|Three-Dimensional, Quantitative in vitro Assays of Wound
Wound healing in vivo
is a dynamic process involving
the coordinated regulation of cell proliferation, cell
migration, cell traction, and apoptosis (Clark, 1996).
For instance, during dermal wound healing, inflammatory
cells are induced to infiltrate a wound site primarily
by factors released from platelets. Fibroblasts
are stimulated to migrate up a chemotactic gradient of
soluble factors, and possibly a haptotactic gradient of
matrix-bound factors, released by the inflammatory
cells and platelets into a provisional matrix composed
primarily of fibrin and fibronectin. These fibroblasts
proliferate and secrete collagen and other extracellular
matrix molecules to form granulation tissue. The cells
often contract this granulation tissue while continuing
to secrete collagen. Ultimately, the cells die through
apoptosis and leave a dense, collagenous, acellular
scar as a reparative patch. The progression of fibroblast
behavior is dictated in part by cues from the
wound healing environment, such as soluble growth
factors, integrin binding to network proteins, and
mechanical stress associated with wound contraction.
Therefore, it becomes a great challenge to design and
implement bioassays that capture quantitatively the
key features of wound healing in a controlled, but
physiologically relevant manner. This article describes
several assays that allow quantitative evaluation of
fundamental aspects of cell behavior involved in the
wound healing response-cell migration, chemotaxis,
cell traction, and cell proliferation--in controlled environments
with improved physiological relevance. The relevance of the assays is improved by examining
cellular phenomena within three-dimensional (3D)
hydrogels of biopolymers involved in wound healing,
namely type I collagen and fibrin. Many studies
have demonstrated dramatic differences in tissue
cell behavior when cultured in a 3D gel rather than
on a 2D substrate (Bell et al.
, 1979; Nusgens et al.
Trypsin (Product No. T6763), paraformaldehyde
(Product No. 158127), ethylenediaminetetraacetic acid
(EDTA) (Product No. E26282), CaCl2
21075), NaOH (Product No. 72079), bovine fibrinogen
(Product No. 46312), bovine thrombin (Product No.
T4265), and agarose (Product No. A2790) are from
Sigma Chemical Company (St. Louis, MO). Vitrogen
100 bovine type I collagen (Product No. FXP-019) is
from Cohesion Technologies, Inc. (Palo Alto, CA).
Tissue culture medium, penicillin/streptomycin
(pen-strep; Cat. No. 15070063, fungizone (Cat. No.
15240062), HEPES buffer (Cat. No. 15630080), phosphate-
buffered saline (PBS; Cat. No. 10010023), and
L-glutamine (Cat. No. 21051024) are from GIBCO
Laboratories (Grand Island, NY). Fetal bovine serum
(FBS; Product No. SH30073.02) is from HyClone Laboratories
(Logan, UT). Polystyrene beads (Product No.
64130) are from Polysciences, Inc. (Warrington, PA).
Stock Teflon (Product No. B-ZRT-2), stock polycarbonate
(Product No. B-211040), and stock hydrophilic porous polyethylene disk (Product No. B-PEH-060/50)
are from Small Parts (Miami Lakes, FL).
Inverted microscope with computer-controlled
stage and on-stage incubation system, biological hood,
air or CO2
A. Biopolymer Gel Solution Preparations
Type I Collagen Gel (2.0mg/ml)
Collagen gels are prepared by neutralizing stock
type I collagen solution and raising the temperature to
facilitate self-assembly of monomeric collagen into
fibrils and forming an entangled network of fibrils
with interstitial medium (Knapp et al.
- To make 1 ml of collagen, add the following
reagents to a 15-ml conical tube in order in a biological
safety cabinet/laminar flow hood under sterile
conditions: 20 µl 1 M HEPES buffer, 132 µl 0.1 N NaOH,
100 µl 10 X MEM, 60 µl FBS, 1 µl pen/strep, 10 µl L-glutamine,
and 677 µl Vitrogen 100.
- Mix gently by pipetting.
- Keep the solution on ice until ready to prepare
: The final solution should be a light pink
color/red color indicating neutral pH.
B. Fibrin Gels (3.3 mg/ml)
Fibrin gels are prepared by enzymatically cleaving
fibrinogen with thrombin in the presence of Ca2+
(Knapp et al.
- Fibrinogen solution A: Dissolve fibrinogen
powder in a 20mM HEPES-buffered saline solution
to a concentration of 30mg/ml. Pass the solution
through a 0.20-µm filter. Store in 1-ml aliquots at
- Thrombin solution B: Dissolve thrombin (250
units) in 1 ml sterile water and 9ml of PBS. Pass the
solution through a 0.20-µm filter. Store in 100-µl
aliquots at -80°C.
