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Proteínas
TransporteAlbúmina
Canalde potasio Mioglobina
Movimiento
Miosina
Estructura
Colágeno
Histonas
Lisozima
PepsinaPolimerasade DNA
CatálisisRegulacióny
SeñalizaciónFactor detranscripción
Inmuno-gamma-globulina
Insulina
Enlaces de hidrógenoInteracciones de van der WaalsInteracciones electrostáticasInteracciones hidrofóbicas
Red de interacciones• intramoleculares• intermoleculares
+
∑
∑
∑
++−=
++=
+−=
iii
iii
iii
dNVdPSdTdG
dNVdPTdSdH
dNPdVTdSdE
μ
μ
μ
PVTSETSHNPTGGPVENPSHH
NVSEE
i
i
i
+−=−==+==
=
),,(),,(
),,(
( ) ( )
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛Δ+Δ=Δ
−Δ+Δ=ΔΔ−Δ=Δ
0P0
0P0
lnTTCTSS
TTCTHHSTHG
A
B
P2
2
PPP
)()()(⎟⎟⎠
⎞⎜⎜⎝
⎛∂Δ∂
−=⎟⎠⎞
⎜⎝⎛
∂Δ∂
=⎟⎠⎞
⎜⎝⎛
∂Δ∂
=ΔT
TGTT
TSTT
THC
∑+−=−=
−=Δ
iiidNPdVTdSWdQddE
WQEμ
00
≥≥Δ
dSS aisladosistemaunen
1a Ley de la Termodinámica Balance energético
2a Ley de la Termodinámica Direccionalidad o viabilidad
∑
∑−<<
−==
iii
iii
dNPdVWdTdSQd
dNPdVWdTdSQd
μ
μ
leirreversib
reversible
000
<>=
dSdSdS
imposibleleirreversib
reversible
A
B
entorno
sistemaenergía
(Q,W)
0≥+= es dSdSdS
0=+= es dEdEdE
0≥−=+=TQddS
TQddSdS s
se
s
0≥− ss QdTdS
constanteVsi00 ≤=−≥− sssss dFTdSdEdETdS
constantePsi00 ≤=−≥− sssss dGTdSdHdHTdS
Supongamos que el sistemano es aislado, pero es cerrado
0,0,0,
≤≤≥
s
s
s
dGPTdFVTdSVE
constantesconstantesconstantes
STHGPVFTSHPVTSEG
sNPTGG
ΔΔΔ
Gibbdelibreenergía),,(
−=+=−=+−=
=
∑++−=++−−=i
iidNVdPSdTPdVVdPSdTTdSdEdG μ
BA 0BA 0,
BA 0
→<↔=
→/>
favorableprocesoequilibrioconstantes
favorablenoproceso
dGdGPTdG
A
B
exergónicaaendergónic
exotérmicaaendotérmic
00
00
<Δ>Δ
<Δ>Δ
Δ−Δ=Δ
GG
HH
STHG
-16
-12
-8
-4
0
4
kcal
/mol
ΔG ΔH -TΔS
( ) RSRTHRTGeq eeeK /// 000 ΔΔ−Δ− ==
ΔH cambio de energía almacenada en enlaces e interaccionesrefleja número, tipo y calidad de enlacesΔH < 0 ⇒ si T ↑, entonces Keq ↓ΔH > 0 ⇒ si T ↑, entonces Keq ↑
ΔS medida de desordenrefleja orden-desorden en enlaces, flexibilidad conformacional y solvatación
BA ↔
( )RTGPPT /expcte, ii Δ−∝⇒
iestados,...,1,0 Pni ⇒=
1ni
0ii =∑
=
=
P…
G0ii GGG −=Δ
exp(-ΔGn/RT)ΔGnGnn
exp(-ΔGi/RT)ΔGiGii
10G00
exp(-ΔG/RT)ΔGGi
( ) ( )∑=
=
Δ−=Δ−
=ni
0ii
ii /exp/exp RTGQ
QRTGP
función de partición
Sistema ergódico ⇒ AA =
∑=
=
=ni
0iii APA promedio de colectividad
∫ ′′=+∞→
t
ttdtA
tA
0)(1lim promedio temporal
En general, iAA ∀≠ ,i
A propiedad observable del sistema ⇒ ¿ medida de A ?
QRTG ln−=Δ
( ) ( )∑∑ Δ−=Δ−=i
ii
ii RTGRTHQ /exp/expω
( )Q
RTGP ii
/exp Δ−=
( )T
TGT
TQRTH
∂Δ∂
−=∂
∂=Δ
/ln 22
TG
TQTQRS
∂Δ∂
−=⎟⎠⎞
⎜⎝⎛
∂∂
+=Δlnln
ΔSnΔHnΔGnn
ΔSiΔHiΔGii
0000
ΔSΔHΔGi
( )Q
RTGP ii
/exp Δ−=
( )
QNPNN
QRTGNPNN i
ii
1
/exp
00 ==
Δ−==
( )∑ Δ−=i
i RTGQ /exp
( )RTGNN
ii /exp0
Δ−=
⎪⎪⎭
⎪⎪⎬
⎫
∑∑ ==i
i
i
i
CC
NNQ
00
Equilibrio Conformacional
( )RTGPPT /expcte, ii Δ−∝⇒
iestados,...,1,0 Pni ⇒=
1ni
0ii =∑
=
=
P
…
G0ii GGG −=Δ
],...)[],[,,,,(ii LDpHPTGG μΔ=Δ
][])([ 0ii DmGDG −Δ=Δ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
++Δ=Δ
−
−
=∑ pHpKa
pHpKa
ij
j
RTnGpHG,
1,
101
101ln)(1j
j0ii
( ))/ln()()()()( im,iP,im,iim,iP,im,ii TTCTSTTTCTHTG Δ+Δ−−Δ+Δ=Δ
⎟⎟⎠
⎞⎜⎜⎝
⎛
++
+Δ=Δ][1][1
ln])([iB,
B,10ii LK
LKRTGLG
Estudio de estabilidad de proteínas
• Bioquímica y BiofísicaInteracciones intramolecularesPlegamiento de proteínas
• BiotecnologíaIngeniería de proteínasSensores moleculares
• BiomedicinaEnfermedades conformacionales
• FarmacologíaFormulación de fármacosControl de calidad
Conformación nativa ≡ conformación de mínima energíaestructurada, estable, funcional, activa
• temperatura moderada• ausencia de agentes denaturalizantes• pH moderado
Pérdida de la Conformación Nativa
• pH ácido• temperatura extrema• agentes desnaturalizantes• hidrólisis• mutaciones
En un contexto dado, la estructura primaria de unaproteína determina su estructura tridimensional, que corresponde a un mínimo energético
Cuantificación dela estabilidad
Energía requerida paradesestabilizar la estructuratridimensional molecular
Técnicas Experimentales:
• Espectroscopía (UV, F, CD, NMR, FTIR)• Calorimetría (DSC)
• Propiedad con diferentes valores para cada estado• Señal medida proporcional al avance del proceso de desplegamiento• Información global o local
Espectroscopía
20 40 60 80 1000
10
20
30
40
50
60
Señ
al E
spec
trosc
ópic
a
Temperatura (oC)
30 40 50 60 70 80 90
0
2000
4000
6000
8000
<ΔC
P>ex
cess (c
al/K
·mol
)T (oC)
0°C
100°C
Calorimetría Diferencial de Barrido
Medida de la capacidad calorífica de una disolución de macromolécula en función de la temperatura
Desplegamiento Cooperativo Reducción del númerode estados accesibles
Estados parcialmente plegados no son significativamente poblados
0 2 4 6 8 10
20
40
60
80
100
120
Señ
al E
spec
trosc
ópic
a
[Urea] (M)
20 40 60 80 1000
10
20
30
40
50
60
Señ
al E
spec
trosc
ópic
a
Temperatura (oC)
20 40 60 80 100
0
2
4
6
8
10
12
14
<ΔC
P> (k
cal/K
·mol
)
Temperatura (oC)
?
