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Flow birefringence and flexibility of desoxyribonucleic acid (DNA) molecules
Flow birefringenee of D N A molecules
2193
REFERENCES 1. L. B. SOKOLOV and T. L. KRUgLOVA, Vysokomol. soyed. 2: 704, 1960 2. V. V. KORSHAK, T. M. FRUNZE and L. V. KOZLOV, Izvest. Akad. N a u k SSSR, Otd. k_him. Nauk, 2062, 1962 3. V. V. KORSHAK, T. M. FRUNZE and L. V. KOZLOV, Izvest. Akad. N a u k SSSR, Otd. khim. Nauk, 2226, 1962 4. L. V. TURETSKII, L. B. SOKOLOV and V. Z. NIKONOV, Sb. Geterotsepnye vysokomolekularnye soyedineniya. (in: "Heterochain High Polymers".) Izdat. " N a u k a " 107, 1964 5. S. M. LIPATOV, Fiziko-khimiya kolloidov. (The Physical Chemistry of Colloids.) Gos. Khim. Izdat., 1948 6. L. B. SOKOLOV and L. V. TURETSKII, Vysokomol. soyed. 6: 346, 1964 7. P. REHBINDER, Z. phys. Chem. 111: 447, 1924 8. A. B. TAUBMAN, Dissertation, 285, 1948 9. A. A. ABRAMZOV, Yu. L. KIYANOVSKAYA and L. Ya.' KREMNEV, Zhur. priklad. Khim. 37: 2314, 1964 10. L. B. SOKOLOV, T. V. KUDIM and L. V. TURETSKH, Vysokomol. soyed. 3: 1370, 1961
FLOW BIREFRINGENCE AND FLEXIRILITY OF DESOXYRIBONUCLEIC ACID (DNA) MOLECULES* V. N . T S V E T K O V , L . N . A N D R E Y E V A a n d L . N . K V I T C H E N K O H i g h Polymer Institute, U.S.S.R. A c a d e m y of Sciences
(Received 10 March 1965)
OUR previous works [1, 2] reported the study of An and the directional angle of the flow birefringenee of DNA fragments obtained by ultrasonic disintegration. It showed that the difference between the main polarizations, 71--72, of DNA molecules increased with the molecular weight of the sample, M, in accordance with the optical propetries of the semi-rigid chains [3]. To obtain quantitative data on the flexibility of DNA molecules, we continued our dynamic flow birefringenee experiments and also extended these to a larger number of samples, and over a wider range of molecular weights. The DNA fragments were obtained by subjecting DNA solutions to ultrasonic and enzymic disintegration. SAMPLES AND DETERMINATION METHODS Samples of t h y m u s D N A were obtained b y a method dissolved earlier [4]. The source of ultrasound was a 3 W / c m a quartz generator. The DNA-DI~aze reaction was carried out in a 0.04 molar solution of tris-HC1, 0.008 molar MgC11 and 0.2 molar NaC1 of p H ~ 7-5. Neither the ultrasonic nor the enzymic destruc* Vysokomol. soyed. 7: No. 11, 2001-2005, 1965.
2194
V. N. T S V E T K O V
et al.
tion was accompanied b y any pronounced hypochromic effect, thus showing t h a t the molecules were not denatured b y their disintegration. The viscosity of the solutions was measured in a modified Zimm vise0meter [5, 6]. As one can see from Figs. 1 and 2, using (t/r--1)/c<10 , its dependence on the gradient of the rate g a n d concentration c is practically non-existent. This makes it possible to determine the reduced viscosity of the DNA solutions, which is less t h a n expected, in an Ostwald
n
--
0
~
~
0
6 0
0
24.0 o o"
u
o
16.0
=~
X o
o
0 0
i~
x
× u-
I
0
I
O'OZ c~9//00cm3
Fro. 1. (n,-De-.o/C(A) as a function of concentration c for a n u m b e r of DNA fragments solutions obtained by enzymic degradation (test I).
