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Cell Seeding Guidelines
Millicell®-24 Cell Culture Insert Plate
Optimizing cell seeding protocols and densities is extremely important to ensure good cell attachment and growth in Millicell®-24 cell culture insert plates. Initially testing a range of seeding densities is recommended. The following guidelines are designed to be carried out in a single device and can be performed using automation. Millicell®-24 plates with a 0.4 µm polycarbonate (PCF) membrane or a 1.0 µm polyester (PET) membrane, which allows the cells to be visualized during the seeding and growth stages, were used in this protocol. Materials and Reagents
- Millicell®-24 cell culture insert plates (PCF or PET membrane) — Merck cat. nos. PSHT 010 R5, PSRP 010 R5
- Tissue culture flasks
- Steriflip-GP or Stericup-GP filter units — Merck cat. no. SCGP 005 25 or SCGP U11 RE
- 0.02% EDTA — Merck cat. no. 20-307
- 1x Trypsin/EDTA — Merck cat. no. SM-2002-C or SM-2003-C
- Cell culture media — Merck cat. no. SLM-022-B
- Sterile 1 mL pipette tips, pipettors, microfuge/centrifuge tubes and basins
- Hemocytometer or other cell counter
Note: Although the following methods have been optimized for seeding and feeding adherent epithelial cell lines such as Caco-2 and MDCK, they contain the basic principles for handling the plate using any method or cell line. Methods Optimization of Seeding Density
- Expand and cultivate cells in T-75 flasks in a cell culture incubator set at 37°C, 5–6% CO2 and 95% relative humidity. Allow cells to reach 80–90% confluence before detaching and passaging. Do not allow cells to become over confluent (>90%) as this will impact subsequent monolayer formation on the Millicell®-24 plates.
Note: The number of cell passages can affect the formation of an optimal monolayer. It is therefore recommended that Caco-2 cells be subjected to no more that 20 passages before a new line is established. Similarly, MDCK cells should be subjected to no more that 40 passages.
- Aspirate the media, rinse the cultivated cells in T-75 flasks with 5 mL 0.02% EDTA and incubate for 3–5 minutes. After aspiration of the 0.02% EDTA, add 1.5 mL of the trypsin/EDTA solution. Incubate at 37°C for approximately 5 to 15 minutes or until the cells detach and float. This can be confirmed by periodic visual inspection of the flasks.
- Once the cells are detached, add fresh cell culture medium and mix until all cell clumps are dispersed. Count the cells using a hemocytometer or other cell counter to determine the cell number and pass cells accordingly to maintain stock of cell line. Mix cells frequently to ensure accurate counts.
*The guidelines in this protocol are specific to Millicell®-24 cell culture plates. If using single-well inserts or Millicell®-96 cell culture plates, modifications must be made to these guidelines. Please refer to the recommended working volumes table to adjust liquid additions based on product selection.
Note: To optimize the seeding density of a cell line, it is recommended that a range of cell concentrations across the plates be used in replicates of 6 or 8.
- In sterile centrifuge tubes, dilute the cell solution with medium to enable the plating of a range of seeding densities. A good starting point to determine seeding density is calculated by multiplying the present cell density by the fold increase or decrease in surface area.
Example: If the seeding density for the 9 mm Millicell® inserts (surface area=0.3 cm2) is 60,000 cells/well then multiply 60,000 by 2.3 to calculate the seeding density for Millicell®-24 cell culture insert plates (surface area=0.7 cm2).
0.7 cm2/0.3 cm2=2.3 60,000 cells/well x 2.3=138,000 cells/well
A suitable range might therefore encompass 120,000–160,000 cells/well, depending on individual cell lines used. The following table lists Merck’s optimized densities (in terms of three different units) for seeding 3 day MDCK and 21 day Caco-2 cell monolayers.
Note: If starting without any prior platform, initially bracket a range of seeding densities around the values listed in the “Cell Seeding Density Conversion” table.
Note: Achieving a uniform cell suspension when initially plating the cells will promote a more consistent monolayer across the 24 wells. This may be particularly difficult when seeding multiple plates. Frequent mixing is recommended to minimize the risk of cells settling to the bottom, resulting in an inaccurate distribution of cells across the wells or plates.
