Biological and mathematical modeling of melanocyte development.

Abstract

We aim to evaluate environmental and genetic effects on the expansion/proliferation of committed single cells during embryonic development, using melanoblasts as a paradigm to model this phenomenon. Melanoblasts are a specific type of cell that display extensive cellular proliferation during development. However, the events controlling melanoblast expansion are still poorly understood due to insufficient knowledge concerning their number and distribution in the various skin compartments. We show that melanoblast expansion is tightly controlled both spatially and temporally, with little variation between embryos. We established a mathematical model reflecting the main cellular mechanisms involved in melanoblast expansion, including proliferation and migration from the dermis to epidermis. In association with biological information, the model allows the calculation of doubling times for melanoblasts, revealing that dermal and epidermal melanoblasts have short but different doubling times. Moreover, the number of trunk founder melanoblasts at E8.5 was estimated to be 16, a population impossible to count by classical biological approaches. We also assessed the importance of the genetic background by studying gain- and loss-of-function β-catenin mutants in the melanocyte lineage. We found that any alteration of β-catenin activity, whether positive or negative, reduced both dermal and epidermal melanoblast proliferation. Finally, we determined that the pool of dermal melanoblasts remains constant in wild-type and mutant embryos during development, implying that specific control mechanisms associated with cell division ensure half of the cells at each cell division to migrate from the dermis to the epidermis. Modeling melanoblast expansion revealed novel links between cell division, cell localization within the embryo and appropriate feedback control through β-catenin.

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RESEARCH ARTICLE
INTRODUCTION
Mice with a defined background display a similar uniform coat
color. This indicates that there is no major variation in melanocyte
production during development throughout the entire body or
between individuals. Therefore, the mechanisms of melanocyte
production must be tightly regulated to provide a defined number
of cells: initially there are a very limited number of progenitors and
subsequently thousands of cells (Mintz, 1967; Wilkie et al., 2002).
Melanocytes are derived from neural crest cells, a transient
population of cells arising from the dorsal part of the neural tube
(Le Douarin and Kalcheim, 1999). In the truncal region of the
mice, founder melanoblasts are determined around E8.5-E9.5 (Pla
et al., 2001; Thomas and Erickson, 2008). From E10.0, precursor
melanoblasts arising from founder melanoblasts can be visualized
as single cells throughout development. From E10.5, the
melanoblasts begin to spread from the migration staging area
(MSA) through the dermis and migrate along a dorsolateral
pathway between the ectoderm and the dorsal surface of the
somites (Wehrle-Haller and Weston, 1995). Initial observations by
Mayer in 1973 suggested that some of these melanoblasts migrate
on E13.5 from the dermis to the epidermis where they continue to
proliferate and migrate actively (Mayer, 1973). Then, between
E15.5 and E16.5, clusters of melanoblasts form progressively as
they move into the developing hair follicles. Finally, melanocytes
reside in the dorsal part of the hair matrix and their renewal after
birth is assured by melanocyte stem cells in the bulge and their
transit amplifying cells.
Mice with a non-uniform pigmentation pattern are the result of
mutations in genes that control the melanoblast developmental
program: the affected genes may be involved in determination,
proliferation, migration, differentiation or other processes. Mouse
mutants (natural, physically/chemically induced or genetically
engineered) are an invaluable resource for identification of the key
proteins that regulate melanoblast development, including proteins
produced either in the developing skin or by the melanoblast itself.
More than 80 genes have been specifically implicated in
melanocyte development, although their precise functions and the
times at which they exert their functions are in most cases unknown
(Lamoreux et al., 2010) (http://www.espcr.org/micemut/#cloned).
These genes encode a variety of proteins, including growth and
differentiation factors, metalloproteinases, and signaling and
transcription factors. These proteins are produced by melanoblasts
or by cells in the surrounding environment (Yamaguchi and
Hearing, 2009). Wnts are locally produced factors that are believed
to play a crucial role in melanoblast determination. Inactivation of
Development 138, 3943-3954 (2011) doi:10.1242/dev.067447
© 2011. Published by The Company of Biologists Ltd
1Institut Curie, Centre de Recherche, Developmental Genetics of Melanocytes,
91405 Orsay, France. 2CNRS UMR3347, 91405 Orsay, France. 3INSERM U1021,
91405 Orsay, France. 4Laboratoire Mathématiques Appliquées aux systèmes, Ecole
Centrale Paris, Grande Voie des Vignes, 94235 Chatenay-Malabry Cedex, France.
5INSERM U895, Equipe 1, 28 Avenue de Valombrose, 06107 Nice Cedex 2, France.
6Max-Planck Institute of Immunobiology, Department of Molecular Embryology,
D-79108 Freiburg, Germany. 7Ludwig Institute for Cancer Research, University of
Oxford, Oxford OX3 7DQ, UK. 8Centre de Mathématiques et de leurs applications,
Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235
Cachan Cedex, France.
*These authors contributed equally to this work.
‡Authors for correspondence (lionel.larue@curie.fr; veronique.delmas@curie.fr)
Accepted 16 June 2011
SUMMARY
We aim to evaluate environmental and genetic effects on the expansion/proliferation of committed single cells during embryonic
development, using melanoblasts as a paradigm to model this phenomenon. Melanoblasts are a specific type of cell that display
extensive cellular proliferation during development. However, the events controlling melanoblast expansion are still poorly
understood due to insufficient knowledge concerning their number and distribution in the various skin compartments. We show
that melanoblast expansion is tightly controlled both spatially and temporally, with little variation between embryos. We
established a mathematical model reflecting the main cellular mechanisms involved in melanoblast expansion, including
proliferation and migration from the dermis to epidermis. In association with biological information, the model allows the
calculation of doubling times for melanoblasts, revealing that dermal and epidermal melanoblasts have short but different
doubling times. Moreover, the number of trunk founder melanoblasts at E8.5 was estimated to be 16, a population impossible to
count by classical biological approaches. We also assessed the importance of the genetic background by studying gain- and loss-
of-function b-catenin mutants in the melanocyte lineage. We found that any alteration of b-catenin activity, whether positive or
negative, reduced both dermal and epidermal melanoblast proliferation. Finally, we determined that the pool of dermal
melanoblasts remains constant in wild-type and mutant embryos during development, implying that specific control mechanisms
associated with cell division ensure half of the cells at each cell division to migrate from the dermis to the epidermis. Modeling
melanoblast expansion revealed novel links between cell division, cell localization within the embryo and appropriate feedback
control through b-catenin.
