0 1992 Wiley-Liss, Inc.

Cytometry 13:155-162 (1992)

In Vivo Measure of Average Bacterial Cell Size From a Polarized Light Scattering Function Burt V. Bronk, Willem P. Van De Merwe, and Marc Stanley U S . Army Chemical Research Development and Engineering Center, A.P.G. (B.V.B.), and Uniformed Services University of the Health Sciences, Bethesda (W.P.V.D.M., M.S.) Received for publication May 10, 1991; accepted October 5, 1991

A particular combination of elements of the Mueller matrix for scattering of polarized light given by

suspension of the same bacteria in the stationary (starving-smaller cells) phase of growth. Microscopic measurements were made to determine, for each case, the average dimensions of the bacterial population. Graphs were then plotted of is measured vs angle at a wavelength of the peak positions from the Mueller ma633 nm for randomly oriented suspen- trix function plots vs either cell length or sions of several species of bacteria in dif- cell diameter. The function was shown to ferent stages of growth. (This combina- be strongly correlated with cell diameter tion of elements is dominated in the under the conditions of this experiment present measurements by the behavior of and poorly correlated with cell length. the normalized S,, matrix element, as is The measurements were shown to have a indicated by the notation defined on the sensitivity to changes in average diameright side of the equation.) The resulting ter of about 20 nm. graph in each case shows an oscillating function of angle. This function is com- Key terms: Light scattering, bacterial dipressed toward smaller angles when the mensions, cell size, polarized light, Muelbacteria are in the exponential phase of ler matrix functions, angular scattering growth in comparison with results for a function

INTRODUCTION Light scattering is well-known to biologists through the useful and simple laboratory practice of measuring optical density as an indicator of the number density of a suspension of cells. The possibility of using more detailed information from the angular scattering pattern for a suspension was demonstrated by the rough agreement of the predictions of Rayleigh-Gans scattering theory with measurements of the angular distribution of the scattered light from bacterial cells (7,101. Although, for dilute suspensions of bacterial cells, most of the light scattering is already concentrated in the forward direction, it was seen that suspensions having, on average, larger cells, tend to enhance the forward scattering further still. More detailed experiments and theory showed that the angular dependence of the scattered intensity could be correlated with the dimensions and refractive index of bacterial cells (12,131and have more recently been used to obtain a refractive index distribution within individual bacterial cells and spores in an aqueous environment (9).

It has been indicated by a number of authors that polarized light scattering has the potential for yielding a great deal more information about the scatterers than is obtainable from a scattering pattern for unpolarized light (eg., 2, 6). Polarized light measurements are usually discussed in terms of the four components, (I, Q , U, V), of the Stokes vector describing a polarized or partialy polarized beam of light. The elastic scattering properties of a particle or collection of particles are then fully described by the 4 x 4 matrix called the Mueller matrix which connects the incident and scattered Stokes vectors according t o the following equation: r

1 i

us vs

I::]

i r

r

= l S l L

SlZ s13

SZZ s 2 3 524 s31 s 3 2 s33 8 3 4 s21

i

ui

(1)

s41 s42 s43 s44

where the incoming Stokes four vector on the right is acted on by the matrix representing the scatterer to give the Stokes vector for the scattered light on the left

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BRONK ET AL.

