1

FRET imaging and statistical signal processing reveal positive and negative feedback

loops regulating the morphology of randomly migrating HT-1080 cells.

Katsuyuki Kunida,1 Michiyuki Matsuda,

1,2 and Kazuhiro Aoki

2,3, *

1 Department of Pathology and Biology of Diseases, Graduate School of Medicine, Kyoto

University, Sakyo-ku, Kyoto 606-8501, Japan

2 Laboratory of Bioimaging and Cell Signaling, Graduate School of Biostudies, Kyoto

University, Sakyo-ku, Kyoto 606-8501, Japan

3 PREST, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama

332-0012, Japan

* Author for correspondence (k-aoki@lif.kyoto-u.ac.jp)

Running title: Feedback loops in random cell migration.

Key words: Rac1, FRET, feedback, adaptation

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Summary

Cell migration plays an important role in many physiological processes. Rho GTPases (Rac1,

Cdc42, RhoA) and phosphatidyl inositols have been extensively studied in directional cell

migration. However, it remains unclear how Rho GTPases and phosphatidyl inositols

regulate random cell migration in space and time. Here, we attempt to address this issue by

fluorescence resonance energy transfer (FRET) imaging and statistical signal processing.

First, we acquired time-lapse images of random migration in HT-1080 fibrosarcoma cells

expressing FRET biosensors of Rho GTPases and phosphatidyl inositols. We developed an

image processing algorithm to extract FRET values and velocities at the leading edge of

migrating cells. Auto- and cross-correlation analysis suggested the involvement of feedback

regulations among Rac1, phosphatidyl inositols, and membrane protrusions. To verify the

feedback regulations, we employed an acute inhibition of the signaling pathway with

pharmaceutical inhibitors. The inhibition of actin polymerization decreased Rac1 activity,

indicating the presence of positive feedback from actin polymerization to Rac1. Furthermore,

treatment with PI3-kinase inhibitor induced an adaptation of Rac1 activity, i.e., a transient

reduction of Rac1 activity followed by recovery to the basal level. In silico modeling that

reproduced the adaptation predicted the existence of a negative feedback loop from Rac1 to

actin polymerization. Finally, we identified MLCK as a convincing factor for the negative

feedback. These findings quantitatively demonstrate positive and negative feedback loops

that are comprised of actin, Rac1 and MLCK, and account for the ordered patterns of

membrane dynamics observed in randomly migrating cells.

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Introduction

Cell migration is an essential process in a wide variety of biological phenomena, such as

embryonic development, wound repair, immune surveillance, tumor cell invasion and

metastasis in mammalian cells (Lauffenburger and Horwitz, 1996). Extracellular cues elicit

the various intracellular responses in the organization of both the actin and the microtubule

cytoskeletons. It is widely accepted that the major driving force of migration is the extension

of a leading edge protrusion or lamellipodia, cell body contraction, and detachment of

adhesions at the cell rear (Rajakulendran et al., 2009). All these steps involve the assembly,

disassembly, and reorganization of the actin cytoskeleton, which are coordinated both in

space and time (Mitchison and Cramer, 1996) (Rajakulendran et al., 2009).

The molecular mechanisms of cell migration have been extensively studied in tissue

culture cells. Rho GTPases and lipid kinases have been identified as key regulators of cell

migration. The best-characterized function of Rho GTPases is in the regulation of actin

dynamics: RhoA increases the actomyosin contractility, whereas Rac1 and Cdc42 induce the

polymerization of actin to form lamellipodial and filopodial protrusions, respectively (Ridley,

2001). Phosphatidyl inositols, which are composed of a D-myo-inositol-1-phosphate linked

via its phosphate group to diacylglycerol, are phosphorylated and dephosphorylated by

phosphatidyl inositol kinases and phosphatases, generating distinct phosphoinositide species

(Saarikangas et al., 2010). Among them, phosphatidyl inositol trisphosphate (PI(3,4,5)P3) and

phosphatidyl inositol bisphosphates (PI(3,4)P2 and PI(4,5)P2) regulate reorganization of actin

cytoskeleton by providing a membrane-binding platform for a variety of proteins, including

guanine nucleotide exchange factors (GEFs) for Rho GTPases and actin filament nucleating

proteins (Saarikangas et al., 2010). With the advent of a myriad of fluorescent proteins,

genetically encoded biosensors have been increasingly utilized to visualize the activities of

Rho GTPases and phosphatidyl inositols (Aoki et al., 2008; Miyawaki, 2003). In particular,

live cell imagings with biosensors based on the principle of Förster (or fluorescence)

resonance energy transfer (FRFT) have uncovered the spatio-temporal dynamics of these

molecules in migrating cells (Itoh et al., 2002; Kurokawa and Matsuda, 2005; Nishioka et al.,

2008) .

Morphological polarization is required for cell migration, enabling cells to turn

intracellularly generated forces into net cell body translocations, i.e., a clear distinction

between cell front and rear (Lauffenburger and Horwitz, 1996). It has been suggested that

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intrinsic mechanisms of intracellular signaling systems with their kinetic fluctuations or noise

suffice to emerge this front-rear polarization during the locomotion of eukaryotic motile cells.

For example, spatially homogenous stimulation with a chemoattractant, at least for

neutrophils, induces a front-rear polarity with a change in filamentous actin (F-actin)

distribution from azimuthal symmetry around the cell rim to concentration within a particular

region (Coates et al., 1992; Lauffenburger and Horwitz, 1996). In addition, even in the

absence of concentration gradients of external stimuli, ordered patterns of cell shape are

observed in Dictyostelium, flies and mammalian cells, such as directional migration,

oscillation behavior of membranes, and lateral traveling waves along the cell boundary

(Dobereiner et al., 2006; Machacek and Danuser, 2006; Maeda et al., 2008; Weiner et al.,

2007). The Turing’s reaction-diffusion model is one of the most supported models for the

formation of ordered patterns in migrating cells (Gierer and Meinhardt, 1972; Kondo and

Miura, 2010; Otsuji et al., 2010). On the basis of a framework in the reaction-diffusion model,

self-enhancing positive and negative feedback regulations play a pivotal role in the

autonomous emergence of an ordered pattern. It is suggested that PI(3,4,5)P3, Rac1 and actin

cytoskeleton are part of a positive feedback loop that can initiate polarization (Peyrollier et al.,

2000; Srinivasan et al., 2003; Wang et al., 2002; Weiner et al., 2002). However, contrary to

these models, rapid activation of endogenous Rac1 proteins triggered effective actin

polymerization but failed to activate phosphatidyl inositol 3-kinase (PI3-K) to generate

PI(3,4,5)P3 or induce cell polarization (Inoue and Meyer, 2008). Furthermore, the molecular

mechanisms of such negative feedback loops remain largely unknown. Here we attempt to

identify molecular mechanisms of positive and negative feedback loops underlying the

random migration of mammalian cells by utilizing FRET imaging with statistical signal

processing.

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Results

Time-lapse imaging of Rho GTPases, phosphatidyl inositols, and F-actin in randomly

migrating HT-1080 cells.

We aimed to elucidate the molecular networks of Rho GTPases and phosphatidyl inositols in

randomly migrating mammalian cells by time-lapse imaging. In this study, we used human

HT-1080 fibrosarcoma cells, which exhibited a high motility and invasiveness, as a model

system of spontaneous random migration (Hoffman, 2005; Itoh et al., 2002). All experiments

presented below employed the use of the time-lapse images of HT-1080 cells 1 hour after

seeding on collagen-coated glass-bottom dishes to induce spontaneous migration. The HT-

1080 cells expressing biosensors were imaged every 1 min for 2 hours in order to minimize

photo-toxicity and photo-bleaching.

We first examined the activity of the Rho GTPases Rac1, Cdc42 and RhoA in

migrating HT-1080 cells by using the FRET biosensors Raichu-Rac1, Raichu-Cdc42, and

Raichu-RhoA, respectively. As reported previously (Itoh et al., 2002; Kraynov et al., 2000;

Nalbant et al., 2004), Rac1 and Cdc42 were locally activated at lamellipodia and membrane

ruffles at the leading edge, and inactivated at the retracting tail of migrating cells (Fig. 1A,B;

supplementary materials Movies 1, 2). On the other hand, activation of RhoA was observed

at both the leading edge and retracting tail (Fig. 1C; supplementary material Movie 3). This

result was also consistent with the previous findings (Kurokawa and Matsuda, 2005; Pertz et

al., 2006).

The spatio-temporal localization of phosphatidyl inositols was also visualized with the

FRET biosensors (Aoki et al., 2005; Nishioka et al., 2008), Pippi- PI(3,4,5)P3, Pippi-

PI(3,4)P2, and Pippi-PI(4,5)P2. PI(3,4,5)P3 was accumulated at the leading edge of migrating

HT-1080 cells (Fig. 1D; supplementary material Movie 4), supporting the previous report that

PI(3,4,5)P3 recruits and activates guanine nucleotide exchange factor(s) for Rac1and

Cdc42(Aoki et al., 2005; Schmidt and Hall, 2002). PI(3,4)P2 and PI(4,5)P2 were also found to

be accumulated at the front of migrating HT-1080 cells (Fig. 1E,F; supplementary material

Movies 5, 6). The increase in PI(3,4)P2 and PI(4,5)P2 at the lamellipodia of migrating cells

could be attributed to the rapid turnover of these lipids (Nishioka et al., 2008).

We also examined the accumulation of F-actin in HT-1080 cells with Lifeact-EGFP, a

marker of F-actin (Riedl et al., 2008). To correctly evaluate the accumulation of F-actin at

membrane ruffles and pseudopodia (Dewitt et al., 2009), DsRed-express fused with a nuclear

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export sequence (ERed-NES) was coexpressed with Lifeact-EGFP, and used as a reference of

the volume of cytoplasm. The leading edge of migrating cells demonstrated a higher ratio of

Lifeact-EGFP signal to ERed-NES signal, clearly showing the actin polymerization (Fig. 1G;

supplementary material Movie 7). Notably, a negative control of the FRET biosensor, which

included a Cdc42 and Rac1 interacting binding (CRIB) domain of PAK1 and RhoA, did not

show any spatial or temporal change of FRET signal in HT-1080 cells (Fig. 1H).

Of note, lateral propagation of membrane protrusion and retraction were frequently

observed around the cell periphery of migrating HT-1080 cells (Fig. 1, arrows), implying the

possibility that common mechanisms underlie the ordered pattern of membrane dynamics as

observed in the migration of other eukaryotic cells (Dobereiner et al., 2006; Machacek and

Danuser, 2006; Maeda et al., 2008).

Quantification of morphological dynamics by auto-correlation analysis.

