Supplement
ot
the Progress
ot Theoretical
Phys1cs, No. 11, 19()1
Roles of the Hydrogen Bond System in Biologically
Important Molecules
Reikiti ITOH
Kobayasi Institute of Physical Research, Kokubunzi, Tokyo
Abstract
It has been pointed out by several observations that the hydrogen bond
system may have important roles in the biological macromolecular substances.
In this paper we will review the speculative picture of such system on the
view-point of physical considerations, while up to the present it seems not to
be clearly established yet. In the former part of this paper, experimental data
will be given for such measurements as X-ray diffraction, infrared absorption,
electron spin resonance, ultraviolet absorption and so on. Later, the phase
transition in the kinetic rate measurement of thermal reaction of macromolecules
and also their functional abilities will be discussed using the hypothetical model
of protein which has the operative function analogous to that of the computing
machine.
§1. Introduction
Living system has two kinds of particular nature from the molecular
theorectical standpoint.
One of these is the complex static structure of
the macromolecules which construct the living cells as an important component of them.
The other is their dynamical properties whereby the
functions of the cells and of the organisms as a whole are achieved.
Though there exist many kinds of macromolecules in the living systems,
the typical important molecules are proteins and nucleic acids on account
of their roles in biosynthesis and in cell divisions. The so-called globular
proteins such as enzymes, antibodies, hemoglobins, albumines, globlines
and so on, are known to have important roles in the chemical reactions
in vivo, and the nucleic acids have the particular importance in the
reproductions of the organism, and genetic and growth processes.
In this article we discuss the static structure of these ·molecules and
give some considerations on their functional abilities paying attention to
the hydrogen bond system in them.
§2. Experimental support of hydrogen bond
a) X-ray
X-ray diffraction data play very important roles in the
present knowledge of structures of proteins or nucleic acids, though the
latter data are less certain.
10
lt Itoh
It has been pointed out thaea) the molecular parameters determined
for amides can be applied for the proteins, and the hydrogen bond is an
important ordering element in the crystals of macromolecules. There are
many possible arrangements of the molecular con:figulations in crystal, and
then the precise prediction of molecular arrangements is not to be expected.
0
0
The bond lenght. of NH· .. O varies from 2.67 A to 3.07 A, and the bond
angles range from 95° to 165° for N···O=C, and from 100° to 130° for
0 ... N-C. There exist in general two forms of molecular arrangements of
polypeptides, i. e., proteins, which have been termed a and S, respectively,
after Astbury.
Pauling and Corey 1b) suggested that under some conditions
globular proteins seem to be converted into the form similar to that of
S-keratin, and they proposed the a-helix as a basic feature of their
structure.
In such structure, polypeptide chain runs helically on the
cylindrical surface with 3.7 residues per turn of 5.4 A pith, which is solidi:ficated by three hydrogen bonds: ···O=C-NH· .. O=C-HN···O=C-NH···.
These hydrogen bonds play an important role in the functional ability
Kendrew 2) determined the primary structure of
of protein molecules.
myoglobin by the X-ray diffraction data.
The secondary and the tertiary
structure of protein and, hence, their specific characters are directly
related to the sequence of amino acids in the main chain.
These steric
structures of polypeptide chain are held by the hydrogen bonds which
control the internal rotation of amino acids.
Astbury, Watson and Crick/n and Langridge 4) played important parts
in the establishment of the molecular structure of DNA (dioxyribonucleic
acid) from X -ray data.
Their cyclic bases are essentially co planer in
which the bond lengths of NH· .. O and NH .. ·N are 2.85 A and 3.00 A,
respectively, and their bonds are nearly linear: bond angles are less than
about 15 °.
The bond length of NH · · ·0 is sometimes smaller than the
above value: it is about 2.82 A. It has been confirmed that DNA has the
so-called double helix structure in which two DNA-chains run to opposite
directions from each other, with ten basic radical pairs in a periodical
sequence of 33.7 A. Langridge 4) determined a possible model, which fitted
in with the intensities of the pattern of X-ray diffraction, from a few models
calculated from the supposed helical· arrangement.