- Add 1 aliquot of fibrinogen solution A to 5ml
20mM HEPES-buffered saline to make a 5-mg/ml
- In a separate vessel, add one aliquot of thrombin
solution B to 1 ml unsupplemented M-199 no serum
and 15µl of 2M CaCl2 solution to make solution C.
- Prepare cell suspension D in cell culture medium
with the cell concentration six time the desired final
concentration. Solution D will be diluted 1:6.
- Keep the solutions separated and on ice until you
are ready to prepare the assay.
- To make the fibrin gel, mix one part of thrombin/
Ca2+ solution C, one part of cell suspension D,
and four parts of fibrinogen solution A. Mix gently
by pipetting and fill the assay chamber quickly.
Frequently, mixing of fibrin and collagen solutions
generates many bubbles, which can affect the geometry
and rheology of gels and blur microscopy images.
To limit bubbles, apply a vacuum to conical tubes
holding the solutions (for collagen, degas the solution
after mixing but before gelation, for fibrin, degas the
fibrinogen solution, thrombin solution, and cell culture
medium before mixing) to draw dissolved air out of
solution and into the vacuum. Make sure that the
solution is not too close to the top of the conical tube
(10ml or less).
Because the fibrin gel can form quickly, add the fibrinogen
solution last and pipette the mixed solution
into the assay chamber quickly.
Disrupting forming gels can affect structural and
rheological properties that are important for cell
behavior assays. Take care when handling the gels
during and after formation.
The following assays were developed to examine
phenomena associated with dermal wound healing
and therefore incorporate dermal fibroblasts as the cell
of choice. However, the assays can be adapted easily
for other cell types (e.g., smooth muscle cells or corneal
fibroblasts.) The key is to maintain tight control over
cell populations and the cell density used in the assays,
as cell behavior can vary widely from passage to
passage, and cell density dramatically affects the
potential for cell-cell signaling, which, if not
accounted for, can cloud results. Cell densities delineated
below are recommended but should be optimized
according to the cell type and the phenomena
to be studied.
V. CHEMOTAXIS ASSAY
Chemotaxis experiments are performed in a conjoined
3D gel system (Knapp et al.
, 1999; Moghe et al.
1995). Manufacture of chemotaxis chambers and
image analysis are involved. The experiments require
machining of chemotaxis chambers (see later). The
chambers allow the generation of a gradient of a
protein/growth factor-sized diffusible species (Fig. 1).
Briefly, one-half of the chamber is filled with collagen
or fibrin solution and a defined concentration of
chemotactic species, and the other, initially separated by a thin divider, is filled with an equal volume of
biopolymer solution with a defined density of cells of
interest. After removing the divider, a gradient of the
species is formed in the gel with cells.
|FIGURE 1 Schematic of linear chemotaxis chamber preparation. The chamber consists of a hollow, plexiglass
box that is sealed to a standard glass slide with vacuum grease. A Teflon plate divides the chamber
into two sections.
(A) One side of the chamber is filled with biopolymer gel with a defined concentration of
chemotactic factor. For collagen assays, the chamber is placed in the incubator, and the biopolymer solution
is allowed to gel.
(B) The Teflon divider is removed, and the other half of the chamber is filled with biopolymer
solution with a defined cell concentration. The chamber is returned to the incubator to facilitate gelation.
(C) Initially, all of the chemotactic factor is in the left half of the chamber, and the cells in the right half
are oriented randomly. (D) Over time, the soluble factor diffuses into the right half, and the cells (if responsive
to the soluble factor) reorient and migrate in the direction of the gradient.
|FIGURE 2 Mechanical drawing of linear chemotaxis chamber. The chamber is machined from plexiglass
(polycarbonate) and is 1.3cm high. A Teflon plate (1.2 × 0.05 × 2cm) is also required to fit into the notched
area and divide the chamber in half.
- Have chemotaxis chambers (at least 6-10)
machined according to Fig. 2.
- Chambers are designed to fit on top of a standard
microscope slide (7.5 × 2.5cm).
- Chambers have a groove at the midline for a thin,
- Thoroughly clean chambers with soapy water
and autoclave prior to each use
- Sterilize all chambers and glass slides.
- Under sterile conditions, secure bottom of
chamber to glass slide with vacuum grease.
- Place Teflon dividers into grooves.
- Prepare solutions for assay (either fibrin or
- Each chamber requires ~3.5 ml biopolymer solution,
which should be divided into two equal
volumes of 1.75 ml/chamber.
- Add enough chemotactic factor to one of the
volumes of the solution to generate the desired
final concentration. Generally for growth factors,
the working range is 0.1-100 ng/ml. This is now
called "solution A."
- Add cells to the other half of the solution to a
final concentration of 10,000 cells/ml. This is
now called "solution B."
- Add 1.75ml of solution A to one-half of each
chamber. This should fill the half approximately 3 mm.
- Secure another glass slide to the top of each
chamber and place the chambers in a humidified incubator
until gelation/self-assembly is complete.
