Upload
lyhuong
View
265
Download
1
Embed Size (px)
Citation preview
!"#$$%&#"'#()'*+#,$,&#"'
-./012)3(#1%&$'
BIOCH 590: Biomacromolecules Spring 2010
Copyright: Jianhan Chen
Key references: 1. Chapter 2 of van Holde (2nd Ed.)
-./012)3(#1%&$'
• -./'40#(&.'25'$&%/(&/'+.#+')/$&0%4/$'+./'4/.#6%20'25'1#7/0'
#()'+0#($5201#,2($'4/+8//(')%9/0/(+'5201$'25'/(/0:3'2('+./'
1#&02$&2;%&'"/6/"<''
• !"#$$%&#"'+./012)3(#1%&$'
– =/$&0%4/'+./'$3$+/1'%('+/01$'25'4>"?';02;/0,/$'
– @'$/+'25'A#8$'25'-./012)3(#1%&$'
– @4$+0#&+B'4>+':/(/0#""3'#;;"%"/'– =2/$'(2+'1#?/'0/5/0/(&/'+2'+./'1%&02$&2;%&')/+#%"$'
• *+#,$,&#"'+./012)3(#1%&$'C$+#,$,&#"'1/&.#(%&$D'
– E1;.#$%F/'G42721H>;I'#;;02#&.'
– J026%)/'"%(?$'4/+8//('1%&02$&2;%&')/+#%"$'C+3;%&#""3'(2+'1/#$>0#4"/D'+2'
1#&02$&2;%&';02;/0,/$'C1/#$>0#4"/D'
– K(&0/#$%(:"3'%1;20+#(+B'4>+')2'(2+'0/;"#&/'&"#$$%&#"'+./012)3(#1%&$'
L'C&D'M%#(.#('!./('
N>()#1/(+#"'!2(&/;+$'
• *3$+/1'C#""'1#+/0%#"$'%(62"6/)'%('+./';02&/$$'>()/0'$+>)3D'#()'
$>002>()%(:$'C+./'0/$+'25'+./'>(%6/0$/D'
– O;/('6$'&"2$/'C+0#($5/0'25'1#7/0D'
– =%#+./01#"'6$'#)%#4#,&'C+0#($5/0'25'./#+D'
– EP;#()#4"/'20'&2($+#(+H62">1/'C+0#($5/0'25'820?D'
– K$2"#+/)'C(/%+./0'1#7/0'(20'/(/0:3'/P&.#(:/D'
• *+#+/'25'+./'$3$+/1'
– @'+./012)3(#1%&'$+#+/')/Q(#4"/'2("3'520'$3$+/1$'#+'/R>%"%40%>1'
• @'&2()%,2('%('8.%&.'/R>%"%40%>1'/P%$+$'4/+8//('+./'$3$+/1'#()'%+$'
$>002>()%(:$'8%+.'0/$;/&+'+2'2(/'20'120/'$3$+/1'6#0%#4"/$'
– *3$+/1'6#0%#4"/$S'/P+/($%6/'#()'%(+/($%6/'
• ;0/$$>0/'CJD'#()'62">1/'CTD'
• +/1;/0#+>0/'C-DS'#('#4$+0#&+'R>#(,+3B'1/#$>0/)'%()%0/&+"3'C2!B'NB'UB'VD'
– K)/#"':#$S'JT'W'('X-B'+.>$'-'W'JTY(X'C#4$2">+/'+/1;/0#+>0/D'
• &2(&/(+0#,2('C!DS'#('%(+/($%6/'6#0%#4"/'C0/"#,6/'R>#(,+3D'C&D'M%#(.#('!./(' Z'
N%0$+'A#8'25'-./012)3(#1%&$'
• !2($/06#,2('25'/(/0:3S'./#+'CRDB'820?C8DB'#()'C%(+/0(#"D'/(/0:3'CED'
• K(+/0(#"'/(/0:3'CED'– [#&02$&2;%&#""3S'2("3')/Q(#4"/'2('0/"#,6/'$&#"/'C$//'ER'#426/D'
– [%&02$&2;%&#""3S'1>",;"/'&2(+0%4>,2($'%(&">)%(:S'?%(/,&B'6%40#,2(#"B'
02+#,2(#"B'C&./1%&#"D'42()%(:B'(2(H42()/)'%(+/0#&,2(B'(>&"/%'
C+3;%&#""3'(2+'0/"/6#(+'%('&./1%$+03Y4%2&./1%$+03D'&21;2(/(+$'
– @'5>(&,2('25'$+#+/''• =/;/()$'2('+./'$+#+/'2("3B'0/:#0)"/$$'25'+./';#+.'25'#00%6#"'
– K5'2("3'J')T'820?B'
C&D'M%#(.#('!./(' \'
!