It seems that RNA
(ribonucleic acids) hardly have the ability of crystallization.rn Experiments
show that TMV (tobacco mosaic virus) protein has the helical rod structure
of which the diameter js about 40 A with an empty in its center. 5 )
b) Infrared abs01·ption Measurement of infrared absorption has
made the contributions of four kinds in the consideration of proteins.
They show the presence of N-H groups which construct the hydrogen
bonds in proteins and have the ability to distinguish between the intraand the inter-molecular hydrogen bonds in their solutions.
They suggest
0
0
Roles of the 1-lydrogen Bond System in Biologically Important Molecules
71
the trans configuration of substituted amide group and, when polarized
infrared light is used, they give the information about the orientation of
the bond moment.
If amide residue forms hydrogen bond, vibrational
frequencies of N-H group are shifted to the lower one, i.e., the characteristic
frequency of 3450.......,3500 cm- 1 moves to 3200.......,3350 cm- 1. The characteristic
frequencies of amide I and II are shifted from 1630 cm- 1 to 1659 cm- 1
and from 1520 cm- 1 to 1540 em-\ respectively, when the polypeptide
chain changes its structure from the extended configuration to the a-helix
configuration. 7) Therefore, the intra· and inter-molecular interactions of
polypeptide chains are considered as the weak perturbations. The spectra
show no indication of the 0-H vibration in hydrogen bond, so it is
suggested that the amide group does not have a high percentage of enol
form.
In the case of DNA, Tsuboi8) has measured the characteristic absorp·
tion of 1710 cm- 1 of nucleotide in calf thymus DNA. Since the strectching
vibration of C=O in the base pairing between cytosin and guanine and
that of C = N in the base pairing between adenine and thymine were
1720 cm- 1 and 1700 em-\ respectively, he suggested that the existence of
1710 cm- 1 absorption gave the evidence of the presence of base pairing
in the DNA molecules. Both microsomal RNA and S-RNA (soluble-RNA)
have 1705 cm- 1 absorption which show the base pairs in native NaRNA. 8>
This seems, however, to be due to the particular structure something like
a loop structure.*
c) Other experiments Besides the X-ray and infrared measurements,
there are several chemical evidences for the presence of hydrogen bonds
in the biological macromolecules. Those are the experiments, for example,
of PH-titration curve,36 > chemical action of urea which breaks the hydrogen
bond but not the covalent bonds, effect of the ionic strength or PH on
the absorption of ultraviolet light, especially of 2600 A, its hypochromic 37 )
effects by PH and temperature 35 ) in solution and so on.
Detailed
informations of these experiments will be given elsewhere in this
publication.
§3. Electronic consideration
It may be evident that experiments on the electron spin resonance
can give the informations on the structure of native proteins in addition
to the informations from the observation of X-ray diffraction and infrared
absorption.
Hausser9) pointed out that the native protein can be looked
* This is confirmed by the hypochromic effect observed in ultraviolet absorption of RNA
in solution where hydrogen bonded (or, base paires) helix structure is considered to be
partially in the single-stranded configuration of RNA molecule.6l
72
R. ltoh
upon as semiconductor which has conductivity along the chain of hydrogen
bonds perpendicular to the main polypeptide chains. Electron mobility
results in the narrowing of the absorption lines and in disappearing of
the hyperfine structures which is due to the very efficient mechanism of
recombination of the electrons with the corresponding holes. Since in the
denatured proteins the network of the hydrogen bonds which form the
conduction bands may be disordered as will be discussed later, the
electrons may lose their mobility, and the experimental results are similar
as those obtained from amino acids excepting the hyperfine structures.
Blumenfeld, Kalmanson,10 J and Gordy 11 J observed the doublet resonance in
certain irradiated proteins.
It was also suggested that the intensities of
resonance absorption was much stronger in denatured proteins than in
natural ones.
On the other hand, Evans and Gergely 12 J proposed that
there occured in protein molecules the overlap interaction of molecular
orbitals between the n-eletrons across the hydrogen bonds, which were
effective to produce the overlap conduction band due to such n-elecrons.