coli) were used. The first was E . coli K12 with heatinducible lamda virus prophage in the main chromosome, (E. coli K12lamda) originally obtained from Dr. L.S. Baron of the Walter Reed Army Institute of Research (1).We have deposited the strain in the American Type Culture Collection (ATCC 49539) because this strain's characteristics make it convenient as a standard for physical measurements. In particular, following a brief heat shock a t 42"C, i t shows a sharper and more complete induction than other strains containing the lambda prophage which we have tested. A second strain of this same species used in these experiments was E . coli Bir (ATCC 12407). The other bacteria studied are Staphylococcus epidermidis (Staph ep.ATCC 1461, Bacillus megaterium (B. meg.-ATCC 136321, a non sporulating strain of this bacillus, and Bacillus subtilis (B. sub.-ATCC 9372). Three different media were used and are expressed per liter of distilled water. LB broth contsins 10.0 g NaC1, 10.0 g tryptone (Difco 01231, and 5.0 g yeast extract (Difco 0127) with measured pH -6.9; Medium M1 has 2.0 g NH4C1, 6.0 g Na,HP04 (anhydrous), 3.0 g [Ss4 + Sl4)KSl1+ SL3)= (s34/sl,) (2) obtained using the polarization modulation technique NaC1,0.25 g MgS04.7H,0, and 2.0 g glucose. (The Mg described above. The approximation indicated in equa- salt and glucose solutions are autoclaved separately.) tion (2) becomes a n equality for a spherically symmet- The medium is brought to pH 7.0 after autoclaving. ric ensemble of scatterers (eg., a non optically-active, Medium M265 contains 12.45 gm Difco heart infusion randomly oriented collection of cylinders, [lo]).Accord- broth, 5.4 gm Difco nutrient broth and 2.5 gm yeast ing to our measurements, i t held well for a randomly extract. (The media used for the growth of the various oriented suspension of Escherichia coli (E. coli) bacte- bacteria are indicated in Table 2.) For this study, all bacterial cells were grown a t 37°C ria. We will therefore denote the above quantity by in a shaker bath with vigorous shaking so that mixing (S34iS11)' hereafter in this paper. From the detailed of air was always near the maximum available for aerdefinition for the elements of the Stokes vector (3) one can show t h a t the S,, matrix element probes the phase obic growth. The doubling time for E . coli Bir was -50 shift in scattered light between electric field vectors min in M1. The following procedure was followed to parallel and perpendicular to the scattering plane. This prepare bacteria both for the light scattering experimatrix element, normalized as in equation (2), has thus ments and prior to spreading the cells on slides for far been the most interesting one giving reproducible microscopy. The procedure was chosen as the simplest differences between different suspensions of bacterial one to give reproducible results. Cells were spun down from growth medium a t -3000 g for 8-10 min and then cells (11). resuspended with vigorous vortexing for about a We have previously shown that very good quantitative reproducibility can be achieved for (S,,/S,,)' as a minute into sterile saline (SS) a t a n optical density function of theta for separate growths of the same bac- (OD) at 600 nm < 0.1 for scattering, or a somewhat terial strain grown in two different laboratories with higher density for microscopy. For Staph. ep, cells only, measurements obtained on two separately constructed some ultrasonication was used to break up large instruments (11).We also showed that the graph of clumps. This procedure did not produce any apprecia(S34iS11)Lvs theta appeared to become compressed in ble change in the scans of the scattering function, (S34/ the forward scattering direction and developed addi- Sll)'. The SS consists of 0.9% NaCl at pH 5.7-5.8. Several comparisons are made in this paper of retional peaks in the backward scattering direction a s the wavelength of the scattered light became shorter, sults for log phase vs stationary phase cells. In order to or the cells became larger. In the present study, we have reproducibility of the size distributions for log extend and quantify our earlier observations by corre- phase growth, cells were always grown for more than lating changes in the angular scattering pattern with five doublings without interruption with OD < .05. (see cellular dimensions obtained by optical microscopy for [4J for a more complete discussion of why this is necessary for a well-defined log phase). Stationary phase is several bacterial species. not generally as well-defined. For the purpose of the MATERIALS AND METHODS present study, stationary phase cells were harvested Biological for the experiment a t 18 hrs (* 1 hr) after having Several species of bacteria were used for the experi- reached a n OD of 0.5 following growth through log ments reported here. Two strains ofEscherichia coli (E. phase. This gives a reproducible condition for each spe-

side of the equation. This formulation and several examples of Stokes vectors and matrix elements for simple cases are given in reference (3).Each element of the matrix is a function of the scattering angle, theta, which is measured between the direction of the incoming light and the scattering direction. The matrix elements are, however, independent of the azimuthal angle for a n isotropic suspension of particles. The S,, element of the matrix represents the scattering for unpolarized light. All of the Mueller matrix elements can be measured using the technique of photoelastic modulation of the incoming light together with lock-in amplification (2, 3, 5). The photoelastic modulation refers to the transformation of the state of the incoming light through intermediate elliptically polarized states alternately to left and right circularly polarized at the natural frequency (50 kHz) of a periodically stressed quartz block which acts as a variable retarder. In the present paper we discuss measurements of the particular combination of matrix elements

POLARIZED LIGHT SCATTERING AND BACTERIAL SIZE

157

Table 1 Comparison of Manufacturers Electron Microscope us Present Optical Measurements of Micron Sized Latex Beads" Manufacturers value (um) 2.95 k 0.13 1.06 t 0.01 0.6 i 0.003

Present measurement ( u.m) 3.14 0.10 1.03 5 0.10 0.59 2 0.05

*

Number of beads measured 15

51 51

"The error indicated for the present measurement is standard deviation.

cies and medium, but not exact biological comparability between two bacterial species or the same species grown in two media.

