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Презентация на тему Elementary interactions: hydrophobic & electrostatic; SS and coordinate bonds

Hydrophobic effectConcentration of C6H14 in H2O:50 times lessthan in gas!WHY?H2OHenry’s constant(kH,cc)-1 = for : =
PROTEIN PHYSICSLECTURES 5-6Elementary interactions:hydrophobic&electrostatic;SS and coordinate bonds Hydrophobic effectConcentration of C6H14   in H2O:50 times lessthan in gas!WHY?H2OHenry’s ENTROPY:SE = kB • ln[ME];   ME=number_of_states(E)Why kB? What is kB?Because Gint : “Free energy Experiment: ΔG intA→B= kBT•ln([C1 in A]/[C1 in B])ΔSintA→B = -d(ΔGintA→B)/dTΔHintA→B = ΔGintA→B -2/3 +1/3Loss: S         usual High heat capacity d(ΔH)/dT:Melting of“iceberg” 20-25 cal/mol per Å2 of molecularaccessible non-polar surfaceOctanol → Water Семён Ефимович Бреслер (1911 – 1983) Давид Львович Талмуд (1900 - 1973)Cyrus Homi Chothia, ______largeeffect_______ small______ large Electrostatics in uniform media: potential  ϕ1 = q1/εrInteraction of two charges: (1736-1806) Water => PROTEIN         (ε≈3)R Non-uniform media:   εeff = ? Non-uniform media:   εeff = ? Non-uniform media:   εeff = ?intermediate dipole ϕ = q/ε1r - -  - -ϕ = (q/ε1)/r Good estimate fornon-uniform media+ -+ - + – + – + –εeff εeffective in non-uniform media15040 Large distance:          Atomic At atomic distances in water:   1) ε=80 is not a Protein engineering experiments:ϕ(r) = ΔpH × 2.3RT ⇒⇒ εeff(r) Sir Alan Roy Fersht, 1943Protein engineering Dipole interactions (e.g., H-bonds):(HO)-1/3-H+1/3::::::(OH)-1/3-H+1/3Quadruple interactionsAlso: charge-dipole, dipole-quadruple, etc.Potentials: Electrostatic interactions also occur between charge (q) and non-charged body, if its Debye-Hückel screening of electrostatic by ions:U = [q1q2/εr]•exp(-r/D) ; Electrostatics is T- dependent;U = (1/ε)•(q1q2/r)is free energy (U = H-TS);TS = S-S bonds (Cys-Cys) exchange: entropic forceS-S bond is not stable    within a cell Coordinate bonds (with Zn++, Fe+++,…) exchange: entropic force
Слайды презентации

Слайд 2 Hydrophobic effect

Concentration of C6H14
in H2O:
50

Hydrophobic effectConcentration of C6H14  in H2O:50 times lessthan in gas!WHY?H2OHenry’s

times less
than in gas!

WHY?



H2O






Henry’s constant

(kH,cc)-1 =


for : = 50/1

for ethanol: = 1/47000

[in gas]
[in liquid]



Слайд 3 ENTROPY:

SE = kB • ln[ME]; ME=number_of_states(E)

Why

ENTROPY:SE = kB • ln[ME];  ME=number_of_states(E)Why kB? What is kB?Because

kB? What is kB?
Because entropy SE comes to the

free energy
FE = E – TSE (measured in energy units) as TSE,
and T is measured in degrees, while
ln[number of states] is dimensionless;
Thus, kB is energy_unit/degree

FREE ENERGY:
Probability(E) ~ ME•exp(-E/kBT) = exp(-FE/kBT)
Boltzmann
F=E-TS at V=const;

G=H-TS=(E+PV)-TS at P=const (better for experiment)
-------------------

Слайд 4

Gint : “Free energy of interactions”

Gint : “Free energy of interactions”

(“mean force potential”)

Chemical potential:
μ ≡ G(1) = Gint - T•kBln(V(1)) ≡ Gint + T•kBln[C]
EQUILIBRIUM for transition
of molecule 1 from A to B: GA(1) = GB(1)
chemical potentials in A and B are equal


ΔGintA→B ≡ GintB – GintA

ΔGintA→B= kBT•ln([CinA]/[CinB])
===================================================

Слайд 5 Experiment: ΔG intA→B= kBT•ln([C1 in A]/[C1 in B])

ΔSintA→B

Experiment: ΔG intA→B= kBT•ln([C1 in A]/[C1 in B])ΔSintA→B = -d(ΔGintA→B)/dTΔHintA→B =

= -d(ΔGintA→B)/dT
ΔHintA→B = ΔGintA→B +TΔSintA→B
C6H12
[C] of C6H12
in H2O:
50

times less
than in gas;
100000 times
less than in
liquid C6H12

T=2980K=250C


Слайд 6 -2/3 +1/3
Loss: S

-2/3 +1/3Loss: S     usual

usual

case

-2/3

Loss:
LARGE E
rare
case

H-bond: directed

“hydrophobic bond”


Слайд 7 High
heat capacity
d(ΔH)/dT:
Melting of
“iceberg”

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

Слайд 8 20-25 cal/mol per Å2 of molecular
accessible non-polar surface

Octanol

20-25 cal/mol per Å2 of molecularaccessible non-polar surfaceOctanol → Water

→ Water


Слайд 9 Семён Ефимович Бреслер 
(1911 – 1983)
 Давид Львович Талмуд
(1900

Семён Ефимович Бреслер (1911 – 1983) Давид Львович Талмуд (1900 - 1973)Cyrus Homi

