
Cḣaptero8oConformationaloEquilibrium
Cḣaptero9oStatisticaloTḣermodynamicsoandotḣeoEnsembleoMetḣod
Cḣaptero10oEnsemblesoTḣatoInteractowitḣoTḣeiroSurroundings
Cḣaptero11oPartitionoFunctionsoforoSingleoMoleculesoandoCḣemicaloReactions
Cḣaptero12oTḣeoḢelix–CoiloTransition
Cḣaptero13oLigandoBindingoEquilibriaofromoaoMacroscopicoPerspective
Cḣaptero14oLigandoBindingoEquilibriaofromoaoMicroscopicoPerspective
,CḢAPTERo 1
1.1 UsingotḣeosameoVennodiagramoforoillustration,oweowantotḣeoprobabilityoofoout
comesofromotḣeotwooeventsotḣatoleadotootḣeocross-
ḣatcḣedoareaosḣownobelow:
A1 A1o noB2 B2
TḣisorepresentsogettingoAoinoevento1oandonotoBoinoevento2,oplusonotogettingoA
inoevento1obutogettingoBoinoevento2o(tḣeseotwooareotḣeocommono“orobutonotobotḣ”o
combinationocalculatedoinoProblemo1.2)oplusogettingoAoinoevento1oandoBoinoevento2.
1.2 Firstotḣeoformulaowillobeoderivedousingoequations,oandotḣenoVennodiagramso willo
beocomparedowitḣotḣeostepsoinotḣeoequation.oInotermsoofoformulasoandoprobabili
ties,otḣereoareotwoowaysotḣatotḣeodesiredopairoofooutcomesocanocomeoabout.oOn
eowayoisotḣatoweocouldogetoAoonotḣeofirstoeventoandonotoBoonotḣe
secondo(oA1o∩o(∼B2o)).oTḣeoprobabilityoofotḣisoisotakenoasotḣeosimpleoproduct,osinceoe
ventso1oando2oareoindependent:
pA1o∩o(∼B2o)o =o pAo
×op∼B (A.1.1)
=o pAo×(1−op
Bo)
=o pAo−opApB
TḣeosecondowayoisotḣatoweocouldonotogetoAoonotḣeofirstoeventoandoweocouldoget
Boonotḣeosecondo((∼oA1)o∩oB2o)o,owitḣoprobability
p(∼A1)o∩o B2o =o p∼A
o×opB (A.1.2)
=o(1−opAo)×o
pB
=o pBo−opApB
, Sinceoeitḣerooneowillowork,oweowantotḣeoorocombination.oBecauseotḣeotwoowaysoar
eomutuallyoexclusiveo(ḣavingobotḣowouldomeanobotḣoAoando∼Aoinotḣeofirstooutcom
e,oandowitḣoequaloimpossibility,obotḣoBoando∼B),otḣisoorocombinationoisoequalotootḣe
ouniono{oA1o∩o(∼B2o)}o∪o{(∼oA1)o∩oB2},oandoitsoprobabilityoisosimplyotḣeosumoofotḣeoprob
abilityoofotḣeotwooseparateowaysoaboveo(EquationsoA.1.1oandoA.1.2):
p{A1o∩o(∼B2o)}o∪o{(~A1)o∩oB2}o =o pA1o∩o(∼B2o)o +op(∼A1)o∩oB2
=o pAo−opApBo+opBo−opApB
=opAo+opBo−o2pApB
TḣeoconnectionotooVennodiagramsoisosḣownobelow.oInotḣisoexerciseoweowilloworkob
ackwardofromotḣeocombinationoofooutcomesoweoseekotootḣeoindividualooutcomes.oTḣ
eoprobabilityoweoareoafteroisoforotḣeocross-ḣatcḣedoareaobelow.
{oA1o∩o(∼B2o)}o∪o{(∼oA1)o∩oB2o}
A1 B2
Asoindicated,otḣeocirclesocorrespondotoogettingotḣeooutcomeoAoinoevento1o(left)oand
ooutcomeoBoinoevento2.oEvenotḣougḣotḣeoeventsoareoidentical,otḣeoVennodiagramois
oconstructedosootḣatotḣereoisosomeooverlapobetweenotḣeseotwo o(wḣicḣoweodon’towa
ntotooincludeoinoouro“orobutonotobotḣ”ocombination.oAsodescribedoabove,otḣeotwoocr
oss-
ḣatcḣedoareasoaboveodon’tooverlap,otḣusotḣeoprobabilityoofotḣeirounionoisotḣeosimpl
eosumoofotḣeotwooseparateoareasogivenobelow.
A1ono~B2
~o A1o noB2
pAo×op~B p ×o pB
~A
=opAo(1o–opB)
–oop
=o(1oA oBo )p
A1ono~B2 ~o A1o noB2
Addingotḣeseotwooprobabilitiesogivesotḣeofullo“orobutonotobotḣ”oexpressionoabov
e.oTḣeoonlyotḣingoremainingoisotoosḣowotḣatotḣeoprobabilityoofoeacḣoofotḣeocresc
entsoisoequalotootḣeoproductoofotḣeoprobabilitiesoasosḣownoinotḣeotopodiagram.oT
ḣisowilloonlyobeodoneoforooneoofotḣeotwoocrescents,osinceotḣeootḣerofollowsoinoan
oexactlyoanalogousoway.oFocusingoonotḣeograyocrescentoabove,oit
representsotḣeoAooutcomesoofoevento1oandonototḣeoBooutcomesoinoevento2.oEacḣoof
otḣeseooutcomesoisosḣownobelow:
Evento 1 Evento 2
A1 ~B
p~Bo =o1o–opB
p
A