To quantitatively evaluate the morphological changes, the edge velocity of membrane

displacement was quantified at the whole cell periphery by a modified mechanical model

(Machacek and Danuser, 2006). Briefly, the distance between a window on the cell periphery

at time T and that at time T+1 was measured by processing time-lapse images (Fig. 2A,B;

supplementary material Fig. S1). Then, the edge velocity was calculated and represented in a

heat map as a function of the time and the sampling window around the cell periphery (see

Materials and Methods for details) (Fig. 2C). Although there existed apparent heterogeneity

of the pattern in the edge velocity map among migrating HT-1080 cells, we often recognized

a periodic pattern, as shown in Fig. 2C. In almost all cases, migrating cells exhibited one

protrusion and one retracting tail, indicating the acquisition of front-back polarity even in the

absence of a concentration gradient of external stimuli.

We next classified the migration pattern of HT-1080 cells by applying auto-

correlation analysis to the edge velocity map (Dobereiner et al., 2006; Maeda et al., 2008).

The auto-correlation function (ACF) in Fig. 2D represents the wave-like pattern,

demonstrating the occurrence of the lateral membrane wave along the cell boundary. With the

temporal ACF (Window no. = 0, dashed line in Fig. 2D), three parameters, t0, tmin, and

tmax, were defined as shown in Fig. 2E. The pattern of ACF map and threshold criteria of t0

value (t0 > 30 min) were utilized to classify the pattern of morphological dynamics into four

categories: wave-like, oscillatory, directional, and non-classifiable mode (Maeda et al., 2008)

(see Materials and Methods in detail) (Fig. 2F; supplementary material Movie 8). Almost half

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of HT-1080 cells demonstrated the wave-like mode of migration (Table 1). Furthermore, the

velocity of the lateral membrane wave, VL, was calculated as 4.2 ± 2.1 m/min by dividing

the length of the cell periphery by tmax. These results suggested the existence of an intrinsic

signaling network that established an ordered pattern of morphological dynamics without

external stimuli. Notably, the expression of FRET biosensors per se did not significantly

perturb the mode of cell migration in HT-1080 cells (supplementary material Fig. S2).

Therefore, in the following study, we examined a molecular mechanism for generating wave-

like motion in randomly migrating HT-1080 cells.

Quantification of correlation and time delay between morphological change and

signaling by cross-correlation analysis.

To identify a hierarchical connection among Rho GTPases, phosphatidyl inositols, and

morphological change, we used a cross-correlation analysis and characterized their temporal

correlation (Machacek et al., 2009; Tsukada et al., 2008). The cross-correlation function

(CCF) between edge velocity (Fig. 3A) and Rac1 activity (Fig. 3B) was calculated with Rac1

activity being fixed as described in the Materials and Methods (Fig. 3C). Temporal CCF was

also extracted (Fig. 3C, dotted line) to analyze the lag time of signaling and morphological

change (Fig. 3D; supplementary materials Fig. S3 and Table S1).

The positive peak value of the cross correlation coefficient was obtained with a time

delay of - 2.2 min (95% confidence interval (CI), -3.0 to -1.4 min) from Rac1 activity,

indicating that the edge velocity was increased prior to the increase in Rac1 activity and vice

versa (Fig. 3E). On the other hand, taking the interval of image acquisition (every 1 min) into

account, the Cdc42 activity was slightly delayed or nearly synchronized with morphological

change (time delay of - 1.3 min, 95% CI, -2.2 to -0.5 min) (supplementary material Fig. S4A).

RhoA activity did not demonstrate any correlation with edge velocity (peak value of 0.082)

(supplementary material Fig. S4B). This was likely because the high RhoA activity at both

protrusion and retraction during cell migration marginally contributed to the overall

correlation, leading to an offset of the net correlation coefficient value (Kurokawa and

Matsuda, 2005). Furthermore, F-actin accumulation was coupled to the edge velocity with a

time delay of - 0.25 min (95% CI, -1.5 to 1.0 min) (Fig. 3F). We have time-lapse imaged

Rac1 activity and F-actin accumulation every 30 sec in migrating HT-1080 cells,

demonstrating the time delay values of – 2.6 min (95% CI, -3.3 to -1.5 min) and – 0.9 min

(95% CI, -1.4 to -0.4 min) for Rac1 activity and F-actin, respectively (supplementary

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materials Fig. S5 and Table S1). These values are consistent with those obtained by imaging

with the time interval of 1 min. Of note, we previously demonstrated that EGF-induced Rac1

activation preceded the lamellipodial extension in Cos1 cells (Kurokawa et al., 2004). Thus,

the role of Rac1 appears to be different between growth factor-induced and stochastic

membrane protrusions.

Cross-correlation analysis revealed that PI(3,4,5)P3 accumulation was almost

synchronized with membrane protrusion (time delay of -1.1 min, 95% CI, -1.8 to -0.5 min)

(Fig. 3G). The downstream metabolites, PI(3,4)P2, demonstrated a time delay of -1.6 min in

comparison to the edge velocity (95% CI, -2.3 to -0.8 min) (supplementary material Fig.

S4C). Meanwhile, PI(4,5)P2 accumulation was delayed 1.4 min (95% CI, -2.0 to -0.7 min)

(supplementary material Fig. S4D). In migrating MDCK cells, phosphatidyl inositol 5-kinase

and PLC-, but not PI3-K, mainly contribute to the distribution of PI(4,5)P2 at lamellipodia of

the leading edge, suggesting a possible role of phosphatidyl inositol 5-kinase and PLC- in

random migration in HT-1080 cells (Nishioka et al., 2008). As expected, the negative control

FRET biosensor did not show any significant correlation with edge velocity (Fig. 3H).

In brief, the cross-correlation analysis showed sequential relationship among signaling

molecules and morphological change in the following temporal order: (1) PI(3,4,5)P3

accumulation and morphological change (polymerized actin localization), (2) PI(3,4)P2

accumulation and Cdc42 activation, and (3) Rac1 activation.

Perturbation analysis of the signaling pathway

Rac1 induces actin reorganization and, consequently, lamellipodial formation (Hall, 1998).

According to this scheme, the delay in Rac1 activation shown in Fig. 3 implies a positive

feedback regulation from actin polymerization to Rac1 in migrating HT-1080 cells. To

explore this assumption, we examined the effects of the F-actin depolymerizers Latrunculin B

and Cytochalasin D on PI(3,4,5)P3 accumulation and Rac1 activity. Latrunculin B (Fig.

4A,B) and Cytochalasin D (supplementary material Fig. S6A,B) treatment did not induce any

change of PI(3,4,5)P3 level, but were associated with a decrease in Rac1 activity (Fig. 4C,D).

These results indicated that actin polymerization activated Rac1 by a positive feedback

mechanism. Cdc42 activity was not suppressed by Latrunculin B or Cytochalasin D treatment

(data not shown), although the reason for this finding remains unknown. Therefore, we

focused on only Rac1 activity in the following study. Next, we investigated another positive

feedback mechanism from Rac1 to PI3-K (Aoki et al., 2007; Weiner et al., 2002) by the

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inducible translocation technique (Inoue et al., 2005). Rapamycin triggers heterodimerization

formation of a Lyn N-terminal sequence-tagged FRB (LDR) with an FKBP-fused protein.

Upon Rapamycin treatment, FKBP-Tiam1 was translocated to the plasma membrane, and

consequently activated Rac1within 2 min, followed by the lamellipodia formation (Fig. 4E,G).

However, rapid activation of Rac1 did not increase the PI(3,4,5)P3 level (Fig. 4F,H). These

findings demonstrated that the positive feedback pathway composed of Rac1 and PI3-K did

not contribute to the signaling network in migrating HT-1080 cells as reported in HL-60

neutrophils (Inoue and Meyer, 2008).

The results of auto-correlation analysis, which showed a wave-like pattern of

membrane dynamics, prompted us to investigate a negative feedback loop among Rac1,

phosphatidyl inositols and morphological change. We found that treatment with a PI3-K

inhibitor, LY294002, induced an immediate and transient decrease in Rac1 activity to below

the basal level, and suppressed lamellipodial protrusions (Fig. 4J,L). Interestingly, Rac1

activity and the morphological repression returned to the basal levels within 20 min even

though PI(3,4,5)P3 was sustained at low levels for at least 30 min after treatment with

LY294002 (Fig. 4I,K). We confirmed these findings by using another PI3-K inhibitor, PIK-

93 (Knight et al., 2006) (supplementary material Fig. S6C,D).

Prediction of a network topology consisting of PI3-K, Rac1 and F-actin

The transient Rac1 suppression by PI3-K inhibition may be caused by adaptation, i.e., the

ability of the signaling network to reset itself after responding to a stimulus. A recent study

revealed that an adaptation emerges from only two major topologies of a signaling network: a

negative feedback loop with a buffering node and an incoherent feed forward loop with a

proportioner node (Ma et al., 2009). This study urged us to explore possible kinetic models in

PI3-K, Rac1 and actin polymerization modules by considering the following two constraints:

(1) the inhibition of actin polymerization induces a sustained decrease in Rac1 activity, and

(2) Rac1 activity and actin polymerization adapt to PI3-K inhibition. Because Rac1 activation

did not affect PI3-K, we set PI3-K as an input. Actin polymerization was set as an output for

the membrane protrusion. In preliminary simulations, Rac1 was located between PI3-K and

actin-polymerization (supplementary material Fig. S7). None of the models derived from this

topology could fulfill the aforementioned constraints because actin polymerization cannot

positively regulate Rac1.

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Therefore, four models of possible networks with an additional “node” were

constructed to reproduce the experimental results obtained by cross-correlation and

perturbation analyses (Fig. 5A). In these models, we considered that actin polymerization

corresponded to the edge velocity. The numerical simulation in every proposed models

reproduced the effect of actin polymerization inhibitors and PI3-K inhibitors on the change in

Rac1 activity—namely, sustained decrease and adaptation, respectively (Fig. 5B in Model A

and supplementary materials Fig. S8-10 in Model B-D and Tables S2-5).

Role of MLCK as a buffering node among PI3-K, F-actin and Rac1 signaling modules

To distinguish these four models, we searched for candidate molecules that might act as

nodes in the signaling scheme. In particular, we focused on negative regulators for actin

reorganization and Rac1 signaling, and found that myosin light chain kinase (MLCK) and/or

its target signaling played a role in a buffering node of the network. To visualize MLCK

accumulation, the high molecular weight isoform of human MLCK1 tagged with GFP at the

N-terminus, hereafter referred to as EGFP-Long-MLCK, was expressed in HT-1080 cells

(Poperechnaya et al., 2000). EGFP-Long-MLCK demonstrated clear accumulation at not only

the retracting tail, but also the leading edge of migrating HT-1080 cells (Fig. 6A). The

temporal CCF demonstrated a positive peak of correlation efficiency at the time delay of

approximately -4.0 min (95% CI, -4.9 to -3.1 min) (Fig. 6B, arrow). Furthermore, the

negative correlation coefficient peak was obtained at the positive time delay of around 0.5

min (95% CI, -0.8 to 1.8 min) (Fig. 6B, arrowhead). These delay timing values did not

correlate with the expression level of EGFP-Long-MLCK, negating the artificial effect of

over-expression of Long-MLCK on the migration in HT-1080 cells (supplementary material

Fig. S11). To validate the relationship between MLCK and Rac1, we examined whether rapid

activation of Rac1 induced translocation of MLCK to the periphery of the membrane. As

expected, Rapamycin-induced hetero-dimerization between LDR and FKBP-Tiam1 activated

Rac1, which in turn increased the level of localization of EGFP-Long-MLCK at the

peripheral membrane (Fig. 6C, arrows) with a delay of 4.6 min (Fig. 6D). In addition,

treatment with an MLCK-inhibitor, ML-7, induced a rapid increase in Rac1 activity (Fig.

