1

Program* Please click on the lecture title to open the abstract.

1st August

13:30-13:40

Opening Address Hiroshi Matano (Meiji University)

Welcome Greeting
13:40-13:50
Ikuko Hara-Nishimura, D. Sc. (Director, Yamada Science Foundation)

13:50-14:00

Opening Session

14:00-15:00

15:00-15:30

Session 2

15:30-16:30

16:30-17:30

Information from Organizing Committee

Diversity of Biological Patterns and Forms in Nature I
Chair：Philip K. Maini (University of Oxford, UK)

Philip Ball (Science writer, London, UK)
Symmetry breaking from Physics to Biology

Break

Diversity of Biological Patterns and Forms in Nature Ⅱ
Chair：Hiroshi Matano (Meiji University)

Philip K. Maini (University of Oxford, UK）
Modelling collective cell behaviour in development and disease

Shigeru Kondo (Osaka University)
How organisms transform 2D patterns into 3D forms

22nd August

Session 3

10:00-10:45

Diversity of Biological Patterns and Forms in Nature Ⅲ
Co-Chair：Toshio Sekimura (Chubu University) and Haruhiko Fujiwara (The University of Tokyo)

Haruhiko Fujiwara (The University of Tokyo)
Mechanisms and evolution of Female-limited Batesian mimicry in Papilio butterflies

Toshio Sekimura (Chubu University)
10:45-11:30(1) A model for pattern formation and (2) population dynamics of the mimetic butterfly Papilio
polytes in the Sakishima Islands, Japan: Mathematical analysis and Computer simulations

11:30-11:45

11:45-12:30

12:30-13:30

Session 4

13:30-14:15

14:15-15:00

15:00-15:45

Break

H. Frederik Nijhout (Duke University, USA)The development and evolution of butterfly wing patterns: finding the primitive pattern

Lunch

Morphology and Evolution
Chair：Tomohiko Yamaguchi（Meiji University）

Reiko Kuroda (Chubu University)
Snail coiling: CRISPR editing of a single gene turns righties into lefties

Sylvain Gerber (Muséum National d'Histoire Naturelle, France)
Morphospace approaches to evolution: Geometric and developmental considerations

Takao Ubukata (Kyoto University)
Functional morphospace analysis of molluscan shells3

15:45-16:00

Break

16:00-16:45

Short talks

16:45-18:00

Poster Session

18:00-20:00

Banquet

3rd August

Session 5

10:00-10:45

10:45-11:30

11:30-11:45

11:45-12:30

12:30-12:40

Mathematical modeling for Patterns and Forms in Nature
Co-Chair：Hiraku Nishimori（MIMS） and Ken-ichi Nakamura (MIMS)

Hiroyuki Shima (University of Yamanashi)
Mechanical Optimality Hidden in the Structure of Plants

Oliver Steinbock (Florida State University, USA)
Spiral patterns and morphology in chemical systems

Break

Hiraku Nishimori (Meiji University)
Autonomous Workload Regulation Mechanism in Foraging Ants

Closing Address Hiraku Nishimori (Meiji University)4Symmetry breaking from physics to biology
Philip Ball
What is the developmental source of biological form? The question
preoccupied natural philosophers from Aristotle to William Harvey
to Rudolf Virchow, and it remains debated today. Early ideas assumed
that biological form was either already manifest in some way within
the embryo – the preformationist idea, famously illustrated by the
Dutch mathematician and microscopist Nicolaas Hartsoeker’s
drawing of the homunculus in a sperm in the seventeenth century –or emerged via the guidance of a kind of life force or soul, as Aristotle asserted: theessentially teleological position called epigenesis. We might now regard both theories
as sleights of hand designed to circumvent rather than to explain what is now seen as
an example of symmetry breaking.

With the emergence of modern genetics, questions about form in biology became
questions about genes: the phenotype of the developing organism was considered to be
programmed by the genotype. DNA could in this view be regarded as a kind of
informational homunculus: form already existed in the embryo, but in an encoded
format, which Erwin Schrodinger famously called the “code-script” of life.

In his approach to the origins of embryogenesis, Alan Turing was thus going against thegrain. It may be partly for this reason that his 1952 paper on morphogenesis had little
impact for several decades. His approach follows the physical scientist’s instinct toexpress the problem at hand in the simplest possible terms, and then to explore what
the minimal requirements are of a model that captures the essential phenomena. Turing
pointed out that the question of how an embryo develops and acquires shape and form
– bilateral symmetry, say, and the budding of limbs – seemed indeed to be one of
spontaneous symmetry-breaking.
In this presentation I shall set out to explore how, by expressing the question in thismanner, Turing aligned it with what is arguably the major theme of twentieth-century
physics.

Perhaps the first intimation of the role of symmetry in physical processes was
expressed in 1894 by Pierre Curie in a paper titled “On symmetry in physicalphenomena”. Here he asked the question: what is the relationship between the physicaland the symmetry properties of a system? Curie stated the fundamental principle ofsymmetry breaking by saying that some phenomena occur when a symmetry isremoved: he said that “asymmetry is what creates the phenomenon”.
In Curie’s doctorate in the early 1890s on magnetism, he reported that ferromagnets
such as iron will lose their magnetism when heated: this falls to zero at a temperature
now called the Curie temperature. The onset of spontaneous magnetization by coolingthrough the Curie temperature occurs when random orientations of the atomic spins
due to thermal motion switch to a collective state of mutual alignment.

This phase transition was studied in the 1920s using the Ising model, a lattice model
developed by Wilhelm Lenz and his student Ernst Ising. It was soon appreciated that the5same model could be used to represent the transition between the gaseous and liquidstates of matter, as investigated in the 1870s by Johannes Diderik van der Waals. Herethe presence of a particle at a point in the lattice denotes the liquid, while its absence
denotes a gas. Cooling a magnet through its Curie temperature then looks equivalent tocooling a fluid through its critical point, where the uniform symmetry of thesupercritical state breaks to permit two distinct phases of differing density.