- After gelation, remove chambers from the incubator
and, again under sterile conditions, remove the
- Mix solution B by pipetting to ensure uniform
distribution of cells and fill the empty half of the
chamber with 1.75 ml of solution B.
- Replace top glass slide, ensuring a good seal,
and place back in humidified incubator for 24-36 h
- At desired time points (typically 12-36h after
gelation), place chamber under microscope and
capture images of all cells through the thickness of the
gel. This should be done with sufficient objective
power (4× or greater) to observe the orientation of
cells. This is facilitated greatly using automated
microscopy/confocal microscopy with a motorized
stage to build a mosaic, but can be done by hand if necessary.
With automation, a projection mosaic of the gel containing cells is generated incorporating all planes
throughout the thickness of the gel.
- For each cell, using standard image analysis
packages (such as NIH Image), draw a line segment
representing the prevailing orientation of the cell (Fig.
3) and calculate and record the angle, 0 (from 0° to 90° the line segment makes with the horizontal axis, which
represents the direction of the chemotactic gradient.
- For each cell, calculate sin2(θ)
- Determine the average value of sin2(θ) for all of
the cells in a given chamber. In other words,
where n represents the number of cells (Fig. 3).
In the case of no chemotactic factor, cells should
be oriented randomly. Therefore, the average angle
should be 45° and Φ = 0.5. For a pure chemotactic
response, θ = 0° and 9 = 0. Generally, values of Φ < 0.5
signify a chemotactic response, but results should be
analyzed statistically after measuring the response in
Helpful Hints and Pitfalls
|FIGURE 3 Chemotaxis analysis. (A) After a period of time (or at regular intervals, if desired), a composite,
mosaic image of the cell-populated half of the chamber is captured and projected into one image. (B) The
orientation of each cell is defined by tracing the long axis of the cell with a line. (C) The orientation of each
line is compared to the orientation of the gradient via the angle θ. The response of the population is then
evaluated using Eq. (1).
- Control experiments should include no chemotactic
factor, as well as uniform chemotactic factor
(half-loading in both solution A and solution B).
- If imaging requires a large block of time, gels
can be fixed with 2-4% paraformaldehyde to ensure
equal exposure times to chemotactic gradients across
- To avoid settling of cells to the bottom of the gel
due to gravity, prewarm solution B to ~28-30°C prior
to filling the second half of the chamber. This is more
crucial for experiments with collagen.
- Alignment of cells in the direction of the gradient
may indicate a negative chemotaxis response. If the polarity of the cells cannot be determined easily, it is
necessary to record the migration of the cells to
confirm that they migrate toward the source of the
factor (positive chemotaxis or chemoattraction) or
away from the source (negative chemotaxis or
A similar assay can be developed to study chemotaxis
toward peptide fragments much smaller than a
growth factor (e.g., RGD) (Fig. 4) (Knapp et al.
Because these species are much smaller, they diffuse
more rapidly and would equilibrate in concentration
if the linear chambers described earlier were used. By
maintaining a divider between the two halves with a
small notch in the divider, diffusion across the two
halves is restricted and gradients can be maintained
for at least 24 h.
- Machine chambers identical to those described
earlier, but add a small notch to the Teflon divider.
- When preparing the chamber, include a glass
coverslip alongside the Teflon divider.
- Fill one-half of the chamber with biopolymer solution
with a defined concentration of the peptide
sequence and allow to gel.
- Fill the other half with biopolymer solution with
defined cell concentration and allow to gel.
- Remove coverslip, but leave notched Teflon divider
in place. This should create radial gradients (see
- Transfer to microscope and quantify as described
previously, with the exception that the direction of
the gradient is now radially outward from the notch.
VI. CELL TRACTION ASSAY
|FIGURE 4 Schematic of radial chemotaxis assay for small chemotactic molecules. The assay is similar to
the linear chambers, except that the Teflon divider remains in the chamber and has a small notch to restrict
diffusion between the two halves. A glass coverslip prevents premature diffusion.
Simple cell traction assays can be performed with
either mechanically constrained, stressed gels or
unconstrained, unstressed gels in various geometries
(Neidert et al.
, 2002; Ehrlich and Rajaratnam, 1990).
This section describes the simplest one to implement -
cylindrical disks (Neidert et al.
, 2002; Tuan et al.
The geometry is a hemisphere initially, but evolves to
a cylindrical disk shape as the cell traction proceeds.
- With a sterile scribe, score a 1-cm-diameter circle
in each well of a six-well plate.
- Prepare collagen or fibrin solution with a final
cell concentration between 10,000 and 500,000
- Carefully pipette 0.5ml collagen or fibrin solution
into the scored region. The scratch in the culture
plate should force the solution to maintain shape.
- Carefully place the plate in an incubator and
allow solution to gel.
