Molecular weights of coliphages and coliphage DNA

J. Mol. Biol.

(1970) 54, 547-556

Molecular Weights of Coliphages and Coliphage DNA II. Measurement of Diffusion Coefficients Using Optical Mixing Spectroscopy, and Measurement of Sedimentation Coefficients STUART B. DUBIN, GEORGE B. BENEDEK Center for Materials

Xcience and Engineering,

and Department

of Physics

Massachusetts Institute of Technology Cambridge, Mass. 02139. 1J.S.A. FRANK C. BANCROFT~ AND DAVID Graduate Department

Brandeis University,

FREIFELDER

of Biochemistry

Waltham, Mass. 02154, U.S.A.

(Received 23 March 1970) The molecular weights of the coliphages T4, T5 and T7 have been determined by measurement of their diffusion coefficient (D) and sedimentation coefficients (8). D WLW determined using the new technique of optical mixing spectroscopy. Valuem of DzO,w for T4, T5, T7, and X phages were found to be (in units of 10m7 cm2/sec) 0.295 f 0.003, 0.397 f 0.004, 0.603 & 0.006, and 0.497 &- 0.005 respectively. Values of S”ao,W were found to be (in Svedbergs) 890 3 15, 615 f 10, 463 f 8, and 360 f 10, respectively. Using values of V from the preceding paper Bancroft & Freifelder (1970) the phage molecular weights for T4, T5, and T7 were then calculated to be (in millions) 192.5 & 6.6, 109.2 & 4.0, and 50.4 5 1.8. From the percentage DNA in these phages (Bancroft & Freifelder, 1970) the molecular weights of T4, T5, and T7 DNA ware found to be (in millions) 105.7 & 3.8, 67.3 & 3.1, and 258 f 1.0.

1. Introduction It is well known that the molecular weight of a macromolecule can be determined from measurements of the diffusion coefficient (D), the sedimentation coefficient (S), and the partial specific volume (a). In this paper we report accurate measurements of the diffusion coefficient and the sedimentation coe6cient for the coliphages T4, T.5, T7 and X. In the preceding paper (Bancroft & Freifelder, 1970) measurements of d and the ratio of the mass of DNA to that of the total phage are presented for T4, T5 and T7. Combining these seperate measurements, the molecular weights of both the phages and their DNA have been determined accurately. This program has become feasible because of the development of a new method for the precise measurement of the diffusion constant (Dubin, Lunacek & Benedek, t Present address: Department 10027, U.S.A.

of Biological

Sciences, Columbia 647

University,

New York,

N.Y.

548

S. B. DUBIN

ITAL.

1967). This method uses a “self-beating spectrometer” to measure the extremely narrow spectrum of laser light quasi-elastically scattered from a solution of macromolecules and is particulary favorable for large macromolecules such as bacteriophages for which the spectral power density of the scattered light is very large. In the present experiments it has been possible to measure D with an accuracy of about 1% in times as short as one hour or less. Conventional methods for the measurement of D are often unsatisfactory for such large macromolecules because the diffusion is so slow as to require measurement times of the order of days during which the temperature must be kept spatially and temporally quite constant. In the present method, precise temperature control is unnecessary since the self-beating spectrornet,er is insensitive to convection so long as the bulk flow of liquid is uniform across the illuminated volume, as observed at the phototube. This fact alone is of sufficient value to warrant general adoption of this t’echnique to measure D of high molecular weight material.

