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RESEARCH ARTICLE DEVELOPMENTAL BIOLOGY
A shark-inspired general model of tooth morphogenesis unveils
developmental asymmetries in phenotype transitions
Roland Zimma,1 ID , Fidji Berioa,b ID , Mélanie Debiais-Thibaudb, and Nicolas GoudemandaID
Edited by Günter Wagner, Yale University, New Haven, CT; received October 5, 2022; accepted February 7, 2023
Developmental complexity stemming from the dynamic interplay between genetic
and biomechanic factors canalizes the ways genotypes and phenotypes can change in
evolution. As a paradigmatic system, we explore how changes in developmental factors
generate typical tooth shape transitions. Since tooth development has mainly been
researched in mammals, we contribute to a more general understanding by studying the
development of tooth diversity in sharks. To this end, we build a general, but realistic,
mathematical model of odontogenesis. We show that it reproduces key shark-specific
features of tooth development as well as real tooth shape variation in small-spotted
catsharks Scyliorhinus canicula. We validate our model by comparison with experiments
in vivo. Strikingly, we observe that developmental transitions between tooth shapes
tend to be highly degenerate, even for complex phenotypes. We also discover that the
sets of developmental parameters involved in tooth shape transitions tend to depend
asymmetrically on the direction of that transition. Together, our findings provide a
valuable base for furthering our understanding of how developmental changes can lead
to both adaptive phenotypic change and trait convergence in complex, phenotypically
highly diverse, structures.
tooth development |mathematical modeling |phenotypic diversity |morphospace |evo-devo
The striking diversity of complex shapes is one of nature’s key features biologists seek
to understand. This plethora of different phenotypes is underpinned by a diversity of
interacting developmental mechanisms, yet some developmental systems are capable of
generating especially large phenotypic variation. Thus, studying such developmental
systems will allow better associations between specific changes in development with
the phenotypes they generate. Although modifiable developmental processes involve
different kinds of heritable and nonheritable factors, this approach has traditionally been
termed “genotype–phenotype mapping” (GPM) and has been applied to both general
and specific developmental systems (1–6). While GPMs in specific systems facilitate a
detailed developmental interpretation of variation found within organisms, populations,
and related species, generalized GPMs offer an opportunity to explain patterns, trends,
and biases observed across different developmental systems.
Teeth are a paradigmatic example of a specific structure displaying a vast amount of
adaptive diversity, which was likely pivotal for the successful diversification of vertebrates.
Besides usually varying between taxa, teeth often show conspicuous shape variation within
a species or even within an individual’s jaws, suggesting that there are multiple accessible
ways to modify and fine-tune development locally. This has motivated researchers to
explore how variation in developmental factors can be linked to certain aspects of
mammalian tooth shape variation, both experimentally and in silico (1, 7, 8).
In addition, teeth and denticles are documented across most of the vertebrate
phylum (9–11), offering an opportunity to link developmental and phenotypic variation
to macroevolutionary trends. However, the vast majority of studies has focused
on mammalian tooth development, where many relevant genetic pathways and the
mechanisms of their interaction with different tissues have hence been described (12–15).
Recently, research has begun unveiling features of tooth development in elasmobranchs,
one of the phylogenetically most distant clades from mammals to exhibit important
tooth variation (10, 16–18). Studying their dentitions might even provide a glimpse on
how teeth emerged from ancestral, more general forms of ectodermal appendages, as
elasmobranch integuments are covered by an array of tooth-like denticles (19).
Although many odontogenetic processes can be considered conserved between mam-
mals and elasmobranchs (20–22), there are evident differences. Odontogenesis in mam-
mals tends to take place much more deeply within the oral tissue than in elasmobranchs
(23), where teeth form superficially and continuously, exhibiting a “conveyer-belt”–like
fashion of permanent tooth replacement (16, 24). In mammals, reciprocal signaling
Significance
Elucidating the developmental
origins of phenotypic variation
remains a central aim for
evo-devo research. Teeth are
particularly rich structures
exhibiting abundant phenotypic
diversity. Here, we chose an
interdisciplinary approach to
explore what changes in
developmental factors may
underlie typical transitions
between shark tooth shapes
within and between individuals.
Using a realistic computational
model, we unveil some counter-
intuitive features of such
transitions: high disparity of
developmental mechanisms even
for complex phenotypes and
significant direction-dependent
differences of the developmental
factors involved. We hypothesize
that these properties may be
general to complex animal traits.
Thus, our analysis contributes
to explain the importance of
contingency and prevalence of
convergence in trait evolution.
Author contributions: R.Z., F.B., M.D.-T., and N.G.
designed research; R.Z. and F.B. performed research;
R.Z. contributed new reagents/analytic tools; R.Z. and
F.B. analyzed data; and R.Z., M.D.-T., and N.G. wrote the
paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
Copyright ©2023 the Author(s). Published by PNAS.
This article is distributed under Creative Commons
Attribution-NonCommercial-NoDerivatives License 4.0
(CC BY-NC-ND).
1To whom correspondence may be addressed. Email:
zimm.roland@gmail.com.
This article contains supporting information online
at http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.
2216959120/-/DCSupplemental.
Published April 7, 2023.