This connection was arguably the first glimpse of universality in physics: the idea that
there is a deep parallel between systems that look superficially as though they sharenothing in common. It stems from the fact that many-body behaviour often does notdiscriminate between the fine differences in the natures of those bodies: all that matters
are the general features of how they interact, such as how many neighbours feel the
influence of each body and the dimensionality of the system.
The 1956 proposal by Tsung Dao Lee and Chen Ning Yang that the weak interaction
might break left-right symmetry (parity violation), experimentally confirmed by ChienShiung Wu that same year in experiments on beta decay, opened the path for theunification of the electromagnetic and weak interactions. The idea was developed in the
1960s by Sheldon Glashow and Abdus Salam, who had to introduce the symmetry
breaking by hand. Their theory predicted three massive new bosons, later identified
with the W and Z bosons that mediate the weak force, along with the massless photon.
In the later 1960s Steven Weinberg showed how this symmetry breaking could happen
spontaneously. The theory was verified by the discovery of the W and Z bosons in
CERN’s Proton-Antiproton Collider in 1983.

This Nobel-winning work on electroweak symmetry breaking was intimately tied up
with the theory of the Higgs field and the Higgs boson. The fundamental insight herecame in the late 1950s from theoretical physicist Yoichiro Nambu, who saw an analogy
between the theory of superconductivity and quantum field theory. The idea won
Nambu the 2008 Nobel prize for “the discovery of the mechanism of spontaneous
broken symmetry in subatomic physics”. But Nambu’s work raised new problems, and it
was by resolving them in the early 1960s that Peter Higgs and others concluded thatspace is permeated by the Higgs field, which exerts a drag on the particles and soaffords them mass.
Turing’s work on morphogenesis takes on a different complexion when consideredagainst this context. Symmetry breaking is, one might say, nature’s way of making manyfrom one: of developing complexity out of simplicity. In this way it offers a kind of orderand form for free: a distinction between a here and a there in what was initially ahomogeneous system. Biology, it is now clear, exploits this source of organization to
produce structure at scales well beyond the molecular. Turing’s mechanism is just one
among several now known to feature in the living world at scales ranging from thecellular to the ecological.
The broader question is how the palette of shapes and patterns available fromspontaneous symmetry breaking interacts with natural selection. To what extent canevolution adapt and modify Turing structures, for example? Are all such structures
necessarily adaptive at all? Or are we too readily tempted, when we see order andregularity in biology, to attribute a function to it? Might some of it, at least, represent
nothing more than the intrinsic creative potential in the natural world?
6

Modelling collective cell behaviour in development and disease
Philip K. Maini
Wolfson Centre for Mathematical Biology, Mathematical Institute,
Oxford, UK
maini@maths.ox.ac.uk

Synopsis: Understanding collective movement is a major and important challenge. In
the context of cell movement, we present two case studies: (i) cancer and (ii) neuralcrest (normal development). Using partial differential equation models, and hybrid cellbased models, we show how modelling can increase our understanding of collective cell
invasion and migration.
Collective movement occurs throughout nature across a multitude of scales, from thelong-distance movement of whales, to flocking starlings, to bacterial pattern formation.
Understanding what are the hallmarks of collective movement is still an open question.
With colleagues, I have been studying this problem in the context of cell movement andI will present some results from this work in the context of disease spread and normal
development. Understanding how cancer cells invade tissue is an important part ofpreventing the disease spreading. Several models have been proposed for this.
Recently, we proposed a partial differential equation model for this phenomenon inwhich cells co-operate. That is, instead of having a generalist population that canovercome obstacles and invade, we consider two specialist populations. In this context,
we consider two barriers to invasion: normal cells and the extracellular matrix, and we
consider two cancer cell types: one that produces lactic acid that can kill normal cells,
and one that produces matrix-degrading enzymes. We analyse the travelling wave
behaviour of this system via linear stability analysis and numerical simulation. We thenanalyse in more detail show a simplified sub-model, with degenerate cross-diffusion anda continuum of steady states, and find that it poses challenging problems for travellingwave analysis.
We then study normal development in the context of the cranial neural crest. These arecells that leave the neural tube and migrate to form part of the skull. Neural crest cells
give rise to many parts of the body and nearly one-third of birth defects arise fromabnormal behaviour of neural crest cells. Moreover, neural cells are the precursors ofmelanocytes, which can form melanoma, one of the most aggressive cancers. We use ahybrid cell-based model as an hypothesis testing and hypothesis generating tool and, ina long-standing collaboration with experimental colleagues, we have uncovered new
biological insights concerning this process. Some of these results will be presented.

7Blank page8

How organisms convert 2D patterns into 3D
Keisuke Matsuda1, Hiroki Gotoh2, Haruhiko Adachi1, Yasuhiro Inoue3 &Shigeru Kondo1*
1
2
3:Osaka University, Frontier Biosciences,:Shizuika University, Faculty of Science,:Kyoto University, Faculty of Technology* skondo@fbs.osaka-u.ac.jp, 81-6-6879-7975,

