Articles Anal. Chem. 1995, 67, 3405-341 1
Side Excitation of Fluorescence in Ultrathin Slab Gel Electrophoresis Danhua Chen,t Mark D. Petemon,t Robert L. Brwnley, Jh,t Michael C. Giddings,t Eric C. Buxton,t Michael Westphall,t Lloyd Smith,* and Lloyd M. Smiih*pt Depaltment of Chemistty, Universify of Wisconsin, Madison, Madison, Wisconsin 53706, and Lawrence Berkeley Laboratoty, Berkeley, Califomia 94720
Recent work has demonstrated the advantages of ultrathin slab gel electrophoresisfor fluorescence-basedautomated DNA sequence analysis. The increased heat transfer efficiencyof the thin (typically 50-100 pm) gels permits higher electric fields to be employed with concomitant increases in separation speed. Issues arise, however, in introducing the laser beam used for fluorescence excitation into the thin gels. This paper presents methods for bringing the excitation beam into the thin gels from the side. ' h i s permits a low-powerair-cooledargon ion laser source to be utilized and produces much lower fluorescence and scattering background than alternative a p proaches. The beam is effectively trapped between the plates due to the high efficiency of reflection at the lowangle grazing incidence of the beam. A theoretical model describing beam throughput was developed which agrees well with experimental observations. In this model, attenuation of the beam intensity is attributed to four factors: aperturing at the entrance of the gel; reflective losses upon entrance into the gel; scattering during transmission through the gel; and reflective losses occurringupon successive "bounces" of the beam &omthe gelglass interface during propagation of the beam. Electrophoresis in thin gels provides increased heat transfer efficiency, permitting larger electric fields to be employed with correspondingly more rapid separations.'V2 This is of particular interest in the area of fluorescence-based automated DNA sequence analysis, where there is a tremendous need for increased throughput from sequencing in~truments.~Kostichka et al. demonstrated an order-of-magnitudeincrease in separation speed for fluorescencebased DNA sequencing in ultrathin slab gels.* In their work, 18 samples were loaded across an 18 mm width of a 75 pm ultrathin gel, which was cooled from the bottom with a +
University of Wisconsin.
:Lawrence Berkeley Laboratory.
(1) Drossman, H.; Luckey, J. A; Kostichka, A J.; D'Cunha, J.; Smith, L. M. Anal. Chem. 1990,62, 900-903. (2) Brumley, R L.; Smith, L. M. Nucleic Acids Res. 1991,19, 4121-4126. 59(3) Hunkapiller, T.; Kaiser, R J.; Koop, B. F.; Hood, L.Science 1991,254, 67. (4) Kostichka, A J.; Marchbanks, M. L.; Bmmley, R L;Drossman, H.; Smith, L. M. Bio/Technologv 1992,10, 78-81.
0003-2700/95/0367-3405$9.00/0 0 1995 American Chemical Society
water jacket. The horizontal sequencihggel was illuminated from above with a beam from an argon ion laser. The beam was expanded into a line across the gel perpendicular to the direction of DNA migration using a cylindrical lens system, and directed into the gel at Brewster's angle, -34" from the horizontal, to minimize reflections from the glass surface and to maximize light entering the gel. Although this means of exciting the fluorescence was adequate for proof of principle, the approach has two major problems. Fit, -2.5 W of 514 nm laser power was employed to excite fluorescence across the 18 mm region imaged. To excite fluorescence over the 75 mm width available in the electrophoresis cell with a comparable excitation power density, a much larger and more expensive laser would be needed. The size and expense of the laser source would compromise substantially the utility of the technology for routine sequence analysis. Second, the passage of the excitation beam through the glass plates and coolant excites considerable fluorescence and scattering leading to a high background signal. This high background signal increases noise and thereby decreases the detection sensitivity of the system. An alternative approach to fluorescence excitation in DNA sequence analysis is to bring the excitation laser beam into the gel from the ~ i d e (Figure ~ , ~ 1). This permits a comparable excitation power density to be obtained from a much lower power laser, as the excitation beam cross section is much smaller. It also greatly decreases background light, as the beam does not pass through the glass or coolant exciting background. This approach has been used successfully for conventional sequencing gels about 400 pm in thickness and is employed in commercial sequencing instruments from Hitachi and Pharmacia. However, the fundamental properties of Gaussian laser beams introduce problems when one tries to pass the beam through an ultrathin gel. The tighter the focus of the beam, the shorter the distance over which the focus can be maintained. For example, beam profiles calculated as described in ref 7 show that in free space the beam diameter can only be maintained below 71 pm over a region 2 x 7.6 mm = 15.2 mm long (see Table 1). Also, a good 1
(5) Ansorge, W.; Sproat, B.; Stegemann, J.; Schwager, C.; Zenke, M. Nucleic Acids Res. 1987,15,4593-4602. (6) Kambara, H.; Nishikawa, T.; Katayama, Y.; Yamaguchi, T. Bio/Technologv 1988,6,816-821. (7) Self, S. A APPI. Opt. 1983,22, 658-661.
