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Protocol

Immersion Freezing of CellMonolayers for Cryo-Electron Tomography

Guenter P. Resch,1,4 Marlene Brandstetter,1 Veronika I. Wonesch,1,2 and Edit Urban3

1IMP-IMBA-GMI Electron Microscopy Facility, Institute of Molecular Biotechnology, 1030 Vienna, Austria2University of Applied Sciences Wiener Neustadt, 2700 Wiener Neustadt, Austria3Institute of Molecular Biotechnology, 1030 Vienna, Austria

INTRODUCTION

Cryo-transmission electron microscopy (cryo-TEM) is not limited to the visualization of suspendedmacromolecules in their native hydrated state. It can also be used to elucidate the molecular architectureof peripheral parts of adherent cells: After cultivation of the cells directly on EM grids, they are physicallyfixed by immersion freezing to yield cells embedded in thin, crystal-free layers of frozen water.Subsequently, specimens can be visualized using cryo-electron tomography (cryo-ET). This protocol out-lines the production of protein-coated gold particles as suitable fiducial markers for electron tomogra-phy, and how to cultivate cells on grids with a carbon support film. It also describes how to freezecells to obtain optimal and reproducible results using the Leica EM GP immersion freezer, and how toassess the results.

RELATED INFORMATION

For a brief introduction to cryo-EM, immersion freezing, the instrumentation available for this purpose,and the Leica EM GP in particular, see Immersion Freezing of Biological Specimens: Rationale, Prin-ciples, and Instrumentation (Resch et al. 2011a). Another protocol that describes immersion freezing ofsuspended specimens, such as nonadherent cells, viruses, macromolecular complexes, and liposomes isalso available (Immersion Freezing of Suspended Particles and Cells for Cryo-Electron Microscopy[Resch et al. 2011b]). Parts common to both protocols were duplicated so that each protocol wouldbe self-contained.

MATERIALS

It is essential that you consult the appropriate Material Safety Data Sheets and your institution’sEnvironmental Health and Safety Office for proper handling of equipment and hazardous materialsused in this protocol.

Reagents

Bovine serum albumin (BSA; Sigma) (5 mg/mL stock in 5 mM NaH2PO4 [pH 5])Cell culture mediumCells of interestColloidal gold, 10 nm (410.011 from Aurion, Wageningen, The Netherlands; EMGC10 from BBIn-

ternational, Cardiff, UK)Ethane gas, 99.995% (4.5; e.g., Air Liquide)Liquid nitrogen (LN2), 99.95% (3.5; e.g., Air Liquide)NaH2PO4 (200 mM, pH 5)

4Corresponding author ([email protected]).Cite as: Cold Spring Harb Protoc; 2011; doi:10.1101/pdb.prot5643 www.cshprotocols.org

© 2011 Cold Spring Harbor Laboratory Press 815

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Equipment

Cell culture setupCentrifuge (for 1.5-mL reaction tubes to be centrifuged at 40 000 g)Cryo-grid boxes with lid, either 15- × 15-mm square (Ted Pella 160-44) or 14-mm diameter round

(Leica Microsystems 16706039; Ted Pella160-40)Each of these boxes can accommodate four grids.

Glow discharge unit, either:

• Bal-Tec SCD005 sputter coater (now Leica Microsystems, Vienna, Austria) with the Autarget removed

This provides more gentle discharge; it is used for thin continuous carbon.

• Instrument built according to Aebi and Pollard (1987)

This is stronger and renders the films more hydrophilic, but should only be used for very stable films such asQuantifoil.

Gold (Au) 200 mesh grids with a carbon support film with small holes (Quantifoil R 1/4, availablefrom Quantifoil Micro Tools GmbH [www.quantifoil.com])

Hair dryer (e.g., Steinel HG 2000 from VWR International) or Leica EMCTDdrying platform (availablefrom mid-2011 on)

Leica EM GP main unit (Leica Microsystems, Vienna, Austria; see Immersion Freezing of BiologicalSpecimens: Rationale, Principles, and Instrumentation [Resch et al. 2011a]) set up in a well-ventilated area with low environmental humidity and good lightingThe instrument can be upgraded with a number of options:

• The foot switch (16654925) makes the workflow more comfortable; it takes the user to the next step in thefreezing cycle.