PNAS 2023 Vol. 120 No. 15 e2216959120 https://doi.org/10.1073/pnas.2216959120 1 of 10
between epithelial and mesenchymal compartments of the tooth
bud will lead to the formation of an epithelial signaling center
termed enamel knot. Enamel knots will both promote peripheral
proliferation and a local switch to differentiation which induces
cusp formation. In sharks, this specialized structure has been
claimed to be either absent or present in a significantly different
form (18, 25). The positioning of future cusps has been
suggested to be controlled by a Turing mechanism (26). In
this mechanism, pro-proliferative morphogens, e.g., Fgfs and Shh
(fibroblast growth factors and Sonic hedgehog) (27–29), and
antiproliferative morphogens, e.g., Bmps bone morphogenetic
proteins (30), form a signaling network giving rise to a spatially
stable morphogen expression pattern, as predicted theoretically
(26, 31, 32). While the mostly colocalized expression patterns of
Fgf, Shh and Bmp genes in rodent tooth germs are in line with
a classic Turing mechanism (33–36), expression domains of the
homologous genes appear as mutually exclusive in sharks (18, 25).
Surprisingly, the development of some shark skin denticles has
been suggested to have more similarities with mammalian than
shark oral teeth (18).
The richness of data on rodent tooth development allowed a
mathematical model of mammalian odontogenesis to be built:
ToothMaker (8). It has been a versatile tool to learn about the
relationship between developmental and phenotypic variation in
various mammalian contexts, as well as some aspects of evolution
of complex traits (1, 8, 37, 38). Yet, as ToothMaker was conceived
to encapsulate features of mammalian tooth development, we
implemented some changes in order to properly account for
odontogenesis in other clades. Thus, we built a more generalized
version of this model capable of encompassing characteristics of
shark tooth development, besides mammalian odontogenesis.
We used this model to understand how development can give
rise to characteristic tooth shape shifts within catshark dentitions
which, in addition, are reminiscent of tooth shape changes
across sharks. In particular, these changes comprise different
cusp numbers and relative cusp shapes, which may vary along
the jaw axis (39) or between species (40). Previous work in mice
suggested that it is easier to produce simple than complex teeth
(41). Thus, using an in silico approach that allows us to explore a
general tooth morphospace, we attempted to learn whether this
observation is a general feature of tooth development and how
difficult it is to evolve complex, adaptive tooth phenotypes.
Results
A Generalized Reaction-Diffusion GRN Topology Provides a
Means to Reproduce Features of Shark Tooth Development.
The original signaling kernel of ToothMaker consists of one
molecular activator and its inhibitor, exploiting their capacity
of spatially stable pattern formation via a classic activator–
inhibitor-type Turing reaction–diffusion mechanism. Since in
such networks, the inhibitor’s expression relies on the activator’s
presence (31), both molecules’ expressions center in the same
spot, thereby not accounting for spatially exclusive expression
patterns, as observed in sharks (18, 25). However, another class of
reaction–diffusion mechanisms, the so-called substrate-depletion
mechanisms, is characterized by out-of-phase localization of
activatory and inhibitory agents (31, 42).
Thus, we changed the original signaling kernel to a three-
agent signaling network capable of reproducing the characteristic
spatiotemporal patterns of Fgf, Shh, and Bmp. In this network
(Fig. 1B), S1(analogous to Fgf ) activates both the S3(analogous
to Shh) signal (43, 44) and the auto-stabilizing S2(analogous to
Bmp) signal (19, 45–48), with S2(Bmp) acting as an inhibitor of
the S1(Fgf ) signal (49) and, conditionally (50), as an inhibitor
of the S3(Shh) signal.
Under this model, in silico teeth showed enhanced S3and S1
(Shh and Fgf ) signaling in the tips of nascent cusps, while S2
(Bmp) signaling was seen to localize basally to those tips, due to
the negative interactions between S2and S3(cf. Fig. 1A). Thus,
we conclude that our model is in line with the developmental
features characteristic of catshark odontogenesis.
From a theoretical perspective, the implemented changes
into the signaling network allowed its dynamics to shift from
AC
D
B
Fig. 1. The mathematical model reproduces features of shark dentitions. (A) Tooth development in silico. Columns show modeled tooth shapes at different
developmental time points, where darker color shades represent local signaling intensity of S1,S2, and S3(Fgf, Bmp or Shh) expression (cf. refs. 10, 17, 18, and
25). Yellow arrowheads point to characteristic basal localization of S2(Bmp). (B) Signaling network dynamics of the shark tooth model. The interactions of S1,S2,
and S3, in analogy to Fgf, Bmp, and Shh (cf.refs. 10, 17, 18, and 25), and secondary activator (Sec) pathways are indicated as networks where black arrows denote
activatory and red bars denote inhibitory interactions. Connections whose activity is threshold-dependent are drawn with dotted lines. The presumptive range
of action of the signaling molecules is indicated by idealized colored bands above a gray epithelial–mesenchymal interface of the developing tooth bud. (C)
In silico shark tooth shapes encompass dental diversity in S. canicula. Juxtaposed example pairs of CT-scanned (Left) and modeled (Right) teeth. The modeled
teeth were found by random parameter screens in a generic in silico 5-cusp tooth. CT scans were taken from ref. 40. (D) Ectopic increase of Fgf3 and a1activity
simplifies tooth shapes in vivo and in silico. Left : CT scans of example S. canicula hatchling teeth without (Upper) and with (Lower )Fgf 3-coated bead. Middle/Right:
In the model, baseline S1-activation (by the parameter a1) is present. We increased a1to two-fold in a 3-cuspid and a 5-cuspid in silico tooth.
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a classic activator–inhibitor system to a substrate-depletion
system where S2can act as an activator of its substrate S1.
