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180o)
)90o
Morikis, Roy, Newlon, Scott, Jennings (2002) European Journal of Biochemistry.
Hydrophobicity vs charges
Electrosta&c calcula&ons using con&nuum dielectric models for proteins
The activation helix-coil transition
Morikis, Elcock, Jennings, McCammon (2003) Biophysical Chemistry
His108 His132
His137
His119
His121
Catalytic site His108 His132
His137
His119
His121
Catalytic site
GART Helix-coil transition & catalysis
NSP In association with BioMed Central © 2004 New Science Press Ltd new-science-press.com
Catalytic triad. The catalytic triad of aspartic acid, histidine and serine in (a) subtilisin, a bacterial serine protease, and (b) chymotrypsin, a mammalian serine protease. The two protein structures are quite different, and the elements of the catalytic triad are in different positions in the primary sequence, but the active-site arrangement of the aspartic acid, histidine and serine is similar.
Functional motif Identifying motifs from sequence alone is not straightforward
His40 Ser195
Asp194
Ile16
Profactor
His40 Ser195
Asp194
Ile16
Zymogen
His40 Ser195
Asp194
Ile16
Ile16
Profactor Zymogen
&
His57
Ser195
Asp102
Profactor
His57
Ser195 Asp102
Zymogen
His57
Ser195 Asp102
Profactor Zymogen &
Profactor
Arg218
Asp189
Ser195
Zymogen
Arg218
Asp189
Ser195
Profactor Zymogen
&
Arg218
Asp189
Ser195
Arg218
Profactor Zymogen1HFD 1FDPa
pK(app) pK(app)Ile16 7.5 7.3 7.4His40 6.3 2.5 2.8His57 6.3 8.6 8.0
Asp102 4.0 -0.7 1.5Asp189 4.0 0.2 2.7Asp194 4.0 -2.0 -0.6Arg218 12.0 14.8 14.2
Res. No. pK(model)
Factor D: Interactions between residues with unusual pKa values
Histidine acid-base equilibrium (backbone & side chain)
backbone Side chain backbone
pKa values for free amino acids in solution
Acidic residues: C-ter: 3.8 Asp: 4.0 Glu: 4.4 Cys: 8.3 (non S-S bonded) Tyr: 9.6
Basic residues: His: 6.3 N-ter: 7.5 Lys: 10.4 Arg: 12.0
Ka AH A– + H+
RT
ionG
e
Δ−
=+−
=[AH]
]][H[AaK
[AH]][AlogapKpH
−+=
alogKapK −=Henderson-Hasselbalch
]log[HpH +−=
Side Chains
0 2 4 6 8 10 12 14-12-10-8-6-4-2024
25mM 50mM 75mM 100mM 125mM 150mM
0 2 4 6 8 10 12 14-60
-40
-20
0
20
40
60
Q(C3d-CR2) Q(C3d) Q(CR2) ΔQ
pH and ionic strength effect on association C-ter Asp Glu
His N-ter
Tyr Lys Arg
Cha
rge
ΔΔ
Gio
n (kc
al/m
ol)
pH
Isoelectric points 50 mM
Δ<Q>=0
)QQQ(RT.pH
)pH(G
CRdCCR:dC
assoc
23233032 〉〈−〉〈−〉〈
=∂
Δ∂
Morikis & Zhang (2006) J Non-Cryst Solids
Tanford, 1970
Free proteins in random diffusion
Encounter complex
Final complex
Recognition
Long-range interactions:
electrostatic macrodipoles
Binding
Long-range electrostatic interactions Short-range interactions:
Electrostatic, hydrophobic, H-bond, van der Waals specific residues
Removal of H2O from interface Local structural rearrangements
Association = Recognition + Binding
+ :
Association
ΔG1,ion(pH) ΔG2,ion(pH) ΔGcomplex,ion(pH)
ΔG(neutral)
ΔG(pH)
–
+ + – + – +
–
+
–
+ –
+
–
+ – +
+ –
+
– + +
–
+ – + – +
Neutral
Ionized
Ionization process
–
+ –
+
–
+ – + +
–
+ – +
+
–
–
0 2 4 6 8 10 12 14-60
-40
-20
0
20
40
60
Q(C3d-CR2) Q(C3d) Q(CR2) ΔQ
Cha
rge
pH0 2 4 6 8 10 12 14
-60
-40
-20
0
20
40
60
Q(C3d-CR2) Q(C3d) Q(CR2) ΔQ
Cha
rge
pH0 2 4 6 8 10 12 14
-12
-8
-4
0
4
8
12
25mM 50mM 75mM 100mM 125mM 150mM
ΔΔ
Gio
n(k
cal/m
ol)
pH0 2 4 6 8 10 12 14
-12
-8
-4
0
4
8
12
25mM 50mM 75mM 100mM 125mM 150mM
ΔΔ
Gio
n(k
cal/m
ol)
pH
Morikis & Zhang (2006) J Non-Cryst Solids
uf ion
G−
ΔΔ
0.1 M
1 M
2 3 4 5 6 7-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
AMS D7N D7K
2 3 4 5 6 7-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
AMS D7N D7K
pH pH
D3
E38 E47
E9 D23 D7