KEY WORDS: Mitf, Dct, b b-Catenin, Melanoblast, Mouse
Biological and mathematical modeling of melanocyte
development
Flavie Luciani1,2,3, Delphine Champeval1,2,3, Aurélie Herbette1,2,3, Laurence Denat1,2,3, Bouchra Aylaj4,
Silvia Martinozzi1,2,3, Robert Ballotti5, Rolf Kemler6, Colin R. Goding7, Florian De Vuyst4,8, Lionel Larue1,2,3,*,‡
and Véronique Delmas1,2,3,*,‡
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both Wnt1 and Wnt3a in mice leads to the absence of melanoblasts,
whereas overexpression of Wnt1 in murine NCC results in
expansion of the number of melanoblasts in vitro (Dunn et al.,
2000; Ikeya et al., 1997). Specific mutation of b-catenin, the central
component of canonical Wnt signaling, in NCC confirms the role
of this pathway in melanoblast determination (Hari et al., 2002).
However, the effect of the Wnt/b-catenin signaling pathway on
melanoblast expansion and localization during development in the
skin has not been investigated.
b-Catenin is central to several developmental processes.
Numerous studies using genetic approaches have revealed that this
protein is important in multiple cellular functions, including
proliferation, cell fate, survival and differentiation (Grigoryan et
al., 2008). b-Catenin is involved in a wide variety of cellular
mechanisms owing to its various different binding partners and its
cellular localizations at the membrane, in the cytoplasm or in the
nucleus. At the plasma membrane, b-catenin is associated with
cadherin and controls cell-cell adhesion. In the nucleus, b-catenin
interacts with the LEF/TCF factor to regulate gene transcription
and more than 100 b-catenin targets have been identified
(http://www.stanford.edu/~rnusse/pathways/targets.html).
epithelial cells, gain-of-function studies using mutants with
stabilized b-catenin have shown that this protein can induce cellular
proliferation with frequent transformation (Grigoryan et al., 2008).
In the melanocyte lineage, the expression of a stabilized form of b-
catenin induces a reduction of pigmentation (Delmas et al., 2007).
This hypopigmentation may be due to a reduction of
melanoblast/melanocyte numbers, a reduction of melanin
production and/or melanosome transport/transfer. Some b-catenin
targets, such as c-myc and cyclin D1, induce proliferation and are
ubiquitously produced. Moreover, in melanocytes and in melanoma
in culture, b-catenin directly regulates the expression of Mitf-M (the
M form of the microphthalmia protein) (Dorsky et al., 2000;
Takeda et al., 2000). Mitf-M is a basic helix-loop-helix zipper
transcription factor restricted to neural crest-derived melanocytes
and considered to be the master gene of this lineage. Depending on
MITF-M gene activity, the protein affects proliferation by inducing
Met, Cdk2, p21 and p16: Met and Cdk2 induce proliferation and
p21, and p16 induces cell cycle-arrest (Carreira et al., 2005; Du et
al., 2004; Loercher et al., 2005; McGill et al., 2006). Moreover,
Mitf-M may interact with LEF1 or with b-catenin, affecting their
transcriptional activities (Schepsky et al., 2006; Yasumoto et al.,
2002).
The aim of this study was to evaluate the spatial and temporal
distribution of melanoblasts in dermis and epidermis during mouse
development and to examine the cell-autonomous aspect of
melanoblast proliferation in wild-type and b-catenin mutant animals.
In
MATERIALS AND METHODS
Transgenic mice
Mice with a conditional deletion of the gene encoding b-catenin (Ctnnb1)
were generated by mating Tyr::Cre transgenic mice (Delmas et al., 2003)
with animals homozygous for a floxed allele of b-catenin, with LoxP sites
flanking exons 2 to 6 (bcat) (Brault et al., 2001). The construction of
transgenic mice producing stabilized b-catenin in melanocytes has been
described previously (Delmas et al., 2007). All mutant and transgenic mice
were backcrossed more than ten times to C57BL/6. All animals were
housed in specific pathogen-free conditions at Institut Curie, in line with
French and European Union law.
Whole mount and skin sections
The bcat* and bcat mice were crossed with Dct::lacZ (Mackenzie et al.,
1997) and Rosa26R mice (Soriano, 1999), and the resulting embryos were
collected. The number of lacZ-positive cells (melanoblasts) was determined
on each side of embryos (Yajima et al., 2006). Skin from 1-week-old mice
was fixed in 4% paraformaldehyde, dehydrated and embedded in paraffin.
Paraffin-embedded sections (7 mm) of skin or of a carefully orientated
embryo were stained with Hematoxylin and Eosin, and examined by light
microscopy.
Quantification of melanin
Melanin content in hair follicles was measured by spectrophotometry. Hairs
were collected and weighed, and 1.5 mg samples were treated with 1.5 ml
of 1 M sodium hydroxide at 85°C for 4 hours to dissolve the melanin;
absorbance was measured at 475 nm (Larue et al., 1993).
Immunostaining
Melanocyte proliferation was analyzed by BrdU labeling in vivo, with
embryos at various stages of development. The mother was given two 50
mg/ml BrdU injections at 20-minute intervals and killed 2 hours later.
Embryos were collected and fixed by overnight incubation in 4% PFA.
They were incubated in 30% sucrose for 12 hours, and then 30% sucrose
with 50% OCT compound for 5 hours and finally in 100% OCT. For
immunofluorescence, sections were treated as described elsewhere (Puig
et al., 2009). Conventional fluorescence photomicrographs were obtained
with a Leica DM IRB inverted routine microscope or a Leica confocal laser
scanning microscope. Figures were assembled with ImageJ. The Mann-
Whitney test was used to compare groups and the significance of
differences is indicated: ****P<10–5; ***P<10–4; **P<10–3; *P<10–2; ns,
non significant.
Cell culture, transfection and adenovirus infection
HEK293 cells and FO-1 cells were cultured in Dulbecco’s minimal
essential medium supplemented with 10% of fetal calf serum. Cells were
transiently transfected as previously described (Delmas et al., 2007).
Adenoviruses containing gfp alone or gfp and Mitf have been described
elsewhere (Gaggioli et al., 2003).
Mathematical model construction and methodology
Two balance equations involving the cell flux from the dermis to
epidermis, which is unknown, are given:
dnd,θ
dt
According to our observations (see Appendix in the supplementary
material), we have two important pieces of information: (1) the total
number of melanoblasts, n, increases exponentially; and (2) the progress
of fraction of melanoblasts in the dermis, y, through time is sigmoidal (or
S-shaped). Consequently, we can establish equations for nand y, both
unknown variables of interest, which are now linked to two equations. The
yequation involves the rate of decrease of the fraction of melanoblasts in
the dermis:
and yitself. The nequation involves the rate of increase of melanoblasts
in the dermis and epidermis:
and nitself. The two rates involved in the yand nequations can be
estimated from the experimental data:
c(t)  dlog(ne,(t) / nd,(t)) / dt (7)
and
dlog(n(t)) / dt m(t) . (6)
After ‘feeding’ the Eqns 13 and 14 with the experimental data, these two
novel equations are independent of the melanoblast flux. The explanation
of the ‘feeding’ is given elsewhere (Aylaj et al., 2011). Note that yand n
= μd,θ(t)nd,θ(t) − Φθ t, nd,θ(t), ne,θ(t)
() (1)
dne,θ
dt
= μe,θ(t)ne,θ(t) + Φθ t, nd,θ(t), ne,θ(t)
(). (2)
dyθ
dt
= −cθ(t)yθ(t) 1− yθ(t)
()
(13)
dnθ(t)
dt
= μθ(t)nθ(t) (14)
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Development 138 (18)
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fit the experimental data almost perfectly. Now, we have three unknowns
(growth rate in the dermis, growth rate in the epidermis and the flux factor)
and two equations:
c(t) (t) + me,(t) – md,(t) (4)
and
?(t)  (y(t))md,(t) + (1 – y(t))me,(t) . (5)
The ‘third equation’ for the three unknowns can be generated from the
confidence interval for the flux factor:
min (t) ≤ (t) ≤ max (t) (10)
(see Appendix in the supplementary material). In conclusion, the problem
can by solved through a probabilistic approach.