"E = q # w dE =$q -$w
!
dE ="q - PdV="q if constant V
#E = qv
E(+.#";3'
• E(+.#";3'C!"#$%&DS'#'$+#+/'5>(&,2('+.#+'&#;+>0/$'/(/0:3'&.#(:/'#+'&2($+#(+'J'
• N20'"%R>%)';.#$/';02&/$$/$'C12$+'4%2&./1%&#"';02&/$$/$DB')T'%$'
$1#""'#()'+.>$'!E']'!^'
C&D'M%#(.#('!./(' _'
!
dE ="q - PdVd(E +PV ) = dE +PdV +VdP
="q - PdV +PdV +VdP= "q+VdP
dH = "q+VdP= "q if constant P
#H = qp
• K(+/0(#"'/(/0:3'%$'0/"#+/)'+2'R6B'8.#+'#42>+'R
;`'
^/$$a$'A#8'
• E(+.#";3'%$'#'$+#+/'5>(&,2(<'-.>$B'+./'/(+.#";3'&.#(:/'25'#'0/#&,2('%$'+./'$#1/'0/:#0)"/$$'25'8.#+';#+.8#3'%$'+#?/('+2'
#&.%/6/'+./';02)>&+$B'%</<B'2("3'+./'$+#0+'#()'/()'$+#+/$'1#7/0'
+2'+./'0/#&,2(B'(2+'+./'%()%6%)>#"'$+/;$'4/+8//(<'
C&D'M%#(.#('!./(' b'
Given:
B2O3(s) + 3H2O(g) ! 3O2(g) + B2H6(g) "H = +2035 kJ H2O(l) ! H2O(g) "H = +44 kJ H2(g) + (1/2)O2(g) ! H2O(l) "H = -286 kJ 2B(s) + 3H2(g) ! B2H6(g) "H = +36 kJ
Find the "H of:
2B(s) + (3/2)O2(g) ! B2O3(s)
Answer: "H = -1273 kJ
c2"+F1#(('=%$+0%4>,2('
• @'$+#,$,&#"'6%/8'25'+./'$3$+/1'#+'12"/&>"#0'"/6/"'
– [2"/&>"/$'C25'+./'$#1/'?%()D'8%+.%('+./'$3$+/1'#0/'%()%$,(:>%$.#4"/'
– @+'#':%6/('121/(+B'/#&.'12"/&>"/'1%:.+'0/$%)/'%('2(/'25'+./';2$$%4"/'
)%$&0/+/'1%&02$&2;%&'$+#+/$'''8%+.'&200/$;2()%(:'/(/0:3'"/6/"'/%''
– N20'6/03'"#0:/'$3$+/1'C0/1/14/0'@62:#)02'd>14/0S'b<eLPfeLZD'#+'
/R>%"%40%>1B'2("3'12$+';024#4"3'$+#+/'%$'0/"/6#(+<'
• c2"+F1#((')%$+0%4>,2(S'$;/&%Q/$'+./'12$+';024#4"/'C%</<B'
/R>%"%40%>1D';024#4%"%+3'25'24$/06%(:'#'&/0+#%('/(/0:3'$+#+/'#+'
#'$;/&%Q/)'+/1;/0#+>0/''
– (cS'c2"+F1#(('&2($+#(+'CWf<Zgeb_eZ'h'feHLZ'M'UHfDi''(
cWXYd
@'
– -./'12$+'5>()#1/(+#"'0/"#,2($.%;'%('$+#,$,&#"'1/&.#(%&$'C20'
$+#,$,&#"'+./012)3(#1%&$'
C&D'M%#(.#('!./(' j'!
Pi "e#ei / kBT
=/0%6#,2($'25'c2"+F1#(('=%$+0%4>,2('CfD'
• !2($%)/0'#'+.0//H$+#+/'$3$+/1'C/fB'/
LB'/
ZD<'@+'#':%6/('-B'"/+k$'
80%+/')28('+./';024#4%"%+3'25'Q()%(:'+./'$3$+/1'%('+./$/$'
$+#+/$'#$';fB';
L'#()';
Z<'''
• *%(&/'/(/0:3'%$'#'0/"#,6/'R>#(,+3B';%Y;
l'W'5C/
%H/
lD''
• ;ZY;
L'W'5C/
ZH/
LDW'5C/
ZH/
fDY5C/
LH/
fD'
• <<<'+.%$'1/#($'+.#+'5CPm3D'W'5CPD'5C3D'
• n.#+'?%()'25'5>(&,2(#"'5201'82>")':%6/'0%$/'+2'$>&.'