Microscopy Photographs of the bacterial cells were obtained using a Zeiss Photomicroscope I11 with phase contrast optics a t a magnification of either 400 in air or 1,000 with oil immersion. Photographs were made with Kodak T-max 100 Professional film and projected on a screen for measuring diameters and lengths of cells. Dust free slides manufactured by Erie Scientific in Portsmouth, NH were designated as #M1100w 3 x 1 superfrosted and were ordered from Port City Diagnostics Inc in Wilmington, N.C. 28412. Slides were prepared with poly-1-lysine solution, catalog no. p8920 from Sigma Diagnostics in St. Louis, Mo to immobilize the bacteria. Photographs of the cells were projected and measured individually on a macroscopicscale. The measurementsfrom each set of photographs were calibrated against a projected photograph of the stage micrometer from the microscope at

FIG.1. E . coli Kl2lambda photoaaphed in vivo in saline suspension. (A) Logarithmic phase of growth. The average cell length is about 6 pm. (B) Stationary phase. The average cell length is about 2 cLm,Bar = 18 cLm.

Scattering Angle (degrees) FIG.2. Scattering function vs angle for E. coli KlZlambda. The solid line corresponds to a suspension of log phase cells. The dotted line is for stationary phase.

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BRONK ET AL.

Table 2 Average Bacterial Dimensions From Optical Micrographs" Bacteria E. coli K12lamda E. coli Kl2lamda E . coli Blr E . coli Blr Staph. ep. Staph. ep. B. meg. €3. meg. B. sub. B . sub.

Stage L S L S L

S L

S

L S

Medium LB LB M1

M1

M265 M265 LB LB LB LB

Length hrn) 6.37 +- 1.49 1.94 2 0.33 2.54 i 0.52 1.60 t 0.28 -

8.09 ? 2.69 5.89 ? 1.94 6.52 t- 1.53 2.92 0.75 _+-

Diameter ( wm) 1.15 -t 0.10 0.97 1 0 . 1 0 0.78 2 0.11 0.60 0.08 1.27 -+ 0.10 1.01 2 0.11 1.41 ? 0.14 1.46 -+ 0.14 0.87 k 0.09 0.75 2 0.11

*

Volume

hm3) 6.22 1.20 1.09 0.40 1.07 0.54 11.90 9.05 3.70 1.18

Counts 149 149 324 300 212 150 167 230 345 311

Lgeo

1.84 1.06 1.03 0.73 1.03 0.81 2.28 2.08 1.55 1.06

Volumes computed assuming cylindrical rods with spherical end caps of same radius as rod except for the Staph. ep. which were approximated as spheres. LKeo= Cells in groups were counted singly whenever a clearly defined septum or indentation divided them from an attached neighbor. Thus, the lengths given in this table are in a few cases considerably less than group lengths of objects in the suspension. Lengths for rods are tip to tip. It should be noted that a single representative (spherical) diameter was selected for speed and simplicity in the measurements of Staph. ep. although the shapes are probably more accurately represented by a short prolate ellipsoid.

the values and standard deviations obtained is given in Table 1. We conclude that we can get reproducibility to better than -0.1 km by this means. While electron microscopy offers better resolution than this, we have observed bacterial cell volumes to shrink by a factor of two to three in the preparation for that measurement. (Compare volumes for E . coli Bir in M1 medium given in Table 2 with those presented in Table 1, r41.1 Our experience was corroborated by telephone conversations with C. Woldringh of University of Amsterdam. See also (8). We concluded that optical microscopy in the same saline suspension a s is used for the scattering measurements is much closer to the in vivo situation.

