Proteiinien rakenne ja laskostuminen
Harjoitus
Outi Heikkinen
Rg radius of gyration
-
gives information about the global conformation of a molecule
rms distance from each atom of the molecule to their centroid
2
 N 

 N ri 
R g    r j      N 
 i 1 N 
 j 1 

-
-
1
2
ri, rj = position vectors of atoms i and j
N = number of atoms
Rg can be estimated for a globular protein or protein domain:
Nresidues number of amino acid residues
0.38
Rg (estim)  2.2 Nresidues
Measurement by small-angle X-ray scattering
Rg is not a geometrically specific quantity  particular target value of Rg – not a specific
structure
Reference: Kuszewski, Gronenborn & Clore (1999) Improving the Packing and Accuracy
of NMR Structures with a Pseudopotential for the Radius of Gyration, J. Am. Chem. Soc.
121, 2337-2338.
R2 spin-spin relaxation rate constant or transverse relaxation rate constant
-
decay of the transverse magnetization in the xy-plane
Mx-y
t
-
Bloch equations:
dM x , y (t )
  R2 M x , y (t )
dt
M x , y (t )  M x , y (0) exp(  R2t )
-
Spin-spin relaxation time constant
T2 
-
1
R2
R2 is approximately proportional to the overall rotational correlation time c of the protein
(depends on the molecular mass and the shape of protein)
1
J ( ) 
c
1  ( c ) 2
R2  4 J (0)  3J ( N )  ...
-
(homogenous) linewidth ∆υFWHH in an NMR experiment:
∆υFWHH = R2/π (Hz)
FWHH = full-width at half height
Spin label
-
paramagnetic label incorporated into the protein structure
o chelated metal ions (heme group)
o stable organic radicals e.g nitroxides attached to reactive amino acid side chains
Protein
S S
Cysteine
residue
N
O
-
induces a distance dependent paramagnetic relaxation enhancement effect on nuclei
nearby
 K
r   sp
 R2
-

3 c 
 4 c 


1   h2 c2 

1
6
r = the distance between the nuclear spin and the electron spin
τc = the correlation time for the electron-nuclear interaction
ωh = the Larmor frequency of the nuclear spin
R2sp = the paramagnetic relaxation enhancement
R2sp = R2* - R2
R2* = the transverse relaxation rate constant for paramagnetic species
R2 = the transverse relaxation rate constant for diamagnetic species
K = 1/15·S(S+1)γ2g2β2
S = the electron spin
γ = the nuclear gyromagnetic ratio
g = the electronic g factor
β = the Bohr magneton
provides long-range distance, tens of angstroms, restraints for protein structure
determination by NMR in contrast to short, few angstroms, inter proton distances
Reference: Battiste & Wagner (2000) Biochemistry 39, 5355-5365
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