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Understanding Electrostatics in Protein Physics: Charge Interactions and Energetics

This lecture delves into the electrostatic interactions of charges in proteins and surrounding media. Key topics include the potential created by charges, interactions between charged particles, and the impact of the dielectric constant (ε) in both uniform and non-uniform media. The lecture discusses the significant differences in electrostatic energy at atomic distances in water (ε ≈ 80) compared to vacuum (ε ≈ 1) or protein interfaces. Important concepts like Debye-Hückel screening, charge-dipole interactions, and their temperature dependencies are explored, making it essential for understanding protein behavior in biological systems.

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Understanding Electrostatics in Protein Physics: Charge Interactions and Energetics

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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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