0 " 4 J" 0
o
0 L
~ 7"0
,,
'
0
Q .....
°'-'1
v
1 ~'Q
l 3"0
j
s•
I
50~0
9, see Fro. 2. (tl,--1) as a function of the grsdient of rate g for D N A fragment solutions obtained by enzymic degre~lation (test I): Concentration c as g/100 cma; 1--0-019; 2~0.023; 3--0.038. viscometer, assuming that (0r--1)/c equals the intrinsic viscosity It/]. The birefringence was measured by the usual method in dynamo-optimeters with an internal rotor. The length of the two instruments used was 6.6 and 3.0 em respectively, the aperture width 0.8 and ().3 m m respectively. These instruments were made of polyethylene. The determined birefringence was i n all eases negative and proportional to the gradient of rate g in the range studied. The DNA concentrations were determined from the phosphorus content after hydrolysis with 0-5 molar HC10,. The DNA-DNaze reaction was carried out direetly in the dynamic optimeter b y introducing the required a m o u n t of DNaze into the solution. The samples (about 3.5 em s) were taken for viscometric determinations directly from the instrument. The reaction con-
Flow birefringence of DNA molecules
2195
ditions were selected so that decomposition did not influence the anisotropy and viscosity of the solution during the 6-10 min required for measuring An/g and ~r. Figures 3 and 4 illustrate ~n[g and t/r as functions of time and are based on tests II and III of an enzymic decomposition of DNA. The duration of these tests was 6-8 hours. RESULTS AND ASSESSMENT
The molecular weights of the samples were calculated from [7] using the formula: [~]~1.45× 10-eM 1"12 [7], obtained by Doty for the range 0.3× l0 B to 7.5 × l0 s. The values of [n]/[7] = ~n/g~o(~r -- 1) were calculated from the experimental values of An/g and the corresponding t/r values from Figs. 3 and 4 at a certain point of time. Figure 5 is a diagram of function [n][[tl]=f/(M ). The results, represented by different points refer to the different methods of disintegrating the DNA. The experimental points (although showing a considerable scatter, owing to the incompletely known identity of the samples) are fairly closely grouped around the curve which reaches its m a x i m u m in the range of molecular weights of several millions and then changes into a straight line which runs parallel with the axis M. This means t h a t the hydrodynamic and optical properties of the DNA molecules are identical with those of the Gaussian statistical coil model. Rigid coils like those of the DNA molecule have an insignificant anisotropy of the macro-form [8] and the limiting value of specific [n]/[t/] will be the sum of two members, in which the first will be proportional with the particular anisotropy of the macromolecule, the second with t h a t of its microform [8].
1.0
1'0 0
100
200 300 Time, rnin
4O0
5O0
FIO. 3. Changes of the relative viscosity t/r of DNA solutions as a function of time during enzymic degradation. /--test I; 2--test HI.
2196
V. 1~. TSVETKOVeta/. AR xlO8
0"/8
0.12
t~06
0
200
O0
0
400 600 Time, rnin
800
FIQ. 4. Changes of birefringence of DNA solutions during enzymic degradation. /--test I; 2--test II; 3--tes~ III.
Mo~lim[n--][~/]
45lcT4~(n~q-2)~×s[l(aii_az)(l_3sin2@)q_ns
M]2~NAv °(-~)i J
(i)
where an--a I is the difference between the main polarizations of the bases, ~ the angle formed by the density and the axis of the coiled part in which this base is situated, S the number of nucleotide pairs in the segment, ~ the specific partial volume, and ns the refractive index of the solvent. By assuming ~----80° and aii--a I to be --186 × 10-~5 cm 3, and using the value calculated from the tensor additivity of polarization as a function of the DNA monomer bond [8] together with the specific [n]/[~] found from (1), one can find S and thus also the persistent length of the bispiral DNA chain, a=½S× 3.4 A. The value of a, produced by this method, was equal to 330 A. The value of [n]/[~] decreased with decreasing molecular weight, thus indicating a deviation of the optical properties of the molecules from those of the Ganssian chains. The experimental function [n]/[~l]=f(M) can be compared with the theoretical [9] produced by using the theory of optical anisotropy of persistant chains [3]. Length a, according to [9], can be determined from the intersect A of the experimental curve [n]/[~]=f(M) with the line running parallel to the abscissa at a distance equal to (1/3). lira [n]/[~/]. The projection of the M-~vo
point of intersect onto the abscissa will equal the contour length of the molecule, L~2.5a.