- Pipette 300 µL of cells at each seeding density into the appropriate filter wells of the Millicell®-24 plates (see “Range of Feeding Densities” figures). Pipette 28 mL of cell culture medium into the single-well feeder plate via the large access hole located at the lower right of the plate. Alternatively, disassemble the filter plate from the feeder plate. Place the filter plate on a sterile surface in a laminar flow hood and add medium directly to the feeder plate. Gently reassemble the two components and place in the cell culture incubator.
Note: Cells seeded onto the Millicell®-24 plate should be placed in an incubator that provides adequate humidity control. A cell culture incubator with electronic humidity control is recommended. If this is not possible, plates should be placed with a water pan in an incubator that will not be opened frequently.
Millicell®-24 Culture Plate — Cell Seeding Density Conversions
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Cells per cm2
|
Cells per mL (0.4 ml.)
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Cells per Well
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21-day Caco-2 Seeding Density |
85,700 |
150,000 |
60,000 |
3-day MDCK Seeding Density |
714,000 |
1,250,000 |
500,000 |
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Cell Feeding Guidelines
Note: Replacing the growth medium every other day is recommended for optimal cell growth. The most critical part of removing and replacing the medium in the Millicell®-24 plate is to avoid damaging the monolayer of cells and the filter on which they are supported. This can be accomplished using a sterile 1 mL pipette tip and utilizing the apical assist feature.
- Aspirate the medium from the feeder plate (basolateral) using a sterile 1 mL pipette tip via the large access hole or, after disassembly of the filter plate from the feeder plate.
- Aspirate the medium from the filter wells using the apical assist feature. Use care not to contact the filter inside the wells when removing or adding medium. Add back 300 µL growth medium to the filter wells (at the apical assist) before adding back the 28 mL of medium to the feeder plate (basolateral).
Note: If setting the filter plate down on the hood surface using the filter plate "feet", it is recommended to let the whole assembly sit idle in the hood for 15 seconds after removing it from the incubator. Disassembly of the plate after 15 seconds will minimize the potential for droplet formation on the underside of the membrane, which may contact the hood surface.
Note: Evaluation of seeding densities is usually performed by testing the integrity of the monolayer with trans-epithelial electrical resistance (TEER) measurements, by evaluation of the transport of lucifer yellow (LY) or by using standard drug compounds.
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Monolayer Integrity Measurements and Drug Transport Guidelines
Millicell®-24 cell culture insert plate is a 24-well general purpose device designed to support cell growth, attachment, differentiation, or other desired applications. The procedure described below details how to measure the formation of a differentiated cell monolayer and the rate of drug transport across the cell barrier. All procedures are designed to be carried out in a single device and, if desired, can be performed using automation for cell seeding, cell feeding, washing, and other experimental procedures. Materials and Reagents
- Millicell®-24 cell culture insert plate (PCF or PET membrane ) — Merck cat. nos. PSHT 010 R5, PSRP 010 R5
- Millicell® ERS System—Merck cat. no. MERS 000 01
- 24-well receiver plate—Merckcat. no. PSMW 010 R5
- 24-well feeder tray—Merck cat. no. PSSW 010 R5
- Lucifer Yellow, 100 µg/mL concentration
- Hanks balanced salt solution (HBSS)
- Radioactive drug transport:
- Wallac/Perkin Elmer 96-well flexible plate
- Microbeta® Trilux® Counter or equivalent
- Scintillation cocktail
Note: Although the following methods have been optimized for monolayer integrity and cell based drug transport on epithelial cell lines such as Caco-2 or MDCK, they can be applied to any applicable cell system. Methods Measurements of Monolayer Integrity A. Trans-Epithelial Electrical Resistance (TEER)
- At the end of the desired growth period, remove the plates from the incubator and allow them to equilibrate to room temperature (approximately 0.5 hours).
- Measure the electrical resistance across the monolayer using the Millicell® ERS system. Position the probe such that the shorter prong is immersed in the media inside the filter well and the longer prong is placed through the basolateral access hole into the media in the growth plate.
Record the electrical resistance for each well. Take care not to touch the filter during TEER measurements, as it can damage the cell monolayer. Note: If applicable, background TEER may be recorded in wells without cell monolayers, and can be subtracted from the raw TEER values with cells. B. Lucifer Yellow (LY) Rejection
- Using the same methodology as when feeding, rinse the monolayer three times with 300 µL HBSS in the apical wells and 28 mL in the feeder tray.