Estabilidad ΔG Energía de Gibbs de estabilizacióno desplegamientoDiferencia de energía de Gibbs entre el estado nativo y el estadodesplegado
][][
ln
NUK
KRTG
=
−=Δ
⎩⎨⎧
↓↑Δ
⇒↑K
GdEstabilida
⎩⎨⎧
<>Δ
⇒1
0Estable
KG
UN ↔
NU GGG −=Δ
Equilibrio de desplegamiento o desnaturalización
No se obtiene información cinéticaNo se consideran procesos irreversibles
G
N
UTS
ΔG‡ΔG
UN ↔
↔
Enlaces de hidrógenoInteracciones de van der WaalsInteracciones electrostáticasInteracciones hidrofóbicasEntalpía de solvataciónEntropía de solvataciónEntropía conformacional
ΔG = ΔH - TΔS
El papel del agua es extremadamente importante
Balance entre estado nativo y desplegado, tomando como referencia la interacción con el solvente
Desplegamiento de dos estados
⎪⎪
⎩
⎪⎪
⎨
⎧
+=
+=
+=
KKP
KP
KQ
1
11
1
U
N
KΔGGU
10GN
exp(-ΔG/RT)ΔGGi
UN ↔
],...)[],[,,,,( LDpHPTGG μΔ=Δ
][])([ 0 DmGDG −Δ=Δ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
++Δ=Δ
−
−=
=∑ pHpKa
pHpKa
RTnGpHGUj,
Nj,
101
101ln)(mj
1jj
0
( ))/ln()()()()( mPmmPm TTCTSTTTCTHTG Δ+Δ−−Δ+Δ=Δ
⎟⎟⎠
⎞⎜⎜⎝
⎛
++
+Δ=Δ][1][1
ln])([UB,
NB,0
LKLK
RTGLG
Desnaturalización Térmica
( ))/ln()()()()( mPmmPm TTCTSTTTCTHTG Δ+Δ−−Δ+Δ=Δ
)()( mm TTHTH =Δ=Δ )()( mm TTSTS =Δ=Δ
P2
2
PPP ⎟⎟
⎠
⎞⎜⎜⎝
⎛∂Δ∂
−=⎟⎠⎞
⎜⎝⎛∂Δ∂
=⎟⎠⎞
⎜⎝⎛∂Δ∂
=ΔT
GTTST
THC
KRTTG ln)( −=Δ
⎪⎪
⎩
⎪⎪
⎨
⎧
Δ=Δ
==
=
⇒=Δ
m
mm
UNm
)()(
21
1
0)(
TTHTS
PP
K
TG
ΔH(Tm) > 0 Ruptura de interacciones de van der WaalsRuptura de enlaces de hidrógenoSolvatación de grupos polares y apolares
ΔS(Tm) > 0 Libertad conformacionalSolvatación de grupos polares y apolares
ΔCP > 0 Solvatación de grupos polares y apolares
ΔCP = cte
ΔCP = a + bT + cT2
0 20 40 60 80 1000
10
20
30
40
50
60
Señ
al E
spec
trosc
ópic
a
Temperatura (oC)
UUNN APAPA +=
( )TbaA NNN +=
( )TbaPA UUUU +=
( ) ( )( ) ( )( )( ) RTTTCTSTTTCTH
RTTTCTSTTTCTH
eTbaeTbaA /)/ln()()()(
UU/)/ln()()()(
NNmPmmPm
mPmmPm
1 Δ+Δ−−Δ+Δ−
Δ+Δ−−Δ+Δ−
++++
=
0 20 40 60 80 1000
10
20
30
40
50
60
Señ
al E
spec
trosc
ópic
a
Temperatura (oC)
ΔH(Tm) 101 ± 2 kcal/molTm 60.69 ± 0.04 °CΔCP 2.2 ± 0.7 kcal/K⋅mol
0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
P N, P
U
Temperatura (oC)
∫
∫Δ
=Δ
Δ=Δ
1
0
1
0
Pm
Pm
)(
)(
T
T
T
T
dTTC
TS
dTCTH
40 60 80-2
0
2
4
6
8
10
12
14
<Δ
CP>
(kca
l/K·m
ol)
Temperatura (oC)40 60 80
0
30
60
90
120
150
180
<ΔH
> (k
cal/m
ol)
Temperatura (oC)
∫ Δ=ΔT
TdTCH
0P
TmΔCP
ΔHcal
HPHPHPH
Δ=
Δ+Δ=Δ
U
UUNN
)()( mPm TTCTH −Δ+Δ
( ) P2
2
2P
P 11C
KK
RTH
KK
TH
C Δ+
+Δ
+=⎟⎟
⎠
⎞⎜⎜⎝
⎛∂Δ∂
=Δ
40 60 80
0
2
4
6
8
10
12
14
<ΔC
P> (k
cal/K
·mol
)
Temperatura (oC)
( )
TQRTH
RTGQ
∂∂
=Δ
Δ−+=ln
/exp1
2
( ))/ln()()()()(
mPm
mPm
TTCTSTTTCTHTG
Δ+Δ−−Δ+Δ=Δ
40 60 80
0
2
4
6
8
10
12
14
<ΔC
P> (k
cal/K
·mol
)
Temperatura (oC)
Tm 60.75 ± 0.03 °CΔH(Tm) 102 ± 0.3 kcal/molΔCP 2.51 ± 0.02 kcal/K⋅mol
-40 -20 0 20 40 60 80 100-10
-5
0
5
10
ΔG (k
cal/m
ol)
Temperatura (oC)
STG
RTH
TK
Δ−=⎟⎠⎞
⎜⎝⎛∂Δ∂
Δ=⎟
⎠⎞
⎜⎝⎛
∂∂
P
2P
ln
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛ΔΔ
−−Δ−Δ=Δ
⎟⎟⎠
⎞⎜⎜⎝
⎛ΔΔ
−==Δ
mP
mmPm
mP
mmSmax
)(exp1)(max
)(exp
TCTHTCTHG
TCTHTTT
T
GT
GST
Δ⇒=Δ max0
Tmax ΔG
P2
2
P ⎟⎟⎠
⎞⎜⎜⎝
⎛∂Δ∂
−=ΔT
GTC
Tm
30 40 50 60 70 80 90-20-15
-10
-5
05
10
ΔG(k
cal/m
ol)
Temperatura (oC)
0
3
6
9
12
<Δ
CP>
(kca
l/K·m
ol)
0.00.2
0.40.6
0.81.0
Frac
ción PN PU
Enlaces de hidrógenoInteracciones de van der WaalsInteracciones electrostáticasInteracciones hidrofóbicas
0 20 40 60 80 100-20
-15
-10
-5
0
5
10
ΔG
ΔG (k
cal/K
·mol
)
Temperatura (oC)
-250-200-150-100-50050100150200
ΔH
, -TΔ
S (k
cal/K
·mol
)
ΔH -TΔS
Tm
TH TS
+
-
estabilizado entálpicamente
estabilizado entrópicamente
Estabilidad “marginal”Dificultad para cálculos predictivos
ΔG = ΔH - TΔSP
mHH
maxSS
)(0)(
0)(
CTHTTTH
TTTS
m
GT
ΔΔ
−=⇒=Δ
=⇒=Δ Δ
Posible justificación de una estabilidad no muy elevada:
Razones para una estabilidad no muy baja:
• Permitir cierta flexibilidad y dinámica relacionadascon la función molecular• Posibilitar la degradación mediante proteasas• Impedir cinética de plegamiento lenta con intermedios de plegamiento muy estables• Evitar la aparición de estructuras incorrectamenteplegadas estables (trampas cinéticas)
• Estados parcial- o totalmente desplegadossignificativamente poblados (inactivos y susceptiblesde degradación)
30 40 50 60 70 80 90
0
1
2
3
4
5
6 Subtype B Subtype A Subtype C Subtype G
<ΔC
P> (k
cal/K
·mol
)
Temperatura (oC)
mWT
mWT
m )()( TTSTG ΔΔ≈ΔΔ
)()()( WTm
WTWTm
MUTWTm TGTGTG Δ−Δ=ΔΔ
WTP
MUTP CC Δ≈Δ
Diferencias de estabilidad
Problema: ΔG= ΔG(T)
Utilizar una temperatura común
( )WTm
MUTm
WTm
WT
XXXGX
XGG −⎟
⎠⎞
⎜⎝⎛∂Δ∂
−=Δ⎟⎠⎞
⎜⎝⎛∂Δ∂
−≈ΔΔ
-40 -20 0 20 40 60 80 100-30
-20
-10
0
10
20
30
ΔG (k
cal/m
ol)
Temperatura (°C)
Tm
Estabilidad a elevada y baja temperatura
¿ Qué proteína es más estable ?
