Cellular self-organization by autocatalytic
Michael Junkin1, Siu Ling Leung1, Samantha Whitman2, Carol C. Gregorio2and Pak Kin Wong1,3,*
1Department of Aerospace and Mechanical Engineering,2Department of Cell Biology and Anatomy, and3Biomedical Engineering IDP and BIO5
Institute, University of Arizona, Tucson, AZ 85721 USA
*Author for correspondence (firstname.lastname@example.org)
Accepted 11 July 2011
Journal of Cell Science 124, 4213–4220
? 2011. Published by The Company of Biologists Ltd
Myoblasts aggregate, differentiate and fuse to form skeletal muscle during both embryogenesis and tissue regeneration. For proper muscle
function, long-range self-organization of myoblasts is required to create organized muscle architecture globally aligned to neighboring
tissue. However, how the cells process geometric information over distances considerably longer than individual cells to self-organize into
well-ordered, aligned and multinucleated myofibers remains a central question in developmental biology and regenerative medicine. Using
plasma lithography micropatterning to create spatial cues for cell guidance, we show a physical mechanism by which orientation
information canpropagatefor alongdistancefromageometricboundarytoguidedevelopmentofmuscletissue.Thislong-rangealignment
occurs only in differentiating myoblasts, but not in non-fusing myoblasts perturbed by microfluidic disturbances or other non-fusing cell
types. Computational cellular automata analysis of the spatiotemporal evolution of the self-organization process reveals that myogenic
fusion in conjunction with rotational inertia functions in a self-reinforcing manner to enhance long-range propagation of alignment
information. With this autocatalytic alignment feedback, well-ordered alignment of muscle could reinforce existing orientations and help
promote proper arrangement with neighboring tissue and overall organization. Such physical self-enhancement might represent a
fundamental mechanism for long-range pattern formation during tissue morphogenesis.
Key words: Myogenesis, Morphogenesis, Tissue engineering, Self-organization
Myoblasts differentiate from single cells into multinucleated
muscle fibers during the course of myogenesis. This self-
organization process is spatiotemporally regulated and involves
multiple steps including proliferation, specification, alignment,
fusion and myofibrillogenesis (Yaffe and Feldman, 1965). During
this process, myoblasts must modify spatial cellular arrangement
over distances considerably longer than an individual cell without
a central coordinator or a blueprint to proceed from a disordered
state of individual,undifferentiated cells into well-ordered,aligned
and multinucleated myotubes (Blanchard et al., 2009; Bryson-
Richardson and Currie, 2008; Nelson, 2009). Many details of how
such information is physically coordinated over a long distance
remain unknown and represent fundamental questions in cell
biology. Understanding the physical aspects of the myogenic self-
organization process will also have profound impacts on various
myogenic diseases and regeneration processes. For example,
abnormalities of muscle fibers and myofibril structures due to
genetic and environmental factors are the underlying causes of
various myopathies, including centronuclear myopathy (Jungbluth
et al., 2008) and muscular dystrophy (Kanagawa and Toda, 2006).
Physical factors in the microenvironment, such as tissue stiffening
caused by muscular dystrophy, are also known to influence the
result of satellite cell regeneration (Scime et al., 2009). Moreover,
the ability to manipulate the tissue morphogenic process will
enable the creation of microengineered tissue constructs and novel
Tissue morphogenic processes are generally regulated by
a combination of numerous physicochemical factors, such as
morphogens, cell–cell contacts, microenvironments and cell
mechanics (Elsdale and Wasoff, 1976; Garfinkel et al., 2004;
Green and Davidson, 2007; Gregor et al., 2010; Keller, 2002;
2010; Ruiz and Chen, 2008; Technau et al., 2000; Turing, 1952).
Nevertheless, relatively little is known about the roles of physical
factors in the regulation of the tissue morphogenic process. For
instance, an unsolved aspect of the development process that
is known to regulate cellular self-organization during tissue
generation is the positional information at physical boundaries.