RESULTS
Spatial and temporal melanoblast distribution
during development
To study in detail the patterns of melanoblast expansion during
development, we used the Dct::lacZ reporter mice in the C57BL/6
background; in these mice, melanoblasts can be labeled with X-gal
from E10.5 onwards (Fig. 1A). We determined the number of
melanoblasts in the truncal region covering somites 13-25 (Fig.
1B). A box and whiskers plot was used to indicate the degree of
dispersion and the skewness of the data (Fig. 1C). Melanoblasts
were evenly distributed in the truncal region of all embryos
analyzed, and the map of the progression of melanoblasts did not
vary substantially between embryos at any stage of development.
The numbers of melanoblasts differed by a factor of less than two
between embryos, with a mean and a median that were almost
identical. The logarithm in base 2 (Ln2) of the number of
melanoblasts was plotted against developmental stage and non-
linear regression used (Fig. 1D). The mean number of melanoblasts
followed a perfect exponential expansion with a correlation
coefficient (r) of 0.99931, which places the correlation into the
‘strong’ category. The overall melanoblast doubling time (t) was
determined from the exponential regression equation where the
exponent, 1.0275, represents (Ln2/t)–1: the doubling time between
E10.5 and E15.5 was 0.67 days (16 hours).
Whole-mount studies give a general view of melanoblast
development but do not allow the visualization of melanoblasts
specifically in the two skin compartments: the epidermis and
dermis. Therefore, we prepared transverse sections from the truncal
region and X-gal-stained melanoblasts (Fig. 2A). For each stage,
melanoblasts were counted in each section and recorded according
to their location (Fig. 2B,C). In the epidermis, the number of
melanoblasts per section increased with time (from 0 to 320),
whereas in the dermis, the number of melanoblasts per section
3945
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Melanoblast proliferation in vivo
Fig. 1. Quantification of melanoblast numbers and doubling time of melanoblasts during development. (A)Spatiotemporal view of
mouse embryo truncal melanoblasts from embryonic day 9.5 (E9.5) to E15.5. Blue and white dots correspond to melanoblasts (mb) expressing or
not expressing lacZ under control of the Dct promoter, respectively. (B)Macroscopic observations of Dct::lacZ embryos at E11.5, E13.5 and E14.5,
with the melanoblasts stained with X-gal for b-galactosidase activity. Note that the melanoblast density in the invaded region does not increase
significantly from E13.5 to E15.5. (C)Box and whiskers plot of melanoblast numbers during development. Values are numbers of melanoblasts on
two sides of the embryo in the trunk region between the front and back limbs (somites 13-25, limits shown as black lines in photographs in B). The
number of embryos counted is indicated in brackets, and means are represented by white lines in the blue boxes. Bars indicate the non-atypical
minimum and maximum for each day of development. (D)The log number of melanoblasts plotted against the time of development. The plot is
perfectly linear, and allows the determination of melanoblast doubling time (t), which is given in hours. MSA, migrating staging area.
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remained fairly constant over time (from 7 to 13). We used these
data to estimate the total melanoblast population in the epidermis
and dermis in the truncal region at each stage of development: we
multiplied the total number of melanoblasts (defined by the whole
mount study, see Fig. 1) by the percentage of melanoblasts present
in the relevant compartment and divided by 100 (see Fig. S1 and
Table S1 in the supplementary material; Fig. 2D,E). For example,
E12.5 embryos contained a mean of 1062 melanoblasts in the
truncal region and 42.7% of them were located in the epidermis.
Therefore, the epidermis contained (1062?42.7/100) 454
melanoblasts in this defined area. The results indicated substantial
melanoblast expansion in the epidermis throughout development
and in the dermis during two distinct phases. From E10.5 to E12.5,
a phase of expansion of melanoblasts was observed, followed by a
plateau (Fig. 2D,E). By E13.0, more than half the melanoblasts
were located in the epidermis (see Table S1 and Fig. S2 in the
supplementary material). We next analyzed whether this pattern of
melanoblast development was influenced by altering the level of
b-catenin, a protein that controls numerous cellular process in
various cell lineages during development.
b b-Catenin levels affect pigmentation
We investigated the function of b-catenin in the melanocyte lineage
in vivo, using a genetic approach involving somatic loss- and gain-
of-function of the gene once melanoblasts are determined. Mice
lacking b-catenin (Tyr::Cre/°; b-cateninlox(ex2-6)/lox(ex2-6)bcat)
RESEARCH ARTICLE
Development 138 (18)
Fig. 2. Dermal and epidermal
distribution of melanoblasts.
(A)Sections through the trunk of
embryos at E11.5, E12.5 and E13.5.
Melanoblasts (mb), identified as X-gal-
positive cells, are observed in both
compartments of the skin: epidermis (ep)
and dermis (de). (B,C)The number of
epidermal (B) and dermal (C)
melanoblasts per section was determined
between embryonic days E11.5 and
E15.5 between the two limbs for b-
catenin loss-of-function (bcat in green),
wild-type (wild type in blue) and gain-of-
function (bcat* in red) embryos. The
mean cell number is represented by the
white line in colored boxes and is
indicated above. Bars indicate the non-
atypical minimum and maximum for
each day of development. (D,E)The total
number of epidermal (D) and dermal (E)
melanoblasts was estimated from E10.5
onwards (see details in Fig. S1 and Table
S1 in the supplementary material). neand
ndare the number of melanoblasts in
epidermis and dermis, respectively, on a
given embryonic day. nWMdenotes the
mean number of melanoblasts defined
by whole mount. ne/s, nd/sand nt/sare the
mean number of epidermal (e), dermal
(d) and total (te+d) melanoblasts per
section (s), respectively. Error bars
indicate s.d.
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and mice producing a low level of stabilized b-catenin
(Tyr::b-cat*/°bcat*) in melanocytes were generated in a C57BL/6
background. We first determined the effect of the protein on coat
color. Both b-catenin mutants had an altered coat color: bcat mice
had a white coat and bcat* mutants had a gray coat (Fig. 3A).
