Pattern regulation in the stripe of zebrafish suggests
an underlying dynamic and autonomous mechanism
Motoomi Yamaguchi*†, Eiichi Yoshimoto‡, and Shigeru Kondo*‡§*Laboratory for Positional Information, RIKEN Center for Developmental Biology, 2-2-3 Minatojima-Minamimachi, Chuo-ku, Kobe 650-0047, Japan
Edited by Hans Meinhardt, Max-Planck-Institut für Entwicklungsbiologie, Tübingen, Germany, and accepted by the Editorial Board January 22, 2007
(received for review September 6, 2006)

The mechanism by which animal markings are formed is an intriguing problem that has remained unsolved for a long time. Oneof the most important questions is whether the positional information for the pattern formation is derived from a covert prepattern or an autonomous mechanism. In this study, using the zebrafish as the model system, we attempted to answer this classic
question. We ablated the pigment cells in limited areas of zebrafish
skin by using laser irradiation, and we observed the regenerationof the pigmentation pattern. Depending on the area ablated,different patterns regenerated in a specific time course. The regenerated patterns and the transition of the stripes during theregeneration process suggest that pattern formation is independent of the prepattern; furthermore, pattern formation occurs by
an autonomous mechanism that satisfies the condition of ‘‘local
self-enhancement and long-range inhibition.’’ Because the zebrafish is the only striped animal for which detailed molecular
genetic studies have been conducted, our finding will facilitate theidentification of the molecular and cellular mechanisms that underlie skin pattern formation.
local self-enhancement and long-range inhibition 兩 pigment patterns 兩reaction– diffusion mechanismAnimals exhibit a wide spectrum of pigment patterns. Although it has been attracting considerable interest for longtime (1, 2), the mechanism underlying the emergence of thesepatterns remains largely unknown.
In his pioneering paper in 1952 (3), Alan Turing showed thatvarious spatial patterns arise in a system in which two substances
react and diffuse at different rates. This system is now commonly
termed as the reaction–diffusion (RD)¶ system, and it has
become the standard for theoretically studying of biologicalpattern formation (4, 5). To form the stationary patterns, thesystem needs to satisfy a necessary condition, ‘‘local selfenhancement and long-range inhibition’’ (6–9). Recent molecular genetic experiments corroborated the existence of suchcondition during the events in biological pattern formation(9–11).
Using computer simulations, theoretical studies have shownthat a variety of characteristic animal skin patterns can be
reproduced by RD mechanism (12–15). Nevertheless, the similarity of the patterns made by the computer simulation is notenough to prove that the RD mechanism underlies the pigment
pattern (16, 17). Therefore, it is desired to identify the molecular
network that controls the pigment pattern formation.
Recent studies have focused on the stripe pattern of zebrafish
as the model system to investigate the mechanism of animal
pigmentation (18–20). Many genes related to the pigmentationof zebrafish have been identified (21–27), and investigations on
the functions of these genes are underway (28–33). However, astrong theoretical premise is necessary to develop a complex
molecular network that can explain the pattern formation. If it
is shown that the RD mechanism underlies the stripes ofzebrafish, the mechanism can be used as the working hypothesis
to investigate the network.

