Figure 3.10 shows a typical ESR spectrum of stearic acid spin probe in lipid
bilayer membranes. Order parameter, S zz is defined as following equation by use of
T xx ¼ T yy in a case of nitroxide radical.
S zz ¼
T==-⊥
T zz À T xx þ T yy
À
Á¼ 3 cos
2
γ
À
Á À 1
S zz varies from À
1
2 to 1 and the value shows angular range of averaged molecular
motion of nitroxide radical. Small value of S zz shows isotropic motion of nitroxide
radical and the motion can be approximated as a motion of sphere (radius ¼r). And
Einstein‘s relation, τ C ¼
4πr
3
kT η is applied to this Brownian motion. This equation
shows relationship between viscosity η and rotational correlation time τ C. And
following equations are derived from theory of line width, ΔH of ESR spectrum
and the correlation time, τ C.
ΔH ¼ τ C (A + B Á m + C Á m
2
), where ‘m’ is quantum number of nucleus, and A, B
and C are constant. It becomes possible to obtain viscosity of lipid bilayer membrane
and biomembranes by use of spin probe. Real equation to obtain viscosity is τ C
¼ 1 À
h 0
ð Þ
h m
ð Þ
3πgβΔH 0
ð Þ
h c 1 mÀc 2 m 2
ð
Þ where h(m) are height and width of each peak, respectively.
c 1 ¼
16π β
j jH
45h
T zz À T xx
ð
Þ g zz À
g xx þ g yy
2
3.6.1.2 TEMPO Parameter
TEMPO (2,2,6,6,-tetramethylpiperidine-1-oxyl) is small molecular weight and volatile spin probe. When TEMPO is added to biomembranes or dispersion of lipid
membranes, the probes are partitioned between aqueous phase and lipid phase of the
membranes (Fig. 3.11). Rapid motion of TEMPO averages hyperfine splitting to
2T
2T
Fig. 3.10 ESR spectrum
Values of 2Tk and 2T⊥ for
order parameters of axial
symmetric rotation are
obtained in ESR spectrum
38
3 Methods for Physical Properties of Biomembranes and Cells