ΔH(Tm) 180 kcal/molΔS (Tm) 0.54 kcal/(K⋅mol)ΔCP 5.0 kcal/(K⋅mol)
ΔH (Tm) 350 kcal/molΔS (Tm) 1.05 kcal/(K⋅mol)ΔCp 8.0 kcal/(K⋅mol).
40 60 80
0
2
4
6
8
10
12
14
<ΔC
P> (k
cal/K
·mol
)
Temperatura (oC)
Tm 60.75 ± 0.03 °CΔH(Tm) 102 ± 0.3 kcal/molΔCP 2.51 ± 0.02 kcal/K⋅mol
-40 -20 0 20 40 60 80 100-10
-5
0
5
10
ΔG (k
cal/m
ol)
Temperatura (oC)
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛ΔΔ
−−Δ−Δ=Δ
⎟⎟⎠
⎞⎜⎜⎝
⎛ΔΔ
−==Δ
mP
mmPm
mP
mmSmax
)(exp1)(max
)(exp
TCTHTCTHG
TCTHTTT
T
GT
Tmax ΔG
P2
2
P ⎟⎟⎠
⎞⎜⎜⎝
⎛∂Δ∂
−=ΔT
GTC
TmTf
0)()( fm =Δ=Δ TGTG
mSfHm
2m
f 22-3
TTTTT
TT −≈≈
-60 -40 -20 0 20 40 60 80 100 120-50
-40
-30
-20
-10
0
10
20
ΔG (k
cal/m
ol)
Temperatura (oC)
TmTf
Desnaturalización Fría
Para una proteína globular típica:
Tm ~ 50-70 °CΔH(Tm) ~ 80-120 kcal/molΔCP ~ 2-3 kcal/K·molΔG(25 °C) ~ 5-10 kcal/molTmaxΔG ~ 20-30 °CTf < 0 °C
Desplegamiento de tres estados
K1K2ΔG1+ΔG2
K2ΔG2
K1ΔG1
10exp(-ΔGi/RT)ΔGii
Q = 1 + K1 + K2 + K1K2
( )Q
RTGP /exp ii
Δ−=
= (1 + K1) (1 + K2)
K1K2ΔG1+ΔG2
K1ΔG1
10exp(-ΔGi/RT)ΔGii
Q = 1 + K1 + K1K2
( )Q
RTGP /exp ii
Δ−=
≠ (1 + K1) (1 + K2)
20 40 60 80 100
0
2
4
6
8
10
<ΔC
P> (k
cal/K
·mol
)
Temperatura (oC)
?
20 40 60 80 100
0
50
100
150
200
250
<ΔH
> (k
cal/m
ol)
Temperatura (oC)
∫ Δ=ΔT
TdTCH
0P
0 20 40 60 80 100
-20
-10
0
10
ΔG1ΔG2ΔG1+ΔG2
ΔG(k
cal/m
ol)
Temperatura (oC)
02468
10
<ΔC
P>(k
cal/K
·mol
)
0.00.20.40.60.81.0
Frac
ción PN
PI
PU P ∼ 0
Reducción del númerode estados accesibles
20 40 60 80 100
0
2
4
6
8
10
12
<Δ
CP>
(kca
l/K·m
ol)
Temperatura (oC)
¿Transición de dos estados ?
20 40 60 80 100
0
50
100
150
200
250
300
<ΔH
> (k
cal/m
ol)
Temperatura (oC)
∫ Δ=ΔT
TdTCH
0P
Tests de dos estados
• Superposición de las curvas de desplegamiento obtenidas con diversas técnicas (espectroscopía)
• Valor del cociente (calorimetría)cal
vH
HH
ΔΔ
Refolding
FluorescenciaCD (far UV)
Dos estados Tres estados
Genzor et al. Protein Science (1996) 5, 1376-1388 Irún et al. J. Mol. Biol. (2001) 306, 877-888
¡ Cuidado !
• Superposición de curvas obtenidas con distintas técnicas es condición necesaria pero no suficiente
• Espectroscopía nos informa de comportamiento global y/o local
• Transición de dos estados implica total cooperatividad (ausencia de otros estados parcialmente plegados)
• Errores y ruido en las medidas pueden enmascarar algunos detalles y fenómenos
cal
maxP2
mvH
4H
CRTHΔ
>Δ<=Δ
2
lnRT
HT
K Δ=
∂∂
1
1
1
cal
vH
cal
vH
cal
vH
>ΔΔ
<ΔΔ
=ΔΔ
HHHHHH unidad cooperativa ≡ molécula (dos estados)
unidad cooperativa < molécula (estados intermedios)
unidad cooperativa > molécula (nativo está asociado)
van’t Hoff enthalpy
20 40 60 80 100
0
2
4
6
8
10
12
<ΔC
P> (k
cal/K
·mol
)
Temperatura (oC)
ΔHcal 144.3 kcal/molTm 63.5 ºC< ΔCP>max 10.2 kcal/K·mol
ΔHvH 63.4 kcal/molΔHvH/ΔHcal 0.44
0 20 40 60 80 100
-20
-10
0
10
ΔG1ΔG2ΔG1+ΔG2
ΔG(k
cal/m
ol)
Temperatura (oC)
02468
1012
<ΔC
P>(k
cal/K
·mol
)
0.00.20.40.60.81.0
Frac
ción PN PI
PU P ≠ 0
20 40 60 80 100
0
4
8
12
16
20
24
28
<ΔC
P> (k
cal/K
·mol
)
Temperatura (oC)
30 40 50 60 70 80 90
0
10
20
30
40
50
<Δ
CP>
(kca
l/K·m
ol)
Temperatura (oC)
ΔHvH /ΔHcal 1ΔHvH/ΔHcal 0.5
Tm 60ºC 60ºCΔH(Tm) 200 kcal/mol 2 × 100 kcal/molΔCP 4 kcal/K·mol 2 × 2 kcal/K·mol
2m
vH
4m
RTH
TP
TT
N Δ−=
∂∂
=
0 20 40 60 80 100-40
-30
-20
-10
0
10
20
ΔG (k
cal/m
ol)
Temperatura (oC)
0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
Frac
ción
Nat
iva
Temperatura (oC)30 40 50 60 70 80 90
-50
0
50
100
150
200
250
300
350
<ΔH
> (k
cal/m
ol)
Temperatura (oC)
K1K2kΔG1+ΔG2+ΔgK2kΔG2+ΔgK1kΔG1+Δg10
exp(-ΔGi/RT)ΔGii
Q = 1 + kK1 + kK2 + kK1K2
( )Q
RTGP /exp ii
Δ−=
Dos dominios interaccionantes
≠ (1 + kK1) (1 + kK2)
0 20 40 60 80 10005
101520253035404550
<ΔC
P> (k
cal/K
·mol
)
Temperatura (oC)
k Δg (kcal/mol)1 010-1 1.410-2 2.710-3 4.110-4 5.510-5 6.810-6 8.310-7 9.5
85.0vH ≈ΔΔ
calHH
0 20 40 60 80 100
Temperatura (oC)
Frac
ción
k = 1 Δg = 0 independenciak ≠ 1 Δg ≠ 0 cooperatividad
0 20 40 60 80 10005
101520253035404550
<ΔC
P> (k
cal/K
·mol
)
Temperatura (oC)
0 20 40 60 80 1000.00
0.25
0.50
0.75
1.00
Temperatura (oC)
0.00
0.25
0.50
0.75
1.00
Frac
ción
k Δg (kcal/mol)1 010-6 8.3