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A characteristic property of the stationary patterns generated
by RD mechanism is the ability to self-regulate the pattern andtheir robustness against perturbations (34). For instance, innumerical simulations, if enlargement of the field is introduced
by increasing the number of cells in which the reaction occurs,
the stripes or spots do not enlarge accordingly; in fact, theintrinsic size is retained by the splitting or insertion of new stripesor spots (1). Such dynamic rearrangement was really observed
during growth in the skin of the growing marine angelfish
Pomacanthus imperator (35). This observation strongly suggested
that the stripe patterning of this angelfish is based on an
autonomous mechanism such as an RD system. Unfortunately,in the case of the zebrafish, the stripes do not show such dynamic
rearrangements during the course of the growth of the fish. New
stripes formed during body growth are simply added to theoutermost stripe (19, 36). However, if the RD mechanism also
controls the pigment pattern of zebrafish, it should be possible
to induce some dynamic rearrangement by introducing an artificial perturbation.
By using a pulse laser system with an attached microscope, wewere able to ablate two types of pigment cells, namely, black
melanophores and yellow xanthophores, without causing any
serious damage to the other cells in and around the target region.
As suggested by molecular genetic studies (32, 37–40), thesepigment cells play a major role in pigment pattern formation, andif so, the loss of these pigmented cells in a defined region would
disturb the stationary ‘‘pattern.’’
Based on the above assumption, we first ablated all of thepigment cells in a wide region of the body trunk to erase theentire ‘‘pattern,’’ and then observed the regeneration process totest whether the zebrafish stripes are independent of any prepattern. Subsequently, to observe the dynamic nature of the pattern,
we observed the transition of the stripes in the area adjacent tothe ablated region. Finally, we demonstrated that the time courseand final regenerated patterns correspond precisely to those
expected if the underlying mechanism is assumed to be RD.

Author contributions: M.Y. and S.K. designed research; M.Y. performed research; E.Y.
analyzed data; and M.Y. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS direct submission. H.M. is a guest editor invited by the Editorial Board.
Freely available online through the PNAS open access option.
Abbreviation: RD, reaction– diffusion.
†Present address: Laboratory for Evolutionary Morphology, RIKEN Center for Developmen-

tal Biology, 2-2-3 Minatojima-Minamimachi, Chuo-ku, Kobe 650-0047, Japan.
‡Present address: Division of Biological Science, Graduate School of Science, Nagoya

University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan.
§To whom correspondence should be addressed. E-mail: skondo@bio.nagoya-u.ac.jp.
¶Although we used the regular term ‘‘RD mechanism’’ in this article, it should be noted thatthe ability to generate patterns is restricted to a specific class of reactions; for example,
those in which self-enhancement is coupled with a long-ranged antagonistic effect (6).
This article contains supporting information online at www.pnas.org/cgi/content/full/
0607790104/DC1.
© 2007 by The National Academy of Sciences of the USA

www.pnas.org兾cgi兾doi兾10.1073兾pnas.0607790104

Fig. 2. Rearrangement process of the ventralmost stripe of both zebrafish
and computer simulation. (A–D) Pattern rearrangement induced by partial
ablation of the stripes in zebrafish. Images were captured at 13 (A), 16 (B), 20(C), and 23 (D) days after ablation of the melanophores in the dorsalmost andthe central black stripes (arrowheads). Although new melanophores frequently appeared in the ablated area during the first week of experimentation, these were ablated around 24-h intervals. Subsequently, the development of new melanophores within this region became less frequent. As aresult, this region was filled with only xanthophores, and the remaining
ventralmost stripes (arrow) began to curve and move upward into the area(A–D). (See also SI Movie 1.) (E–H) Computer simulation of the stripe rearrangement. Used equations are identical with that used in Fig. 1. Horizontal
stripes were set as the initial pattern in the 80 ⫻ 80 field. The white indicatesan area where a concentration of the assumptive activator (u in the equations)is the highest, whereas the black shows the highest concentration area ofassumptive inhibitor (v in the equations). Subsequently, with the ‘‘paint tool,’’which was used to erase the contents of the target region, we manually erased
a part of the stripes to form a large region where the activator is absent.
Simulation captures were produced after 1,000 (E), 2,000 (F), 3,000 (G), and
4,000 (H) iterations, respectively [see the details of the simulation in Materials
and Methods (Computer Simulation)].

Results

Experiment 2: Pattern Rearrangement Induced by Partial Ablation of
the Stripes. Another specific property of the stationary pattern

Experiment 1: Regeneration of Stripes Without an Inherent Prepattern. We used young 20-day-old fish for the ablation experiment.

