Download Lecture 6 - The Protein Physics Laboratory

PROTEIN PHYSICS
LECTURE 6
Electrostatics in uniform media:
potential 1 = q1/r
Interaction of two charges:
U = 1q2 = 2q1 = q1q2/r
 = 1 vacuum
  3 protein
  80 water
Protein/water interface
In non-uniform media:
At atomic distances:
=?
=?
CHARGE
inside
PROTEIN
Water => vacuum:
U  +100 kcal/mol
Water => PROTEIN
R  1.5 - 2 Å
U  +30 - 40 kcal/mol
CHARGE inside
PROTEIN:
VERY BAD
Non-uniform media:
eff = ?
ΔU = q2/2r
≈40
U = q1q2/effr =
(q1/1)(12/r)
(q2/2)
+++
– – –
Good estimate for
non-uniform media
eff ≈ 200 !!
effective
in nonuniform
media
Large distance:
 = 80
Atomic distance:
=?
intermed.
“vacuum”, ε~1?
but absence
of intermed.
dipoles can
only increase
interaction…
At atomic distances in water:
 = 80 is not a bad approximation
(much better than  = 1 or 3 !!)
(salt does not dissolve at <40 at 3Å)
  30-40 at 2-3Å
2.5 [pH]  2.3RT = 6RT = 3.5 kcal/mol at 2.5-3Å
Protein engineering experiments:
(r) = pH  2.3RT  eff(r)
Dipole interactions
(e.g., H-bonds):
Quadruple interactions
(HO)-1/3-H+1/3::::::(OH)-1/3-H+1/3
Also: charge-dipole, dipole-quadruple, etc.
Potentials:
dipole ~ 1/r2
quadruple ~ 1/r3
Electrostatic interactions also occur between
charge (q) and non-charged body if itsr 2
differs from the media’s 1:
4
U ~ q • [(1 - 2)/(12)] • V • (1/r )
at large
In water: repulsion of charges from non-polar
molecules (since here 1>>2);
in vacuum (where 1<2) : just the opposite!
r
Debye-Hückel screening
of electrostatic by ions:
U = [q1q2/r]•exp(-r/D) ;
in water: D = 3Å•I-1/2;
Ionic strength I = ½iCi(Ziion)2 .
Usually: I  0.1 [mol/liter]; D  8Å.
Electrostatics is an example of a multi-body
(charge1, charge2, media, ions) interaction
e.g.:
electrostatics with Debye-Hückel screening:
U = [q1q2/r]•exp(-r/D)
Electrostatics is T-dependent;
U = (1/)•(q1q2/r)
is free energy;
TS = T•(-dU/dT) = -T• [d(1/)/dT]•(q1q2/r) =
= [dln()/dlnT]•U
in water: when T grows from 273o to 293oK (by 7%),
 decreases from 88 to 80 (by 10%):
TS ≈ -1.3 U; H  -0.3U
In water the entropic term (-TS) is the main
for electrostatics!
S-S bonds (Cys-Cys)
exchange
Coordinate bonds (with Zn++, Fe+++,…)
CHARGE near the surface of PROTEIN
Electric field in
non-uniform media = ??
EXERSIZE:
charge near the surface of conductor (metal)
______________________________________
______________________________________
electric field
goes to high 
CHARGE near the surface of PROTEIN
non-uniform media:
electric field avoids low 
CHARGE
q
near the surface of PROTEIN
q
q
nonuniform
media
At atomic distances:
=?