ABSTRACT:The question, "How are organisms formed?" is one of the central questions in developmental
biology. In the past 30 years, embryological experiments and mathematical modeling studies
have revealed the mechanisms by which individual genes are expressed in specific regions,the so-called principles of pattern formation. However, those principles deal, for the mostpart, only with the division of fixed fields into regions. In actual morphogenetic phenomena,
pattern formation and the expansion and deformation of the field proceed simultaneously. As
such, it is extremely difficult to model such a situation, because the two different elements
affect each other.
To circumvent these difficulties, it is useful to study phenomena in which cellular changes
and field deformation occur at different times. We believe that the deformations associatedwith molting in exoskeletal organisms serve this purpose.
Late morphogenesis in exoskeletons occurs through molting. During molting, (1) grooves areformed in the intracellular layer in advance, and (2) large-scale deformation occurs by
expanding these grooves. The process (2) is a purely physical process because it occurs in ashort time. By measuring the number, depth, and direction of the grooves, the final 3D
structure can be calculated from the groove pattern.
On the other hand, process (1) is a biological process, in which the position and angle of thewrinkles are determined in a two-dimensional cell sheet, which is a kind of pattern formation.
We first examined the beetle horn primordium. Beetle pupae have huge horns, but in larvae
the horn primordia are compactly folded in the head. Reproducing the folding of theprimordium from serial sections and extending it with physical calculations, the structure of
the pupal horn emerged. This indicates that the three-dimensional morphology of the horns isalready completed by the folding pattern of the primordium. Furthermore, by examining thewrinkle patterns corresponding to the various parts of the horns, part of the logic behind thecreation of the three-dimensional form was revealed.
We are currently studying the folding patterns of the helmets of treehoppers, which havemore complex and diverse three-dimensional structures, through which we expect toelucidate how the complex structures of insects are designed.

9Sequential photos of Japanese beetle pupation. Giant horns emerge in just 100 minutes.
Because of the extremely short time, this deformation is thought to be due to the physicalunfolding of the folded cell sheet.

Scientific Reports volume 11, Article number: 1017 (2021)

Relationship between wrinkle patterns in cell sheets of horn precursors and 3D morphology
after unfolding.

Zoological Letters volume 6, Article number: 3 (2020)
Scientific Reports volume 7(1), Article number13939 (2017)10

Mechanisms and evolution of female-limited
Batesian mimicry in Papilio butterflies
Haruhiko FUJIWARA
University of Tokyo (Emeritus Professor)
haruh@edu.k.u-tokyo.ac.jp

To deceive predators, palatable species often resemble color patterns and morphology ofunpalatable species, which is called Batesian mimicry. Many animals employ the Batesian
mimicry, which mechanisms and evolution remain largely unknown. In two closely related
swallowtail butterflies, Papilio polytes and P. memnon, there are two types (mimetic and nonmimetic coloration) females, while males show non-mimetic pattern. The female-limited
Batesian mimicry of these butterflies attract public interest from Darwin and Wallace’s era.
In both species, mimetic phenotype is superior to non-mimetic and known to be controlled bya single autosomal locus (H in polytes and A in memnon). Thus, the mimetic female genotype
is HH or Hh (AA or Aa) and non-mimetic is hh (aa), while all males with any genotype are
non-mimetic. Fisher RA (1930) suggested that this polymorphic female-limited mimicry is
regulated by “supergene”, which is a cluster of multiple genes tightly linked together.
Recent genome projects revealed many supergenes involved in various complex adaptive
phenomena, but the functional unit of supergene has not been clarified in any cases. We haveidentified the mimicry supergene locus (H for P. polytes and A for P. memnon) in a region
around doublesex (dsx) of chromosome 25 (1): The region includes several genes, dsx, UXT,
U3X (only for polytes) and Nach-like, which sequences are highly diversified between H andh (A and a) due to recombination suppression, caused by chromosomal inversion in P. polytes
but probably by repetitive sequences without inversion in P. memnon (2, 3). To identify thefunctional unit of mimicry supergene, we performed knock-down of candidate gene function
by electroporation mediated RNAi in mimetic female wings of P. polytes. We found that dsxH was responsible for switching from the non-mimetic to mimetic traits, and that not only
UXT within highly diversified region (HDR) but also sir2 adjacent to HDR affected the wing
pattern (4). Furthermore, it was suggested that U3X regulates both dsx-H and UXT
expression. These results indicate that dsx-H works as a mimicry gene and other flanking
genes as modifier and that functional unit of mimicry supergene is expanded to a wider
region than we thought before. In the symposium, I also discuss how two mimicry supergenes
in Papilio species have evolved.

11References(1) Nishikawa, H. et al. (2015) A genetic mechanism for female-limited Batesian mimicry in
Papilio butterfly. Nat Genet 47, 405-409.
(2) Iijima, T. et al. (2018) Parallel evolution of Batesian mimicry supergene in
two Papilio butterflies, P. polytes and P. memnon. Sci Adv 4, eeao5416.
(3) Komata, S. et al. (2022) Genomic architecture and functional unit of mimicry supergene infemale limited Batesian mimic Papilio butterflies. Philos Trans R Soc Lond B Biol Sci. B
377 (1856), 20210198.
(4) Komata, S. et al. (2023) Functional unit of supergene in female-limited Bastian mimicry of
Paplio polytes. Genetics 223, iyac177.

12(1) A model for pattern formation and (2) population
dynamics of the mimetic butterfly Papilio polytes
in the Sakishima Islands, Japan:
Mathematical analysis and Computer simulations
Toshio Sekimura
Chubu University, Japan(1) A model for pattern formation
Butterfly wing pigmentation patterns are one of the most spectacular and vivid examples ofpattern formation in biology. They have attracted much attention from experimentalists andtheoreticians, who have tried to understand the underlying genetic, chemical and physicalprocesses that lead to patterning. In this paper, I present a brief review of this field by firstconsidering the generation of the localised, eyespot, patterns and then the formation of moreglobally controlled patterns. We present some new results applied to pattern formation on
the wing of the mimetic butterfly Papilio dardanus and Papilio polytes.

The African female limited mimetic butterfly Papilio dardanus

13(2) Population Dynamics of the mimetic Butterfly Papilio polytes in the SakishimaIslands, JapanI next present a mathematical model for population dynamics of the mimetic swallow
butterfly Papilio polytes in the Sakishima Islands, Japan.
(Introduction) P. polytes is a mimetic swallowtail butterfly species widely distributed
across India and Southeast Asia, including Southeast of China, the Philippines, Taiwan,
and the Ryukyu Islands of Japan (Clarke and Sheppard, 1972). P. polytes exhibits thefemale limited polymorphism, that is, the female is polymorphic, whereas the male ismonomorphic and exhibits a white bar on the black hind wing. In the Ryukyu Islands
located in the southwest of Japan, the female of P. polytes has two different forms, themimetic form f. polytes and the non-mimetic form f. cyrus resembling the monomorphic
male in appearance. The form f. polytes mimics the unpalatable butterfly Pachiliopta
aristolochiae as a mimetic model, which has a large white area in the center, and a row
of submarginal red spots on the black hind wing. Mimicry in the female of P. polytes isknown to be Batesian mimicry. Batesian mimicry is one of the most interesting
biological phenomena in nature.