Analytical Chemistry, Vol. 67, No. 19,October 1, 1995 3405
Figure 1. Overview diagram of fluorescence-based ultrathin slab gel electrophoresis system. The electrophoresis plates are 10 cm wide by 30 cm long, and the distance from the sample well to the detection region is 20 cm (see refs 1 and 2 for a more complete description).
Table 1. Depth ofFocus (DOF) Calculations
beamwidth
at focusa (um) 1 10 25 50 75 100 150 200
F(calcd)l (mm) 2.0
20 so 99 150
__
200 3M) 400
DOF (mm) 3.1 ~~
310 1.9 7.6 17 31
69 120
beam width
at edge of DOF (Irm) 1.4
14 35 71 110 140 210 280
The beam width at locus is taken as 2wo. where wo is the beam halfwdth at the waist: in the case of a round beam, w , is the beam radius lea SI. F is the focal lenmh of the lens. which is deoendent upon the 6pot sue required. Depth of f O N S is defined he& as the distance to where the beam diameter is the square root of 2 times larger than it is at the beam waist.
quality optical interface has to be incorporated into the el&* phoresis cell to permit the excitation light to be directed into the gel without distortion or loss. We describe here input optics and an optical interface that permit the laser excitation beam to be introduced into an ultrathin slab gel with high efficiency and reproducibilityand little distortion. The high efficiency of grazing incidence reflection is shown to effectively trap the beam between the glass plates, resulting in a high throughput of the laser energy. The beam properties are characterized experimentally and theoretically with good agreement.
EXPERIMENTAL SECTION Optics. Figure 1 shows an overview diagram of the f l u o r e cencebased horizontal ultrathin gel electrophoresis sequencing system employed for these experiments. The system consists of a laser excitation source, input optics for the laser excitation beam, a gel electrophoresis assembly, collection-imaging optics, and a CCD detector and associated computer system. The present system differs from that previously described4 in that it employs a larger area CCD chip (1024 x 1024 pixels, Tektronix 1024TKS, Princeton Instruments Inc., NJ) and the prism-wedge assembly @roomer, Islip, NY) was assembled into a single unit rather than as two separate pieces. The fluorescence collection lens is a Hasselblad (150 mm, ~2.8) and is used in conjunction with a secondary Nikkor lens (50 mmJl.2) to provide a demagnifcation of 3; thus an objective area 3 in. across is imaged onto the 1in. CCD detector. In addition, the input optics have been redesigned 3406
Analytical Chemisfy, Voi. 67, No. 19, October 1, 1995
to permit the excitation beam to enter the gel from the side, as described in detail below. Critical factors include (a) cleanly iniroducingthe beam into the gel with minimum loss or scattering, (b) minimizing the width of the beam across the gel, in order to maximize resolution of the DNAfragment~,8,~ and (c) minimizing power loss as the beam propagates through the gel. Parts A-C of Figure 2 show diagrams of the input optics and electrophoresis cell. An Omnichrome multiline argon ion laser (American Laser Corp., Salt Lake City, UTI operating primarily at 514 and 488 nm with a waist (Gaussian beam radius at l/ez intensity) of 0.298 mm was used for these experiments. The beam is directed into a spherical lens (No. BK7 PCX, 4 = 25.4 mm,f= 200 mm, Newport Corp., Fountain Valley, CA) positioned to focus at the center of the gel (Figure 2B). A second cylindrical lens (No. BK7 CKX 100, @ = 50.8 mm,f= 100 mm, Newport) focuses the beam further only in the vertical direction to a spot coinciding with the side of the glass plates holding the gel. Thus, the focused beam has two waists: a vertical waist at the entrance to the glass plates and a horizontal waist centered in the gel. The location of the vertical waist minimizes aperturing losses at the entrance to the gel, whereas the location of the horizontal waist minimizes the beam width across the gel to the extent permitted by the Gaussian beam properties. The small acrylamide chamber shown in Figure 2 provides an optical interface for entry of the laser beam into the gel. The chamber consists of a piece of plexiglass 3.4 cm wide x 0.6 cm thick x 1.5 cm high into which a rectangular notch 0.9 cm wide x 1.2 cm high has been milled to yield a U-shaped piece. Afusedsilica microscope slide 0.96 nun thick (the entrance window) glued to one side closes that side of the chamber, and a 0.85 mm thick silicon rubber gasket cut to the same shape as the plexiglass is glued to the other to provide a seal. The chamber (gasket side toward the gel) is placed against the side of the gel and secured by means of two thumbscrews affixed to the