proteins in aqueous environment. And lipid molecules assemble to form lipid bilayer
membranes and show phenomena of statistical thermodynamics such as phase
transition and phase separation. Differential scanning calorimetry observes equilibrium of statistical system, but most functions of living organisms is fulfilled in
non-equilibrium state. Dynamics of molecules and biological system are observed
by various physical techniques such as ESR, NMR and fluorescence spectroscopy,
and some of these techniques are developed to become imaging methods to observe
the phenomena directly.
3.2 X-ray Crystallography
The best contribution of X-ray crystallography in life science is elucidation of double
strand structure of DNA. Most important functional molecule is protein that is
synthesized according to genetic information on DNA. There is a concept, ‘function
is on structure’. And the first 3dimensional structure of protein was determined by
contributions of Max Pertz and John Kendrew using X-ray diffraction of hemoglobin. Incident X-ray beams scatter by electron of each atom. The scattered beam of
specific angle is enhanced in regular structure of crystal to give a diffraction pattern.
And the diffraction pattern is shown by Brag condition, λ ¼ 2d Á sin θ where d, λ and
θ are distance between crystal planes, wavelength of X-ray and incident angle to
lattice plane, respectively.
3.2.1 Principle of X-ray Diffraction
Resolution of optical microscope is determined by equation of d ¼ 0:61
λ
N:A: , where d
λ and N.A. are minimum distance for distinguishing two points, wavelength of
observing light and numerical aperture of objective lens, respectively. This means
that observation depends on wavelength of light. X-ray diffraction method using
X-ray of 0.1 nm wavelength makes possible to observe smaller structure compared
to optical microscope using ~300 nm light. When molecules are arranged regularly
in crystal, unit of regular structure in crystal is called unit lattice. Structure of the
crystal is composed of unit lattices translated x, y and z directions, resulting in
diffraction lattice. Incident X-ray beams are scattered discretely to h, k and l of
diffracted X-ray in reciprocal lattice space. Structure factor, that is relationship
between diffracted X-ray and position coordinate of an atom in the crystal is
shown by equation F hkl
ð Þ ¼
X N
j¼1
f j e
À2πi hx j þky j þlz j
ð
Þ , where x j , y j and z j , f j are
coordinates of each atom in jth molecule and atomic scattering factor of jth molecule.
30
3 Methods for Physical Properties of Biomembranes and Cells
membranes and show phenomena of statistical thermodynamics such as phase
transition and phase separation. Differential scanning calorimetry observes equilibrium of statistical system, but most functions of living organisms is fulfilled in
non-equilibrium state. Dynamics of molecules and biological system are observed
by various physical techniques such as ESR, NMR and fluorescence spectroscopy,
and some of these techniques are developed to become imaging methods to observe
the phenomena directly.
3.2 X-ray Crystallography
The best contribution of X-ray crystallography in life science is elucidation of double
strand structure of DNA. Most important functional molecule is protein that is
synthesized according to genetic information on DNA. There is a concept, ‘function
is on structure’. And the first 3dimensional structure of protein was determined by
contributions of Max Pertz and John Kendrew using X-ray diffraction of hemoglobin. Incident X-ray beams scatter by electron of each atom. The scattered beam of
specific angle is enhanced in regular structure of crystal to give a diffraction pattern.
And the diffraction pattern is shown by Brag condition, λ ¼ 2d Á sin θ where d, λ and
θ are distance between crystal planes, wavelength of X-ray and incident angle to
lattice plane, respectively.
3.2.1 Principle of X-ray Diffraction
Resolution of optical microscope is determined by equation of d ¼ 0:61
λ
N:A: , where d
λ and N.A. are minimum distance for distinguishing two points, wavelength of
observing light and numerical aperture of objective lens, respectively. This means
that observation depends on wavelength of light. X-ray diffraction method using
X-ray of 0.1 nm wavelength makes possible to observe smaller structure compared
to optical microscope using ~300 nm light. When molecules are arranged regularly
in crystal, unit of regular structure in crystal is called unit lattice. Structure of the
crystal is composed of unit lattices translated x, y and z directions, resulting in
diffraction lattice. Incident X-ray beams are scattered discretely to h, k and l of
diffracted X-ray in reciprocal lattice space. Structure factor, that is relationship
between diffracted X-ray and position coordinate of an atom in the crystal is
shown by equation F hkl
ð Þ ¼
X N
j¼1
f j e
À2πi hx j þky j þlz j
ð
Þ , where x j , y j and z j , f j are
coordinates of each atom in jth molecule and atomic scattering factor of jth molecule.
30
3 Methods for Physical Properties of Biomembranes and Cells