k = 1
k = 10-6
0 20 40 60 80 100-30-25-20-15-10
-505
10152025
ΔG1 ΔG2 ΔG1+ΔG2
ΔG1+Δg ΔG2+Δg ΔG1+ΔG2+Δg
ΔG (k
cal/m
ol)
Temperatura (oC)
05101520253035404550
<ΔC
P> (k
cal/K
·mol
)
Reducción del númerode estados accesibles
Cooperatividad ⇒ No aditividad
Todd et al. J. Mol. Biol. (1998) 283, 475-88
Unión de Ligandosy
Estabilidad de Proteínas
UN ↔
0
0
TU
0T
N
1][][
11
][][
KK
PUP
KPNP
+==
+==
00
0
ln][][
KRTGNUK
−=Δ
=K0
K0ΔG0
10exp(-ΔGi/RT)ΔGii
Q = 1 + K0
( )Q
RTGP /exp ii
Δ−=
NL
L
UN+↔
( )][1ln
][1][11
][][
][][][
0
0
LKRTGG
LKK
LKNU
NLNUK
a
aa
++Δ=Δ
+=
+=
+=
0
0
TU
0T
N
][11][][
][1][1
11
][][][
KLKK
KK
PUP
KLKLK
KPNLNP
a
a
a
++=
+==
+++
=+
=+
=
K0
Ka
K0ΔG0
Ka[L]ΔGbind
10exp(-ΔGi/RT)ΔGii
Q = 1 + Ka[L] + K0
( )Q
RTGP /exp ii
Δ−=
0 20 40 60 80 100-12-8-4048
12
ΔG(k
cal/m
ol)
Temperatura (oC)
02468
1012
<ΔC
P>(k
cal/K
·mol
)
0.00.20.40.60.81.0 1:0
1:1 1:5 1:25 1:125
P U
Ka 10-6 M-1
[L]T/[P]T
G
−RTln(1+Ka[L])
UL
L
UN+
↔
( ) ( )
( )][1ln
][1][1][][
][][][
0
0
LKRTGG
LKKLKNU
NULUK
a
aa
+−Δ=Δ
+=+=+
=
( )( )( )][11
][11][
][][
][111
11
][][
0
0
TU
0T
N
LKKLKK
KK
PULUP
LKKKPNP
a
a
a
+++
=+
=+
=
++=
+==
K0
Ka
K0Ka[L]ΔG0+ΔGbind
K0ΔG0
10exp(-ΔGi/RT)ΔGii
Q = 1 + K0(1+Ka[L])
( )Q
RTGP /exp ii
Δ−=
0 20 40 60 80 100
-12-8-4048
ΔG(k
cal/m
ol)
Temperatura (oC)
02468
<ΔC
P>(k
cal/K
·mol
)
0.00.20.40.60.81.0
P U
G
−RTln(1+Ka[L])
ULNL
LL
UN++
↔
⎟⎟⎠
⎞⎜⎜⎝
⎛
++
+Δ=Δ
++
=++
=++
=
][1][1
ln
][1][1
][1][1
][][
][][][][
U,
N,0
N,
U,0
N,
U,
LKLK
RTGG
LKLK
KLKLK
NU
NLNULUK
a
a
a
a
a
a
( )( )
( )][1][1][1
1][][][
][1][1][1
11
][][][
U,0
N,
U,0
TU
U,0
N,
N,
TN
LKKLKLKK
KK
PULUP
LKKLKLK
KPNLNP
aa
a
aa
a
++++
=+
=+
=
++++
=+
=+
=
K0
Ka,N Ka,U
G
−RTln(1+Ka,N[L])
−RTln(1+Ka,U[L])
20 40 60 80 100-20-15-10-505
10
ΔG (k
cal/m
ol)
Temperatura (oC)
048
121620
<ΔC
P> (k
cal/m
ol)
Estabilización de proteínas
ΔΔH 2.5 kcal/molΔΔS 2.5 kcal/mol
mWT
mWT
m )()( TTSTG ΔΔ≈ΔΔ
Estabilización de proteínas
• Enlace disulfuro intramolecular• Interacción catión-π• Resíduo con mayor propensión helicoidal• Carga positiva en extremo C de α-hélice• Carga negativa en extremo N de α-hélice • Rellenado de cavidad intramolecular• Optimización de carga electrostática• Neutralización de enlaces de hidrógeno superficiales
ΔΔH, ΔΔS ⇒ ΔΔG > 0
Estudio de unión de ligandos
• Bioquímica y BiofísicaInteracciones intramolecularesPlegamiento de proteínas
• BiotecnologíaIngeniería de proteínasMotores moleculares
• BiomedicinaInhibidores y activadoresEnfermedades conformacionales
• FarmacologíaControl de calidad
ΔG = ΔH – TΔSconf-PR – TΔSconf-Inh – TΔSsolv
• Cómo interaccionan M y L entre sí?• Cómo interaccionan M y L con el disolvente?
Interacciones M-L• van der Waals• enlaces de H• de/protonación
Desolvatación
Ganancia de entropía debido a la desolvatación
Pérdida de entropía debido a una pérdida de grados de libertad
Tipos de interacciones:
M + L ↔ ML
M + nL ↔ MLn
mM ↔ Mm
mM + L ↔ MmL
Mm + L ↔ mML
Técnicas experimentales
Método 1
• Diálisis• Ultracentrifugación analítica
Método 2
• Espectroscopía• Calorimetría
Diálisis
2111
2121
22
11
][][][][][
][][][][
][][][
LLLLML
LLLL
MLLL
TT
L
T
T
−=−=
=⇒==
+=
μμ
⇒ concentraciones en equilibrio
Ultracentrifugación
molecular peso⇒= WβM0)( eCrC
Distribución de pesos molecularesen disolución ⇒ concentraciones en equilibrio
Espectroscopía
seña
l
concentración de ligando
KB ≡ 1/KD 2
lnRT
HTKB Δ
=∂
∂
Calorimetría
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
ΔH
n
KB ≡ 1/KD
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
MLLM ↔+
( )1][][ −−Δ= iii MLMLHVq
( ) ( )/RTGΔexp/RTHΔexpωPPT, iiii −=−∝⇒constant
iPn1,...,0,i ⇒= states
1Pn
0ii =∑
=
…
G [ML]][MLRTlnGGGΔ i
0ii −=−=
exp(-ΔĜn/RT)ΔĜnĜnn
exp(-ΔĜi/RT)ΔĜiĜiI
10Ĝ00
exp(-ΔĜ/RT)ΔĜĜi
( ) ( )∑=
−=−
=n
0ii
ii /RTGΔexpZ
Z/RTGΔexpP
partition function or binding polynomial
pH,...)(T,fSTΔHΔGΔ iiii =−=
Binding and Linkage: Functional Chemistry of Biological Macromolecules. J. Wyman and S. Gill. Ed. University Science Books
ergodic system → AA =
∑=
=0i
iiAPA ensemble average
∫ ′′=+∞→
t
0tt)dtA(
t1limA time average
A observable property of the system → measurement of A?