Flow birefringence of DNA molecules
2197
The finding of point A is in our case linked with a fairly large error, because the experimental points of curve 1 showed considerable scatter. However, an extrapolation of curve I to the point of intersect with the line will give an M~ ~(150±25).103 on the abscissa when A is projected onto it; this makes the
[.] ~o~-~ [,7]
o
, ,,,"
°I°
O
1000
@?
~
~" ~-'~-T'~_ n]
o
O
•
o
ob
I
6"0
I
100 MxlO
Fio. 5. Birefringence of fragmented DNA solutions having different molecular weights:/--curve [n]/[q]=] (M) drawn through experimental points: a = fragments obtained by treating DNA solutions with DNaze; b=fragments obtained by treatment with ultrasound; 2--molecular anisotropy curve of 71--71 as a function of x=L/a; 3--initial sector of the theoretical [nil[ill=f(M) curve. contour line of the bispiral DNA chain segment L~=(735~125) A, and the persistant chain then has a=0.4, L~=(2904-50) /~, which is in good agreement with the 330 A obtained above from lira [n]/[~]. The obtained value of a is also M-~oo
in good agreement with t h a t found by using hydrodynamic methods [10]. It is twice as large as that found for the persistant length of the nitrocellulose molecule [11] and is evidence of the greater rigidity of the bispiral DNA structure. The a of DNA is, at the same time, only ~-1/3 that of the persistant length of the a-spiral in poly-7-benzyl-L-glutamate [12]. Curve 3 in Figure 5 represents the initial part of the theoretical [n]/[~]=f(M) curve [9] which, after extrapolation (dotted line), joins the experimental curve 1. Curve 2 represents the dependence of the equilibrium anisotropy of the macromolecule, 71--7~, on M [3]. In accordance with theory [9], the second curve should be situated below the first over the whole range of M when specific F1--72 and [n]/[~] values are used together. CONCLUSIONS
(1) The flow birefringence, [n] and the viscosity [7] of solutions containing the ultrasonic or enzymic disintegration fragments of DNA, having a molecular weight ranging from 0.2 to 11 x 106, was studied.
2198
V . N . TSVETKOVeta/.
(2) The e x p e r i m e n t a l [n]/[##] values increased with increasing molecular weights of t h e samples a n d the curve of f u n c t i o n [n]/[##]= f ( M ) r e a c h e d a m a x i m u m a t larger M, t h e n continuing as a straight line parallel with axis M. A comparison of this curve with t h e theoretical [3] of molecular a n i s o t r o p y 7,--72 as a function of molecular weight showed this second curve to be s i t u a t e d below the first over t h e whole range of M w h e n m a x i m u m values of 7,--72 a n d [n]/[~] were used together, which was in accordance with the t h e o r y [9]. (3) T h e use of the theoretical a n i s o t r o p y of D N A m o n o m e r chain [8] a n d the consideration o f the micro-form effect [8] gave the specific [n]/[~] for larger values of M; this was used to calculate the persistant chain length a. I t was f o u n d to be 330 A. (4) T h e value of a, o b t a i n e d b y other, i n d e p e n d e n t methods, appears to have been o b t a i n e d in the range of small M [9]. This gave a persistant chain length of a----290 A. These two values m u s t be t a k e n as identical within the limits of experimental error.
