HHMI meeting, FOLDING

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PROTEIN PHYSICS LECTURES 9-10 Secondary
structures
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coil
r ________ L
1cos?
1 cos?
lth2gt (Mr)r LMr h M1/2

V M3/2
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Main secondary structures
4
Experimental study of secondary structure X-ray
crystallography
NMR spectroscopy (cross-peaks)
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Experimental study of secondary structure
Far UV CD spectra (peptide groups)
IR spectra (amid I, CO bond)
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H-bonds
Helices Right and Left
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Right ?-helix
Right 310-helix
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ALA, etc. GLY only
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???, twisted
???, twisted
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Mirror-asymmetric amino acids
mirror-asymmetric twist of ?-sheets
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?-turns
?-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
EKINSmv2/2 - does not depend on coordinates S
SCOORD SKIN
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?-helix
homo-polypeptide ?F? F? - Fcoil
(n-2)fH - nTS? -2fH n?(fH - TS?)


fINIT fEL fEL elongation (
? 0) ? -0.5?kBT Ala
--- ? 1.5?kBT Gly fINIT initiation
(gtgtkBT) ? exp(-fINIT/kBT) initiation (?ltlt1)

0.001
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Average lengths n0 of helix and coil regions at
mid-transition (when fEL0,
fINITgtgtkBT)
N
n
E? fINIT n?fEL
n is small fINIT -TkBlnn?n gt 0 insertion
of coil is unfavorable n is large fINIT
-TkBlnn?n lt 0 insertion of coil is favorable
EQUILIBRIUM ?G 0 fINIT -T2kBlnn0 0
? n0 ? exp(fINIT/2kBT) ?-1/2 gtgt 1
? exp(-fINIT/kBT) ltlt 1
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Width of helix-coil transition When fEL
changes IF n0 ?fEL ltlt - kBT, i.e., fEL/kBT
ltlt - 1/n0 stable helix IF n0 ?fEL gtgt kBT
i.e., fEL/kBT gtgt 1/n0 unstable helix,

stable coil
n0
n0
Transition width ? fEL/kBT 4/n0 4?1/2
fEL0 if ? 50 for very long chain n0 ?
? 0 when chain is shorter than n0
n0 ? ?-1/2 ? 30
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TIME of coil-helix transition Barrier for
initiation ?F fINIT Time to initiate helix
in given place t1 ? ? exp(?F/kBT) ? ? ?
-1 ?n02 ? 110 ns Time to initiate helix
in any of n0 places tINIT_H n0-1 ? ? ?
exp(?F/kBT) ?n0 100 ns To extend helix to n0
residues tEL_H n0 ? ? ? ? ? ? -1/2 100
ns tHELIX 200 ns
n0 ?-1/2
n0
/
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TIME of coil stable ?-hairpin
transition Barrier for initiation ?F fTURN ?
fINIT_? Time to initiate ?-hairpin with turn
in the middle of the chain t1 ? ? ?
exp(?F/kBT) ? ? n0-2 3000 ns Time to
extend ?-hairpin to n residues tEL_?-HAIRPIN ?
n ? ? 100 ns t?-HAIRPIN 3000 ns
fTURN
1
n
/
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TIME of coil ?-sheet transition (when hairpin
is unstable)
fTURN
fEDGEf?
f? lt 0 fEDGE f? gt 0
f?
F
f?N fTURN lt 0 ? Nmin fTURN/(-f?)
F fTURN 2Nmin(fEDGEf?) fTURN 2 fTURN
fEDGE /(-f?)
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TIME of coil ?-sheet transition
F 2 fTURN fEDGE /(-f?) ? ? when (-f?) ? 0
Time to initiate ?-sheet folding t1 ? ?
exp(?F/kBT) ? ? when (-f?) ? 0 !!
Fopt(M) 2 fTURN fEDGE /(-f?) - fTURN
f? lt 0 fEDGE gt -f?
fTURN
fEDGEf?
F
f?
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Average lengths n0 of helix and coil regions at
mid-transition (when fEL0)
N
of ends ? regions n ? N/? ?/2 helices,
1?/2 coils when fEL0 ?E E(?2) - E(?)
fINIT S(?)/kB lnN(N-?1) / ?1
?S/kB S(?2) - S(?)/kB ? 2lnN/? 2ln(n)
(when Ngtgt?) EQUILIBRIUM ?G ?E-T?S0 fINIT
-T2kBlnn0 0 ? n0 ? exp(fINIT/2kBT)
?-1/2

(when ?ltlt1)
n
n
E? fINIT n?fEL