At this age, the primary formation of the pigment stripes iscomplete. By using laser irradiation, we ablated all of themelanophores and xanthophores on the left side of the bodytrunk above the anal fin base; subsequently, we observed theirregeneration process. Approximately 24 h after laser ablation, allof the pigment cells in the region were visibly dead, and thepigment debris was released into the hypodermis (data notshown). Within 3 days, the debris disappeared, and the ablated
region became pigment-free. Approximately 1 week after theablation, several melanophores and xanthophores appeared in arandom manner throughout the ablated area (Fig. 1A). Approximately 10 days after the ablation, the regenerated pigment cells
began to segregate (Fig. 1B). Subsequently, regions in which
either melanophores or xanthophores were predominant
emerged. Gradually, the delineation between the different cellular regions became more prominent (Fig. 1 B and C), and aclear striped pattern was regenerated ⬇3 weeks after ablation(Fig. 1D). The width of the resultant stripes was similar to theoriginal one. However, the stripes displayed a variable orientation (Fig. 1D). This regenerated stripe pattern was relatively
stable regardless of its orientation and permanently maintained.
To simulate the regeneration of the stripe pattern, we used the
Gierer–Meinhardt model of RD equations (6, 8), which is one of
the activator–inhibitor type of the RD model (details areavailable in Materials and Methods). The sequence of patternregeneration that was predicted by using the simulation (Fig. 1
E–H) was similar to the regeneration pattern observed in live
zebrafish (Fig. 1 A–D) both in its process and resultant pattern.
In both the live zebrafish and simulation, the regenerated stripes
retained the original spacing (Fig. 1 D and H). However, incontrast to the standard anterior–posterior direction of theunaffected stripes, the orientation of the regenerated stripes wasmore or less arbitrary (Fig. 1 D and H).
Yamaguchi et al.

formed by the RD mechanism is the dynamic regulation of thepattern (34). Therefore, if the original stripe width was artificially changed, the adjacent stripes are expected to orient
themselves to recover the original width. To test this hypothesis,
we selectively ablated the melanophores in the dorsalmost andthe central black stripes (arrowheads in Fig. 2A). During the firstweek of experimentation, new melanophores frequently appeared in the ablated region; these were ablated around 24-hintervals. Because of the continual elimination of melanophores,
the xanthophores gradually developed and filled the region;
furthermore, the development of new melanophores within thisregion became less frequent. Eventually, a large area was filledwith only xanthophores (Fig. 2 A).
At the beginning of the experiments, the ventralmost black
stripe (arrow in Fig. 2 A) comprised a narrow strip of melanophores that thickened during the first week [supporting information (SI) Movie 1]. This early states were identical to thatobserved in the control fish. However, during the second week,
the remaining ventralmost stripes began to curve and move
upward toward the dorsal region (Fig. 2 A and B). This moving
stripe formed a bell-shaped pattern that filled the vacant space(Fig. 2 C and D). The shape and width of stripe remained
permanently (SI Movie 1). This experiment was performed on
three individuals. In the other two cases, the ventralmost stripe
moved dorsally and connected with the anterior terminal of thecaudal central stripe, and the width of the stripe remained thesame (SI Movies 2 and 3). In all cases, the rearranged patterns
were permanent and quite stable.
The equations and parameters used for the simulation in thisexperiment were identical to those used in the first simulation(details are available in Materials and Methods). Horizontal
stripes were set as the initial pattern and erased the contents ofthe target region. The results observed for the simulation (Fig.
2 E–H) were quite similar to those observed in the real experiment (Fig. 2 A–D).
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Fig. 1. Regeneration process of the stripes of both zebrafish and computer
simulation. (A–D) Regeneration of stripes without an inherent prepattern inzebrafish. Images were recorded after 1 week (A), 10 days (B), 2 weeks (C), and3 weeks (D) after ablation of both melanophores and xanthophores in thewide region above the anal fin base. At the beginning of the regeneration,
melanophores and xanthophores were randomly distributed in the ablatedarea (A). Then, each type of pigment cell became to segregate their distribution (B and C), and the stripe pattern without original anterior–posterior
direction was regenerated (D). Note that this regeneration was achieved byautonomous migration of pigment cells. (E–H) Time-lapse captured images of
the regeneration process outputted by computer simulation. We used the
Gierer–Meinhardt model (6, 8), which is one of the activator–inhibitor type of
RD models, for the simulation. Equations and the details for simulation areavailable in Materials and Methods (Computer Simulations). The white indicates an area where a concentration of the assumptive activator (u in theequations) is the highest, whereas the black shows the highest concentration
area of assumptive inhibitor (v in the equations). Parameters were selected tofacilitate the stripe formation. The parameter c, which causes saturation ofself-enhancement of the assumptive activator in the equation, is crucial tostripe formation (8). As the initial condition for pattern regeneration, we set
a horizontal stripe pattern in the 256 ⫻ 128 field. For the ablation, the central
region was replaced by a random pattern. Captures were produced after 500(E), 1,000 (F), 3,000 (G), and 10,000 (H) iterations, respectively.