6E,F).Thus, a reaction from Rac1 to MLCK accounted for a mechanism of buffering node,

which was postulated in Model A (Fig. 5). Finally, we examined the involvement of ROCK,

which was well-known to regulate myosin contractility (Totsukawa et al., 2004). ROCK

inhibitor, Y27632, was added to the media of HT-1080 cells expressing Raichu-Rac1 to

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observe whether or not Y27632 increased Rac1 activity as ML-7 does. Unexpectedly,

however, Y27632 did not significantly alter Rac1 activity, although Y27632 induced typical

morphological changes in ROCK inhibition: long protrusions and a sickle-cell shape

(supplementary material Fig. S12). These results strongly supported the negative feedback

loop in Model A, in which the MLCK pathway acted as a buffering node for the negative

feedback.

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Discussion

In this study, we have revealed a signaling network comprised of positive and negative

feedback regulations among PI3-K, actin polymerization, Rac1, and MLCK in randomly

migrating HT-1080 cells (Fig. 7A). On the basis of the auto- and cross-correlation analyses,

we can summarize the relative delay timing in comparison to edge velocity change (Fig. 7B)

and the process of signaling and membrane protrusion/retraction as follows (Fig. 7C). In the

first phase of protrusion, the edge velocity takes a positive value, indicating membrane

extension and actin polymerization (0 min). Simultaneously or slightly after membrane

protrusion, PI(3,4,5)P3 is accumulated at the tip of the protrusion. In the second phase, after

the initiation of membrane extension (2 min), Rac1 activity is increased. In the third phase (4

min), MLCK accumulates at the tip of the leading edge in a Rac1-dependent manner, and

consequently decelerates the edge velocity via actin reorganization. According to the results

of the auto-correlation analysis, the lateral membrane wave revolves around the cell

periphery with a periodicity of 40 min. Thus, the edge velocity, Rac1 activity, and MLCK

localization reach a peak at 10, 12, and 14 min, respectively. Meanwhile, the edge position of

the cell periphery is described by integrating the edge velocity value, and demonstrates a

peak at 20 min after the start of the increase in edge velocity (Fig. 7C, grey line). The latter

half of the process, i.e., retraction, represents the same sequential process in which the edge

velocity and molecular activities show negative and low values, respectively.

We propose that a reaction-diffusion system of the signaling network generates the

lateral propagation of waves around the cell periphery (Kondo and Miura, 2010). The

positive feedback loop from Rac1 to actin polymerization amplifies the increase in the edge

velocity and the lamellipodia protrusion. This actin polymerization signal diffuses laterally

along the cell periphery. Meanwhile, the negative feedback loop comprising MLCK as a

buffering node and Rac1 as the input, respectively, retracts the membrane with a time delay.

Consistent with this idea, Otsuji et al. have reported a mass-conserved reaction diffusion with

positive and negative feedback loops, which reproduces characteristic behaviors of

membrane dynamics including lateral wave propagation (Otsuji et al., 2010). Our data

provide a molecular basis for their mathematical modeling. Furthermore, Arai et al. have

found that self-organized waves of PI(3,4,5)P3 are generated spontaneously on the membrane

of Dictyostelium cells in the presence of Latrunculin B, and have developed a reaction

diffusion model that recapitulates the relaxation oscillator of phosphatidyl inositols dynamics

with positive and negative feedback loops (Arai et al., 2010). This model differs from the

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present models of HT-1080 cells in terms of the signaling hubs: Phosphatidyl inositols play a

central role in the positive and negative regulations in Dictyostelium cells, whereas Rac1 acts

as a signaling hub of two feedback loops as observed in HT-1080 cells. Of note, the velocity

of lateral membrane wave in this study, c.a. 4 m/min (Table 1), was comparable to those in

mouse embryonic fibroblasts (2.4 m/min), fly cells (0.72 m/min), T cells (0.33 m/min)

(Dobereiner et al., 2006), and Dcityostelium cells (2-4 m/min as roughly calculated from

(Arai et al., 2010)), implying the presence of general molecular mechanisms underlying the

random migration of eukaryotic cells.

One of the key findings in this study was that a negative feedback loop from Rac1 to

MLCK enables the system of actin reorganization to adapt to external perturbations. We

assumed that GTP-Rac1 recruits MLCK to the edge of membrane protrusions either directly

or indirectly, leading to the retraction of the peripheral plasma membrane by increasing the

actomyosin contractility. Consistent with this model, MLCK localizes at the leading edge of

lamellipodia in mouse embryonic fibroblasts, and regulates the periodic lamellipodial

contractions (Giannone et al., 2004). The long MLCK directly binds to actin filaments in

vitro and in interphase cells, and these bindings are mediated by five DXRXXL motifs

(Poperechnaya et al., 2000; Smith et al., 2002). The inhibition of ROCK by Y27632 did not

alter Rac1 activity (supplementary material Fig. S12), suggesting two possibilities of the

molecular mechanisms of the negative feedback: First, the negative feedback from MLCK to

Rac1was mediated through myosin that was regulated by MLCK, but not ROCK. There are

many reports showing spatial and functional discrepancies of myosin regulations between

MLCK and ROCK (Totsukawa et al., 2004). Second possibility is that myosin-independent

MLCK activity mediates the negative feedback from MLCK to Rac1. Consistent with this

hypothesis, it has been reported myosin-independent effect of MLCK on migration of

mammalian cells (Kudryashov et al., 1999; Niggli et al., 2006). In disagreement with the

negative feedback model, the rapid and global activation of Rac1by FKBP-Tiam1 and LDR

upon Rapamycin stimulation resulted in global lamellipodial extensions (Fig. 4E,F). This

discrepancy is presumably attributable to the difference of strength and duration in Rac1

activation between randomly migrating cells and cells expressing FKBP-Tiam1. Robust and

sustained activation of Rac1 by the FKBP-Tiam1 translocation system may cause inactivation

of MLCK through phosphorylation by PAK, which is a downstream effector of Rac1

(Sanders et al., 1999). On the other hand, it has been reported that PAK directly

phosphorylates Ser19 of MLC and induces an increase in actomyosin contraction in

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endothelial cells (Chew et al., 1998; Zeng et al., 2000). Therefore, future studies will be

needed to further evaluate the spatial and temporal regulation of MLCK activity in migrating

cells.

Evidence of a pathway from the actin cytoskeleton to Rac1 was provided by cross-

correlation analysis (Fig. 3) and by the Latrunculin B-induced decrease of Rac1 activity (Fig.

4). In this context, we should note that Rac1 induces actin polymerization and formation of

lamellipodia (Hall, 1998) (Fig. 4E,F). These data imply the existence of a positive feedback

loop between the actin cytoskeleton and Rac1. Although it remains unknown how the actin

cytoskeleton regulates Rac1 activity, we can adduce several presumable mechanisms of the

positive feedback loop. Some GEFs acting on Rac1, such as FGDs, Frabin (Nakanishi and

Takai, 2008), and Asef2 (Sagara et al., 2009), interact with F-actin directly or indirectly.

These GEFs are candidates for molecules playing a role in the positive feedback. Furthermore,

focal complexes and adhesions induced by Rac1 at lamellipodia recruit the Cas/Crk/DOCK

signaling complex (Cote and Vuori, 2007; Meller, 2005), and lead to the further activation of

Rac1 in a manner consistent with the positive feedback. Such positive feedback regulation

among PI(3,4,5)P3, Rac1, and actin has been well characterized in Dictyostelium cells,

neutrophils and PC12 cells (Aoki et al., 2007; Iijima et al., 2002; Merlot and Firtel, 2003;

Weiner et al., 2002). In contrast with these earlier works, PI(3,4,5)P3 was not involved in the

positive feedback in the present model (Fig. 7). Consistent with this, Inoue et al. have shown

with HL-60 neutrophils that rapid activation of endogenous Rac1 proteins triggers effective

actin polymerization in the absence of PI-3K activation and increase in PI(3,4,5)P3 (Inoue

and Meyer, 2008).

Cross-correlation analyses have been applied to understand how Rho GTPases

coordinate the morphodynamics (Machacek et al., 2009; Tsukada et al., 2008). Tsukada et al.

have demonstrated, using the edge evolution tracking (EET) method, that the change in cell

edge velocity precedes the activation of Rac1 and Cdc42 with a time delay of ca. 6 and 8 min,

respectively (Tsukada et al., 2008). In contrast, Machacek et al. have shown with a

sophisticated image processing technique that Cdc42 and Rac1 are activated approximately

40 sec after the increase in the edge velocity (Machacek et al., 2009). Differences in the

values of the time delay among these studies and our study, 2.2 min for Rac1, may arise from

two reasons; the differences in image processing algorithms and the use or not of a

classification system for the modes of cell migration. With respect to the first reason,

Machacek et al. analyzed the local area of the cell periphery, i.e., only the protrusive area,

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with image sets acquired by shorter time interval, 10 sec, than ours, 1 min. We, instead,

focused on the global membrane dynamics of protrusion and retraction in the entire cell

periphery of migrating HT-1080 cells. This could cause larger time delay values than those

obtained in Machacek’s study. With respect to the second reason, we classified the modes of

cell migration into four categories – wave-like, oscillatory, directional, and unclassifiable –

and analyzed only the cells that were categorized into the wave-like migration. In contrast,

Tsukada et al. did not use any categorization. Time-delay values obtained from directionally

migrating cells became much greater than those of the cells migrating in the other modes.