;02;/0+3`'
• V'/P;2(/(,#"'5>(&,2($o'• V';
%'W'"'/P;'C'H'#'/
%D''
• V'+.%$'%$'/P#&+"3'8.#+'C(2+'.28D'c2"+F1#((')/0%6/)'f_e'3/#0$'
#:2o'K+'+>0($'2>+'+.#+'#'W'fY?c-'
C&D'M%#(.#('!./(' g'
=/0%6#,2($'25'c2"+F1#(('=%$+0%4>,2('CLD'
• !2($%)/0%(:'#('%$2"#+/)'$3$+/1'25')*8%+.'#'+2+#"'/(/0:3'0/$+0%&+/)'+2'EW+,'8./0/'/#&.';#0,&"/'1%:.+'#&&/$$'/(/0:3'
"/6/"$'#0/'-,.*8%+.*-"/.*0.*1.*V'''' '-/*$*-0*$*-1$**2*"*)*
' ',*-0*$*1,*-1*$*3,*-3*$'V'W'+/''
• c2"+F1#((';2$+>"#+/)'+.#+'%5'2(/'&#('24$/06/'$>&.'#('
#$$/14"3'26/0'#'"2(:';/0%2)'25',1/B'/#&.'1%&02$+#+/'8%""'
2&&>0'8%+.'/R>#"';024#4%"%+3'#()'+.#+'2(/'8%""'Q()'+.#+'+./'
(>14/0'25'2&&>00/(&/$'520'#(3';#0,&>"#0'$/+'25')%$+0%4>,2('%$'
;02;20,2(#"'+2'+./'(>14/0'25'&200/$;2()%(:'1%&02$+#+/$B'
8.%&.'%$':%6/('43S*
C&D'M%#(.#('!./(' p'
!
W =N!
n0!n1!n2!...
=/0%6#,2($'25'c2"+F1#(('=%$+0%4>,2('CLD'
C&D'M%#(.#('!./(' fe'
• @'&#$/'25'dWjB'EWj/B'+./'+2+#"'(>14/0'25';2$$%4"/'$+#+/$S'fjfb'
!
W1 =7!1!"6!
=5040720
= 7
!
W10 =7!
1!"1!"2!"3!=504012
= 420
=/0%6#,2($'25'c2"+F1#(('=%$+0%4>,2('CLD'
C&D'M%#(.#('!./(' ff'
• N20'6/03'"#0:/'dB'2("3'+./'12$+';024#4"/'1%&02$+#+/'1#7/0$o'
• [#P%1%F/'n'20'/R>%6#"/(+"3'"('n'8%+.'d'#()'E'0/$+0%&,2('
=/0%6#,2($'25'c2"+F1#(('=%$+0%4>,2('CLD'
C&D'M%#(.#('!./(' fL'
=2/$'%+'1#?/';.3$%&#"'$/($/ '̀
• q%6/('+./'+82'$+#+/'$3$+/1'$.28('+2'+./'0%:.+'
*-$*4*,5678,9(:;****-8*4*,56*7*,9(:;*
C&D'M%#(.#('!./(' fZ'
e
-e
!
P+ =exp -ei /kT( )
exp -e /kT( ) + exp ei /kT( )
P" =exp ei /kT( )
exp -e /kT( ) + exp ei /kT( )
• n./('+/1;/0#+>0/'%$'(/#0'F/02'C-HreDB'6$'!'eB'68'!f'
• n./('+/1;/0#+>0/'#;;02#&./$'%(Q(%+3B'p+ = p- = 0.5'
J#0,,2('N>(&,2('
• q%6/('+./'c2"+F1#((')%$+0%4>,2(B'+./';024#4%"%+3'25'24$/06%(:'
#(3'/(/0:3'$+#+/'%$':%6/('#$S'
• s'%$')/Q(/)'#$'+./'C&#(2(%&#"D';#0,,2('5>(&,2('• K5'&2($%)/0%(:')/:/(/0#&3'25'/(/0:3'$+#+/$'
• !2(+#%($'#""'%(5201#,2('#42>+'+./'$3$+/1'C:%'#()'/
%Do'@""'
&"#$$%&#"'+./012)3(#1%&$'R>#(,,/$'&#('4/')/0%6/)'5021's'
• ^28'+2'&21;>+/'s`'
– -./203'#()'$%1>"#,2('
C&D'M%#(.#('!./(' f\'
!
Pj =n j
N=exp "e j /kT( )exp -ei /kT( )
i#
=1Qexp "e j /kT( )
!
Q = gi exp -ei /kT( )i"
*+#,$,&#"'-./012)3(#1%&$'
• -./012)3(#1%&'/($/14"/$S'#'&2""/&,2('25'%)/(,&#"'>(%+$'
C%</<B'#+21$'20'12"/&>"/$D'25'#'$3$+/1'
– @'+./20/,&#"'&2(&/;+'+.#+'0/"#+/'1%&02$&2;%&';02;/0,/$'+2'
&200/$;2()%(:'+./012)3(#1%&$';02;/0,/$'
– ER>%6#"/(&/'25'/($/14"/'#6/0#:/'#()',1/'#6/0#:/'
• !#(2(%&#"'/($/14"/S'dB'T'#()'-'#0/'&2($+#(+'
• CK(+/0(#"D'/(/0:3'E'W'tErWdt/r'
C&D'M%#(.#('!./(' f_'
!