2. Measurement of the D&.&on Coefficient from the Spectrum of the Scattered light : Theory Because of the newness of this technique, the underlying theory will be presented briefly. A more detailed discussion has been presented by Dubin et al. (1967), and by Clark, Lunacek & Bcnedek (1970). It is well known that the intensity of the light scattered from a solution of macromolecules can provide information on the molecular weight of the scatterers provided that the scattered intensity can be reliably extrapolated to the forward scattering direction. For large molecules this extrapolation is often quite uncertain. In our experiments we measure the spectrum of the scattered light. The spectral width is directly proportional to the diffusion constant of the scattering macromolecules. In previous papers the physical origin of this spectrum has been described both from a macroscopic, continuum point of view (Dubin et al., 1967) and from a microscopic, random walk point of view (Clark et al., 1970). The spectral width of the scattered light is so narrow ( 5 10 kHz) that a laser light source having high spectral purity must be used for the incident light. Also an ultra-high resolution spectrometer such as the self-beating optical mixing spectrometer (Ford & Benedek, 1965; Forrester, 1961) is required t,o observe the spectrum of the scattered light. The principles that underly this method for measuring macromolecular diffusion coefficients can be expressed briefly as follows. As is indicated in Figure 1, light of wave vector k, is allowed to fall on an assemblage of macromolecules each of which, at some time t, is located at the position r,(t). The intensity of the light scattered with wave vector k is determined at each instant of time by the superposition of the phases of the waves scattered by each of the molecules at the various positions r,(t). The intensity of the scattered light fluctuates randomly about the value of the mean intensity because the phase of the light waves scattered by each molecule is constantly changing as the particle undergoes a random walk. The phase of the wave scattered by a particle at rj relative to a point at the origin (0) is easily seen to be 4, = (k, - k) * rl(t) 3 K * r,(t). The difference K = k, - k is defined as the “scattering vector.” The magnitude of this vector is

MOLECULAR

WEIGHTS

OF COLIPHAGES

649

recorder

FIG. 1. So&taring geometry and block diagram of self-bating

qectrometer.

where 13is the angle between the wave vectors of the incident and scattered light (k, and k), 72is the index of refraction of the solution, and h is the wavelength of the incident light in vacuum. Because of the continually changing arrangement of particles the intensity I(t) of the scattered light fluctuates randomly. This random variable I(t) can be characterized by its spectral power density or by its correlation function. If rO is the “correlation time” beyond which intensity fluctuations at t are uncorrelated with those at t + 7, then the width of the spectrum [(AU) l,Z] of the intensity flucturttions is related to rC by the condition

where (Aw),,, is the half-width at half-maximum in radians per second. We may therefore find the spectral width of the scattered light intensity by estimating the magnitude of TV.* the correlation time for the random fluctuations in I(t). This is done by recognizing that 7Cis the time required for each particle to diffuse so far that its new phase after diffusion has changed on the mean square by an amount 2 N 1. Since @=

(K * Ar,(t))2 z K2Ari(t),

and since the mean square change in position Ari(t) (that of K) in a random walk process is given by

elong any psrticular

direction

we see that the condition for the time rC is ii?+4

-K2DrC.

The spectral width of the intensity fluctuations

is therefore 2~r(Av)~,~=[(Aw),,, = l/r,,

650

8. B. DUBIN

- DKa. In fact an exact calculation (Clark et al., 1970)

ET AL.

of the effect shows the rigorous result to be

where Av, ,2 is the half width at half maximum in Hertz. Detailed calculation also shows that if the molecule is small compared to the light wavelength and undergoes isotropic random walk, the line shape is Lorentzian whose normalized form is given by G(v) =

(2DK2/2r) 2 7 va + (2DK2/2~)2 I OF

(3)

with

I;G(v)dv

= 1.

In all the present experiments the line shapes were found to be accurately Lorentzian so that the value of the diffusion constant D could be deduced unambiguously from the line width, since the scattering vector K is known via equation (1) from the scattering angle 0 and the index of refraction of the solution. The spectrum of the intensity fluctuations is found experimentally by measuring the spectrum of the fluctuations in the photocurrent from a phototube which is illuminated by the scattered light. This spectrum is obtained with the aid of an audio frequency spectrum analyzer and the spectrum is recorded on a strip-chart recorder. Discussion of this method for spectral analysis is to be found in Clark et al. (1970) and in Materials and Methods of this paper.