FIG.3. B . subtilis cells photographed in vivo in saline suspension. (A) Log phase cells of average length about 6.5 Fm.(B) Stationary phase cells of average length about 3 Fm. Bar = 15 Fm.

the same magnification. As a check of our resolution, we measured latex beads obtained from Sigma Chemical Co. using the same procedures as for the bacteria. These beads had been calibrated by the original manufacturer using electron microscopy. A comparison of

Scattering Instrumentation The experimental setup has been described in detail elsewhere (eg., 3 , 5 ) . In brief, a linearly polarized laser beam is passed through a photoelastic modulator, causing the polarization to rotate between left and right circular polarization a t a frequency of 50 kHz. For the present experiments, the HeNe laser line of 633 nm was used with about 1/2 mW of power. The modulated beam passes through the liquid suspension containing the sample in a cylindrical quartz cuvette (19 mm i.d., 22 mm 0.d.) with a flat face -5 mm wide for the laser beam to enter and exit. Dull black paper was used to reduce extraneous reflections a t glass-air interfaces. The scattered light is passed through a linear polarizer and then detected by an RCA 1P21 photomultiplier tube. The signal is detected by lock-in amplification a t 50 kHz, and the DC component of the PMT is kept constant by electronically servoing the high voltage. The signal is expressed as a percent of the maximum value obtained after placing a quarter waveplate in a direction close to forward scattering and adjusting it for maximum signal. The scattering curve (S34/S,l)'is obtained a s a function of angle by rotating the arm carrying the phototube, a t a rate of 15 degimin, about

159

POLARIZED LIGHT SCATTERING AND BACTERIAL SIZE

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&

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*

e

m

m

*. **

I

I

I

I

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30

60

90

120

150

Scattering Angles (degrees) FIG.4. Scattering function vs angle for B.subtzlzs cells. The solid line again corresponds to log phase cells; the dotted, stationary phase. 140

120

a vertical axis through the cylindrical sample cuvette. The propagation direction of the incoming laser beam defines the zero scattering angle, with 180 degrees defined by direct back-scattering. The signal is averaged over 3 seconds t o reduce electronic noise and noise from the sample (eg., clumps of cells).

RESULTS In Figure 1, the photomicrographs of E . coli h KlBlamda in log phase (Fig. la> and in stationary rn Q, phase (Fig. l b ) at the same magnification clearly show a reduction in average cell size as the bacteria adapt to 0) starvation in stationary phase. a 80 From an analysis of measurements of several hundred cells, we observed that the diameters of the cells, a 0) as well as the lengths, become smaller in stationary S phase for this bacterial strain in rich medium. In Fig60 ure 2 , the scattering curves for these bacteria are shown. The graph of (S,,/SI1)* intensity vs angle is an oscillating function with several maxima and minima. The pattern for the larger, log-phase cells appears similar to that for the stationary phase bacteria, but is 40 shifted toward forward scattering angles. In a previous study (11)we found a general trend corresponding to this observation by recording this graph for several different laser wavelengths while 20 studying a single suspension of these bacteria. As the 0.6 0.8 1.o 1.2 1.4 1.6 wavelengths became shorter, corresponding to a scaling up in size of the cells, the pattern increased in complexity and appeared compressed toward forward Diameter (microns) angles. In the present study, we vary the actual cell FIG.5. Locations of maxima and minima of the plots of (S:34/Sllli vs sizes by using different bacteria and different condiaverage diameters of bacteria. Average peak locations for a single tions of observation. bacterial species and conditions occur in line vertically above the The average dimensions of the bacterial cells (and average diameter (See Table 2) corresponding to that cell type. The different eymbols correspond to families of peaks which evidently cor- other statistical information) is presented for each case respond to one another. studied in Table 2 . In every case, the log phase cells are 100

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160

BRONK ET AL. 140

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100

100

80

80

60

60

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E v)

E.