Papilio polytes and the numerical simulation result of fore and hind wings

14

The development and evolution of butterfly wing patterns:
finding the primitive pattern
Fred Nijhout
Department of Biology
Duke University
Durham, NC 27708
hfn@duke.edu

Synopsis: The color patterns of butterflies and moths constitute a highly evolved system ofvisual communication used in sexual signaling, camouflage, warning, territoriality andmimicry. These patterns are based on extensive modifications of a groundplan of three pairsof bands. The ancestors of this pattern can be found as far back as the dragonflies, which
are among the first winged insects, and model simulations will illustrate how this could have
happened.
Outline: The development and evolution of butterfly wing patterns have been extensively
studied over the past 30 years. Much of our understanding of the structure of these color
patterns derives from the classical work of Schwanwitch (1924) and Süffert (1927). Theseauthors independently derived the diversity of color patterns in the butterfly Family
Nymphalidae, from a common ”groundplan” composed of three parallel pairs of bands thatrun from the anterior to posterior margin of the wing. Each pair of bands has a characteristic
pigmentation pattern and is called a symmetry system because the pigments of the bands
mirror each other. Subsequent work by these authors and their associate showed that the“nymphalid groundplan” (Figure 1) applies widely to other Families of butterflies and to
many moths as well.

Figure 1. The Nymphalid Groundplan iscomposed of 3 sets of bands called thebasal-, central- and border- symmetry
systems. In some butterflies and moths the
bands are un-interrupted, as in the left
panel, but in most cases the bands are
disrupted by the vein system (as in the rightpanel), which compartmentalizes thepattern into semi-independent
developmental units (after Nijhout, 1991).

15

A long-standing question in this field is whether the Nymphalid Groundplan somehow
represents the primitive butterfly wing pattern from which all others were derived. The
butterflies are phylogenetically within the moths, so if there is a primitive pattern of
Lepidoptera, it needs to be sought among the moths. Recently, Schachat and Brown (2016)
studied the color patterns of the Micropterigidae, the most basal group of moths, anddeduced that their color patterns were based on a system of 5-6 parallel bands. In many
moths and butterflies the crossbands are interrupted by the wing veins and appear as a rowof spots, and it is still an open question whether bands arose from rows of spots or whetherrows of spots came from broken bands.
In my presentation I will show that the primitive color pattern from which the mothpatterns evolved arose long before the evolution of the Lepidoptera. Color patterns of the
caddis flies (Trichoptera) and scorpion flies (Mecoptera) all resemble those found in thebasal moths. I will show that these patterns are all based on variations on a set of 6 parallel
bands, and that this basic patterning system can be found in the earliest winged insects,
represented today by the dragonflies (Odonata).
A simple reaction-diffusion system can readily generate three symmetry systems, that canbe visualized as either 3 pairs of bands or 6 identical bands (e.g. the yellow stripes in Figure
2).

Figure 2. Pattern of threesymmetry systems formed
by a substrate-depletion
model of reactiondiffusion.

I will show that from this banding system, a lateral inhibition mechanism can, in turn,generate much of the diversity of spotting and banding patterns that we see in the
dragonflies and other patterned insect wings, including the Lepidoptera.
References:
Nijhout, H. F. (1991). Development and Evolution of Butterfly Wing Patterns. Washington D.C.
Smithsonian Press.
Schachat, S.R. and Brown, R.L., 2016. Forewing color pattern in Micropterigidae (Insecta:
Lepidoptera): homologies between contrast boundaries, and a revised hypothesis for theorigin of symmetry systems, BMC Evolutionary Biology. 16, 116.
Schwanwitsch, B. N. (1924). On the groundplan of the wing-pattern in nymphalids and certain otherfamilies of rhopalocerous Lepidoptera. Proceedings of the Zoological Society of London B, 34,
509–528.
Süffert, F. (1927). Zur vergleichende Analyse der Schmetterlingszeichnung. Biologisches Zentralblatt,47, 385–413.

16

Snail coiling: CRISPR editing of a single gene turns
righties into lefties
Reiko Kuroda
Frontier Research Institute, Chubu University, Japanrkuroda@isc.chubu.ac.jp
Synopsis

The establishment of left-right (l-r) body asymmetry is a key biologicalprocess which is strictly regulated genetically. We have demonstrated
unequivocally that the handedness of the freshwater snail Lymnaea (L.) stagnalis isdetermined by the single maternal diaphanous gene Lsdia1. The gene operates at the one-cellstage to set the chirality and dictates the entire chiromorphogenesis programme across thelevels of biological hierarchy. We have also revealed that mechanical micromanipulation
during the 3rd cleavage to reverse the spiral-cleavage direction creates mirror-image animals.
Abstract

