Extracellular matrix and cell migration: locomotory characteristics of
MOS-11 cells within a three-dimensional hydrated collagen lattice
P. B. NOBLE
Cell Tracking and Reconstruction Laboratory, Department of Oral Biology, Faculty of Dentistry and Department of Physiology, Faculty of
Medicine, McGill University, Montreal, Quebec HJA 2B2, Canada
Summary
The locomotory trajectories of MOS-11 cells migrating in a three-dimensional hydrated collagen
lattice have been determined using a computerassisted optical sectioning unit. The trajectories
have been quantified using a three-dimensional
continuous-time Markov probability theory consisting of eight directional states and one stationary state; in the latter the cells are not locomoting. Markov analysis shows that these cells
are locomoting in a random manner with regard
to direction and remain stationary for about
three times as long as they are locomoting.
Analysis of persistence also implies random locomotion. Compilation of the distribution of angles
between steps reveals that the cells exhibit a
predilection for turns around 30° and 150° on
either side of the previous step. Time-lapse video
recordings show that the cells are bi-polar with
ruffling membranes at opposite poles. Ruffling,
and hence locomotion, occurs alternately at one
pole and then the other, which -would account for
the distribution of angles encountered. The mean
speed of the cells was of the order of 3 ^un min"1
including the time stopped and approximately
twice this if the time stopped (state 0) is not
included. The results obtained provide base-line
data on the locomotory characteristics of MOS-11
cells locomoting in a l-2mgml - 1 collagen gel. It
is now possible to study the role of various matrix
components in cell locomotion. Such studies are
of importance to embryology, wound healing,
host defence mechanisms and the invasion of
cancer cells.
Introduction
Cell locomotion is of some importance to many
aspects of cell behaviour in embryology, wound healing, host defence mechanisms and cancer. In order to
study cell locomotion in gels we have devised a
computer-driven optical sectioning unit that can provide thex,^, z coordinates of cells at given times, from
which the three-dimensional trajectories can be deduced (Noble & Levine, 1986). From these trajectories several parameters can be computed that permit
a quantitative description of cell locomotion. In the
study reported here, locomotory characteristics of
MOS-11 cells incorporated into a three-dimensional
collagen gel are described.
Over the past few years, there has been a steady
increase in the number of reports on the behavioural
properties of cells both on and within hydrated
collagen lattices. Many of these reports show that
collagen gels offer a more physiological environment
for cells as exemplified by their morphology, which
very closely resembles that seen in vivo (Elsdale &
Bard, 1972; Allen et al. 1984). The importance of a
three-dimensional matrix for cell differentiation has
also been reported (Loring et al. 1982; Hall et al.
1982; Kramer, 1985). Apart from a few attempts to
study the invasiveness of tumour cells and leucocytes
by measuring how far a given cell can migrate into the
gel, little research has been done on the locomotory
capabilities of cells within three-dimensional systems
(Hastonefa/. 1982; Schor et al. 1982, 1983).
Journal of Cell Science 87, 241-248 (1987)
Printed in Great Britain © The Company of Biologists Limited 1987
Key words: extracellular matrix, cell migration, collagen
lattice.
Materials and methods
Cell preparation
The MOS-11 cell used in this study are derived from neo
simian virus 40 (SV40)-transformed 3T3 cells (Southern &
241
MIRROR
c<
V7.CONDENSER
J STAGE * GEL
MENU
TERMINAL
MONITOR
STEPPER
MOTOR
1CAMERA
FOCUSSING
CONTROL
CPU
PI-80
STEPPER MOTOR
ZOMPUPRO
8-16
EOIS 1100
HARD DISK
CONTROLLER
SYNCH. DRIVER
Fig. 1. A schematic drawing of the optical sectioning unit. The synchronized driver as shown is used if film or video
recording devices are used. For real time, synchronization is achieved by software between the CPUs.
Berg, 1982). They were grown and maintained in minimum
essential medium (Earle's salts) containing foetal calf serum
10 %, 0-2 mM-glutamine and 5000 units of penicillin and 1 %
(v/v) of streptomycin (5000/igml" 1 ). Stock cultures were
maintained at 37°C in a CO2 incubator. Cells were removed
from tissue-culture flasks using trypsin (l:250)/EDTA
(0 - 2gl~') mixture. After washing in media, the cells were
resuspended in media prior to incorporation into the threedimensional hydrated collagen lattice. Control experiments
were performed using MOS-11 cells incorporated into a gel,
then fixed with 1% glutaraldehyde (J.B.E.M. Services,
Montreal) in Hank's balanced salt solution. These experiments provide a measure of the stability and reproducibility
of the optical sectioning system.