• A binocular (“viewing system;” 16706433) mounted in front of the environmental chamber can be used toclosely monitor the filter paper alignment and the blotting process. In practice, however, it is not beingused much.

• The forceps adjusting tool for the quick-lock forceps (16706442) and the filter paper punch (16706443)come in very handy when using different types of forceps or filter paper (and can help to save money onconsumables).

Leica EM GP accessories:

• GP quick-release forceps (set of two, well aligned to each other; one piece: Leica Microsystems16706435)

• Special forceps with insulation coating (set of two; Leica Microsystems 16701955)

• Cryo-transfer container (Leica Microsystems 16706439)

• Cryo-tool with M4 thread (Leica Microsystems 16701958)

• Secondary cryogen liquefier (Leica Microsystems 16706438)

• Filter paper for blotting, either Whatman No. 1 filter paper with precut hole (Leica Microsys-tems 16706440) or self-made filter paper of any type with an outer diameter of 55 mm anda central 15-mm hole, made with a filter paper punch (see above)

Light microscope slides (e.g., VWR International 631-9461)LN2 dewar vessels, 1-L (e.g.,VWR International)LN2 specimen storage systemMultiwell dishes, sterile (six- or 12-well; VWR International 734-0991 or Nunc 734-2156)Pipette tip (200-µL) or hollow needle (if Leica liquefier is not used; see Step 33)Pressure regulator for ethane gas, 50-mbar (GDK)Screwdrivers (or Allen key) to open/close cryo-grid boxesSyringeTubing for ethane gas

• Silicone tubing, 3-mm ID, 1-mm wall for the Leica liquefier

• Tygon R-3603 tubing, 5-mm ID, 1.5-mm wall from Saint-Gobain/Performance Plastics for aneedle or pipette tip

Tweezers, long (300-mm; e.g., VWR International)Vortex mixer

www.cshprotocols.org 816 Cold Spring Harbor Protocols

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METHOD

Preparation of BSA-Coated Gold Colloid

To avoid aggregation of the gold fiducials on a tomography sample, use commercially available protein-coated gold (Gar-valov et al. 2006; Lucic et al. 2007) or prepare a BSA-saturated gold colloidal stock as described here.

1. Mix 39 volumes of 10 nm colloidal gold with 1 volume of 200 mM NaH2PO4 (pH 5.0). Vortex.

2. Add BSA from a stock solution of 5 mg/mL in 5 mM NaH2PO4 (pH 5.0) at a dilution of 1:20 to thebuffered gold. Mix it well. Incubate it for at least 15 min at 4˚C.

3. Centrifuge the gold colloid for 1 h at 40 000g at 4˚C.4. Discard the supernatant. Resuspend the red pellet in the desired buffer or medium to yield the same

volume as before centrifugation.

5. Repeat the centrifugation step.

6. Collect the final pellet in buffer or medium (about one-tenth of the original volume) and store it at4˚C.

7. Before freezing, test the distribution and the possible aggregation of gold particles in the freshly pre-pared stock on a glow-discharged carbon-coated grid in the TEM.

Pretreatment of EM Grids

Before cultivating cells on grids, glow discharge (plasma clean) grids in air to render the carbon support film morehydrophilic.

8. Place the grids to be discharged with the carbon film side facing up onto a clean glass slide.

9. Place the glass slide into the vacuum chamber of the glow discharge device and evacuate accordingto the instructions.

10. Expose the grids for 30–60 sec to the homogeneous purple discharge.On the SCD005, use a current of 20 mA; on the homemade device (Aebi and Pollard 1987), set the high-frequencygenerator to full power.

11. Vent the vacuum chamber carefully so as not to blow away the grids.

12. Use the grids as soon as possible, but in any case within 1 h.

Cultivation of Adherent Cells on Grids

13. Glow discharge Quantifoil R 1/4 200 mesh Au grids.Copper ions are cytotoxic and nickel negatively influences the alignment of TEMs, so do not use grids from thesematerials for cell culture!

14. (Optional) Prior to plating of the cells, a matrix coating can be applied onto the carbon film as forglass coverslips.

15. Prepare an appropriate dilution of cells in multiwell cell culture dishes. For six-well dishes, use 3mL ofcell suspension per well; for 12-well dishes, use 1 mL.

16. Place the grids with the carbon film side facing up into the wells.For ease of handling, place only one grid into each well.

