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Equilibrium density gradient ultracentrifugation: A simple computer program for routine DNA analysis
CO~1IMI:NIC.4TlONS Equilibrium
Density
A Simple
Gradient Computer
Routine
DNA
with the determination of sedimentation coefiicient,s. The present program has been designed for equilibrium density gradient runs; it is written in Fortran IV, the most, practical and common language, and is 82 cards lollg. The computer gives the buoyant density, the ‘;, of Guanine + Cytosine and the molecular weight within a compilation time of 2 sec. The use of this program does not involve familiar knowledges in computation.
Ultracentrifugation: Program
0%
for
Analysis’
Equilibrium density gradient ult,racentrifugation is one of the most useful methods in the study of nucleic acids (Hearst and Vinograd, 1961). In the case of DNA, a single run gives generally two parameters; the buoyant density and a very
6
dm d2
=‘3
FIG. 1. Parameters of densitometer tracings; RE, external reference hole; dl ,df ,da , distances between RE and bands 1, 2, and 3; see text for definition of g. DNA has been extracted from cold-stressed mature seeds of Cucumis ?neZo; bands 1, 2, and 3 are, respectively, the classical chromosomal DNA(N), the nucleolar satellite DNA(N1) and the new-discovered, G + C rich, nuclear “satellite” DNA(Nh). See Q&tier, Guill& and Vedel for further details. coarse estimation of its molecular weight; it must be emphasized that this last value has no absolute significance and is only useful in comparing different samples. However, the obtained molecular weight represents a minimum one, according to the always possible heterogeneity in density. On the other hand, the base composition of DNAexpressed as y. of Guanine + Cytosine-is linearly related to the buoyant density (Schildkraut, Marmur, and Doty, 1962) and thus can be easily determined. The use of a computer in analytical ultracentrifugation has been recently reviewed (Trautman, 1966); the most part of the programs deals 1 Cards with procedure to our address.
are available
by request
Analytical ultracentrifugations are performed on a Spinco model E equipped with UV optics. Densitograph tracings of the plates are recorded by Joyce-Loebl double-beam microdensitometer. Compilation is carried out on the Univac 1108 supplied with a high speed printer. Symbols used. p, Density of solvant; 8, buoyant, density of a polymer; OM, that of the marker; r’, distance to the axis of rotation; d, distance to the external reference hole; R,, distance between axis of rotation and external reference hole; W, angular velocity; T, absolute temperature; R, gas conallowing to calculate the stant; 00, coefficient density gradient in an aqueous solution of salt; c, standard deviation of polymer distribution. Program. The photographs represent the content of the cell magnified A times. Two kinds of
REAL NT(7i ,~~~~~IW~~MW~~MW~,MW~,MW~ DIMENSION R~~OT(~),RHOPT(~~),TT(~~) DATA N~/1.3626~1~3718~1~3810~1~39~~~1~3994~1~406b~~~4132~ DATA RHOT/1~3~05~1.4005~1.~0U4~1.b0U3~1.7002~1~800~~1~8~01/ J~TA kH0PT/1.1500~1.20o0,1.25V0,~.3000~1.3500~1.~0n0~1~~5~0~
D1.50~0~1.5b0u~1.~J~~1.b50~~.1.70~@~~.7500~1.8~0G~~~b50~~ DATA
ii/2.491.1.94R~1.715,I.54b,].43U~1.346~1.2~6~~.245~1*21~?