Translated by K. A. ALLEN REFERENCES
1. V. N. TSVETKOV, L. N. ANDREYEVA, and V. I. 8ISENKO, Sb. Molekulyarnaya biofizyka). (Collection, Molecular Biophysics.) 110, 1965 2. V. N. TSVETKOV, V. Ye. ESKIN and S. Ya. FRENKEL', Struktura makromolekul v rastvorakh. (Macromolecular Structure in Solutions.) Izdat. ,,!~auka", Moscow, 619, 1964 3. V. N. TSVETKOV, Vysokomol. soyed. 4: 894, 1962 4. J. S. COLTER, R. A. BROWN and K. A. O. ELLEM, Biochim. biophys. Aeta 55: 31, 1962 5. V. N. TSVETKOV and E. V. KORCHEYEVA, Vestnik Leningr. Gos. Univ. 22: No. 4, 1965 6. B. ZIMM and D. CROTHERS, Proc. Nat. Acad. Sei. USA. 48: 905, 1962 7. P. DOTY, B. Mc GILL, and S. RISE, Proc. Nat. Acad. ScL USA 44: 411, 1958 8. V. N. TSVETKOV, Vysokomol. soyed. 5: 740, 1963 9. V. N. TSVETKOV, Vysokomol. soyed., 7: 1968, 1965 10. L E. HEARST and W. H. STOCKMAYER, J. Chem. Phys. 37: 1425, 1962 11. V. N. TSVETKOV, I. N. SHTENNIKOVA, N. A. MEZHERITSKAYA and L. SI BOLOTNIKOVA, Sb. Tsellyuloza i eye proizvodnye (Collection, Cellulose and its Derivatives.) Izd. Akad. Nauk SSSR, 74, 1963 12. V. N. TSVETKOV, I. N. SHTENNIKOVA, Ye. I. RYUMTSEV and G. I. OKHR1MENKO, Vysokomol. soyed. 7: 1104, 1965
2193
REFERENCES 1. L. B. SOKOLOV and T. L. KRUgLOVA, Vysokomol. soyed. 2: 704, 1960 2. V. V. KORSHAK, T. M. FRUNZE and L. V. KOZLOV, Izvest. Akad. N a u k SSSR, Otd. k_him. Nauk, 2062, 1962 3. V. V. KORSHAK, T. M. FRUNZE and L. V. KOZLOV, Izvest. Akad. N a u k SSSR, Otd. khim. Nauk, 2226, 1962 4. L. V. TURETSKII, L. B. SOKOLOV and V. Z. NIKONOV, Sb. Geterotsepnye vysokomolekularnye soyedineniya. (in: "Heterochain High Polymers".) Izdat. " N a u k a " 107, 1964 5. S. M. LIPATOV, Fiziko-khimiya kolloidov. (The Physical Chemistry of Colloids.) Gos. Khim. Izdat., 1948 6. L. B. SOKOLOV and L. V. TURETSKII, Vysokomol. soyed. 6: 346, 1964 7. P. REHBINDER, Z. phys. Chem. 111: 447, 1924 8. A. B. TAUBMAN, Dissertation, 285, 1948 9. A. A. ABRAMZOV, Yu. L. KIYANOVSKAYA and L. Ya.' KREMNEV, Zhur. priklad. Khim. 37: 2314, 1964 10. L. B. SOKOLOV, T. V. KUDIM and L. V. TURETSKH, Vysokomol. soyed. 3: 1370, 1961
FLOW BIREFRINGENCE AND FLEXIRILITY OF DESOXYRIBONUCLEIC ACID (DNA) MOLECULES* V. N . T S V E T K O V , L . N . A N D R E Y E V A a n d L . N . K V I T C H E N K O H i g h Polymer Institute, U.S.S.R. A c a d e m y of Sciences
(Received 10 March 1965)
OUR previous works [1, 2] reported the study of An and the directional angle of the flow birefringenee of DNA fragments obtained by ultrasonic disintegration. It showed that the difference between the main polarizations, 71--72, of DNA molecules increased with the molecular weight of the sample, M, in accordance with the optical propetries of the semi-rigid chains [3]. To obtain quantitative data on the flexibility of DNA molecules, we continued our dynamic flow birefringenee experiments and also extended these to a larger number of samples, and over a wider range of molecular weights. The DNA fragments were obtained by subjecting DNA solutions to ultrasonic and enzymic disintegration. SAMPLES AND DETERMINATION METHODS Samples of t h y m u s D N A were obtained b y a method dissolved earlier [4]. The source of ultrasound was a 3 W / c m a quartz generator. The DNA-DI~aze reaction was carried out in a 0.04 molar solution of tris-HC1, 0.008 molar MgC11 and 0.2 molar NaC1 of p H ~ 7-5. Neither the ultrasonic nor the enzymic destruc* Vysokomol. soyed. 7: No. 11, 2001-2005, 1965.