17. After seeding, examine the density and the current state of the cells regularly under phasecontrast microscopy.One or two cells per grid square on a 200-mesh grid is optimal for cryo-observation. To obtain adequately spread cells, itmay take from a few hours up to even overnight, depending on cell type.

18. Once the desired state of the cells is reached, process the grids further as described below.

Preparation of the Instrument

19. Power on the main unit.


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20. Transfer the black secondary cryogen container into its cup-shaped holder. Remove any grids thatare left inside.It is mandatory to use this inner container in order to remove the secondary cryogen before baking out the instrument!

21. Position the transfer container holding a marked and empty cryo-grid box onto its platform.

22. Insert a new piece of filter paper, and mount it on the magnetic holder with the metal ring provided.Confirm the corresponding warning message on the touch screen.

23. Using a syringe, fill the water container for the humidifier with 60 mL of water. Close the valve andattach the tubing to the back side of the humidifier.

24. Press the environmental parameters display to show controls. Set the chamber temperature TC,humidity HR, and cryogen temperature to the desired values. Keep the following points in mind:

i. The chamber temperature is generally set to the temperature at which cells are cultivated.

ii. To avoid evaporation of the solvent, the humidity is typically set to 90% or above.

iii. The temperature of the secondary cryogen should be set to the lowest value that just pre-vents solidification of the secondary cryogen (e.g., −185˚C).

25. To set up the position of the filter paper relative to the grid, pick up a blank grid with one of the quick-lock forceps that will be used for freezing. In the “Load forceps” position, attach the forceps to theinterlock protruding from the bottom of the environmental chamber. Go to the “Setup” page ofthe software.

26. With the environmental chamber lowered, adjust the horizontal position of the filter paper (i.e.,the pressure exerted onto the grid for blotting; “Blotter Setting”). We use a position wherethe grid is bent slightly by the filter paper pressing against it. If the blot sensor (Step 31) is tobe used, this position has to be set up as well, as it is used as reference point for the sensormeasurements!As the grid can be rotated around the vertical axis, there are two slightly different positions to set up: one with theforceps in “home” position, the other one rotated by 180˚. Use home position for setup.

27. Adjust the vertical position of the grid relative to the filter paper (“Grid Blot Position”).We prefer a position in which the upper edge of the filter paper and the upper edge of the grid coincide.

28. If you intend to use the “Transfer” position for lifting the grid to the surface of the secondary cryogenbefore transferring it to the grid box, set up the desired vertical position of the grid relative to thecontainer (e.g., just at the level of the secondary cryogen surface).

29. In “Setup,” “Settings,” set the TF heater (which produces a stream of gaseous nitrogen through theworking area to prevent contamination) to full power, unless you are planning to use the GP for avery long time without refilling the LN2. Increase the power of the window heater if you cannotsee the grid/filter paper contact clearly due to a fogged front window.

30. Return to the main screen. Reset the filter paper counter to “10” to have the full number of blottingpositions available.

31. Open the program list and set up/select a program suitable for freezing your specimen.For single blot, up to 10 different programs including the parameters explained below can be saved. Each specimen willrequire its own, optimized program. If there is any previous experience frommanual freezing a cell line, start with similarconditions.

i. Disable rotation of the grid around the vertical axis (first two check boxes).This feature is not required if the grid carrying the cells is picked up in the right orientation.

ii. Activate the sensor unless it does not work with the setup of your specific experiment.

iii. Leave the option “A-Plunge” active to automatically plunge the specimen after blotting,unless your thin liquid film after blotting requires some special treatment.

iv. Set the Preblot time to 0 sec.


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v. Blot time (the time the filter paper contacts the grid for blotting liquid): Allowed values arefrom 0 to 60 sec in 0.1 sec steps; 1.0 sec to 3.0 sec are good starting values for most celllines (see Table 1).

vi. Postblot time (an optional time after blotting but before plunging the specimen, used forequilibration of the liquid layer [Iancu et al. 2007]).We obtain very even ice layers without this additional wait time.

32. Cool down and fill the 1-L dewar at the base of themain unit with 2L of LN2. Bring the LN2 level up tothe grid at the bottom of the working area. Wait for the vigorous bubbling of the LN2 to stop. Fill thetransfer container holding the grid box with LN2 and close it with its lid.

