and collided molecules, respectively. On the other hand, diffusion constant, D is
shown by Stokes-Einstein equation as follows. D ¼
kT
6πηR where k and η are
Boltzmann constant and solvent viscosity, respectively. Therefore, chemical reaction
depends on viscosity of solvent, temperature, size of molecules in addition to
concentration of molecules. Biomembrane is dynamic structure and molecular
components of it show rotational diffusion and lateral diffusion. Receptor on
biomembrane surface binds ligand to make conformational change and diffuses to
bind effector protein for transmitting received signal to enzymic signaling system.
This diffusion process depends on fluidity (viscosity) of lipid bilayer membrane.
And it was shown in adrenalin-induced activation of glycolysis system. In this
system, energy supply is promoted through activation of glycolysis when adrenalin
receptor binds adrenalin. The complex of adrenalin-adrenalin receptor collides with
adenylate cyclase through G-protein. Adenylate cyclase raises level of cyclic AMP
(cAMP) in the cell to regulate enzyme activity. Relationship between collision
frequency and lateral diffusion rate on biomembranes was analyzed from fluidity
change of the biomembranes in reaction system as follows. HR þ E !
k b
HRE
ð
Þ!HR
þE
0 where HR, E and E
0 are receptor binding hormone, enzyme and activated enzyme,
respectively. HR and E collide with rate constant k b in red blood cell of turkey.
Membrane fluidity of the blood cells was changed by addition of cis-vaccenic acid.
And viscosity at 25
C was lowered from 6 poise to 4 poise and corresponding diffusion
constant of β-adrenalin receptor increased from 4.0 Â 10
À11 cm
2
/sec to 9.0 Â 10
À10 cm
2
/sec [2]. Velocity of diffusion-controlled process between substrate and enzyme in
stationary state on two-dimensional space is shown as following equation.
v ¼
substrate
½
enzyme ½
N A
4πD S, E
ln
π
4 Enzyme
½
N A
À
Á 1
2 1
a
where N A , D S,E and a are Avogadro’s
number, relative diffusion coefficient and length of active part, respectively. Chemical
reaction between substrate and enzyme is bimolecular reaction and velocity is shown as
v ¼ k b [E][R T ] where [E] and [R T ] are concentration of adenylate cyclase and whole
concentration of receptor, respectively. v ¼ k observed ¼ [E] is obtained from constant
concentration of receptor. And v observed ¼ N A 4πR T
Ã
lnπ R T N A
½
1
2 1
a Á
c
η is obtained from
D ¼
kT
6π ¼
c
η , therefore specific activity of adenylate cyclase becomes zero at 6.1 poise of
membrane viscosity. This result indicates that k observed depends on η and that the
activation of adenylate cyclase is diffusion-controlled process.
6.2 Phase Separation of Biomembranes and Biological
Functions of Cell
Biomembranes are a key area for biological functions. One of major components of
biomembranes, lipid molecules show phase separation correlated with phase transition. Phase transition observed in temperature acclimation of cells regulates function
of proteins through varicosity (fluidity) of lipid membranes. On the other hand, it is
considered that phase separation affects functions of proteins by making
82
6 Physical Properties of Biomembranes and Cellular Functions
shown by Stokes-Einstein equation as follows. D ¼
kT
6πηR where k and η are
Boltzmann constant and solvent viscosity, respectively. Therefore, chemical reaction
depends on viscosity of solvent, temperature, size of molecules in addition to
concentration of molecules. Biomembrane is dynamic structure and molecular
components of it show rotational diffusion and lateral diffusion. Receptor on
biomembrane surface binds ligand to make conformational change and diffuses to
bind effector protein for transmitting received signal to enzymic signaling system.
This diffusion process depends on fluidity (viscosity) of lipid bilayer membrane.
And it was shown in adrenalin-induced activation of glycolysis system. In this
system, energy supply is promoted through activation of glycolysis when adrenalin
receptor binds adrenalin. The complex of adrenalin-adrenalin receptor collides with
adenylate cyclase through G-protein. Adenylate cyclase raises level of cyclic AMP
(cAMP) in the cell to regulate enzyme activity. Relationship between collision
frequency and lateral diffusion rate on biomembranes was analyzed from fluidity
change of the biomembranes in reaction system as follows. HR þ E !
k b
HRE
ð
Þ!HR
þE
0 where HR, E and E
0 are receptor binding hormone, enzyme and activated enzyme,
respectively. HR and E collide with rate constant k b in red blood cell of turkey.
Membrane fluidity of the blood cells was changed by addition of cis-vaccenic acid.
And viscosity at 25
C was lowered from 6 poise to 4 poise and corresponding diffusion
constant of β-adrenalin receptor increased from 4.0 Â 10
À11 cm
2
/sec to 9.0 Â 10
À10 cm
2
/sec [2]. Velocity of diffusion-controlled process between substrate and enzyme in
stationary state on two-dimensional space is shown as following equation.
v ¼
substrate
½
enzyme ½
N A
4πD S, E
ln
π
4 Enzyme
½
N A
À
Á 1
2 1
a
where N A , D S,E and a are Avogadro’s
number, relative diffusion coefficient and length of active part, respectively. Chemical
reaction between substrate and enzyme is bimolecular reaction and velocity is shown as
v ¼ k b [E][R T ] where [E] and [R T ] are concentration of adenylate cyclase and whole
concentration of receptor, respectively. v ¼ k observed ¼ [E] is obtained from constant
concentration of receptor. And v observed ¼ N A 4πR T
Ã
lnπ R T N A
½
1
2 1
a Á
c
η is obtained from
D ¼
kT
6π ¼
c
η , therefore specific activity of adenylate cyclase becomes zero at 6.1 poise of
membrane viscosity. This result indicates that k observed depends on η and that the
activation of adenylate cyclase is diffusion-controlled process.
6.2 Phase Separation of Biomembranes and Biological
Functions of Cell
Biomembranes are a key area for biological functions. One of major components of
biomembranes, lipid molecules show phase separation correlated with phase transition. Phase transition observed in temperature acclimation of cells regulates function
of proteins through varicosity (fluidity) of lipid membranes. On the other hand, it is
considered that phase separation affects functions of proteins by making
82
6 Physical Properties of Biomembranes and Cellular Functions