Discussion
Stripes are one of the common patterns displayed by many
animals (41). The zebrafish pattern is especially interesting
because complete and detailed molecular genetic data regarding
their patterns are expected to be available in the near future (18,
42–45). In contrast to the stripes on the tropical marine-fish
Pomacanthus imperator (35), those of the zebrafish appear to be
fixed to the skin. However, our perturbation experiments haverevealed that the mechanism underlying the pattern formation ofzebrafish is highly dynamic and autonomous. This finding narrows down the possible theoretical models that form the basis of
the molecular data of the stripe pattern.
In this study, we simulated pattern formation by using an
RD-based model; in this model, diffusion serves as the processof signal transfer. However, it is also possible to generate similar
spatial patterns with other modes of signaling; e.g., by mechanical pressure (mechanochemical model) (46), cell movement(chemotaxic model) (47), and neuronal signaling (neural model)(48). Because these models share the same mathematical basis,
which is ‘‘local self-enhancement and long-range inhibition’’(6–9), it is difficult to determine the most appropriate mechanism by comparing their simulations with the macroscopic
pattern changes observed. We presume that diffusion is the most
likely basis of the long-range signaling in the skin; however, thisassumption must be corroborated by experimental identificationof the corresponding signaling molecule.
In the first experiment, we ablated all of the pigment cells ina large region to remove the original pattern. In the early stagesof regeneration, the two types of pigment cells (melanophores
and xanthophores) appeared in a random manner regardless ofthe pattern of the original stripes (Fig. 1 A); this suggests that theprecursor cells of either pigment cell type were not distributed
according to any particular prepattern. Gradually, the two cell
types segregated into their respective stripes, which retained
their original spacing (Fig. 1 B and C). However, the orientationand position of the regenerated stripes (Fig. 1D) did notresemble those of the original stripes. This clearly indicates thatat least until this stage, there were no other controlling signals
at work; e.g., those derived from the overall gradient of somemorphogen or hidden anatomical structures. Obviously, stripe
formation was driven by local interactions and, as demonstrated
by our simulations, displayed the typical time course of RD
reactions. By using the temperature-sensitive alleles of fms
receptor tyrosine kinase, which is expressed by xanthophores andis essential for melanophore survival and migration into stripes(25), it has been demonstrated that the haphazard stripes areregenerated when xanthophores are restored in both anal andcaudal fins originally occupied only by melanophores (32). Thissuggests that the essentially identical mechanism is at work in thefins.
Because the RD mechanism can determine only the spacing
and not the direction of the stripes (5, 49), it is reasonable thatthe regenerated stripe patterns lose their horizontal orientation
when regeneration starts from a random pattern (Fig. 1 A–D). At
the onset of the patterning process, RD mechanisms are highly
sensitive against any local cue that induces the symmetry breaking (50). To generate the directional stripes, some additional
conditions are required (e.g., directional initial distribution or
directional diffusion of components) (51, 52). It is suggested thatthe initial organization of the melanophores, which appear along
the horizontal myoseptum (19), in the juvenile fish acts as initialconformation and may enforce making the directionality of
stripes.
In the second experiment, it has been shown that the stripe ofzebrafish reacted to the artificially introduced partial perturbation in the stripes with the dynamics estimated by RD model(Fig. 2). According to the findings of our simulation, the dynamic
4792 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0607790104