Sections from 1-week-old pups revealed gray pigmentation in the
hair bulb of bcat* mice, rather than the dark pigmentation of the wild
type. Pigmentation was absent from bcat mice (Fig. 3B). Hairs
from transgenic bcat* mice had lighter pigmentation than wild type
(Fig. 3C), although the melanin was distributed uniformly from the
root to the apex as observed for wild-type hairs. This indicates that
the transfer of melanin from the melanocytes to the keratinocytes
was not altered. The hypopigmentation resulted from smaller
amounts of melanin in transgenic bcat* than wild-type hairs (Fig.
3D). Melanin was absent from bcat hairs. Therefore, it is likely that
the hypopigmentation of the coat observed in the b-catenin mutants
was due to abnormally low pigment production, rather than to
defects either in the distribution of melanin or in melanin transfer to
the keratinocyte and hair shaft. Tail and ear pigmentation of b-
catenin mutant mice was similar to that of the coat: gray for bcat*
and white for bcat (Fig. 3E and data not shown).
Melanoblast expansion in the epidermis is
strongly altered in both b b-catenin mutants
We tested whether the pigmentation deficiency in b-catenin mutant
mice was associated with an abnormally small number of
melanocytes. We determined the number of melanoblasts produced
during development of the melanocyte lineage in mice generated
by crossing Dct::lacZ/° mice (Dct::lacZ mice) with bcat* and
bcat mice (Fig. 4). On E10.5, when the transgenes (bcat* and
Cre) start their expression, the numbers of melanoblasts were
similar in all mice. By E11.5, there were fewer melanoblasts in
bcat* than in wild-type embryos; this difference increased with
time. From E12.5, the number of melanoblasts in bcat mice was
lower than in wild type. Overall, the number of bcat, wild-type
and bcat* melanoblasts increased at each stage but the rates of
increase differed between the genotypes. The differences in
numbers of melanoblasts present during development reflected the
differences in coat color observed between the genotypes after
birth. Consequently, the number of melanoblasts seemed to account
for the coat-color phenotype.
We analyzed the number of melanoblasts in epidermis and
dermis for each genotype to determine the potential differences
in expansion in the two compartments. We calculated the total
number of melanoblasts in epidermis and dermis as described
above (see Fig. S1 and Table S1 in the supplementary material).
In the epidermis, the number of melanoblasts increased with
time. The most substantial increase was in wt mice and the
smallest in bcat mice (Fig. 2B,D). In the dermis, the total
numbers of melanoblasts remained low for all genotypes, but
was nevertheless smallest in b-catenin mutants (Fig. 2C,E).
Overall, melanoblast numbers in the epidermis and dermis of b-
catenin mutants were lower than in the wild type. However, the
effect of b-catenin mutants was greater in the epidermis than in
the dermis. This suggests that melanoblast expansion is
particularly dependent on b-catenin signaling in the epidermal
compartment.
b b-Catenin level affects the proliferation of
melanoblasts
The reduction of melanoblast number in b-catenin mouse
mutants could be a consequence of several cellular processes:
increased apoptosis, loss of differentiation, transdifferentiation
(changes in cell fate) and/or decreased proliferation. The number
of apoptotic melanoblasts was determined by testing for the
presence of cleaved caspase 3 in b-catenin mutants and wild-
type embryos from E12.5 to E14.5 (see Fig. S3 in the
supplementary material). No apoptotic melanoblasts were
detected in the epidermis in wild-type or in b-catenin mutants.
Very few apoptotic melanoblasts were found in the dermis of
wild type and b-catenin mutants at E12.5 and E13.5. It appears
that the amount of apoptosis did not significantly differ between
in bcat, wild-type and bcat* melanoblasts. Similar results were
obtained by TUNEL (data not shown). We previously showed
3947
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Melanoblast proliferation in vivo
Fig. 3. b b-Catenin activity controls hair pigmentation. (A)Photograph of b-catenin loss-of-function (white), wild-type (black) and gain-of-
function (gray) adult mice. (B)Histological section of 1-week-old skin with Hematoxylin and Eosin staining. Note the pigmentation of hair follicles:
white (bcat), black (wt) and gray (bcat*). (C)Macroscopic observations of dorsal hair follicles for the three genotypes. The pigmentation matches
the corresponding hair follicles exactly. Note that pigmentation is regular and homogeneous for each hair. (D)Spectrophotometric measurement
indicates a lower than wild-type melanin content in bcat* hair and an absence of melanin from bcat hair. Data are mean±s.e.m. (E)Tail
photographs for the three genotypes.
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that no transdifferentiation or loss of commitment was observed
for bcat* melanoblasts (Delmas et al., 2007). We then analyzed
differences in the fate of melanoblast-committed cells between
those lacking b-catenin (bcat) and wild type. We compared the
numbers of blue cells in Dct::lacZ (staining for melanoblasts)
and Tyr::Cre/°; Rosa26R/+ (staining for defloxed cells)
embryos. There was no difference between the two genetic
backgrounds, suggesting that the absence of b-catenin did not
affect cell differentiation or fate (data not shown). To test
whether the coat color phenotype of bcat and bcat* mutants is
a consequence of a reduction of melanoblast proliferation, we
carried out bromodeoxyuridine (BrdU) labeling assays on
embryos collected from E12.5 to E14.5. The numbers of BrdU-
labeled melanoblasts were determined in epidermis and dermis
for each genotype (Fig. 5). In the epidermis, for each
developmental stage analyzed, the number of BrdU-positive
melanoblasts was lower in b-catenin mutants than in wild type.
The difference was greater for the cells lacking b-catenin than
for those that expressed the stabilized form of b-catenin. In the
wild-type embryos, a lower percentage of dermal melanoblasts
than of epidermal melanoblasts had incorporated BrdU. This
suggests that the proliferation rate is higher in the epidermis than
in the dermis. A similar difference was also observed for bcat*
melanoblasts, but it was less pronounced than for wild type.
Finally, bcat melanoblasts presented an overall low level of
BrdU incorporation in both compartments. These findings reveal
that the proliferation of wild-type melanoblasts is faster than that
of bcat* melanoblasts, and much faster than that of bcat
melanoblasts. In conclusion, the lower numbers of bcat and
bcat* melanoblasts are mainly due to a reduction of proliferation,
and not due to apoptosis, loss-of-differentiation or
transdifferentiation.
Modeling melanoblast proliferation in the skin
during development
To investigate bcat, wild-type and bcat* melanoblast proliferation
in developing skin, we developed a mathematical model to estimate
the doubling time of dermal and epidermal melanoblasts. In the
truncal region, founder melanoblasts are determined from the
neural crest around E8.5-E9.5 and can be easily detected from
E10.5 in a Dct::lacZ background. In both compartments, dermal
and epidermal melanoblasts can theoretically undergo proliferation,
apoptosis, loss-of-differentiation or/and transdifferentiation.