33. Condense the secondary cryogen (ethane)—there are two ways to do that:

Using the Leica Liquefier

i. Connect the liquefier to the ethane bottle and place it over the secondary cryogen cup. (Con-trary to the manual, we recommend not to cool the instrument with the liquefier in place, asthis might trap humidity in the secondary cryogen container!) The temperature reading ofthe secondary cryogen container will rise. Pour LN2 over the liquefier to speed up coolingand wait for the temperature to equilibrate at the preset value.

ii. Fully open the main valve of the ethane bottle. Open the needle valve on the ethane bottleslowly. After some time, white gas and subsequently liquid ethane will fill the secondarycryogen container.

iii. Close all valves when the container is full. Do not overfill; excess ethane might freeze theliquefier onto the secondary cryogen container.

iv. Remove the liquefier carefully and place it into the small Styrofoam container provided byLeica for safe transport.

Using a Pipette Tip (or a Needle)

i. Cut off the fine end of a 200-µL pipette tip and connect it to the tubing on the ethane bottle.

ii. Wait for the temperature of the cryogen container to equilibrate to the preset value (e.g.,−185˚C).

iii. Hold the pipette tip to the bottom of the secondary cryogen container and slowly open themain and the needle valve of the ethane bottle. At the beginning, whitish gas fills thechamber, and the sound of bubbling ethane can be used to control tip position and toadjust the flow rate. Within 1 min, the rising level of liquid ethane is visible. Pay attentionto the temperature of the secondary cryogen container as it increases during ethane conden-sation: If the temperature rises above –160˚C, close the needle valve and wait for the cryogencontainer to return to the preset temperature. Resume ethane condensation.

Table 1. Summary of freezing conditions for various cell lines

Sample Grids Pretreatment Temp. Humidity Volume Preblot Blot Postblot Ref.

B16 mousemelanoma cells

Au 200 mesh, QFR 1/4

Glowdischarge

37˚C 90% 4 μLmedium

0 sec 2–3 sec fromback side

0 sec

Troutkeratocytes


Glowdischarge

RT 90% 4 μLmedium


0 sec Urban et al.(2010)

CAR goldfishfibroblasts


Glowdischarge

27˚C 90% 4 μLmedium


0 sec Urban et al.(2010)

All specimens were blotted once with Whatman No. 1 filter paper and plunged into liquid ethane cooled to just above thefreezing point.


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iv. When the level of liquid ethane reaches the rim of the secondary cryogen container, move thepipette tip above the ethane surface. Ethane gas flows out of the tip, replacing residual liquidethane that could cause burns.

v. Close the needle valve and the main valve of the ethane bottle.

34. Wait until the environmental chamber has reached the preset temperature and humidity. Keep theworking area covered, but not as tightly as to stop the gas flow.

35. Prepare another (dewar) vessel with LN2 for refilling the transfer container.

Freezing Grids

36. Bring the instrument to the “Load Forceps” position.

37. With the quick-release forceps, pick up the grid with the cell monolayer directly from the cell culturedish so that cells will face away form the filter paper when blotting. Close the black slider only to thefirst notch.

38. Immediately add 4 µL of prewarmed medium supplemented with fiducials for cryo-ET from Step6. To avoid dramatic changes in the osmolarity of the surrounding medium, do not use plain col-loidal gold sol.

39. Attach the quick-release forceps to the interlock and lower the environmental chamber.

40. Press “Blot (S)/A-Plunge” to trigger the freezing cycle.The blotting mechanism will be triggered.

41. Follow the blotting process closely to observe any irregularities. Check if large patches of carbon filmare left on the filter paper.After the postblot delay, the grid will be plunged into the secondary cryogen.

42. Once the specimen is frozen, the chamber will lift up. From now on, approach the specimen withprecooled tools only!

43. (Optional) Advance to the “transfer position” of the grid. This is slightly higher than the freezing pos-ition and allows one to blot off liquid ethane with a piece of filter paper.

44. Open the lid of the transfer container with precooled forceps.

45. Disconnect the forceps from the grid plunger. To avoid damaging the grid at the wall of the second-ary cryogen container, hold the forceps at the level of the black slider and tilt it out of thebeveled interlock.

46. Transfer the grid in one quick movement into the transfer container filled with LN2. Do not exposethe grid to the humidity of the air; do not lift it any higher than the gray ring surrounding theworking area.