Despite the fact that regulation through positional information
at boundaries has been seen in vivo to influence myogenic
developmental processes such as axis formation, initiation of
myogenesis and alignment of reintroduced mesenchymal stem
cells to existing muscle tissue (Cossu et al., 1996; Green et al.,
2004; Rowton et al., 2007; Shake et al., 2002), the details of how
physical boundaries guide tissue organization remain unclear. By
contrast, myoblasts aggregate, differentiate, and fuse over time,
and their physical size and properties evolve during the
differentiation process (Engler et al., 2004b; Stya and Axelrod,
1983). The effects of these physical changes of the cells on
the organization of myotubes during myogenesis have not been
With the advent of microfluidics and micropatterning
techniques, systematic manipulation of various physical and
Research Article 4213
Journal of Cell Science
microenvironments with high spatiotemporal resolution (Kim
et al., 2009; Nelson et al., 2006; Wong et al., 2008). For example,
topographical and chemical cues have been demonstrated to
guide the alignment of cardiac or skeletal muscles (Charest et al.,
2007; Feinberg et al., 2007). However, most of these studies
focus on guiding cell alignment with local cues instead of
exploring the inherent self-organization ability of myoblasts.
To understand the effects of global geometric cues and
long-range alignmentof myotubes,
(Junkin et al., 2011; Junkin et al., 2009; Junkin and Wong,
2011). This allows us to systematically perturb the environmental
factors and cell–cell interactions for elucidating the regulatory
processes in myogenic self-organization. Here, we demonstrate a
physical mechanism by which alignment information from a
geometric boundary can propagate over long distances to guide
the organization of muscle tissue. Understanding the details
of how muscle tissue forms from individual cells will have
regenerative medicine and systems theory (Mahmud et al.,
2009; Parrish and Edelstein-Keshet, 1999; Zheng et al., 2006).
factorscan beachieved incontrolled
Geometric constraints guide alignment of myotubes
To investigate the myogenic self-organization process within a
geometric context, we studied the organization of myoblasts
constrained in microscale patterns. The micropatterning was
achieved by plasma lithography, which produces spatial cues on
polystyrene substrates by means of selective exposure of the
surface to plasma treatment (Fig. 1A; supplementary material Fig.
S1). The self-organization of C2C12 mouse myoblasts (Fig. 1B)
and primary chick skeletal myoblasts (Fig. 1C) were studied on
line patternscreatedon polystyrene
differentiated myotubes aligned in parallel with the line patterns
despite the large distance of the cells from the geometric
boundaries. Additionally, we
myoblasts that differentiated on the plasma lithography-patterned
lines possessed characteristics of functional myotubes, including
the presence of well-developed sarcomeres (Fig. 1D), and the
ability to spontaneously twitch after 4–5 days of differentiation
(supplementary material Movie 1). During the alignment process,
myoblasts near the boundary of the line pattern were observed to
first elongate and align to the boundary, and myoblasts adjacent to
an elongated myoblast then polarized along the same direction
(supplementarymaterialFig. S2). Quantitative measurementofthe
cell alignment angle at different locations from the boundary
result, the alignment information appeared to propagate from the
boundary to neighboring cells and the myoblasts self-organized
into myotubes that aligned in parallel with the line patterns. These
results suggest myoblasts can use geometric cues for guiding the
In the experiment, the presence of well-developed sarcomeres
(Fig. 1D) and spontaneous twitching of myoblasts were observed
after 4–5 days of differentiation (supplementary material Movie
1). Quantification of twitching and sarcomere formation,
nevertheless, was not undertaken systematically because the
dynamic alignment process was the focus of the current study.
The patterns that were used in our experiments consisted of
alignment cues connected to unpatterned areas that also
possessed cells. The presence or absence of neighboring cells
could potentially influence the development process. As a
comparison, we additionally cultured myocytes on isolated
patterns of finite length, not surrounded by masses of
unpatterned cells at the ends. These cells also displayed
alignment to patterns and fusion. This suggests that the
alignment and fusion processes observed in this study are not
sensitive to the cells connected in the unpatterned regions.