Moreover, melanoblasts cross the basement membrane from the
dermis to the epidermis but there is no evidence of a reverse flow
of melanoblasts from epidermis to dermis in normal conditions. We
showed that melanoblasts do not die, do not transdifferentiate and
do not lose their differentiation. On the basis of these findings, we
constructed a simplified model of melanoblast proliferation as
depicted in Fig. 6A,B and detailed in the Appendix in the
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Development 138 (18)
Fig. 4. b b-Catenin activity affects melanoblast production. (A)Macroscopic observations of the trunk region of bcat, wild-type and bcat*
E14.5 embryos. Note that melanoblasts are less abundant in both b-catenin mutants than in wild type, and in bcat than in bcat*. Scale bar:
100mm. (B)The number of X-gal-positive cells in bcat, wild type and bcat* from E10.5 to E15.5 was determined by eye on both sides of embryos
in the trunk region. The mean X-gal-positive cell number is shown by the white line in the colored boxes and is given above them; the non-atypical
minimum and maximum are shown for each day of development by the vertical bars. Melanoblast doubling times (t) were determined (as in Fig. 1)
and indicated for each type of mutant and wild-type mice.
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supplementary material (Eqns 1-19). The number of founder
melanoblasts, which are located in the MSA is nd,(0), which is
equal to n0. At that time, there are no melanoblasts in the
developing epidermis, i.e. nd,(0)0. The numbers of melanoblasts
(n) in the dermis (d) and epidermis (e) at a particular time (t) of
development are nd,(t) and ne,(t), respectively, with n(t)  nd,
(t) + ne,(t). The parameter  represents the dependence on b-
catenin activity. The flow (t) of melanoblasts from the dermis to
epidermis is, unfortunately, unknown and cannot currently be
determined experimentally. We have three initial unknowns, which
are the two doubling times (t) of the melanoblasts (that in the
dermis and that in the epidermis) and the flow of the cells from the
dermis to the epidermis. We have determined two values: the
numbers of melanoblasts in the dermis and epidermis at a given
time. These two values are not sufficient to solve the problem. The
flow of melanoblasts from the dermis to the epidermis cannot be
determined experimentally for technological reasons. Therefore, we
estimated several cellular characteristics (whether the cells are or
are not cycling, relative rates of proliferation, apoptosis and
transdifferentiation/loss-of-differentiation), and used these data to
solve the problem. Rather than three required equations to
determine the three unknowns, two equations (Eqns 1 and 2),
which can be obtained easily, were used. Thus, the rationale of the
mathematical model was to link the doubling times t(t) [or
proliferation rate m(t), td,(t)  log(2)/md,(t), te,(t) – log(2)/me,
(t) Eqn 3] with the flow of the cells [or the flow factor (t)] on
the basis of the relationship of compatibility existing between
unknowns (t)  c(t) – me,(t) + md,(t) (Eqn 4) (see Appendix
in the supplementary material) (Aylaj et al., 2011). These
unknowns can be defined as follows: me, (t) is the rate of
proliferation of melanoblasts in the epidermis, corresponding to the
inverse of the doubling time in the epidermis me,(t)  log(2)/te,
(t) (Eqn 3), md,(t) is the rate of proliferation of melanoblasts in the
dermis, corresponding to the inverse of the doubling time in the
dermis md,(t)  log(2)/td,(t) (Eqn 3), (t) represents the speed
at which a melanoblast crosses from the dermis to epidermis, and
c (t) represents the rate of decline in the number of dermal
melanoblasts. The global rate of melanoblast proliferation m(t)
can be broken down into the rate of proliferation of the dermal
melanoblast fraction y(t) and the rate of proliferation of the
epidermal melanoblast fraction (1 – y(t)): m(t)  (y(t))md,
(t)+(1 – y(t)) me,(t) (Eqn 5). The values of y(t) are given in
Table S1 in the supplementary material. m(t) can be calculated
from the total number of melanoblasts ndefined biologically using
the differential equation m(t)dlog (n(t))/dt (Eqn 6), c(t) can be
calculated from the number of melanoblasts in the epidermis (ne)
and in the dermis (nd) defined biologically using the differential
equation c (t)  dlog(ne, (t)/nd, (t))/dt (Eqn 7). These two
differential equations were solved using MATLAB. Note that the
mathematical model fits the biological data (Fig. 6B). If we were
able to measure (t), we would be able to determine me,(t) and
md,(t) from the equations me,(t)  m(t) + y(t) (c(t) – (t))
(Eqn 8), and md,(t)  m(t) – (1– y(t)) (c(t) – (t)) (Eqn 9),
which are derived from Eqns 4 and 5. Therefore, we now have two
equations with three unknowns. As stated above, we cannot
determine  (t) from biological experiments. However, it is
possible to estimate lower and upper bounds for (t) (min (t)
and max (t) from biological information, and in particular the
BrdU incorporation experiment which indicates the proliferation
rate of melanoblasts (Fig. 5; see Fig. S4 in the supplementary
material). We established two limits for me,(t) and md,(t): the
proliferation rate in the epidermis is (1) greater than or equal to that
in the dermis me,(t)≥ md,(t) and (2) equal to or less than three
times that in the dermis 3 md,(t)≥ me,(t). These biological limits
3949
RESEARCH ARTICLE
Melanoblast proliferation in vivo
Fig. 5. Melanoblast proliferation is dependent on b b-
catenin signaling. (A)Immunostaining of Dct::lacZ embryo
using anti-b-galactosidase (red), anti-BrdU (green) antibodies
and DAPI (blue). Images are merged to reveal proliferating
melanoblasts. (B)Determination of proliferation rate for
Dct::lacZ-positive cells between E12.5 and E14.5 in bcat, wild-
type and bcat* embryos. Between 20 and 107 sections, derived
from two to four embryos from independent litters, were
analyzed for each embryonic stage and each genotype.
Statistical significance was calculated with the Mann-Whitney
test and is indicated: ****P<10–5, ***P<10–4, **P<10–3, ns,
non significant.
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3950
are not stringent and allow high flexibility of the model. We
introduced these biological limits (me,(t)≥ md,(t), 3 md,(t)≥ me,
(t)≥ m(t)) into Eqns 4 and 9, and thereby generated Eqn 10: 
min (t) ≤ ≤ max (t), where min (t)  max (0, c(t) – 2m
(t)/3–3 y(t)) (Eqn 11) and max (t)  c(t) (Eqn 12) (see Fig.
S4 in the supplementary material). As the value of c(t) is known,
max (t) can be determined. Similarly, as m(t) and y(t) are
known, min (t) can be determined. The minimum and maximum
rates of proliferation of melanoblasts in the epidermis (me,min (t),
me, max (t)) and dermis (md, min (t), md, max (t)) can be
determined from the known min (t) and max (t) from the
following equations:
me,max (t)  m(t) + y(t) (c(t) – min (t)) ,
me,min (t)  md,max (t)  m(t) and
md,min (t)  m(t) – (1– y(t)) (c(t) – min (t)) .
