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

Hydrophobic effect Concentration of C 6 H 12 in H 2 O: 50 times less than in gas! WHY? H2OH2OH2OH2O

G int : “Free energy of interactions” G int : “Free energy of interactions” (“mean force potential”) (“mean force potential”) Chemical potential: Chemical potential:  G (1) = G int - Tk B ln(V (1) )  G int + Tk B ln[C] EQUILIBRIUM for transition of molecule 1 from A to B: G A (1) = G B (1) chemical potentials in A and B are equal chemical potentials in A and B are equal  G int A  B = G int B – G int A  G int A  B = k B Tln([C inA ]/[C inB ]) ===================================================

Experiment:  G int A  B = k B T ln([C 1 in A ]/[C 1 in B ])  S int A  B = -d(  G int A  B )/dT  H int A  B =  G int A  B +T  S int A  B C 6 H 12 [C] of C 6 H 12 in H 2 O: 50 times less than in gas; times less than in liquid C 6 H 12 T=298 0 K=25 0 C

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

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

20-25 cal/mol per Å 2 of molecular accessible non-polar surface Octanol  Water

______largeeffect _______ small small______ large large

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 (ε  3) (ε  3) R  Å  U  kcal/mol CHARGE inside PROTEIN: VERY BAD CHARGE inside insidePROTEIN Water => vacuum:  U  +100 kcal/mol

Non-uniform media:  eff = ?

 = q /  1 r

 = (q /  1 )/r

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

 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: 1)  =80 is not a bad approximation (much better than  = 1 or 3 !!) (salt does not dissolve, if  <50 at 3Å!) (salt does not dissolve, if  <50 at 3Å!) 2) [H] 1/2 = [H] 1/2 =  e -  G el /RT   at ~2.5Å!   at ~2.5Å!  G el = 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/  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 its  2 differs from the media’s  1 : U ~ q [ 1/  2 – 1/  1 ] 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! 22VV22VVV 11

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

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 S-S bond is not stable within a cell within a cell

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

 = q / r  1