- After gelation, fill each well with 2.5 ml of culture
medium with defined concentrations of the desired
- If the assay is for unstressed gels, with a sterile,
flat spatula, gently pry the gels off of the bottom
surface so that they are "free floating."
- Transfer the plate to a microscope and measure
the thickness of the gel. When using a microscope
equipped with motorized focus, this is done most
easily by focusing on the top of the gel, recording the
motor position, and then focusing on the bottom of the gel and determining the change in motor position,
and therefore the thickness. For unstressed gels, also
measure the diameter of the gel. (The diameter should
remain unchanged for stressed gels.)
- Return the gels to the incubator.
- Repeat measurement performed in step 7 at
regular intervals of your discretion. Once every 1-2 h
is generally sufficient for a short duration (12-24h
experiment. Once every 4-6h is sufficient for longer
duration experiments. Return the samples to the incubator
immediately after recording the thickness.
- After completion, normalize results by the original
dimension and plot percentage compaction vs
time for the various conditions.
VII. CELL MIGRATION
- Gel thickness measurements reflect the gel rheology
(and possibly cell proliferation) as much as cell
traction. An intrinsic measure of the latter can be
obtained by analyzing data using a mechanical model
for cell-matrix interactions (Barocas et al., 1995;
Barocas and Tranquillo, 1997a,b).
- If only measurements are desired for the constrained
case, the sample can be attached to a force
transducer (Eastwood et al., 1996; Kolodney and
- Cell alignment that typically results during the
contraction of mechanically constrained gels can
complicate the interpretation of data (Barocas and
Time-lapse cell migration assays in a 3D matrix can
be performed to evaluate cell migration in two or three
dimensions (Knapp et al.
, 2000; Shreiber et al.
, 2001, 2003). Both techniques require an automated image
analysis system and an XY motorized stage. Motorized
focus is advantageous for evaluation in 2D and is
required for 3D.
Generally, it is advised to perform each experimental
condition in triplicate. For instance, if the assay
was to determine the effects of PDGF-BB on fibroblast
migration and the experiment called for testing cells in
the presence of 0, 10, 20, and 50ng/ml, then 12 wells
would be needed.
The migration assay can be performed in practically
any assay chamber. It is written here for a 96-well plate
In these assays, data are recorded to fit to the persistent
random walk model of cell migration (Dunn
and Brown, 1987). This model implies that cell migration
is purely random over long periods of time, but
can have persistent direction over short period of
times. To assess cell migration, there are three parameters,
two of which are independent: persistence time,
P; cell speed, S; and cell motility, bt. These three parameters
are related via calculation of the mean-squared
displacement (MSD) of the cells:
= number of dimensions tracked (two for X-Y
tracking, three for X-Y-Z tracking).
Assays can be designed to improve measurement
accuracy of any of these three parameters (Dickinson
and Tranquillo, 1993); it is left to the researcher to
decide which is most appropriate and design accordingly.
Briefly, in order to evaluate the persistence time
accurately, cell positions must be recorded at a time
lapse significantly less than the actual persistence
time in order to observe the directed motion of the cell.
For example, if the persistence time of a cell is estimated
to be 30min (on average it changes direction in
its motion every half-hour), then to observe this phenomenon,
cell position must be monitored at a
minimum every 5-10min, as the cell will appear to be
moving randomly without any directional persistence.
However, if the position of each cell needs to be
recorded every 5min, then the total number of cells
that can be monitored is decreased. (More images of
wells of a 96-well plate or individual cells can be captured
in 10min than in 5min.) Thus, the amount of
data that is averaged to determine S, P, and µ is
decreased. The timing of the imaging sequence must
be determined by the individual laboratories and can
be influenced by the imaging hardware and software
and the inherent motility of the cells. Generally, this
timing issue is negligible for 2D analysis and only becomes a problem in 3D, where each cell is generally
monitored individually with high magnification.
Both 2D and 3D analyses require complex image
analysis codes that can perform object identification
and/or correlation. Many software packages now
include such algorithms, and they can also be programmed
by the individual laboratories. The actual
codes will differ according to the software packages,
and presentation of a code is beyond the scope of this
article. A brief outline for 2D and 3D is presented.
The general steps are the same for 2D and 3D analysis
for preparing the assays.
- Prepare collagen or fibrin solution with a final
cell concentration between 7500 and 30,000 cells/ml
and 5000-10,000 10-µm polystyrene after beads/ml.
Beads serve as fiduciary markers to allow measurement
of any drift in the stage or movement of the gel.
They are especially crucial for 3D, high-magnification
tracking and analysis.
- Pipette 100ml of collagen or fibrin solution into
a well of the 96-well plate. Fill as many wells as warranted
to complete the experimental test matrix.
- Carefully place the plate in an incubator and
allow solution to gel.