Preparation of collagen gels
Collagen gel was reconstituted from lyophylized type 1
collagen (Sigma) by dissolving in slightly acid distilled water
at a concentration of 2mg per ml. To lml of collagen
solution was added 0-125ml of 10 X MEM, 0-062ml of
sodium bicarbonate (4"4%) and 0-050 ml of foetal calf
serum. All the solutions were kept on ice to prevent
polymerization of the collagen (Elsdale & Bard, 1972).
Finally, cells were added at an appropriate concentration in
medium so that the final concentration of collagen was
l - 2 m g m r ' . The mixture of collagen and cells was then
pipetted gently into a tissue culture flask and placed in a CO2
incubator at 37°C. Within 3-5 min, the collagen had polymerized to a firm gel with the cells suspended randomly
throughout. Medium was then pipetted carefully into the
flask to cover the gel. Gels prepared in this manner were of
the order of 200/im thick. An area of the gel was selected for
study and the flask fastened firmly to the microscope stage
with tape to prevent subsequent movement. A cover was
placed over the flask into which 5 % CO^balance air was
242
P. B. Noble
passed at a rate of 100-200 ml min '. A Sage air curtain was
used to maintain the temperature at 37°C. Optical sectioning
was then initiated as described below.
A computer-assisted optical sectioning unit has been
developed that can track cells as they locomote within a
three-dimensional collagen gel. The output from this unit
consists of the x, y and z coordinate positions of the cells, at
specified time intervals, from which the three-dimensional
trajectories can be computed and analysed (Noble & Levine,
1986). Briefly, the tracking unit consists of a programmable
interface (two Z80 microprocessors), designed and built at
McGill University, which regulates the operation of a
stepper-motor attached to the fine focusing control of a Wild
M40 inverted microscope. The interface also communicates
with a CompuPro 8-16 computer (Intel 80286/80287/Z80H
microprocessors) (Fig. 1). The number of optical slices (a
section) to be taken through the gel, the inter-slice distance
(in ixm), the number of sections to be taken and the intersection delay time are all programmable via the interface.
The interface instructs the CompuPro to digitize the camera
image at each slice level (Cat 100, Digital Graphics, California). The cells to be tracked are selected by light-pen in the
slices of the first section, after which the process of tracking
is automatic for the number of sections required. After one
section (say 10 slices) there will be in the computer memory
10 times 32 k bytes. During the intersection delay time, only
those pixels representing the x, y and 2 coordinates of the
cells are retained stored on a hard disk, clearing the
computer memory for the next set of digitized slice images.
The cells are tracked by placing a cube (an electronic
tracking window) around each cell of such dimensions that
the cells cannot locomote beyond the confines of the cube
between sections. The cube's dimensions are determined by
video time-lapse recording of the cells within a three-
dimensional gel and estimating the maximum speed attained. From this information the dimensions of the cube
can be programmed into the tracking system. The JC, y and z
coordinates of each cell within its cube at each point in time
(section) are obtained using an n-dimensional converging
squares algorithm, in this case n = 3, developed by O'Gorman & Sanderson (1984). This algorithm recursively selects
the centre of a cell, notes the x, y and 2 coordinates and recentres the tracking cube around the new cell position before
the next section is digitized and the process repeated. Thus,
as more sections are completed, a file of x, y and 2
coordinates is gradually built up for each cell. These
coordinate positions describe the three-dimensional trajectories of the cells. Further details of the cell tracking
methodology have been published (Noble & Levine, 1986).
Time-lapse video recordings were made using MOS-11
cells grown on plastic tissue culture dishes and in thin
(80 /im) deep three-dimensional hydrated collagen lattices.
The purpose was twofold; (1) to estimate the speed of the
cells in order to define the tracking parameters required for
setting up the optical three-dimensional tracking unit; and
(2) to have a visual record of cell behaviour for comparison
with the data obtained from the cell tracking unit. Timelapse video recordings were accomplished using GYYR
TLC2001 and Panasonic NV8050 time-lapse video recorders. Images were captured at 1-min intervals via Panasonic Newvicon cameras (WV-1S50) attached to a Wild M40
and Leitz Diavert inverted microscopes. Bright-field optics
were used at a magnification of XS4. Cultures were maintained at 37 °C by a Sage air curtain in an atmosphere of 5 %
COz/balance air.
Data analysts
Analysis of the x, y and 2 coordinates was performed using a
three-dimensional version of our Markov method (Noble et
al. 1979; Noble & Lewis, 1979). In this case, instead of four
directional states and one stationary state, we now have eight
directional states and one stationary state.