47. Place the grid into the right slot of the grid box and release it from the quick-lock forceps.

48. Refill LN2 in the transfer container, if required—the grid box should always be covered with LN2.Keep the secondary cryogen cup covered with the plastic lid provided by the manufacturer so asnot to mix liquid ethane and LN2! Close the transfer container.

49. Watch out for any warning messages issued by the GP. Keep the following points in mind:

i. If necessary, refill the humidifier with 20 (!) mL water.

ii. Refilling LN2 in the main dewar is only required when a warning is displayed (<25%).

iii. If you need to replace the filter paper, allow new filter paper to equilibrate with the humidityin the environmental chamber.This can improve the reproducibility of freezing and the evenness of the resulting ice layer.


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50. Warm up all cold and frosted tools with a hair dryer to avoid contamination of the specimen or thecryogens with ice crystals.

Shutting Down the Instrument

51. With a precooled screwdriver or Allen key, close the grid box.

52. Refill the transfer container with LN2 and close it.

53. Precool the handle with the M4 thread. Attach it to the specimen transfer container.

54. Lift the transfer container out of the working area and into a dewar filled with LN2. Then, transfer thefrozen grids either directly to the cryo-TEM or to a LN2 storage container for later use.

55. Remove the container holding the secondary cryogen with insulated forceps and place it into thesmall Styrofoam box. Allow evaporation to occur in a safe place.

56. Discard the filter paper. Leave the door of the environmental chamber open.

57. Drain the residual water from the water container.

58. Switch on a 1 h bake-out cycle.The timer will start once the LN2 level in the dewar has dropped to 0%.

The bake-out is not intended to sanitize the environmental chamber after freezing pathogenic specimens. Alternativemeans of decontamination such as ultraviolet (UV) irradiation of the reflective interior of the chamber, gas sterilization,or wiping with ethanol have to be tested, taking into account that most components inside the environmental chamberare not removable.

59. Once the bake-out cycle is complete (at most 1.5 h), switch off the instrument.

TROUBLESHOOTING

A number of troubleshooting issues concerning the operation of the Leica EM GP and specimen prep-aration for cryo-TEM in general have been discussed in Immersion Freezing of Suspended Particlesand Cells for Cryo-Electron Microscopy (Resch et al. 2011b).

Problem: Cells are disrupted or deformed.Solution:Damaged cells have been reported in a number of studies (Small et al. 2008; Lepper et al. 2009;

Urban et al. 2010), with a possible dependence on the cell line used. To minimize these problems,remember the following:

• handle the grids with extreme care• transfer the grids as quickly as possible to avoid any temperature shift and osmotic change in the

small volume on the grid• blot the cells from the back side at high humidity

Nevertheless, it is crucially important to critically assess the condition of the frozen cells (also see theDiscussion) and possibly to reconsider the choice of cell line.

Problem: Gold fiducials are aggregated.Solution: Use fresh protein-coated gold and add it right before blotting.

DISCUSSION

To localize regions of interest, we prepare low-magnification (�140×), minimal-dose montages of ourcryo grids using SerialEM (Mastronarde 2005) or Leginon (Suloway et al. 2005). This allows us toassess cell density and ice thickness. An optimal result in terms of evenness of cell spreading and ice thick-ness is shown in Figure 1A. Grid squares that have been selected at low magnification are then checkedat higher magnification (e.g., 1350×) at appropriate underfocus and very low electron exposure. Atthis magnification, cell bodies and even finer cell extensions accessible for tomography become visible(Fig. 1B). Only at high magnification (>20 000×) can the specimen finally be checked for successful


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vitrification, the presence of nanometer-size contamination (Immersion Freezing of SuspendedParticles and Cells for Cryo-Electron Microscopy [Resch et al. 2011b]), and the distribution of thegold fiducials.

