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 interfaceIn 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]••UUin 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