However, we do not rule out the possibility that the cells in the
unpatterned areas might influence the twitching behavior and
sarcomere development. Another factor that has been reported to
be relevant to sarcomere development is adhesion (Engler et al.,
2004a; Griffen et al., 2004; Sen et al., 2011). In our experiments,
cell adhesion to patterned substrates was not investigated during
the alignment process, although we observed that alignment as
guided by patterns did not differ between different cell layers,
Length-scale dependence of the alignment process
To systematically investigate the alignment process, line patterns
from 50 mm to 500 mm in width were created to test the length-
scale dependence of the alignment process. The myoblasts
generally aligned to the line patterns for all widths (Fig. 1E). For
pattern widths that were 50 mm or smaller, most of the cells
aligned with the line patterns immediately after cell seeding. For
larger patterns, the portion of cells that aligned to the line patterns
increased gradually over time towards a steady state value. The
extent of alignment was found to be influenced by pattern size
because wider patterns tended to not align as well over time.
Examination of the temporal evolution of the alignment angles
revealed that the time constant of the process increased linearly
with the width of the line patterns (Fig. 1F). The fraction of
multinucleated cells was also examined and was found to
be similar for all pattern widths examined (,70%). These
observations further support the idea that the physical boundary
guides the alignment of the myoblasts and the orientation
information can propagate from the geometric boundary to guide
the alignment of myotubes.
Long-range alignment of myoblasts in
The dependence of the alignment process was further studied in a
semi-infinite domain created by plasma lithography (Fig. 2A).
This consisted of creating a large (millimeters in size)
hydrophobic area with straight edges surrounded by a larger
hydrophilic area. The result was compared with that from cells
grown on homogeneously plasma-treated substrates (Fig. 2B).
The myoblasts, in both cases, self-organized into aligned
domains: groups of myotubes aligned in similar directions over
the course of myotube formation (,1 week). Myoblasts cultured
on homogeneous substrates developed into multiple aligned
domains without preference to the orientation of each domain,
similarly to polycrystalline materials. The dimension of the
alignment domains could be over 600 mm. By contrast, myotubes
that formed near a pattern edge became well aligned along the
boundary, and the distance away from the edge where alignment
was preserved was taken as an estimate of the length scale that
the geometric cue propagated (Fig. 2C). Cell angles remained
Journal of Cell Science 124 (24)4214
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aligned to the orientation of the geometric boundary for a
distance approximately 1000±250 mm before alignment started to
decay and become randomized. Alignment of myoblasts far away
from the boundary (i.e. &1000 mm) resembled the behavior
of cells on homogeneous substrates, which form multiple
aligned domains in random directions. Other cell types, such
as fibroblasts, are also known to self-organize into multiple
alignment domains by contact guidance (Edelstein-Keshet and
Ermentrout, 1990; Nubler-Jung, 1987), and so experiments were
also performed using 3T3 mouse embryonic fibroblasts. When
3T3 fibroblasts were grown on the semi-infinite domain, the
alignment angle, however, decayed rapidly away from the edge
in approximately 200 mm (Fig. 2D), and did not show the long-
range propagation of orientation information observed in
differentiating myoblasts. To study the underlying mechanisms
responsible for the long-range propagation of orientation
information, the alignment experiments were performed inside
a microfluidic channel to perturb any possible morphogen
gradient created in the extracellular space (supplementary
material Fig. S4). Initially, fresh differentiation medium was
continuously perfused into the microchannel. Under this
condition, the alignment relative to the boundary decayed
rapidly (Fig. 2E), similarly to the alignment of 3T3 fibroblasts.
It should be noted that the myoblasts did not fuse, owing to the
removal self-generated growth factors required for initiating the
fusion process (Florini et al., 1991). Interestingly, re-circulating
the culture medium resumed cell fusion and the long-range
alignment of myotubes (data not shown). This suggests that
morphogen gradients in the extracellular space are unlikely to be
responsible for the long-range propagation of the alignment
information because the continuous fluid flow should disrupt the
formation of a morphogen gradient. In addition, shear stress does
not have an observable influence on the long-range alignment
process because when re-circulating of the culture medium was
carried out, the extended alignment was present. Myoblasts were
also grown in medium that lacked sufficient calcium, which
inhibits fusion of myoblasts (Knudsen and Horwitz, 1977).