D67
D80
R78
R33 K54 K86
R6
K63
R93
R30
Improvement of Fibronectin stability: Scaffold for Monobody design
Mallik, Zhang, Koide, Morikis (2008) Biotechnology Progress
ufneutralG −Δ
ufG −Δ
fionGΔ u
ionGΔ
ufneutralG −Δ
ufG −Δ
fionGΔ u
ionGΔ
+ –
+–+
––
+–+–––++
–+
++–
ΔG (neutral)h-c
ΔG (pH)h-c
ΔG (pH)h,ion ΔG (pH)c,ion
h: helix c: coil
neutral
ionized
Folded à Unfolded Helix à Coil
pH dependence of conformational transitions
Isoelectric focusing Isoelectric point (pI): pH at which the biomolecule (or ampholyte) has zero charge It is used to separate biomolecules Suppose that we can create, in a gel or capillary, a stable pH gradient between the anode and cathode Molecules would migrate until each reached the pH equaled its pI Bands would form at different points in the pH gradient Bands would remain sharp, as if a biomolecule diffused away from its pI position it would experience a force pulling it back
How such a pH gradient can be established and maintained? The cathode and anode departments become basic and acidic, respectively through the reactions
22
2
442
22
OeHOHHeH
++→
→+−+
−+
Electrolysis of water The pH changes resulting from these reactions are confined to regions near the electrodes Ampholytes with lower pI concentrate near the anode, whereas those with higher pI concentrate near the cathode
Proteomics experiment: MS fingerprinting
2D gel electrophoresis: separation according to charge (pH) & molecular weight
Peptide sequencing by tandem MS spectrometry (MS/MS)
CID: collision-induced dissociation In a chamber filled with a neutral gas (Ar or Xe) that breaks the peptide backbone
Tandem MS: coupling of two or more experiments
TOF: Time-of-flight mass spectrometer
Positive ions of the substance to be analyzed
21
2
221
/
mZeESv
ZeESmv
⎟⎠
⎞⎜⎝
⎛=
=
2
21
2
2
⎟⎠
⎞⎜⎝
⎛=
⎟⎠
⎞⎜⎝
⎛==
DteES
Zm
DZeESm
vDt
/
Field region
Ion generation
Units: Daltons 1 Da = 1 g/mol
Mass spectrometry (MS) of biomolecules Determination of biomolecular mass Determination of biomolecular sequence Protein identification (proteomics) Study of conformational transitions, protein folding, and protein interactions in combination with H/D exchange
Mass spectrometry (MS) of biomolecules Measures degradation products resulting from their collisions with electrons à molecular ions Does not actually measure mass but m/Z (mass over charge) ratio Molecular ions with smaller masses or larger # of charges have higher velocity, which is used to resolve various molecular species according to m/Z
The molecule of interest as a charged ion is placed into the gas phase, then the molecular species must be separated according to their masses, and finally the molecular ions must be detected
Difficulty in ionizing proteins compared to small molecules For small molecules: we simply heat the sample For proteins: MALDI or ESI MALDI: matrix-assisted laser desorption/ionization à Molecular mass measurement à Study of proteins up to 300,000 molecular mass ESI: electrospray ionization à Molecular mass & sequence determination à Study of proteins up to 500,000 molecular mass
Very small amounts of sample à ESI MS: femtomole-picomole à NanoESI MS: zeptomole-femtomole à MALDI MS: femtomole
Example of MALDI spectrum Molecular mass measurement
More than one ionic species are obtained Integral fraction of that with Z=1
ESI MS
Electrostatically-charged nozzle
Solute & solvent
Droplets accelerate away from the tip – solvent evaporates – charge concentration become high & Coulombic forces overcome surface tension – resulting in dispersion of the drop into a spray of smaller droplets.
