Secondary structures

Сентябрь 14, 2022

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Физика
Secondary structures

Содержание

2. coil r = ________ L 1+cosα 1– cosα = (Mr)•r = LM•r |h| ~ M1/2 V
3. Linus Carl Pauling (1901-94) — Nobel Prizes: 1954, 62 Werner Kuhn (1899 - 1963) Robert Brainard
4. Main secondary structures
5. H1 NMR spectroscopy (cross-peaks) Experimental study of secondary structure X-ray crystallography
6. Far UV CD spectra (peptide groups) IR spectra (“amid I”, C=O bond) Experimental study of secondary
7. Helices: Right and Left H-bonds
8. Right α-helix Right 310-helix
10. ALA, etc. GLY only
12. β↑↑, twisted β↓↑, twisted
13. Mirror-asymmetric amino acids – mirror-asymmetric twist of β-sheets
14. β-turns β-bulge
15. collagen triple helix
16. Secondary structure transitions We may consider only potential energy, etc.: E ⇒ ECOORD M ⇒ MCOORD
17. α-helix homo-polypeptide: ΔFα = Fα - Fcoil = (n-2)fH - nTSα = = -2fH + n×(fH
18. α-helix homo-polypeptide: ΔFα = Fα - Fcoil = (n-2)fH - nTSα = = -2fH + n×(fH
19. Average lengths n0 of helix and coil regions at mid-transition (when fEL=0, fINIT>>kBT): N n Eα
20. Width of helix-coil transition When fEL changes: IF n0 ×fEL IF n0 ×fEL >> +kBT; i.e.,
21. TIME of coil-helix transition Barrier for initiation: ΔF# = fINIT; Time to initiate helix in given
22. TIME of coil – stable β-hairpin transition Barrier for initiation: ΔF# = fTURN ≈ fINIT_α; Time
23. TIME of coil – β-sheet transition (when hairpin is unstable) fβ fTURN fEDGE+fβ fβN + fTURN
24. TIME of coil – β-sheet transition fβ fTURN fEDGE+fβ F# F# = 2 fTURN fEDGE /(-fβ)
25. The End
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coil

r = ________ L
1+cosα
1– cosα
= (Mr)•r = LM•r

|h| ~ M1/2
V ~ M3/2

→

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Linus Carl Pauling (1901-94)
— Nobel Prizes: 1954, 62
Werner Kuhn (1899 -

1963)

Robert Brainard Corey
(1897 –1971)

Herman Russell Branson
(1914 –1995)

Random coil:

α-helices and β-sheets:

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Main secondary structures

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H1 NMR
spectroscopy
(cross-peaks)
Experimental
study of secondary structure
X-ray crystallography

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Far UV CD spectra
(peptide groups)
IR spectra
(“amid I”, C=O bond)
Experimental study of

secondary structure

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Helices:
Right and Left
H-bonds

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Right
α-helix
Right
310-helix

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ALA, etc. GLY only

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β↑↑,
twisted
β↓↑,
twisted

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Mirror-asymmetric amino acids –
mirror-asymmetric
twist of β-sheets

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β-turns
β-bulge

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collagen triple helix

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Secondary structure transitions
We may consider
only potential energy, etc.:
E ⇒ ECOORD
M

⇒ MCOORD
S(E) ⇒ SCOORD(ECOORD )
F(E) ⇒ FCOORD , etc.

Separation of potential energy
in classic (non-quantum) mechanics:
E = ECOORD + EKIN; EKIN=Σmv2/2 - does not depend on coordinates
S = SCOORD + SKIN

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α-helix
homo-polypeptide:
ΔFα = Fα - Fcoil = (n-2)fH - nTSα =

= -2fH + n×(fH - TSα)
||==========|| ||========================||
fINIT fEL
fEL: elongation ( ≈ 0) :
≈ -0.5⋅kBT Ala --- ≈ +1.5⋅kBT Gly
s = exp(-fEL/kBT): s = 2 – 0.2
fINIT =-2fH: initiation (>>kBT)
σ = exp(-fINIT/kBT): σ<<1 (~0.001)

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α-helix
homo-polypeptide:
ΔFα = Fα - Fcoil = (n-2)fH - nTSα =

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Average lengths n0 of helix and coil regions at
mid-transition (when

fEL=0,
fINIT>>kBT):

Eα = fINIT + n×fEL

positional entropy
n is small: fINIT -T•kBln[n×n] > 0: insertion of coil is unfavorable
n is large: fINIT -T•kBln[n×n] < 0: insertion of coil is favorable
EQUILIBRIUM: ΔG = 0:
fINIT -T•2kBln[n0] = 0 ⇒ n0 ≈ exp(+fINIT/2kBT) = σ-1/2 >> 1

σ = exp(-fINIT/kBT) << 1

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Width
of helix-coil transition
When fEL changes:
IF n0 ×fEL << -

kBT, i.e., fEL/kBT << - 1/n0: stable helix
IF n0 ×fEL >> +kBT; i.e., fEL/kBT >> + 1/n0: unstable helix,
stable coil

~n0

n0 ≅ σ-1/2 ≈ 30

Transition width: Δ[ fEL/kBT ] ~ 4/n0 = 4σ1/2

fEL=0 if %α = 50%
for very long chain
n0: %α → 0
when chain is
shorter than n0

~n0

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TIME of coil-helix transition
Barrier for initiation:
ΔF# = fINIT;
Time to initiate helix

in given place:
t1 = τ × exp(+ΔF#/kBT) = τ × σ -1= τn02 τ ~ 1–10 ns
Time to initiate helix in any of n0 places:
tINIT_H = n0-1 × t1 = τn0 ≡ τ × σ -1/2 ~100 ns
To extend helix to n0 residues:
tEL_H = n0 × τ ≡ τ × σ -1/2 ~100 ns
tHELIX ~ 200 ns

~n0

n0 = σ-1/2

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TIME of coil – stable β-hairpin transition
Barrier for initiation:
ΔF# = fTURN

≈ fINIT_α;
Time to initiate β-hairpin
with turn in the middle of the chain:
t1 ≈ τ × exp(+ΔF#/kBT) = τ × n02 ~ 3000 ns
Time to extend β-hairpin to n residues:
tEL_β-HAIRPIN ≈ n × τ ~ 100 ns
tβ-HAIRPIN ~ 3000 ns

fTURN

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