Without calcium, cell fusion and long-range propagation were
again not observed, and the alignment behavior resembled that of
fibroblasts (Fig. 2F).
homogeneous substrates could self-organize into multiple
alignment domains (Fig. 2B). This suggests that the alignment
of myoblasts does not require local cues and is probably an
inherent self-organizing property of myoblasts. However, the
long-range alignment of myoblasts cannot be fully explained by
the contact guidance mechanism, which was observed in
fibroblasts (Edelstein-Keshet and Ermentrout, 1990; Nubler-
Jung, 1987). Unlike the long-range (,1000 mm) alignment of
differentiating myoblasts, the alignment of 3T3 fibroblasts
decayed and randomized within a short distance (approximately
200 mm) from the geometric boundary (Fig. 2D). Cell densities
were also measured and found to be similar in all experiments
(data not shown). Additionally, significant layering of myocytes
on top of each other was not observed, as reported in other studies
(Griffen et al., 2004; Sen et al., 2011). Additional or alternative
mechanisms, therefore, are required to explain the long-range
alignment of myoblasts. Because the surface that the cells
contacted was uniform, the long-range alignment of myotubes
observed was different from that previously reported because of
local topographic (Charest et al., 2007) or chemical signals
(Feinberg et al., 2007), which provide short-range alignment cues
on the dimension of a cell to guide the alignment. Interestingly,
the long-range alignment only
myoblasts that can be fused into myotubes in the experiments.
Rapid decay of the alignment angle from boundaries was
occurs for differentiating
Fig. 1. Self-organization of myoblasts and geometric alignment of myotubes on plasma patterned substrates. (A) Plasma lithography to create chemical
patterns for guiding cell alignment. Areas exposed to plasma (pink) present surface functional groups that facilitate cell adhesion, whereas areas shielded by
PDMS (blue structure) prevent cell adhesion. (B) C2C12 mouse myoblasts, and (C) primary chick myoblasts guided on line patterns form linear, aligned myotubes
parallel to the boundaries. (D) Sarcomeres in patterned primary chicken skeletal muscle fibers. F-actin is labeled by phalloidin (green), Z-discs by a-actinin (blue)
and M-line by titin T114 (red). (E) The temporal evolution of myoblasts aligned to the line patterns with different widths. (F) Time constants of myoblast
alignment on different pattern widths. Error bars in E and F are s.d. and s.e. of the mean, respectively.
Journal of Cell Science
observed for all non-fusing cells such as 3T3 fibroblasts and
myoblasts that are perturbed by microfluidic disturbance or low
calcium medium (Fig. 2D–F).
Long-range propagation of alignment information
Our data suggest that the long-range propagation of alignment
information only occurs with differentiating myoblasts that can
fuse into myotubes. However, it is unclear how myoblast fusion
can affect the long-range alignment of myotubes. To investigate
the roles of myoblast fusion in the alignment process, we
measured the physical properties of differentiating myoblasts
(Fig. 3). In particular, live images at various stages of the fusion
process were captured to evaluate rotational and linear motions
and their dependence upon fusion. The angular motion decreased
rapidly with the size of the cells (Fig. 3A,B). In other words, the
rotational inertia – the resistance of the cell to rotate – increased
with the cell size. However, the displacement of myoblasts
showed only weak correlation with cell size (Fig. 3C,D). Other
measurements of linear motion, including the ratio of distance
traveled parallel and perpendicular to the interface, and velocity
data, also did not show any correlation with cell length or to
position relative to pattern edge (data not shown). Because
rotational inertia changed with the size of cells, the ability of
differentiating myoblasts to adjust relative to surrounding cells
decreased during the differentiation process. We therefore
hypothesized that rotational inertia could serve as a mechanism
forthe enhanced propagation
To test the possibility that myogenic fusion in conjunction with
rotational inertia functions in a self-reinforcing manner to
enhance long-range propagation of orientation information, a
cellular automata model was developed to evaluate the alignment
of myoblasts under geometric constraints resembling the
experimental conditions (Ermentrout and Edelstein-Keshet,
1993). In the cellular automata model, each cell, which is
surrounded by a grid of 565 neighboring cells, was subjected to
a decision on whether or not to align. Alignment would proceed if
most of the surrounding cells were aligned to a high degree, and
Fig. 2. Spatiotemporal evolution of cell
alignment in semi-infinite domains.
