Bien 249 w14 Project Supplement

Titra&ons  in  Biology    

Why  charge  is  important  in  biology?  

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  

A  protein  surrounded  by  water  creates  dielectric  boundaries  

The  electrosta&c  poten&al  generated  by  a  protein    

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

Backbone acid-base equilibrium for free amino acids

NH3+

COO-

NH2

COOH

Histidine acid-base equilibrium (backbone & side chain)

backbone Side chain backbone

Histidine tautomers

Rare

neutral charged neutral

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

Graphical demonstration

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

Example

Example O’Farrell technique (2D)

Charge

Molecular weight

Proteomics experiment: MS fingerprinting

2D gel electrophoresis: separation according to charge (pH) & molecular weight

Properties of proteolytic enzymes

Strategy for determining protein sequence from proteolytic fragments

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

Matrix absorbs strongly at the laser wavelength

MALDI MS

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.

ESI MS Example 1: peptide

ESI MS Example 2: protein

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

Electrostatic fields

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

−

−

−

= ×

= ×

= ×

= ×

freepair

AH f↓ΔU

neutral

AHp

ΔU free

# →##ΔU pair

# →##

Af−

↓ΔUcharged

Ap−

++

H +

H +

ΔU∑ = 0

For acidic amino acid:

How about for basic amino acid? How about for desolvation?

Hint for class example