electrophoresis cell assembly. The electrophoresiscell glass plates thus form the back wall of the entrance chamber. In this region, the spacer material that separates the two plates (defining the gel thickness) has been removed (for further detail on the process of gel preparation see ref 10). During the gel-pouing process, the freshly prepared and as yet unpolymerized polyacrylamide solution seeps from between the glass plates into the chamber. Additional gel solution is added to the chamber to fill it after the seepage has slowed. Polymerization of the gel material in the chamber occurs in parallel with that between the plates, thus forming a continuum of gel material between the chamber and the electrophoresis cell. The edges of the upper and lower electrophoresis cell plates are beveled to a 45" angle at the position of beam entry and derivatized by a 2 min treatment with a solution of 0.5% [y-(methacryloxy)propylltrimethoxysilane (Sigma Chemical Co., St. Louis, MO) in 2 0 1 ethanol-acetic acid to increase adhesion of the gel to the glass. This treament stabilizes the gel-glass interface, which must be intact for proper entry of the laser beam between the glass plates. The laser beam enters the chamber perpendicular to the entrance window with the waist of the laser beam in the vertical dimension positioned at the back wall formed hy the upper and lower gel (8) Luckey, 1. A Smith, L M. A n d Ckem. 1 9 9 3 , 6 5 , 2 8 4 - 2 8 5 0 . (9) Luckey, J. A Nonis. T. B.; Smith. L M. J. Pkp. Chn. 1993, 97.3067-
3075. (10) Smith, L M.; Bmmley, R L:Buxion, E.; Giddings. M.; Marchbanks, M.; Tong. X. High Speed Automated DNA Sequencing in Ultra Thin Slab Gels. In Metkodr in Emynologv, in press.
A
B
w e
H 1Cm
C
Wndw
w e
H 1Cm
Figure 2
Diagram of input optics and optical interface.
plates. Gels employed in these studies were 4% total acrylamide with 5% bisacrylamide crosslinker and 7.5 M urea, unless otherwise specified. Beam Attenuation Measurements. To measure the W o n of excitation light that passes through the gel, in some experiments, a second optical interface on the opposite side of the gel was employed to permit exit of the excitation beam. The power was measured with a Newport Model 820 laser power meter before entering and after exiting the gel. In the latter case, to exclude light propagating through the glass plates from being measured as well, a pinhole aperture adjusted to the beam size was placed directly in front of the power meter photosensor. The gel is usually bubble free. In rare cases, bubbles appear in the area where the laser beam passes through. In this case, either the laser beam is moved to an adjacent position to avoid scattering caused by the bubbles or a new gel is prepared. Relative standard
deviations for the beam throughput measurement are generally -1-2%. Gel scattering Measurements. The amount of beam attenuation due to scattering of the excitation light in the gel was measured as follows: five 13 mm i.d. glass tubes, 1,2,5, 10, and 20 cm in length, were used to measure the scattering loss. A microscope cover glass (No. 1%54OA, Fisher Scientific Corp., Pittsburgh, PA) was glued at one end of each tube with silicone sealant @ow Corning Corp., Midland, MI). The polyacrylamide gel mixture was prepared and poured into each tube. A second microscope cover glass was af6xed to the other end of the tubes using petroleum jelly (Anderson Laboratories, Inc., Fort Worth, TX). Gel polymerization was allowed to proceed for 2 h or more. The collimated (unfocused) beam of the argon ion laser was passed through each gel tube along the long axis, and the beam intensity before and after passage through the gel was measured Analytical Chemistry, Vol. 67, No. 19, October 1, 1995
3407
with the power meter for several d ~ e r e ntube t lengths. Control experiments using pure water instead of acrylamide gel were also performed. The decrease in beam intensity results from reflective losses at the two windows as well as scattering losses during propagation through the gel. Both gel and water showed the expected logarithmic relationship between tube length and the amount of light lost by scattering. The logarithmic relationship is consistent with Beer‘s law, A = -log(Z/Z,) = EbC, and the data yield values for EC of 0.00478 cm-1 for gel (13 = 0.996) and 0.000 434 cm-’ for water (Z = 0.972). With this information, the loss due to scattering of the laser beam as it passes through the slab gel is readily calculated. Refractive Index Measurements. An ABBE-3L refractometer (Milton Roy Co., Rochester, NY) was used to measure refractive indexes @Is) of both polymerized and unpolymerized acrylamide gels containing varying amounts of urea