2194
V. N. T S V E T K O V
et al.
tion was accompanied b y any pronounced hypochromic effect, thus showing t h a t the molecules were not denatured b y their disintegration. The viscosity of the solutions was measured in a modified Zimm vise0meter [5, 6]. As one can see from Figs. 1 and 2, using (t/r--1)/c<10 , its dependence on the gradient of the rate g a n d concentration c is practically non-existent. This makes it possible to determine the reduced viscosity of the DNA solutions, which is less t h a n expected, in an Ostwald
n
--
0
~
~
0
6 0
0
24.0 o o"
u
o
16.0
=~
X o
o
0 0
i~
x
× u-
I
0
I
O'OZ c~9//00cm3
Fro. 1. (n,-De-.o/C(A) as a function of concentration c for a n u m b e r of DNA fragments solutions obtained by enzymic degradation (test I).
0 " 4 J" 0
o
0 L
~ 7"0
,,
'
0
Q .....
°'-'1
v
1 ~'Q
l 3"0
j
s•
I
50~0
9, see Fro. 2. (tl,--1) as a function of the grsdient of rate g for D N A fragment solutions obtained by enzymic degre~lation (test I): Concentration c as g/100 cma; 1--0-019; 2~0.023; 3--0.038. viscometer, assuming that (0r--1)/c equals the intrinsic viscosity It/]. The birefringence was measured by the usual method in dynamo-optimeters with an internal rotor. The length of the two instruments used was 6.6 and 3.0 em respectively, the aperture width 0.8 and ().3 m m respectively. These instruments were made of polyethylene. The determined birefringence was i n all eases negative and proportional to the gradient of rate g in the range studied. The DNA concentrations were determined from the phosphorus content after hydrolysis with 0-5 molar HC10,. The DNA-DNaze reaction was carried out direetly in the dynamic optimeter b y introducing the required a m o u n t of DNaze into the solution. The samples (about 3.5 em s) were taken for viscometric determinations directly from the instrument. The reaction con-
Flow birefringence of DNA molecules
2195
ditions were selected so that decomposition did not influence the anisotropy and viscosity of the solution during the 6-10 min required for measuring An/g and ~r. Figures 3 and 4 illustrate ~n[g and t/r as functions of time and are based on tests II and III of an enzymic decomposition of DNA. The duration of these tests was 6-8 hours. RESULTS AND ASSESSMENT
The molecular weights of the samples were calculated from [7] using the formula: [~]~1.45× 10-eM 1"12 [7], obtained by Doty for the range 0.3× l0 B to 7.5 × l0 s. The values of [n]/[7] = ~n/g~o(~r -- 1) were calculated from the experimental values of An/g and the corresponding t/r values from Figs. 3 and 4 at a certain point of time. Figure 5 is a diagram of function [n][[tl]=f/(M ). The results, represented by different points refer to the different methods of disintegrating the DNA. The experimental points (although showing a considerable scatter, owing to the incompletely known identity of the samples) are fairly closely grouped around the curve which reaches its m a x i m u m in the range of molecular weights of several millions and then changes into a straight line which runs parallel with the axis M. This means t h a t the hydrodynamic and optical properties of the DNA molecules are identical with those of the Gaussian statistical coil model. Rigid coils like those of the DNA molecule have an insignificant anisotropy of the macro-form [8] and the limiting value of specific [n]/[t/] will be the sum of two members, in which the first will be proportional with the particular anisotropy of the macromolecule, the second with t h a t of its microform [8].