Therefore, the use of classification caused shorter delay timing in our study than Tsukada’s

studies. Notably, we assumed that the proposed feedback regulations among Rac1, actin

cytoskeleton and MLCK took place in both protrusions and retractions in migrating HT-1080

cells for the following reasons: (1) Data obtained from cross-correlation analysis at the front

of migrating cells contributed to the total correlation coefficient value to a similar extent as

that obtained at the back of migrating cells. (2) We did not recognize any difference of

correlative relationship of Rac1/Cdc42 activities and edge velocity between the front and

back of cell movements; namely, at the front, increase in edge velocity preceded increase in

Rac1 activity, whereas, at the back, decrease in edge velocity preceded decrease in Rac1

activity. It was also noted that correlation-based multiplexing approach should be carefully

applied to the system with feedback interactions (Sabouri-Ghomi et al., 2008). In our study

the delay timing obtained by correlation analysis was within 2.2 min for Rac1 (Fig. 3);

whereas, the effect of feedback regulation appears at 4-6 min later (Fig. 6). Thus, it is

unlikely that the feedback regulation interferes with the correlation analysis.

By employing image processing, statistical analysis, and pharmacological

perturbations, this study has demonstrated the molecular mechanisms underlying the ordered

membrane dynamics in randomly migrating eukaryotic cells. A pivotal question to be

answered is what factors initiate the increase in edge velocity prior to Rac1 activation. Our

data showed that PI(3,4,5)P3 accumulated concomitantly with the increase in edge velocity

(Fig. 3). Additionally, it has been recently reported that membrane curvature induces actin

polymerization through EFC/F-BAR proteins and the N-WASP-WIP complex (Takano et al.,

2008). In line with this finding, maximal F-actin assembly was observed about 20 sec after

maximal edge advancement (Ji et al., 2008). These results suggest the involvement of lipid

regulation, which serves as a trigger for membrane protrusion. Further studies will be needed

to uncover the molecular mechanism of the dynamics in migratory cells.

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Materials and Methods

FRET biosensors

The plasmids encoding FRET biosensors have been described as follows: Raichu-

Rac1/1011x, pRaichu-Cdc42/1054x (Itoh et al., 2002), pRaichu-RhoA/1294x (Nakamura et

al., 2005; Yoshizaki et al., 2003), pPippi-PI(3,4,5)P3/1747x, pPippi-PI(3,4)P2/1759X(Aoki et

al., 2005; Sato et al., 2003), pPippi-PI(4,5)P2/1758X (Nishioka et al., 2008), and pRaichu-

Pak-Rho/1110x, a negative control (Kurokawa and Matsuda, 2005).

Cells, plasmids and reagents

HT-1080 cells were purchased from the American Type Culture Collection or the Japan Cell

Resource Bank, and maintained in DMEM (Sigma-Aldrich, St. Louis, MO) supplemented

with 10% fetal bovine serum (FBS). The cells were plated on 35-mm glass-base dishes

(Asahi Techno Glass, Tokyo, Japan), which were pre-coated with collagen type I (Nitta

Gelatin Inc., Osaka, Japan). Plasmids were transfected into HT-1080 cells with

Lipofectamine 2000 according to the manufacturer’s protocol (Invitrogen, San Diego, CA).

cDNA of Lifeact, a 17-amino-acid peptide (Riedl et al., 2008), were subcloned into

pCAGGS-EGFP vector. EGFP-Long-MLCK was a kind gift from Dr. Anne R. Bresnick

(Poperechnaya et al., 2000). Expression plasmids for ERed-NES, LDR (Lyn11-targeted FRB),

FKBP and FKBP-Tiam1 have been described previously (Aoki et al., 2007; Inoue et al.,

2005). cDNA for FKBP-iSH2 was subcloned into pCAGGS-GST vector to obtain pCAGGS-

GST-FKBP-iSH2 (Inoue and Meyer, 2008). LY294002 were obtained from Sigma-Aldrich

(St. Louis, MO). Latrunculin B, Cytochalasin D, ML-7 and Y27632 were purchased from

Calbiochem (La Jolla, CA). PIK-93, which is a PI3K inhibitor, was obtained from

SYMANSIS (NZ, CA). Rapamycin was purchased from LC Laboratories (Woburn, MA).

Time-lapse FRET imaging

Images for FRET imaging were obtained and processed by using essentially the same

conditions as previously reported (Aoki and Matsuda, 2009). Briefly, HT-1080 cells

expressing biosensors were suspended by trypsin, plated on collagen-coated 35-mm glass-

base dishes, and waited at approximately one hour after plating. During plating, the culture

medium was replaced with phenol red-free DMEM/F12 containing 10% FBS, and overlaid

with mineral oil to prevent evaporation. Cells were imaged with an inverted microscope

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(IX81; Olympus, Tokyo, Japan) equipped with a x60 objective lens (Olympus), a cooled

CCD camera (Cool SNAP-K4; Roper Scientific), an LED illumination system (CoolLED

precisExcite; Molecular Device), an IX2-ZDC laser-based autofocusing system (Olympus)

and an MD-XY30100T-Meta automatically programmable XY stage (SIGMA KOKI, Tokyo,

Japan). The following filters were used for the dual emission imaging studies: excitation

filters, 435/20 for CFP and FRET (Olympus), S492/18x for GFP (Chroma), and 580AF20 for

RFP (Omega Optical, Brattleboro, VT); dichroic mirrors, XF2034 for CFP and FRET

(Omega), and 86006bs for GFP and RFP (Chroma); emission filters, 480AF30 for CFP

(Omega), 535AF26 for FRET and GFP (Omega), and 635DF55 for RFP (Omega). The

exposure time was 400 msec for CFP and FRET images when the binning was set to 4×4.

After background subtraction, FRET/CFP ratio images were created with MetaMorph

software (Universal Imaging, West Chester, PA), and represented by the intensity modulated

display mode. In the intensity-modulated display mode, eight colors from red to blue are used

to represent the FRET/CFP ratio, with the intensity of each color indicating the average

intensity of FRET and CFP.

Mapping of velocity and molecular activity in the leading edge

The velocity of the leading edge in migrating HT-1080 cells was calculated by a mechanical

model with some modifications (Machacek and Danuser, 2006). The process was divided

into two steps: (1) image processing and (2) velocity calculating.

(1) Image processing: First, FRET or GFP images were binarized by the threshold

value, which was determined arbitrarily to identify the cell edge (supplementary material Fig.

S1A,B). Second, an Erode operation was applied to the binarized images three times to

reduce the noise of the periphery (supplementary material Fig. S1C). Third, the outline of the

eroded images was captured the line-scanning to correct the data of 2D coordinates and

FRET/CFP ratio values of the cell periphery (supplementary material Fig. S1D). These

processes were implemented by MetaMorph software (Universal Imaging). There was no use

of interior positions, only the edge positions.

(2) Velocity calculating: First, the data of XY coordinates and FRET/CFP ratio values,

which were obtained by the image processing, were normalized to 200 sampling windows.

Second, to quantify the edge velocity, the window that was located at an angle of 0 degrees

from the centroid was set as an initial point (Fig. 2A). Third, normal vectors were obtained

along the cell boundary (supplementary material Fig. S1E). Normal vector angles were

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affected especially in the region with strong boundary deformation (Machacek and Danuser,

2006). Therefore, fourth, the normal vector angles were corrected by averaging angles of 5

backward and 5 forward vectors (supplementary material Fig. S1F). Lastly, by using the

averaged vectors, the boundary displacement at the time of T was obtained by calculating the

minimum distance from the point at the time of T to the point at the time of T + 1, and

divided by the interval time of imaging to obtain the edge velocity (supplementary material

Fig. S1G). We denoted the matrices of edge velocity and molecular activity/localization as

{M(x, t)| 0 ≤ x ≤ 200, 0 ≤ t} and {F(x, t)| 0 ≤ x ≤ 200, 0 ≤ t}, respectively. These processes

were implemented by Matlab software (version R2010b; The Mathworks Inc., Natick, MA).

Correlation analysis

The auto- and cross-correlation analysis was performed essentially as described previously

(Maeda et al., 2008). The auto-correlation functions of M(x, t) and F(x, t), and the cross-

correlation function between M(x, t) and F(x, t) are defined as

tx

tx

tx

txttxxtx

,

2

ave

,aveave

M),(M

M),(MM),(M,ACF

21

21

,

2

ave,

2

ave

,aveave

F),(FM),(M

F),(FM),(M,CCF

txtx

tx

txtx

txttxxtx

,

where the numbers Mave and Fave indicate the average value of M(x, t) and F(x, t),

respectively. The operator < >x,t denotes the averages over time and over space. The range of

calculation is the entire period of measurement in time and space from 0 to 200. Correlation

analyses were implemented by Matlab software.

Classification of migration pattern

Patterns of random migration in HT-1080 cells, i.e., wave-like, oscillatory, directional, and

non-classifiable migration, were categorized based on the ordered pattern of auto-correlation

function in edge velocity, as shown in Fig. 2F. First, non-classifiable disordered pattern of the

auto-correlation function was discriminated from the other migration patterns. Then,

directional migration was classified as a value of t0 > 30 min defined as a threshold criteria

in the temporal auto-correlation function (Space = 0, dashed line in Fig. 2D). Finally, wave-

like migration was distinguished from oscillatory migration by the typical wavy shapes in the

auto-correlation function.

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Modeling and numerical simulation

All kinetic reactions in Model A to D (Fig. 5) were described by ordinary differential

equations based on Michaelis-Menten kinetics. Equations and parameters in Model A to D

are listed in supplementary materials Tables S2-5, respectively. Numerical simulation was

performed by Matlab software. To achieve the adaptation, we presumed one constraint: The

reaction rates and Michaelis constants of the buffering node (knode and Kmnode) were set to

small values as compared with their substrate in order to saturate their reaction rates (Ma et

al., 2009).

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Acknowledgments

We thank A.R. Bresnick for the plasmids and Y. Sakumura for the helpful discussion. Y.

Inaoka, K. Hirano, R. Sakai, A. Katsumata, N. Nonaka, and A. Kawagishi are also to be

thanked for their technical assistance. We are grateful to the members of the Matsuda

Laboratory for their helpful input. K.K. was supported by a Grant-in-Aid for JSPS Fellows.

K.A. was supported by the JST PRESTO program. M.M. was supported by the Research

Program of Innovative Cell Biology by Innovative Technology (Cell Innovation) from the

Ministry of Education, Culture, Sports, and Science (MEXT), Japan. The authors have no

competing financial interests to declare.

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Yoshizaki, H., Ohba, Y., Kurokawa, K., Itoh, R. E., Nakamura, T., Mochizuki, N., Nagashima,

K. and Matsuda, M. (2003). Activity of Rho-family GTPases during cell division as visualized with

FRET-based probes. J.Cell Biol. 162, 223-232.

Zeng, Q., Lagunoff, D., Masaracchia, R., Goeckeler, Z., Cote, G. and Wysolmerski, R. (2000).

Endothelial cell retraction is induced by PAK2 monophosphorylation of myosin II. Journal of Cell

Science 113 ( Pt 3), 471-82.