They gave the following energy gap between valence and conduction
bands, that is, using the three different models it was estimated as 3.2 ev,
3.5 ev, and 4.8 ev respectively. According to Kasha' s discussion13J and the
results of Eley et al./ 4 J it is evident that pure protein molecules should
be electric insulators and may have photoconductivity but not semiconductivity.
As for the mechanism of such behavior, Kasha has had an idea
of extrinsic electronic conductivity caused by the new levels which arises
in the term schema from the presence of lattice imperfections or impurity
centers similar to those in organic semiconductor.
If the existence of
such trapping centers is true,* it is reasonable to consider that they play
an important role in electronic conduction.
The resonance overlap or
the resonance integral of n-electrons across the hydrogen bonds should be
smaller than those across the ordinary covalent bond of conjugated
system. Then, the electron transfer in the bond systems of macromolecules
may be considered to be done via non-adiabatic processes rather than via
adiabatic processes, and to be due to the process of the so-called hopping
type or something like a polaron motion15J analogous to some organic
semiconductors.
§4. Phase transition in macromolecules with ordered structure
Several experiments show the presence of phase transition in which
the ordered structure of the system of macromolecules is changed, which
* In the bond ruptured state of hydrogen bonds, the unit peptide bond may behave as
something like a radical or a biradical because it has one or two odd electrons.
Then such
a bond may play a role of the electron trapping center, and may give new energy levels in
the polypeptide chain system.
11.oles of the Ifyrlrogen Botul System hi Biologically jmportant Molecules
13
seems to be caused by the breakage of hydrogen bonds or their confor·
mation changes. Light scattering experiments suggest that the dissociation
of double-stranded helix DNA is caused by the breakage of about two
It is
base pairings/6 > that is, the rupture of about ten hydrogen bonds.
obtained
noteworthy that the transition point, 85°C, of DNA conformation
by the measurement of the extinction coefficient of ultraviolet (2600 A)
8
absorption* consists with that by the infrared observation by Tsuboi, > that
is, by the disappearance of band, 1680 em-\ of NaDNA in D20 which
indicates the breakage of base pairs. There are some other evidences for
the phase transition such as the viscosity change depending on PH of
solution, the change in the critical wave length of rotatory dispersion,
the existence of melting point of synthetic polynucleotide helix, the
change of stranding number, two or three, in the sedimentation equilibrium
in the density gradient, and so on.** On the other hand, RNA molecule
dose not show the phase transition in the ultraviolet measurement
though there will be partial base pairing in the random coil configuration
in its solution.
0
§5. Denaturation and hydrogen bond
Denaturation of natural protein or nucleic acid is considered to be
the disorganization of their structure by the rupture of vital intramolecular
This defintition is in accord with the earlier
bonds which stabilize it.
interpretation by Mirsky and Paulingm in which they emphasized the key
In this connection,
role of the hydrogen bonds in protein reaction.
18
Lumry and Eyring > distinguished among several different arrangements of
hydrogen bonds, for example, those in the states of reversible and irreversible denaturation, and they proposed the term "conformation changes"
for these changes. In some respect the denaturation may be regarded as
Although the isolated
the quasi phase transition in the molecular level.
secondary bonds may be continually broken in random by the thermal motion
such bond may be normally reformed in the same configuration and the
structure of the molecule as a whole may be maintained by the constraints
If many disturbances arise at the same
imposed by neighbor bonds.
instance, there may be a chance of the improper formation of bonds, and
the molecular structure may be changed into an irreversible, disordered
This model gives a satisfactory interpretation of thermodynamical
state.
as well as kinetic data for the thermal denaturation of proteins and
nucleic acids.
* In
0
the case of copolymer of polyadeninenucleotide, ultraviolet absorption of 2520 A shifts
to 2570 A after its dissociation into single strand.16)
** In these measurements, the optical density may correspond to the base stacking absorption, while the optical rotatory dispersion to the secondary structure of the molecule.
74
it 1toh
Using the said model Platzman and Franck111) explained the effect of
temperature on radiation sensitivity. When the effect of ionization or
excitaion is subcritical for denaturation, its effect may become critical at
elevated temperatures because of the argumented probabililty that the
ambient thermal disorder can supplement the radiation effect and bring it
help to surpass the threshold for denaturation.