-m 2 Q)

20

20

0

2

4

6

8

10

Length (microns)

0

1

2

3

Lgeo(microns)

FIG.6. (A) Peaks are plotted vs average cell length as in Figure 5 but do not show a clear correlation in this case. (B) Peaks are plotted vs L,, Le., the cube root of the cell volume) in the same manner.

greater in length than the stationary phase cells for the same strain with the same growth conditions. The statistical errors indicated in the table are standard deviation. Standard deviations of the mean (i-e., dividing the standard deviation by the square root of the number of counts) would give a more accurate representation of the uncertainty for the average lengths, but would indicate an unrealistically small value for the uncertainty of the average diameters (See Table 1). In Figure 3, photomicrographs of B. s u b t i h cells in log and stationary phase are shown. However, while the log-phase cells are substantially longer, we see from Table 2 that the diameters of the log phase cells are about the same as the diameters of the stationary phase B. s u b t i h cells. A comparison of the (S,,/SI1)* scan for log and stationary phase is shown in Figure 4. It indicates that there is very little shift in the location of the peaks from one scan t o the other although the microscopically measured length of the cells changes considerably (Table 2). The log phase scans were repeated twice and the stationary phase scans, three times, giving the same result. The replicate experiments were done with separate bacterial growths. Considering the large change in length, this suggests that

diameter rather than length is the primary factor in determining the location of the peaks. A somewhat different observation was made for the experiments with B . megaterium. These cells reduce their average length by about 25% in changing from log to stationary phase, but increase slightly or stay the same in diameter. In that case, there was some movement of the peaks outward as the cells decrease in length. (Graph not shown.) The extremum located rougly at 60 degrees moved to about 64 degrees for that experiment. In Figure 5, the angles for the peak location for the maxima and minima of the (S,JSI1)* scattering function are plotted vs the cell diameter determined microscopically for each type of bacteria in the particular condition of growth for which the measurement was made. To understand this graph, note that a vertical line of points represents the extrema obtained in a single experiment from a single graph like those shown in Figures 2 and 4.The experiment may be identified by comparing the average cellular dimension on the horizontal axis with the data in Table 2 . We note that in each case, a family of points forms. (A family of points is denoted by a single symbol in the figure.) This suggests that the extrema move roughly linearly toward

POLARIZED IAIGHTSCATTERING AND BACTERIAL SIZE

smaller angles as the cell diameters on average become larger. A similar analysis in which peak locations were plotted against average cell length is attempted in Figure 6a. Lines connecting the peaks which were indicated to be in a single family by Figure 5 were drawn, but it appears that bacterial cell length is not well correlated with peak location. One reason for the good correlation of peak location with diameter but not with cell length is probably that the cells are randomly oriented in liquid suspension, and the path length of the light across the cell is what determines the phase change for polarized light. The difference in these phase changes for two orthogonal polarizations is measured by S34.It is apparent that the distance sampled by various photons traversing a bacterial cell is more often close to a cell’s diameter than to its length. An additional reason for the poor correlation with length may be that the distribution of lengths is typically broader than that for the diameters in these experiments, which would tend to smear any length dependent features of the graphs. A quantity with the dimensions of length which incorporates information from both bacterial dimensions but weighs the diameter more heavily than the length is Lgeo = (V~lume)”~. This quantity is plotted against the locations of the maxima and minima in Figure 6b and is seen t o show a good correlation with the peak location (the data for Staph. ep. log phase has been omitted to achieve this fit).

DISCUSSION For the present experiments, the bacterial diameter is the average cellular dimension most clearly correlated with angular locations of the peaks in the graphs of (S34/SlJ‘. A good correlation is also achieved for the average dimension represented by Lgeo. We would like to discuss briefly the errors inherent in the various measurements. The peak locations of the plots such as in Figures 2 and 4 are reproducible from experiment to experiment to within about a degree. Since the signal is very small, some drift in the vertical location of the graphs occurs as may be seen in these figures. While the Mueller matrix functions are probably more interesting for back-scattering than for scattering in the forward direction, it is difficult to reproduce signals for scattering a t angles greater than about 120 degrees a t this time with our set-up. Some reasons for this are additional reflections from our cuvette and a weaker signal combined with greater sensitivity to small changes for the function in back-scattering. The fluctuations indicated in Table 2 are standard deviations, and for the lengths at least are indicative of the wide breadth of the size distribution for growing log phase cells. The procedure for estimating a standard error of the mean would suggest that the errors in the averages are generally less than one or two percent. Our experience in comparing counts taken on different days, however, suggests that this is overoptimistic and