F1.197~~.190~1.190~1.199~1.215~1.23~~ 1 2
RLAD Zr~lDt~~KM~RX1,St,~X2~S2,~X3,SlrRX4~S4~RXS~S5 FOR\?Al ( 1 Azl7.4 VI=44UDO
~:((2*3.1416*~1/60)**2) a=1 oouooo c=1oouooooob 3=10000000 DO 3 1=1#6 ii(N-NT(Il)2iJ,10~3
10 11 12 13 14
IF(R~~-R~OPT(I))50,3GIr3 CUNT~NUE T=lT(l) GC TO 200
T=rT~i-l~t(lTT~I~-TT~I-l~~r(HnO-HnOPT~I-l~~/~RHDPT~I~-RHO~T~I-l~~~29 IF (RX11 r21Lv
30
25 100
DO 13 1=1,14
53 200
n7 0% 09
19 20 21 22 23 24 25 26 27 29
RHO=dtiOT(I)
50
Oh
15 16 17 18
CONTINUE
3 IU
13
c2 03 04 05
tl:D~,t~1./2~~~~l./~T~C~l*V~~~~7.3-~RXl/A~~**2~-~~7.3-~R~/A~~**2~~~31
Cl:~C1-1.b6~~/~.OCO98 ~wl=~d.314~D*29~~/~~~Sl/A~*(1./D1~*~~./Dl~*~l./~T*C~~*~~**2~*~~7.3F(Hkll/Al*~21*d) IF (Rnrl ,212, 32:0~+(1./2)+((1./(T*C))+V+(((7.3-(RX2/A))**2)-~~7.3-(R~/A))**2)))36 C~~~~~-1.66Ul/Ci.OUO93 Mwz=(~.31r*~*29U)/~1~52/A)**2)*(l./D2)*(l./(T*C))*(V**2)*((7.3F(RXZl/Ahc2) *al ,212, Ii (RX31 ~3=~~l+(l./il*~(1./~TtC))*V*(~~7.3-tRX3/4))**2)-((7.3-(R~/A))~*2)))41 :3=(33-1.6b~l/l~rUC098
1:
(d&4)
32 33 34 35 37 38 39 4U 42
,212,
~r=3~~+(1./2)r((l./(T+C))*v*(((7.3-(RX4,A~~**2)-~~7.3-~R~,A~~**2~~~~~ :4;(;4-1.66~)/U.~iO96
~~,~~=(~.3t~*~*i~B)/(((~U/A)**2)**2)*(1./D4)*(l./(l*C))*~~**2)*((7*3-
47
48
F(Rr4)/Al+rZ1*81 Ii (HA51 ,312, DS=D~~tIl./~)*((i:/(T*C))*V*((7.3-(RX5/A))**2)-(~7.3-(R~/A))~*2)))51 C~:(~S-1.6bD)/U.U009~~ ~,~~=(b.314*0*~90)/(((ij/k)t+2)*(1./D5)*(l./(T~C)~*lV**2)*((7.3-
119 6,
FZ~16X~Fb.4,29X~F5.2~34X#F6.2,2X,RHk!ILLI~NS.l1 BD
65
52 53
212
21.5
214 0 XBT
67
FIG. 2a. The designed program in Fortran IV; the number at right of each card is its relative position in the pack for rapid relocation. Cards 18-23 make linear interpolation to transform the refraction index (N) into the corresponding CsCl density (RHO); Cards 24-29 make linear interpolation to transform RHO into the corresponding coefficient p” (T). Cards 4-9 are the tables of N, RHO, and T values. Cards 30-54 calculate the buoyant density, the base composition and the minimum molecular weight of each DNA (cards 35,40,45, and 50 shunt the program if the number of bands is <5). Initial data and results are, respectively printed by Cards 5661 and 62-66. The data cards are put after the : X&T one. 686
G87
COMRIUNICATIONS
>TOP
h.“Pk‘
FIG. 2b. Printing
of the results,
parameters are taken into account for calculations: (a) Speed and temperature are set by the operator; and (b) initial density of the solution, position, and width of bands. It is generally necessary to calculate the distance between band and axis of rotation by the relation r = (n, - d)/A. With this program, measuring d is sufficient (Fig. 1). On the other hand, if the speed of rotation is voluntarily-or accidently-altered, it is sufficient to change one card; so it is with the coefficient of magnification A. Two cards must be changed for a different temperature; a different salt alters four cards. Procedllre. Refraction index of CsCl is determined (25”, XNao) after the run. The density of the marker is known. The cl and (r values of each band are measured on the densitometer tracings; g is equal to the half-width of the peak at 0.606 times its height, assuming the gaussian distribution of the polymer. These cards-called “data cards”-are put after the pack of “program cards” (see Fig. Za). Compiled by the computer, they make the following calculations, in 2 set : (1) Calculation of initial CsCl density, according to the International Critical Tables; (2) calculation of the corresponding coefficient p:, according to the table published by Ifft, Voet, and Vinograd (1961); (3) calculation, for each DNA, of the buoyant density . . 0 = 8.~ + $$(l/pj)wz(rz - r.~z); the base composition . . . 7’0 of G + C = (0 - 1X60)/ 0.00098, according to Schildkraut, Marmur, and Doty (1962); the minimum molecular weight . . . MW = RT/a2(l/0) (de/dr)&, with (c@/dr) =
as listed
by the Univac
1108.