- Add 300 µL of LY solution to each well in the filter plate.
- Add 600 µL HBSS to each well of a 24-well receiver tray.
- Assemble the filter plate and 24-well receiver plate and incubate for 1–2 hours at 37°C.
- Remove the filter plate from the receiver plate and place the receiver plate into a fluorescent plate reader. Determine the LY fluorescence using an excitation wavelength of 485 nm and an emission wavelength of 535 nm.
- Calculate the percent of LY rejection across the cell monolayer by measuring fluorescence in the receiver plate as compared to an ‘equilibrium’ standard.
Note: The standard plate should consist of 4 wells with 600 µL HBSS (blank) and 4 wells with 200 µL LY (100 µg/mL) + 400 µL HBSS (equilibrium samples).
Cell Drug Transport Template (Four Compounds, Three Replicates) Filter Plate (Apical) Template
300 µL Drug 1 |
300 µL Drug 1 |
300 µL Drug 1 |
300 µL Drug 2 |
300 µL Drug 2 |
300 µL Drug 2 |
300 µL HBSS |
300 µL HBSS |
300 µL HBSS |
300 µL HBSS |
300 µL HBSS |
300 µL HBSS |
300 µL Drug 3 |
300 µL Drug 3 |
300 µL Drug 3 |
300 µL Drug 4 |
300 µL Drug 4 |
300 µL Drug 4 |
300 µL HBSS |
300 µL HBSS |
300 µL HBSS |
300 µL HBSS |
300 µL HBSS |
300 µL HBSS |
Receiver Plate (Basolateral) Template
600 µL Drug 1 |
600 µL Drug 1 |
600 µL Drug 1 |
600 µL Drug 2 |
600 µL Drug 2 |
600 µL Drug 2 |
600 µL HBSS |
600 µL HBSS |
600 µL HBSS |
600 µL HBSS |
600 µL HBSS |
600 µL HBSS |
600 µL Drug 3 |
600 µL Drug 3 |
600 µL Drug 3 |
600 µL Drug 4 |
600 µL Drug 4 |
600 µL Drug 4 |
600 µL HBSS |
600 µL HBSS |
600 µL HBSS |
600 µL HBSS |
600 µL HBSS |
600 µL HBSS |
Calculate the LY rejection using the following equation: Find the LY passage using this equation: Example: If the measured values for each of these solutions were: Then the percent LY passage would equal: The calculated LY rejection would therefore be: Note: The cell seeding protocol is commonly optimized by choosing the density that results in the highest average electrical resistance with the least variability (e.g., lowest CV) combined with the lowest LY passage. After the seeding density has been optimized, monolayer integrity can be tested using TEER reading, LY rejection, or transport of a paracellular drug compound such as atenolol or mannitol. Note: We do not recommend performing LY rejection in tandem with drug transport as it may interfere with radiometric or LC/MS analysis. It is recommended to run LY post drug transport to assess the integrity of the monolayer. Cell-based Drug Transport
- After the desired cell growth period, remove the Millicell®-24 plate from the incubator and determine the electrical resistance for each well (as described above). Wash the monolayer, exchanging the volume three times using sterile HBSS, pH 7.4. After washing, remove the buffer from the filter plate and feeder tray.
- Transfer the filter plate to a 24-well transport analysis plate.
- To determine the rate of drug transport in the apical to basolateral direction, add 300 µL of the test compounds to the filter well. Drug concentrations typically ranging from 10 µm to 200 µm may be used (achieve desired concentration using HBSS, pH 7.4 or an alternative buffer of desired pH).
- Fill the wells of the 24-well receiver plate with 600 µL buffer.
- To determine the rate of drug transport in the basolateral to apical direction, add 600 µL of the test compounds to the 24-well receiver plate.
- Fill the filter wells (apical compartment) with 300 µL of buffer.
- Combine the filter and receiver plates once all drugs and buffer have been added. Begin timing the experiment.
- Incubate at 37°C shaking at 60 rpm on a rotary shaker. Typical incubation times are 1 to 2 hours. We recommend a 2-hour incubation for optimal results.
- For LC/MS analysis: At the end of the incubation, remove a fixed volume (typically 50–100 µL) directly from the apical and basolateral wells (using the basolateral access holes) or by disassembling the plates. Transfer the volume to a clean plate.