and acrylamide. Gel solutions were prepared without added TEMED catalyst and the RIs of the unpolymerized solution were measured. Subsequently, TEMED was added and the gel was allowed to polymerize overnight. Since polyacrylamide gels polymerize poorly when in contact with air, the tubes were cut in half and slices were taken from the middle of the gel to minimize the effects of contamination by unpolymerized gel. For RI measurements, each slice was pushed between the two glass plates of the refractometer,breaking the slice up into fragments. In three sets of measurements, each of 10 gels, the relative standard deviation of the measured RI was less than 0.03%,similar to that obtained from pure liquids. This high degree of reproducibility confirms the absence of a problem due to air bubbles or other artifacts resulting from the disruption of the gel when placed into the refractometer cell. Calibration of the refractometerwith distilled water yielded an RI of 1.3325, reasonably close to the literature value of 1.3330 for room-temperature water.” The results of duplicate measurements in which urea and acrylamide concentra tion are varied were obtained. The RI was found to be linearly dependent upon the concentrations of both polyacrylamide and urea, with observed values of 1.404, 1.405, 1.406,1.409, and 1.413 at 3.5, 4, 5, 6, and 8% total polyacrylamide (of which 5% is bisacrylamide cross-linker; urea held fixed at 7.5 M) and 1.377, 1.385, 1.392, 1.401, and 1.405 at 4, 5, 6, 7, and 7.5 M urea (total polyacrylamide held fixed at 4%),respectively. A value of 1.405, corresponding to a 4%acrylamide gel containing 7.5 M urea, was used for the refractive index of the gels employed in the experiments described here. THEORY
suggests that it is not feasible to utilize from-the-side excitation in such thin gels without an unacceptable attenuation in power due to the spreading and subsequent decreased power density in the beam. This result is in contrast, however, to visual observations made on the system. Using the input optics and optical interface described above, the laser beam does enter the gel cleanly and to the eye appears to propagate across the gel without excessive loss. Total internal reflection is not the explanation for this, as the gel RI of 1.4045is less than 1.517 RI of the BK7 glass plates. An alternative possibility considered was that the laser beam is reflecting off of the gel-glass interface with high efficiency due to the low angle of incidence. Reflection efficiency calculations using the Fresnel equations (see, for example, ref 12) were consistent with this idea. For example, at an angle of incidence of 0.7 mad, 99.32% of the incident radiation will reflect from the gel-glass interface, using the refractive indexes above. To explore this hypothesis further, it was of interest to calculate the predicted transmission of the excitation beam through the gel, which would involve a number of successive reflections, with a certain loss from each reflection. These calculations are as follows: Beam Throughput Calculations. A ray entering the gel at a given angle will be attenuated at each gel-glass interface reflection by an amount which may be calculated using the Fresnel equations: The number of bounces N is given by
N = l8/a
(1)
where 1 is the width of the gel, 8 is the ray input angle, and a is the gel thickness. The reflection efficiency of this ray is given by the Fresnel equations, which to 6rst order in small grazing angle yield
E,” = El(1 - 468) €L =
n1
(n; - n;)l’’
(1polarization)
(I1polarization)
(2)
where E, is the reflected electric field amplitude, E, is the incident electric field amplitude, nl is the gel refractive index, and n2 is the glass refractive index. The total transmission efficiency for this ray after N bounces is then given by
To be able to employ from-the-side fluorescence detection effectively for these ultrathin gel systems, it is essential that the laser excitation beam be introduced into and propagated through the gel with minimal loss of power. The electrophoresis cell employed is 10 cm wide, and desirable gel thicknesses are in the range of 50-100 ~ m The . ~values in Table 1 show the problem that arises in trying to maintain such a tightly focused Gaussian beam over an extended region. For example, as mentioned above, a Gaussian beam focused to a 50 pm diameter diverges to 71 pm only 7.6 mm away in free space; thus, maintaining the beam diameter below 71 pm can only be accomplished for a region 1.5 cm long, much less than the desired 10 cm. This observation ~
~
(11) CRC Handbook of Chemistry and Physics, 68th ed.; Weast, R C., Ed.: CRC Press, Inc.: Boca Raton, FL,1987-88; p E-372.