(A,B) Myoblast alignment near an
interface (A) and on a homogeneous
surface (B) at days 1 (top), 4 (middle) and
8 (bottom). Color maps of alignment angle
(left) and the corresponding micrographs
of cells (right). (C–F) Representative
measurements for propagation of
geometric orientation information with
fusing myoblasts (C), 3T3 fibroblasts (D),
myoblasts inside a microchannel, which
was supplied with fresh differentiation
medium to block fusion (E), and
myoblasts in medium without calcium to
block fusion (F). PS, polystyrene.
Journal of Cell Science 124 (24)4216
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partial alignment was executed if a lesser number of cells
were aligned (supplementary material Fig. S5). The increase in
rotational inertia due to cell fusion was incorporated into the
model because aligned cells, similarly to a long cell having the
same angle over its whole length, are less likely to rapidly
rotate. Using the cellular automata model, the propagation of
the alignment information from the boundary can be observed
(Fig. 4A,B, and supplementary material Movie 2) and closely
resembled the experimental observation (Fig. 2A). The model
was able to capture the spatial distribution of the self-
organization process with a geometric boundary (compare
Fig. 2C,D and Fig. 4C,D). Furthermore, the model successfully
described the formation of multiple alignment domains observed
in homogeneous substrates (supplementary material Movie 4;
Fig. 2B). For non-fusing cells, only short-range alignment could
be observed in the numerical study (supplementary material
Movie 3) similarly to our experiments (Fig. 2D–F). We have also
applied the model to describe the length scale dependences and
time constants of myoblast alignment to line patterns of different
widths (Fig. 4E,F). The portions of cells that are aligned to the
line patterns gradually increase toward steady state values, with
time constants linearly increasing with the pattern width. Despite
the simplicity of the model, the numerical data are in excellent
agreement with our experiment results (Fig. 1E,F). These data
indicate that the cellular automata model successfully describes
the spatiotemporal distribution of myogenic self-organization
providing a model to understand the self-organization process.
In this study, we observed that orientation information can
propagate for a long distance from a geometric boundary during
myogenic self-organization. This long-range alignment process can
be understood within a biomechanical context. In particular,
examining the temporal evolution of the cellular automata model
revealed that myogenic fusion in conjunction with rotational inertia
can serve as an autocatalytic mechanism to enhance long-range
propagation of orientation information. During the alignment
process, cells near the geometric boundary first align as a result
of contact guidance (Brock et al., 2003; Edelstein-Keshet and
Ermentrout, 1990) (Fig. 2A; supplementary material Fig. S2 and
Movie 2). Cells near aligned cells tend to align with the elongated
cells and polarized cells fuse with each other, which increases the
rotational inertia of the cells. Then, the increase in rotational inertia
further facilitates the alignment and fusion of nearby cells. The
rotational inertia functions in an autocatalytic, or self-enhancing,
manner to propagate the alignment information from the boundary.
In fact, the increase in the size of aligned domains during
differentiation was observed consistently in our experiment where
myoblasts were fused with and without geometric guidance
(Fig. 2A,B). For non-fusing cells, the rotational inertia does not
increase autocatalytically. Therefore, the cells are more likely to
align in random directions as a result of the small rotational inertia
and the alignment information from the boundary can only
propagate for a short distance, as shown in both experiments and
numerical simulation (Fig. 2D–F and Fig. 4D). In addition to non-
fusing fibroblasts, microfluidic perturbation and medium with low
calcium, which prevented myoblasts fusion, were applied to
modulate the rotational inertia of myoblasts in our experiment,
Fig. 3. Dependence of motion on cell fusion. (A,B) Total angular movement
in relation to cell length. (C,D) Measurement of total distance moved in
relation to cell length. Measurements record motion taking place between
successive image capture intervals and were recorded after 7 days of fusion.
Fig. 4. Cellular automata modeling of autocatalytic alignment feedback
during myogenic self-organization. (A,B) Myoblast alignment calculated
using the cellular automata model at days 1 and 8. (C,D) Propagation of
geometric orientation information of fusing cells (C) and non-fusing cells
(D) estimated using the model. (E) Simulation of alignment on line patterns
with different widths. (F) Time constants of myotube alignment on different
Journal of Cell Science
and both conditions demonstrated only short-range alignment,
which is consistent with our model. Collectively, the fusion of
myoblasts in conjunction with the increase in rotational inertia
provides a physical mechanism for the long-range alignment
observed only in differentiating myoblasts.