161

we would estimate a larger error due t o the difficulty in judging the location of the edge of the cells. Thus, we estimate our uncertainty for both length and diameter to be -0.1 pm for the averages. Again we would like to emphasize that while the physical process of electron microscope measurements provides much better resolution than does measurement with an optical microscope, one is limited in using the electron microscope for sizing cells because of the shrinkage which occurs in preparation for that procedure. This shrinkage does not occur in the present procedure in which measurements were made with optical microscopy of bacteria in saline solution. The correlations we have obtained from the scattering measurements suggest that a rather precise measure of changes in average cell dimension is obtainable from graphs such as those presented here. If one uses the linear fit to the peak location vs diameter given in Figure 5 , one obtains for the fourth curve up from the bottom a value of D(lengthiD(ang1e) - 0.02 pm per degree. Since our measurements are reproducible to about a degree, this suggests we can observe changes of about 20 nm in average cellular dimension with this method. (We note that the ability t o observe such small changes does not imply an absolute accuracy of the same order.) The use of shorter wavelengths for similar experiments would improve the sensitivity of the measurement still further. The measurements described in this paper were achieved after a quick change of the suspending medium from that used for growth to a simple saline solution. If the growth medium is free of debris and the cells do not agglutinate, the measurements may be made directly in the growth medium with no clean-up procedure required. From this we conclude that the present measuring technique will be useful to quantify small changes in average cell size in real time. Preliminary experiments with bacterial suspensions damaged by heat or UV radiation have shown this to be the case (4).

ACKNOWLEDGMENTS We would like to thank Professor C. Woldringh of the University of Amsterdam for several discussions on the measurement of cellular dimensions. We would also like to express our appreciation for the encouragement and interest in our research of our late friend. Dr. H. Kubitschek.

LITERATURE CITED 1. Baron LS, Penido E, Ryman IR, Falkow S: Behavior of coliphage lambda in hybrids between E. coli and salmonella. J Bacteriol 102221433, 1970. 2. Hickel WS, Davidson JF, Huffman DR, Kilkson R Application of polarization effects in light scattering: A new biophysical tool. Proc Natl Acad Sci USA 73:486-490, 1976. 3. Bohren CF, Huffman DR: Absorption and Scattering of Light by Small Particles. John Wiley & Sons, New York, 1983. 4. Bronk BV; Van De Merwe WP, Huffman DR: Polarized light scattering as a means for detecting subtle changes in microbial populations. In: Modern Techniques for Rapid Microbiological Analysis, Nelson W (ed). VCH Publishers, New York, 1991, in press.

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5. Hunt AJ, Huffman DR. A new polarization-modulated light scattering instrument. Rev Sci Instrum 44:1753-1762, 1973. 6. Johnston RG, Singham SB,Salzman GC: Polarized light scattering. Comm Molec Cell Biophys 5171-202, 1988. 7. Koch AL, Ehrenfeld E: The size and shape of bacteria by light scattering measurements. Biochim Biophys Acta 165:262-273, 1968. 8. Trueba FJ, Woldringh CL: Changes in cell diameter during the division cycle of Escherichia coli. J Bact 142869-878, 1980. 9. Ulanowski Z, Ludlow IK, Waites WM: Water content and size of spore components determined by laser diffractometry: FEMS Microbiol. Lett. 40:229-232. 1987.

10. Van de Hulst HC: Light Scattering by Small Particles. John Wiley & Sons, New York, 1957, Dover Edition, New York, 1981. 11. Van De Merwe WP, Huffman DR, Bronk BV: Reproducibility and sensitivity of polarized light scattering for identifying bacterial suspensions. Appl Opt 285052-5057, 1990. 12. Wyatt PJ: Identification of bacteria by differential light scattering. Nature (Lond.) 221:1257-1258, 1969. 13. Wyatt PJ: Cell wall thickness, size distribution, refractive index ratio and dry weight content of living bacteria. Nature (Lond.) 226:277-270. 1970.

In vivo measure of average bacterial cell size from a polarized light scattering function.

A particular combination of elements of the Mueller matrix for scattering of polarized light given by (S34 + S14)/(S11 + S13) identical to (S34/S11)++...
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