Pj =1Qexp "e j /kT( ) =
1Qexp "#e j( )
e = e jj$ Pj =
1Q
e jj$ exp "#e j( )
= "d lnQd#
= kBT2 d lnQdT
*;2(+#(/2>$'J02&/$$/$'
• X/#"H820")';02&/$$/$'.#6/'#'(#+>0#"')%0/&,2('25'&.#(:/<''– ^/#+'+0#($5/0$'5021'.%:.'-'+2'"28'-'
– CK)/#"D':#$'$;2(+#(/2>$"3'Q""$'>;'#""'+./'#&&/$$%4"/'62">1/'
• E(/0:3'#()'/(+.#";3')2'(2+';026%)/'%(5201#,2('$>&.'
)%0/&,2(#"%+3'25'&.#(:/<'
– @426/';02&/$$/$'2&&>0'(#+>0#""3'%('%$2"#+/)'$3$+/1$'8./0/'/(/0:3'
)2/$'(2+'&.#(:/'CN%0$+'A#8'25'-./012)3(#1%&$D'
• n.#+'R>#(,,/$'82>")'./";'>$'+2';0/)%&+'+./')%0/&,2('25'
&.#(:/'%('&21;"/P'$3$+/1$`''
– !"#$%#&''#&()*"#+,)(&($'$"-o'• !2(&/;+'25'/(+02;3'#()'*/&2()'A#8'25'-./012)3(#1%&$'
– O0%:%(#"'&2(&/;+'&21/$'25'$+>)%/$'25'./#+'/(:%(/'C&2(6/0$%2('4/+8//('
./#+'#()'820?D'
– *+#,$,&#"')/0%6#,2(S';026%)/$'/(+02;3'#'+#(:%4"/'1/#(%(:'
C&D'M%#(.#('!./(' fb'
E(+02;3'
• @'1/#$>0/'25'%(+/0(#"'./#+'&2(+/(+B'20B'+./'>(#6#%"#4%"%+3'25'#'
$3$+/1a$'/(/0:3'+2')2'820?'C*WR0/6Y-D<'
• c#$/)'2('+./'$#1/'"2:%&'+.#+'%$'>$/)'520')/0%6%(:'c2"+F1#(('
)%$+0%4>,2(B'/R>%"%40%>1'#8/'+2'"%/'8./0/'+./';024#4%"%+3'%$'#+'
1#P%1>1<'
C&D'M%#(.#('!./(' fj'
E(+02;3'
• *+#,$,&#"')/Q(%,2('CfDS'<*"*(=*>-*?************************************CfD'– EP+/($%6/S'*'W'*
f'm'*
L'
– @'5>(&,2('25'$+#+/'C#$'n'%$D'
• *+#,$,&#"')/Q(%,2('CLDS'''''''''''''''''''''''''''''''''''''''''''''''''''''''''CLD'
• -82')/Q(%,2($'#0/'/R>%6#"/(+''
C&D'M%#(.#('!./(' fg'
!
S = "kB pi ln pii#
!
W =N!
n0!n1!n2!...
lnW = (N lnN " N) " (ni lnni " nii# )
= N lnN " ni lnnii#
X/"#,2('25'!"#$$%&#"'#()'*+#,$,&#"'E(+02;3'
• -./'$+#,$,&#"')/Q(%,2('25'/(+02;3'+.>$';026%)/$'#'&"/#0"3')/Q(/)'1%&02$&2;%&'1/#(%(:'25'+./'&"#$$%&#"'/(+02;3<'
C&D'M%#(.#('!./(' fp'
!
dS = kBd lnW = "kBd ni lnnii#
= "kB lnnidnii# (remember dni
i# = 0)
ni = n1 exp("ei /kBT) (in reference to e1 = 0)
lnni = lnn1 "eikBT
dS = kBeikBTi
# dni =1T
eii# dni =
dqrev
T
X/"#,2('+2'J#0,,2('N>(&,2('
C&D'M%#(.#('!./(' Le'
!
S = "kB pi ln pii#
= "kBe"ei / kBT
Qln e
"ei / kBT
Qi#
= kB (lnQ+ E /kBT)
=$$T
kBT lnQ( )
= "$A$T
!
E = "d lnQd#
= kBT2 d lnQdT
!
A = "kBT lnQ
A: Helmholtz free energy
n.#+')2/$'/(+02;3'&#;+>0/ '̀
• !200/&+'%(+/0;0/+#,2($S'#$':%6/('43'+./')/Q(%,2($''– @'1/#$>0/'25'%(+/0(#"'./#+'&2(+/(+'C+./'>(#6#%"#4%"%+3'25'#'$3$+/1a$'
/(/0:3'+2')2'820?D'
– @'$+#,$,&#"'1/#$>0/'25'+./';024#4%"%+3'520'#':%6/('1#&02'$+#+/'
– @'1/#$>0/'25'>(&/0+#%(+3'C5021'%(5201#,2('+./203D'
• !2(5>$%(:Y%(&200/&+'%(+/0;0/+#,2($'– @'1/#$>0/'25'G)%$20)/0I'20'G0#()21(/$$I'
– @'1/#$>0/'25'G&21;"/P%+3I'
C&D'M%#(.#('!./(' Lf'
!
