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Pulsatile contractions and pattern formation in excitable active gels
Michael F. Staddon,1Edwin M. Munro,2, 3 and Shiladitya Banerjee4, ∗
1Center for Systems Biology Dresden, 01307 Dresden, Germany
2Department of Molecular Genetics and Cell Biology, University of Chicago, Chicago, IL 60637, USA
3Institute for Biophysical Dynamics, University of Chicago, Chicago 60637, IL, USA
4Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense,
generate and transmit mechanical forces. The cortex can exhibit a wide range of dynamic behaviours, from gen-
erating pulsatory contractions and traveling waves to forming highly organised structures such as ordered fibers,
contractile rings and networks that must adapt to the local cellular environment. Despite the progress in charac-
terising the biochemical and mechanical components of the actin cortex, our quantitative understanding of the
emergent dynamics of this mechanochemical system is limited. Here we develop a mathematical model for the
RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an ac-
tive polymer gel, to investigate how the interplay between chemical signalling and mechanical forces govern the
propagation of contractile stresses and patterns in the cortex. We demonstrate that mechanical feedback in the
excitable RhoA system, through dilution and concentration of chemicals, acts to destabilise homogeneous states
and robustly generate pulsatile contractions. While moderate active stresses generate spatial propagation of
contraction pulses, higher active stresses assemble localised contractile structures. Moreover, mechanochemical
feedback induces memory in the active gel, enabling long-range propagation of transient local signals.
Introduction.– The actin cortex is an adaptive active ma-
terial that dynamically regulates its mechanical properties to
maintain or change cell shapes [1–4]. Actin cortex can display
a wide range of dynamic behaviours from driving intracel-
lular pulsatory contractions [5,6] to cellular-scale polarized
flows [5,7,8] and assembling protrusive or contractile struc-
tures during cell motility and cytokinesis [9,10]. These be-
haviours must adapt to the cell’s local environment and devel-
opmental stage. For instance, cellular-scale pulsatile contrac-
tions are often observed during developmental morphogene-
sis, where pulsatile contractions act as a mechanical ratchet
to sequentially alter cell size and shapes [11–14], leading to
tissue bending or elongation [15]. At the intracellular level,
these pulses can occur with chaotic spatiotemporal dynam-
ics [5,16,17], or can have periodic spatiotemporal struc-
tures as seen in surface contraction waves in Xenopus em-
bryos [18,19]. In other physiological contexts, stable con-
tractile structures are needed, as in the assembly of an acto-
myosin purse-string during wound healing [20], or the forma-
tion of a contractile ring during cytokinesis [21,22]. While
the biochemical pathways underlying actomyosin dynamics
are known, the ways in which actomyosin-driven forces feed-
back to upstream chemical signals to govern cytoskeletal be-
haviours remain poorly understood [4].
Alan Turing, in his seminal paper, demonstrated that
reaction-diffusion systems can autonomously generate a wide
variety of spatiotemporal patterns observed in nature, but
noted that mechanical forces may also play an important role
in pattern formation [23]. In recent years, purely biochemi-
cal models have been proposed for actomyosin pattern forma-
tion. RhoA and its downstream effectors of actin and myosin
have been shown to form an activator-inhibitor system that ex-
hibits excitable dynamics and oscillations [17,24,25]. Here
autocatalytic production of the activator RhoA leads to lo-
cal accumulation of the inhibitor F-actin, which in turn lim-
its the spreading of activators. This triggers the next cycle
of autocatalytic production of RhoA, resulting in traveling
waves [24,25]. Since F-actin diffusion is negligible compared
to RhoA, this model cannot spontaneously generate Turing
patterns. By tuning RhoA production rates locally, static pat-
terns of RhoA can be generated. This raises the question if
actomyosin patterns strictly rely on biochemical cues or can
spontaneously and robustly emerge via interactions with an
active mechanical medium.
Mechanochemical feedback in the cytoskeleton is another
mechanism for generating spatiotemporal patterns [26–29].
Active gel models of the cytoskeleton have suggested that pul-
satory patterns can emerge from contractile instabilities driven
by a positive feedback between active stress and advective
flows generated by a stress regulating chemicals such as actin
and myosin [28,30,31]. These contractile instabilities cluster
myosin into a few high concentration regions, but regulating
myosin contraction with an independent RhoA oscillator can
prevent the collapse of myosin and sustain oscillations [32].
