PROTEIN PHYSICSPROTEIN PHYSICS

LECTURE 6LECTURE 6

Electrostatics in uniform media: Electrostatics 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

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 = ? = ?

Good estimate forGood estimate fornon-uniform medianon-uniform media

U = qU = q11qq22//effeffr =r =

((qq11//11))((1212/r/r))((qq22//22)) ++ ++ ++

–– – – – –

ΔΔU = qU = q22//2r2r

effeff ≈ 200 !!≈ 200 !!

≈40

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: = 80 is not a bad approximation= 80 is not a bad approximation

(much better than (much better than = 1 or 3 !!) = 1 or 3 !!)

(salt does not dissolve at (salt does not dissolve at <40 at 3<40 at 3ÅÅ))

30-40 at 2-330-40 at 2-3ÅÅ

2.5 [pH] 2.5 [pH] 2.3RT = 6RT = 3.5 kcal/mol at 2.3RT = 6RT = 3.5 kcal/mol at 2.5-2.5-33ÅÅ

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 itsr if itsr 22

differs from the media’s differs from the media’s 11::

U ~ U ~ qq • • [([(11 - - 22)/()/(1122)] )] •• 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!

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

e.g.:e.g.:

electrostatics with Debye-Helectrostatics with Debye-Hückel screening: ückel screening:

U = [U = [qq11qq22//r]r]••exp(-r/D)exp(-r/D)

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

Coordinate bonds (with ZnCoordinate bonds (with Zn++++, Fe, Fe++++++,…) ,…)

CHARGE near the surface of PROTEINCHARGE near the surface of PROTEIN

Electric field in Electric field in non-uniform media = ??non-uniform media = ??

EXERSIZE:EXERSIZE:charge near the surface of conductor (metal)charge near the surface of conductor (metal)

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electric field electric field goes to high goes to high

CHARGE near the surface of PROTEINCHARGE near the surface of PROTEIN

non-uniform media:non-uniform media:electric field avoids low electric field avoids low

CHARGE CHARGE qq near the surface of PROTEINnear the surface of PROTEIN

non-non-uniform uniform mediamedia

qq

qq

At atomic distances: At atomic distances: = ? = ?