Since interactions between the signals are defined by parameter
values, it is theoretically possible to adjust these so that classic
activator–inhibitor dynamics, where signals coincide spatially,
emerge again. An in-depth analysis of the network topology
reveals that it shows structural features associated with relatively
large Turing spaces—the proportion of parameter combinations
allowing for Turing pattern emergence—possibly explaining why
it was found by our morphospace exploration and why it might
provide developmentally and evolutionarily robust patterning
dynamics (42, 51). Since the model encompasses, by suitable
parameterization, the mammalian tooth development dynamics
as well, it can be considered general.
The Model Recapitulates Natural and Experimentally Induced
Shape Variation. Next, we explored to which extent the model
can help understand some of the natural variation of S. canicula
dentition. In this species, tooth shapes vary both between
populations, sexes, ages, and within jaws (40, 52), comprising
cusp numbers between 1 and 7, symmetrical and asymmetrical
teeth, as well as different cusp heights and different height ratios
between neighboring cusps in multicuspid teeth (cf. SI Appendix,
Fig. S1). Catshark cuspidity (cusp number) tends to increase
from medial to distal teeth, which appears reminiscent of within-
jaw cuspidity trends in other shark species and even in many
mammals (21, 39, 40, 52, 53).
By exploring different combinations of the developmental
model parameters, we found variants that closely resembled
typical 1-cuspid, 3-cuspid, 5-cuspid, and other multicuspid teeth
in S. canicula (Fig. 1D). We also found that different parameter
combinations were capable of producing very similar tooth
shapes.
In order to corroborate the model further, we tested if it
accounts for phenotypic variation resulting from experimen-
tally changed signaling. Although many signaling pathways
are involved in tooth development, we hypothesized that Fgfs
are particularly interesting, as interfering with Fgf signaling
has been reported to lead to conspicuous effects in other
ectodermal appendages. Ectopic Fgfs partially rescue cusp relief
in ectodysplasin mutant mice (54) and increase proliferation
in developing dental tissues in mice (55) and zebrafish (56),
while ectopic Fgf inhibitors reduced denticle size, or prevented
their formation, in the dorsal midline in sharks (57). In other
ectodermal organs, the effects of ectopic Fgf differed (58–61), so
we concluded that elucidating its effect on shark odontogenesis
may be insightful.
Similar to previous studies (54, 57), we implanted beads
coated with Fgf 3 into the dental laminae of S. canicula embryos
(40). Teeth in treated laminae displayed significantly fewer cusps
(averages control = 3.1, treatment = 2.3, P-val = 0.008), more
abnormal accessory cusps (control = 0.09, treatment = 0.59,
P-val = 0.018), and more undermineralized teeth (control =
0%, treatment = 25.9%, P-val = 0.01). In summary, most tooth
buds treated with Fgf 3 showed underdeveloped or undeveloped
accessory cusps.
To reproduce the bead experiments in silico, we ectopically
increased S1(Fgf ) concentration in the model in a transcription-
independent manner. Ectopic increase in S1led to a reduction
of tooth complexity, and even moderate addition of S1activity,
such as a 2-fold increase of the parameter a1, prevented accessory
cusps from forming. We observed this for different in silico teeth
with different cusp numbers (Fig. 1D), suggesting that the model
robustly reproduces the global effect of increased Fgf signaling,
in line with the observation in real shark tooth development.
Developmental Transitions Tend to Be Highly Degenerate. We
then wanted to understand which parameter combinations
have to be changed in order to transform biologically relevant
phenotypes into another. Since phenotypic changes within
catshark dentitions commonly involve changes in cuspidity, we
attempted to transform a characteristic 3-cuspid in silico tooth
into a characteristic 5-cuspid tooth shape, and vice versa. To this
end, we picked a 3-cuspid and a 5-cuspid tooth from the ensemble
of modeled teeth most similar to chosen real teeth of S. canicula
(cf. SI Appendix,Methods: Morphological Distances). From each
starting morphology, we produced a large set of random variants,
which we compared to the other (target) shape. Variants were
then ranked by similarity to the target (SI Appendix, Fig. S4).
Since different combinations of developmental parameters pro-
duced similar phenotypes, we measured parameter-phenotype
degeneracy (Fig. 2B; here defined as the parameter disparity
per morphological disparity). This was done by calculating
the average parameter distance (the Hamming distance, cf. SI
Appendix,Methods: Size of Phenotypic Regions) between any
two variants that were similar enough to the target shape (the
“opposite” tooth shape), for different similarity rank thresholds
theta (Fig. 2Band SI Appendix, Fig. S6). The average parameter
disparity saturated quickly, approaching the global average of
the entire set of variants already for similarity rank thresholds of
around theta = 60. Representing random associations between
parameters and phenotypes, we performed bootstraps of random
pairs of variants as a negative control. Although degeneracy for
5-to-3 cuspid transitions tended to stay below this control, it
remained largely within its 0.95 CI for 3-to-5 cuspid transitions.
In contrast, a positive control, representing a perfect correla-
tion between parameter dissimilarity and phenotypic distance,
differed substantially from the degeneracy in our ensemble data
(cf. Fig. 2B). This suggested a high degeneracy for a complex
phenotype (5-cuspid) which was supported by a comparison of
degeneracies across the entire ensemble of variants (SI Appendix,
Fig. S6). We also visualized the distribution of similar variants
within the morphospace using a principal component analysis
(PCA) of normalized developmental parameters. Variants with
high phenotypic similarity to the target shape localized in
different parts of the morphospace, without any discernible
clustering (Fig. 2A). Using a Hotelling’s T2 test, we found
no difference between those clusters and the remainder of the
variants in the morphospace (all P-values <2e-16, except 100
best fits (P-value = 0.00256) and 200 best fits (P-value = 3.2e-7)
of 3-cuspid variants against the 3-cuspid target shape). Thus, our
results imply that specific associations between developmental (or
genetic) parameter variations and specific phenotype transitions
tend to be intrinsically difficult to establish, as many and
very different combinations of parameter values led to similar
phenotypic results.