For radiolabeled drug evaluation: Remove 25 µL or applicable volume from each compartment and transfer to a plate containing 100 µL of scintillation fluid. Mix, then determine the radioactivity per sample using a Multiwell Plate Scintillation Reader such as the Trilux from Perkin Elmer. Add 25 µL of your initial drug to 100 µL of scintillation fluid to obtain your standard counts. Calculating Drug Transport Rates The apparent permeability, in units of centimeter per second, can be calculated for Millicell®-24 plate drug transport assays using the following equation. Where: VA=the volume in the acceptor well Area=the surface area of the membrane (0.7 cm2 for Millicell®-24 plates) Time=the total transport time in seconds. For radiolabeled drug transport experiments the CPM units obtained from the Trilux Multiwell Plate Scintillation Counter are used directly for the drug acceptor and initial concentrations such that the formula becomes: Note: Caco-2 or MDCK monolayer differentiation is evaluated by the transport of compounds that are effluxed, such as digoxin and vinblastine. The (B to A)/(A to B) ratios are good measurements of expression and localization of P-glycoprotein (P-gp) to the apical plasma membrane. Optimization of seeding densities may also be assessed by monolayer differentiation. Note: The growth, integrity and differentiation of the cell monolayers need to be carefully monitored when optimizing the assay for use in a drug transport analysis. Many factors may contribute to the assay variability. Note that the cell passage number and culture medium can influence how the cells perform on the Millicell®-24 cell culture plate. These factors may cause a shift in the behavior of both tight junction formation and polarized expression of membrane proteins, as the cell passage number increases. How this will ultimately affect the measurement of drug transport rates needs to be carefully considered in the experimental design. References
- Artursson, P., Karlsson, J. (1991) Correlation between oral drug absorption in humans and apparent drug permeability coefficients in human intestinal epithelial (Caco-2) cells. Biochem. Biophys. Res. Comm. 175:880–85.
- Artursson, P. (1990) Epithelial transport of drugs in cell culture. I: A model for studying the passive diffusion of drugs over intestinal absorptive (Caco-2) cells. J. Pharm. Sci. 79:476–82.
- Artursson, P., Palm, K., and Luthman, K. (2001) Caco-2 monolayers in experimental and theoretical predictions of drug transport. Adv. Drug Deliv. Rev. 46:27–43.
- Bailey, C.A., Bryla, P., Malick, A.W. (1996) The use of intestinal epithelial cell culture model, Caco-2, in pharmaceutical development. Adv. Drug Deliv. Rev. 22:85–103.
- Arena, A.A., et.al. (2005) Development of a higher throughput, permeability model system using MDR1-transfected MDCK cells in 24- and 96-well formats. 2005 American Association of Pharmaceutical Sciences Annual Meeeting, Nashville, TN.
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Sodium Fluorescein Permeability Assay
The following is a specific protocol adapted from: Tchao, Ruy, Progress in In Vitro Toxicology 6 (2). It is a MDCK cell monolayer integrity test performed on Millicell®-HA cell culture insert using sodium fluorescein. This assay is suited to score the irritancy of compounds and mixtures that are miscible in water, most commonly soaps and detergents. These results have been correlated to Draize eye irritancy scores or Average Maximum Draize (AMD) scores.** The assay may be used to establish rank orders of the irritancy of soaps and detergents and may potentially be used to assess and predict irritancy-related compounds. Other diluents may be substituted for less miscible materials. Suggestions include coconut oil, mineral oil, and dimethyl sulfoxide (DMSO). Corn oil, cotton seed oil, soy bean oil, and mineral oil (heavy and light) have shown no adverse effects in this assay. Sodium dodecyl sulfate (SDS) in homogenized mineral oil produced an effect similar to SDS in Hank’s Balanced Saline Solution (HBSS). This test quantitatively determines the integrity of in vitro MDCK cell to cell junctions in an epithelial monolayer. It has been shown that increased permeability of compounds is related to increased irritancy. The irritancy of unknown samples is determined by comparison to an SDS positive control. This assay also allows evaluation of cell recovery after injury. For example, disruption of tight junctions (without cell detachment and loss) will require two to four hours for complete recovery. If cell detachment and loss occur, the recovery may require several days depending on the severity of the injury. A limitation of the assay is that it can not be used to test compounds of extreme pH (lower than pH 3 or higher than pH 11) due to the buffering capacity of the diluent used. In general, compounds at these extreme pH levels are by definition considered irritants and therefore would not be tested. *This section contains a protocol for sodium fluorescein. Information on immunofluorescence and Lucifer Yellow is available in the Fixing and Staining section of the Handbook. **All Draize test scores were obtained from the Soap and Detergent Association. Merck was not involved in Draize eye irritancy testing. Materials and Reagents
- 24-well tissue culture plates (3 plates for each compound)
- 12 mm Millicell®-HA cell culture inserts. Merck cat. no. PIHA 012 50
- MDCK epithelial cells
- T-75 tissue culture flasks
- MEM media with 10% fetal bovine serum and gentamycin, 1 µg/mL
- Hanks' Balanced Salt Solution (HBSS)
- Trypsin-Versene™
- Sodium Fluorescein, 1mg/vial
[Adapted from Tchao, Ruy, Progress in In Vitro Toxicology 6 (2)]:
- Grow MDCK cell line in T-75 culture flask with MEM (10% FBS, 1 µg/mL gentamycin) and pass at weekly intervals using trypsin-versene.
