Estimating the Size of Onion Epidermal Cells From Diffraction Patterns

Estimating the Size of Onion Epidermal Cells from Diffraction PatternsJeffrey R. Groff

Citation: Phys. Teach. 50, 420 (2012); doi: 10.1119/1.4752048 View online: http://dx.doi.org/10.1119/1.4752048 View Table of Contents: http://tpt.aapt.org/resource/1/PHTEAH/v50/i7 Published by the American Association of Physics Teachers

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420 The Physics Teacher Vol. 50, OctOber 2012 DOI: 10.1119/1.4752048

Figure 1 is a light micrograph showing onion epidermal cells on a prepared glass microscope slide stained to enhance the contrast of cell walls and nuclei.6 The onion epidermis consists of a single layer of relatively large cells forming a protective skin between each segment of the onion. Note that individual epidermal cells have relatively transparent cell bodies and opaque cellulose cell walls. The cells are elongated and the longitudinal (long) axes of neighboring cells tend to line up, but the cells are staggered along their transverse (short) axes forming a brick-like pattern. Due to this struc-ture and the sufficiently uniform width of the cells along the transverse axis, the epidermis acts like a one-dimensional transmission diffraction grating and produces diffraction patterns like the one shown in Fig. 2 when a laser beam passes through the tissue. By analyzing these diffraction patterns, the transverse width of individual onion epidermal cells can be estimated as described below.

Estimating the Size of Onion Epidermal Cells from Diffraction Patterns Jeffrey R. Groff, Institute of Environmental and Physical Sciences, Shepherd University, Shepherdstown, WV

Bioscience and premedical profession students are a major demographic served by introductory physics courses at many colleges and universities. Exposing these students to biological applications of physical prin-ciples will help them to appreciate physics as a useful tool for their future professions. Here I describe an experiment suit-able for introductory physics where principles of wave optics are applied to probe the size of onion epidermal cells. The epidermis tissue is composed of cells of relatively uniform size and shape (Fig. 1) so the tissue acts like a one-dimen-sional transmission diffraction grating. The diffraction pat-terns generated when a laser beam passes through the tissue (Fig. 2) are analyzed and an estimate of the average width of individual onion epidermal cells is calculated. The results are compared to direct measurements taken using a light microscope. The use of microscopes and plant-cell tissue slides creates opportunities for cross-discipline collaboration between physics and biology instructors.

Exploiting the wave nature of light to study biological structure and function

The principles of wave optics are a powerful tool for probing microscopic structure in biology. Perhaps the most famous example of the application of these principles to a bio-logical problem is the use of x-ray crystallography to study the structure of DNA. Watson and Crick relied on x-ray diffrac-tion images of crystalized DNA taken by Rosalind Franklin to infer the double-helical structure of DNA.1, 2 Principles of wave optics have also been used to study the mechanisms of muscle contraction. Muscle cells are composed of bundles of long, tubular structures called myofibrils, which in turn are composed of subunits called sarcomeres that appear as repeating, regularly spaced light and dark bands under a mi-croscope. During muscle contraction, sarcomeres shorten as the actin and myosin protein filaments inside slide past one another. Diffraction studies have been performed using both visible light to study the dynamics of sarcomere shortening, and shorter wavelength x-rays to study the mechanics of the actin and myosin proteins during muscle contraction.3, 4 Technical challenges make it impractical to study crystalline DNA and sarcomeres in introductory physics, although three-dimensional helical structures can be studied by substituting a red laser for x-rays and a mechanical pen spring for DNA molecules.5 It is a challenge to find a biological material that can be studied using the diffraction principles taught in in-troductory physics. However, after testing dozens of prepared microscope slides, I discovered a suitable two-dimensional tissueonion epidermis.

Fig. 1. Light micrograph of stained onion epidermal cells on a prepared slide.6 The locations of a cell nucleus and a cell wall are indicated. The cell-wall spacing is relatively regular along the transverse (short) axis of the cells so the tissue acts like a one-dimensional transmis-sion diffraction grating.

Fig. 2. Example interference pattern formed on a screen when a red laser beam (l = 65010 nm) passes through a slide containing onion epidermis.6 First- and second-order maxima are clearly visible on either side of the bright zeroth-order central maximum.


The Physics Teacher Vol. 50, OctOber 2012 421

The experiment consists of systematically changing the distance between the onion epidermal cells and the screen (L) and measuring the distance between the second-order maxima (m = 2) on either side of the central maximum of the diffraction pattern. Interpreting Fig. 4, this distance is 2y. The angular position of the second-order fringes (q2) is always small. Therefore, we can take advantage of the small-angle approximation sin q < tan q = y/L and using Eq. (1) write

dy /L < ml . (2)

The largest angle observed in the data presented below was q2 = 1.14

o so this small-angle approximation introduces error less than 0.02%. Multiplying both sides of Eq. (2) by 2L/d yields

2y < (2ml/d)L. (3)

A plot of the measured values of 2y as a function of L yields a line with a slope that is approximately 2ml/d.