However recent studies suggest a negative feedback loop be-
tween actomyosin and RhoA [17,24,25], raising the question
of how the feedback between RhoA and actomyosin mechan-
ics are regulated to generate flows and patterns.
Here we develop a mathematical model for an excitable
signalling network comprising RhoA and actomyosin, em-
bedded in an active mechanical medium, to study how the
feedback between biochemical signalling and mechanical
stresses regulate patterns and flows in the actin cytoskeleton.
We specifically ask how pulsatory flows arise from the
coupling between a fast diffusing activator (RhoA) and a
slow diffusing inhibitor (actomyosin), how mechanochemical
feedbacks stabilise contractile instabilities into localised
patterns, and how active stresses propagate local contractile
signals. We find that mechanical feedback acts to destabilise
stationary states to robustly generate pulsed contractions.
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2
At high contractile activity, stable patterns of actomyosin
emerge. Furthermore, the system encodes memory of tran-
sient perturbations that allows local signals to be translated
into propagating contraction waves or stable patterns.
Mechanical feedback generates robust pulsatile contractions.
– To elucidate the role of mechanical feedback in the dy-
namic behaviours and instabilities in the actin cortex, we first
study a coarse-grained three-element ODE model for the cou-
pling between RhoA, actomyosin and mechanical strain in the
actomyosin network. Our model draws from recent experi-
ments on Xenopus oocytes [24] and C. elegans embryos [17]
that suggest that actomyosin pulsation is regulated by the ex-
citable dynamics of RhoA GTPase – the upstream regulator
of actomyosin tension and turnover. Local autocatalytic ac-
tivation of RhoA drives rapid initiation of pulses, followed
by actomyosin recruitment. As actomyosin concentrations in-
crease, F-actin dependent accumulation of the RhoA GTPase-
activating proteins RGA-3/4 terminate the pulse through a de-
layed negative feedback [17]. This activator-inhibitor cou-
pling between RhoA-GTP (concentration r) and actomyosin
(concentration m) is described by the following dynamics:
˙r=Rr(r, m)−r˙u
1 + u,(1)
˙m=Rm(r, m)−m˙u
1 + u,(2)
where Rrand Rmdefine the rates for the assembly of RhoA
and actomyosin, and u(t)is the mechanical strain (Fig. 1a).
Here the effect of F-actin and myosin are represented by a
single species – actomyosin – that encompasses the inhibitory
feedback supplied by F-actin as well as active force generation
by myosin (see below). The second term on the right hand
sides of the above equations arise from mass conservation –
concentrations increase as the cell contracts and decreases as
the cell relaxes, providing an additional mechanical feedback
between RhoA and actomyosin. The chemical reaction rates
are given by:
Rr(r, m) = S+arn
An+rn−gmr
G+r,(3)
where Sis the applied stimulus (or basal rate of RhoA pro-
duction) representing the activity of Rho-GEF, ais the rate of
autocatalytic production of RhoA, nis a Hill coefficient, and
gis a negative feedback parameter arising from F-actin-driven
accumulation of RGA-3/4 that lowers the level of RhoA-GTP.
The rate of actomyosin production is given by:
Rm(r, m) = Sm+kar2−kdm, (4)
where Smis the basal rate of actomyosin production, kais the
actomyosin assembly rate and kdis the disassembly rate. The
chemical reactions are coupled to mechanical deformations in
the cytoskeleton, described as an active viscoelastic material
with strain u(t)and dynamics given by:
Eu +η˙u=−σa
m
m0+m,(5)
Inhibitor
Strain
Activator
a
g
S
a
RhoA
acto-
myosin
100
RhoA Concentration r
10-1
100
101
Actomyosin Concentration m
10-2
10-4 10-2 100
RhoA Concentration r
100
101
10-1
10-2
10-4 10-2
0 100 200 300
Time (s)
0.0
0.5
1.0
1.5
2.0
Actomyosin Concentration m
Quiescent
Excitable
Pulsatile
Contractile
0.0 0.2 0.4
Active Contractile Stress σa/E
0.00
0.01
0.02
0.03
0.04
0.05
0.06
Applied Stimulus S [s-1]
Pulsatile
Contractile
(a) (b) (c)
(d) (e)
Excitable
actomyosin nullcline
trajectory
RhoA nullcline
Actomyosin Concentration m
FIG. 1. Mechanical feedback sustains pulsatile contractions in ex-
citable active medium. (a) Feedback loop schematic of the system.