A[M]
AV[M]
T
T
=
=
value observed
value observed
RTlnZΔG −=
( )∑ −=i
i /RTGΔexpZ
( )Z
/RTGΔexpP ii
−=
( )T
/TΔGT
TlnZRTΔH 22
∂∂
−=∂∂
=
TΔG
TlnZTlnZRΔS
∂∂
−=⎟⎠⎞
⎜⎝⎛
∂∂
+=
( )Z
/RTGΔexpP ii
−=
( )
Z1NPNN
Z/RTGΔexpNPNN
00
iii
==
−==
( )∑ −=i
i /RTGΔexpZ
( )/RTGΔexpNN
i0
i −=
⎪⎪⎭
⎪⎪⎬
⎫
∑∑∑ ===i
i
i 0
i
i 0
i
[M]][ML
CC
NNZ
0,0
0,5
1,0
1,5
2,0
n LB
ln([L]/1M)
∑
∑
=
=== n
0ii
n
0ii
T
BLB
][ML
]i[ML
[M][L]n
Number of ligand moleculesbound per macromolecule
nnlim LB[L]=
+∞→
0.0
0.5
1.0
1.5
2.0
n LB
[L] (M)
nnF LB
B =
0nlim LB0[L]
=+→
0ln[L]nLB ≥
∂∂
Binding and Linkage: Functional Chemistry of Biological Macromolecules. J. Wyman and S. Gill. Ed. University Science Books
( )
( )
∑ ∏
∑
∏
=
∗∗∗
=
∗
=
−
∗
=
∗
∗
+++=⎟⎟⎠
⎞⎜⎜⎝
⎛=
+++==
−=
−====
=
−==
n
0i
2211
ii
1jj
221
n
0i
ii
ii
iii
i1i
ii
i
1jji
1-i
ii
iii
i
...[L]KK[L]K1[L]K
...[L]β[L]β1[L]βZ
ln[L]RTiΔGGΔ
/RTGΔexp[ML]
][ML[L]βββKKβ
][L][ML][MLK
/RTΔGexp[M][L]
][MLβ overall association constants
step-wise association constants
∑
∑
∑
∑
∑∑
=
=
=
=
==
==
==
n
0i
ii
ii
n
0in
0ii
n
0ii
LB
n
0i
ii
n
0i
i
[L]β
[L]βi
][ML
]i[MLn
[L]β[M]
][MLZ
∑∑
∑∑
=
=
=
=
Δ=Δ
=⎟⎠⎞
⎜⎝⎛∂∂
=
===⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂
=
n
0iii
n
0ii
ii
[L]P,
2
n
0ii
n
0i
ii
TP,LB
HPZ
H[L]β
TlnZRTΔH
iiPZ
i[L]β
ln[L]lnZn
Measurement of thermodynamic binding parameters: ΔG, KA, ΔH, ΔS
• Direct measurement of equilibrium concentrations (method 1)
• Measurement of signal proportional to advance of reaction (method 2)
BT
BLB
B
Fn[M][L]n
F
==
∝signal
STΔΔHΔGRTΔH
TlnK
ΔGK[ML][M],[L],
2A
A
−=
=∂
∂→→
sign
al
ligand concentration
STΔΔHΔGRTΔH
TlnK
ΔGΔH,K
2A
A
−=
=∂
∂→→model
ln[L]lnZnLB ∂∂
=
TLBT [M]n[L][L] +=
TiiiTTLB [M]P][MLP[L]0[L][M]n[L] =→→→=−+
conservation or balance equation
∑∑
∑∑
==
==
===
===
0iii
0iiiTT
0iii
0iiiTT
]A[MLAP[M]A[M]
]A[MLVAPV[M]AV[M]
value observed
value observed
Note: The free species concentrations are unknown; we only manage total concentrations
∑∑==
===0i
iji0i
iji,jT,jjT,jT, HΔ][MLVHΔPV[M]ΔHV[M]Q
∑
∑
=
=
⎟⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−=
⎟⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−=⎟
⎠⎞
⎜⎝⎛ −−=
0ii1-jiji
0ii1-ji,ji,jT,1-jT,jT,j
ΔHVv1][ML][MLV
ΔHVv1PPV[M]
Vv1QQQ
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
0[L][M]n[L] jT,jT,jLBj =−+j
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−=
⎟⎠⎞
⎜⎝⎛ −=
j
0jT,
j
0jT,
Vv11[L][L]
Vv1[M][M]
( )
( )∑
∑
∑∑
=
=
==
−+=
−+=
===
0i0iji0jT,
0i0ijT,ji,0jT,
0iiji
0iiji,jT,jT,j
AA][MLAM][
AA[M]PA[M]
A][MLAP[M]A[M]A
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Sp
ectro
scop
ic S
igna
l (a.
u.)
[Ligand]T (μM)
0[L][M]n[L] jT,jT,jLBj =−+
j
jvVjv[L][L]
jvVV[M][M]
Vv11[L][L]
Vv1[M][M]
0jT,
0jT,
j
0jT,
j
0jT,
+=
+=
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−=
⎟⎠⎞
⎜⎝⎛ −=
Ligand binding to a simple protein
A single binding site
Binding affinity ΔG Gibbs energy for complex formationGibbs energy difference between free and bound states
[M][L][ML]K
RTlnKΔG
A
A
=
−=
⎩⎨⎧
↑↓
⇒↑KΔG
Affinity⎩⎨⎧
><
⇒1K
0ΔGBinding
MLLM ↔+
MML GGGΔ −=
G
MG
MLG
ΔG − RTln[L]0ΔĜi
K[L]1
exp(−ΔĜi/RT)i
K[L]1K[L]n
K[L]1Z
LB +=
+=
MLLM ↔+
ΔHVv1[ML][ML]VQ 1-jjj ⎟
⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−=
0[L][M]n[L] TTLB =−+
K[L]1K[L]nLB +
=
K[L]1Z +=
TT [M]K[L]1
K[L][ML][M]K[L]11[M]
+=
+=
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
nΔH,K,
0.0 0.5 1.0 1.5 2.0 2.5 3.0
-20
-16
-12
-8
-4
0
-8
-4
0
0 30 60 90 120 150 180 210
time (min)
dQ/d
t (μc
al/s
)
[2'CMP]T/[RNase A]T
Q (k
cal/m
ol o
f inj
ecta
nt)
Bovine Pancreatic Ribonuclease A2’CMP
KA 2.9·106 M-1
ΔH -19.3 kcal/moln 1.02
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
0.0
2.0
4.0
6.0
8.0
10.0
0.0
0.5
1.0
0 30 60 90 120 150 180 210
time (min)
dQ/d
t (μc
al/s
)
[PPT]T/[STI]T
Q (k
cal/m
ol o
f inj
ecta
nt)
Soybean Trypsin InhibitorPancreatic Porcine Trypsin
KA 1.5·106 M-1
ΔH 8.4 kcal/moln 1.2
Ligand binding to a “complex” protein
Two binding sites
ΔG2 − 2RTln[L]
ΔG1 − RTln[L]
0ΔĜi
β1[L]
β2[L]2
1exp(−ΔĜi/RT)i
221
221
LB
221
[L]β[L]β1[L]2β[L]βn
[L]β[L]β1Z
+++
=
++=
2ML2LM ↔+
⎟⎟⎠
⎞⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−+
⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−=
21-j2j2
11-jjj
ΔHVv1][ML][ML
ΔHVv1[ML][ML]VQ
0[L][M]n[L] TTLB =−+
221
221
LB [L]β[L]β1[L]2β[L]βn
+++
=
221 [L]β[L]β1Z ++=
T221
22
2
T221
1T2
21
[M][L]β[L]β1
[L]β][ML
[M][L]β[L]β1
[L]β[ML][M][L]β[L]β1
1[M]
++=
++=
++=
0.0
1.0
2.0
3.0
4.0
0 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 1.0 2.0 3.0 4.0
0.0
0.2
0.4
0.6
0.8
1.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
222
111
n,ΔH,βn,ΔH,β
1β4β
1β4β
1β4β
21
2
21
2
21
2
>
<
=
First, perform data analysis with model-free general formalism.Then, once the system is classified, then, apply site-specific models.