1.0
1'0 0
100
200 300 Time, rnin
4O0
5O0
FIO. 3. Changes of the relative viscosity t/r of DNA solutions as a function of time during enzymic degradation. /--test I; 2--test HI.
2196
V. 1~. TSVETKOVeta/. AR xlO8
0"/8
0.12
t~06
0
200
O0
0
400 600 Time, rnin
800
FIQ. 4. Changes of birefringence of DNA solutions during enzymic degradation. /--test I; 2--test II; 3--tes~ III.
Mo~lim[n--][~/]
45lcT4~(n~q-2)~×s[l(aii_az)(l_3sin2@)q_ns
M]2~NAv °(-~)i J
(i)
where an--a I is the difference between the main polarizations of the bases, ~ the angle formed by the density and the axis of the coiled part in which this base is situated, S the number of nucleotide pairs in the segment, ~ the specific partial volume, and ns the refractive index of the solvent. By assuming ~----80° and aii--a I to be --186 × 10-~5 cm 3, and using the value calculated from the tensor additivity of polarization as a function of the DNA monomer bond [8] together with the specific [n]/[~] found from (1), one can find S and thus also the persistent length of the bispiral DNA chain, a=½S× 3.4 A. The value of a, produced by this method, was equal to 330 A. The value of [n]/[~] decreased with decreasing molecular weight, thus indicating a deviation of the optical properties of the molecules from those of the Ganssian chains. The experimental function [n]/[~l]=f(M) can be compared with the theoretical [9] produced by using the theory of optical anisotropy of persistant chains [3]. Length a, according to [9], can be determined from the intersect A of the experimental curve [n]/[~]=f(M) with the line running parallel to the abscissa at a distance equal to (1/3). lira [n]/[~/]. The projection of the M-~vo
point of intersect onto the abscissa will equal the contour length of the molecule, L~2.5a.
Flow birefringence of DNA molecules
2197
The finding of point A is in our case linked with a fairly large error, because the experimental points of curve 1 showed considerable scatter. However, an extrapolation of curve I to the point of intersect with the line will give an M~ ~(150±25).103 on the abscissa when A is projected onto it; this makes the
[.] ~o~-~ [,7]
o
, ,,,"
°I°
O
1000
@?
~
~" ~-'~-T'~_ n]
o
O
•
o
ob
I
6"0
I
100 MxlO
Fio. 5. Birefringence of fragmented DNA solutions having different molecular weights:/--curve [n]/[q]=] (M) drawn through experimental points: a = fragments obtained by treating DNA solutions with DNaze; b=fragments obtained by treatment with ultrasound; 2--molecular anisotropy curve of 71--71 as a function of x=L/a; 3--initial sector of the theoretical [nil[ill=f(M) curve. contour line of the bispiral DNA chain segment L~=(735~125) A, and the persistant chain then has a=0.4, L~=(2904-50) /~, which is in good agreement with the 330 A obtained above from lira [n]/[~]. The obtained value of a is also M-~oo
in good agreement with t h a t found by using hydrodynamic methods [10]. It is twice as large as that found for the persistant length of the nitrocellulose molecule [11] and is evidence of the greater rigidity of the bispiral DNA structure. The a of DNA is, at the same time, only ~-1/3 that of the persistant length of the a-spiral in poly-7-benzyl-L-glutamate [12]. Curve 3 in Figure 5 represents the initial part of the theoretical [n]/[~]=f(M) curve [9] which, after extrapolation (dotted line), joins the experimental curve 1. Curve 2 represents the dependence of the equilibrium anisotropy of the macromolecule, 71--7~, on M [3]. In accordance with theory [9], the second curve should be situated below the first over the whole range of M when specific F1--72 and [n]/[~] values are used together. CONCLUSIONS
(1) The flow birefringence, [n] and the viscosity [7] of solutions containing the ultrasonic or enzymic disintegration fragments of DNA, having a molecular weight ranging from 0.2 to 11 x 106, was studied.