&r/p2 (Baldwin, 1959; Hearst and Vinograd. 1961). Results are printed as follows (Fig. 2b): (1) listing of all initial data (refraction index, calculated CsCl density, density of marker, d and d of each DNA); (2) listing of density, o/o of G + C and minimum molecular weight of each DNA. This program has been designed for analytical ultracentrifugations with up to five DNAs plus the marker per cell, and is routinely used in our laboratory since 1 yr. REFERENCES BALDWIN, R. L., Proc. Natl. Acad. hi. 46, 939 (1959). HEARST, J. E., AND VINOGRAD, J., Proc. Natl. Acad. Sci. 47,999 (1961). IFFT, J. B., VOET, D. H., AND YINOGRAD, J., J. Phys. Chem. 66, 1138 (1961). QU~TIER, F., GUILL~, E., AND VISDEL, F., Compt. Rend. Acad. Sci. 266, 735 (1968). SCHILDKRAUT, C. L., MARMUR, J., .\ND DOTY, P., J. Mol. Biol. 4, 430 (1962). TRAUTMAN, R., in “Fractions” (Beckman, ed.), vol. 2, (1966). FRANCIS Q&TIER ETIENNE GUILLI~ LISE LEJUS Laboratoire de Physiologic Ve!gdtale associk au CNRS Facultt! des Sciences 91 -Orsay, France Received October 25, 1968; accepted November 14, 1968.
Density
A Simple
Gradient Computer
Routine
DNA
with the determination of sedimentation coefiicient,s. The present program has been designed for equilibrium density gradient runs; it is written in Fortran IV, the most, practical and common language, and is 82 cards lollg. The computer gives the buoyant density, the ‘;, of Guanine + Cytosine and the molecular weight within a compilation time of 2 sec. The use of this program does not involve familiar knowledges in computation.
Ultracentrifugation: Program
0%
for
Analysis’
Equilibrium density gradient ult,racentrifugation is one of the most useful methods in the study of nucleic acids (Hearst and Vinograd, 1961). In the case of DNA, a single run gives generally two parameters; the buoyant density and a very
6
dm d2
=‘3
FIG. 1. Parameters of densitometer tracings; RE, external reference hole; dl ,df ,da , distances between RE and bands 1, 2, and 3; see text for definition of g. DNA has been extracted from cold-stressed mature seeds of Cucumis ?neZo; bands 1, 2, and 3 are, respectively, the classical chromosomal DNA(N), the nucleolar satellite DNA(N1) and the new-discovered, G + C rich, nuclear “satellite” DNA(Nh). See Q&tier, Guill& and Vedel for further details. coarse estimation of its molecular weight; it must be emphasized that this last value has no absolute significance and is only useful in comparing different samples. However, the obtained molecular weight represents a minimum one, according to the always possible heterogeneity in density. On the other hand, the base composition of DNAexpressed as y. of Guanine + Cytosine-is linearly related to the buoyant density (Schildkraut, Marmur, and Doty, 1962) and thus can be easily determined. The use of a computer in analytical ultracentrifugation has been recently reviewed (Trautman, 1966); the most part of the programs deals 1 Cards with procedure to our address.