What if the binding sites are different, but they display cooperativity?
Extra-thermodynamic considerations (e.g. structural features) may help in deciding which model applies.
Identical and independent binding sites
Non-identical and independent binding sites,or negative cooperativity
Positive cooperativity
Homotropic Interaction Heterotropic Interaction
[M], [A], [MA], [MA2] [M], [A], [B], [MA], [MB], [MAB]
Binding Cooperativity in Proteins
4nn
log[L]n
log[L]nn
nlogn
Hill
2nn
LB
2nn
LB
LB
Hill
LB
LB
=∂∂
∂
⎟⎟⎠
⎞⎜⎜⎝
⎛−
∂=
=
=
Quantifying binding cooperativity
Hill coefficient
Binding capacity
• Measure of the ability for accepting or delivering large quantities of ligand for relatively small changes in ligand concentration
• Efficiency of biochemical signal transduction (response to changes in ligand concentration)
0 ≤ nHill < 1 negative cooperativitynHill = 1 independent binding1 < nHill ≤ n positive cooperativity
0 1 2 3 4 5
0
2
4
6
Q (k
cal/m
ol o
f inj
ecta
nt)
Molar Ratio
β1 5.5·104 M-1
ΔH1 -1.9 kcal/molβ2 4.2·109 M-2
ΔH2 9.9 kcal/mol
4β2/β12 5.4
nHill 1.40
cAMP Receptor Protein + cAMP
Gorshkova et al. (1995). Journal of Biological Chemistry 270 21679-21683
0.0 0.5 1.0 1.5 2.0
0.0
0.2
0.4
0.6
0.8
1.0
[ML i] /
[M] T
nLB
ML
M ML2
0 1 2 3 4
-10
-5
0
Q
(kca
l/mol
of i
njec
tant
)
Molar Ratio
β1 3.0·106 M-1
ΔH1 -10.1 kcal/molβ2 2.4·1012 M-2
ΔH2 -19.1 kcal/mol
4β2/β12 1.1
nHill 1.02
R. solanacearum Lectin + α-Methyl-Fucoside
Kostlanova et al. (2005). Journal of Biological Chemistry 280 27839-27849
0 1 2 3 4
-10
-5
0
Q (k
cal/m
ol o
f inj
ecta
nt)
Molar Ratio
β1 1.0·107 M-1
ΔH1 -9.5 kcal/molβ2 5.4·1013 M-2
ΔH2 -15.0 kcal/mol
4β2/β12 2.2
nHill 1.19
Human Transferrin + Fe3+
Lin et al. (1993). Biochemistry 32 9398-9406
0 1 2 3 4 5 6 7 8
-15
-10
-5
0
Q
(kca
l/mol
of i
njec
tant
)
Molar Ratio
β1 3.3·104 M-1
ΔH1 -23.8 kcal/molβ2 2.6·109 M-2
ΔH2 -33.2 kcal/mol
4β2/β12 9.6
nHill 1.51
H. vulgaris Hemocyanin + Caffeine
Menze et al. (2001). Journal of Experimental Biology 204 1033-1038
0 1 2 3 4
-10
-5
0
Q
(kca
l/mol
of i
njec
tant
)
Molar Ratio
β1 4.6·105 M-1
ΔH1 -9.5 kcal/molβ2 1.4·1010 M-2
ΔH2 -18.1 kcal/mol
4β2/β12 0.27
nHill 0.68
Cyanovirin + Manα1→2Man
Bewley et al. (2001). Journal of the American Chemical Society 123 3892-3902
0 1 2 3 4
-5
0
5
Q (k
cal/m
ol o
f inj
ecta
nt)
Molar Ratio
β1 2.5·107 M-1
ΔH1 3.4 kcal/molβ2 3.3·1012 M-2
ΔH2 -2.5 kcal/mol
4β2/β12 0.022
nHill 0.26
O. nova d(T4G4T4G4) + Telomere Binding Protein α Subunit N-domain
Buczek and Horvath. (2006). Journal of Molecular Biology 359 1217-1234
0 1 2 3 4 5 6 7
-8
-4
0
Q (k
cal/m
ol o
f inj
ecta
nt)
Molar Ratio
β1 3.1·104 M-1
ΔH1 -21.9 kcal/molβ2 3.3·109 M-2
ΔH2 -45.3 kcal/mol
4β2/β12 14.1
nHill 1.56
E. carinatus Ecarpholin S + Suramin
Zhou et al. (2008). Biophysical Journal 95 3366-3380
Ligand binding to a “complex” protein
Two nonidentical and independentbinding sites
ΔG1+ΔG2 − 2RTln[L]ΔG2 − RTln[L]ΔG1 − RTln[L]
0ΔĜi
K1[L]K2[L]
K1K2[L]2
1exp(−ΔĜi/RT)i
( ) ( )( )
( )( ) [L]K1
[L]K[L]K1
[L]K[L]KK[L]KK1
[L]K2K[L]KKn
[L]K1[L]K1[L]KK[L]KK1Z
2
2
1
12
2121
22121
LB
212
2121
++
+=
+++++
=
++=+++=
2ML2LM ↔+
( )⎟⎟⎠
⎞+⎟
⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−+
⎟⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−+
⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−=
211-jj
21-jj
11-jjj
ΔHΔHVv1[LML][LML]
ΔHVv1[LM][LM]
ΔHVv1[ML][ML]VQ
0[L][M]n[L] TTLB =−+
( )( ) 2
2121
22121
LB [L]KK[L]KK1[L]K2K[L]KKn
+++++
=
( ) 22121 [L]KK[L]KK1Z +++=
( ) ( )
( ) ( ) T22121
221
T22121
2
T22121
1T2
2121
[M][L]KK[L]KK1
[L]KK[LML][M][L]KK[L]KK1
[L]K[LM]
[M][L]KK[L]KK1
[L]K[ML][M][L]KK[L]KK1
1]M[
+++=
+++=
+++=
+++=
0.0
1.0
2.0
3.0
4.0
0 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 1.0 2.0 3.0 4.0
0.0
0.2
0.4
0.6
0.8
1.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
222
111
n,ΔH,Kn,ΔH,K
Ligand binding to a “complex” protein
Two identical and independent binding sites
2ΔG − 2RTln[L]ΔG − RTln[L]ΔG − RTln[L]
0ΔĜi
K[L]K[L]
K2[L]2
1exp(−ΔĜi/RT)i
( )
K[L]12K[L]
[L]K2K[L]1[L]2K2K[L]n
K[L]1[L]K2K[L]1Z
22
22
LB
222
+=
+++
=
+=++=
2ML2LM ↔+
