protein physics lectures 5-6 elementary interactions: hydrophobic & electrostatic;
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PROTEIN PHYSICS LECTURES 5-6 Elementary interactions: hydrophobic & electrostatic; SS and coordinate bonds. Hydrophobic effect. Concentration of C 6 H 12 in H 2 O: 50 times less than in gas! WHY?. H 2 O. G int : “ Free energy of interactions ” - PowerPoint PPT PresentationTRANSCRIPT
PROTEIN PHYSICSPROTEIN PHYSICS
LECTURES 5-6LECTURES 5-6
Elementary interactions:Elementary interactions:hydrophobichydrophobic
&&
electrostatic;electrostatic;SS and coordinate bondsSS and coordinate bonds
Hydrophobic effectHydrophobic effect
Concentration of CConcentration of C66HH1212
in Hin H22O:O:
50 times 50 times lesslessthan in gas!than in gas!
WHY?WHY?
HH22OO
GGintint : “: “Free energy of interactionsFree energy of interactions””
(“mean force potential”)(“mean force potential”)
Chemical potential: Chemical potential:
GG(1)(1) = G = Gint int - T- T••kkBBln(Vln(V(1)(1)) ) G Gint int + T+ T••kkBBln[C] ln[C]
EQUILIBRIUM for transition EQUILIBRIUM for transition
of moleculeof molecule 11 fromfrom A A toto B: B: GGAA(1) (1) = G= GBB
(1) (1)
chemical potentials inchemical potentials in AA andand BB are equalare equal
GGintintAAB B = G= Gintint
B B – G– GintintAA
GGintintAABB= k= kBBTT••ln([Cln([CinAinA]/[C]/[CinBinB])])
======================================================================================================
Experiment: Experiment: GG intint
AABB= k= kBBTT••ln([Cln([C11 inin AA]/[C]/[C11 inin BB])])
SSintintAABB = -d( = -d(GGintint
AABB)/dT)/dT
HHintintAABB = = GGintint
AABB +T +TSSintintAABB
CC66HH1212
[C] of C[C] of C66HH1212
in Hin H22O:O:
50 times 50 times lesslessthan in gas;than in gas;100000 times 100000 times less less than in than in liquid Cliquid C66HH1212
T=298T=29800K=25K=2500CC
-2/3-2/3 +1/3 +1/3
Loss: Loss: S S usual usual casecase
-2/3-2/3
Loss: Loss:
LARGE LARGE EE rare rare casecase
H-bond: directedH-bond: directed
““hydrophobic bond”hydrophobic bond”
High High heat capacity heat capacity d(d(H)/dT:H)/dT:Melting ofMelting of““iceberg”iceberg”
20-25 cal/mol per 20-25 cal/mol per ÅÅ22 of molecular of molecularaccessible non-polar surfaceaccessible non-polar surface
Octanol Octanol Water Water
____________largelargeeffecteffect
______________ smallsmall
____________ largelarge
ElectrostaticsElectrostatics in uniform media: in uniform media:
potential potential 11 = q = q11//rr
Interaction of two charges: Interaction of two charges:
U = U = 11qq22 = = 22qq11 = q = q11qq22//rr = 1 vacuum= 1 vacuum 3 protein3 protein 80 water80 water Protein/water interfaceProtein/water interface
In non-uniform media:In non-uniform media: = ? = ?
At atomic distances:At atomic distances: = ? = ?
Water => PROTEINWater => PROTEIN ((εε3)3)
RR 1.5 - 2 1.5 - 2 ÅÅU U +30 - 40 kcal/mol +30 - 40 kcal/mol
CHARGE inside CHARGE inside PROTEIN: PROTEIN: VERY BADVERY BAD
CHARGECHARGE insideinsidePROTEINPROTEIN
Water => vacuum: Water => vacuum: UU +100 kcal/mol +100 kcal/mol
Non-uniform media: Non-uniform media: effeff = ? = ?