Asymmetry Between Tooth Shape Transitions. The high de-
generacies prevented a clear association between specific pa-
rameters and shapes. Therefore, we assessed if any parameters
were mutated more often within sets of in silico variants with
high similarity to the target shape. We quantified parameter
enrichments both for phenotypic transitions from 3-cuspid
to 5-cuspid teeth and the reverse (Fig. 3). We found that
some morphogen interaction strengths mostly involving S3
(Shh) signaling were changed more often than expected by
PNAS 2023 Vol. 120 No. 15 e2216959120 https://doi.org/10.1073/pnas.2216959120 3 of 10
A B
Fig. 2. The generative tooth morphospace is highly degenerate. (A) Principal Component Analysis of parameter changes in the generative morphospace. We
show the distribution of variants between the first four PCs, for 3-to-5-cuspid transitions (N= 6,262) and vice versa (N= 3,267); colors indicate grouped similarity
to target shapes (by rank threshold). Convex hulls are drawn for phenotypic regions around the target shapes. Good fit variants are distributed all over the
morphospace with hulls commensurate to the entire morphospace. (B) Regions in the morphospace tend to be highly degenerate. Variants were ranked by
phenotypic similarity to their target. Variant subsets were defined by similarity below a threshold rank. For different such thresholds, here ordered along the
x-axes, the average Hamming distance between the parameter values of all variant pairs within the respective subset is associated on the y-axis (normalized for
subset size and total average parameter distance for all variants). Averages are plotted in dark blue for variants of 3-cusp teeth ranked by their similarity to a
target 5-cusp tooth and in red for the opposite. We performed bootstraps of 400 permutations. The resulting area is plotted in gray whose darkness represents
density, with the 0.95 and 0.99 confidence intervals as dashed lines. The borders of these areas are smoothened using a Bezier algorithm. As a positive control,
we also randomly picked 400 variants and ranked, for each of them, all other variants by parameter similarity to them. We then used this rank instead of
the phenotypic similarity rank threshold and proceeded as described above. Results are plotted in turquoise. This way, we emulate the hypothetical case of
phenotype-based distance being perfectly correlated with parameter-based distance. Since the blue and red curves are distant from the turquoise area, we
conclude that this correlation is low and the overall disparity of different sets of parameters mapping to the same phenotype is high, especially for the 3-to-5
cusps transitions.
chance. This was also true for some parameters that define the
mechanical properties of the tissue underlying the tooth bud
(Fig. 3A). On the other hand, other parameters such as upstream
activation, differentiation, epithelial growth, and spatial biases
were changed less frequently than expected by chance. For some
parameters, however, enrichment depended on the direction of
the phenotypic transition (Fig. 3A).
To quantify direction-dependent enrichment differences, we
divided, for each parameter, enrichment in the 3- to 5-cuspid
variants sample by enrichment in the opposite variants sample
and inverted the ratio if it was below one (Fig. 3B).
We found the enrichment asymmetry in our experiment to
be significantly larger than in a bootstrap control (P= 0.00214);
Fig. 4A).
To quantify this difference, we then used a sample of 200
random shapes (verifying a comparable phenotypic distance)
as control target shapes and compared their parameter enrich-
ments, individually, with the enrichments from 3-to-5 and
5-to-3 cuspid teeth. Surprisingly, the distributions between
the two-way enrichment and the positive control enrichment
asymmetries were not significantly different from one another
(P= 0.4725), suggesting that the difference in developmental
parameters between “forward” and “backward” variants is about
as large as between sets of parameter changes that lead to
two completely different phenotypes, for a given approximate
phenotypic distance. We did not find any significant difference
(P= 0.6) between the best-fit variants and random variants from
the entire set, although the former tended to be slightly more
asymmetric.
To make sure that this result was not a mere artifact of neutral
parameter changes, we quantified the phenotypic difference that
each parameter change contributed to. In total, less than 20%
of mutations led to phenotypic changes that we considered
insignificant, suggesting that the asymmetry we measured was
not driven by a major percentage of mutations of negligible
phenotypic impact (cf. SI Appendix, Fig. S5).
Anisotropy Differences Between Phenotypic Regions. To better
understand this finding, we investigated the extent to which
phenotypes were more sensitive to changes in some parameters
relative to others. If a given phenotype is equally sensitive to
all relative parameter changes, we would call the associated
region of the parameter space isotropic, allowing for equally
large parameter changes without altering the phenotype. An
isotropic region of the parameter space associated with a particular
phenotype would appear circular in shape (In addition, it
might be reasonable to assume that most robust “wild-type”
phenotypes would tend to be found at the center of such a
circular region, cf. ref. 62). Otherwise, we call it anisotropic.