To the extreme, the minimum doubling times in the epidermis
are equal to the doubling times in the dermis, although this
depends on the non stringent limits that we decided. The average
rate of proliferation is simply calculated from the minimum and
maximum rates of proliferation with mmean (t)  (mmin (t) +
mmax (t))/2. The average doubling time is the inverse of the
average rate of proliferation (Eqn 3) and is presented in Table 1.
At E14.5, the doubling time for wild-type epidermal
melanoblasts was estimated by this model to be 18 hours. By
analyzing whole mounts, we estimated that the doubling time of
the melanoblasts to be 16 hours (Fig. 1). The results obtained
from whole-mount data and from the mathematical model are
thus in agreement. Moreover, from E13.5, most of the
melanoblasts are located in the epidermis, and therefore the
doubling time estimated from the whole mount principally
reflects the proliferation of epidermal melanoblasts. At E14.5,
the doubling time for wild-type dermal melanoblasts was
estimated to be 28 hours (Table 1). Mathematical (28 hours
versus 18 hours) and biological (BrdU experiments) data show
that the doubling time in the dermis is longer than that in the
epidermis. Indeed, the biological data indicate that melanoblasts
proliferate faster in the epidermis than in the dermis for all
genotypes from E13.5, and the mathematical model proposes
values for the doubling time. This indicates that the surrounding
environment is important for the proliferation of the cells. We
estimated the doubling times of bcat epidermal and dermal
melanoblasts to be 49 hours and 74 hours, respectively, and of
bcat* epidermal and dermal melanoblasts to be 23 hours and 31
hours, respectively (Table 1). Melanoblasts in the dermis interact
mostly with fibroblasts and those in the epidermis, mostly with
keratinocytes. Both interactions are mostly mediated by
cadherins. The lack of b-catenin in melanoblasts affects E-
cadherin localization at the cell-cell contact and influences Mitf-
M expression (Fig. 7 and data not shown). The slight increase in
b-catenin activity in bcat* melanoblasts does not affect cell-cell
adhesion but increases signaling (Fig. 7 and data not shown).
Consequently, the effects on the doubling time of bcat*
RESEARCH ARTICLE
Development 138 (18)
Fig. 6. Estimation of epidermal and
dermal melanoblast doubling times for
each genotype from a mathematical
model. (A)Melanoblast fate in epidermis and
dermis. In the dermis, Dct::lacZ+cells (blue)
arise from Dct::lacZ–cells (white). The
number of melanoblasts at the initial time
point (E8.5), is represented by nd,(0)  n0for
the dermis and ne,(0)  0 for the epidermis.
The parameter  represents the dependence
on b-catenin activity. The flow, (t) of
melanoblasts from the dermis to epidermis is,
unfortunately, unknown. (B)Comparison
between data and solution of the ratio model
log10(ne,(t)/nd,(t). Comparison between
measurements (squares) and mathematical
model (solid line) after parameter
identification. Ratio of epidermal to dermal
melanoblasts for bcat (green), wild-type
(blue) and bcat* (red) mice.
Table 1. Estimation of the doubling times (t t ) of dermal (de)
and epidermal (ep) melanoblasts for each genotype based on
an estimation of   at E14.5
 bcat
ep deep
t mean48.66 73.8317.58
s.d.1.0424.200.23
t min35.7149.5517.29
t max49.55148.6618.03
The lower and upper bounds of were deduced from BrdU experiments (see Fig.
S4 in the supplementary material). These bounds allow the determination of the
minimum (mmin), maximum (mmax) and average (mmean) rates of proliferation.
From these rates of proliferation, tcan be calculated using Eqn 3. The extreme
values of the doubling times t min and t max calculated from the lower and upper
bounds for are indicated. On the basis of the mathematical model, we cannot
formally exclude the possibility that is equal to lower or upper bounds (these
values are consistent with the model). However, biological data provides evidence
that the proliferation rates of melanoblasts in the dermis are never higher than those
in the epidermis. At E14.5, the rates of melanoblasts proliferation in the epidermis
are higher than that in the dermis (see Fig. S4 in the supplementary material). Note
that the minimum and maximum for the doubling times of bcat in the dermis are
quite divergent. This is mainly due to the small numbers of melanoblasts in bcat
mutant embryos.
Wild type bcat*
deepde
27.71
8.59
18.03
54.09
22.83
0.41
22.68
23.23
30.87
6.39
23.24
43.90
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melanoblasts are likely to be mainly due to effects on b-catenin
signaling, and the effects on the doubling time of bcat
melanoblasts are presumably due to the lower b-catenin
signaling and cell-cell adhesion.
Assuming that the doubling time of melanoblasts follows the
same general rules during this period (E8.5 to E15.5), the number
of founder melanoblasts (n0; independent of max (t)) can be
estimated to be about 16 (for further details see the Appendix in the
supplementary material). This means that on one side of the
embryos there is roughly one founder melanoblast for about two
somites. This value is consistent with the presence of a limited
number of founder melanoblasts and with previous estimations
(Mintz, 1967; Wilkie et al., 2002).
Mitf-M is regulated by the b b-catenin level in
melanoblasts
To investigate the molecular basis of the transcriptional effect of
the b-catenin level on the proliferation of melanoblasts in vitro and
in vivo, we analyzed the expression of Mitf-M, a specific target of
b-catenin implicated in melanoblast and melanocyte proliferation.
We analyzed the effect of an increasing amount of Mitf-M by
infecting melanocytic cells in vitro with adenovirus expressing
Mitf-M or, as a control, GFP. Cells infected with MITF-M showed
less thymidine incorporation than controls (Fig. 7A), indicating that
increasing the Mitf-M level inhibits cell proliferation. When the
amount of Mitf-M was reduced in melanocytic cells in vitro by the
use of an siRNA directed against Mitf (Fig. 7B), proliferation was
affected and the length of G1 phase was clearly increased. These
findings are consistent with previous in vitro studies (Carreira et
al., 2005; Carreira et al., 2006). We then used Q-RT-PCR to
determine the amount of Mitf-M mRNA per melanoblast in wild
type and b-catenin mutant embryos (E10.5 to E13.5). At E10.5,
wild-type and b-catenin-mutant melanoblasts contained similar
amounts of Mitf-M. However, between E11.5 and E13.5, Mitf-M
mRNA was more abundant in bcat* melanoblasts and less
abundant in bcat melanoblasts than in wild-type melanoblasts
(Fig. 7C). Thus, the level of Mitf-M gene expression correlates with
the amount/activity of b-catenin in melanoblasts during
development, indicating also that b-catenin is a major regulator of
Mitf-M expression during melanoblast expansion. Furthermore, the
upregulation of Mitf-M leads to an increase in tyrosinase
expression in bcat* melanoblasts (Fig. 7D).