The pronounced thermal
sensitivity observed is explained by this property. For an another example,
it is known that the thermal inactivation of DNA by heating can partly
recover unless the rate of cooling is so rapid that the disorganized
molecule can not afford to tie with each other by the reformation of
ruptured hydrogen bonds.16)
Denaturation may cause the change in some of the following properties,
that is, solubility, biological activity, molecular size and shape, and
susceptibility to enzymatic reactions. We guess that there will be several
conformations of protein which correspond respectively to each of these
properties and in each conformation there will be a different critical
number of hydrogen bonds which should be broken to cause the denaturation.
The following Tables I, II and III show the critical number of
hydrogen bonds which should rupture for the denaturation of the proteins
and nucleic acids obtained from the data of thermal inactivation rates.
Table I. Thermal inactivation data and critical number of hydrogen bond breakages.
Enzymes
vv,r ~},~h
r.
1
1
Mol wt
AF
25,000
35,000
35,000
37,000
36,500
1
-0.91
0.16
1.3
0
fW
-~
Chymotripsinogen
Pepsinogen
Tripsine
..aH
(Kcal/mol)
57.3
99.6
143
31
67.6
AS
(e. u.)
PH
180
316
432
93
213
3.0
2.0
3.0
7
6.5
Temp
&H/5
&S/16
40
45.·5
11
20
28
6
14
11
20
27
6
13
45.5
45
44
These are for the reactions in the reversible transformation where the tertially structure is
rearranged by the secondary bond breakage and is measured by solubility. (See ref. 18.)
Table II. Thermal inactivation data and critical number of hydrogen bond breakages .
&F
.::tH
(Kcal/mol)
Enzymes
24.0
25.7
25.1
26.2
24.7
Pancreatic lipase
Tripsine
Entrokinase
Tri psinkinase
Pancreatic proteinase
I
i
45.4
40.2
42.2
44.3
37.9
.dS
(e.u.)
&H/5
..dS/7
68.2
44.7
52.8
57.6
9
8
8
9
8
10
6
8
8
I
These are for the irreversible inactivation reaction,l8l PH=6"'7, t°C=40-60.
-
Roles of the }Jydrogen Bond System in Biologically important Molecules
75
Table III. Thermal inactivation data and critical· number of hydrogen bond breakages
Enzymes
Insuline
Tri.psine
Pepsin
Peroxidase (milk)
Ovalbumine
Hemoglobin
Yeast invertase
l
Mol wt
12,000
24,000
37,000
40,000
43,000
68,000
120,000
\
(Kcj~mol)
35.6
40.2
55.6
185
132
75.6
110
l
4S
(e u)
11.9
22.4
56.5
233
158
76.5
131.5
4H/5
7
8
11
37
26
15
22
4S/6
2
4
9
39
26
13
22
These are data reported by Platzman and Frank19l using Stern's.
In these tables, .JF is the free energy difference, .JH is the enthalpy of
activation, both in Kcal/mole, and .JS is the entropy of activation in
entropy unit. Stern20 > proposed a calculation of the number of hydrogen
bonds which have been ruptured in the activated complex, i. e., the
critical number of hydrogen bonds which should be broken in order to
put its conformation into disord erby assuming the average energy requirement of 5 Kcal/mole, the hydrogen bond energy and the average entropy
increment of 6 e.u. for the irreversible inactivation reaction. As is shown
in these Tables, the calculated critical number of hydrogen bonds are
almost the same in both from the energy value and from the entropy
value, except in case of small proteins in Table III. In such calculation we
assume the average value of entropy change of breakage of hydrogen
bond to be 7 e. u. in Table II and 16 e. u. in Table I.
A large value of
entropy change in Table I will be considered to be due to a number of
unnecessary breakages of hydrogen bonds which will be restored normally
in the reversible process of transformation and also considered as indicat·
ing the more entropy change in the change of solubility than in the
inactivation of enzyme proteins. Cox and Peacocke 21 > presented a simplified
mathematical attack on the denaturation which seemed to have promise.