A major finding in this study is that myoblasts propagate
global geometric alignment cues by local autocatalytic alignment
architecture. The interplays between autocatalytic alignment
feedback and geometric cues were therefore investigated by
means of creating arbitrary shapes for myoblast differentiation
(Fig. 5). Myotubes formed on large patterns show the ability of
myoblasts to follow geometric cues in the microenvironment, as
seen by curved myotubes formed as a result of juxtaposed
geometric cues (Fig. 5A). The limit of geometric guidance can be
seen by patterns with sharp corners, and small radii of curvature
where myotubes are not able to completely follow the pattern and
sharp edges become smoothed out when myotubes form
(Fig. 5B,C). The overall tendency for myotube alignment and
domain growth, however, is
alignment feedback favors not only production of well-ordered
structures but also correction of local misalignment to ensure that
globally well-aligned structures needed for proper tissue function
are achieved. This can be seen in myoblasts differentiating on Y-
shape patterns, in which multiple segments of muscle can connect
smoothly (Fig. 5D). This is likely to have an important role
during embryogenesis where muscle does not form in isolation
but in conjunction with neighboring tissues whose structure could
provide the spatial cue to provoke alignment feedback (Cossu
et al., 1996; Green et al., 2004; Rowton et al., 2007; Shake et al.,
2002; Yaffe and Feldman, 1965). Well-ordered alignment of
orientations and help to promote proper development of
neighboring tissue and overall organization.
Autocatalysis, or self-enhancement, is a hallmark in pattern
formation where initial inputs become amplified by the action of
individual cells to produce higher-order structure (Ermentrout
and Edelstein-Keshet, 1993; Meinhardt, 1982). Most established
morphogens and surface receptors, are biochemical in nature.
Our results suggest that physical factors can also be used in
cellular self-organization, such as the autocatalytic alignment
feedback mechanism observed in myoblast differentiation.
Physical autocatalytic feedback is then probably involved in
guiding the formation of other types of tissue, because adhesion
and boundaries are crucial parts of many morphogenic processes.
musclecould then reinforceexistingaxesand
Materials and Methods
polydimethylsiloxane (PDMS) molds (Dow Corning Sylgard 184) placed in
conformal contact with polymer surfaces to selectively shield the substrates from
the effects of air exposure (Junkin et al., 2011; Junkin et al., 2009; Junkin and
Wong, 2011; Keyes et al., 2008). The patterning was done at room temperature in a
plasma chamber (PDC-001, Harrick Plasma) at 150 Pa, with a radio frequency
power of 29.6 W for 10 minutes. Selective exposure to the plasma results in a cell-
sensitive chemical pattern that guides cellular attachment and movement. 3D
molds were made using replica molding from photolithographically patterned
masters. After plasma patterning, the surfaces were placed under UV for
10 minutes before cell seeding.
to guidecellattachment were generatedusing3D
Cell culture and primary cell preparation
Cell lines, CRL-1772 mouse myoblast (C2C12) and ATCC CRL-1658 mouse
embryo fibroblasts (3T3) were obtained from the American Type Culture
Collection (ATCC). C2C12 cells were used from passage 3–10. Differentiation
of C2C12 cells was induced upon reaching a confluence of 80–90% by switching
Fig. 5. Effect of myogenic differentiation on
geometrical patterns for investigating the
relationship between spatial cues and alignment
feedback. (A–D) Phase-contrast images of myotubes
formed on circular (A,C), square (B) and Y-shaped
(D) patterns of different sizes.
Journal of Cell Science 124 (24) 4218
Journal of Cell Science
to a medium with 5% horse serum that was exchanged every other day. Calcium-
free culture and differentiation media were identical to normal medium except for
the use of calcium and magnesium-free DMEM and the addition of 270 mM
ethylene glycol tetraacetic acid (EGTA) (Neff et al., 1984). All cell lines were
maintained under standard conditions and media formulations per ATCC
guidelines unless otherwise specified. Primary cells comprising embryonic chick
skeletal myoblasts were maintained and isolated as originally described (Almenar-
Queralt et al., 1999; Gregorio and Fowler, 1995) and were cultured in DMEM
(Invitrogen) supplemented with 10% ‘selected’ FBS (Sigma), 4% chick embryo
extract and 1% antibiotics and antimycotics.