0.0 1.0 2.0 3.0 4.0 5.0 6.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
⎟⎟⎠
⎞⎟⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−+
⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−=
H2ΔVv1][ML][ML
ΔHVv1[ML][ML]VQ
1-j2j2
1-jjj
0[L][M]n[L] TTLB =−+
22
22
LB [L]K2K[L]1[L]2K2K[L]n
+++
=
22[L]K2K[L]1Z ++=
T22
22
2
T22T22
[M][L]K2K[L]1
[L]K][ML
[M][L]K2K[L]1
2K[L][ML][M][L]K2K[L]1
1[M]
++=
++=
++=
nΔH,K,
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
Ligand binding to a “complex” protein
Two identical and cooperative binding sites
2ΔG+Δg − 2RTln[L]ΔG − RTln[L]ΔG − RTln[L]
0ΔĜi
K[L]K[L]
αK2[L]2
1exp(−ΔĜi/RT)i
22
22
LB
22
[L]Kα2K[L]1[L]K2α2K[L]n
[L]Kα2K[L]1Z
+++
=
++=
2ML2LM ↔+
( )( )
( )( )
[L]K1[L]K
[L]K1[L]K
[L]Kα2K[L]1[L]K2α2K[L]n
[L]K1[L]K1[L]Kα2K[L]1Z:1 α if
[L]K1[L]K
[L]K1[L]K
[L]Kα2K[L]1[L]K2α2K[L]n
[L]K1[L]K1[L]Kα2K[L]1Z:1 α if
2
2
1
122
22
LB
2122
2
2
1
122
22
LB
2122
++
+=
+++
=
++=++=
<
++
+≠
+++
=
++≠++=
>
αβ4β
21
2 =
nonidentical independent binding sites are equivalent toidentical binding sites with negative cooperativity
( )⎟⎟⎠
⎞+⎟
⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−+
⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛ −−=
ΔhH2ΔVv1][ML][ML
ΔHVv1[ML][ML]VQ
1-j2j2
1-jjj
0[L][M]n[L] TTLB =−+
22
22
LB [L]Kα2K[L]1[L]K2α2K[L]n
+++
=
22[L]Kα2K[L]1Z ++=
T22
22
2
T22T22
[M][L]Kα2K[L]1
[L]Kα][ML
[M][L]Kα2K[L]1
2K[L][ML][M][L]Kα2K[L]1
1[M]
++=
++=
++=
0.0
0.5
1.0
1.5
2.0
0 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 1.0 2.0 3.0 4.0
0.0
0.2
0.4
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
0.0
0.5
1.0
1.5
2.0
0 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 1.0 2.0 3.0 4.0
0.0
0.2
0.4
0.6
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
1α>
1α<
Δhα,nΔH,K,
Δhα,nΔH,K,
A
B
+
Equilibrio conformacional modulado por unión de ligando
A
][11
][][
]][[][][
][][][
][][
LKAB
LAKAB
ALABK
ABK
AA
L
+=
+=
+=
=
L
( )][1ln
][11
LKRTGG
LKKK
AL
A
L
++Δ=Δ
+=
+
Unión de ligando modulada por equilibrio conformacional
A A
B
L
][1
1
][1
][1][
][][][][
][1][
][][][
LK
K
LK
K
KLKLK
BALAALF
LKLK
ALAALF
L
L
L
LBBL
L
LBL
++
+=++
=++
=
+=
+=
( )KRTGGK
KK
LBL
LBL
++Δ=Δ+
=
1ln1
+
+++
Equilibrio de unión modulado por la unión de otro ligando
][][1
1
][][1
][][1][
][][][][
][1][
][][][
LXK
K
LXK
K
XKLKLK
MXMLMMLF
LKLK
MLMMLF
X
L
X
L
XL
LXB
L
LB
++
+=
++=
++=
+=
+=
( )][1ln
][1
XKRTGG
XKKK
XLXL
X
LXL
++Δ=Δ
+=
0.0 2.5 5.0 7.5 10.0
0.0
0.4
0.8
1.2
F B
[L] (μM)
1E-3 0.01 0.1 1 10
0.0
0.4
0.8
1.2
F B
ln([L]/1μM)
KL = 107 M-1
KX = 105 M-1
[X] = 10-4 M
Isothermal Titration Calorimetry&
Differential Scanning Calorimetry
Adrián Velázquez Campoy
+
Every biological process can be decomposed in a sequence of sequential and/or simultaneous elemental processes
Binding Equilibrium
Conformational Equilibrium
BA
Peq CSHKG ΔΔΔΔ ,,,,
⎩⎨⎧<>
−=Δfavorable0
eunfavorabl0EnergyGibbs AB GGG
Gibbs energyEquilibrium constantEnthalpyEntropyHeat Capacity
BA
eqKRTG ln−=Δ
STHG Δ−Δ=Δ
PP T
HC ⎟⎠⎞
⎜⎝⎛∂Δ∂
=Δ
Peq CSHKG ΔΔΔΔ ,,,,
PP T
STC ⎟⎠⎞
⎜⎝⎛∂Δ∂
=Δ
⎟⎟⎠
⎞⎜⎜⎝
⎛Δ+Δ−−Δ+Δ=Δ
0000 ln)()()()(
TTCTSTTTCTHTG PP
⎩⎨⎧<>
−=Δfavorable0
eunfavorabl0EnergyGibbs AB GGG
SH
KG eq
ΔΔ
Δ
,
,
environmental variablesT, pH, ionic strength, solutes
information about the inter- and intramolecular interactions involved in the process
Two calorimetric techniques can be used to perform an exhaustive thermodynamic characterization of binding and conformational equilibrium processes:ITC Determination of Enthalpy, Affinity, Entropy and
of Binding.
DSC Characterization of Thermodynamic Stability.
ΔH, Ka, n, ΔG, ΔS, ΔCP
ΔH, Tm, ΔCP, ΔS, ΔG, K
MLLM ↔+
UnfoldedNative ↔
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
30 40 50 60 70 80 90
0
2000
4000
6000
8000
<ΔC
p>ex
cess (c
al/K
·mol
)
Temperature (oC)
Isothermal Titration Calorimetry
Isothermal Titration Calorimetry
R S
ΔTR ΔT=TS-TR
Isothermal Titration Calorimetry
dQ/dt 0 100 200 300
2.0
3.0
4.0
5.0
dQ/d
t (μc
al/s
)
time (s)
adiabatic chamber
Peltierelement
The measured signal is the amount of heat per time unit, dQ/dt, that must be provided or removed in order to keep ΔT null.