They used a statisitcal method for finding the number of hydrogen bonds
which should have been simultaneously broken to denature the DNA
molecule.
Calculated number of hydrogen bonds, 10,......,50, is very small
compared with the total number of hydrogen bonds, of the order of 20,000
in a molecule.
On the other hand, Kauzman22 > listed some values of .JH
and JS for denaturation ranging from 50 to 60 Kcal/mole and from 200 to
400 e. u., respectively, for several proteins.
Platzman and Franck19> proposed a mechanism of radiation damage of
macromolecules in which the dielectric absorption is considered to depend
on the polarization of vibration in the hydrogen bond system after the
ionization, in which the breakage of hydrogen bonds and the denaturation
may come out.
They also pointed out the possibility of denaturation by
R.ltoh
76
the molecular isomerization after its excitation. The former is supported
by the presence of low frequency absorption of infrared region of about
300 cm- 1 in the proteins and nucleic acids,23 ) while the latter is confirmed
by the rotatory dispersion measurement by Murakami24 ) who reported the
change of critical wavelength of 1850 A and 2600 A for native and
denaturated DNA's, respectively. Since there is no non-bonding n-electron
in the base paired conformation of DNA, the presence of the absorption,
2600 A, which is attributed to n-n transition of unpaired base groups, may
show the occurrence of isomerization due to the breakage of hydrogen
bonds or base unpairization. In addition it is suggestive that the irradiation
of near ultraviolet, i. e., 3.4 ev to cell, results in causing cancer, which
may be a kind of denaturation and has attributed to conformation of
proteins due to the keto-enol tautomerization. 25 )
Watson and Crick, 3) and Overend and Peacocke 26 ) proposed that the
hydrogen bonding plays a role in the genetic duplication of nucleic acid.
If we interrupt the process of base pairing in the DNA synthesis in cell
division by any one of the following methods, that is, deamination reaction, trivial loss of proton in the base by basic reaction, ionization by
irradiation, reduction, excitation and so on, the resultant DNA molecules
have a chance of changing the base sequence and hence the daughter
cells have a chance to cause mutation, since any base to which hydrogen
bond formation is impossible, wiH be put out from the base pairing. 16 )
In this point of view, the hydrogen bonds between bases are considered
as an important factor in the presence of DNA activity.
0'
0
0
§6. Functional ability of macromolecules
Dynamical and functional abilities of macromolecules are only inadequately explained by the simple physical mode] which corresponds to the
static chemical structure.
In order to explain their dynamical nature
27
Shimanouchi ) proposed the so-called computer model of protein as a
working hypothesis.
He regarded the protein molecule as a small computing machine.
An element of such computer is considered to be a
peptide bond, -CO-NH-, and there exist 153 units of such bonds in a
molecule of myoglobin protein, and more than 300,000 units in a molecule
of self-reproducible TMV protein.
Connections among these units are
considered to be made by the hydrogen bonds between peptides and by
the hydrogen bonds and n-electron system between peptide and side
chain. In the case of myoglobin, output heme group is connected with
histidine side chain by the hydrogen bond system.
In such case the
surrounding conditions such as PH of the medium, partial pressure of
oxygen, some secretions from muscle and the situation of the contact
Roles of the Hydrogen Bond System in Biologically Important Molecules
77
with muscle fiber, etc. are considered as input actions, and the output is
the information on the attachment or release of oxygen to or from heme.
Our previous work28 ) on the effect of hydrogen bond upon infrared
absorption spectra allows us to add some considerations to this proposed
model of protein.
The proton in the hydrogen bond has a set of
quantized energy states of vibration due to the resonance interaction
between double minimum of potential.
The effects of hydrogen bond on
the infrared absorption of N-methyl-acetamide, such as red shift, strengthening of the intensity, and increment of half width, were explained semiquantitatively with the resonance interaction between the normal state and
the proton transferred state of vibration of molecule, just analogous to
the case of the charge transfer spectra of molecular complex. The proton
transfer is closely connected with the electron transfer through the
participation in the conjugated systems and should be treated as an acidbase reaction problem from the broader point of view.