- Place inserts into a 24-well culture plate containing 0.5 mL media per well. One 24-well plate can be used to test a compound at six concentrations in quadruplicate.
- Seed 1.5×105 cells per insert; confluency should occur in 3 days. Test for monolayer before proceeding. During this incubation period the media should be changed daily.
- When cultures are confluent, remove media and rinse inserts with HBSS.
- Place inserts into a new 24-well plate containing 0.5 mL HBSS and a specific amount of the test compound. Incubate at 24°C for 15 minutes.
- Decant solution and wash inserts three times, each with 1 mL HBSS.
- Place inserts into a new 24-well plate containing 0.5 mL HBSS. Add 0.5 mL HBSS containing 0.02% sodium fluorescein to the apical side of the inserts. Incubate at 24°C for 30 minutes.
- Remove inserts and fix for examination via light and electron microscopy.
- Dilute sodium fluorescein solution in each well to 3 mL and measure in a spectrophotometer at 490 nm.
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Visualization and Microscopy
The Microscopic Examination of Samples Can Be Performed in Three Modes:
- Viewing from below the plate (through transparent PET or CM membranes)
Millicell® devices using PET or CM membrane have been designed to allow visualization of cells from below using an inverted microscope. For viewing live cells, microscopic observations can be made through the receiver or plastic plate containing media. In order to focus on the cells, the microscope objective (typically 5–20X) must have an appropriate working distance. (For objective specifications, visit the websites listed in the Microscope Objective Information section.) Fixed cells that do not require to be visualized in media can be viewed directly without the receiver plate. However, care should be taken not to contaminate the objective with liquid residue (media, mounting fluid) on the membrane.
- Viewing from above the plate (Millicell® 6-well inserts, Millicell®-24 cell culture insert plates)
Some cell culture platforms can allow the cells to be viewed in a conventional microscope directly from above using low magnification. Cells can be visualized through the lid to maintain sterility or with the lid removed for fixed cells or when maintenance of sterility is not required. Working distances of the objective must be longer when reading from above compared to when reading from below. If using immunofluorescence, it is recommended to use a mounting fluid that contains an anti-fade additive to prevent photobleaching.
- Visualizing membranes on microscope slides (for higher magnification or withobjectives with short working distances [less than 2 mm])
The membrane can be removed from each well for microscopic evaluation. This allows for higher magnification examination and storage of the slides for future use.
For visualizing from above the membrane, typically 5–20X objectives are used that have at least a 13.59 mm (A) or a 18.03 mm (B) working distance when viewing without or with the lid, respectively. For visualizing from below the membrane, 5–20X objectives are used that have at least a 2 mm (C) working distance. To prepare membranes on microscope slide
- Remove the membrane from the well using a sharp scalpel to make a small incision in the edge of the membrane. Carefully cut along the inside of the well wall for approximately one quarter of the well diameter. Using forceps (Merck cat. no. XX62 000 06), carefully hold the membrane while continuing to cut around the well diameter to remove membrane. Alternatively, a cork borer may be used to remove the membrane. Note: Use care to prevent membrane from curling.
- Place the membrane disk, cells facing up, onto a microscope slide.