- After gelation, fill each well with 100ml of cell
culture medium with twice the defined concentration
of the desired soluble factor(s) to yield the correct final
- Transfer the plate to an inverted microscope
that includes an automated image analysis system
and motorized stage, potentially motorized focus,
and an environmental chamber to maintain proper
humidity and CO2 concentration. Air-buffered media
can be used (e.g., M199) if on-stage CO2 regulation is
The followings steps are used for analysis of migration
in 2D (without automated focus).
- Using a 10× objective, select a focal plane that is
consistent among all of the wells.
- Move the stage from desired well to well and
record images of each well. Build a mosaic image
if necessary. Develop a numbering scheme to save
the images (e.g., [date]_[condition]_[sample]_[image
number]). Be sure to record the centroid position of
each well so that the computer can move the microscope
stage to those same positions at future time
- Determine the total duration of an individual
interval, and the total number of intervals, which
define the overall length of the time-lapse experiment.
Be certain that your system is capable of capturing the
desired number of images required for one complete interval in the time allocated. Generally, intervals
should be as short as possible, so it frequently helps
to work backward and determine how quickly the
desired number of images can be captured. In this case,
be sure to include a safety factor (usually a minute or
two is sufficient to ensure that all required images are
- Instruct the computer to return to each position,
in sequence, record an image(s) of the well, move to
the next position, etc. After the last picture in one interval
has been recorded, the computer should instruct
the stage to wait until the beginning of the next time
interval to return to the first well. For instance, if a time
interval is 10 min and all pictures from an interval are
captured in 8 min, the computer should wait 2min to
begin the next interval instead of immediately beginning
the next time interval. Maintaining a consistent
time interval simplifies data analysis greatly.
- Object identification can be performed during
an experiment or off-line. In either case, the general
scheme is the same: (a) capture image and (b)
filter image to accentuate "objects," i.e., cells and
Filtering usually involves
- Equalizing contrast.
- Low-pass filter.
- Edge detection filter (e.g., Sobel).
- Generating a binary image based on an appropriate
- Rejecting objects that are too big and/or too small.
- Recording the centroid position of objects, and
correlating those positions, and possible shapes to
the previous interval to track individual cells
properly. Shape matching is not necessarily
advised for tracking cells, as they change morphology
during migration, but will certainly work
- Tabulate the cell/bead positions in a text file in a
rational sequence. Include a flag to represent
whether the object is a bead (1) or a cell (0). For
Interval 1, Well 1, Object (cell or bead) 1, Type of object
(Cell = 0, Bead = 1), Xposition 1, Yposition 1
Interval 1, Well 1, Object 2, Type, Xposition 1,
Yposition 1 . . .
Interval 1, Well 2, Object 1, Type, X1, Y1
Interval 1, Well 2, Object 2, Type X1, Y1 ...
Interval 2, Well 1, Object 1, Type X2, Y2
Interval 2, Well 1, Object 2, Type X2, Y2...
Proceed to step 10.
Use the following steps for analysis of migration in
3D (must have automated focus).
- Use the lowest power objective that generally
allows you to focus on any object so that it is the only
object in the volumetric field of view (FOV). To do this:
- Scan through the sample until you find an object.
- Maneuver the stage so that the object is in the
center of the FOV and in focus.
- Make sure that the object is the only one in the
volume immediately surrounding that object in
all directions (including the focal plane, Z).
- Recenter and focus the object and record the
position of the stage and focus on the computer
- Select the cells and beads to track. Optimally,
search for a bead with many (at least three to four; the
more the better) cells within 200-400µm of the bead,
but not within the FOV. The motion of that bead would
then represent the local absolute motion of the stage
and gel to allow the subtraction of any convective
effects that occur due to gel contraction.
- Find a bead that is the only object in its volumetric
- Scan the regions immediately outside that FOV
for cells. Find beads with multiple cells in the
immediately adjacent FOV.
- Return to the bead. Focus and center the bead
and then record the X, Y, Z position with the
- Move to the cells in the adjacent volumes, focus
and center each cell, and record the X, Y, Z position
of each cell.
- Proceed to another bead and repeat
As with 2D tracking and analysis, there are opportunity
costs that allow the optimization of the number
of assay conditions, the number of beads/cells tracked
per condition, and the duration of a single interval.
This optimization is even more crucial for 3D tracking.
Ideally, at least 20-30cells are tracked for each
- When finished identifying the final object to be
tracked, program the computer to return the stage to
the first cell.
- Execute an autofocus routine to focus the object.
If it has moved from the center, recenter.
- Run the object identification algorithm (see earlier
discussion) to locate the centroid of the object.
- Record the position of the object and write the
position of the object to a database. Include a flag
to represent whether the object is a bead (1) or a
cell (0). For instance: Interval #, Well #, Object
#(cell or bead), Type (Cell = 0; Bead = 1), Xposition,
- Automatically move to the next object and repeat
until all objects are recentered.