3951
RESEARCH ARTICLE
Melanoblast proliferation in vivo
Fig. 7. A fine balance between b b-catenin and Mitf levels is required for melanoblast proliferation. (A)FO-1 melanoma cells were infected
with various amounts of adenoviruses encoding GFP-Mitf-M fusion protein and GFP as a control. The proliferation rate of FO-1 melanoma cells was
arbitrary (ru), evaluated from thymidine incorporation. Percentages of infection were determined directly under a microscope equipped for
epifluorescence (white diamonds, right panel). Adenovirus was inactivated for 1 hour at 56°C. (B)Melanoma cell lines were either transfected with
control or Mitf siRNA or not transfected. The percentage of cells in each phase of the cycle (G1, S and G2/M) was evaluated by standard FACS
analysis. ***P<10–4. (C,D)The amount of Mitf-M (C) and tyrosinase (D) cDNA amplified from embryo skin is expressed relative to the number of
melanoblasts. The Mitf-M (or Tyr) per melanoblast ratios for mutants are given relative to those for wild type defined as 1. Error bars indicate s.d.
(E)Activities of top, cyclin D1 and Myc luciferase reporters in HEK293 cells, which do not produce Mitf, in the presence or absence of bcat* and/or
Mitf-M. Three independent luciferase assays were performed in duplicate; errors bars represent s.d.
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The increase in Mitf-M level may have an additional effect on
melanoblast proliferation through its direct interaction with b-
catenin. Indeed, the interaction between MITF-M and b-catenin
can redirect b-catenin transcriptional activity toward Mitf-
specific target genes (Schepsky et al., 2006). Although the effect
of the MITF-M and b-catenin interaction was not investigated on
natural b-catenin target genes, this finding suggests that
transcriptional activation mediated by b-catenin in the
melanocyte lineage may be modulated by the increased in MITF-
M levels. To establish the effect of MITF-M on expression of the
Myc and cyclin D1 genes, both well-known targets of b-catenin
involved in proliferation, we evaluated their promoter activities
in the presence of b-catenin with or without Mitf-M expression.
We measured the activation of a luciferase reporter driven by the
cyclin D1 and Myc promoters following expression of b-catenin,
Mitf-M or both. The cyclin D1 and Myc promoter activities were
stimulated by the presence of b-catenin, but Mitf-M expression
alone had no effect. Interestingly, expression of Mitf-M
abolished the transactivation driven by b-catenin (Fig. 7E).
Therefore, the transactivation activity of b-catenin may be
inhibited by an increased Mitf-M level. Possibly, cells expressing
an activated form of b-catenin contain an increased level of Mitf-
M, leading to a reduction in cyclin D1 and Myc, and
consequently to a diminution in proliferation, which explains the
phenotype observed in bcat* mice. In addition, in the absence of
b-catenin, the transcription of all its targets is reduced leading to
a severe proliferation defect in these cells, potentially explaining
the phenotype observed in bcat mice.
DISCUSSION
Melanoblasts are a specific type of cell that displays extensive
cellular proliferation during development. Melanoblasts colonize
the dermis, epidermis and the hair follicle sequentially. In each
compartment, they are exposed to a large variety of developmental
cues. We show here that the number and the localization of
melanoblasts are very well defined, resulting in tight control over
melanoblast expansion, both spatially and temporally, with minimal
variation in cell number and distribution in the skin. By paying
careful attention to embryo stage and precise determination of
melanoblast number, we revealed that melanoblast numbers were
highly consistent from one embryo to another at any given stage.
The model allowed estimation of the number of founder
melanoblasts and the doubling time of melanoblasts in the dermis
and the epidermis. To challenge the mathematical model, we used
gain- and loss-of-function b-catenin mutants in a C57BL/6
background to modify b-catenin activity. b-Catenin is essential for
the determination of the melanocyte lineage (Hari et al., 2002).
Therefore, we modified b-catenin expression at around E10.5, after
determination in this lineage. We showed that the gain-of-function
using bcat* mice and the loss-of-function using bcat mice each
led to a coat color phenotype: bcat* mice were hypopigmented and
bcat mice were white. The lack of pigmentation for bcat mice
was not so surprising in light of the functions of b-catenin in other
lineages. However, the hypopigmentation observed in bcat* mice
was puzzling. It appears that the modification of b-catenin
production in both directions affects cell proliferation but does not
interfere significantly with apoptosis or cell fate. In epithelial cells,
cyclin D1 and Myc, two proteins promoting cell proliferation, can
be directly induced by b-catenin. In melanocytes, in addition to
cyclin D1 and Myc another direct b-catenin target, Mitf-M, also
controls cell proliferation (Bismuth et al., 2005; Carreira et al.,
2005; Carreira et al., 2006; Garraway et al., 2005; Loercher et al.,
2005). However, the only evidence that Mitf has a role in
melanoblast proliferation in vivo is very indirect (Hornyak et al.,
2001). We showed that the transcriptional activity of b-catenin on
its cellular proliferative targets can be inhibited by Mitf-M. Thus,
in bcat* melanoblasts, b-catenin induces the expression of Mitf-M,
which in turn exerts a negative feed-back control by inhibiting b-
catenin transcriptional activity on cyclin D1 and Myc promoters,
and therefore cell proliferation. By way of their close
interconnection, b-catenin and MITF-M not only direct
melanoblast cell fate but also coordinate cell proliferation during
development.
Establishment of the melanocyte lineage
The localization and the number of melanoblasts during
development were first studied by in situ hybridization using
probes for Mitf, Kit, Pax3 and Sox10 (Thomas and Erickson,
2008). Subsequently, Dct::lacZ transgenic mice were used to
visualize melanoblasts during development from E10.5 (Mackenzie
et al., 1997). The use of Dct::lacZ mice appears to have a
sensitivity similar to that of in situ hybridization experiments, but
this method is faster and more convenient for double or triple
staining. Previous studies indicated that melanoblast numbers
increase substantially during development (Hornyak et al., 2001;
Mackenzie et al., 1997; Silver et al., 2008; Van Raamsdonk et al.,
2004). However, these various studies did not examine cell number
or dermal/epidermal distribution in detail. After backcrossing
Dct::lacZ mice towards C56BL/6 mice, we were able to provide a
precise description of melanoblast number and location from E10.5
to E15.5. We focused our analysis on the trunk because this region
shows less complexity in terms of melanoblast expansion than the
cephalic, vagal or sacral regions; in particular, it has a lower density
of melanoblast founders (Fig. 1) (Mackenzie et al., 1997; Wilkie et
al., 2002).