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Figure legends

Fig. 1. Spatio-temporal activity maps of signaling molecules in randomly migrating HT-

1080 cells. HT1080 cells transfected with the plasmid encoding indicated biosensors were

imaged for CFP and FRET every 1 min. FRET/CFP ratio ranges in IMD mode are shown at

the right of each image. The scale bar is 10 m. (A-F, H) Montage images show the

spontaneous cell migration of HT-1080 cells expressing the biosensors Raichu-Rac1 (A),

Raichu-Cdc42 (B), Raichu-RhoA (C), Pippi-PI(3,4,5)P3 (D), Pippi-PI(3,4)P2 (E), Pippi-

PI(4,5)P2 (F), and Raichu-PAK-Rho (H). (G) The montage image represents the ratio of

Lifeact-EGFP to ERed-NES.

Fig. 2. Quantification of morphological dynamics by auto-correlation analysis. (A) Left

and middle panels show the cell boundaries extracted by image processing at the time of T

and T+1, respectively. The window with the angle of 0 in polar display is defined as an initial

window. The right panel indicates the merged cell boundary with edge velocity (see Materials

and Methods; supplementary material Fig. S1). Red and blue lines represent the positive and

negative velocity at each window, respectively. (B) Edge velocities are plotted as a function

of the window number (Window no.) between the frame T and frame T+1 (A, left and right

panel, respectively). (C) Edge velocity is represented as a function of the sampling windows

and time. Red and blue indicate protrusion and retraction, respectively. (D) The auto-

correlation function of the edge velocity map is shown as a function of the shift of the

sampling window (Window no.) and the shift of time (Time). (E) The temporal auto-

correlation function (Window no. = 0, dotted line in D) is plotted as a function of Time.

t0, tmin, and tmax are shown as red dots (see Results). (F) Representative heat maps of

auto-correlation coefficients, which were classified into wave-like, oscillatory, directional,

and non-classifiable migrations, are shown as a function of Window no. and Time.

Fig. 3. Quantification of the dynamics between morphological change and signaling

molecules by cross-correlation analysis. (A and B) Edge velocity (A) and Rac1 activity, i.e.,

the FRET/CFP ratio value (B), are represented as a function of the sampling windows and

time. (C) The cross-correlation function between edge velocity and Rac1 activity is

represented as a function of Window no. and Time. The edge velocity map was shifted to

obtain the cross-correlation function. (D) The temporal cross-correlation function (Window

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no. = 0, dotted line in C) is plotted as a function of Time. The maximum value of the

temporal cross-correlation coefficient is obtained at a time lag of -2 min from Rac1 activation

(arrowhead), indicating that membrane protrusion is initiated 2 min before Rac1 activation.

(E-H) The temporal cross-correlations between edge velocity and Rac1 activity (E), F-actin

(F), PI(3,4,5)P3 (G), and a negative control (H) are shown for individual cells (gray). Red

lines indicate the average temporal cross-correlation function; N = 6 (Rac1), N = 8 (F-actin),

N = 7 (PI(3,4,5)P3), and N = 5 (negative control). See supplementary materials Fig. S3 and

Table S1 for the details.

Fig. 4. Perturbation analysis of PI3-K-Rac1-Actin signaling by chemical inhibitors. (A-

D) HT-1080 cells expressing Pippi-PI(3,4,5)P3 (A) or Raichu-Rac1 (B) were treated with 100

nM Latrunculin B, and imaged every 1 min. FRET images at the indicated time points after

latrunculin B addition are shown in IMD mode. Ratio ranges in IMD mode are shown at the

right of each image. The scale bar is 10 m. (C and D) FRET/CFP ratios of Pippi-PI(3,4,5)P3

(C) or Raichu-Rac1 (D) for the individual cells (black) were expressed by measuring the

increase over the basal activity, which was averaged over 10 min before Latrunculin B

addition. Red lines indicate the average FRET/CFP ratio; N = 4 (C), N = 9 (D). (E-H) HT-

1080 cells expressing LDR and FKBP-Tiam1 with Raichu-Rac1 (E) and Pippi-PI(3,4,5)P3 (F)

were treated with 100 nM Rapamycin, and imaged every 1 min. FRET images are shown in

A and B. The scale bar is 10 m. (G and H) FRET/CFP ratios of Raichu-Rac1 (G) and Pippi-

PI(3,4,5)P3 (H) for the individual cells (black) and their average (red) are shown as described

in C and D; N = 10 (G), N = 7 (H). (I-L) HT-1080 cells expressing Raichu-Rac1 (I) and

Pippi-PI(3,4,5)P3 (J) were treated with 20 M LY294002, and imaged every 1 min. FRET

images are shown in A and B. The scale bar is 10 m. (K and L) FRET/CFP ratios of Raichu-

Rac1 (K) and Pippi-PI(3,4,5)P3 (L) for the individual cells (black) and their average (red) are

shown as described in C and D; N = 9 (G), N = 10 (H).

Fig. 5. In silico modeling and simulation of PI3-K-Rac1-Actin signaling. (A) On the basis

of the results in Fig. 4C, D, K, and L, four possible models were considered. Model A and

Model B included a negative feedback loop with a buffering node (case 1). Model C and

Model D included an incoherent feedforward loop with a proportioner node (case 2). All

these models assume the existence of a hypothetical “node” molecule. (B) Ordinary

differential equations in Model A were described by the Michaelis-Menten scheme, and

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numerically solved. Left and right graphs show the time course of PI(3,4,5)P3 (orange), F-

actin (green), Rac1 (red), and node (blue) as a function of time after PI3-K inhibition and

actin polymerization inhibition, respectively. PI3-K inhibition decreases 90% of the PI3-K

level at time 0. On the other hand, actin polymerization inhibition reduces the F-actin level to

0 at time 0. All reactions and parameters are shown in supplementary materials Tables S2-5.

Fig. 6. Identification of MLCK as a buffering node of the negative feedback loop. (A)

HT-1080 cells expressing the long isoform of MLCK fused with EGFP (EGFP-Long-MLCK)

and ERed-NES as a cytoplasmic reference were imaged every 1 min. EGFP and ratio images

at the indicated time points are shown. Ratio ranges in IMD mode are shown at the right of

each image. The scale bar is 10 m. (B) Temporal cross-correlation between edge velocity

and Long-MLCK localization are shown for individual cells (gray). Red lines indicate

average temporal cross-correlation function; N = 6. (C and D) HT-1080 cells expressing LDR

and FKBP-Tiam1 with EGFP-Long-MLCK and ERed-NES were treated with 100 nM

rapamycin, and imaged every 1 min. The ratio images are shown in A. Arrow heads indicate

the accumulation of EGFP-Long-MLCK after Rapamycin treatment. The scale bar is 10 m.

(D) The mean EGFP-MLCK/ERed-NES ratios at the cell periphery (red and green circles) or

FRET/CFP ratios of Raichu-Rac1 over the whole cell (blue circles) are represented by

measuring the relative increase as compared with the reference value at 0 min of Rapamycin

addition. FKBP-Tiam1 and FKBP were used as Rac1 activator (blue and red) and control

(green), respectively. Blue and red lines represent curves fitted with single exponential

function, and rac1 and mlck are their time constants. Bars represent SD; N = 5 (Rac1), N = 6

(MLCK), and N = 5 (control). (E and F) HT-1080 cells expressing Raichu-Rac1 were treated

with 20 M ML-7, an MLCK inhibitor, and imaged every 1 min. FRET images are shown in

Fig. 1A. The scale bar is 10 m. (F) FRET/CFP ratios of Raichu-Rac1for the individual cells

(grey) and their average (red) are shown as described in Fig. 4D; N = 5.

Fig. 7. Signaling network in randomly migrating HT-1080 cells. (A) Schematic

representation of the signaling network among PI3-K, actin polymerization, Rac1, and

MLCK is shown as a pathway diagram. Negative and positive feedback loops are expressed

in blue and red dashed boxes, respectively. (B) Cross-correlation coefficients of Rac1, F-actin,

PI(3,4,5)P3, and MLCK (maximum and minimum) are plotted as a function of relative timing

from edge velocity change. Bars represent 95% confidence intervals. (C) The sequential order

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of edge velocity (actin polymerization), Rac1, MLCK, and edge position are shown as a

function of time. The edge position of the cell periphery is obtained by integrating the edge

velocity value. The time shifts of Rac1 and MLCK from edge velocity are 2 min and 5.5 min,

respectively. Based on the results of auto-correlation analysis, the lateral membrane wave

revolves around the cell periphery with a periodicity of 40 min.

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PI(3,4,5)P3 (FRET/CFP)

Rac1 (FRET/CFP)

0.9

1.80 (min) 20 10

0.90

1.650 (min) 20 10

Cdc42 (FRET/CFP)

1.3

2.0

RhoA (FRET/CFP)

1.2

2.2Actin (Lifeact-EGFP/NES-ERed)

0

15

Negative control (FRET/CFP)

0.9

2.2

PI(3,4)P2 (FRET/CFP)

0.80

1.55

PI(4,5)P2 (FRET/CFP)

1.05

1.65

0 (min) 20 10

0 (min) 20 10

0 (min) 20 10

0 (min) 20 10

0 (min) 20 10

0 (min) 20 10

A

B

C

D

E

F

G

H

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∆Time (min)

Oscillatory

1.0

-0.50 60-60

0

100

-100

Δ W

indo

w n

o.

Δ W

indo

w n

o.

Δ W

indo

w n

o.

× 0200

1

50

100

150

=-

T+1T

∆Time (min)

1.0

-0.50 60-60

0

100

-100

∆ W

indo

w n

o.

Auto-correlation coefficient Auto-correlation coefficient Auto-correlation coefficient Auto-correlation coefficient

Auto-correlation coefficient

Window no.0 100 200

-8.0

8.0

0

Protrusion

Retraction

-4.0

4.0

Time (min)

Win

dow

no.

0 60 1200

200

100

Wave-like

1.0

-0.50 60-60

0

100

-100

Δ W

indo

w n

o.

∆Time (min)

Non-classifiable

1.0

-0.5

0 60-60

0

100

-100

∆Time (min)

Directional

1.0

-0.50 60-60

0

100

-100

∆Time (min)

Δtmin

∆Time (min)0 10

Aut

o-co

rrel

atio

nco

effic

ient

1.0

-0.5

0

0.5

20 30

ΔtmaxΔt0

● ● ●

Edge velocity (µm/min)

Edg

e ve

loci

ty (µ

m/m

in)

A B

C D E

F

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Cro

ss-c

orre

latio

n co

effic

ient

30

0

-0.4

-0.2

0.4

0 2010-20-30 -10

0.2

Negative control

∆Time (min)

protrusionBefore

protrusionAfter

Cro

ss-c

orre

latio

n co

effic

ient

30

0

-0.4

-0.2

0.4

0 2010-20-30 -10

0.2

Actin

∆Time (min)

protrusionBefore

protrusionAfter

-0.3 min

E F

G H

▼ ▼0.6

0

-0.4

-0.2

0.4

0.2

0 2010-20-30 -10Cro

ss-c

orre

latio

n co

effic

ient

∆Time (min)

Rac1

protrusionBefore

protrusionAfter

-2.2 min

30

▼

Cro

ss-c

orre

latio

n co

effic

ient 0.6

0

-0.4

-0.2

0.4

0.2

0 2010-20-30 -10

PI(3,4,5)P3

∆Time (min)

protrusionBefore

protrusionAfter

-1.1 min

30

-4.0

4.0

Time (min)

Win

dow

no.