Here, we define anisotropy as the relative difference in sen-
sitivity to different developmental parameters (or their linear
combinations) for a given phenotype. As a way to quantify
4 of 10 https://doi.org/10.1073/pnas.2216959120 pnas.org
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Fig. 3. Parameter enrichment and asymmetry. We isolated the 10% variants of a typical 3-cuspid in silico tooth with the lowest phenotypical distance to a
typical 5-cuspid target tooth, and vice versa (cf. Fig. 2). (A) For either experiment, we show how often each parameter was mutated relative to what would be
expected by chance, i.e., enrichments (0 represents average value expected by chance). Bar heights represent change normalized by standard deviations (SDs).
(B) To calculate the asymmetry of enrichments, we divided, parameter-wise, the ratio between both enrichments. Ratios below one were inverted. Ratios are
shown in logscale (2). Colors encode different parameter types, as shown by the Inset. Significance was assigned by comparison to a null-model (105simulations)
and is indicated by asterisks (*:0.01<P<0.05; **:0.001<P<0.01; ***:P<0.001).
anisotropy, we measured parameter value differences between
all pairs of variants within the same phenotypic region (defined
by rank threshold). Parameter-wise ranges were then defined
as absolute maxima or average differences. Then, we compared
parameter ranges within the phenotypic regions around the 3-
and the 5-cuspid target shapes. These calculated ranges varied
substantially between the parameters (SI Appendix, Fig. S8),
while epithelial growth rates occupied relatively large ranges, this
was less so for biophysical parameters. Conspicuous differences
between the two sets of best-fit variants were recorded for many
developmental parameters, including epithelial growth rates,
tissue adhesion, tissue rounding, diffusion rates of S2(Bmp) and
S3(Shh), apical-basal biases, and mesenchymal growth rates (SI
Appendix, Fig. S8). We then calculated the parameter-wise ratios
between the parameter ranges of the two phenotypic regions. Our
measurements showed substantial disparity between these ratios,
indicating a large difference between the two corresponding
phenotypic regions in their dependence on specific parameter
variation. In every instance, the anisotropy between the two
phenotypic regions proved significantly higher (Fig. 4Band SI
Appendix, Fig. S8) than the respective negative controls.
Discussion
Shark Tooth Development in the Wider Context of Ectoder-
mal Appendages. Ectodermal organs have been considered one
paradigm of adaptive diversity across vertebrates (63–66). Under-
standing how the mechanisms of their development have evolved
and how they are capable of producing a multitude of different
structures and phenotypes is therefore a key question of evo-devo
research (9, 19, 61, 67–73). As our study was built on a more
general model of odontogenesis, it investigates developmental
differences in a conserved structure between two phylogenetically
distant branches of vertebrates whose last common ancestor lived
more than 415 Ma ago (11, 74).
Although our proposed network of three interacting signaling
pathways is still substantially simplified compared to the com-
plexity and size of real regulatory networks, we found it sufficient
to account for key developmental dynamics and observed features
of odontogenesis in S. canicula, including spatiotemporal patterns
of key morphogen pathways (10, 18). The implemented changes
to the structure of the original model designed to encapsulate
mammal-specific odontogenesis exemplify how developmental
systems may switch their patterning modes by developmental
systems drift during evolution (42, 75, 76). A recent study
explained ontogenetic shifts in shark tooth cusp number using the
mammal-specific version of ToothMaker (25), highlighting con-
served aspects of tooth development. Here, we have showed that
our generalized odontogenetic network is capable of generating
specific tooth variation characteristic of within-species variation
(heterodonty) in S. canicula (40, 77) and possibly in other species
(77, 78). Besides, it is in accordance with GRNs proposed for
the development of other ectodermal organs (19, 57, 79–81).
Developmental studies in ectodermal organs largely support
a simplifying effect of Fgf on several ectodermal organs and
can thus be considered in line with our observations in shark
teeth (58, 59, 61). A striking difference, however, emerges
when comparing the effects of ectopic Fgf on odontogenesis
between catshark and both rodents and zebrafish, representing
diverged branches within the osteichthyan clade. Although
the commonalities with other ectodermal organs point to an
overall high degree of conservation in the morphogenetic kernel
that orchestrates patterning of ectodermal appendages, opposite
effects of increased Fgf signaling between chondrichthyan and
osteichthyan (incl. tetrapods) teeth (54–56) suggest that specific
morphogen functions can diverge in a process of developmental
systems drift (76) without affecting the overall developmental
process or its capacity of generating phenotypic variation.
This means that morphological correspondence between two
structures in divergent clades may not be a sufficient criterion
to infer developmental commonalities. Thus, functionally and
histologically similar structures may have evolved several times
within vertebrates from a general, presumably odontode-like,
ancestral appendage, due to a highly modular and plastic set of
developmental mechanisms.