Most animals display external bilateral symmetry, but the structure and position of thevisceral organs show asymmetries that are determined genetically. To reveal the still
unknown mechanism of the establishment of left-right body asymmetry, we have chosen towork on the freshwater snail L. stagnalis, which has several unique characteristics. 1) Boththe dextral and the sinistral strains within a species are found in the wild with 98% of thesnails dextral and 2% sinistral. 2) The asymmetry is displayed both externally and internally.
3) Snail handedness depends on the direction of spiral cleavages of the embryos, as wasreported as early as 1894.1) 4) The snail is a hermaphrodite, and hence both self-crossing andcrossing can occur. This makes the genetics more versatile and informative.
Fig. 1 shows three left-right pairs of L. stagnalis: a) a pair in the wild, b) one created bymechanical manipulation and c) the sinistral one is created by CRISPR/Cas9 genome editingof the dextral one. Contrary to what has been believed, temporal and spatial cytoskeletal
dynamics for the left- and right-handed snails within a species are not mirror images of eachother. Thus, during the third cleavage, helical spindle inclination (SI) and spiral blastomere
deformation (SD) are observed only in the dominant dextral embryos at metaphase-anaphase,whereas in the recessive sinistral embryos, helicity emerges during the furrow ingression(Fig. 2)2). We have constructed the congenic F10 strain that on average has inherited 99.9%of the sinistral-derived genome and only 0.1% of the dextral strain-derived genome. All thedextral embryos oviposited by F10 animals that inherited the dextrality gene(s) within the
0.1% of the dextral-derived genome exhibited dextrotropical rotation with SD/SI at the 3rdcleavage and without exception grew to possess dextral body shape. Equally, all the sinistralembryos oviposited by F10 animals that do not inherit the dextrality-determining gene(s)showed levotropical rotation without SD/SI, and grew to possess the sinistral body shape,

17

again without exception. These findings strongly suggested that dextrality is determined by asingle gene or by genes at closely linked loci.3)
We carried out positional cloning and identified that Lsdia1 is the strongest candidate genefor the handedness determination. There are tandemly duplicated Lsdia1 and Lsdia2 genes
whose proteins share 89.4% amino acid similarity. In the sinistral strains, both Lsdia1 alleles
had a frameshift mutation early in the coding region (c.184delC) that leads to protein
truncation.4) Further, knocking out the Lsdia1 gene using CRISPR/Cas9 produced sinistrallycoiled offspring generation-after-generation in the otherwise totally-dextral genetic
background, if biallelic frameshift mutations had occurred (Fig. 1c).5) We could show that thegene sets the chirality at the one-cell stage, the earliest observed symmetry-breaking event
linked to body-handedness in the animal kingdom. The gene dictates the entire
chiromorphogenesis programme across the levels of biological hierarchy wherein the early
intra-cellular chirality is superseded by the inter-cellular chirality during the 3rd cleavage,
leading to asymmetric nodal/Pitx expressions and then to organismal body handedness.5)
In parallel, we revealed that mechanical micromanipulation during the 3rd cleavage toreverse the spiral cleavage direction creates mirror-image animals (Fig. 1b, 2). The
expression site of the nodal/Pitx genes was inverted by mechanical micromanipulation. (Fig.
2).6)
Diaphanous genes are present in all the Eukaryotes, and therefore, our work featuringformin-controlled early onset of chirality in L. stagnalis may provide new insight on unifying
mechanisms of l-r body plan formation in animals.
a) Sinistral andDextral in naturec) Sinistral created byb) Created by
CRISPR/Cas9 from Dextral
micromanipulation

NatureNature2004 journal cover

2009

2019 journal coverFig.1 Three l-r pairs in the wild (a) and created (b, c).
Offspring reverts
to the originalchirality

Fig.2. Breaking of mirror-image relationship,and l-r inversion by mechanical manipulation.

References

1. Crampton, H. E. Annals of the New York Academy of Sciences, 8, 167-170 (1894).
2. Shibazaki, Y., Shimizu, M. & Kuroda, R. Curr. Biol. 14, 1462-1467 (2004).
3. Kuroda, R. Quarterly Reviews of Biophysics, Discovery, 48, 445-452 (2015).
4. Kuroda, R. et. al., Scientific Reports, 6, 34809 (2016).
5. Abe, M. & Kuroda, R., Development,146 Dev175976 (2019).
6. Kuroda, R. et al., Nature 462, 790-794 (2009).

18

Morphospace Approaches to Evolu�on:Geometric and Developmental Considera�ons
Dr. Sylvain GerberIns�tut de Systéma�que, Evolu�on, Biodiversité (ISYEB), Muséum na�onal
d'Histoire naturelle,
CNRS, SU, EPHE-PSL, UA, 57 rue Cuvier, CP50, 75005 Paris, Francesylvain.gerber@mnhn.fr

Synopsis
The biological no�on of morphospace is examined from its conceptual and analy�caldimensions. We review the diverse morphospace geometries encountered in the literatureand their implica�ons for the interpreta�ons of morphological paterns. We also show how
considera�ons of organismal development suggest novel mathema�cal structures to endow
the set of morphological variants with evolu�onarily meaningful no�ons of accessibility.

Main text
The no�on of morphospace is both of conceptual and empirical importance in biology andpaleobiology. Conceptually, it has entailed cri�cal discussions about the rela�ve prevalence of
selec�ve forces, varia�onal constraints, and historical con�ngencies in shaping paterns ofmorphological evolu�on. Empirically, morphospaces have proven powerful quan�ta�ve tools
to document and analyze morphological paterns in various research areas, from compara�veanatomy and systema�cs, to func�onal morphology and large-scale studies of clade dynamics.
A morphospace is generally understood as the depic�on of morphological variants as points
in an abstract space in such a way that the rela�ve proximity of points expresses themorphological similarity of variants. Here, we discuss whether this way of conceiving
morphospace is always warranted in empirical studies or even adequate for all researchques�ons. Two main aspects pertaining to morphospace geometry are considered: (i) the
poten�al misinterpreta�on of the geometry induced by some morphometric descriptors and(ii) a no�on of evolu�onary accessibility among variants derived from the developmental
representa�on of morphological traits.
Morphospace narra�ves o�en include statements about distance (between morphologicalvariants) and direc�on (of morphological change) indica�ng that an inner-product geometry(generally the dot product of Euclidean geometry) is assumed for the morphospace. However,
not all morphospaces are equipped with the metric proper�es that one tends to intui�vely
atach to the no�on of ‘space’ [1,2]. So-called ‘theore�cal morphospaces’ are par�cularly

19prone to such non-metric geometries [2]. Raup’s iconic shell coiling morphospace is taken as
an example to illustrate this phenomenon and discuss its implica�ons for biological inferences.
In paleobiology, the use of discrete character data does lead to metric morphospaces(assuming no missing data), but their Hamming-like geometry is some�mes overlooked [3]. In
par�cular, the morphospace and its mul�variate ordina�on are o�en confused for one another,invi�ng the use of inappropriate methodologies for their analyses (Fig. 1A).