In our previous
29
paper ) it has been pointed out that the acid-base characters of some
protonated aromatics are changed by the excitaion of their n:-electrons,
and this fact is well known by the comparison of the photochemical absorp·
tion and emission data after and before excitation. In such cases it is
suggested that the change in acidity (or basicity) corresponds to that in
the n:-electron density of protonated atoms after and before the excitation ..
The increase of n-electron density on the donor atom will induce the
proton to attract more closely through the strengthened a-bond.
In this
connection, the site of proton may be determined by the n:-electron density
of donor (or acceptor) atom in th~ hydrogen bond system. In the excited
state of n-electron the proton may be given a chance to approach to the
neighboring peptide in the ground state, and as such peptide is in the
excited state, the proton will go back to the original position or will be
pushed to the next neighbors.
Since the energy transfer in protein is
explained by the exciton transfer30 ) or sensitized resonance transfer 31 ) in
some cases, it will be possible to consider the exciting process as a basis
for these transfers.
In CO-myoglobin complex it is well known that CO
is released by the absorption of either ultraviolet in protein or visible
light in hemin. 33 ) Considering the excitation as an input, the site of
proton will be selected at each step of its transfer.
However, since the
chemical reaction, such as reduction-oxidation or acid-base reactions, may
often act as an input action, one should take the electron transfer or
proton transfer as a basic process in the initial action.
It is not so
unnatural to suppose here that the proton transfer and the rr-electron
transfer between donor and acceptor have a complemental relation.
The
well-known effect of hydrogen bond on the near ultraviolet absorption
spectra of some aromatics 32 l in solution will give a subtle base to this
R. Itoh
78
consideration.
Namely, the separation of the proton in the substituted
group, 0.02 A, can cause some parent molecules to stabilize it energetically in the order of 0.1 ev.
Though it may seem as a perturbation, the
change in the position of proton site will make a drastic change of the energy
of n-·electrons in the peptide bond.
This closed connection will give the
essential part of excitation and will result in the determination of the
proton site in the chain. As a final case of input action, we consider the
conduction of the electrons or the holes donated from the outside.
Such
electrons or holes will pass either due to the so-called hopping process
discussed in the previous part of this paper or through something like
the low-lying molecular exciton band in the sense of Kasha's model.
Which is the case depends on the situation that such electrons or holes
act either as a combined particles leading to the dissociation of the exciton
by its trapping or as independent particles moving through the wider
overlapping excited orbital.
These imput actions will give the sign of "yes" or "no" as a reply
of the unit element of a computer.
It is noteworthy that Shimanouchi
has suggested the correspondence between three hydrogen bonds in a-helix
turn unit and the three codes in the parametron computer for operating
"a:nd" or "or".
As a consequence, initial actions will be converted to
proton transfer where the stretching vibrations of donor and acceptor in
the chain will help the transfer of the information via transfer of electron
and hence via that of proton, though he considers the proper vibration
as the main possibility.
0
References
1a)
lb)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
G. C. Pimentel and A. L. McClellan, The Hydrogen Bond, W. H. Freeman and Company,
1960.
L. Pauling, R. B. Corey and H. R. Branson, Proc. Nat. Acad. Sci. U. S. 37 (1951), 205,
235.
J. C. Kendrew et al., Nature 181 (1958), 662; Proc. Roy. Soc. A253 (1959), 70; Rev.
Mod. Phys. 31 (1959), 94.
J, D. Watson and F. H. C. Crick, Nature 171 (1953), 737, 964.
R. Langridge, H. R. Wilson, C. W. Hooper, M. H. F. Wilkins and D. D. Hamilton, J.
Mol. Biol. 2 (1960), 19, 38.
H. Kakudo, Report at the 3rd Meeting on Biophysics held at Research Institute for
Fundamental Physics, Kyoto University, Kyoto, Aug., 1960.