Specific Parameter Changes Can Be Associated with Shape
Variation. The finding that specific parameters were altered
significantly more often than by chance in silico (Fig. 3 and
SI Appendix, Fig. S8) does not necessarily imply that aspects of
real development corresponding to those parameters contribute
critically to tooth heterodonty in shark dentitions. However, they
PNAS 2023 Vol. 120 No. 15 e2216959120 https://doi.org/10.1073/pnas.2216959120 5 of 10
A
BC
Fig. 4. Phenotypic transitions tend to be asymmetrical. (A) Parameter enrichment asymmetries are significant. Magenta lines represent sorted parameter-wise
enrichment asymmetries. Gray boxplots display a negative control consisting of 2,000 bootstrap permutations of the same data. Turquoise boxplots represent
a positive control for which different sets of variants were identified as approximately equidistant to both the 3-cusp and the 5-cusp targets. Ratios between
parameter enrichments in these variants and the 3-to-5-cusp or 5-to-3-cusp best-fit variants were calculated, representing parameter enrichment differences
between unrelated morphologies. Golden boxplots represent the ratios between the sets of best-fit variants and randomly chosen sets of variants; 2,000
permutations were performed. (B) Anisotropy: among the 100 and 200 best-fit variants, we calculated the average parameter distances between any pair of
variants within those sets. This was performed for the 3-to-5-cusp variants and the reverse experiment. For each parameter, the ratio between the values
from both corresponding experiments was calculated. Sorted range ratios of all parameters were plotted as a magenta line. Gray boxplots represent, as a
negative control, 2,000 bootstrap permutations from the respective sets of variants. Golden boxes resulted from 2,000 bootstrap permutations based on the
entire ensemble of variants. The farthest outliers are not shown. (C) Abstract representation of asymmetry and anisotropy of phenotypic regions. Phenotypic
regions A and B are plotted as diffuse clouds of patches of the corresponding color in a reduced morphospace consisting of different combinations of values
of parameter1 (p1) and parameter2 (p2). Phenotype A is more sensitive to changes in p1 than p2, while the reverse is true for phenotype B, suggesting both
their phenotypic regions are anisotropic. Transiting from region B to region A will, therefore, critically depend on adjusting p1, while p2 may be altered to most
values without phenotypic effects. The reverse transition, from Ato B, will mostly depend on fine-tuning p2. Thus, we can expect to observe an asymmetry in
the enrichments of parameter-wise changes.
represent a starting point about where to look for developmental
features associated with shape variation. Diffusion rates, for
instance, have been linked developmentally to the number of,
and distance between, emergent cusps (15, 26), yet they did only
emerge as enriched in 5 >3 transitions. Where diffusion ranges
were changed, their values were found to be of similar magnitude
(i.e., narrow parameter ranges, cf. SI Appendix, Fig. S8). This
can be explained by a high sensitivity of reaction–diffusion
dynamics to altered diffusion rates (31, 32, 51, 75, 82), which
can easily disrupt the overall tooth shape, unless they are modified
concordantly in both the activator and inhibitor. Thus, the more
fine-tuned changes required to produce a specific 5-cuspid shape
did not involve many diffusion rate modifications. Signaling
interactions, however, especially those that involve S3(Shh), were
found to be altered frequently (Fig. 3), suggesting that their fine-
tuning might be essential for stable Turing patterns and fine-
tuning cuspidities. Another study reproduced some of the effects
of ectopically modified Wnt on catshark cuspidity by mainly
modifying the autoactivation rate of the activator within the
reaction–diffusion kernel of ToothMaker (25), adding evidence
that the signaling interactions can be powerful tools to generate
different cuspidities.
In mammals, a central role of tissue biomechanics has been
explored with respect to the capacity of forming secondary
cusps (83). In line with this, we found tissue downgrowth and
adhesion, which define the specific deformations of mesenchyme
and epithelium during odontogenesis, to be strongly enriched
in our experiments. Conversely, other parameters like epithelial
growth rate and spatial biases, some of which were even associated
with heterodont seal tooth changes in another in silico study (8),
did appear as depleted in our enrichment analysis. We attribute
this to a high sensitivity of morphological features to changes
in those parameters, leading to rather disruptive effects of their
modification.
When trying to associate certain parameters with possible
mechanisms that may explain heterodont variation, we have to
take into consideration the likelihood that analogous features of
real development can actually change within the spatial tissue
context of the jaw. Thus, we might argue that differences in
tissue growth might result from gradients of growth factors
within the jaw (84, 85), and that changes in some biomechanic
parameters might reflect different tissue thicknesses at different
specific positions, making those parameters interesting candidates
for explaining heterodont variation.
6 of 10 https://doi.org/10.1073/pnas.2216959120 pnas.org
Morphological Transitions Are Degenerate with Respect to
Developmental Mechanisms. This study shows that not only
are there multiple ways to build a specific phenotype but even
any substantial clustering of dominant parameter combinations
can be elusive. Degeneracy was found to be high even for complex
phenotypes, implying that regions of specific phenotypes within
the larger morphospace tend to be vast and patchy. In other
words, attributing specific and compact parts of the morphospace
to specific phenotypes, and vice versa, may often reflect reality
poorly.
Intriguingly, similar 5-cuspid teeth issuing from 3-cuspid teeth
show even higher parameter disparity than any randomly picked
pair of tooth variants. This might, ultimately, reflect that 3-cuspid
teeth are morphologically simpler than 5-cuspid teeth: simpler
phenotypes emerge from a larger number of parameter combina-
tions, implying that the majority of random variants of a 3-cuspid
parent will display barely changed morphologies (1, 86) that fill
the parameter space densely. Conversely, almost any random
modification to developments producing complex phenotypes
will either lead to simpler or very different phenotypes. This could
also be the chief reason why more parameters had to be adjusted
to reproduce a multicuspid tooth shape than a unicuspid one in
a study using ToothMaker (25), and in another study, several
signaling pathways had to be fine-tuned in order to increase
cuspidity in mouse molar in vitro cultures (41). Consequently, a
much larger part of the successfully developed (i.e., nonfailing)
variants of the 5-cuspid parent than of the 3-cuspid parent will
look phenotypically similar to their target. Thus, the density
and average parameter similarity will be higher in the former
set, as reflected by the lower overall degeneracy. The latter, on
the other hand, representing an overall rarer phenotype, will
constitute dispersed islands within the morphospace, surrounded
by regions of mostly simpler shapes (1, 86) (Fig. 4C). Although
those islands might be well connected and contiguous, it is very
unlikely that a random parameter exploration will uncover those
spurious and reticulate connections, leading to the impression of
high dispersion and degeneracy.