Figure 1. (A) Morphospace representa�on from discrete character data; (B) Accessibility structure
mapped onto a morphospace.

Historically, methodological approaches to morphospace construc�on have typically aimed for
metric topologies deﬁned at the morphological level, organizing variants according to theirmorphological similarity. This choice may be subop�mal for addressing some important
evolu�onary ques�ons however, since morphological distance among variants can be a poor
predictor of their evolu�onary accessibility (Fig. 1B). We show how a gene�c or developmental
representa�on of morphological characters allows the deﬁni�on of accessibility among
variants and enriches the explanatory power of morphospace with regards to the role ofconstraints and selec�on in morphological evolu�on [4].
References[1] Huttegger, S. M., & Mitteroecker, P. (2011). Invariance and meaningfulness in phenotype
spaces. Evolutionary Biology, 38, 335-351.
[2] Gerber, S. (2017). The geometry of morphospaces: lessons from the classic Raup shellcoiling model. Biological Reviews, 92(2), 1142-1155.
[3] Gerber, S. (2019). Use and misuse of discrete character data for morphospace and disparity
analyses. Palaeontology, 62(2), 305-319.
[4] Gerber, S. (2014). Not all roads can be taken: development induces anisotropic accessibility
in morphospace. Evolution & Development, 16(6), 373-381.

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Functional morphospace analysis of molluscan shells
Takao Ubukata

Kyoto University

ubukata@kueps.kyoto-u.ac.jp

Morphospace is a powerful tool for large-scale comparison of morphology across a number of
species.

Morphospaces are geometric spaces in which a particular organic form can be plotted withreference axes chosen to represent morphological parameters.

Abstraction of essential

morphological traits allows us to summarize complex morphological variation into a few
dimensional morphospace. If a functional performance can be assessed for a set of organic shapes
accommodated in the morphospace, the relationship between the functional performance andmorphological traits can be visualized as a surface on the morphospace which mimics an adaptive
landscape. The functional morphospace allows us to predict which shape is common or rare fromthe view point of functional morphology. Such a prediction can be readily tested for
paleontologists by referring actual fossil records. The present talk introduces a couple of casestudies on evolutionary morphology of fossil and extant molluscan shells using morphospaces basedon theoretical morphologic models.
In the first topic on bivalve shell morphology, geometric constraints of bivalve shell form
derived from space conflict between umbones of both valves are discussed. A functional
morphospace analysis of bivalve shells using a theoretical morphologic model revealed that the
space conflict between umbones restricts morphological diversity of bivalve shell of each groupdepending on hinge morphology. A characteristic type of ligament evolved in a heteroconch
bivalve in the late Mesozoic may has allowed the clams to develop an adaptive shell shape forburrowing through their macroevolution.
The second topic on shell form of gastropod snails focuses on a functional trade-off between
postural stability and efficiency of shell construction. The result of a functional morphospace
analysis of gastropod shells revealed that mechanical stability of a snail while creeping and theamount of shell material necessary for shell construction both depend on shell shape and are hardly
compatible with each other. The aperture of snail is often inclined to the coiling axis particularly inthe species living in the environment with less buoyancy and calcium carbonate. The results

21suggest that the aperture inclination downward relaxes the functional trade-off between postural
stability and efficiency of shell construction.
The subject of the third topic on cephalopods focuses on the functional properties for theirnektonic mode of life. The functional morphospaces constructed using a theoretical model
representing planispiral cephalopod shells clearly shows a functional trade-off between hydrostaticand hydrodynamic efficiencies: a shell form which minimizes a form drag acting on the shell whileswimming readily maximizes the density of the totally produced shell. The results ofmorphometric analyses indicates the followings. Nautilids tend to be optimized for hydrostatics incomparison with other groups.

Some ammonoid groups seem to be optimized for hydrodynamic

efficiency. Tarphycerid cephalopods tend to have high scores of postural stability. The results
suggest that the macroevolutionary pattern is clearly different among cephalopod phylogenies.
Morphospaces constructed through geometric morphometric and multivariate analyses appear
to be potentially useful for a functional morphospace analysis.

Evolutionary morphology based onmorphospace analysis can be facilitated by big-data analyses using morphological databases.
Combining the conventional functional morphospace analyses and their potentially relevant
techniques is an interesting subject of future research.

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4

Mechanical Optimality Hidden in the Structure of Plants
Hiroyuki Shima
University of Yamanashi, Japanhshima@yamanashi.ac.jp