K. !so, see ref. 5).
A. Elliott and E. ]. Ambrose, Nature 165 (1950), 921.
M. Tsuboi, see ref. 5).
K. H. Hausser, Radiation Research Supplement 2 (1960), 480.
L. A. Blumenfeld and A. E. Kalmanson, Biofizika 3 (1958), 87.
vV. Gordy et al., Proc. Nat. Acad. Sci. U. S. 41 (1955), 983; 46 (1960), 1124, 1137.
M. G. Evans and J. Gergely, Biochim. et Biophys. Acta 3 (1949), 188.
M. Kasha, Rev. Mod. Phys. 31 (1959), 162.
Roles of the Hydrogen Bond System in Biologically Important Molecules
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
79
D. D. Eley et al., Nature 162 (1948), 819; Trans. Farad. Soc. 49 (1953), 79; 51 (1955),
1529.
I. Oshida and Y. Ooshika, private communication. Also see N. V. Riehl, Zhnr. Fiz.
Kim. 6 (1955), 959; 7 (1955), 1152.
D. C. Northrop and 0. Simpson, Proc. Roy. Soc. A234 (1956), 124.
L. E. Lyons, J, Chem. Soc. (1957), 5001.
T. Holstein, Annals of Phys. 8 (1959), 325, 343.
K. Iso, see ref. 5).
A. E. Mirsky and L. Pauling, Proc. Nat. Acad. Sci. U. S. 22 (1936), 439.
R. Lumry and H. Eyring, J. Phys. Chern. 58 (1954), 110.
R. L. Platzman and J. Frank, Symp. on Information Theory in Biology, ed. by H. P.
Yockey, R. L. Platzman and H. Quastler, Perg. Press, N. Y., 1959.
A. E. Stern, Advances in Enzynwlogy, ed. by F. F. Nord, 9 (1949), 25.
R.. A. Cox and A. R. Peacocke, J, Poly~ Sci. 23 (1957), 765.
W. Kauzman, Denaturation oj Protein and Enzymes, John Hopkins Press, Baltimore,
1954.
T. Miyazawa, see ref. 5).
H. Murakami, J. Chern. Phys. 27 (1957), 1231.
0. Schmidt, Naturwiss. 29 (1941), 146.
W. G. Overend and A. R. Peacocke, Endeavour 16 (1957), 90.
T. Shimanouchi, Kagaku (Science) 30 (1960), 39; Buturi (J. Phys. Soc. Japan) 15
(1960), 565, both in Japanese.
I. Oshida, Y. Ooshika and R. Miyasaka (Itoh), J. Phys. Soc. japan 10 (1955), 849.
R. Itoh, J, Phys. Soc. Japan 14 (1959), 1224.
M. Kasha, Rev. Mod. Phys. 31 (1959), 162.
Th Forster, Disc. Farad. Soc. No. 27 (1959), 7; Radiation Research Supplement 2
(1960), 326.
S. Nagakura and H. Baba, J. Chern. Soc. Japan Pure Chern. Sect. 71 (1950), 610; 72
(1951), 3, 219, in Japanese.
H. Tsubomura, ibid. 73 (1951), 841, 920, in japanese.
R. Miyasaka (Itoh), Busseiron Kenkyu No. 62 (1953), 94, in Japanese.
]. Frank and R. Livingston, Rev. Mod. Phys. 21 (1949), 505.
P. Doty, A. Wada, ]. T. Yang and E. R. Brout, ]. Poly. Sci. 23 (1957), 851.
P. Doty, Rev. Mod. Phys. 31 (1959), 107.
J. R. Fresco and P. Doty, j. Amer. Chern. Soc. 79 (1957), 3928.
S. A. Rice and P. Doty, J, Arner. Chem. Soc. 79 (1957), 3937.
S. A. Rice, Rev. Mod. Phys. 31 (1959), 69.
C. Tanford, Symp. Protein Structure, John Wiley and Sons Inc., N. Y., 1957.
A. Wada, ]. Chern. Soc. Japan Pure Chern. Sect. 79 (1958), 1393, in Japanese.
P. Doty et al., Ann. N. Y. Acad. Sci. 81 (1959), 693.
G. Telsenfeld and A. Rich, Biochim. et Biophys. Acta 26 (1957), 457.