Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
PROTEIN PHYSICS LECTURE 6 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 R 1.5 - 2 Å U +30 - 40 kcal/mol CHARGE inside PROTEIN: VERY BAD Non-uniform media: eff = ? ΔU = q2/2r ≈40 U = q1q2/effr = (q1/1)(12/r) (q2/2) +++ – – – Good estimate for non-uniform media eff ≈ 200 !! effective in nonuniform media Large distance: = 80 Atomic distance: =? intermed. “vacuum”, ε~1? but absence of intermed. dipoles can only increase 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) 30-40 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): Quadruple interactions (HO)-1/3-H+1/3::::::(OH)-1/3-H+1/3 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 itsr 2 differs from the media’s 1: 4 U ~ q • [(1 - 2)/(12)] • V • (1/r ) at large In water: repulsion of charges from non-polar molecules (since here 1>>2); in vacuum (where 1<2) : just the opposite! r Debye-Hückel screening of electrostatic by ions: U = [q1q2/r]•exp(-r/D) ; in water: D = 3Å•I-1/2; Ionic strength I = ½iCi(Ziion)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 = [q1q2/r]•exp(-r/D) 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 ≈ -1.3 U; H -0.3U In water the entropic term (-TS) is the main for electrostatics! S-S bonds (Cys-Cys) 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 q q nonuniform media At atomic distances: =?