Plants of various morphology (shape) can be found in nature. These diverse shapes are believed tobe the result of the evolution of plants, which cannot move, to adapt to the surrounding environment.
In this talk, I will particularly focus on the shapes of three plant types: i) bamboo [1-4], ii) butterbur,
and iii) muskmelon [5]. First, I will demonstrate how the shapes of bamboo and butterbur, which areboth tall and hollow plants, are optimal for supporting their own weight. Next, I will explain that therind of muskmelons develops a mesh pattern with a certain geometric property, which may be used by
farmers as a visual indicator of optimum sweetness of flesh; this is a consequence of a farmer seeking
the optimum sweetness of the flesh.
i) Optimal structure of bamboo
Bamboo is the fastest-growing plant worldwide. This rapid maturity stems from their hollow
structures, which require less material to develop, thereby promoting rapid growth. One critical
disadvantage of hollowness is the propensity to easily collapse under external forces such as wind,rain, and self-weight. To overcome this limitation, bamboos generate a sequence of “circular plates”
within the long cavity. The plates stiffen the culm locally; therefore, numerous plates from the bottom
to the top of the bamboo enhance the stability of the culm. However, this is not a case of “the more,
the better”, because an excessive number of plates will inhibit the growth rate of the bamboo plant.
Therefore, the number of plates has to be “neither too many nor too few”. This trade-off between
stability and growth rate implies an optimum number of stiffening plates that bamboo has acquired
over millions of years of evolution.
Against this backdrop, our research group has explored the optimum solution to this issue by
investigating wild bamboo groves in Japan. Analysis of the measurement data showed that a single
universal law explaining the interdependence between the preferred number of stiffening plates andtheir ideal arrangement along the culm governs the growth of bamboo [3]. Specifically, the density at
which fibers are embedded increases as it gets closer to the outer skin. This universal law thus provides
a design criterion, endowing less material and high strength to wild bamboos, which are advantageous
for survival over competing tree species.
Surprisingly, another mechanism lurks in the cross-section of the bamboo to increase its stability
as a whole. It is bamboo fiber. Inside the bamboo, many long fibers are embedded in the longitudinal
direction. These fibers are called "vascular sheaths" in biological terminology, and they act as straws
that convey water and nutrients vertically. The structural mechanics theory revealed that this fiber
plays an important role in the mechanical properties of bamboo. If a part of the cross-section ofbamboo is cut and observed using an electron microscope, it can be seen that the fibers are not
evenly23

distributed over the entire cross-section. Specifically, the closer it is to the outer skin, the more fibers
are embedded. We were able to prove within the scope of the elastic approximation theory that bygathering many reinforcing fibers near the outer skin of the bamboo, the bamboo as a whole is lesslikely to bend [4]. This result indicates that the bamboo makes its own body stronger by efficiently
arranging a limited number of reinforcing fibers inside the cross-section.
ii) Optimal cross-section of butterbur petiole:
There are many plant species with hollow stems and petioles, including those belonging to thefamily Poaceae. One of the reasons why many plant species have hollow tubular structures is thought
to be the structural stabilization provided by hollowness. A tube with a hollow cross-section deforms
less than a solid tube (filled) with the same cross-section. Thus, it can support its own weight by using
minimal resources. In addition, by choosing the optimal cross-sectional shape (circular, polygonal,etc.) according to the growth environment, the resistance to the most influential mechanical loads(crosswind, self-weight of stems, weight of petals, etc.) increases.
From this perspective, the plant that we focused on in this study was the Japanese butterbur, a typeof wild grass. A close examination of the cross-section of the stem of the Japanese butterbur reveals
that it has a shape similar to that of a horse's hoof, which is rarely seen in other plants. We hypothesizedthat this peculiar horseshoe-shaped stem cross-section is the optimal structure for supporting large
leaves at the tip of the stem. We have verified this hypothesis both experimentally and theoretically.
iii) Geometric law of mesh pattern of melon skin:
The surface of muskmelons, which is representative of high-grade melons, has a fine mesh pattern(net). It is empirically known that the appearance of this mesh pattern correlates with the quality of
melons and is used as an important indicator for quality evaluation at production sites. However, only
a few studies have investigated the geometric properties of melon nets.
Our research group took photographs of several muskmelons sold at a retail store (for quality
assurance) and investigated the shape and size of the small green peel fragments separated by white
reticular stripes. Calculating the areas of these small peel fragments, obtaining the probability
distribution curves of the areas, and normalizing them, it was found that the distribution curves wereon a common curve regardless of the type and size of individual melons [5]. Furthermore, this common
probability distribution curve was derived from fracture mechanics theory. This discovery suggests
the possibility of non-destructive identification and evaluation of melon quality using mesh pattern
imaging.

References[1] H. Shima, A. Inoue, and M. Sato: “Bamboo: A Mechanically Optimum Design in Nature”, Chapter
1 in Book: “Bamboo Science and Technology” (Springer, 2023) ISBN: 978-981-99-0014-5[2] A. Inoue and H. Shima: “Survival time of Princess Kaguya in an air-tight bamboo chamber”, Forma
33, 1-5 (2018) [https://forma.katachi-jp.com/frame/33.html][3] H. Shima, M. Sato and A. Inoue: “Self-adaptive formation of uneven node spacings in a wildbamboo”, Physical Review E 93, 022406 (2016)[4] M. Sato, A. Inoue and H. Shima: “Bamboo-inspired optimal design of functionally graded hollow
cylinders”, PLOS ONE 12, e0175029 (2017)[5] Y. Akiba, A. Ishibashi, M. Sato, and H. Shima: “Empirical rule of fruit rind fragmentation inmuskmelon epidermis netting”, Journal of the Physical Society of Japan 91, 104801 (2022)

24

Spiral patterns and morphology in chemical systems
Oliver Steinbock
Florida State University,
Department of Chemistry and Biochemistry,
Tallahassee, FL 32306-4390, USA
E-mail: osteinbock@fsu.edu
Synopsis
This talk will showcase different examples of chemical systems undergoing self-organization far
from the thermodynamic equilibrium. Starting with a brief look at the history of chemical waves
and the work of the field’s pioneers, we will discuss similarities to the growth of unusual
polycrystalline solids called biomorphs and go beyond to the self-propulsion of chemical garden
tubes.
Abstract
Living systems masterfully program molecular events to create macroscopic shapes anddynamics. Can the same be done with inorganic chemistry? I believe the answer is yes if
reactions are kept far from the thermodynamic equilibrium (and your expectations are not toohigh). In my talk, I will introduce several self-organizing chemical systems including theBelousov-Zhabotinsky (BZ) reaction, chemical gardens, biomorphs, and self-propelled catalytic
units capable of swarm-like cooperativity. These examples will illustrate unexpected behaviors
if reactions are allowed to unfold in space and time. Perhaps not surprisingly, similar processes
are used by living systems suggesting system-level interpretations of important biologicalphenomena (e.g. cardiac arrhythmia) and novel approaches to materials science andengineering.
Our discussion of the BZ reaction will focus on three-dimensional patterns and discuss them inthe context of pioneering work by Profs. Stefan Müller, Benno Hess, and Art Winfree. These andother prominent scientists studied two-dimensional spirals, the basic building blocks of scroll
waves that provide the foundation for understanding 3D dynamics. While spiral waves rotate
around point singularities, scroll waves rotate around 1D filaments that move according to theirlocal curvature. Today tomographic methods, numerical simulations, and controlled
manipulations are used to obtain deeper insights into the local pinning to heterogeneities aswell as scroll behavior in gradients. Many of these studies, including the results to bepresented, are motivated by similar phenomena in the ventricles of the human heart and theirlink to sudden cardiac death.