3. Materials and Methods The bacteriophages used in these studies were obtained from the same lots as described in the preceding paper (Bancroft & Freifelder, 1970). The X was X ti1 2004 isolated by R. Thomas. This DNA contains a small deletion of unknown size (J. D. Shalk, personal communication). The sedimentation coefficient of T4 phage was determinedin 0.1 M-N&I, 0.01 M-MgSO,, 0.001 lur-CaCl,, and 0.01 M-Tris-HCl buffer (pH 7.0). All other sedimentation coefficients and diffusion coefficients were determined in the solvents given in Table 1. All experimental runs were performed within 1 hr after filling the scattering cell except in the case of T’i’. Diffusion constant results for this phage were found to be erratic and unreproducible unless the diluted phage solution wss allowed to stand for about 10 hr (at 7°C) after dilution. The source of this problem is not understood but it is noteworthy that the optical density of a T7 phage solution which has been diluted will slowly rise and then level off. Evidently some type of phage-solvent or phage-glass interaction occurs upon dilution but its effects are gone after waiting several hours. The concentrations of diluted phage solutions were determined by measuring the optical density at 26Omn and using the data from Bancroft & Freifelder (1970). At the concentrations used, no difference could be detected between the viscosities of the solvent alone, and the phage-solvent solution, thereby eliminating the possibility of the presence of any free DNA in the experimental solutions. DNase wss therefore not used in these studies. The scattering cells were cleaned in Alconox and rinsed extensively. Approximately 100 ml. of distilled water (20 cell vol.) pretlltered with a 0.22~ Millipore type MF filter was the forced through the cell. The water remaining in the cell was forced out and the cell

MOLECULAR

WEIGHTS

OF COLIPHAUES

661

TABLET Solvents u-sed in the chtemhation

of bacteriophage diffukon and sedimentation wejkients

Bacteriophage

Solvent

T4

o.srVr-N&l O.OOlaa-MgCl, O.OlM-TrisHCl buffer (PH 74)

T6

0.11~N&l O.Olx-MgSO1 0~001r&-c&c1, OvOln-Tris-HCl buffer (PH 7-O)

T7 x

same as T4 O.OlM-MgSO, O*Olrd-Tris-HCl buffer (PH 7.0)

was dried by a stream of dry nitrogen also prefiltered with a 0.22~ filter. Since the system was closed, this process excluded dust from the cell and rendered it ready for filling. Dilute phage solutions were filtered into the scattering cell through specially prepared 0.22~ Millipore filters. To avoid loss of phage by adsorption to the titers, the filters were prewashed in 0.1% bovine serum albumin and then rinsed in distilled water (Davison & Freifelder, 1902). No phage loss was encountered in the filtration as determined by optical density measurement before and after filtration. The filled cells showed no particulate contamination, as determined both by low-angle observation of the scattered light and by observation of the unfocused beam (about 2 mm in diameter) through a to-power microscope. The block diagram of the self-beating spectrometer is displayed in Fig. 1. The f3328A radiation of a Spectra-Physics model no. 125 laser (N 50 mw) is focused in the scattering cell (standard spectrophotometric cuvette). The transmitted laser beam is monitored by a silioon solar cell which controls a servo to ensure constant leer power. Light scattered at an angle 0 is focused onto an RCA 7265 photomultiplier tube, the output of which is analyzed by a General Radio 1900A audio spectrum analyzer. Sinoe the output of this device is proportional to the voltage rather than power spectrum, its output is squared before display on the strip chart recorder. By slowly sweeping the center frequency of the spectrum analyzer the entire self-beat spectrum may be mapped out. About 1 hr is required to obtain the complete spectrum. No temperature controls were used in the determination of the diffusion coefficients. The requirement of precise temperature stability in conventional determinations of D is not necessary with this spectrometer since, to first order, convection currents do not affect this measurement of D (Dubin et al., 1967). All data were taken between 23 and 25”C, and the temperature in the experimental area was constant to better than 0.2 deg. C? during the course of a run ( N 1 hr). Analytical centrifugation was performed in a Spinco model E ultracentrifuge equipped with ultraviolet optica. The following centrifuge speeds were used: T4, 6995 rev∈ T6, 8776 rev./n&; T7 and A, 11,673 rev./min. The sedimentation coefficients were all measured in the range 23 to 26’C, and the temperature was constant to better than O-1 deg. C during each run ( N 0.5 hr). All sedimentation coefficient and diffusion ceofficient data were reduced to standard conditions (ZO’C, water) in the usual manner. Solvent kinetic viscosities were determined