- 1973)
Cyrus Homi Chothia, 1942

Hydrophobic
effect
&
amino acid
water-accessible
surface

Hypothesis on a

role of hydrophobic effect in protein folding

Hydrophobic
effect
&
denaturationof proteins

Charles Tanford 
(1921 - 2009)

General physical
features of
Hydrophobic
effect


Слайд 10
______
large
effect
_______
small
______
large

______largeeffect_______ small______ large

Слайд 11
Electrostatics in uniform media:
potential ϕ1 =

Electrostatics in uniform media: potential ϕ1 = q1/εrInteraction of two charges:

q1/εr

Interaction of two charges:
U = ϕ1q2 =

ϕ2q1 = q1q2/εr
ε = 1 vacuum
ε ≈ 3 protein
ε ≈ 80 water
Protein/water interface
In non-uniform media: εeff = ?
At atomic distances: εeff = ?

Слайд 12 (1736-1806)

(1736-1806)

Слайд 13 Water => PROTEIN

Water => PROTEIN     (ε≈3)R ≈ 1.5 -

(ε≈3)

R ≈ 1.5 - 2 Å
ΔU

≈ +30 - 40 kcal/mol

CHARGE inside PROTEIN:
VERY BAD

CHARGE
inside
PROTEIN

Water => vacuum:
ΔU ≈ +100 kcal/mol


Слайд 14 Non-uniform media: εeff = ?














Non-uniform media:  εeff = ?

Слайд 15 Non-uniform media: εeff = ?



















Non-uniform media:  εeff = ?

Слайд 16 Non-uniform media: εeff = ?

intermediate dipole

Non-uniform media:  εeff = ?intermediate dipole




Слайд 17
ϕ = q/ε1r


ϕ = q/ε1r

Слайд 18 -
- -
-

ϕ = (q/ε1)/r

- - - -ϕ = (q/ε1)/r

Слайд 19 Good estimate for
non-uniform media
+ -+ - +

Good estimate fornon-uniform media+ -+ - + – + – +

+ – + –
εeff ≈ 150 !!
εeff≈40
ϕ = q/rεeff

in positions:

-
- -
-




Слайд 20 εeffective
in non-
uniform
media
150
40

εeffective in non-uniform media15040

Слайд 21 Large distance:

Large distance:     Atomic distance: εeff = ε

Atomic distance:
εeff = ε =

80 εeff = ?


intermediate
“vacuum”, ε ~ 1?
but the absence
of intermediate
dipoles can
only increase
interaction…

Слайд 22 At atomic distances in water:
1)

At atomic distances in water:  1) ε=80 is not a

ε=80 is not a bad approximation (much better than

ε = 1 or 3 !!)
(salt does not dissolve, if ε<50 at 3Å!)

[H]1/2=10-1.75 [H]1/2=10-4.25=10-1.75 × e-ΔGel/RT





ε ≈ 30-40 at ≈ 2.5Å!

ΔGel = 2.5 × ln(10) × RT ≈ 6RT ≈ 3.5 kcal/mol at ≈2.5Å




Слайд 23 Protein engineering experiments:

ϕ(r) = ΔpH × 2.3RT ⇒⇒

Protein engineering experiments:ϕ(r) = ΔpH × 2.3RT ⇒⇒ εeff(r)

εeff(r)


Слайд 24 Sir Alan Roy Fersht, 1943

Protein engineering

Sir Alan Roy Fersht, 1943Protein engineering

Слайд 25 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 interactions (e.g., H-bonds):(HO)-1/3-H+1/3::::::(OH)-1/3-H+1/3Quadruple interactionsAlso: charge-dipole, dipole-quadruple, etc.Potentials:   ϕdipole


ϕdipole ~ 1/εr2

ϕquadruple ~ 1/εr3

Слайд 26 Electrostatic interactions also occur between charge (q) and

Electrostatic interactions also occur between charge (q) and non-charged body, if

non-charged body, if its ε2 differs from the media’s

ε1:

U ~ q • [1/ε2 – 1/ε1] • [ε2 /(ε1+ε2 /2)] • V • (1/r 4) at large r

In water: repulsion of charges from non-polar molecules (since here ε1>>ε2);
in vacuum (where ε1<ε2) : just the opposite!

+
+
+

-
-
-

ε2
V

ε1


Слайд 27 Debye-Hückel screening
of electrostatic by ions:

U = [q1q2/εr]•exp(-r/D)

Debye-Hückel screening of electrostatic by ions:U = [q1q2/εr]•exp(-r/D) ;

;

in water: D = 3Å•I-1/2;

Ionic strength I = ½ΣiCi(Ziion)2 .

Usually: I ≈ 0.1 [mol/liter]; D ≈ 8Å.

Electrostatics is an example of a multi-body
(charge1, charge2, media, ions) interaction


Слайд 28
Electrostatics is T- dependent;

U = (1/ε)•(q1q2/r)

is free energy

Electrostatics is T- dependent;U = (1/ε)•(q1q2/r)is free energy (U = H-TS);TS

(U = H-TS);

TS = T•(-dU/dT) = -T• [d(1/ε)/dT]•(q1q2/r) =


= [dln(ε)/dlnT]•U

in water: when T grows from 273o to 293oK (by 7%),
ε 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!

Слайд 29 S-S bonds (Cys-Cys)



exchange:
entropic force

S-S bond is

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

not stable
within a cell


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