PROTEIN PHYSICS LECTURE 6

Electrostatics in uniform media: potential  1 = q 1 /  r Interaction of two charges: U =  1 q 2 =  2 q 1 = q 1 q 2 /  r  = 1 vacuum  = 1 vacuum   3 protein   3 protein   80 water   80 water Protein/water interface In non-uniform media:  = ? At atomic distances:  = ?

Water => PROTEIN R  Å  U  kcal/mol CHARGE inside PROTEIN: VERY BAD CHARGE inside insidePROTEIN Water => vacuum:  U  +100 kcal/mol

Non-uniform media:  eff = ?

Good estimate for non-uniform media U = q 1 q 2 /  eff r = (q 1 /    1 )  (    12 /r)  (q 2 /    2 ) – – –– – – – – –– – – ΔU = q 2 / 2r     eff ≈ 200 !!    ≈40

 effective in non- uniformmedia

Large distance: Atomic distance:  = 80  = ?  = 80  = ? intermed. intermed. “vacuum”, ε ~ 1? “vacuum”, ε ~ 1? but absence but absence of intermed. of intermed. dipoles can dipoles can only increase only increase interaction… 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)   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): (HO) -1/3 -H +1/3 ::::::(OH) -1/3 -H +1/3 Quadruple interactions Also: charge-dipole, dipole-quadruple, etc. Potentials:  dipole ~ 1/  r 2  quadruple ~ 1/  r 3  dipole ~ 1/  r 2  quadruple ~ 1/  r 3

Electrostatic interactions also occur between charge (q) and non-charged body if itsr  2 differs from the media’s  1 : U ~ q [(  1 -  2 )/(  1  2 )] V (1/ r 4 ) at large r In water: repulsion of charges from non-polar molecules (since here  1 >>  2 ); in vacuum (where  1 <  2 ): just the opposite! in vacuum (where  1 <  2 ) : just the opposite!

Debye-Hückel screening of electrostatic by ions: U = [q 1 q 2 /  r]exp(-r/D) ; in water: D = 3Å I -1/2 ; in water: D = 3Å I -1/2 ; Ionic strength I = ½  i C i (Z i ion ) 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 = [q 1 q 2 /  r]exp(-r/D)

Electrostatics is T- dependent; U = (1/  )(q 1 q 2 /r) is free energy; TS = T (-dU/dT) = -T [d(1/  )/dT](q 1 q 2 /r) = = [dln(  )/dlnT] U = [dln(  )/dlnT] U in water: when T grows from 273 o to 293 o K (by 7%),  decreases from 88 to 80 (by 10%):  decreases from 88 to 80 (by 10%): TS ≈ -1.3 U; H  -0.3 U In water the entropic term (-TS) is the main for electrostatics!

S-S bonds (Cys-Cys) exchange 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 non-uniformmedia q q

At atomic distances:  = ?