are available
by request
Analytical ultracentrifugations are performed on a Spinco model E equipped with UV optics. Densitograph tracings of the plates are recorded by Joyce-Loebl double-beam microdensitometer. Compilation is carried out on the Univac 1108 supplied with a high speed printer. Symbols used. p, Density of solvant; 8, buoyant, density of a polymer; OM, that of the marker; r’, distance to the axis of rotation; d, distance to the external reference hole; R,, distance between axis of rotation and external reference hole; W, angular velocity; T, absolute temperature; R, gas conallowing to calculate the stant; 00, coefficient density gradient in an aqueous solution of salt; c, standard deviation of polymer distribution. Program. The photographs represent the content of the cell magnified A times. Two kinds of
REAL NT(7i ,~~~~~IW~~MW~~MW~,MW~,MW~ DIMENSION R~~OT(~),RHOPT(~~),TT(~~) DATA N~/1.3626~1~3718~1~3810~1~39~~~1~3994~1~406b~~~4132~ DATA RHOT/1~3~05~1.4005~1.~0U4~1.b0U3~1.7002~1~800~~1~8~01/ J~TA kH0PT/1.1500~1.20o0,1.25V0,~.3000~1.3500~1.~0n0~1~~5~0~
D1.50~0~1.5b0u~1.~J~~1.b50~~.1.70~@~~.7500~1.8~0G~~~b50~~ DATA
ii/2.491.1.94R~1.715,I.54b,].43U~1.346~1.2~6~~.245~1*21~?
F1.197~~.190~1.190~1.199~1.215~1.23~~ 1 2
RLAD Zr~lDt~~KM~RX1,St,~X2~S2,~X3,SlrRX4~S4~RXS~S5 FOR\?Al ( 1 Azl7.4 VI=44UDO
~:((2*3.1416*~1/60)**2) a=1 oouooo c=1oouooooob 3=10000000 DO 3 1=1#6 ii(N-NT(Il)2iJ,10~3
10 11 12 13 14
IF(R~~-R~OPT(I))50,3GIr3 CUNT~NUE T=lT(l) GC TO 200
T=rT~i-l~t(lTT~I~-TT~I-l~~r(HnO-HnOPT~I-l~~/~RHDPT~I~-RHO~T~I-l~~~29 IF (RX11 r21Lv
30
25 100
DO 13 1=1,14
53 200
n7 0% 09
19 20 21 22 23 24 25 26 27 29
RHO=dtiOT(I)
50
Oh
15 16 17 18
CONTINUE
3 IU
13
c2 03 04 05
tl:D~,t~1./2~~~~l./~T~C~l*V~~~~7.3-~RXl/A~~**2~-~~7.3-~R~/A~~**2~~~31
Cl:~C1-1.b6~~/~.OCO98 ~wl=~d.314~D*29~~/~~~Sl/A~*(1./D1~*~~./Dl~*~l./~T*C~~*~~**2~*~~7.3F(Hkll/Al*~21*d) IF (Rnrl ,212, 32:0~+(1./2)+((1./(T*C))+V+(((7.3-(RX2/A))**2)-~~7.3-(R~/A))**2)))36 C~~~~~-1.66Ul/Ci.OUO93 Mwz=(~.31r*~*29U)/~1~52/A)**2)*(l./D2)*(l./(T*C))*(V**2)*((7.3F(RXZl/Ahc2) *al ,212, Ii (RX31 ~3=~~l+(l./il*~(1./~TtC))*V*(~~7.3-tRX3/4))**2)-((7.3-(R~/A))~*2)))41 :3=(33-1.6b~l/l~rUC098
1:
(d&4)
32 33 34 35 37 38 39 4U 42
,212,
~r=3~~+(1./2)r((l./(T+C))*v*(((7.3-(RX4,A~~**2)-~~7.3-~R~,A~~**2~~~~~ :4;(;4-1.66~)/U.~iO96
~~,~~=(~.3t~*~*i~B)/(((~U/A)**2)**2)*(1./D4)*(l./(l*C))*~~**2)*((7*3-
47
48
F(Rr4)/Al+rZ1*81 Ii (HA51 ,312, DS=D~~tIl./~)*((i:/(T*C))*V*((7.3-(RX5/A))**2)-(~7.3-(R~/A))~*2)))51 C~:(~S-1.6bD)/U.U009~~ ~,~~=(b.314*0*~90)/(((ij/k)t+2)*(1./D5)*(l./(T~C)~*lV**2)*((7.3-
119 6,
FZ~16X~Fb.4,29X~F5.2~34X#F6.2,2X,RHk!ILLI~NS.l1 BD
65
52 53
212
21.5
214 0 XBT
67
FIG. 2a. The designed program in Fortran IV; the number at right of each card is its relative position in the pack for rapid relocation. Cards 18-23 make linear interpolation to transform the refraction index (N) into the corresponding CsCl density (RHO); Cards 24-29 make linear interpolation to transform RHO into the corresponding coefficient p” (T). Cards 4-9 are the tables of N, RHO, and T values. Cards 30-54 calculate the buoyant density, the base composition and the minimum molecular weight of each DNA (cards 35,40,45, and 50 shunt the program if the number of bands is <5). Initial data and results are, respectively printed by Cards 5661 and 62-66. The data cards are put after the : X&T one. 686