- Initiate the time-lapse loop. The time-lapse loop
essentially performs the same procedures as step 8, but the computer recenters the object. The main steps that
need to be programmed are as follows.
- Move to the recorded XYZ position of an object,
- Search in the Z direction for that object using an
autofocus routine, returning the objective to the
position of best focus. This is the new Z position
of the cell, Zi+1.
- Identify the centroid of the object with the object
- Calculate the X and Y distance between the position
of the centroid and the center of the FOV in
pixels. Convert this to micrometers or stage position
units and add this to the current stage position.
This is the new XY position of the object,
- Move the stage to the new XY position, Xi+1Yi+1,
which you just calculated.
- Proceed to the next object and complete all objects
for a given interval.
- Wait until the duration of the interval is over
before returning to the first object. See 2D tracking
and analysis for an explanation.
- Following completion of the time lapse, proceed
to step 10.
The reasoning behind the high magnification celltracking
algorithm is that in a given time interval, a
cell cannot migrate fast enough to exit the FOV
scanned during the autofocus. By recentering the
object at each time interval, the likelihood of finding
that object successfully in the next interval is maximized
(see Fig. 5 for a schematic of the high magnification
- Cell track analysis. Analysis requires three
general steps: (A) correcting cell tracks for stage error
and gel compaction (cell convection), (B) generating
mean-squared displacement data, and (C) fitting data
to the persistent random walk model.
A. Correcting cell tracks
|FIGURE 5 Schematic of autofocus and cell-tracking scheme for
high magnification tracking in 3D. Initially, cells are focused and
positioned in the center of the field of view. At the next time interval,
the computer-controlled stage and focus move to the previously
recorded position and execute an autofocus routine to locate the cell
and determine the distance moved in the Z direction. A snapshot is
taken, the centroid of the cell is located, and the X and Y distances
moved by the cell are recorded. The process is repeated for the next
and subsequent intervals, always returning the stage to the centroid
recorded at the previous interval for each cell.
B. Calculating MSD
- Subtract initial position for each object from subsequent
positions for that object. Each object should
now begin at 0,0,0.
- Subtract the XYZ position of the bead from XYZ colocalized cells for each time interval.
- Write a new file of corrected object positions.
|MSD = Δx2 + Δy2 + Δz2
|FIGURE 6 Overlapping vs
nonoverlapping intervals for calculating
mean-squared displacement (MSD). In
this example, an object
is imaged five
times (t1-t5) over four time intervals.
Suppose we are
determining the MSD
over two time intervals. With the
interval procedure (top), the
distance traveled by the object during
two time intervals can be measured three
times (solid lines), whereas
nonoverlapping technique, the same
measurement can only
be made twice.
Mean-squared displacement data can be generated
in two manners: overlapping intervals and nonoverlapping
intervals (Fig. 6). Overlapping intervals generates
more data but introduces covariance into the error. Analyses have been formulated to account
for these (and other) complex errors (Dickinson and
Tranquillo, 1993), but a full discussion is beyond the
scope of this article. The two techniques are discussed
briefly, and then we proceed assuming we are using
In an MSD calculation, we generate X-Y
address the question: How far did an object, on
average, migrate over a time interval of a given duration?
In analyzing cell migration, we assume that cells
have no inertia. That is, the fact that a cell is moving
at a particular speed in a particular direction at time 1
has no assumed influence on the speed or direction at
time 2, or any future time. Therefore, to determine the
average distance traveled by a cell over one time interval,
we average all displacements that occurred over 1
time interval. Thus, if the time lapse were four intervals
long (five time points), we would calculate:
= l to t
= 2: MSD1
= 2 to t
= 3: MSD2
= 3 to t
= 4: MSD3
= 4 to t
= 5: MSD4
MSD for 1 time interval = average (MSD1-4)
We then average these over all of the cells in a given
condition to arrive at the MSD value for that number
of time intervals.
The use of overlapping vs nonoverlapping intervals
arises when calculating the MSD over durations
greater than I time interval (Fig. 6). For instance, in the
example just given, if we want to calculate the MSD
that occurs over 2 time intervals, we have two choices:
Option 1: Overlapping intervals
= l to t
= 3: MSD1
= 2 to t
= 4: MSD2
= 3 to t
= 5: MSD3
Option 2: Nonoverlapping intervals
= l to t
= 3: MSD1
= 3 to t
= 5: MSD2
As can be seen, overlapping intervals result in 3 MSD
measurements to average, while nonoverlapping
results in only 2. However, the overlapping intervals
are interdependent; any error that occurs from interval
2 to 3 will be included in the calculation from interval
1 to 3 and from interval 2 to 4. Generally, overlapping
intervals are preferred as the improvement in signalnoise
outweighs the cost of error covariance. Also, as
mentioned, there are statistical means of accounting
for this error in determining cell traction parameters.
