Transcript HHMI meeting, FOLDING

PROTEIN PHYSICS
LECTURES 9-10
Secondary structures
coil
r
<h2> = (Mr)•r = LM•r
1+cos
________
=
L
1– cos
|h| ~ M1/2
V ~ M3/2
Main secondary structures
Experimental
study of
secondary
structure
X-ray
crystallography
NMR
spectroscopy
(cross-peaks)
Experimental study of secondary structure
Far UV CD spectra
(peptide groups)
IR spectra
(amid I, C=O bond)
H-bonds
Helices:
Right and Left
Right
-helix
Right
310-helix
ALA, etc.
GLY only
,
twisted
,
twisted
Mirror-asymmetric
amino acids –
mirror-asymmetric
twist of -sheets
-turns
-bulge
collagen triple helix
Secondary structure transitions
Separation of potential energy
in classic (non-quantum) mechanics:
E = ECOORD + EKIN;
S = SCOORD + SKIN
EKIN=Σmv2/2 - does not depend on coordinates
We may consider
only potential energy, etc.:
E  ECOORD
M  MCOORD
S(E)  SCOORD(ECOORD )
F(E)  FCOORD , etc.
-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 (>>kBT)
 = exp(-fINIT/kBT):
initiation (<<1)
~0.001
Average lengths n0 of helix and coil regions at
mid-transition (when fEL=0,
fINIT>>kBT):
N
n
E = fINIT + nfEL
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: G = 0:
fINIT -T•2kBln[n0] = 0  n0  exp(+fINIT/2kBT) = -1/2 >> 1
 = exp(-fINIT/kBT) << 1
Width
of helix-coil transition
~n0
~n0
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
Transition width: [ fEL/kBT ] ~ 4/n0 = 41/2
n0  -1/2  30
fEL=0 if % =50%
for very long chain
n0: %  0
when chain is
shorter than n0
TIME of coil-helix transition
Barrier for initiation:
n0 = -1/2
~n0
F# = fINIT;
Time to initiate helix in given place:
t1 =   exp(+F#/kBT) =    -1= n02
 ~ 1–10 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:
t
= n       -1/2 ~100 ns
EL_H
0
tHELIX ~ 200 ns
/
TIME of coil – stable -hairpin transition
fTURN
Barrier for initiation:
F# = fTURN  fINIT_;
1
Time to initiate -hairpin
n
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
/
TIME of coil – -sheet transition (when hairpin is unstable)
fTURN
f
fEDGE+f
f < 0
fEDGE+f > 0
F#
fN + fTURN < 0

Nmin = fTURN/(-f)
F# = fTURN +2Nmin(fEDGE+f) + fTURN = 2 fTURN fEDGE /(-f)
TIME of coil – -sheet transition
F# = 2 fTURN fEDGE /(-f) 

when (-f)  0
Time to initiate -sheet folding:
f < 0
t1 =   exp(+F#/kBT)

!!

fEDGE >-f
when (-f)  0
Fopt(M#) = 2 fTURN fEDGE /(-f) - fTURN
fTURN
f
fEDGE+f
F#
Average lengths n0 of helix and coil regions at
mid-transition (when fEL=0):
# of ends: ; region’s n  N/
n
: /2 helices, 1+/2 coils
E = fINIT + nfEL
N
n
when fEL=0: E = E(+2) - E() = fINIT
S()/kB = ln[N•…•(N-+1) / •…•1];
S/kB = [S(+2) - S()]/kB  2ln[N/] =2ln(n) (when N>>)
EQUILIBRIUM: G = E-TS=0:
fINIT -T•2kBln[n0] = 0  n0  exp(+fINIT/2kBT) = -1/2
(when
<<1)