3408 Analytical Chemistry, Vol. 67, No. 19, October 1, 1995
(12) Schwartz, M. Pn’nciples of Electrodynamics; McGraw-Hill Book Co.: New York, 1972; p 268.
(3) The focused Gaussian laser beam may be thought of as a collection of such rays (plane waves) moving in directions given by 2 with amplitudesf(k,,k,,kJ. Thus
r
E =rdx
ei(wt-x7),f(k
X)
ky' kz)
bounces, square the electric field and multiply the number per unit angle (eq 10) by the loss at that angle (eq 3).
(4)
If z is the direction of propagation of the Gaussian beam and y is the direction perpendicular to the gel-glass interface, the angle of interest is 8 = ky/k (small angles). The problem is to determine the density of waves as a function of 8. It is possible to i%d fin the general elliptical case, but, as discussed by Yariv,I3 the x and y behavior can be considered separately. Without loss of generality, we will treat the case of a round beam with waist at z = 0. A convenient starting point is obtained from eq 6.67 of Yariv, with the parameter qo set equal to izo.
E = e-ikze-ln[l+z/izol e ( - i k / Z ) [ ~ / ( z + i z ~ ) I
Here tu0 is the beam radius at the waist, n is the index of refraction, and 1is the wavelength. The Fourier transform of this expression is
Here ZOis the incident beam intensity and I is the attenuated beam intensity after passage between the plates. Solving the integral yields a final expression for the decrease in beam intensity
-I= I+-
Io
[
k2wt2d]-1/2
Angular Alignment Error. Equation 12 gives an expression for the throughput of excitation light when the axis of propagation of the Gaussian beam lies in the horizontal gel plane. In a real optical system there may be, however, some misalignment of the beam. It is therefore of interest to evaluate the effect of alignment error upon beam throughput. In this case eq 11 becomes eq 13, with 8 replaced by 8 - 80,where 80 is the error in direction.
This yields upon integration
The additional attenuation of the beam caused by misalignment is contained in the exponential factor, the preexponential factor being identical to eq 12. It should be noted that the approximation of 4 ~ a N Imade l in the derivation of eq 3 is valid taking E = 2.60, a = 63.5 pm, N = 3.494, and 1 =10 cm yields a value of 4~aN/1= 0.023 07. This approximation will continue to hold true for laser incidence angles below -5 mrad.
yielding upon integration
In this integration the beam is treated as if it were propagating through free space; that is, the confinii effect of the glass plates was neglected. Equation 7 may be further integrated over k, and k, to yield an expression for Ahy),
The ray density dp as a function of angle 8 is given by
dp =f@J dky
To get the total decrease in laser beam intensity after multiple
(9)
Substituting ky = kB yields (13) Yariv, A. Quantum Electronics, 2nd ed.; John Wiley and Sons, Inc.: New York, 1975; pp 110-113.
RESULTS AND DISCUSSION Three factors potentially affecting beam throughput were considered: (a) losses upon entering and/or exiting the gel; (b) losses due to scattering in the gel; (c) losses due to reflective inefficiencies as the beam propagates by reflection through the gel. The first factor, losses upon entering and/or exiting the gel, has two parts: the first part is reflective losses at the air-glass (4.26%)and glass-gel (0.155%)interfaces on the entrance side (see Figure 2) and at their counterparts on the exit side when an exit window is also employed for the purpose of beam power measurements. The total reflective loss upon beam entrance is thus 4.41%,and the same loss is encountered upon beam exit. It may be noted that the reflection upon exit actually increases the power withiin the gel, although it decreases the measured power at a detector outside the gel. The second part is aperture losses Analytical Chemistry, Vol. 67, No. 19, October 1, 1995
3409
Table 2. Calculated and Measured Beam Throughput
spacer thickness
bouncing loss
"
reflective loss 1 Xl (%)
blocking loss
63.5 89 127 152 177 354 531 708 885
4.67 4.67 4.67 4.67 4.67 4.67 4.67 4.67 4.67
13.47 3.62 0.30 0.034 0.028 0 0 0 0
11.52 8.63 6.29 5.33 4.63 2.40 1.62 1.22 0.98
63.5 127 152 177 531 885
4.41 4.41 4.41 4.41 4.41 4.41
13.47 0.30 0.034 0.028 0 0
15.10 8.47 7.23 6.30 2.24 1.36
xz (%)
x 3
scattering loss
(%)
x 4
reflective loss 2
calcd throughput
measd throughput
x 5 (%)
In(%)
(%)
4.67 4.67 4.67 4.67 4.67 4.67 4.67 4.67 4.67