Solid lines indicate biochemical feedback. Dashed lines indicate me-
chanical feedback. (b-c) Trajectory curves and nullclines showing
the fixed points for RhoA (blue) and actomyosin (orange) in the ex-
citable (b) and in the pulsatile regime (c). Black arrows on the trajec-
tory are equally spaced in time. Grey arrows show motion in phase
space. Solid circles represent stable fixed points and the open circle is
the unstable fixed point. (d) Concentration of actomyosin over time
in the quiescent phase (S= 0), excitable phase (S= 0.002 s−1),
pulsatile phase (S= 0.025 s−1), and contractile phase (S= 0.075
s−1). (e) Phase diagram of the system, for varying contractile stress,
σa/E, and applied stimulus, S, with η/E = 5s. See Table I in
Supplemental Material for a list of default parameters in the model.
where Eis the compressional elastic modulus, ηis the vis-
cosity, σa(>0) is the maximum active stress arising from
actomyosin-driven contractions, and m0is the concentration
of actomyosin at half-maximum stress. While the mechan-
ical parameters of the cortex are calibrated from available
data [33], the model comes with several unknown reaction
rate constants that we determine by fitting our model to the
experimental time-series data of myosin and RhoA concen-
trations measured in the C. elegans cortex [17]. With these
parameters calibrated, we simulate the system dynamics nu-
merically [34], for different values of activity Sand σa.
The model yields four distinct dynamic behaviours – qui-
escent, excitable, pulsatile, and contractile, depending on the
magnitude of the applied stimulus, S(Fig. S1). For low S,
the system displays an excitable behaviour – a single pulse
of RhoA, followed by a pulse of actomyosin and contractile
strain buildup, before reaching a steady-state (Fig. 1d). This
excitable behaviour can be visualised in phase space as a tra-
jectory about the intersecting nullclines (Fig. 1b). For this ex-
citable pulse, we observed a loop about the high (r, m)fixed
point before settling to a steady state at the lower fixed point.
As the applied stimulus is increased, other behaviours
emerge (Fig. 1d-e). For a small increase in S, we observe sus-
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3
tained pulsatile contractions, when the RhoA nullcline shifts
up (Fig. 1c), resulting in a single fixed point at high concen-
trations and the system is trapped in a limit cycle. At even
higher values of S, the limit cycle is unstable and the pulse
amplitude decays until the system settles in a contracted state
with high actomyosin concentration and strain. Finally, for
very low applied stimulus, we observe a quiescent mode; both
RhoA and actomyosin steadily increase to a fixed set-point.
While pulsatile contractions are observed in the absence of
contractile stress (σa= 0), we find that including mechanical
feedback helps to sustain oscillations over a wider range of
the parameter space (Fig. 1e). As actomyosin drops after
a pulse, the cell relaxes, further reducing both actomyosin
and RhoA concentrations away from a fixed point, allowing
another pulse to occur. Pulsatile contractions have been im-
plicated in coordinating cell shape changes via a mechanical
ratchet [35–37]. Mechanical feedback may be important in
enabling robust control of this morphogenetic ratchet.
Spatial propagation of pulsatile flows and pattern formation.–
To investigate the role of active mechanical stresses and RhoA
signalling on the spatiotemporal regulation of actomyosin
flows, we develop a continuum active gel model of the actin
cortex, coupled to the excitable RhoA signalling network
(Fig. 1a). The actin cortex is modelled as a one-dimensional
Maxwell viscoelastic material, behaving elastically at short
times and remodelling over longer time scales. Local balance
of viscoelastic forces with cytosolic drag and actomyosin-
generated active contractile forces can be written as:
γ(v+τ˙v) = η∂2
xv+σa∂xm
m0+m,(6)
where v(x, t)is the actin flow velocity, γis the frictional drag
coefficient, τis the timescale for viscoelastic relaxation, ηis
the viscosity, σais the active contractile stress, and m0is the
actomyosin concentration at half-maximum stress.