After cell specification, melanoblasts spread and start to
proliferate in the dermis. From E12.5 to E15.5, most of the cells in
the dermis and epidermis are cycling (Ki67 positive, a marker of
cycling cells, data not shown) and the number of melanoblasts in
the dermis remains fairly constant. These cells are not dying or
changing cell fate. These observations suggest that a regular flow
of cells crosses the basement membrane between the dermis and
epidermis. It suggests that the rate of migration from dermis to
epidermis is similar to the rate of proliferation in the dermis. This
is consistent with an asymmetric division of dermal melanoblasts:
after each cell division, one cell stays in the dermis and one
migrates to the epidermis. However, we cannot exclude the
possibility that there is a constant rate of emigration without
selectivity in which cell emigrate. How the flow of melanoblasts
from the dermis to the epidermis is controlled remains unknown,
but the following three parameters are undoubtedly involved: the
intrinsic capacity of melanoblasts to pass from the dermis to the
epidermis; attraction/repulsion of the melanoblasts that migrate
from the dermis to the epidermis (including the chemo-attraction);
and the quality of the basement membrane that separates the dermis
from the epidermis. There is possibly asymmetric cell division such
that one of the daughter cells is competent to cross the basement
membrane immediately after mitosis (or at the beginning of G1)
and the other daughter cell is not. The crossing daughter cells
would then be those inheriting components that allow the migration
from the dermis to the epidermis. These components may be linked
(protein at the membrane) or not linked (a particular combination
of transcription factors) to the shape of the cells and/or to local
degradation of the basement membrane.
RESEARCH ARTICLE
Development 138 (18)
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The first epidermal melanoblasts are observable at E11.5. This
means that the flow from the dermis to the epidermis starts at
around that time and continues until E15.5 or later. In the two b-
catenin mutants used in this study, dermal melanoblasts in the
embryos were cycling and the number of dermal melanoblasts
remained constant. Therefore, b-catenin does not appear to affect
the asymmetric division and does not seem to contribute to the
control of melanoblast migration from the dermis to the epidermis.
Doubling time of dermal and epidermal
melanoblasts
By E12.5, almost half of all melanoblasts are in the epidermal
compartment where they proliferate actively. The increasing
melanoblast count in the epidermis results from both the division
of these cells in this compartment and the continuous flow of
dermal melanoblasts. However, at later stages, the number of
melanoblasts coming from the dermis is negligible compared with
the number of melanoblasts proliferating in the epidermis. Using
our experimental findings for melanoblast numbers and locations,
we established a mathematical model of the proliferation of these
cells in both skin compartments, allowing melanoblast doubling
times to be estimated. Using this mathematical model, we were
able to determine the in vivo doubling time of wild-type and
mutant murine melanoblasts in two independent compartments
(epidermis and dermis), which are separated by a physical barrier.
We could determine the number of cells in each compartments at
different time of development (from E11.5 to E15.5), but it is not
yet technically possible to evaluate the flow of melanoblasts
going from the dermis to epidermis. Other mathematical models
have already been established to determine the proliferation
features for cells in culture or in vivo (Chou et al., 2010; Di
Garbo et al., 2010; Hyrien et al., 2010; Tabatabai et al., 2011;
Tomasetti and Levy, 2010). However, none of them brings clear
values of doubling times of their considered cells, as we do. They
do not challenge their mathematical models with mutants, as we
do. This challenge was certainly of a great importance. We first
developed a linear model, which gave reproducible values for the
doubling times of wild-type and bcat* melanoblasts.
Unfortunately, this mathematical model was not reproducible and
produced erratic results for bcat. We therefore decided to
develop a generic mathematical model fitting any mouse mutant
from white to black, with all possible intermediates. The
mathematical model presented is nonlinear, which is biologically
relevant. This nonlinear model generates reproducible values for
the doubling times of wild-type, bcat* and bcat melanoblasts. It
should be noted that the doubling time of wild-type melanoblasts
was similar with both linear and non linear mathematical models.
Similar findings were obtained for bcat* melanoblasts. The
methodology developed here is a compromise between expected
balance equations, behavior and feature extractions from data, and
validation of data fitting. The mathematical model, combined
with the biological information (BrdU experiments), indicated
that melanoblasts proliferate more rapidly in the epidermis than
in the dermis. In addition, using the b-catenin mutant mice, we
could show that melanoblast proliferation would be dependent on
cell-cell adhesion and signaling in both compartments. We
conclude that both surrounding environment and genetic context
influence the proliferation rate of melanoblasts during
development. Those findings are consistent with those of
Kunisada, suggesting that specific factors influence melanocyte
survival/growth/differentiation as a function of their location in
the skin (Aoki et al., 2009). This model provided no evidence,
either mathematical or experimental, for a second major wave of
melanoblast production, at the body location and stages of
development analyzed (Adameyko et al., 2009; Jordan and
Jackson, 2000).
A novel mathematical approach to evaluate the
number of founder melanoblasts
The number of founder melanoblasts has been a subject of
discussion over the years. This number has been estimated either
by observing transversal coat color stripes in adult mice derived
from aggregating morulae of various genetic backgrounds, or by
analyzing melanoblast number/distribution revealed by X-gal
staining in mosaic embryos (Mintz, 1967; Wilkie et al., 2002). We
estimated that the doubling time of melanoblasts in the dermis
between E10.5 and E15.5 was about 28 hours. If we assume that
founder melanoblasts are determined at E8.5 in the truncal region
and that the doubling times of progenitors and migrating
melanoblasts are similar from E8.5 to E15.5, the mathematical
model indicates that there are about 16 founder melanoblasts in the
truncal region, which is consistent with previous genetic findings
suggesting that there is a small number of founder melanoblasts in
the trunk (Mintz, 1967). In the cephalic and vagal regions, we
estimated that the number of founder melanoblasts would be larger,
consistent with the findings of Wilkie et al. (Wilkie et al., 2002).
In conclusion, this biological and mathematical modeling may
help to elucidate the function of mutated proteins during
melanocyte development in a particular environment and can be
used to predict the proliferative status of other genetically modified
melanoblasts. In this specific case, the gain- and loss-of-function
of b-catenin revealed that b-catenin affects melanoblast
proliferation, but not migration from the dermis to the epidermis.
Two other signaling pathways, those involving endothelin and Kitl
and its receptor, are involved in the proliferation/survival of
melanoblasts in the dermis and epidermis in vivo. It would be
interesting to evaluate the respective importance of these three
signaling pathways during the establishment of the melanocyte
lineage.
Acknowledgements
We are grateful to I. Jackson for providing a mouse strain (Dct::lacZ mice) and
to I. Davidson for comments on the manuscript. We thank all members of the
animal colony and imaging facilities of Institut Curie. We also thank Y.
Bourgeois, F. Cordelières and H. Harmange. We thank T. Eguether for technical
assistance. F.L. was supported by fellowships from MENRT, SFD and LNCC-
Essonnes. L.D. was supported by fellowships from LNCC-Oise and ARC. This
work was supported by LNCC (Oise et Nationale – labellisation), INCa and
Cancéropole IdF.
Competing interests statement
The authors declare no competing financial interests.
Supplementary material
Supplementary material for this article is available at
http://dev.biologists.org/lookup/suppl/doi:10.1242/dev.067447/-/DC1
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