S = "kB pi ln pii#S = kB ln W
!#"&>"#,2('25'E(+02;3'
• EP#1;"/S'%$2+./01#"'/P;#($%2('25'%)/#"':#$'5021'Tf'+2'T
L'
C&D'M%#(.#('!./(' LL'
1. Classical approach
!
dE = dq " dw = 0
dq = dw = PdV = RT dVV
#S =qrevT
= R dVV
= R ln V2V1
$
% &
'
( ) V1
V2*
2. Statistical approach: V1 = n1 V0 V2 = n2 V0
!
W1 " n1N W2 " n2
N
#S = kB lnW2 $ kB lnW1
= kB ln n2N
n1N
%
& '
(
) * = R ln n2
n1
%
& '
(
) * = R ln V2
V1
%
& '
(
) *
*/&2()'A#8'25'-./012)3(#1%&$'
• K('#('%$2"#+/)'$3$+/1B'/(+02;3'0/#&./$'1#P%1>1'#+'
/R>%"%40%>1'C+./'12$+';024#4"/')%$+0%4>,2(D<'K('#(2+./0'820)B''
!*re';026%)/$'#'&0%+/0%2('520'$;2(+#(/2>$'&.#(:/'C2("3'%5'%('#('%$2"#+/)'$3$+/1B'%</<B'8%+.2>+'/(/0:3'/P&.#(:/'%('+./'5201'
25'./#+'20'820?D<'
C&D'M%#(.#('!./(' LZ'
G=/0%6#,2(IS'#+'/R>%"%40%>1B'#('%(Q(%+/$%1#"'&.#(:/'%$'
0/6/0$%4"/<'
K('#))%,2(B'520'%$2"#+/)'$3$+/1B'@#We.*@AWe<'-.>$B'
+./0/520/B'/(+02;3'%$'/%+./0'#+'1#P%1>1'20'1%(%1>1<'!
dE = dq " dw = TdS " PdV
!
dS = 0
N0//'E(/0:%/$'
• @+'&2($+#(+'J'#()'-'CdJ-DS')J'W')-'W'e'' ' 'T')J'u'*')-'W'e ' ' ' ')E'W'-')*'u'J')T'
' ' 'CT')J'u'*')-'D'm')E'u'C-')*'u'J')TD'W'e'
' ' ')E'm'T')J'm'J')T'u'C'*')-'m'-')*D'W'e'
' ' ')'C'E'm'JT'u'-*'D'W'e'
• K5'8/')/Q(/'#'(/8'R>#(,+3'q'W'E'm'JT'u'-*'W'^'u'-*B''' ' ')q'W'e'''''''520'#'0/6/0$%4"/';02&/$$'#+'dJ-'
• q'%$'0/5/00/)'+2'#$'Gq%44$'50//'/(/0:3IB'8.%&.'%$'#+'1%(%1>1'#+'
/R>%"%40%>1'>()/0'dJ-'&2()%,2('C12$+'&2112(D<'
• *%1%"#0"3B'^/"1.2"+F'50//'/(/0:3B'@'W'E'u'-*B'%$'#+'1%(%1>1'#+'
/R>%"%40%>1'>()/0'dT-'&2()%,2(<'
• -./'50//'/(/0:%/$';026%)/'+./')%0/&,2('25'$;2(+#(/2>$'&.#(:/$'>()/0'&200/$;2()%(:'&2()%,2($<'
C&D'M%#(.#('!./(' L\'
N0//'E(/0:3'#()'J024#4%"%+3'
• X/1/14/0B'5021'+./'$+#,$,&#"'1/&.#(%&#"';2%(+'25'6%/8B'
)%0/&,2('25'$;2(+#(/2>$';02&/$$/$'%$':%6/('43'+./')%0/&,2('25'
1#P%1>1';024#4%"%+3<'
– 520'%$2"#+/)'$3$+/1$B'+./';024#4%"%+3'25'#'1#&02H$+#+/'%$':%6/('43'
/(+02;3<'%</<B'n'W'/P;'C'*Y?cD''
C&D'M%#(.#('!./(' L_'
• N20'#'$3$+/1'&2>;"/)'8%+.'dJ-'&2()%,2($B''
• N20'#'$3$+/1'&2>;"/)'8%+.'dT-'&2()%,2($B'
!
Pi "exp(#Gi /RT) = exp(#Hi /RT)exp(Si /R)
!