rearrangement of the stripe of zebrafish occurred because, withrepeated irradiation, the ability of the melanophores to recover
the maximum level of activity from a low level was abolished.
This was included in the simulation by eliminating the production of the baseline activator that would allow de novo triggeringof the following reactions. Because inhibitor was not producedin the nonactivated region, the activation spread from theexisting stripe into the nonactivated region, and this process led
to the movement of the stripe.
The equations in the RD model usually comprise two or threediffusible substances that play multiple roles (3–8). To use theoretical models in a working hypothesis for future molecular genetic
experiments, it is essential to detect what the variables in theequations represent in the real system. In the case of zebrafish,
many experimental data have shown that the mutual interaction
between melanophore and xanthophore plays the key role in the
stripe formation (32, 37–40). In the mutant zebrafish lacking oneof the two kinds of pigment cells, the remaining pigment cells form
only a rudimentary pattern, whereas introduction of one pigment
cell type into a mutant possessing only the other type is sufficient
to make an original stripe pattern (32). From the experiments
manipulating the melanophore number by making the interspecifichybrids, it is suggested that evolutionary changes in the pigment cellnumber have contributed to the pattern alteration (39, 40). Fromthese experimental data, it seems reasonable to assume that the two
types of pigment cells play the role of the substances in the RD
model. If so, any gene mutation that changes the interaction
between the pigment cells may change the pattern. This is equivalent to the change of a parametric value in the RD equation. It isnotable that the allelic differences in the pigment pattern of leopard
mutant are well reproduced by the RD simulation varying only asingle parametric value (53). Recently, some mutant genes thatcause the abnormal pattern have been identified (22–27). Functional analysis of the gene products will provide us the substantialreference to construct the molecular network, which may satisfy thecondition of ‘‘local self-enhancement and long-range inhibition.’’Materials and Methods
Fish Stock. Zebrafish were bred and maintained under standard

laboratory conditions (54). The wild-type strain used was Tü.
The age of the fish used in the experiments was ⬇3 weeks after
hatching, the point at which the first three stripes appear on thebody.
Laser Ablation of Pigment Cells. Before ablation, the fish wereanesthetized by using 0.01% MMS (ethyl-m-aminobenzoate
methanesulfonate) and mounted on a chamber glass slide.
During ablation, fish were always maintained under moist conditions with a weaker anesthesia than full anesthetization. Ablation was performed by using a 365-nm multiple light pulse laserfrom the MicroPoint pulse laser system (Photonic Instruments),
which was focused to a ⫻40 objective on a microscope. In
general, each pigment cell was broken down sufficiently by four
to five laser pulses. Cell death from ablation was checked thenext day, and remnants were ablated if there were any.
Time-Lapse Observations and Recordings. The fish used in experiments were maintained individually. Captured time-lapse imagesof pattern regeneration and/or striping dynamics of the ablated
regions were recorded every day by using a digital camera
mounted on a dissecting microscope at a fixed magnification.
These recordings were continued for a duration of ⬇50–60 days.
Computer Simulations. The differential equation (Gierer–
Meinhardt model) (6, 8) used was
Yamaguchi et al.

dv⫽ u2 ⫺ v ⫹ Dv⌬v,
dt
where u and v are the concentrations of hypothetical factors. u
and v act as the activator and the inhibitor, respectively. Parameters were a ⫽ 0, b ⫽ 1.2, c ⫽ 0.4, Du ⫽ 1 ⫻ 10⫺2, and Dv ⫽ 20 ⫻10⫺2. To adjust the parameters so as to form the stripes, it is
crucial that the saturation level of the self-enhancement ofactivator (parameter c) is adjusted appropriately (8). We set asc ⫽ 0.4. With smaller or larger value of c, the resulting pattern
becomes spots or network.
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duu2⫽ a ⫺ bu ⫹⫹ Du⌬udt
v共1 ⫹ cu2兲