The directional states are specified in the following
manner; referring to Fig. 2:
State
1
2
3
4
S
6
7
Coordinate definition
+x, +y, +z
—x, +y, +z
—x, —y, +z
+-v, -y, +2
+x, +y, —z
8
+x, -y, - 2
-x, +y, - 2
-x, -y,
-z
State 0 has the same definition as previously reported in
our two-dimensional Markov method; namely, that the cell
is stationary. The three-dimensional Markov method provides information on the ultimate direction that the cells will
take, as well as how often the cells stop locomoting and for
how long. Other information includes the transition probabilities of going from one state to another and the time spent
in each state. All in all, the method provides a complete
quantitative description of the three-dimensional zig-zag
path taken by the cells.
Also, from the x, y and 2 coordinates, the speed of cells,
the angle distribution of cell turns, persistence and orientation are computed. Speed is computed in two ways: by
/
/ State
4
.-*' State 8
V
Fig. 2. If the four cubes are pushed together to form one larger cube, which represents the three-dimensional gel, then any
segment of the cell path anywhere within this larger cube having the coordinate characteristics of +x, +y, +2 would be
assigned to state 1; likewise, -x, +y, +z to state 2, etc. Reprinted with permission, from Noble & Levine (1986).
Three-dimensional cell migration
243
Table 2.
Table 1. Eight-state Markov analysis
State
Probability
1
2
3
4
5
6
7
8
0-115
0-110
0133
0-136
0129
0-106
0-129
0-142
A. Eight-state Markov analysis: mean ± s.D.
State
Probability
1
2
3
4
5
6
7
0-119 ±0-028
0-118±0-036
0-117±0-030
0-149 ±0-033
0-140 ±0-026
0-114±0-023
0-120 ±0-028
0-119±0-034
8
dividing the total distance travelled by the time taken and,
by dividing the total distance travelled by the time taken only
while locomoting, i.e. time in state 0 is omitted. The angle
distribution is the number of times a cell proceeds into
specified 15° sectors measured from the direction of the
preceding step with no distinction being made between left
and right turns. Persistence is the direct-line distance
between starting and ending points divided by the actual
cell-path distance. Orientation depicts the total path of the
cell as a vector with magnitude whose direction is specified as
angles with both the x—y plane and the x-axis.
B. Eight-state Markov probability range computed by adding
±2s.D. to mean in A
Results
The angle distribution between successive changes
in cell direction suggests that these particular cells
locomote in a zig-zag fashion, with activity more
pronounced in the 0-30° and especially the 150-180°
ranges on either side of the direction of the previous
step (Fig. 3). The 0° and 180° values imply that the
cell, after stopping (state 0), recommences locomoting
in either the same or the opposite direction. The
proclivity of angular changes around the 150° sector
reflects that the cells are alternating their locomotory
Using glutaraldehyde-fixed cells, the optical sectioning unit gave constant x, y and z coordinates; therefore, any changes in coordinates between sections
truly reflects cell movement. Table 1 shows the results
obtained for an eight-state Markov analysis of 84 cells
tracked within a three-dimensional gel. The data are
pooled from 10 different experiments using the same
cell type and the same concentration of collagen
(l-2mgml~'). The eight-state steady-state probabilities closely approximate the theoretical probabilities for random locomotion, namely 0-125, to
within 10%.
Table 2A shows the mean and standard deviation of
the eight-state steady-state probabilities for the individual directional states. These data are derived from
treating the 10 different experiments by statistical
analysis. Both these analyses show that MOS-11 cells
locomoting within a three-dimensional matrix show
approximate random movement. Table 2B shows the
range of probabilities for each state obtained by both
adding and subtracting the standard deviation from
the mean. For a given state, any value higher or lower
than those given would represent positive and negative
chemotaxis, respectively (Noble et al. 1979).
Analysis of the nine-state Markov method reveals
that the probability of the cells stopping (state 0) is of
the order of six times greater than any of the directional states (Table 3). The waiting time in the eight
directional states is remarkably constant, with visits to
state 0 being about three times longer than to the
directional states (Table 4).
244
P. B. Noble
State
Probability
1
2
3
4
5
6
7
8
0-175-0-063
0-190-0-045
0-177-0-057
0-215-0-083
0-192-0-088
0-160-0-068
0-175-0-064
0-187-0-055
Table 3. Nine-state Markov probability values
State
Probability
0
1
2
3
4
5
6
7
8
0-400±0-121
0-069 ±0-018
0-065 ±0-018
0-069 ±0-022
0-073 ±0-023
0-076 ±0-022
0-075 ±0-021
0-074 ±0-022
0-078 ±0-026
Table 4. Waiting time: nine-state Markov method
State
Waiting time
0
1
2
3
4
5
6
7
8
2-02 ±0-57
0-76 ±0-06
0-76 ±0-09
0-76 ±0-09
0-75 ±0-08
0-76 ±0-08
0-77 ±0-08
0-76±0-12
0-75 ±0-11
activity between the ruffling membranes located at
opposite ends of the bi-polar cell.