Pi "exp(#Ai /RT) = exp(#Ei /RT)exp(Si /R)
*+#,$,&#"'[/#(%(:'25'N0//'E(/0:%/$'
• =%0/&+"3')/Q(/)'43'+./';024#4%"%+3'25'#'1#&02H$+#+/'
• N>0+./0'0/"#+/)'+2'+./';02;/0,/$'25'1%&02$&2;%&'$+#+/$'
+.02>:.'+./';#0,,2('5>(&,2('
• N20'/P#1;"/S''
C&D'M%#(.#('!./(' Lb'
!
S =""T
kBT lnQ( ) = kB lnQ+ kBT" lnQ"T
!
E = "d lnQd#
= kBT2 d lnQdT
!
A = E "TS
= kBT2 d lnQdT
"T(kB lnQ+ kBT# lnQ#T
)
= "kBT lnQ
O+./0'-./012)3(#1%&'J02;/0,/$'
• !"#$$%&#"'+./012)3(#1%&$'0/"#,2($.%;$'&#('4/'>$/)'+2'
)/0%6/)'+./'$+#,$,&#"')/Q(%,2($'25'#""';02;/0,/$'
• N20'/P#1;"/S'
C&D'M%#(.#('!./(' Lj'
!
P = "#A#V$
% &
'
( ) N ,T
= kBT# lnQ#V
$
% &
'
( ) N ,T
H = E + PVG = A + PV
Cv =#E#T$
% &
'
( ) N ,V
Cp =#H#T$
% &
'
( ) N ,P
!
S =""T
kBT lnQ( )!
E = "d lnQd#
!
A = "kBT lnQ
E(+.#";3'#()'E(+02;3'!21;/($#,2('
• !q'W'!^'u'-!*'• !2($%)/0'#('/P#1;"/'25';02+/%('52")%(:S'
$ $ $ $ $ $ $!^5't'e'''!-
5't'e'
f< A28'+/1;/0#+>0/B'!q5'W'!^
5'u'-!*
5't'e'C52")%(:D'
C+./'5#620/)'$+#+/'%$'(2+'+./'120/'G0#()21I')/(#+>0/)'$+#+/oD''
L< @+'52")%(:'+/1;/0#+>0/'-1B'!q
5'W'e'C;
5'W';
>'W'e<_D'
Z< ^%:.'+/1;/0#+>0/B'!q5'W'!^
5'u'-!*
5'r'e'C>(52")%(:D'
C&D'M%#(.#('!./(' Lg'
Enth
alpy
native
denatured
ER>%"%40%>1'!2($+#(+'
• X/1/14/0'+.#+':%6/('#'0/#&,2(S''
' ' ' ' ' ' '@'m'c'W'!'m'='
'+./'R>#(,+3S'U'W'v!wv=wYv@wvcw'%$'#'&2($+#(+'+.#+'%$'&2112("3'0/5/00/)'+2'#$'
#('G/R>%"%40%>1'&2($+#(+I<'c>+'8.3'#'&2($+#(+`''
C&D'M%#(.#('!./(' Lp'
• .,))/S''• N%0$+B'(//)$'+2')/Q(/'#'G$+#()#0)'$+#+/”'C&2112("3'LpgUB'f#+1B'f[D<'
-./('520'#'$2">,2('8%+.'#'&2(&/(+0#,2('v@wB'
' ' ' 'q'W'qe'm'X-'"('Cv@wYv@weD'W'qe'm'X-'"('v@w'
• -./0/520/B $ $ $ $!q'W'!qe'm'X-'"('Cv!wv=wYv@wvcwD'
• @+'/R>%"%40%>1B'!q'W'e<'-.>$B'
' ' ' '!qe'm'X-'"('Cv!wv=wYv@wvcwD'W'e'
' ' ' '!qe'W'H'X-'"('U'
' ' ' 'U'W''v!wv=wYv@wvcw'W'/P;'C'H'!qeYX-D'
-./012&./1%$+03'
• EP;/0%1/(+#"')/+/01%(#,2('25'+./'+./012)3(#1%&'
;#0#1/+/0$'$>&.'#$'!qB'!^'#()'!*<''
• !q'&#('4/')%0/&+"3'&#"&>"#+/)'5021'U/R'
– Ox/(')2(/'43'Qy(:'+2'#',+0#,2('&>06/'
– X/R>%0/'&.22$%(:'#'1/#$>0#4"/'+.#+'0/$;2()$'+2'4%()%(:'20'C4%2HD
&./1%&#"'0/#&,2('
• =/+/01%(#,2('25'!^'#()'!*'– T#(a+'^29'X/"#,2($.%;'– !#"20%1/+03'
– -./203'#()'$%1>"#,2(S'(2+'0/"%#4"/'#+'R>#(,+#,6/'"/6/"'
C&D'M%#(.#('!./(' Ze'
T#(a+'^29'X/"#,2($.%;'
• -./'&"#$$%&#"'#;;02#&.B'0/R>%0/'1>",;"/'1/#$>0/1/(+$'25'U/R'
#+')%9/0/(+'+/1;/0#+>0/$'#()'&/0+#%('#$$>1;,2($'
C&D'M%#(.#('!./(' Zf'
!