C2C12 cells were stained with Alexa Fluor 555 Phalloidin (Invitrogen) to label
actin, FITC-conjugated anti-vinculin (Sigma) to label focal adhesions and sealed
with ProLong Gold Antifade Reagent (Invitrogen) containing 49,6-diamidino-2-
phenylindole (DAPI; Invitrogen) to label nuclei. Alternatively cell membranes
were stained with CellMask Orange (Invitrogen). Primary cells were stained with
primary antibodies including monoclonal anti-a-actinin (Sigma) to mark the Z-
disc, polyclonal anti-titin T114 (Invitrogen) to mark the M-line and Alexa-
Fluor-488-conjugated Phalloidin for F-actin. Secondary antibodies consisted of
Alexa-Fluor-350-conjugated goat anti-mouse IgG (Invitrogen), and Texas-
Red-conjugated donkey anti-rabbit IgG (Invitrogen). Coverslips for primary cells
were mounted onto slides with Aqua Poly/Mount (Polysciences).
Phase-contrast images of cells were captured on an inverted Nikon TE2000-U
microscope using a SPOT camera from Diagnostic Instruments (model 2.2.1).
Fluorescence images were captured on a Leica inverted DMI4000 B microscope
using a Cooke SensiCamQE. Continuous, live-cell images were recorded using a
custom fabricated live-cell apparatus consisting of a microscope stage incubator
(AmScope Model TCS-100) to which a plastic enclosure was added. Normal
atmospheric conditions were maintained by placing water trays to maintain
humidity and by supplying 5% CO2passed through a 0.3 mm in-line filter at a
slight overpressure to the chamber. Continuous imaging was conducted using
either a Nikon TE2000-U or a Nikon Diaphot microscope with an Imaging
Source DMK41AU02 camera. Cells were visually identified with phase-contrast
microscopy by determining cell size and border, and examining morphology in
contrast-enhanced images. Movement of cells was analyzed using a custom
ImageJ macro that tracked a line drawn over the long axis of each cell. Position
data was then exported for analysis and data including length, endpoints, angle
and center point of each cell was followed sequentially over time. Alignment
angle was measured relative to pattern direction with either 90˚ or 180˚
corresponding to the direction of the guidance cue. Time constants for alignment
data were extracted from angle measurements by best fit of data to a first-order
system. Multinucleation of cells was assessed by counting number of nuclei
inside cells with multiple nuclei and comparing with total number of nuclei
Cellular automata modeling
Mathematical modeling was carried out using a MATLAB cellular automata
program that was created to model cell alignment based upon relationships
between a small neighborhood of cells. The program examines angles of cells in a
565 grid and places cells into groups of 10˚bins. The number of cells in each bin
is counted and if ten or more cells fall into the same angle bin then the cell at the
center of the grid assumes the average angle of those ten (or greater) aligned cells.
Otherwise, if between eight and nine cells fall into the same angle bin then the
central cell assumes the average of the angle of the aligned block of cells and its
current cellular angle. Otherwise, if any bin of cells has less than eight cells in it,
then the cell at the center of the 565 grid assumes an 8:1 weighted average of its
own alignment (8) and the average alignment of the cells with the greatest number
in their alignment bin (1). This is then repeated for every cell in the array once per
time step and cellular angle is mapped to a color and displayed. The algorithm for
non-fusing cells is for alignment to neighboring cells without a decision based
upon fusion or a high degree of alignment. During each time step, the central cell
assumes a 2:1 weighted average of the largest aligned bin of cells (2), and the value
of the central cell (1). During all steps of the algorithms, a small random angular
change is either added or subtracted to the cell being analyzed.
This work is supported by the National Institutes of Health Director’s
New Innovator Award [grant number 1DP2OD007161-01]; National
Heart Lung and Blood Institute [grant number HL083146]; the
National Science Foundation [grant number 0855890]; and the
James S. McDonnell Foundation. M.J. is supported by the National
Institutes of Health Cardiovascular Training Grant; the Arizona
Technology Research Initiative Fund; and Achievement Rewards for
College Scientists. Deposited in PMC for release after 12 months.
Supplementary material available online at
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