Genome: the complete spectrum of genetic material of a cell Proteome: the complete protein composition of a biochemical system (e.g. all proteins within a cell) MS determines post-translational modifications à methylation, phospohrylation, glycosylation, etc
Ka AH A– + H+ - = + ] log[H pH
[AH]]][H[AKa
+−
= [AH]][AlogpKpH a
−
+=aa logKpK −=
Henderson-Hasselbalch
1011
01
,aRTG
,a KlnRTGeK −=→=−
2022
02
,aRTG
,a KlnRTGeK −=→=−
alog.elogalogaln 3032==
( ) a,a,ao pKRT.KlnKlnRTGGG Δ=−−=−=Δ 303212
01
02
aP pKRT.G Δ=Δ 30320Perturbation in the ionization free energy:
Change in pKa in response to local electrostatic environment
Favorable Coulombic Interaction:
+ –
Unfavorable Coulobic Interaction:
+ + – –
Desolvation effect (transfer from solvent to hydrophobic environment):
+ –
+ Basic amino acid – Acidic amino acid
Arrows denote shifts in pKa values with respect to the pKa values of free amino acids in solution
Eelectro =q1q2
Dmediumr
ε =Dmedium
Dvacuum
=Dmedium
κε0k = 4πSI unitsDmedium = 4πε0ε
Coulombic energy
Coulomb’s law
Coulomb’s law describes a pairwise interaction The potential energy for a single isolated charge in a dielectric medium is modeled by its self-energy
DreZZVe2
21= 04πε=D
Coulomb’s law does not account for shielding of electrostatic interactions by solvent salt ions à need more elaborate Poisson-Boltzmann treatments Coulomb’s law is typically used in force field potential energies
Sself DR
)Ze(V2
21
= always positive RS is Stokes radius of ion or molecule
Dielectric constant: Polarizability of medium
Self-energy
The self-energy of an ion is given by
Consider the work done to bring a small increment of charge, dq’, to the surface of a sphere, already carrying charge, q’
Uself =1
4πε0εq2
2RS
δU =!qδ !q
4πε0εRS
U =1
4πε0εRS!q d !q = 1
2q2
4πε0εRS0
q
∫
Interactions with environment
Potential energies involving charges &/or dipoles depend on the polarity of the intervening medium Charge/dipole interactions are shielded in a polar medium and thus weakened Vacuum: least polarizable medium with dielectric constant κε0 = 4π 8.85 x 10-12 C2/(J m) κ = 4π ε0: vacuum permitivity ε0 = 8.85 x 10-12 C2/(J m) ß SI units ε0 = 1/(4π) ß esu units Energy: inversely proportional to D Water: D = 78.5κε0 @ room T
ε =Dmedium
κε0
SI units: ε =Dmedium
Dvaccum
=Dmedium
4πε0⇒ Dmedium = 4πε0ε
cgs units: 4πε0 = 1 κ = 4π for unit charge
SI units
• Charge: C • Energy: J • Distance: m • Potential: V = J C-1 • Capacitance: F = C V-1
19
12 2 -10
23 -1
24 -1
0
1.602 10 C
8.854 10 C J m
6.022 10 mol
1.386 10 J m mol4
c
av
av c
e
NN e
ε
πε
−
−
−
= ×
= ×
= ×
= ×
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