lnKeq = "#G0
RT= "
#H 0
RT+#S0
R
• @$$>1%(:'+.#+'!^'#()'!*'#0/'+/1;/0#+>0/'
%()/;/()/(+'C2x/('#'
$+02(:'#$$>1;,2('%('
4%2&./1%&#"Y4%2;.3$%&#"'
;02&/$$/$'
• 'G$#5/0I'+2'&#"&>"#+/'!*WC!^H!qDYX'
!#"20%1/+03'
• G+./'R>#(,+#,6/'1/#$>0/1/(+'25'./#+I'
• =/;/()%(:'2('+./'$/+>;B'/%+./0'B6'20'B
;'
– J024/'!E'C4214D'20'!^'C&2($+#(+';0/$$>0/D'
– c%2&./1%&#"'$3$+/1$'2x/('0/R>%0/'+./'#4%"%+3'+2'
$+>)3'6/03'$1#""'62">1/$'C1%&20&#"20%1/+03D'
• @'&#"20%1/+/0'1/#$>0/$'+./'./#+'%(+2'20'2>+'25'
+./'$#1;"/'
• @')%9/0/(,#"'&#"20%1/+/0'1/#$>0/$'+./'./#+'25'
+./'$#1;"/'0/"#,6/'+2'#'0/5/0/(&/'
• @')%9/0/(,#"'$&#((%(:'&#"20%1/+/0'C=*!D')2/$'
#""'+./'#426/'#()'./#+$'+./'$#1;"/'8%+.'#'
"%(/#0'+/1;/0#+>0/'0#1;'
C&D'M%#(.#('!./(' ZL'
• @'K$2+./01#"'-%+0#,2('!#"20%1/+03'CK-!D'1/#$>0/$'+./'./#+'
#4$204/)'20'0/"/#$/)'43'#'C4%2D&./1%&#"'0/#&,2('
=%9/0/(,#"'*&#((%(:'!#"20%1/+03'C=*!D'
• -./')%9/0/(&/'%('./#+'z28'+2'+./'$#1;"/'#()'#'0/5/0/(&/'#+'+./'
$#1/'+/1;/0#+>0/B'%$'0/&20)/)'#$'#'5>(&,2('25'+/1;/0#+>0/<''
C&D'M%#(.#('!./(' ZZ'
@(#"3$%$'25'=*!'
• [2$+"3'520'12(%+20%(:'./#+'/9/&+$'#$$2&%#+/)'8%+.';.#$/'
+0#($%,2($'#()'&./1%&#"'0/#&,2($'#$'#'5>(&,2('25'
+/1;/0#+>0/'C$>&.'#$';02+/%('52")%(:D'
• c#$%&';02;/0,/$'#0/S'
C&D'M%#(.#('!./(' Z\'
!
Cp = dqp /dT = dH /dT
"H # CpdTT1
T2
$• *>4$+#(,#"'&21;"%&#,2($'
#0%$/')>0%(:'+./'+0#($%,2('
0#(:/'8./0/'#'1%P+>0/'25'
;2+/(,#""3'1#(3'C1%&02HD'
$+#+/$'1%:.+'&2(+0%4>+/'+2'
+./'24$/06/)'C;'#()'
)/&2(62">,2('4/&21/$'
.%:."3'(2(H+0%6%#"'
-82H*+#+/'@(#"3$%$'25'=*!'
C&D'M%#(.#('!./(' Z_'
Native
Denatured
Tm
!
"H 0(Tm ) # "H 0 $ (Cp %Ci)dTTi
T j
&
"S0(Tm ) = "H 0(Tm ) /Tm
• -82H$+#+/'0/6/0$%4"/'+0#($%,2('#$$>1/)'
!
"H 0(T) = "H 0(Tm ) + "CpdTTm
T
#
"S0(T) = "S0(Tm ) + "Cp /T dTTm
T
#
"Cp = Ci $C j
Note: baseline correction often needed.
X/"#,2('+2'+./'6#(a+'^29'E(+.#";3'
• Different assumptions involved in DSC analysis and van’t Hoff relationship. Nonetheless,
C&D'M%#(.#('!./(' Zb'
!
"HDSC0 (T) and "HvH
0 (T) can be related.• Assuming a reversible two-state system, the (base-line corrected)
calorimetry enthalpy change,
!
"Hi0(Tx ) = [Cp (T) #Ci(T)]dT
Ti
Tx
$ = "Ci(T)dTTi
Tx
$
% fi "H % f i "CpdTTi
T j
$
"H j0(Tx ) % # f j CpdT
Ti
T j
$
K(T) =f jf i% #
"H j0(T)
"Hi0(T)
Ti
Tj
Tx
!