- Add 50 µL mounting fluid to the membrane disk and allow it to wet out in order to prevent bubbles under the disk.
- Slowly lower a cover slip onto the membrane at an angle to allow air bubbles to be removed.
Microscope Objective Information Information regarding microscope objective magnification power and working distances can be obtained from individual optical dealers or from the microscope vendors:
Note It is assumed that users of this procedure will be knowledgeable in TEM procedures. Materials and Reagents
- Millicell® Cell Culture Inserts
- Phosphate Buffered Solution (PBS)
- Glutaraldehyde
- Osmium tetroxide
- Sodium cacodylate
- Sucrose, reagent grade
- Calcium chloride
- Lead nitrate
- Sodium citrate/Sodium hydroxide
- Uranyl acetate
- Ethanol
- Flat embedding trays
- Embedding Resin (i.e. EPON812)
- Fine forceps — Merck cat. no. XX66 000 06
- Diamond Knife
- Cork Borer
- Durapore® Filter Disk — Merck
Sample Pictures Living murine embryonic stem cell derived embryoid bodies visualized in a 1 um PET Millicell®-24 device using an Olympus IMT-2 inverted microscope Neuron differentiation of embryonic stem cells in Millicell®-24 1 um PET filter plates. Murine embryonic stem cells were formed into suspended embryoid bodies (EBs), then transferred to 1 um PET Millicell®-24 plates for attachment and differentiation. The photo inset shows the inverted phase contrast through membrane of live EBs in the media. Neural differentiation after netinoic acid treatment of attached EBs was confirmed by anti-neurofilament immunofluoresence. A. Processing/Cell Preparation Note: Steps 1–5 should be done on an intact Millicell® cell culture insert or plate well.
- Wash cells briefly (2 times for 5 minutes each) at room temperature with phosphate buffered solution without fixative.
- Fix cells in 2% glutaraldehyde in 100 mm sodium cacodylate buffer, pH 7.5, at room temperature from 15 minutes to 2 hours.
- Wash cells (2 times for 5 minutes each) in 100 mm sodium cacodylate buffer at room temperature. Note: At this point, cells can be stored in the above buffer with 7 g sucrose/100 mL buffer at 4°C.
- Fix cells in 1% osmium tetroxide in either 100 mm sodium cacodylate or suitable phosphate buffer.
- Dehydrate cells in the following concentrations of ethanol:
Ethanol Concentration Kit (%)
|
Time (minutes)
|
30 |
15 |
50 |
15 |
70 |
15 |
95 |
15 |
100 |
3 x 15 |
Note: Dehydration of Millicell®-HA units should be performed in a metal pan that will be used as the embedding tray due to the tendency of the cellulosic membranes to be less rigid during the dehydration process. Attempts to transfer the membranes during these steps could lead to mechanical damage to the cells.
- For infiltration, EPON812, an EDPON substitution, or LX112 is suitable for both devices (do not use Spurr’s). The following is a general infiltration scheme:
Ethanol Concentration Kit (%)/Tray (% Plastic)
|
Time (minutes)
|
75/25 |
30 on a shaker |
50/50 |
30 on a shaker |
0/100 |
30 each/3x on a shaker |
0/100 |
Overnight |
Note: It is not necessary to use any other agent, such as propylene oxide, with plastic. Propylene oxide will dissolve the cellulosic filters. In addition, the standard inversion/rotation of specimens used in these steps is not advised since either (1) damage to the cell layer or (2) stretching of the cellulosic filter may occur. Mild shaking on a gel shaker apparatus is sufficient for successful infiltration.
Note: Before the next step the membrane must be detached from the surrounding plastic ring. Sometimes this will occur without manipulation since the EPON may loosen the membrane-to-ring bond. If this does not occur, use a sharp scalpel or a cork borer and cut the membrane. It may also help to cut the membrane over a 47 mm filter support disk. Under no circumstances should the membrane be left attached to the ring during polymerization.
- Transfer to fresh plastic and polymerize at 68°C overnight.
B. Sectioning Notes
- Nitrocellulose (HA), polycarbonate (PC) and polyethylene terepthalate (PET) membrane: These membranes can be sectioned in any plane without difficulty.
- CM (Biopore) membrane: The Biopore membrane must be processed in one of two ways based on the final thickness of the section.
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