ResultsFigure 5 shows the distance between the second-order

fringes (2y) as a function of the distance between the onion epidermal cells and the screen (L) for three different onion tissue samples on glass microscope slides. Two are prepared slides obtained from Fischer Scientific of stained onion epidermis manufactured by Johannes Lieder6 and Altay Sci-entific.11 The third is a homemade slide prepared from fresh onion tissue (see preparation details below). The data are fit with least-squares regression lines. Using the slopes of the fits and Eq. (3), we can calculate an estimate of the transverse

Experimental details and analysis

Figure 3 shows the experimental apparatus consisting of PASCO basic optics components: a 1.2-m optics bench, a red diode laser (l = 65010 nm), a viewing screen, and an adjustable lens holder.7-10 The adjustable lens holder is used to hold a glass microscope slide of onion epidermal cells as shown in the inset. Figure 4 is a diagram of the experimental setup showing a laser beam incident on the onion epidermis and the intensity profile of the diffraction pattern that ap-pears on a screen placed down-field from the tissue. If the laser beam is normal to the onion cells, they act like a one-dimensional transmission diffraction grating and the angular location of the mth-order fringe on either side of the central maximum (qm) is given by

d sin qm = m l, (1)

where l is the wavelength of the laser, d is the average spac-ing between the cells along their transverse (short) axis (i.e., an estimate of the transverse cell width), and m = 0, 1, 2, 3, ... is the order of the fringe. The central maximum is assigned m = 0 and q0 = 0

o.

Fig. 3. Experimental apparatus consisting of PASCO basic optics components, a Labomed trinocular microscope, and a ProScope HR USB camera. The inset shows how a prepared microscope slide is held by a PASCO adjustable lens holder.

Fig. 4. Diagram of experimental setup and the intensity profile of the diffraction pattern formed on a screen when a laser beam passes through the onion epidermis. The relationship between the angular position of the mth-order maximum (qm), the wave-length of the laser (l), and the inter-cell spacing (d) is given by Eq. (1). The distance from the onion cells to the screen is L and between the central maximum (m = 0) and the second-order maxima (m = 2) is y.

L (cm)

35.0 45.0 55.0 65.0 75.0 85.0 95.0 105.0

2y (c

m)

1.00

1.50

2.00

2.50

3.00

3.50

4.00

Fig. 5. The distance between the second-order fringes (2y) plot-ted against the distance between the onion epidermis and the viewing screen (L) for prepared slides from Johannes Lieder (crosses)6 and Altay Scientific (open circles),11 and a homemade slide (filled circles). The linear fits to the data are 2y = (0.03380 0.00039)L + (-0.1080.028 cm) (crosses), 2y = (0.03309 0.00019) L + (-0.0180.014 cm) (open circles), and 2y = (0.03966 0.00059) L + (-0.0840.043 cm) (filled circles).


422 The Physics Teacher Vol. 50, OctOber 2012

duces a beam that is not well collimated and is elongated along one dimension. Better results were obtained by blocking part of the beam with an index card taped to the laser housing. This results in sharper maxima but also introduces another dif-fraction pattern that is superposed on the pattern generated by the tissue. However, this does not lead to any difficulty because the fringes caused by the diffraction of the laser beam around the edge of the index card are much closer together than those

caused by the tissue.To prepare the homemade slide used in this experiment,

a fresh onion segment was cut from a whole onion bulb. The epidermis was peeled away from the concave side of the on-ion segment using forceps. The epidermis was placed flat on a glass microscope slide and stained with a few drops of dilute Fast Green in aqueous solution (0.05 g/mL). Fast Green is a cellulose-specific stain used to enhance the contrast of cell walls. The excess stain was washed and wicked away using distilled water and KimWipes. An approximately 1-cm-x-1-cm square was cut from the tissue and mounted on a clean microscope slide using clear nail polish. A few more drops of nail polish were used to place a glass cover slip over the tis-sue. After mounting, the slide was allowed to cure for about a week.

Tissue staining and slide preparation is as much an art as it is a science, and my skills in this area leave much to be desired. For example, nail polish is a strong solvent and re-moved most of the stain from my tissue sample; however, this didnt seem to matter for the experiment. Other slides prepared without stain exhibited diffraction patterns suggest-ing that the cell walls are sufficiently opaque for the onion tissue to act like a diffraction grating without staining. Those who are interested in making their own onion slides have an obvious opportunity to collaborate with the cell biologist at their institution. A good reference for plant-cell staining techniques is Plant Microtechnique and Microscopy by Ruz-in.12 Finally, I suggest that those who purchase professionally manufactured prepared slides should purchase more than they expect they will need. I found the Johannes Lieder and Altay Scientific slides of very high quality, but not all of the slides I purchased worked exceptionally well due to variation in the tissue samples used to prepare them.