S. B. DUBIN

662

ET

AL.

with a Cannon-Manning semimicro viscometer calibrated against double-distilled water (0.26% precision). The solvent densitiee were determined from data in the International Critical Tables assuming additivity of the individual constituent densities. These density values were used both to convert the measured kinetic viscosity values to the solvent viscosity, and to normalize the buoyancy correction to standard conditions. The sedimentation rates were determined from densitometric traces of the photographic plates

obtained with a Joyce-Loebl Recording Microdensitometer. Diffusion coefficients were obtained by performing a least-squares best Lorentzian to the experimentally observed self-beat spectra and hence obtaining the half-width haIf-maximum (d&l,. We then obtained D using equation (2).

fit at

4. Results (a) Bifsusim coeficients Equation (3) described the power spectrum of the light scattered by a solution of macromolecules under the assumption that the molecules diffuse isotropically. However, three of the four phages studied (T4, T5 and A) are quite asymmetric having long thin tails (Williams k Fraser 1953; Cummings, Chapman & DeLong, 1965) so that it is important to determine whether equation (3) is applicable. The self-beat spectrum of the light scattered by T4 was therefore studied as a function of scattering angle for nine angles between 33.9” and 160”. Equation (2) predicts that (Av)~,~should vary linearly with the square of the wave vector over this range and go to zero for K = 0. Figure 2 shows that this is very accurately the case for T4. Hence equation (2)

0

O-I I

O-2 I

0.3 I

@4 I

ml2 (012) 0.6 05 I I

0.7 I

O-8 1

09 I

IO

Corrected to 20" C. water

0

1

2

3 4 5 K= m units of IO'O cm‘?

6

7

FIG. 2. (+)Av~,~ ver8w) Ka for T4 bacteriophage at 30 &ml.

5000

240

220

200

180 160 I40 I20 *-- Frequency (Hz)

100

80

60

40

20

0

Fro. 3. The self-beat speotrum of the light scattered at 0 = 33.9” by T4 bacteriophage at 30 &nl. The open &rcles indicate a Lorentzian fit of half-width 66.2 Hz.

MOLECULAR

WEIGHTS

-

OF COLIPHAQES

653

Frequency ( Hz 1

FIG. 4. The self-beat spectrum of the light scattered at 0 = 160” by T4 bacteriophage The open circles indicate a Lorentzian fit of half-width Bf36Hz.

at 3Opg/ml.

is valid for the very asymmetric phage T4, and thus the other three phages have been studied at only a single scattering angle, namely, 90”. Equation (3) predicts that the power spectrum of the fluctuations in the photocurrent should be Lorentzian. In Figure 3 the self-beat spectrum of the light scattered by T4 phage at an angle of 33.9” is shown. The open circles refer to a least-squares fit with @iv),,, = 652Hz. It’is clear from Figure 5 that the spectrum is indeed accurately Lorentzian. Since the incident light has a frequency of 4.74 x 1014Hz, the resolution (R) of the self-beating spectrometer is seen to be better than R ~10~~. In Figure 4 is shown the self-beat spectrum of the light scattered by T4 at 160” scattering angle. Once again we see the spectrum to be quite accurately Lorentzian with the open circles indicating a least-squares best fit width of (Av),,, = 665Hz. These data indeed indicati the validity of equation (3) over the entire range of angles studied and hence the appropriateness of this method of determining D for phages by light scattering techniques. From the slope of the graph in Figure 2 a value of Dzo,w= (0.295 -&O-003)x lo- I cm2/sec is calculated for T4 phage. The error includes a residual error of approximately 0.5% which arises from the O-2deg. C!fluctuation in the temperature, non-linea,rity in the frequency calibration of the wave analyzer, and 8 0.25% error in the measurement of solvent viscosities. This residual error of O-50/Oappears in all of the results.

i

0

Fm. 6. Dependence

o-2

)

o-4 0.6 Cocxntration

!

