PROTEIN PHYSICS LECTURES 5-6 Elementary interactions: hydrophobic & electrostatic;

PROTEIN PHYSICS LECTURES 5-6 Elementary interactions: hydrophobic & electrostatic; SS and coordinate bonds

Hydrophobic effect Concentration of C6H12 in H2O: 50 times less than in gas! WHY? H2O

Gint: “Free energy of interactions” (“mean force potential”) Chemical potential: m G(1) = Gint - T•kBln(V(1))  Gint + T•kBln[C] EQUILIBRIUM for transition of molecule1from A to B: GA(1) = GB(1) chemical potentials inAandBare equal GintAB = GintB – GintA GintAB= kBT•ln([CinA]/[CinB]) ===================================================

Experiment: GintAB= kBT•ln([C1inA]/[C1inB]) SintAB = -d(GintAB)/dT HintAB = GintAB +TSintAB [C] of C6H12 in H2O: 50 times less than in gas; 100000 times less than in liquid C6H12 C6H12 T=2980K=250C

-2/3 Loss: S usual case -2/3 +1/3 H-bond: directed Loss: LARGE E rare case “hydrophobic bond”

High heat capacity d(H)/dT: Melting of “iceberg”

Octanol  Water 20-25 cal/mol per Å2 of molecular accessible non-polar surface

______ large effect _______ small ______ large

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 (ε3) R  1.5 - 2 Å U  +30 - 40 kcal/mol CHARGE inside PROTEIN: VERY BAD

Non-uniform media: eff = ?

j = q/1r

j = (q/1)/r - - - -

j = q/reff in positions: - - - - eff≈40 +-+-+ –+–+– eff≈ 200 !! Good estimate for non-uniform media

effective in non- uniform media

Large distance: Atomic distance:  = 80 = ? intermed. “vacuum”, ε~1? but absence of intermed. dipoles can only increase interaction…

At atomic distances in water: 1) =80 is not a bad approximation (much better than  = 1 or 3 !!) • (salt does not dissolve, if <50 at 3Å!) • [H]1/2=10-1.75 [H]1/2=10-4.25e-Gel/RT •   30-40 at ~2.5Å! Gel = 2.5  ln(10)  RT  6RT  3.5 kcal/mol at 2.5Å

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/r2 quadruple ~ 1/r3

Electrostatic interactions also occur between charge (q) and non-charged body if its 2 differs from the media’s 1: U ~ q• [1/2– 1/1] •V• (1/r4) at large r In water: repulsion of charges from non-polar molecules (since here 1>>2); in vacuum (where 1<2): just the opposite! 1 + + + - - - 2 V

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

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≈ -1.3U; H  -0.3U In water the entropic term (-TS) is the main for electrostatics!

S-S bonds (Cys-Cys) exchange S-S bond is not stable within a cell

Coordinate bonds (with Zn++, Fe+++,…)

j = q/r1 - - - -

PROTEIN PHYSICS LECTURES 5-6 Elementary interactions: hydrophobic & electrostatic;