2198
V . N . TSVETKOVeta/.
(2) The e x p e r i m e n t a l [n]/[##] values increased with increasing molecular weights of t h e samples a n d the curve of f u n c t i o n [n]/[##]= f ( M ) r e a c h e d a m a x i m u m a t larger M, t h e n continuing as a straight line parallel with axis M. A comparison of this curve with t h e theoretical [3] of molecular a n i s o t r o p y 7,--72 as a function of molecular weight showed this second curve to be s i t u a t e d below the first over t h e whole range of M w h e n m a x i m u m values of 7,--72 a n d [n]/[~] were used together, which was in accordance with the t h e o r y [9]. (3) T h e use of the theoretical a n i s o t r o p y of D N A m o n o m e r chain [8] a n d the consideration o f the micro-form effect [8] gave the specific [n]/[~] for larger values of M; this was used to calculate the persistant chain length a. I t was f o u n d to be 330 A. (4) T h e value of a, o b t a i n e d b y other, i n d e p e n d e n t methods, appears to have been o b t a i n e d in the range of small M [9]. This gave a persistant chain length of a----290 A. These two values m u s t be t a k e n as identical within the limits of experimental error.
Translated by K. A. ALLEN REFERENCES
1. V. N. TSVETKOV, L. N. ANDREYEVA, and V. I. 8ISENKO, Sb. Molekulyarnaya biofizyka). (Collection, Molecular Biophysics.) 110, 1965 2. V. N. TSVETKOV, V. Ye. ESKIN and S. Ya. FRENKEL', Struktura makromolekul v rastvorakh. (Macromolecular Structure in Solutions.) Izdat. ,,!~auka", Moscow, 619, 1964 3. V. N. TSVETKOV, Vysokomol. soyed. 4: 894, 1962 4. J. S. COLTER, R. A. BROWN and K. A. O. ELLEM, Biochim. biophys. Aeta 55: 31, 1962 5. V. N. TSVETKOV and E. V. KORCHEYEVA, Vestnik Leningr. Gos. Univ. 22: No. 4, 1965 6. B. ZIMM and D. CROTHERS, Proc. Nat. Acad. Sei. USA. 48: 905, 1962 7. P. DOTY, B. Mc GILL, and S. RISE, Proc. Nat. Acad. ScL USA 44: 411, 1958 8. V. N. TSVETKOV, Vysokomol. soyed. 5: 740, 1963 9. V. N. TSVETKOV, Vysokomol. soyed., 7: 1968, 1965 10. L E. HEARST and W. H. STOCKMAYER, J. Chem. Phys. 37: 1425, 1962 11. V. N. TSVETKOV, I. N. SHTENNIKOVA, N. A. MEZHERITSKAYA and L. SI BOLOTNIKOVA, Sb. Tsellyuloza i eye proizvodnye (Collection, Cellulose and its Derivatives.) Izd. Akad. Nauk SSSR, 74, 1963 12. V. N. TSVETKOV, I. N. SHTENNIKOVA, Ye. I. RYUMTSEV and G. I. OKHR1MENKO, Vysokomol. soyed. 7: 1104, 1965