The MSD should be calculated for all possible interval
durations. Again, using our 5 time point, 4 interval
example and assuming overlapping intervals we
Over 1 time interval: MSD1 = average of 4 MSD
measurements (1-2, 2-3, 3-4,
Over 2 time intervals: MSD2 = average of 3 MSD
measurements (1-3, 2-4, 3-5)
Over 3 time intervals: MSD3 = average of 2 MSD
measurements (1-4, 2-5)
Over 4 time intervals: MSD4 = 1 MSD measurement
data are then generated as follows
|X = duration
||Y = average MSD over that number of intervals
A full time-lapse experiment would include many
more intervals and therefore a much greater amount
C. Fitting data to the random walk model
easiest way to fit data is to use a program (or write one
yourself) capable of nonlinear regression. Fit X-Y
to Eq. (2) to identify µ and P
). If a nonlinear
regression package is not available, the parameters
can be estimated by recognizing that the MSD vs
duration plot can be separated into two distinct regions:
at short durations, the curve goes as time2
, with slope
, and at long durations the curve goes as time,
with slope ~2nd
µ. An investigator can split MSD curves
into these two regions and then use standard linear
regression to identify cell traction parameters.
Finally, Shreiber et al.
(2003) have detailed a technique
to temporally resolve mean-squared displacement
Potential Pitfalls and Helpful Hints
VIII . MIGRATION/TRACTION
- Do not trust that all objects are tracked appropriately.
Review time-lapse movies of each experiment
and note which objects are lost or switched to a different
object and disregard these cells in data analysis.
- Equation (2) assumes that cells move randomly.
If it appears that cells are not moving randomly,
examine the cell tracks of individual cells (look at all,
not just a few) to visually inspect for any directional
bias. Also, mean-squared displacement data can be
generated for one direction at a time and the MSD in each direction independently fit to Eq. (2). If the migration
is indeed random, then cell migration parameters
should be (within error) the same for analysis of the X direction, the Y direction, and the Z direction.
- Note that in calculating values for MSD, more
measurements go into calculating the average MSD
over one interval than over two intervals, more over
two than over three intervals. Thus, there is generally
more error in the calculation of MSD over long durations
than short durations. This can be accounted for
in the analysis by repeating data for a given duration
to represent the number of samples that were included
in the average calculation.
- The increase in error in the MSD calculation over
long durations can also produce aberrant behavior in
the MSD plot. Specifically, the MSD plot may deviate
from linear behavior as the error in the MSD calculation
increases. These points can be ignored in processing
The combined migration/traction assay allows
assessment of the contractile ability of cells and their
motility (Knapp et al.
, 2000; Shreiber et al.
, 2001, 2003).
It is more technically challenging than either assay is individually and requires machining of special chambers.
A schematic of the chamber is shown in Fig. 7,
but the dimensions are somewhat arbitrary and can be
tuned to the specific need of the investigator. Our
assay chamber consists of a stainless-steel annulus
(2.5 cm o.d., 1.5 cm i.d., 0.6cm thick) with 3-mm holes
located 1 mm from the bottom surface, bored through
the side of the annulus. For stressed gel assays, two
stainless-steel posts (3 mm diameter, 1.2 and 0.8cm in
length) with flared ends fit securely into opposing
holes. On the inside ends of the two posts is glued a 3-
mm-diameter, 1-mm-thick disk of porous polyethylene.
A polycarbonate tube with an inner diameter
matching the diameter of the posts/disks is supported
by the two posts and serves as a mold for the assay.
When the tube is filled with a collagen or fibrin
solution, the solution penetrates the pores to form a
fixed boundary condition upon gel formation. For
unstressed, free-floating gels, the stainless-steel posts
are replaced with polycarbonate posts that are each 1
mm longer to account for the lack of a porous polyethylene
disk. In these cases, the gel forms without a
rigid attachment, and the gel is free to compact uniformly
in all directions.
|FIGURE 7 Individual components of a single traction/migration chamber. The stainless-steel posts and
porous polyethylene discs are used in the stressed, constrained assay. The polycarbonate posts are used in
the unstressed, free floating assay and are slightly longer to accommodate the length lost by not including
the porous polyethylene.
All steps are performed under sterile conditions.
- Prepare collagen or fibrin solution as described
earlier. Be sure to degas the collagen/fibrin.
- Add cells to desired concentration (7500-30,000
- Add beads (7500-10,000beads/ml).
- Prepare culture medium with defined soluble
factors of interest (e.g., 50ng/ml PDGF).
- Under sterile conditions, hold the assay chamber
in one hand with the sheath supported by one
post. Fill the sheath with the gel solution from
- Gently push the opposing post into the mold.