08 (mgnr!)

of DlO,W on phage concentration

IO

I-2

for Tb and T7 bacterlophageb

5. B. DUBIN

554

-

ET

AL.

~ Frequency CkHz)

FIQ. 6. The self-beat spectrum of the light scattered at 0 = 90’ by T7 bacteriophage The open circles indicate a Lorentzian fit of half-width 687 Hz.

at 750 pg/ml.

TABLET Summary of results on bacteriophage mobcuhr weights Phage

D 20.v [(units of 3A-*~m2/sec) I” ‘C

fG3.w (units of 10-13 SIX = Svedberg)

77 Wg)

M Phase (millions)

% DNA

M DNA (millions)

T4

0,295 & 0.003

890 & 15

0.617 f 0.007

192.5 + 6,6

54.9 6.0.5

105.7 k 3.8

T5

0.397 f 0.004

615 f

0.658 + 0.006

109.2 f 4.0

61.7 * 1.7

67.3 & 3.1

T7

0.603 f 0.006

453 & 8

0.639 f 0.006

50.4 & 1.8

51.2 f 0.5

25.8 & 1.0

h

0.497 f 0*005

360 f 10

10

The residual spectral power density indicated at 45 kHz in Figure 4 is due to the flat-shot effect spectrum. The self-beat spectrum is fit above this level to determine the diffusion coefficient (Dubin et al., 1967). The diffusion coefficients of T5 and Ti’ phage were determined at 90” scattering angle for a series of concentrations. As is clear from Figure 5 there is no discernible concentration dependence of the diffusion coefhcient over the range studied, despite the appreciable concentration dependence usually seen for the sedimentation coefficient in this range. Thus from Figure 5, D io,, for T5 and T7 are (0.397 5 0.004) x lo-? cm2/sec and (0.603 f O@OS)x 10e7 cm2/sec, respectively. The self-beat spectrum of the light scattered by T7 at 90” scattering angle and a phage concentration of 0.75 mg/cc is displayed in Figure 6. The open circles again indicate the best Lorent zian fit, with (dv),,, = 687Hz. The fit is seen to be accurately Lorentzian. The diffusion coefficient of X phage was determined at a scattering angle of 90” and found to be D20nw= (0.497 & 0.005) x 10-7cm2/sec. This value was obtained at a phage concentration of 0.20 mg/ml. All of the results of the diffusion coefficients are summarized in column 2 of Table 2 (Dubin & Benedek, 1969). It should be noticed that D for each phage is given in this experiment with an accuracy of 1%. (b) Sedimentation coegicient S20.w was determined for T4, T5, T7 and /\ phage at a series of concentrations as shown in Figure 7. These results were then extrapolated to zero concentration. The following values (in Svedbergs) were obtained for Si,., for T4, T5, T7 and h phage,

MOLECULAR

WEIGHTS I,

900-

I, I r

OF COLIPHAGES I

,

1

/I

I

1 T

I. ‘I

T4 %.w

=(890+15)

x10-'3sec

800-

= (615~10)x10-'3sec .E 6 500v)

T7S$ +-*.w+-*

400-

25 0

=(453*88)~lO-'~sec I;

A s40. ,=(360~10h10-~'3 -~-&-----A

:

/ 20

,

,

,

,

,

40 60 80 Concentration (pg/ml)

FIG. 7. Dependenoe of Sao,r on phage oonoentration Svedberg = lo-= sea).

respectively: and are listed for T4 phage of (300 f 12)

,

WC

,

, 100

for T4, TS, T7 and h bacteriophages

(one

890 + 15, 615 f 10, 453 & 8, and 360 f 10 (Dubin t Benedek, 1969) in column 3 of Table 2. It is noted that the present value of S~,,,/D,,,, of (301 rt ‘7) x 10T5 (sec/cnl)2 is identical to that obtained for T2 phage x lob5 (sec/cm)2 by Cummings & Kozloff (1960).