G87
COMRIUNICATIONS
>TOP
h.“Pk‘
FIG. 2b. Printing
of the results,
parameters are taken into account for calculations: (a) Speed and temperature are set by the operator; and (b) initial density of the solution, position, and width of bands. It is generally necessary to calculate the distance between band and axis of rotation by the relation r = (n, - d)/A. With this program, measuring d is sufficient (Fig. 1). On the other hand, if the speed of rotation is voluntarily-or accidently-altered, it is sufficient to change one card; so it is with the coefficient of magnification A. Two cards must be changed for a different temperature; a different salt alters four cards. Procedllre. Refraction index of CsCl is determined (25”, XNao) after the run. The density of the marker is known. The cl and (r values of each band are measured on the densitometer tracings; g is equal to the half-width of the peak at 0.606 times its height, assuming the gaussian distribution of the polymer. These cards-called “data cards”-are put after the pack of “program cards” (see Fig. Za). Compiled by the computer, they make the following calculations, in 2 set : (1) Calculation of initial CsCl density, according to the International Critical Tables; (2) calculation of the corresponding coefficient p:, according to the table published by Ifft, Voet, and Vinograd (1961); (3) calculation, for each DNA, of the buoyant density . . 0 = 8.~ + $$(l/pj)wz(rz - r.~z); the base composition . . . 7’0 of G + C = (0 - 1X60)/ 0.00098, according to Schildkraut, Marmur, and Doty (1962); the minimum molecular weight . . . MW = RT/a2(l/0) (de/dr)&, with (c@/dr) =
as listed
by the Univac
1108.
&r/p2 (Baldwin, 1959; Hearst and Vinograd. 1961). Results are printed as follows (Fig. 2b): (1) listing of all initial data (refraction index, calculated CsCl density, density of marker, d and d of each DNA); (2) listing of density, o/o of G + C and minimum molecular weight of each DNA. This program has been designed for analytical ultracentrifugations with up to five DNAs plus the marker per cell, and is routinely used in our laboratory since 1 yr. REFERENCES BALDWIN, R. L., Proc. Natl. Acad. hi. 46, 939 (1959). HEARST, J. E., AND VINOGRAD, J., Proc. Natl. Acad. Sci. 47,999 (1961). IFFT, J. B., VOET, D. H., AND YINOGRAD, J., J. Phys. Chem. 66, 1138 (1961). QU~TIER, F., GUILL~, E., AND VISDEL, F., Compt. Rend. Acad. Sci. 266, 735 (1968). SCHILDKRAUT, C. L., MARMUR, J., .\ND DOTY, P., J. Mol. Biol. 4, 430 (1962). TRAUTMAN, R., in “Fractions” (Beckman, ed.), vol. 2, (1966). FRANCIS Q&TIER ETIENNE GUILLI~ LISE LEJUS Laboratoire de Physiologic Ve!gdtale associk au CNRS Facultt! des Sciences 91 -Orsay, France Received October 25, 1968; accepted November 14, 1968.