From an evolutionary perspective, the richness in alternative
paths toward a selective phenotype might explain why certain
aspects of phenotypic variation—such as the common pattern
of increasing cusp numbers toward the distal part of the jaw—
appear to be conserved between sharks and mammals despite
substantial modifications in development (22, 39, 77, 84, 85). If
various combinations of parameters can give rise to the same phe-
notype, it is likely that some drift in the generative factors does not
crucially affect the variational aspects of the phenotypic outcome,
which implies that similar structures might actually be produced
in substantially different ways and that such developmental
divergences might be common. This phenomenon is sometimes
referred to as phenogenetic drift or developmental systems drift
(87), and its occurrence in our simplified in silico model suggests
that it might be an intrinsic property of developmental systems.
On the other hand, the convergence of specific phenotypic traits
will be a rather commonplace phenomenon too (5, 6), as disparate
branches of a specific phenotypic region can be accessed from
many places of the morphospace: Our study shows that we
can expect the parameter disparity of such a region to approach
the parameter disparity of the entire morphospace (cf. Fig. 2A).
Then, the fact that different parts of the same phenotypic region
must be adjacent to very different sets of neighboring regions
also means that a specific mutation might be likely to have
different phenotypic outcomes in two phenotypically conserved,
but developmentally diverged, populations, thus affecting future
evolution (1, 88). Such a developmental degeneracy may even
facilitate the emergence of heterodonty, i.e., phenotypic variation
within the same organism, as it increases the likelihood that
existing patterning cues between different body parts will in
some way connect to the tooth developmental program and
produce the selected variation (85). In the case of Scyliorhinus,
heterodont tooth shape transitions involving changes in cusp
numbers correlate with age, sex, and jaw position (39, 52). Yet,
our theoretical results suggest that the mechanisms underlying
each of those transitions may be different in each instance and that
we should be careful when generalizing or inferring mechanistic
hypotheses even within the same organism (89). Intriguingly,
since real developmental systems feature a much higher number
of morphogen interactions than our model, we should expect
that our observations may be even more significant in real
phenotypes. As intricate developmental mechanisms involving
numerous and heterogeneous developmental factors are rather
commonplace in animals, this finding may, arguably, not be
restricted to odontogenesis, but may be a feature of most dynamic
developmental systems (90).
Previous studies, including theoretical and experimental work
(1, 41, 86), have argued that there should be always more ways to
reduce pattern complexity (e.g., cusp numbers) than to increase it.
From a theoretical point of view (1, 86, 91), this is a consequence
of the difficulty of fine-tuning several parameters required to
build a complex phenotype. Yet, we showed that even in the case
of higher cuspidities, the diversity of apt modifications to the
morphogenetic program is large, providing a fertile playground
for evolutionary drift and adaptations. Therefore, we predict
that our observations would be even more salient in transitions
between the very common unicuspid teeth and any other dental
phenotypes.
Developmental Asymmetries Emerge from the Multidimen-
sional Structure of Development. As one of the key results of this
study, we documented a striking asymmetry between reciprocal
sets of morphogenetic mechanisms. Parameter modifications
leading to reciprocal phenotypic changes were found to be
as different as modifications leading to completely different
phenotypes. Our analysis also proposes a probable explanation
of this finding: The substantial shape anisotropy of phenotypic
regions. This can be better visualized in a simplified morphospace
of two dimensions, whose two axes represent the possible values
of two developmental parameters (represented in Fig. 4C).
Phenotypic regions will then be represented as areas whose main
axes of variation are unlikely to be parallel (or isotropic in the
multidimensional case), meaning that the two phenotypes are
differently robust to variation in each parameter. The more
dimensions a morphospace is composed of, the more unlikely
it is for phenotypic regions to be isotropic, suggesting that real
phenotypic regions might prove to be even more anisotropic than
in our simulations.
Yet, where does this variation in shape and orientation between
phenotypic regions emerge from? We suggest that the degree
of asymmetry and anisotropy between two given phenotypic
regions should be related to the complexity of the respective
developmental system. While relatively simple developmental
systems in which few generative factors additively build a trait
may allow for linear relationships between developmental param-
eters, this assumption cannot hold for complex developments
where heterogeneous generative factors dynamically interact to
produce multitrait phenotypes (92). Interacting mechanisms will
unavoidably involve partially correlated change between devel-
opmental parameters, leading to complex-shaped phenotypic
PNAS 2023 Vol. 120 No. 15 e2216959120 https://doi.org/10.1073/pnas.2216959120 7 of 10
regions and nongradual transitions between adjacent regions.
Whether these hypotheses hold in general and which features
can predict the degree of such asymmetry will be the objective
of future experiments using different phenotypes and different
models.
The low likelihood of reverse evolution has long been known
e.g., Dollo’s law (93, 94). In this study, we have conducted
a systematic exploration of the developmental factors involved
in typical morphological transitions in order to provide insight
about why this is the case. While the results of our study suggest
that morphological convergences should occur commonly, we
also show that multiple trait reoccurrences within a lineage are
likely to involve different underlying developmental factors. We
hypothesize that this follows unavoidably from the fact that
complex interactions of generative factors will create complex
and differently shaped phenotypic regions, thereby crucially
contributing to the central role of contingency in evolution.