"HvH0 (T) = #RT 2 d lnK(T)
dT= #RT 2 "Ci(T)
"Hi0(T)
#"C j (T)"H j
0(T)
$
% & &
'
( ) )
!
Disagreement of "HDSC0 (T) and "HvH
0 (T) indicates non two - state behavior
[#l20'*2>0&/$'25'E0020$'
• !#"%40#,2('• !2(+#1%(#,2('
• *#1;"/';0/;#0#,2('u'.28'$#1;"/'%$'"2#)/)'%(+2'#';#('
– d//)'+2'1%(%1%F/'+./01#"':0#)%/(+'
• X/$%)>#"'$2"6/(+$'#()'12%$+>0/<'
• -./01#"'"#:'
– ^/#,(:Y!22"%(:'0#+/$'– *#1;"/'1#$$'
• J02&/$$%(:'/0020$'
C&D'M%#(.#('!./(' Zj'
K$2+./01#"'-%+0#,2('!#"20%1/+03'
• [2$+"3'>$/)'520'
>()/0$+#()%(:'%(+/0H
12"/&>"#0'%(+/0#&,2($'
• K(&0/1/(+#"'#))%,2('26/0'
,1/'25'#'"%:#()'C20'#'
4%()%(:';#0+(/0D'%(+2'#'
$2">,2('25'#';02+/%('C20'
#(2+./0';#0+(/0DB'>(,"'(2'
/P&/$$'./#+'1/#$>0#4"/'C(2'
120/'50//';02+/%(D'
• [/#$>0/'+./'./#+'0/R>%0/)'
+2'1#%(+#%('+./'
+/1;/0#+>0/'
C&D'M%#(.#('!./(' Zg'
@(#"3$%$'25'K-!'
• [>&.'$%1;"/0'&21;#0/)'+2'=*!'
C&D'M%#(.#('!./(' Zp'
!
q = "H 0(T)nPL = "H 0(T)V[PL]
= "H 0(T)V[PT ]Ka[L]1+ Ka[L]
!
[PL] = [PT ]Ka[L]1+ Ka[L]
P + L PL
!
qi = "H 0(T)V[PT ]Ka[L]i1+ Ka[L]i
#Ka[L]i#11+ Ka[L]i#1
$
% &
'
( )
=/Q(/'#'0#,2'D'W'vA-wYvJ
-wB'Qy(:'25'B
%'6$'X'8%""'3%/")'42+.'U
#'
#()'!^eC-D<''N0//'/(/0:3'#()'/(+02;3'&.#(:/$'+./('52""28<'!
[L]i = 0.5([LT ]" [PT ]± ([LT ]" [PT ]"1/Ka )2 " 4[LT ])
C&D'M%#(.#('!./(' \e'
EMBO reports 8, 1, 63–69 (2007)
the yeast exosome
A%1%+#,2($'25'K-!'
• =%{&>"+'520'$+>)3%(:'6/03'$+02(:'4%()/0$'
– E#&.'%(&0/1/(+#"'25'"%:#()'4/&21/$'&21;"/+/"3'42>()'>(,"';02+/%('%$'
5>""3'&2($>1/)i'(2'+0#($%,2('+2'Q+o'
– |;;/0'"%1%+'U#']'fep'[Hf'
– [%:.+'4/'26/0&21/'43'$2H&#""/)')%$;"#&/1/(+',+0#,2('
C&D'M%#(.#('!./(' \f'
Ka ~ 106 M-1 Ka ~ 1012 M-1
=%$;"#&/1/(+'K-!'
C&D'M%#(.#('!./(' \L'
Nature Protocols 1, - 186 - 191 (2006)
Weak inhibitor strong inhibitor (Ka ~ 1012 M-1)
!#"20%1/+03'520'=0>:'=/$%:('
• c2+.'=*!'#()'K-!'#0/';28/05>"'+22"$'520'24+#%(%(:'+./012)3(#1%&')#+#'&0%,&#"'520')0>:')/$%:('
• ^28/6/0B'42+.'#0/',1/H&2($>1%(:'#()'"#420%2>$'#()'$;/&%#"'
)/$%:($'#0/'(/&/$$#03'520'+./'(//)'25'.%:.H+.02>:.;>+''
– /<:<B'-./012N">20-['+/&.(2"2:3S'"/$$'R>#(,+#,6/''
• n./+./0'4%()%(:'%$'/(+.#";3'20'/(+02;3')0%6/('&#(';026%)/'
%1;20+#(+'%($%:.+$'520'"/#)'2;,1%F#,2('C#()'$>&.'%(52'&#('(2+'
4/'24+#%(/)'5021'$+0>&+>0#"')#+#D'
• X/;"#&/1/(+'K-!'520',:.+'4%()/0$'
C&D'M%#(.#('!./(' \Z'
Ref: “Calorimetry and Thermodynamics in Drug Design” by J. B. Chaires, Annu. Rev. Biophys. 2008. 37:135–51 .