Therefore total TEMPO spin probe in lipid phase¼[C] in lipid phase Á volume of lipid
phase and total TEMPO spin probe in aqueous phase¼[C] in aqueous phase Á volume of
aqueous phase.
3.6.1.3 Spin-Spin Exchange Interaction
Effect of spin-pin exchange interaction between different electron spins appears on
ESR spectrum as concentration of spin probe in a sample increases. Hamiltonian of
this effect is shown by J ij S ij where J ij is exchange integration between interacting
radicals, i and j [6, 7]. The effect appears in widening of ESR spectrum while effect
of the interaction is small. Experimentally, the effect appeared on ESR spectrum is
digitalized asα parameter. And relation between spin probe concentration andα
parameter is obtained (Fig. 3.12). And relation between distributions of spin probes
as ESR spectrum is schematically shown (Fig. 3.13). This technique is used for
measurement of lateral diffusion of lipid spin probe in lipid membranes [7] and
measurement of phase separation of acidic phospholipid by calcium ions [8]. This
technique is also used for measurement of membrane fusion between virus membrane and host cell and membrane fusion of various systems. Decrease of spin-spin
exchange is observed in membrane fusion caused by dilution of spin probes. On the
other hand, increase of spin-spin exchange is observed in phase separation caused by
increase of local concentration of spin probes.
Spin-spin exchange interaction is an effect of quantum mechanics, and overlap of
wave function increases or decreases energy of the system Hamiltonian of nitroxide
radical in spin labeling method is shown as following equations.
H ¼ β
j jS Á g Á H 0 þ hS Á T Á I þ Àβ N
j
jI Á g N Á H 0 þ H exchange þ H dipole
(T xx , T yy , T zz )¼(5.8, 5.8, 30.8) Gauss
(g xx , g yy , g zz )¼(2.0089, 2.0058, 2.0021)
In the equation, term of spin-spin exchange interaction is shown as
H exchange ¼ À 2∑ i < j J ij S i S j where J ij is exchange integration of interacting unpaired
electron i and j. Introducing wave function, Ψ i and Ψ j for unpaired electrons i and j,
respectively, the equation becomes J ij ¼
R Ψ i i
ð ÞΨ j j
ð Þ
e
2
r ij
Ψ i j
ð ÞΨ j i
ð Þdτ i dτ j where |
r ij | is distance between i electron and j electron. Line width, Δν exchange of ESR
spectrum is defined as distance between the maximum and the minimum of first
differential of ESR spectrum under condition of exchange broadening. And
Δν exchange ¼ 2W exchange is obtained. On the other hand, Δ exchang ¼
aH
ð Þ
2
W exchange
is obtained
under condition of exchange narrowing. Exchange frequency for fixed radicals is
W exchange ¼ ν encounter Á p where ν encounter and p are encounter frequency and
probability of exchange for each encounter, respectively. This exchange interaction
is used for measurement of lateral diffusion of lipid molecules [6, 7]. The measurement is carried out by use of spin probe of cholesterol analogue (concentration rage
40
3 Methods for Physical Properties of Biomembranes and Cells
phase and total TEMPO spin probe in aqueous phase¼[C] in aqueous phase Á volume of
aqueous phase.
3.6.1.3 Spin-Spin Exchange Interaction
Effect of spin-pin exchange interaction between different electron spins appears on
ESR spectrum as concentration of spin probe in a sample increases. Hamiltonian of
this effect is shown by J ij S ij where J ij is exchange integration between interacting
radicals, i and j [6, 7]. The effect appears in widening of ESR spectrum while effect
of the interaction is small. Experimentally, the effect appeared on ESR spectrum is
digitalized asα parameter. And relation between spin probe concentration andα
parameter is obtained (Fig. 3.12). And relation between distributions of spin probes
as ESR spectrum is schematically shown (Fig. 3.13). This technique is used for
measurement of lateral diffusion of lipid spin probe in lipid membranes [7] and
measurement of phase separation of acidic phospholipid by calcium ions [8]. This
technique is also used for measurement of membrane fusion between virus membrane and host cell and membrane fusion of various systems. Decrease of spin-spin
exchange is observed in membrane fusion caused by dilution of spin probes. On the
other hand, increase of spin-spin exchange is observed in phase separation caused by
increase of local concentration of spin probes.
Spin-spin exchange interaction is an effect of quantum mechanics, and overlap of
wave function increases or decreases energy of the system Hamiltonian of nitroxide
radical in spin labeling method is shown as following equations.
H ¼ β
j jS Á g Á H 0 þ hS Á T Á I þ Àβ N
j
jI Á g N Á H 0 þ H exchange þ H dipole
(T xx , T yy , T zz )¼(5.8, 5.8, 30.8) Gauss
(g xx , g yy , g zz )¼(2.0089, 2.0058, 2.0021)
In the equation, term of spin-spin exchange interaction is shown as
H exchange ¼ À 2∑ i < j J ij S i S j where J ij is exchange integration of interacting unpaired
electron i and j. Introducing wave function, Ψ i and Ψ j for unpaired electrons i and j,
respectively, the equation becomes J ij ¼
R Ψ i i
ð ÞΨ j j
ð Þ
e
2
r ij
Ψ i j
ð ÞΨ j i
ð Þdτ i dτ j where |
r ij | is distance between i electron and j electron. Line width, Δν exchange of ESR
spectrum is defined as distance between the maximum and the minimum of first
differential of ESR spectrum under condition of exchange broadening. And
Δν exchange ¼ 2W exchange is obtained. On the other hand, Δ exchang ¼
aH
ð Þ
2
W exchange
is obtained
under condition of exchange narrowing. Exchange frequency for fixed radicals is
W exchange ¼ ν encounter Á p where ν encounter and p are encounter frequency and
probability of exchange for each encounter, respectively. This exchange interaction
is used for measurement of lateral diffusion of lipid molecules [6, 7]. The measurement is carried out by use of spin probe of cholesterol analogue (concentration rage
40
3 Methods for Physical Properties of Biomembranes and Cells