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PROTEIN PHYSICS LECTURE 6

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   3 protein

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PROTEIN PHYSICS LECTURE 6

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  1. PROTEIN PHYSICS LECTURE 6

  2. 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:  = ?

  3. 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

  4. Non-uniform media: eff = ?

  5. ΔU = q2/2r ≈40 U = q1q2/effr = (q1/1)(12/r)(q2/2) +++ – – – eff≈ 200 !! Good estimate for non-uniform media

  6. effective in non- uniform media

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

  8. 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

  9. Protein engineering experiments: (r) = pH  2.3RT  eff(r)

  10. 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

  11. 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/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!

  12. 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.

  13. 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)

  14. 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!

  15. S-S bonds (Cys-Cys) exchange

  16. Coordinate bonds (with Zn++, Fe+++,…)

  17. CHARGE near the surface of PROTEIN Electric field in non-uniform media = ??

  18. EXERSIZE: charge near the surface of conductor (metal) ______________________________________ ______________________________________ electric field goes to high 

  19. CHARGE near the surface of PROTEIN non-uniform media: electric field avoids low 

  20. CHARGE qnear the surface of PROTEIN q non- uniform media q

  21. At atomic distances:  = ?

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