0 60 1200

200

100

Edge velocity (µm/min)

Win

dow

no.

Rac1 activity (FRET/CFP)

2.5

1.50 60 120

0

200

100

Time (min)

0.8

-0.40 60-60

0

100

-100

Cross-correlation coefficient

∆Win

dow

no.

∆Time (min)

Rac1

Beforeprotrusion

Afterprotrusion

0 60-60

0.6

0.3

0

-0.3

▼

Cro

ss-c

orre

latio

n c

oeffi

cien

t∆Time (min)

A B

C D

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1 5 10 20０(min)

1.45

3.25

+ Latrunculin B

Rac

1P

I(3,4

,5)P

3R

ac1

PI(3

,4,5

)P3

Rac

1P

I(3,4

,5)P

31 5 10 20０(min)

+ Latrunculin B

0.95

2.3

30Time (min)

-10 0 10 20

1.04

1.00

0.96

0.92

0.88

Nor

mal

ized

FR

ET/

CFP

ratio

Rac1

Time (min)-10 0 10 20 30

1.04

1.00

0.96

0.92

0.88

Nor

mal

ized

FR

ET/

CFP

ratio

PI(3,4,5)P3

1 5 10 20０(min)

+ LY294002

1 5 10 20０(min)

+ LY294002

1.2

1.8

0.85

2.0

1.03

1.00

0.97

0.94

0.91

Time (min)-10 0 10 20 30

Nor

mal

ized

FR

ET/

CFP

ratio

Rac11.02

1.00

0.98

0.96

0.94

Time (min)-10 0 10 20 30

Nor

mal

ized

FR

ET/

CFP

ratio

PI(3,4,5)P3

1 5 10 20０(min)

1 5 10 20０(min)

1.2

2.2

+ Rapamycin

+ Rapamycin 0.7

1.8

1.1

1.0

1.2

1.3

0.9

Time (min)-10 0 10 20 30

Nor

mal

ized

FR

ET/

CFP

ratio

Rac1

1.1

1.0

1.2

0.9

Time (min)-10 0 10 20 30

Nor

mal

ized

FR

ET/

CFP

ratio

PI(3,4,5)P3

A

B

C D

E

F

G H

I

J

K L

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Case1: Negative feedback loop with a buffering node

Case2: Incoherent feedforward loop with a proportioner node

Model A Model B

Model C Model D

Numerical simulation in Model A

PI3-K

Protrusion

Rac1

Node

Actinpolymerization

PI(3,4,5)P3

PI3-K

Protrusion

Rac1

Node

Actinpolymerization

PI(3,4,5)P3

PI3-K

Protrusion

Rac1

Node

Actinpolymerization

PI(3,4,5)P3

PI3-K

Protrusion

Actinpolymerization Rac1

NodePI(3,4,5)P3

Actin polymerizationinhibition

1.0

0.6

0.2

-0.2

Time (min)-10 0 10 20 30

Nor

mal

ized

conc

entra

tion PI(3,4,5)P

F-actinRac1Node

3 3PI(3,4,5)PF-actinRac1Node

1.0

0.8

0.6

0.4

Time (min)-10 0 10 20 30

Nor

mal

ized

conc

entra

tion

PI3-K inhibition

A

B

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+Rapamycin

0 min 4 min

+Rapamycin

0 min 4 min

A B0 (min)

0 (min)

EGFP-MLCK localization

EGFP-MLCK/ERed-NES ratio image10

10

5

5

C D

EF

2 40 (min)

+ ML-7

Rac1

Rac1

Nor

mal

ized

FR

ET/

CFP

ratio

1.08

1.04

1.00

0.96

0.92

Time (min)-10 0 10 20 30

0 20 3010-20-30 -10∆Time (min)

Cro

ss-c

orre

latio

n co

effic

ient

MLCK accumulation

0

-0.2

0.2

-0.4

0.4

0.5 min

▼

-4.0 min

▼

Rac1(Experiment)Rac1(Fitting)

MLCK(Experiment)MLCK(Fitting)

Control

EG

FP-M

LCK

/ER

edN

ES

ratio

Rac1 activity

Time after Rapamycin treatment (min)0 2 4 6 8 10

1.3

1.2

1.1

1.0

0.9

***

1.3

1.2

1.1

1.0

0.9

τrac1=1.1

EG

FP-M

LCK

lo

caliz

atio

n im

age

EG

FP-M

LCK

/E

Red

-NE

S ra

tio ia

mge

τmlck=5.7

▼▼

▼

▼

▼▼

0.5

5.5

0

1.5

1.4

2.3

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A

C

B

1.0

1.5

0

-0.5

0.5

-1.0

-1.50 10 20 30 40

Time (min)

Ral

ativ

e va

lue

Edge velocityRac1MLCKEdge position

PI3-K

Negativefeedback loop

Protrusion

Rac1

MLCK

Actinpolymerization

PI(3,4,5)P3

Positivefeedback loop

-0.4

-0.2

0.0

0.2

0.4

0.6

-2.0 0.0 2.0 4.0 6.0

Cro

ss-c

oeffi

cien

t coe

ffici

ent

Time after edge velocity change (min)

Rac1

Actin

PI(3,4,5)P3

MLCK_Max

MLCK_Min

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Table 1: Classification of migration mode based on the auto-correlation analysis

Wave-like Oscillatory Directional Unclassifiable

Percent (%) 42 6 32 20

Length (m) 124 ± 35.4 126 ± 23.9 126 ± 31.7 129 ± 23.1

t0 (minute) 10.7 ± 7.54 16.8 ± 8.6 48 ± 22.1 39.6 ± 36.6

tmin (minute) 19.9 ± 14.8 14.3 ± 3.2 － －

tmax (minute) 39.8 ± 24.9 29.0 ± 9.8 － －

VL m/minute) 4.2 ± 2.1 4.4 ± 1.0 － －

More than forty cells were analyzed and classified as described in Materials and Methods.

Average values are listed with SD.

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Unit normal vector Averaged vector

cell

T+1T

cell

T

cell

T

Edge velocity

A

E

Binarize

Erode Linescan

FRET or GFP image B

C D

F

G

Fig. S1. Image processing for calculating edge velocity. The procedures for image processing are as follows. FRET (FRET biosensor) or GFP (Lifeact-EGFP and EGFP-Long-MLCK) images (A) are acquired and processed by a binary operation with an arbitrary threshold value (B). The images are treated with an Erode operation to reduce the noise of the cell periphery (C). Then, the outline of the eroded images is captured by line scan to correct the data of XY coordinates and the FRET/CFP ratio value of the cell periphery. The XY coordinates are normalized to 200 sampling windows. Then, normal vectors are obtained along the cell periphery (E). The angles are corrected by averaging angles of 5 backward and 5 forward vectors to obtain averaged vectors (F). By using the averaged vectors, the boundary displacement at the time of T is obtained by calculating the minimum distance from the point at the time of T to the point at the time of T + 1, and divided by the interval time of imaging to obtain the edge velocity.

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0

10

20

30

40

50

60 FRET biosensorsGFP reporters

Frac

tion

(%)

Wav

e-lik

e

Osc

illat

ory

Dire

ctio

nal

Unc

lass

ified

Fig. S2. Effect of the expression of FRET biosensors on the mode of cell migration. The acquired image data were grouped into GFP reporter-expressing cells (N = 39) and FRET biosensor-expressing cells (N = 69). The mode of migration was classified into four categories as described in Materials and Methods. The data show the effect of FRET biosensors on the cell migration is negligible.

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B

C D

E F

G H

A Edge Velocity (μm/min)

Time (min)

2.5

1.50 60 120

0

200

100

Win

dow

no.

-4.0

4.0

Time (min)0 60 120

0

200

100

Cdc42 activity

Win

dow

no.

ΔTime (min)

0.8

-0.40 60-60

0

100

-100

∆ W

indo

w n

o.Cross-correlation

coefficient

60ΔTime (min)

0-60

0.8

-0.4

0

0.4

Cro

ss-c

orre

latio

nco

effic

ient

FRE

T/CFP

ratio

0

4.0

-4.00

200

100

Edge Velocity (μm/min)

Time (min)6020 40

Win

dow

no.

2.2

3.6

Time (min)0 60

0

200

100

RhoA activity

20 40

Win

dow

no.

ΔTime (min)

0.5

-0.20 30-30

0

100

-100 ∆ W

indo

w n

o.

Cross-correlationcoefficient

0.3

-0.1

0.1

0.5

ΔTime (min)0 30-30

Cro

ss-c

orre

latio

nco

effic

ient

FRE

T/CFP

ratio

Edge Velocity (μm/min)4.0

-4.00

200

100

Time (min)0 6020 40

Win

dow

no.

2.2

3.6

Time (min)0 600

200

100

20 40

PI(3,4,5)P3 accumulation W

indo

w n

o.

FRE

T/CFP

ratio

ΔTime (min)

0.5

-0.20 30-30

0

100

-100 ∆ W

indo

w n

o.

Cross-correlationcoefficient

ΔTime (min)0 30-30

0.3

-0.1

0.1

0.5

Cro

ss-c

orre

latio

nco

effic

ient

3.0

-3.00

200

100

Time (min)0 60 120

Edge Velocity (μm/min)

Win

dow

no.

1.2

2.0

0

200

100

PI(3,4)P2 accumulation

Time (min)0 60 120

Win

dow

no. FR

ET/C

FP ratio

ΔTime (min)

0.3

-0.10 60-60

0

100

-100 ∆ W

indo

w n

o.

Cross-correlationcoefficient

ΔTime (min)0 60-60

0.3

-0.1

0

0.1

0.2

Cro

ss-c

orre

latio

nco

effic

ient

4.0

-4.00

200

100

Edge Velocity (μm/min)

Time (min)0 60 120

Win

dow

no.

1.1

1.8

0

200

100

PI(4,5)P2 accumulation

FRE

T/CFP

ratio

Time (min)0 60 120

Win

dow

no.

ΔTime (min)

0.4

-0.10 60-60

0

100

-100

∆ W

indo

w n

o.

Cross-correlationcoefficient

0.4

-0.2

0

0.2

ΔTime (min)0 60-60

Cro

ss-c

orre

latio

nco

effic

ient

Time (min)

4.0

-4.00

200

100

Edge Velocity (μm/min)

0 6020 40

Win

dow

no.