The persistence values computed for the cells
suggest that they are moving in a random manner.
Values approaching 100% would imply that the cells
were locomoting in a highly directional manner,
whereas values toward 0 % imply highly random
locomotion. For the MOS-11 cells a mean persistence
value of 8-97 % ± 5-25 S.D. was obtained.
The speed of the cells was computed in two ways.
The first presents the mean speed over the entire
experimental period and includes the time spent when
the cell is stationary. The second method deletes the
time period in which the cell is stationary (state 0) and
therefore provides a measure of the maximum speed of
which the cell is capable. The mean speed including
600
100
0
state 0 time periods is 3-6 ± 1-8/zmmin ', « = 84;
the mean speed excluding the time in state 0 is
6-24 ± 1-62jLtm. Therefore, the maximum speed attainable by these cells under these environmental
conditions is about twice that computed including the
stops. Table 5 shows an example of the orientation
data obtained for seven cells. The displacement vector
gives the change in x, y and z coordinates and
magnitude (both in pixels) with the angle of vector
orientation with the xy plane and the tf-axis. Note that
for the magnification used in this study one pixel is
equivalent to 3-5 |Um. This type of data is useful for
comparative purposes and lends itself to graphic
representation as a visual summary of cell migrations
within three-dimensional systems.
Visual analysis of time-lapse video recordings of
MOS-11 cells locomoting on two-dimensional surfaces
of a three-dimensional gel have revealed two different
cell types, at least with respect to their locomotory
characteristics. One cell type is rather sessile, with a
tendency to form 'cords'. Cells within a cord move
slowly, and make and break contacts frequently. The
other type of cell seen in two dimensions is an
individualistic cell that only forms cell contacts temporarily and actively locomotes.
In three-dimensional gels, individual locomoting
cells appear to retrace their 'steps' frequently, perhaps
due to the cells using a path of least resistance forged
through the gel during a previous period of locomotion. Cells within a gel are bi-polar, with ruffling
membranes at opposite poles (Fig. 4). Cord formation
also occurs within three-dimensional gels but the cords
are much more stable (Fig. 4). These cords, formed
by cell division and recruitment, occur only after
a considerable time in culture (1 week) and consequently do not interfere with the cell tracking
experiments.
30
60
90
120
150
Angular change between steps (°)
Discussion
Fig. 3. The distribution of angular changes between steps.
Note, no distinction is made between left and right turns.
We have presented quantitative data that characterize
the locomotory trajectories of MOS-11 cells in three-
Table 5. Seven MOS cells: 100 frames
Path description
Persistence (%)
Displacement vector
Magnitude (pixels)
13-41
28-74
18-36
17-97
17-25
18-10
13-40
(-1,4,4)
( - 1 . 1,7)
( 1,3,5)
(-3,3,4)
( 2, 1, 7)
( 0,3,6)
( - 4 , 4, 5)
5-745
7-141
5-916
5-831
7-348
6-708
7-550
Angle with xy
plane (°)
44-1
78-6
57-7
43-3
72-3
63-4
41-5
Angle with .v-axis (°)
-76-0
-450
71-6
-45-0
26-6
900
-45-0
See the text for details.
Three-dimensional cell migration
245
Fig. 4. A - F . A series of photographs taken from the video screen of a time-lapse recording. The darker shapes are cells at
different levels in the gel and are out of the focal plane. The arrows show a bi-polar cell with ruffling membranes occurring
alternately at opposite poles. The asterisks show cord development formed by a combination of cell division and
recruitment. X54.
246
P. B. Noble
dimensional lattices of hydrated collagen. An important point to consider in interpreting three-dimensional
locomotory data is to appreciate the morphology of
these cells as compared to the better-known morphological forms associated with two-dimensional surfaces. The morphological behaviour of these cells is
different depending on whether the cells are locomoting on a two-dimensional surface or or within a
three-dimensional gel. Several reports have commented on this difference, for a variety of cell lines
(Bard & Hay, 1975; Grinnell & Bennett, 1981; Schor
et al. 1983). In a three-dimensional gel the broad
lamellipodium, so prominent on two-dimensional surfaces, is rarely, if at all, seen. The cells within a threedimensional gel are strongly bi-polar, with small
discrete ruffling membranes at opposite ends. This
fact is reflected in the rather specific turn angles
computed from the x, y and z coordinates representing
the steps taken by the cells. The greater number of
turns within the 0-30° and 150-180° segments on
either side of the previous step orientation is not an
unexpected result, considering the location and consistency of the 'locomotory' ruffling membranes. Interpretation of this proclivity to angles around 150°
implies that ruffling and locomotion occur at one end
of the cell only to cease and be initiated at the opposite
pole. This is frequently seen when viewing time-lapse
video recordings of these cells locomoting within a
three-dimensional gel (see Fig. 4). MOS-11 cells
within a three-dimensional gel most probably make
turns around the 90° range when stopped (state 0)
where the cells appear to be less polarized.