(c) Determination of the molecular weights From the sedimentation and diffusion coefficients, the phage molecular weights can be calculated form the Svedberg equation (equation (a)), using the values of the partial specific volumes, G, from Bancroft & Freifelder (1970): (4) where M is the particle molecular weight, p is the solvent density, N, is Avogadro’s number, k is Boltzmann’s constant and T is the absolute temperature. These values of M are presented in column 5 of Table 2. From the weight percentage of DNA in each phage (Bancroft & Freifelder, 1970) the molecular weights of the DNA have also been determined. Only f%,, and D~o.~ have been determined for X phage. Accurate determinations of e and percentage DNA of this phage are not available and are left for the future. It should be noted that the value of M for T7 agrees exceedingly well with the determination in Bancroft & Freifelder (1970). In addition, the values of the molecular weight for T4, T5 and T7 DNA agree well with those obtained by Schmid & Hearst (1969). A general discussion of the reliability and usefulness of these values is presented in the fourth paper in this series (Freifelder, 1970). 5. Conclusion By employing the newly developed techniques of optical mixing spectroscopy the diffusion coefficients (D) of bacteriophages of molecular weight as large as 200 million have been measured with great accuracy. This method is in fact readily applicable

556

S. B. DUBIN

ETAL.

even to far larger molecules. By combining these measurements of D with B conventional determination of S and newly obtained values of 5 and fraction of DNA in each phage, accurate determinations of the molecular weight8 of T4, T5, and T7 phage and their DNA have been presented. This work was supported at the Massachusetts Institute of Technology by the Advanced Research Projects Agency under Contract number SDSO. At Brand&s University the work was supported by grant no. Gm14358 from the US. Public Health Service, grant no. E509 from the American Cancer Society, and contract no. (AT-30-l)-3797 from the Atomic Energy Commission. One of us (F.C.B.) was supported by a postdoctoral fellowship from the U.S. Public Health Service. Another of us (D.F.) is supported by a Career Development Award (no. Gm7617) from the U.S. Public Health Service. Additional support for student assistance came from a Training Grant from the U.S. Public Health Service. This is publication 743 from the Graduate Department of Biochemistry, Brandeis University. REFERENCES Bancroft, F. C. & Freifelder, D. (1970). J. Mol. Biol. 54, 537. Clark, N. C., Lunacek, J. H. & Benedek, G. B. (1970). Amer. J. Phys. 38, 676. Cummings, D. J., Chapman, V. A. & DeLong, S. S. (1965). J. Mol. Biol. 14, 418. Cummings, D. J. & Kozloff, L. M. (1960). Biochim. biophys. Acta, 44, 445. Davison, P. F. & Freifelder, D. (1962). J. Mol. BioZ. 5, 635. Dubin, S. B. & Benedek, G. B. (1969). Biophys. J. 9, A212. Dubin, S. B. Lunacek, J. H. & Benedek, G. B. (1967). Proc. Na,t. Acad. Sk., Wash. 57, 1164. Ford, N. C., Jr. & Benedek, G. B. (1965). Phys. Rev. Letters, 15, 649. Forrester, A. T. (1961). J. Opt. Sot. Amer, 51, 253. Freifelder, D. (1970). J. Mol. BioZ. 54, 567. Schmid, C. W. & Hearst, J. E. (1969). J. Mol. BioZ. 44, 143. Williams, R. C. 8: Fraser, D. (1953). J. Bact. 66, 468.