Myosin-induced F-actin flows advect both RhoA and
myosin, leading to their local accumulation due to convergent
flows or depletion via divergent flows. These advective flows
compete with reaction and diffusion of RhoA and actomyosin:
˙r+∂x(rv) = Rr(r, m) + Dr∂2
xr, (7)
˙m+∂x(mv) = Rm(r, m) + Dm∂2
xm, (8)
where Drand Dmare the diffusion coefficients for RhoA and
actomyosin, taken from Nishikawa et al [32]. The default pa-
rameter for active stress and viscoelastic time scale are taken
from Saha et al [33]. The model equations are then numer-
ically integrated [38] in a periodic box of length L= 10λ,
where λ=pη/γ is the hydrodynamic length scale. As
shown in Fig. 2a-c, the numerical solutions predict a wide di-
versity of dynamic states as the active contractility σ0
a=σa/γ
and RhoA stimulus Sare varied– from stationary patterns to
propagating waves and pulsatile flows (Fig. S2).
At low σ0
a, diffusion dominates over advection, giving rise
to spatially uniform concentration profiles that exhibit ex-
citable, oscillatory, or contractile dynamics (Fig. 2c, top row),
0 10050
Active contractility σa’ [μm2/s]
0.00
0.02
0.04
0.06
Applied Stimulus S [s-1]
050 100
0.00
0.02
0.04
0.06
S [s-1]
0.15
0.20
0.25
Wave Speed [μm/s]
σa’ [μm2/s]
(a) (b)
0
200
400
600
t (s)
0 5 10
x/λ
0
200
400
600
t (s)
0 5 10
x/λ
0 5 10
x/λ
0
Max
Actomyosin Concentration m
(c) Excitable Oscillatory Contractile
Propagating wavesLocalized contraction Pulsatile flows
Wave- like s tates
FIG. 2. Active stress generates spatial patterns and pulsatory flows.
(a) Phase diagram of the dynamic states of the system as a func-
tion of applied Rho stimulus Sand active contractility σ0
a=σa/γ.
Encircled data points correspond to kymographs in panel (c). (b)
Actomyosin wave speed, computed from linear stability analysis of
the model equations, for varying Sand σ0
a. (c) Kymograph of acto-
myosin concentration in different regimes (left to right, top to bot-
tom): excitable, oscillatory, homogeneous contractile, localised con-
tractions, propagating waves and pulsatile flows. See Supplemental
Tables I and II for a list of model parameters.
as observed in the ODE model (Fig. 1). In the absence of me-
chanical feedback, reaction-diffusion alone cannot generate
spatial patterns because the activator, RhoA, diffuses much
faster than the inhibitor, actomyosin (DrDm). When
DrDm, the homogeneous state becomes unstable and
Turing patterns emerge (Fig. S3). This regime, however, is not
realistic for the cortex since Dr> Dm. As σ0
ais increased,
contractile instabilities develop due to local accumulation of
actomyosin, allowing finite wavelength patterns to emerge.
At low Sand high σ0
a, we observe stable localized peaks of
actomyosin and RhoA (Fig. 2c, bottom left). Initially, auto-
catalytic positive feedback of RhoA creates small RhoA con-
centration peaks (Fig. 3a, 1st panel), which in turn produce
actomyosin (Fig. 3a, 2nd panel). As actomyosin begins to
accumulate, large inward flows are generated, further increas-
ing both RhoA and actomyosin concentrations (Fig. 3a, 3rd
panel). Finally, actomyosin-induced inhibition of RhoA re-
sults in RhoA localization on either side of the actomyosin
peak (Fig. 3a, 4th panel), in contrast to Turing patterns where
activators and inhibitors overlap. With no RhoA advection,
RhoA diffuses away from the peak, producing actomyosin
behind it and generates a travelling wave (Fig. S4a). With
no actomyosin advection, actomyosin concentrations remain
too low to prevent RhoA from diffusing and create a uniform
steady state (Fig. S4b). When several contractile actomyosin
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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprintthis version posted February 23, 2021. ; https://doi.org/10.1101/2021.02.22.432369doi: bioRxiv preprint
4
0 2 4
x/λ
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Concentration
024
x/λ
024
x/λ
0 2 4
x/λ
RhoA
acto
myosin
0 2 4
x/λ
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Concentration
024
x/λ 024
x/λ 0 2 4
x/λ
(a)
(b)
Localized contraction
Pulsatile flows RhoA
acto
myosin
t=5s
t=15s t=25s t=35s
t=500s
t=520s t=540s t=565s
FIG. 3. Feedback mechanisms for pulsatile flows and stationary pat-
tern formation. (a) RhoA and actomyosin concentration during local-
ized contraction (σ0
a= 80 µm2/s, S= 0) at t = 5s, 15s, 25s, and 35s
(left to right). (b) RhoA and actomyosin concentration profiles over
a pulsatile flow cycle (σ0
a= 80 µm2/s, S= 0.1s−1) at t = 500s,
520s, 540s, and 565s (left to right). Arrows indicate flow velocity.
foci exist, they attract each other and merge into a single peak.