Reference and
Sample cells
R S
ΔT=TS-TR
Isothermal Titration Calorimetry
dQ/dt
0 100 200 300
2.0
3.0
4.0
5.0
dQ/d
t (μc
al/s
)
time (s)
ΔTR
R S
ΔT=TS-TR
Isothermal Titration Calorimetry
dQ/dt
0 100 200 300
2.0
3.0
4.0
5.0
dQ/d
t (μc
al/s
)
time (s)
ΔTR
R S
ΔT=TS-TR
Isothermal Titration Calorimetry
dQ/dt
0 100 200 300
2.0
3.0
4.0
5.0
dQ/d
t (μc
al/s
)
time (s)
ΔTR
R S
ΔT=TS-TR
Isothermal Titration Calorimetry
dQ/dt
0 100 200 300
2.0
3.0
4.0
5.0
dQ/d
t (μc
al/s
)
time (s)
ΔTR
R S
ΔT=TS-TR
Isothermal Titration Calorimetry
dQ/dt
0 100 200 300
2.0
3.0
4.0
5.0
dQ/d
t (μc
al/s
)
time (s)
ΔTR
R S
ΔT=TS-TR
Isothermal Titration Calorimetry
dQ/dt
0 100 200 300
2.0
3.0
4.0
5.0
dQ/d
t (μc
al/s
)
time (s)
∫=f
o
t
tdt
dtdQQ
ΔTR Total heat released or absorbed during the thermal event
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
Isothermal Titration Calorimetry
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
MLLM ↔+
Isothermal Titration Calorimetry
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
MLLM ↔+
Isothermal Titration Calorimetry
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
MLLM ↔+
Isothermal Titration Calorimetry
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
MLLM ↔+
Isothermal Titration Calorimetry
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
MLLM ↔+
Isothermal Titration Calorimetry
0.0
0.5
1.0
1.5
2.0
2.5
3.00 30 60 90 120
dQ/d
t (μc
al/s
)
time (min)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol)
[Ligand]T/[Macromolecule]T
ΔH
n
Ka ≡ 1/Kd
MLLM ↔+
Isothermal Titration Calorimetry
ITC: Advantages
Complete thermodynamic charaterization: ΔH, Ka, n, ΔG and ΔS
Direct determination of the binding enthalpy (with no additionalassumptions)
Heat is a universal signal
Absence of reporter labels
Non-destructive technique
10 20 30 40
6.0
8.0
10.0
ΔH (k
cal/m
ol)
T (oC)
PP T
HC ⎟⎠⎞
⎜⎝⎛∂Δ∂
=Δ
)()()( 00 TTCTHTH P −Δ+Δ=Δ
Determination of the Binding Heat Capacity
-2 0 2 4 6 8 10
4.0
6.0
8.0
10.0
12.0
ΔH (k
cal/m
ol)
ΔHbufferionization (kcal/mol)
bufferionization
0 HnHHHΔ+Δ=Δ +
Determination of Proton Transfer Processes Coupled to Ligand Binding
ΔH*
ΔHbuffer,ionization
ΔHp
ΔH0 binding enthalpy independent of the buffer
nH+ number of protons exchanged between M-L complex and solution
macromolecule
ligand
protonbuffer
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
2.0
4.0
6.0
8.0
10.0
Q (k
cal/m
ol o
f inj
ecta
nt)
[Ligand]T/[Macromolecule]T
0.0 0.5 1.0 1.5 2.0 2.5 3.0
[Ligand]T/[Macromolecule]T
0.0 0.5 1.0 1.5 2.0 2.5 3.0
[Ligand]T/[Macromolecule]T
time (min)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
time (min)
dQ/d
t (μc
al/s
)
time (min)
7.0][10
T
14
== −
MKMK
a
a
70][10
T
16
== −
MKMK
a
a
7000][10
T
18
== −
MKMK
a
a
ITC: Considerations
riment)hours/expe 2( techniqueanalyticfast mg)1(~sampleofamount
01010 1814
<••
≠Δ•≤≤• −−
HMKM a
Displacement Experiment
Scheme
0 20 40 60 80 100
0.0
0.5
1.0
0 20 40 60 80 100
-1.0
-0.5
0.0
0 20 40 60 80 100
-1.0
-0.5
0.0
Tight-Binding InhibitorWeak-Binding Inhibitor
Tight-Binding Inhibitor displacing the Weak-
Binding Inhibitor
0aK
XaK
aK ][1][0
XKXKHHH X
a
XaX
+Δ−Δ=Δ
][1
0
XKKK X
a
aa +=
Extension of the Practical Limits for Reliable Affinity Determination
-1.0
-0.5
0.0
0 10 20 30 40 50 60 70 80 90 100
0.0 0.5 1.0 1.5 2.0 2.5
-8.0
-6.0
-4.0
-2.0
0.0
Time (min)dQ
/dt (μc
al/s
)Q
(kca
l/mol
of i
njec
tant
)
[Inhibitor]T/[HIV-1 PR WT]T
0.0
0.5
1.0
0 10 20 30 40 50 60 70 80 90 100 110
0.0 0.5 1.0 1.5 2.0 2.5
0.0
2.0
4.0
6.0
8.0
-1.0
-0.5
0.0
0 10 20 30 40 50 60 70 80 90
0.0 0.5 1.0 1.5
-16.0
-12.0
-8.0
-4.0
0.0
Protease Protease + Ac-PepstatinProtease
KNI-764 KNI-764Ac-Pepstatin
0aK
][1
0
XKKK X
a
aa +=X
aK
Measuring High Binding Affinity
pM32
M1030
-1100
=
⋅=
d
a
K
K
Differential Scanning Calorimetry
Differential Scanning Calorimetry
Differential Scanning Calorimetry
30 40 50 60 70 80 90
0
2000
4000
6000
8000
<ΔC
P>ex
cess (c
al/K
·mol
)
T (oC)
R S
ΔTR
ΔT=TS-TR
dQ/dt
T0↑ ΔTS
The measured signal is the amount of heat per time unit, dQ/dt, that must be provided or in order to keep ΔT null.Later, thermal power is converted to heat capacity.
adiabatic chamber
Peltierelement
Reference and
Sample cells
Differential Scanning Calorimetry
30 40 50 60 70 80 90
0
2000
4000
6000
8000
<ΔC
P>ex
cess (c
al/K
·mol
)
T (oC)
R S
ΔTR
ΔT=TS-TR
dQ/dt
T0↑ ΔTS
0°C
100°C
Differential Scanning Calorimetry
30 40 50 60 70 80 90
0
2000
4000
6000
8000
<ΔC
P>ex
cess (c
al/K
·mol
)
T (oC)
R S
ΔTR
ΔT=TS-TR
dQ/dt
T0↑ ΔTS
0°C
100°C
Differential Scanning Calorimetry
30 40 50 60 70 80 90
0
2000
4000
6000
8000
<ΔC
P>ex
cess (c
al/K
·mol
)
T (oC)
R S
ΔTR
ΔT=TS-TR
dQ/dt
T0↑ ΔTS
0°C
100°C
Differential Scanning Calorimetry
30 40 50 60 70 80 90
0
2000
4000
6000
8000
<ΔC
P>ex
cess (c
al/K
·mol
)
T (oC)
R S
ΔTR
ΔT=TS-TR
dQ/dt
T0↑ ΔTS
0°C
100°C
Differential Scanning Calorimetry
30 40 50 60 70 80 90
0
2000
4000
6000
8000
<ΔC
P>ex
cess (c
al/K
·mol
)
T (oC)
R S
ΔTR
ΔT=TS-TR
dQ/dt
T0↑ ΔTS
0°C
100°C
Differential Scanning Calorimetry
30 40 50 60 70 80 90
0
2000
4000
6000
8000
<ΔC
P>ex
cess (c
al/K
·mol
)
T (oC)
R S
ΔTR
ΔT=TS-TR
dQ/dt
T0↑ ΔTS
0°C
100°C
30 40 50 60 70 80 90
0
2000
4000
6000
8000
<ΔC
P>ex
cess (c
al/K
·mol
)
T (oC)
Tm
ΔH(Tm)
ΔCP
UnfoldedNative ↔
Differential Scanning Calorimetry
30 40 50 60 70 80 90
0
2000
4000
6000
8000
<ΔC
P>ex
cess (c
al/K
·mol
)
T (oC)
UnfoldedNative ↔Differential Scanning Calorimetry
∫ >Δ<=Δ f
o
T
T excessPm dTCTH )(
∫>Δ<
=Δ f
o
T
TexcessP
m dTT
CTS )(
⎟⎟⎠
⎞⎜⎜⎝
⎛Δ+Δ−−Δ+Δ=Δ
mPmmPm T
TCTSTTTCTHTG ln)()()()(
0 20 40 60 80 100-12.0
-9.0
-6.0
-3.0
0.0
3.0
6.0
ΔG (k
cal/m
ol)
T (oC)
0 20 40 60 80 100
0
2000
4000
6000
8000
10000
12000
14000
<Δ
CP>
exce
ss (c
al/K
·mol
)
T (oC)
UnfoldedteIntermediaNative ↔↔
Differential Scanning Calorimetry
Unfolded2Native2 ↔
Differential Scanning Calorimetry
40 60 80
0
2000
4000
6000
8000
10000
<ΔC
P>ex
cess (c
al/K
·mol
)
T (oC)0.00 0.02 0.04 0.06 0.08 0.10
60
62
64
66
68
T m (o C
)[Macromolecule]T,monomer (mM)
20 40 60 80 100
0
2000
4000
6000
8000
10000
<ΔC
P>ex
cess (c
al/K
·mol
)
T (oC)0 5 10 15 20
60
63
66
69
72
75
T m (o C
)
[Ligand]T/[Macromolecule]T
( )][1ln0 LKRTGG a++Δ=Δ
Determination of Binding Affinity:Effect of Ligand Binding on the Stability
of the Macromolecule