68.89 79.23 84.06 85.15 85.78 87.81 88.52 88.88 89.09
65.6 74.5 77.6 80.1 82.0 83.9 83.9 85.1 86.4
4.41 4.41 4.41 4.41 4.41 4.41
60.13 74.70 75.91 76.68 80.02 80.74
56.3 68.8 71.9 75.0 78.1 80.3
(%)
Water 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.995 Gel
a
Calculated throughput: I (%) =100(1 - X1)(1 - Xz)(l
10.42 10.42 10.42 10.42 10.42 10.42
- X3)(1 - X4)(1 - &). 125
15
-
8
0
0
8
6 100 n
3
8
Y
50
a
-
a
2 c
0 0 50
n
75
0
25
0 250
500
750
-
n
5
a c
5
0
loo0
a
3 E
O
0
125
3 +
0
O
b
"1 0
75
a c M
10
15
I
loot
I
6
0
W
Y
a
a
50-
fb
e
0 0
751
501 25
0
Thickness (pm)
5
10
15
20
Tilt Angle (milliradians)
Figure 3. Calculated (0)and measured (0)beam throughput as a function of thickness for (A, top) water and (B, bottom) gel.
Figure 4. Calculated (0)and measured (0)beam throughput as a function of angle for (A, top) water and (B, bottom) gel.
upon entering the gel, due to beam power falling outside of the gel cross section. This may be minimized by (i) placing the beam focal waist at the entrance to the gel as diagrammed in Figure 2 and (ii) choosing the beam diameter at the focal waist to be
smaller than the entrance aperture. Use of the two lens input optics described above yields an elliptical spot with a 42.3 pm waist in the vertical direction. The electrophoresis cell was positioned so this waist coincided with the entrance to the gel
3410 Analytical Chemistry, Vol. 67, No. 19, October 7, 1995
plates. In these experiments, the gel spacers employed in the electrophoresiscell were 63.5 pm thick for this elliptical Gaussian beam focused to a vertical waist of 42.3 pm, beam power blocked by the glass plates is calculated to be 13.47%. Quantiiication of the second factor, scattering losses in the gel, was accomplished by measurement of the beam attenuation when a collimated laser beam was passed through an optical cell containing polymerized gel (see Experimental Section). Scattering losses determined in this way correspond to a gel absorbance of 0.00478 absorbance unit (AU) for a 1 cm path length; the absorbance for the 10 cm path length of the electrophoresis cell employed is thus 0.0478 AU, corresponding to a scattering loss of 10.42%.The scattering loss for water is similarly calculated to be 0.995%with the same 10 cm path length. Finally, losses due to reflective inefficiencies during beam propagation may be calculated according to eq 12 above. Table 2 and Figure 3 show the beam transmission efficiency calculated on the basis of these three factors, for several gel thicknesses, along with the measured values. Results are shown for both gel and pure water in the electrophoresis cell. The agreement is fairly good (compare last two columns of Table 2), suggesting that no significant beam attenuation mechanisms have been overlooked and that the proposed mechanism for propagation of the beam is valid. This latter point is substantiated in particular by the observed dependence of beam throughput upon gel thickness, which agrees well with experiment. As neither the reflective nor the scattering components depend upon the gel thickness or the beam waist, most of the interesting
behavior is in the transmissive component described by eq 12. This equation shows that as gel thickness or beam focal radius is decreased, the transmission efficiency also decreases. Importantly, only -40% attenuation of beam intensity is encountered in beam passage through even the thinnest gel studied (63.5 pm). This relatively modest attenuation has only a minor effect upon the fluorescence data quality. It may thus be concluded that the side excitation method is well suited for even these ultrathin gel systems. Beam throughput may be calculated for still thinner gels by the methods described here, permitting the feasibility of side excitation in such systems to be readily assessed. As sensitivity to alignment errors is an important aspect of the instrument design, it is of interest to determine this experimentally and compare the results with those predicted by eq 14. Figure 4 shows calculated and measured throughput for a 63.5 pm thickness of gel or water when the tilt angle is varied from 0 to 12 mrad. Again,the agreement between calculated and measured results is quite good, although some deviation occurs at larger angles; this deviation reflects the small-angle approximation made in eq 3 by the assumption of 4mN/l