ΔTime (min)

0.3

-0.10 30-30

0

100

-100 ∆ W

indo

w n

o.

Cross-correlationcoefficient

ΔTime (min)0 30-30

0.4

-0.2

0

0.2

Cro

ss-c

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nco

effic

ient

2.5

7.0

Time (min)0 60

0

200

100

20 40

Actin

Win

dow

no.

EG

FP/R

FP ratio

Time (min)

2.0

-2.00

200

100

Edge Velocity (μm/min)

0 60 120

Win

dow

no.

Time (min)

0.5

1.4

0

200

100

MLCK accumulation

0 60 120

Win

dow

no.

GFP

/RFP

ratio

ΔTime (min)

0.25

-0.20 60-60

0

100

-100 ∆ W

indo

w n

o.

Cross-correlationcoefficient

ΔTime (min)0 60-60

0.2

-0.2

0

Cro

ss-c

orre

latio

nco

effic

ient

Time (min)

3.0

-3.00

200

100

0 60 120

Win

dow

no.

Edge Velocity (μm/min)

ΔTime (min)

1.0

-0.50 60-60

0

100

-100 ∆ W

indo

w n

o.

Cross-correlationcoefficient

ΔTime (min)0 60-60

1.0

0

-0.5

0.5

Cro

ss-c

orre

latio

nco

effic

ient

0.8

3.5

0

200

100

Negative control

FRE

T/CFP

ratio

Time (min)0 60 120

Win

dow

no.

Fig. S3. Representative data of cross-correlation analysis. Each data set consists of 4 panels: upper left, edge velocity map; upper right, molecular activity/localization map; lower left, cross-correlation function (CCF); lower right, temporal cross-correlation function (TCCF), which corresponds to the white dotted line of CCF. The biosensors are as follows: Cdc42 (A), RhoA (B), PI(3,4,5)P3 (C), PI(3,4)P2 (D), PI(4,5)P2 (E), F-actin (F), MLCK localization (G), and a negative control (H). These data are available upon request.

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Cro

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Cro

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Cro

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Cro

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0.6

0

-0.4

-0.2

0.4

0.2

0 2010-20-30 -10

Cdc42

∆Time (min)30

0.6

0

-0.4

-0.2

0.4

0.2

0 20 3010-20-30 -10

RhoA

∆Time (min)

0.6

0

-0.4

-0.2

0.4

0.2

0 20 3010-20-30 -10

PI(3,4)P2

∆Time (min)30

0.6

0

-0.4

-0.2

0.4

0.2

0 2010-20-30 -10

PI(4,5)P2

∆Time (min)

▼

▼▼

protrusion protrusion

protrusion protrusion protrusion protrusion

BeforeAfterprotrusion

Beforeprotrusion

After

BeforeAfter BeforeAfter

-1.3 min

-1.6 min -1.4 min

A B

C D

Fig. S4. Quantification of the dynamics between morphological change and signaling molecules by cross-correlation analysis. The temporal cross-correlations between edge velocity and Cdc42 activity (A), RhoA activity (B), PI(3,4)P2 (C), and PI(4,5)P2 (D) are shown for individual cells (gray). Red lines indicate the average temporal cross-correlation function; N = 6 (Cdc42), N = 6 (RhoA), N = 7 (PI(3,4)P2), N = 5 (PI(4,5)P2). See supplementary materials Fig. S3 and Table S1 for the details.Jo

urna

l of C

ell S

cien

ceA

ccep

ted

man

uscr

ipt

A

0 2010-20-30 -10

Rac1

30

▼

protrusion protrusionAfter

0.6

0

-0.4

-0.2

0.4

0.2

∆Time (min)

Before

Cro

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ient

-2.4 min

B

0 2010-20-30 -10

Actin

30

▼

protrusion protrusionAfter

0.6

0

-0.4

-0.2

0.4

0.2

∆Time (min)

Before

Cro

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-0.9 min

Fig. S5. Effect of the interval of time-lapse imaging on the cross-correlation analysis. HT-1080 cells expressing Raichu-Rac1 (A) or Lifeact-EGFP and ERed-NES (B) wrer imaged for CFP and FRET every 30 sec to The temporal cross-correlations between edge velocity and Rac1 activity (A), F-actin (B) are shown for individual cells (gray). Red lines indicate the average temporal cross-correlation function; N = 5 (Rac1), N = 5 (F-actin).

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Rac1 PI(3,4,5)P3A B

C D

Time (min)-10 0 10 20 30

1.04

1.00

0.96

0.92

← Cytochalasin DN

orm

aliz

ed F

RE

T/C

FP ra

tio ← Cytochalasin D

-10 0 10 20 30

1.00

0.96

0.92

Rac1 PI(3,4,5)P3

-10 0 10 20 30

← PIK931.04

1.00

0.96

0.92

-10 0 10 20 30

1.04

1.02

1.00

0.98

0.94

0.96

← PIK93

Nor

mal

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FR

ET/

CFP

ratio

Nor

mal

ized

FR

ET/

CFP

ratio

Nor

mal

ized

FR

ET/

CFP

ratio

Time (min)

Time (min)

Time (min)

Fig. S6. Perturbation analysis of PI3-K-Rac1-Actin signaling by chemical inhibitors. (A and B) HT-1080 cells expressing Pippi-PI(3,4,5)P3 (A) or Raichu-Rac1 (B) were treated with 10 µM Cytochalasin D, and imaged every 1 min. FRET/CFP ratios of Pippi-PI(3,4,5)P3 or Raichu-Rac1 for the individual cells (black) were expressed by measuring the increase over the basal activity, which was averaged over 10 min before cytochalasin D addition. Red lines indicate the average FRET/CFP ratio; N = 4 (A), N = 4 (B). (C and D) HT-1080 cells expressing Pippi-PI(3,4,5)P3 (C) or Raichu-Rac1 (D) were treated with 10 µM PIK-93, and imaged every 1 min. FRET/CFP ratios of Pippi-PI(3,4,5)P3 or Raichu-Rac1 for the individual cells (black) were expressed by measuring the increase over the basal activity, which was averaged over 10 min before PIK-93 addition. Red lines indicate the average FRET/CFP ratio; N = 7 (C), N = 5 (D).

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Model 1

PI3-K

Protrusion

Rac1

Node

Actinpolymerization

PI(3,4,5)P3

Fig. S7. Excluded models. Four signaling models are illustrated as in Fig. 5A. These models reproduce an adaptation of Rac1 activity induced by PI3-K inhibition; however, the models cannot represent a decrease of Rac1 activity upon inhibition of Actin polymerization.

PI3-K

Protrusion

Rac1

Node

Actinpolymerization

PI(3,4,5)P3

PI3-K

Protrusion

Rac1

Node

Actinpolymerization

PI(3,4,5)P3

Model 2 Model 3

PI3-K

Protrusion

Rac1

Node

Actinpolymerization

PI(3,4,5)P3

Model 4

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Numerical simulation in Model B

Time (min)-10 0 10 20 30

PI(3,4,5)P3

0.8

1.0

0.6

0.4N

orm

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ed

conc

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30Time (min)

-10 0 10 20

Actin

0.9

1.0

0.8

0.7

1.1

Nor

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co

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Time (min)-10 0 10 20 30

0.9

1.0

0.8

0.7

1.1Rac1

Nor

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ized

co

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Node

Time (min)-10 0 10 20 30

2.0

2.5

1.5

1.0

Nor

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co

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Time (min)-10 0 10 20 30

0.6

1.0

0.2

1.4

Nor

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co

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n

Actin

30Time (min)

-10 0 10 20

0.6

1.0

0.2

1.4

Nor

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co

ncen

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Rac1

10

20

0

Nor

mal

ized

co

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n

Time (min)-10 0 10 20 30

Node

0.6

1.0

0.2

1.4

Nor

mal

ized

co

ncen

tratio

n

Time (min)-10 0 10 20 30

PI(3,4,5)P3

PI3-K inhibition

Actin polymerization inhibitionB

A

Fig. S8. Numerical simulation of Model B. Model B in Fig. 5 was described by the Michaelis-Menten scheme and numerically solved. (A) Each graph shows the time course of PI(3,4,5)P3 (orange, top left), F-actin (green, top right), Rac1 (red, bottom left), and node (blue, bottom right) as a function of time after PI3-K inhibition. PI3-K inhibition decreases to 10% of the PI3-K level at time 0. (B) Each graph shows the time course of PI(3,4,5)P3 (orange, top left), F-actin (green, top right), Rac1 (red, bottom left), and node (blue, bottom right) as a function of time after actin polymerization inhibition reduces the F-actin level to 0 at time 0. All reactions, parameters and simulation conditions are described in supplementary materials Table S3.

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Numerical simulation in Model C

PI3-K inhibition

Actin polymerization inhibitionB

A

30Time (min)

-10 0 10 20

PI(3,4,5)P3

0.8

1.0

0.6

0.4

Nor

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co

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Time (min)-10 0 10 20 30

Actin

0.91.0

0.80.7

1.1

Nor

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co

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0.6

Node

Time (min)-10 0 10 20 30

40

60

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0N

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80

Time (min)-10 0 10 20 30

0.91.0

0.80.7

1.1Rac1

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Time (min)-10 0 10 20 30

0.6

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Actin

30

0.6

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0.2

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co

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Time (min)-10 0 10 20

PI(3,4,5)P3

30Time (min)

-10 0 10 20

0.6

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1.4

Nor

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co

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Rac1

Nor

mal

ized

co

ncen

tratio

n

Time (min)-10 0 10 20 30

Node

0.6

1.0

0.2

1.4

Fig. S9. Numerical simulation of Model C. Model C in Fig. 5 was described by the Michaelis-Menten scheme and numerically solved. (A) Each graph shows the time course of PI(3,4,5)P3 (orange, top left), F-actin (green, top right), Rac1 (red, bottom left), and node (blue, bottom right) as a function of time after PI3-K inhibition. PI3-K inhibition decreases to 10% of the PI3-K level at time 0. (B) Each graph shows the time course of PI(3,4,5)P3 (orange, top left), F-actin (green, top right), Rac1 (red, bottom left), and node (blue, bottom right) as a function of time after actin polymerization inhibition reduces the F-actin level to 0 at time 0. All reactions, parameters and simulation conditions are described in supplementary materials Table S4.