- With vacuum grease, secure a coverslip to the
top and bottom of the chamber and place in an
- Gently flip the chamber every 5 min until the solution
is gelled to prevent cells and beads from settling
to the bottom.
- Remove chamber from incubator, place right side
up, and carefully remove the top coverslip.
- Fill the chamber with medium from step 4.
- With sterile tweezers, gently slide the sheath over
the long post to expose gel to culture medium.
- Replace the coverslip, again securing with vacuum
- Transfer chambers to microscope stage and
prepare tracking algorithm (section VIII,A).
A schematic of the final steps is provided in Fig. 8.
|FIGURE 8 Schematic of cell traction/cell migration assay preparation. Fill the polycarbonate sheath with
the biopolymer solution (+cells and beads) and support with stainless-steel posts, use vacuum grease to cover
top and bottom surfaces with glass coverslips, and transfer to the incubator to facilitate gelation. After gelation,
remove the top coverslip and fill the chamber with culture medium with defined concentrations of
soluble factors of interest. Slide the sheath over the long post to expose the gel to the culture medium. Replace
the top coverslip and transfer to the microscope stage for traction and migration tracking.
The migration/traction assay requires at least an XY
motorized stage. Automated focus is preferred and
rotating objectives are ideal. The routines for tracking
cell migration are identical to those described previously.
To record cell traction, follow initial selection of
cell/bead positions, move the stage to the center of
each chamber, and instruct the computer to build a
mosaic image of the gel at the midplane. This is done
most easily with a low power objective; if available,
use the motorized objective feature to switch objectives
to 2 or 4X. This process should be repeated automatically
at the end of each time interval. A typical time
lapse is run for 12-48h. Typical "before" and "after"
images of the stressed and unstressed assays are
shown in Fig. 9.
|FIGURE 9 Examples of unstressed, free-floating assay (A,C) and stressed, constrained assay (B,D).
Migration-traction assays are prepared as described and are nearly identical after initial preparation. (A)
Free-floating cylindrical gel at time = 0. The gel was formed by supporting a sheath with smooth-ended polycarbonate
(B) Contstrained cylindrical gel at time = 0. The gel was prepared by filling an identical
sheath that is supported by stainless-steel posts with porous polyethylene discs glued to the ends (outside
field of view). The biopolymer solution penetrates the pores to form a fixed boundary condition upon gelation.
Following incubation, cells that are entrapped in the gel exert traction and compact the gel. (C) Without
physical constraints to compaction, the free-floating, cylindrical gel compacts (roughly) uniformly. (D) In contrast,
the physical connection to the posts via the porous polyethylene prevents the constrained gel from compacting
in the axial direction. The result is pure radial compaction and subsequent fiber and cell alignment.
The characteristic "hourglass" shape results. In both cases, the degree of cell traction is related to the amount
of gel compaction, measured as the decrease in radius at the midplane of the sample.
Cell migration and traction analyses are performed
as before. For traction, measure the diameter at the
midplane of the gel at each time point. The fixed,
stressed gel should form an hourglass during cellmediated
gel compaction, so the diameter measurement
should essentially be the middle of the hourglass.
The free floating, unstressed gels should compact uniformly, so the diameter measurement can be taken
from any cross-section. The result is X-Y
data of percentage
compaction vs time, which can be examined
for temporal trends or quantified on the basis of final
midplane compaction and compared to results of the
- Be careful not to introduce bubbles into the assay
that can affect gel compaction and obscure imaging.
- Similarly, do not smear vacuum grease over the
coverslip in an area that will obscure imaging.
- Use hydrophilic porous polyethylene (Small
Parts, Miami Lakes, FL) to ensure good penetration of
the gel-forming solution for the fixed case.
- In the free-floating case, cell traction and/or
convective motion of the culture medium may lead
to rigid body motion of the cylindrical gel. Because
cell migration may be tracked at high magnification,
a small translocation of the gel can result in "losing"
all of the cells during the traction algorithm, as
it is only prepared to follow movements of 0.5
xFOV per interval. Use a low percentage, sterile,
agarose solution (1%) to increase the viscosity of
the culture medium and to reduce the ability for gel
- Similarly, under some conditions (high cell concentration,
certain concentrations of soluble factors,
etc.), gels may compact too quickly to monitor cell
position. Some trial and error is likely necessary to
converge on appropriate conditions.
- Bubbles in the medium can also diminish
imaging capabilities. Degas the culture medium and
be careful when filling and sealing the chambers to
avoid introducing air.
- Strong compaction in the stressed case leads to
fiber alignment in the axial direction, which can lead
to anisotropic migration. It may be necessary to quantify
migration in the individual directions (X,Y, and Z)
for these cases.
- Generally, because of the high variability in cell
lines from culture to culture and passage to passage, it
is recommended to run all experimental conditions in
one set of experiments rather than running all controls
one day, all at one condition the next, and so on.
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