25

Similar nonlinear wave dynamics appear to rule the growth of certain polycrystalline assemblies
known as biomorphs. The smoothly curved and life-like biomorphs form when aqueous
solutions of BaCl2 and silicate react with CO2. The shapes are about 100 μm in size and include
helices, funnels, and urns. The entirely abiotic biomorphs can form from natural spring waters
and constitute intriguing problems for the identification of Earth’s earliest microfossils as wellas the search for life’s remnants on Mars and other planetary bodies.
Lastly, we will present novel results on chemical gardens (CG). In the classical CG experiment,these colorful, hollow precipitate tubes form when a salt crystal is placed into an alkaline
sodium silicate solution. Specific aspects to be covered include a cellular automaton model ofCGs, the involvement of colloidal particles in their growth, and applications as self-propelled
micro-rockets. Our model considers, CG growth based on a simple A+B->C reaction and a lattice
for which each site is exactly one of these three species. We show that the aging of the material
modulates the likelihood of mechanical changes in the position of the solid product C and that astrong preference for changes in the fresh material causes filament (2D) and tube (3D) growth.
The self-propulsion of CG tubes is demonstrated for Mn-containing units in H2O2 solutions. The
tubes are propelled forward by the rhythmic ejection of O2 microbubbles formed in the
catalytic tube cavity. We also observed a characteristic acoustic signature of this propulsionthat allows detailed analyses of the bubble dynamics. These analyses reveal that the tube speed
is determined by the tube diameter (which approximates the step size per bubble) and the
bubble ejection frequency (which is nearly proportional to the H2O2 concentration). Lastly, we
will discuss the swarming behavior of the CG tubes and their interactions with bubble rafts.

References[1]
F. M. Zanotto and O. Steinbock, “Hyperscroll Dynamics: Vortices in Four-dimensional
Networks”, Chaos 31, 053132, 2021.
[2]
P. Knoll, N. Wu, and O. Steinbock, “Spiraling Crystallization Creates Layered Biomorphs”,
Phys. Rev. Materials 4, 063402, 2020.
[3]
B. C. Batista, A. Z. Morris, O. Steinbock, “Pattern selection by material aging: Modelingchemical gardens in two and three dimensions”, Proc. Natl. Acad. Sci. USA 120, e2305172120
2023.

26

Autonomous Workload Regulation Mechanism
in Foraging Ants
Hiraku Nishimori*, Masashi S hi r ai s hi , Osamu Ya m a n ak a
Meiji Institute for Advanced Study of Mathematical Sciences,
Meiji University* Correspondence: nishimor2@meiji.ac.jp

As the basic mechanism to enable task allocation in ant colonies without a leader, theprimary role of the caste system has been discussed [1], through which system, specific tasks
are autonomously assigned to individual workers according to their size, age, and other factors.
Even among specialized ants that are involved in the same task, a hierarchical structure, namely,a heterogeneity of workload is observed.
In the present study, we introduced an experimental system to observe the statisticalbehavior of colonies of ants, Camponotus japonicus, using tiny RFID tags attached to the bodies
of all ants in 5 colonies (Fig.1) [4]. By analyzing the “big data of ant society” focusing on
foraging behavior obtained through more than three months of continuous measurement, wefound various kinds of statistical characteristics of the ant society; i)The emergence of theforaging workload hierarchy, namely, the heterogeneity of the diligence on foraging task, thatobeys a simple mathematical form of distribution, ii)Autonomous workload compensation after
the separation of each colony into two
different groups; the diligent half before
separation, and, the lazy half, and, iii)The
slowly decreasing correlation of rank-orderof diligence with a characteristic durationof a month.
Fig.1 RFID tag is affixed to the center of the redcircle in the enlarged image.

27

As a mathematical model to numerically reproduce the characteristic behavior of social insects; ants
and bees, the response threshold model [3] is widely known. To analytically treat the response model,
we introduce a corresponding master equation. In conjunction with foraging behavioral data obtained
through the above-mentioned long-term observation using tiny RFID tags [4], we found that a masterequation approach is effective in quantitatively describing the statistical features of the collective
foraging-task engagement of ants. Specifically, the following two kinds of statistical characters related
to the autonomous workload compensation in ant colonies were indicated; i) Response threshold θ forstarting the foraging task is not uniformly nor normally distributed but largely skewed among ants ineach colony(Fig.2). ii)Foraging-task in a colony is carried only by a small fraction of workers in a colony.

Fig.2 Estimated distributions of the response threshold f (θ) of the foraging task through the combinatory
analysis of master equation and the experimental outcomes of the goraging activity of Camponotus
japonicus’s colony. The shape of f (θ) varies according to the experimentally unconfirmed values ofparameters, α, β, and δ. However, if β is fixed, the change of α and δ is reflected in s0, then, all graphs
overlap after rescaling.

References[1] E. O. Wilson, Behav. Ecol. Sociobio., 14, 47(1983).
[2] D. Charbonneau et al., PLOS ONE, 12(9), e0184074(2017).
[3] E. Bonabeau et al., Proc.Roy.Soc.Lond.B, 263(1996).
[4] O. Yamanaka et al., Scientific Reports, 9, 1 (2019).

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