For adherent cells, only the region at or just behind the plasma membrane is accessible formicroscopy. With some experience and underfocus, the cell boundary can be easily found (Fig. 1C),the tilt series can be acquired at positions of interest, and tomographic reconstructions can be computed(Fig. 1D). However, the cell has to be assessed carefully for integrity. A number of studies (Small et al.2008; Lepper et al. 2009; Urban et al. 2010) have highlighted that cells are prone to disintegrationupon blotting/plunge freezing. This is supported by recent data from our lab in which we froze cellsgrown on grids, freeze-substituted them, resin-embedded the grids, and sectioned them perpendicularto the substrate (Wonesch and Resch, unpublished data). Althoughmany cells were found intact andwellfrozen, others—presumably in regions with thicker ice—showed significant ice crystal damage. Rupturedplasma membranes, parts of cells drawn through holes, and release of cytoplasmic components into themedium were also observed, highlighting the need for critically evaluating the condition of immersionfrozen cells from any instrument before using them for cryo-ET.

ACKNOWLEDGMENTS

We thank Ian Lamswood, Dr. Reinhard Lihl, Andreas Nowak, andDr. Ruwin Pandithage from LeicaMicro-systems for discussions, andNicole Fellner for her assistance in the EM Facility. Thework of G. P. R. andM.B. was supported by the City of Vienna/Zentrum fuer Innovation und Technologie through the Spot ofExcellence grant “Center of Molecular and Cellular Nanostructure.” E.U. is supported by the AustrianScience Fund (FWF project P21292-B09 to J. V. Small).

FIGURE 1. Cryo-electron micrographs and tomographic reconstructions of CAR goldfish fibroblasts grown on perforatedcarbon grids and frozen according to the method outlined in this protocol. Images and zero-loss filtered tilt series wereacquired on an FEI Tecnai G2 F30 Helium at 300 kV acceleration voltage. (A) An exemplary low-magnification montageof a major part of the grid with cells embedded in an evenly thin ice layer. (B) Medium-magnification micrographshowing cell bodies (asterisks) and thin regions of the cells accessible for electron tomography (arrowheads). (Reprintedfrom Resch et al. 2010 with permission from Elsevier © 2010.) (C ) High-magnification projection image of the thin periph-eral region (lamellipodium) of a fish fibroblast imaged at low dose. (D) A 4.8-nm thick tomogram section of the lamellipo-dium shown in C after reprojection of the tilt series. The plasma membrane and the network of long and straight actinfilaments are clearly visible (from Urban et al. [2010]). Bar (D) = 250 nm (also applies to C ).


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Garvalov BK, Zuber B, Bouchet-Marquis C, Kudryashev M, Gruska M,Beck M, Leis A, Frischknecht F, Bradke F, Baumeister W, et al.2006. Luminal particles within cellular microtubules. J Cell Biol174: 759–765.

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Lepper S, Merkel M, Sartori A, Cyrklaff M, Frischknecht F. 2009.Rapid quantification of the effects of blotting for correlation oflight and cryo-light microscopy images. J Microsc 238: 21–26.

Lucic V, Kossel AH, Yang T, Bonhoeffer T, Baumeister W, Sartori A.2007. Multiscale imaging of neurons grown in culture: from lightmicroscopy to cryo-electron tomography. J Struct Biol 160: 146–56.

Mastronarde DN. 2005. Automated electron microscope tomographyusing robust prediction of specimen movements. J Struct Biol 152:36–51.

Resch GP, Urban E, Jacob S. 2010. The actin cytoskeleton inwhole mount preparations and sections. Methods Cell Biol 96:529–564.

Resch GP, Brandstetter M, Pickl-Herk AM, Königsmaier L, Wonesch VI,Urban E. 2011a. Immersion freezing of biological specimens:Rationale, principles, and instrumentation. Cold Spring HarbProtoc doi: 10.1101/pdb.top118.

Resch GP, Brandstetter M, Königsmaier L, Urban E, Pickl-Herk AM.2011b. Immersion freezing of suspended particles and cells for cryoelectron microscopy. Cold Spring Harb Protoc doi: 10.1101/pdb.prot5642.

Small JV, Auinger S, Nemethova M, Koestler S, Goldie KN, Hoenger A,Resch GP. 2008. Unravelling the structure of the lamellipodium.J Microsc 231: 479–485.

Suloway C, Pulokas J, Fellmann D, Cheng A, Guerra F, Quispe J, Stagg S,Potter CS, Carragher B. 2005. Automated molecular microscopy:the new Leginon system. J Struct Biol 151: 41–60.

Urban E, Jacob S, Nemethova M, Resch GP, Small JV. 2010. Electrontomography reveals unbranched networks of actin filaments inlamellipodia. Nat Cell Biol 12: 429–435.


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