At higher Sand moderate σ0
a, we observe propagating
waves and pulsatile flows (Fig. 2c, bottom). A higher level
of excitation in RhoA generates a localized actomyosin peak
with high contractility. Away from the actomyosin peak,
RhoA concentrations are higher and are advected towards ac-
tomyosin (Fig. 3b, 1st panel). Advected RhoA produces ac-
tomyosin as it moves, such that the newly assembled acto-
myosin generates flows away from the centre, reducing the
actomyosin concentration at the centre (Fig. 3a, 2nd panel).
Once the initial contraction dissipates, the two remaining ac-
tomyosin peaks merge, completing a cycle (Fig. 3a, panels
3-4). In propagating states, we observe periodic RhoA pulses,
but as σ0
ais increased, actomyosin pulses generate large con-
tractile flows that advect neighboring pulses, creating chaotic
motion. Here, advection is necessary for the waves to form
(Fig. S4d). Without advection of RhoA however, we may
still observe waves, since the actomyosin generated by RhoA
forms clusters that travel with RhoA (Fig. S4c). However,
these waves display much less chaotic motion when compared
to the system with advection (Fig. 2c, bottom right).
Linear stability analysis of the continuum model reveals
the role of active stress in destabilising the homogeneous
state of the system (Fig. 2b, Fig. S5). At low S, three fixed
points exist (Fig. 1b), with the lower fixed point being stable
for high σ0
a. As Sis increased, the RhoA nullcline shifts up
until only one fixed point remains and the system enters the
pulsatile regime (Fig. 1c). Increasing σ0
aleads to contractile
instabilities that manifest as propagating waves and pulsatile
flows (Fig. 2c). While active stress is required for wave
propagation, higher σ0
aleads to lower wave speeds (Fig. 2b).
Response to local bursts of contractile activity.– While our
model can capture many of the dynamic states observed in
the actin cortex, cells must have the ability to actively switch
between flowing and contractile states during physiological
0246810
x/λ
0
200
400
600
800
1000
t (s)
0246810
x/λ
0.00
0.25
0.50
0.75
1.00
1.25
RhoA Concentration r
0246810
x/λ
06020 40
Active Contractility σa’ [μm2/s]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Mean RhoA Concentration
06020 40
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
RhoA-Input Cross-correlation
(a)
(b) (c) Memoryless Transient
Memory
High
Memory
σa’=12.5 σa’=25 σa’=50
Stimulus
ON
Active Contractility σa’ [μm2/s]
FIG. 4. Response to local bursts of contractile activity. (a) Kymo-
graph of Rho concentration upon local transient application of Rho
stimulus: S= 0.03 s−1inside box (dashed rectangle) and S= 0
outside box, for different values of active stress: (left) bistable front
propagation for σ0
a= 12.5µm2/s, (middle) solitons for σ0
a= 25
µm2/s, and (right) localised contraction for σ0
a= 50 µm2/s. (b)
Spatially averaged RhoA concentration, 300s after the application
of stimulus. (c) Correlation between RhoA concentration and input
stimulus S(x, t), averaged over the last 120s.
transitions. Such state transitions may be triggered by a local
up-regulation in RhoA activity, which may be induced in re-
sponse to mechanical forces or by cell cycle checkpoints. It is
unclear how local bursts in RhoA activity spatially propagates
or for how long the effects of the signal persist.
To understand how RhoA signals can propagate through
space and induce state transitions, we locally turned on RhoA
activity and examined the output response. Starting from rest
with no applied stimulus (S= 0), an increased stimulus is ap-
plied at the central region (S= 0.03 s−1) (Fig. 4a). By chang-
ing active stress in the system, we are able to regulate both the
ability for the input RhoA to propagate in space, and for the
system to remember the spatial location of the signal. We
observed three distinct phases (Fig. 4a): (i) propagation of a
bistable front, where the memory of the signal location is lost
and a global increase in RhoA concentration is observed, (ii)
a soliton phase with transient spatial memory, and (iii) a high
memory phase where a stable RhoA pattern is maintained.