= q= q//11rr
- - - -- - --
= (q= (q//11)/r)/r
Good estimate forGood estimate fornon-uniform medianon-uniform media
++ --++ -- ++
–– ++ –– ++ ––
effeff ≈ 200 !!≈ 200 !!
eff≈40
= q= q//rreffeff in positions: in positions:
-- - -- - --
effectiveeffective
in non-in non-uniform uniform mediamedia
Large distance: Atomic distance:Large distance: Atomic distance:
= = 8080 = ? = ?
intermed.intermed. “ “vacuum”, vacuum”, εε ~~ 11?? but absence but absence of intermed.of intermed. dipoles can dipoles can only increaseonly increase interaction…interaction…
At atomic distances in water:At atomic distances in water: 1) 1) =80 is not a bad approximation (much better than =80 is not a bad approximation (much better than = 1 or 3 !!) = 1 or 3 !!) (salt does not dissolve, if (salt does not dissolve, if <50 at 3<50 at 3Å!Å!))
2)2) [H][H]1/21/2=10=10-1.75-1.75 [H] [H]1/21/2=10=10-4.25-4.25 ee--GGelel/RT/RT
30-40 at 30-40 at ~2.5~2.5Å!Å!
GGelel = 2.5 = 2.5 ln(10) ln(10) RT RT 6RT 6RT 3.5 kcal/mol at 3.5 kcal/mol at 2.52.5ÅÅ
Protein engineeringProtein engineering experiments: experiments:
(r) = (r) = pH pH 2.3RT 2.3RT effeff(r) (r)
DipoleDipole interactions interactions (e.g., H-bonds):(e.g., H-bonds):
(HO)(HO)-1/3-1/3-H-H+1/3+1/3::::::(OH)::::::(OH)-1/3-1/3-H-H+1/3+1/3
QuadrupleQuadruple interactions interactions
Also: charge-dipole, dipole-quadruple, etc.Also: charge-dipole, dipole-quadruple, etc.
Potentials: Potentials: dipoledipole ~ 1/ ~ 1/rr2 2 quadruplequadruple ~ 1/ ~ 1/rr33
Electrostatic interactions also occur between Electrostatic interactions also occur between charge (charge (qq) and non-charged ) and non-charged bodybody if its if its 22 differs differs
from the media’s from the media’s 11::
U ~ U ~ qq • • [[1/1/22 – – 1/1/11] ] •• VV •• (1/ (1/rr
44) ) at largeat large r r
In water: repulsion of charges from non-polar In water: repulsion of charges from non-polar molecules (since here molecules (since here 11>>>>22)); ;
in vacuum in vacuum (where (where 11<<22)) : just the opposite!: just the opposite!
++
++
++
--
--
--
22
VV
1
Debye-HDebye-Hückel screening ückel screening of electrostatic by ions:of electrostatic by ions:
U = [qU = [q11qq22//r]r]••exp(-r/D) exp(-r/D) ; ; in water:in water: D = 3Å• D = 3Å•II-1/2-1/2;;
Ionic strength Ionic strength I = I = ½½iiCCii(Z(Ziiionion))2 2 . .
Usually:Usually: II 0.1 [mol/liter] 0.1 [mol/liter]; ; D D 8Å. 8Å.
Electrostatics is an example of a multi-bodyElectrostatics is an example of a multi-body((charge1charge1, , charge2charge2, , mediamedia, , ionsions) interaction) interaction
Electrostatics is T-Electrostatics is T- dependent;dependent;
U = (1/U = (1/))••(q(q11qq22/r)/r)
is free energy;is free energy;
TSTS = T = T••(-dU/dT) = -T(-dU/dT) = -T•• [d(1/[d(1/)/dT])/dT]••(q(q11qq22/r) =/r) =
= [dln(= [dln()/dlnT])/dlnT]••UU
in water: when in water: when TT grows from 273 grows from 273oo to 293 to 293ooK (by 7%),K (by 7%),
decreasesdecreases from 88 to 80 (by 10%): from 88 to 80 (by 10%):
TSTS ≈ -≈ -1.31.3 U; H U; H -0.3 -0.3 UU
In water the entropic term (In water the entropic term (-TS-TS) is the main) is the mainfor electrostatics!for electrostatics!
S-S bonds (Cys-Cys)S-S bonds (Cys-Cys)
exchangeexchange
S-S bond is not stableS-S bond is not stable within a cellwithin a cell
Coordinate bonds (with ZnCoordinate bonds (with Zn++++, Fe, Fe++++++,…) ,…)
- - - -- - --
= q= q//rr11