AcknowledgmentsI would like to acknowledge Carol Plautz and Carl Bell of the Shepherd University biology department for sharing some of their knowledge of plant-cell staining techniques. This work was supported in part by West Virginia Higher Education Policy Commission Division of Science and Research Grant No. HEPC.dsr.10.10, an EPSCoR innovation grant for the acquisition of biophysics instrumentation for curricular enhancement, research, and outreach.

width of the onion cells (d). Table I summarizes these esti-mated cell widths for each tissue sample. Also summarized is the cell widths estimated from micrographs similar to Fig. 1. The micrographs were taken using a ProScope HR USB camera connected to a Labomed trinocular microscope (see Fig. 3). Cell widths were measured in pixels using the mea-surement tool supplied by the open source image manipula-tion program GIMP and converted to centimeters using a micrograph of a 1-mm stage micrometer taken with the same camera and microscope.

SummaryThe results obtained using the Johannes Lieder prepared

slide and the homemade slide agree within the margin of uncertainty with the direct measurements taken using the microscope. However, the results obtained using the Altay Scientific slide do not agree. I attribute this lack of accuracy to the difficulty of obtaining a micrograph (for direct mea-surements) of the exact location where the laser beam passed through the tissue. If the area photographed using the micro-scope and the laser-beam target area do not coincide, then the two estimates may differ simply because the average size of the onion cells is different at different locations on the slide. The laser-beam target area was easy to locate on the home-made slide due to the presence of imperfections (air bubbles), which served as spatial markers. It was more difficult to lo-cate the target area on the professionally manufactured and blemish-free prepared slides.

Variable onion-cell size may introduce experimental un-certainty, but this lab involves what was once living tissue, and biology, often by virtue of its complexity, is a messy sci-ence from a quantitative perspective. Nevertheless, physical principles are increasingly becoming important tools for bi-ologists and should be embraced by bioscience students. Un-fortunately, undergraduate biology curriculums often fail to emphasize this. This makes it important for physics instruc-tors to demonstrate to the bioscience students in their courses the usefulness of physics to the study of biological problems. This laboratory provides an opportunity to do just that.

SuggestionsThe PASCO red-diode laser used in the experiment pro-

Table I. Estimated transverse width of onion epidermal cells obtained from three differ-ent tissue samples through analysis of diffraction patterns (first row) and direct mea-surements from micrographs (second row). The micrograph measurements are reported as mean standard deviation (top) and mean standard error (bottom). The number of cells measured to calculate each mean was 22, 57, and 40 for the Johannes Lieder, Altay, and homemade slide, respectively.

Johannes Lieder

Altay Homemade

d (cm) from diffraction experiment 76.9 1.5 mm 78.6 1.3 mm 65.6 1.4 mm

d (cm) from micrograph measure-ments

76.9 8.2 mm

76.9 1.7 mm

67.8 9.3 mm

67.8 1.2 mm

64.4 7.8 mm

64.4 1.2 mm


The Physics Teacher Vol. 50, OctOber 2012 423

References1. F. Crick and J. Watson, A structure for deoxyribose nucleic

acid, Nature 171, 737738 (1953).2. R. E. Franklin and R. G. Gosling, Molecular configuration in

sodium thymonucleate, Nature 171, 740741 (1953).3. Y. Yeh, R. J. Baskin, R. L. Lieber, and K. P. Roos, Theory of

light diffraction by single skeletal muscle fibers, Biophys. J. 29(3), 509522 (1980).

4. V. Lombardi, G. Piazzesi, M. Reconditi, M. Linari, L. Lucii, A. Stewart, Y. B. Sun, P. Boesecke, T. Narayanan, and T. Irving, X-ray diffraction studies of the contractile mechanism in single muscle fibres, Phil. Trans. of the Roy. Soc. Lond. B: Biol. Sci. 359(1452), 18831893 (2004).

5. Gregory Braun, Dennis Tierney, and Heidrun Schmitzer, How Rosalind Franklin discovered the helical structure of DNA: Experiments in diffraction, Phys. Teach. 49(3), 140 (March 2011).

6. Epidermis of Allium cepa (onion) prepared slide 5101c. Jo-hannes Lieder GmbH & Co. KG.

7. Adjustable lens holder OS-8474. PASCO scientific; www.pasco.com.

8. 1.2 m optics bench OS-8508. PASCO scientific.9. Viewing screen OS-8460. PASCO scientific.10. Red basic optics diode laser OS-8525A. PASCO scientific.11. Onion bulb epidermis w.m. prepared slide 7182.030. Altay Sci-

entific; www.altayscientific.com.12. Steven E. Ruzin, Plant Microtechnique and Microscopy (Oxford

University Press, 1999).

Jeffrey Groff is an assistant professor of physics in the Institute of Environmental and Physical Sciences at Shepherd University. He earned his PhD in applied science with a focus in computational biophysics from the College of William and Mary in 2008. He joined the faculty at Shepherd University in 2009 after spending a year at Gettysburg College as a visiting assistant professor of [email protected]

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Estimating the Size of Onion Epidermal Cells From Diffraction Patterns

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