At low active stress (σ0
a= 12.5µm2/s), RhoA is excited
into a pulsatile state within the activation region, while spread-
ing laterally through diffusion (Fig. 4a, left). A front of highly
concentrated RhoA travels away from the source, increasing
the total RhoA and actomyosin in the system (Fig. 4b). This
is reminiscent of a bistable front propagation in classical ex-
citable systems [39,40], where the system switches to the high
concentration stationary state (Fig. 2c).
As active stress is increased, we find that mechanical feed-
back is able to tune the properties of the biochemical system
away from classical excitable systems. At moderate active
stress (σ0
a= 25 µm2/s), RhoA pulses spread out as two soli-
tons before annihilating as they meet (Fig. 4a, middle), as
seen in surface contraction waves [18]. In contrast to classi-
cal excitable systems, actomyosin generated behind the RhoA
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wavefront increases its own concentration through contractile
flows. This region of highly concentrated actomyosin behind
the wave acts as a barrier that inhibits RhoA, preventing the
system from switching to the high fixed point, and instead cre-
ates a soliton. Such a barrier can be seen at σ0
a, although it is
too weak to prevent diffusion, with the band of reduced RhoA
concentration behind the wavefront (Fig. 4a, left).
At high active stress (σ0
a= 50 µm2/s), the contractile forces
within the activated region are strong enough to maintain a
spatially localized state that persists after the activation, re-
maining stationary in a fixed location at the centre of activa-
tion (Fig. 4a, right). This suggests a potential mechanism for
cells to direct the locations of contractility. Without the guid-
ance of RhoA activation, the system in this parameter regime
is incapable of spontaneously forming a stable pattern.
To quantify the input-output relationship of the system, we
measured the correlation between the input signal and the out-
put RhoA concentration at long times (Fig. 4c). At low σ0
a,
RhoA spreads outwards, leading to a loss of correlation be-
tween input and the output signal, akin to a memoryless sys-
tem. For the soliton case, the shape of the input signal is
remembered, resulting in a negative correlation as the waves
travel away from the source. Finally, in the spatially patterned
phase, a high-memory state emerges where RhoA remains lo-
calized at the centre of activation, with a strong positive corre-
lation between the input and the output. These results suggest
that mechanical stresses play an important role in biochemical
signal propagation, and in retaining the spatial memory of ac-
tivity. For low active stress, signals propagate the fastest with
global changes in contractility and no memory of the spatial
location of the signal. As active stress is increased, we observe
contraction waves propagating away from the source, display-
ing transient memory. At higher stresses, a high memory state
develops, where transient local RhoA activations create local-
ized contractile states.
Discussion.– Chemical signalling and mechanical forces are
both essential to regulate the dynamics of the cellular actin
cortex. We demonstrate that mechanochemical couplings are
necessary to generate waves, patterns and pulsatile dynamics
in the actin cytoskeleton, with mechanical feedback helping
to robustly sustain pulsatile contractions, and provide a new
mechanism for spatial patterning of RhoA and actomyosin,
distinct from classical Turing patterns [23]. At low RhoA ac-
tivity and high contractile activity, actomyosin forms station-
ary patterns, with RhoA localized on either side of the acto-
myosin peak. At moderate RhoA activity and stress, we ob-
serve periodic waves of actomyosin which annihilate before
new wavefronts are generated in regions with low actomyosin
concentration (Fig. S2c). This is reminiscent of RhoA waves
in starfish eggs [16]. As contractile activity is increased, the
waves of actomyosin become highly peaked, generating pul-
satile dynamics (Fig. S2c), reminiscent of pulsed contractions
observed in the C. elegans cortex [5]. Besides generating
patterns and flows, the level of active contractile stress reg-
ulates the system’s response to local RhoA signals, enabling
phase transitions and memory entrainment as the activity is
increased. Together, these results show the importance of con-
sidering both mechanical forces and chemical reactions when
modelling the actin cortex, and present several ways for cells
to alter their dynamic mechanical behaviour.
∗shiladtb@andrew.cmu.edu
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