Given the fact that cells can orientate and locomote
along fibres (contact guidance) it is difficult to assess
the extent to which orientation of the collagen fibrils
contributes to these angular changes.
The persistence data show that these cells take a
very tortuous path. Video time-lapse recording of
these cells locomoting in thin three-dimensional collagen gels (approximately 80 jj.m thick) reveals that the
cells appear to locomote back and forth, continually recrossing their path. Again, this is a consequence of the
alternating of activity between ruffling membranes.
Perhaps there is a tendency to re-use part of an existing
track, as it presents a path of least resistance through
the gel. The interpretation of the persistence data is in
keeping with the angle-distribution data discussed
previously.
Analysis of the orientation and displacement of the
cell vectors in three-dimensional space has recently
been shown to be random (Boyarsky & Noble, unpublished data).
Although the mean speed is approximately 3 /im
min" 1 , the cells do not locomote far from their initial
starting point, due to the amount of back-tracking that
takes place. A consequence of this is seen in cultures
that have been used for cell tracking and are maintained for several weeks. In such cases, localized
discrete colonies are formed within the gel. A characteristic of these cells is that they remain stationary for
about three times as long as the period in which they
are locomoting. However, it must be remembered that
this parameter is dependent on the half-cell-diameter
rule and the framing rate chosen (Noble & Peterson,
1974). Nevertheless, it is a valid parameter for comparison when using the same cell type and method
of measurement, albeit in different physiological
conditions.
A Markov analysis from the .x, y and z coordinates
complements the findings for angle distribution and
persistence, which suggest the cells are moving in a
random manner. Both the steady-state probability
values, whether computed from pooled experimental
data or as the mean and standard deviation computed
from the individual experiments, give values close to
the theoretical values for cells moving randomly in
eight directional states, i.e. 0-125. By adding ±2s.D.
to the mean for each of the eight directional states, a
measure of positive and negative chemotaxis can be
made. If, under the appropriate experimental conditions a potential chemotactic substance is located in a
given directional state, then probability values that are
greater than the mean plus two standard deviations
represent positive chemotaxis. Likewise, probability
values less than the mean —2s.D. represent negative
chemotaxis with respect to a given direction (state)
(Noble et al. 1979).
These locomotory parameters computed by the cell
tracking system can be subjected to statistical analyses
that detect the presence of different locomotory
phenotypes within a cell population. Using factor
analysis (SAS/STAT, 1985), evidence for two distinct populations of MOS-11 cells has been found
(Shields & Noble, unpublished data).
The results of the three-dimensional optical tracking system provide quantitative data on the global
locomotory characteristics of MOS-11 cells that do not
conflict with subjective observations of their locomotory behaviour as viewed from time-lapse video.
Within three-dimensional gels, in the absence of
known chemotactic or haptotactic factors, these cells
exhibit random locomotion as computed from Markov, persistence and vector analyses and have a mean
speed of S/zmmin" 1 . The finding that MOS-11 cells
move randomly within a randomly polymerized gel is
not unexpected. However, it does form a baseline of
locomotory parameters from which the effects of
various matrix and cell components can be investigated. Angle distribution data suggest that these cells
turn more frequently within narrow 30° confines, as
dictated by the alternating bi-polar ruffling membranes. Comparison between the data produced by the
Three-dimensional cell migration
247
cell tracking system and those obtained by viewing
time-lapse video recordings gives us confidence that
the tracking system produces quantitative information
that truly reflects cell behaviour within three-dimensional gels. With this tracking system it is now possible
to study the role of various matrix components in cell
locomotory behaviour. This information is relevant to
studies on embryological development, wound healing
and the invasiveness of tumour cells.
I thank Dr J. A. Hassell, Department of Immunology and
Microbiology, Faculty of Medicine, McGill University for
the supply of MOS-11 cells, and Diane Leggett for typing
the manuscript. This work was supported by the Medical
Research Council of Canada (no. MA7742).
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Extracellular matrix materials influence quail neural crest
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