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Numerical simulation in Model D

PI3-K inhibition

Actin polymerization inhibitionB

A

30Time (min)

-10 0 10 20

PI(3,4,5)P3

0.8

1.0

0.6

0.4

Nor

mal

ized

co

ncen

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n

Nor

mal

ized

co

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Time (min)-10 0 10 20 30

Actin

0.9

1.0

0.8

0.7

Time (min)-10 0 10 20 30

0.9

1.0

0.8

0.7

Rac1

Nor

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co

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Node

Time (min)-10 0 10 20 30

0.6

0.8N

orm

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Time (min)-10 0 10 20 30

0.6

1.0

0.2

1.4

Nor

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Actin

30

0.6

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0.2

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Nor

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co

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Time (min)-10 0 10 20

PI(3,4,5)P3

30Time (min)

-10 0 10 20

0.6

1.0

0.2

1.4

Nor

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ized

co

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Rac1

Nor

mal

ized

co

ncen

tratio

n

Time (min)-10 0 10 20 30

Node

0.6

1.0

0.2

1.4

Fig. S10. Numerical simulation of Model D. Model D in Fig. 5 was described by the Michaelis-Menten scheme and numerically solved. (A) Each graph shows the time course of PI(3,4,5)P3 (orange, top left), F-actin (green, top right), Rac1 (red, bottom left), and node (blue, bottom right) as a function of time after PI3-K inhibition. PI3-K inhibition decreases to 10% of the PI3-K level at time 0. (B) Each graph shows the time course of PI(3,4,5)P3 (orange, top left), F-actin (green, top right), Rac1 (red, bottom left), and node (blue, bottom right) as a function of time after actin polymerization inhibition reduces the F-actin level to 0 at time 0. All reactions, parameters and simulation conditions are described in supplementary materials Table S5.

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Sample1Sample2Sample3Sample4Sample5Sample6

4.0

-4

-2

0

2

4

0 2.0MLCK expression level (AU)

×105

-7

-5

-3

-1

Tim

e la

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cr

oss-

corr

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(min

)

Tim

e la

gs o

f min

imum

cr

oss-

corr

elat

ion

(min

)

14.00 2.0

MLCK expression level (AU)×105

Fig. S11. Effect of MLCK expression level on the cross-correlation between MLCK accumulation and morphological change. Time lag values of the maximum (left) and minimum (right) cross-correlation coefficient are plotted as a function of MLCK expression level (arbitrary unit, AU), which is a value of total EGFP-Long-MLCK fluorescence in a whole cell. The regression line through the data points shows y = -0.0093x - 3.7621 (left) and y = -0.0028x + 0.5714 (right) and coefficient of determination indicates 0.0128 (left) and 0.0006 (right).

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0 (min) 10 20 30

+Y27632 1.4

2.2Rac1

1.2

1.1

1.0

0.9-10 0 10 20 30

Nor

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ized

FR

ET/

CFP

ratio

Time (min)

A

B Y27632

Fig. S12. Perturbation analysis of Rac1 signal by ROCK inhibitors. HT-1080 cells expressing Raichu-Rac1 were treated with 30 µM Y27632, and imaged every 1 min. (A) FRET images at the indicated time points after Y27632 addition are shown in IMD mode. Ratio ranges in IMD mode are shown at the right of image. The scale bar is 10 µm. (B) FRET/CFP ratios of Raichu-Rac1for the individual cells (gray) were expressed by measuring the increase over the basal activity, which was averaged over 10 min before Y27632 addition. Red lines indicate the average FRET/CFP ratio; N = 4.

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Table S1: Summary of cross-correlation analyses between edge velocity and molecular activity.

Rac1 Rac1 Actin Actin PI(3,4,5)P3 Cdc42 RhoA PI(3,4)P2 PI(4,5)P2 MLCK (Max) MLCK (Min) NCSampling time 60 sec 30 sec 60 sec 30 sec 60 sec 60 sec 60 sec 60 sec 60 sec 60 sec 60 sec 60 sec

Time lags(Average and SD)

95% Confidence Interval (-2.96, -1.38) (-3.32,-1.48) (-1.49, 0.99) (-1.42, -0.38) (-1.78, -0.50) (-2.19, -0.48) (-3.94, -1.40) (-2.30, -0.84) (-2.08, -0.72) (-4.94, -3.06) (-0.79, 1.79)Peak of TCCF

(Average and SD)95% Confidence Interval (0.33, 0.48) (0.19, 0.38) (0.15, 0.24) (0.16, 0.24) (0.18, 0.31) (018, 0.49) (0.04, 0.12) (0.16, 0.32) (0.20, 0.37) (0.07, 0.23) (-0.30, -0.14)

NA

0.33±0.15 0.08±0.04 0.24±0.09 0.29±0.07 0.04

-4.00±0.89 0.50±1.22

0.15±0.08 -0.22±0.08

-1.33±0.82 -2.67±1,21 -1.57±0.79 -1.40±0.55-2.17±0.75 -2.40±0.74 -0.25±1.49 -0.90±0.42 -1.14±0.69

0.41±0.07 0.28±0.08 0.19±0.05 0.20±0.03 0.24±0.07

Relative time delay from edge velocity was quantified by cross-correlation analysis. The time lag and peak value were obtained from temporal cross-correlation function (Fig. 2) and represented with SD. 95% confidence interval was

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Table S2: Equations and parameters in Model A

Initial conditions of other parameters are follows: [PI3K] = 1.0 (constant), [PTEN] = 1.0 (constant), [GAP] = 1.0 (constant). PI3-K inhibition decreases 90% of the PI3-K level at time 0. Actin polymerization inhibition reduces the F-actin level to 0 at time 0.

kf Kmf

kb Kmb0.1 1.0 Arbitrary0.01 1.0 Obtained by fitting the data in Fig. 4K.0.05 1.0 Arbitrary0.05 1.0 Arbitrary0.01 1.0 Arbitrary0.01 1.0 Obtained by fitting the data in Fig. 4D.0.2 0.001

0.01 0.001

d[PIP3]/dt = kf*[PI3K]*(1-[PIP3])/(1-[PIP3]+Kmf)- kb*[PTEN]*[PIP3]/([PIP3]+Kmb)

These parameters were estimated toreproduce the data in Fig. 4.

d[Node]/dt = kf*[Rac1]*(1-[Node])/(1-[Node]+Kmf)- kb*[Node]/([Node]+Kmb)

d[F-actin]/dt = kf*[PIP3]*(1-[F-actin])/(1-[F-actin]+Kmf)- kb*[Node]*[F-actin]/([F-actin]+Kmb)

d[Rac1]/dt = kf*[F-actin]*(1-[Rac1])/(1-[Rac1]+Kmf)- kb*[GAP]*[Rac1]/([Rac1]+Kmb)

CommentsReactions

Model A

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Table S3: Equations and parameters in Model B

Initial conditions of other parameters are follows: [PI3K] = 1.0 (constant), [PTEN] = 1.0 (constant), [GAP] = 1.0 (constant). PI3-K inhibition decreases 90% of the PI3-K level at time 0. Actin polymerization inhibition reduces the F-actin level to 0 at time 0.

Model Bkf Kmf

kb Kmb0.1 1.0 Arbitrary0.01 1.0 Obtained by fitting the data in Fig. 4K.

kf1=0.03, kf2=0.02 1.0 Arbitrary0.05 1.0 Arbitrary0.01 1.0 Arbitrary0.01 1.0 Obtained by fitting the data in Fig. 4D.0.02 0.001

0.1 0.001

d[Rac1]/dt = kf*[F-actin]*(1-[Rac1])/(1-[Rac1]+Kmf)- kb*[GAP]*[Rac1]/([Rac1]+Kmb)

d[Node]/dt = kf*(1-[Node])/(1-[Node]+Kmf)- kb*[Rac1]*[Node]/([Node]+Kmb)

These parameters were estimated to reproducethe data in Fig. 4.

d[F-actin]/dt = (kf1*[PIP3]+kf2*[Node])*(1-[F-actin])/(1-[F-actin]+Kmf)- kb*[F-actin]/([F-actin]+Kmb)

Reactions Comments

d[PIP3]/dt = kf*[PI3K]*(1-[PIP3])/(1-[PIP3]+Kmf)- kb*[PTEN]*[PIP3]/([PIP3]+Kmb)

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Table S4: Equations and parameters in Model C

Initial conditions of other parameters are follows: [PI3K] = 1.0 (constant), [PTEN] = 1.0 (constant), [GAP] = 1.0 (constant). PI3-K inhibition decreases 90% of the PI3-K level at time 0. Actin polymerization inhibition reduces the F-actin level to 0 at time 0.

Model Ckf Kmf

kb Kmb0.1 1.0 Arbitrary0.01 1.0 Obtained by fitting the data in Fig. 4K.

kf1=0.03, kf2=0.01 1.0 Arbitrary0.06 1.0 Arbitrary0.01 1.0 Arbitrary0.01 1.0 Obtained by fitting the data in Fig. 4D.0.05 0.55

0.05 0.003These parameters were estimated to reproduce

the data in Fig. 4.

Reactions Comments

d[Node]/dt = kf*(1-[Node])/(1-[Node]+Kmf)- kb*[PIP3]*[Node]/([Node]+Kmb)

d[F-actin]/dt = (kf1*[PIP3]+kf2*[Node])*(1-[F-actin])/(1-[F-actin]+Kmf)- kb*[F-actin]/([F-actin]+Kmb)

d[Rac1]/dt = kf*[F-actin]*(1-[Rac1])/(1-[Rac1]+Kmf)- kb*[GAP]*[Rac1]/([Rac1]+Kmb)

d[PIP3]/dt = kf*[PI3K]*(1-[PIP3])/(1-[PIP3]+Kmf)- kb*[PTEN]*[PIP3]/([PIP3]+Kmb)

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Table S5: Equations and parameters in Model D

Initial conditions of other parameters are follows: [PI3K] = 1.0 (constant), [PTEN] = 1.0 (constant), [GAP] = 1.0 (constant). PI3-K inhibition decreases 90% of the PI3-K level at time 0. Actin polymerization inhibition reduces the F-actin level to 0 at time 0.

Model Dkf Kmf

kb Kmb0.1 1.0 Arbitrary0.01 1.0 Obtained by fitting the data in Fig. 4K.0.05 1.0 Arbitrary0.05 1.0 Arbitrary0.01 1.0 Arbitrary0.01 1.0 Obtained by fitting the data in Fig. 4D.0.05 0.003

0.05 0.53d[Node]/dt = kf*[PIP3]*(1-[Node])/(1-[Node]+Kmf)

- kb*[Node]/([Node]+Kmb)These parameters were estimated to

reproduce the data in Fig. 4.

Reactions

d[Rac1]/dt = kf*[F-actin]*(1-[Rac1])/(1-[Rac1]+Kmf)- kb*[GAP]*[Rac1]/([Rac1]+Kmb)

Comments

d[PIP3]/dt = kf*[PI3K]*(1-[PIP3])/(1-[PIP3]+Kmf)- kb*[PTEN]*[PIP3]/([PIP3]+Kmb)

d[F-actin]/dt = kf*[PIP3]*(1-[F-actin])/(1-[F-actin]+Kmf)- kb*[Node]*[F-actin]/([F-actin]+Kmb)

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