Materials and Methods
Mathematical Modeling of Tooth Development. In order to simulate shark
tooth development, we implemented features of shark odontogenesis into
ToothMaker, in which activator–inhibitor dynamics together with tissue growth
and changes in biomechanics lead to morphogenesis of the odontogenic
epithelial–mesenchymal interface (8). Overall, our modification of ToothMaker
is based on the assumption that most of the morphogenetic mechanisms
are conserved between elasmobranchs and mammals, while developmental
systemsdriftmayhavecausedmorphogennetworkstodiverge over evolutionary
time(75,76).Wereplacedits signaling kernel with a three-component signaling
network(S1,S2,S3), each, respectively, representinggeneral featuresoftheFgf,
Bmp, and Shh signaling pathways (Fig. 1B). The signaling factors emulating Fgf
andShhsignalsweredefinedaspromotingepithelialgrowth.Possibleupstream
activation of the signaling pathways was implemented by a constant ai. The
original ToothMaker model induced signaling asymmetrically (in buccolingual
direction) based on cited observations in mice, which we replaced by upstream
activation of the signaling kernel from the center of the initial hexagon.
Furthermore, directed pressure perpendicular to the direction of tooth eruption
by the closely overlaying dental lamina was emulated. SI Appendix,Methods:
Mathematical Modelling, for a detailed description.
Ectopic Modification of Catshark Tooth Development. We tested one
model prediction by ectopically increasing Fgf signaling. This was done experi-
mentally by implanting 100μm-sized Fgf3-coated beads into the odontogenic
lamina of S. canicula embryos and assessing phenotypic effects. In the model,
ectopic changes to the Fgf signal were emulated by changes to upstream
activation of S1, by modifying a1.
Morphospace Exploration. In the first morphospace exploration phase, we
created variants of in silico teeth by introducing random changes to the model
parameters (SI Appendix, Table S1), using a logarithmic probability distribution
betweenaparameter-specificminimum and maximum value (SI Appendix,Table
S2).Variantswere visuallyselectedbasedontheir similaritytogeneralsharktooth
outlines and typical distributions of signaling molecules during development.
Subsequent rounds of parameter mutations were applied to zoom further into
the neighborhoods of selected variants. In the second exploration phase, we
produced large numbers of variants from initial in silico teeth most similar to
typical 3- and 5-cuspid teeth of S. canicula.
Phenotype and Parameter Similarity Quantification. Shape distance be-
tween the2D outlines ofin silico variants andtarget shapes wasquantified using
normalized Euclidean distances between discrete cosine Fourier coefficients.
Analogously, we measured the parameter distances between variants as
normalized Euclidean distance. Parameter degeneracy was assessed as average
parameter distances within sets of variants defined by a threshold phenotype
distance to a target shape.
Parameter Change Enrichment and Range Anisotropies. Starting from
a typical tricuspid tooth shape A, we generated the set A’ of variants and
analogously used a 5-cuspid tooth shape B and its variants as the set B’ of
shapes. Each variant set was sorted by similarity to a target shape: for set A’,
the target shape was shape B, and vice versa. This was done to emulate shape
transformations reminiscent of real toothrows in catsharks. Subsets were then
delimitedbya threshold similarity rank.Thisallowedustocompare the frequency
of parameter changes between A and A’ and B and B’. Parameter-wise ratios
betweentotalcountsof parameter changes in thetwo conditions were calculated
(i.e.,specific enrichments). Enrichments across allparameters werethen ranked,
quantifying the global parameter enrichment asymmetry. Parameter ranges
were measured as the normalized distance between the highest and lowest
value of the respective parameter in an entire set of variants. In analogy to
enrichment asymmetries, we quantified global parameter range anisotropies
by ranking parameter-wise ranges and comparison to a negative control
(by bootstrap). Results were statistically assessed via Kolmogorov–Smirnoff
tests.
SI datasets. Detailed methods and additional tables and figures are provided
in SI Appendix. In addition, the code for the tooth model alongside files
required for its execution and visualization is available under: https://github.
com/RolandZimm/silicoshark/releases/tag/v2.0.Theoutlines of the3-cuspidand
5-cuspid target shapes are provided, too. For further information, please contact
the lead author.
Data, Materials, and Software Availability. All the data necessary to
replicate our results alongside software and morphological data are al-
ready available in the manuscript, its supplementary material, and at an
open repository: https://github.com/RolandZimm/silicoshark/releases/tag/v2.0
(546043138) (95).
ACKNOWLEDGMENTS. This study has been funded by a Deutsche Forschungs-
gesellschaft research fellowship (ZI1809/1-1:1, Proj.432922638) to R.Z. and
a French ANR grant (PLASTICiTEETH) to N.G. We thank Cyril Charles, Jukka
Jernvall, and an anonymous reviewer for helpful feedback on the manuscript.
WeacknowledgetheMRIplatformmember of the national infrastructure France-
BioImaging supported by the French National Research Agency (ANR-10-INBS-
04, “Investments for the future”), the labex CEMEB (ANR-10-LABX-0004), and
NUMEV (ANR-10-LABX-0020) and thank Sylvie Agret and Renaud Lebrun for
their help with microCT imaging.
Author affiliations: aInstitut de Génomique Fonctionnelle de Lyon, Ecole Normale
Supérieure de Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5242, Lyon Cedex
07 69364, France; and bInstitut des Sciences de l’Evolution de Montpellier, University of
Montpellier, CNRS, Institut de la Recherche pour le Développement, Montpellier 34095,
France
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