**3.6 Phyllotaxis**

*Current Topics in Chirality - From Chemistry to Biology*

has not yet been introduced to England.

S or Z is the most reasonable and unequivocal.

gene expression patterns established differently for each species.

species specific trait. *Wisteria sinensis* and Japanese *Wisteria floribunda,* both the attractive ornamental vines, are opposite in this respect. Darwin, who was very interested in twinning plants and made observations on *W. sinensis* stated: "*I have seen no instance of two species of the same genus twinning in opposite directions, and such cases must be rare"* [61]. He could say so because in his times Japanese *Wisteria*

The confusing descriptions of *Wisteria* in botanical literature [63] show clearly that there is a certain problem with definition of a chiral configuration of structures or processes with mirror symmetry in biological systems. *W. sinensis* ascending shoot twins CW when looked at from its base and CCW when looked at from above. The same configuration of this plant twining, in some sources is claimed to be CCW [64] in others CW [65]. In Darwin's words the plant "*moves against the sun*" [61]. Compton and Lack [63] claim that *W. floribunda*:" … has climbing woody stems twining from left to right…", which should not be if it is truly opposite to *W. sinensis*. It all shows the importance of clear convention how the chiral configuration is determined. Moving along the S helix upward is a CW motion whereas descending along the same line we move CCW. While looked at from outside the *W. sinensis* twins from the left to right (Z configuration). It is opposite (S configuration) when looked at from the inside of the growing shoot's helical structure. The same necessity of defining chiral configuration according to specific convention applies to the cellulose microfibrils rotated in the layers of the plant cell secondary wall, to the spiral grain in a tree trunk or to the cells enveloping charophyte oogonia. It seems that definition of the helix chiral configuration, looked at from its outside, as being

Molecular mechanism responsible for the direction of plant climbers twinning is not known. The results of the studies on the *lefty* and *spiral* mutants of the model plant *Arabidopsis thaliana* [40–42] suggest the involvement of the genetic factor. It is possible that the species specific behavior depends on distinct and constitutive

The petal folding in a flower bud, in most of the flowering plants, is clearly chiral. Petals overlap either CCW or CW and this chiral configuration is often later maintained in fully developed flower (**Figure 8**). The direction of petals

**172**

**Figure 8.**

**3.5 Aestivation**

*pinwheel-like corolla of an open flower (right).*

*The chiral CW folding (aestivation) of petals in Hawaiian plumeria's flower bud (left) is maintained in a* 

Among best known chiral phenomena and investigated since the ancient times [66] is helical phyllotaxis – the regular distribution of lateral organs such as leaves or flowers on a plant shoot. Their consecutive primordia, circumferentially equidistant, emerge on the vertically growing shoot apex in the regular intervals. The primordia may be connected with an imaginary line called ontogenetic helix. The helix S or Z configuration depends on whether the process of primordia initiation proceeds CW or CCW. The plantlets growing from seeds have this configuration established at random in the main axis. It is not so, however, in the axes of lateral branches. Their ontogenetic helix may be either concordant (a homodromy case) or discordant (an antidromy case) with that of the supporting axis. It has been found, that even when both phyllotactic correlations occur with the same frequency [67] the supporting axis and the laterals may have the same chirality of vascular sympodia - elements of the internal transport system strongly related to phyllotaxis (**Figure 9**).

The sympodia follow the course of one set of superficial secondary helices - phyllotactic prastichies. Two sets of parastichies running in opposite directions constitute a phyllotactic lattice. This is why even when ontogenetic helices in two axes making up one branching unit are discordant, the axes still may be concordant on the level of their vasculature. The numbers of parastichies in the sets of opposite chiral configuration belong to the mathematical series, the quality of which is associated with the size of circumferential distance between successive primordia. This distance, usually given in an angular measure, is known as divergence angle. The most common is the main Fibonacci series (1,1,2,3,5,8,13…) present in the system with the divergence angle approximating 137,5 degrees or Lucas series (1,3,4,7,11 …) with the angle close to 99,5 degrees. There are also many other divergencies and phyllotactic patterns [68].

#### **Figure 9.**

*Scheme on the left shows how, in the laterals of one coniferous branching shoot, ontogenetic helix may be either S (blue) or Z (red) but orientation of vascular sympodia the same in the whole system. The sympodia chiral configuration depends on their number, which is one of the mathematical series shown below the scheme. H- homodromic, A - antidromic correlations of chiral configurations. Upper right photo shows the righthanded and lefthanded whirls of needles in two coniferous shoots with the same S Fibonacci phyllotaxis. Their opposite chiral configurations, resulting likely from growing shoot rotation, are caused by the different sympodia numbers and orientations shown below.*

#### **Figure 10.**

*Shoot apical meristems isolated from winter buds of balsam fir (*Abies balsamea*) are truly green living crystals. The needle primordia are tightly packed on their lateral surface resembling crystal lattice. The unique case shown here illustrates the atavistic trait of dichotomy, rare in otherwise strictly monopodial conifer.*

Asymmetry of phyllotactic lattice with regard to the shoot axis is most probably responsible for the peculiar twirling of needles frequently seen on the top of coniferous shoot (**Figure 9**). The chirality of these twirls results likely from the growing shoot torsion and is rather related to the orientation of vascular sympodia than to the chiral configuration of ontogenetic helix.

Regularity of primordia initiation resembles crystal growth. The plant apical meristem where the primordia are tightly packed may be called by *licentia poetica*, a living crystal [69] (**Figure 10**). The similarity has been strengthened by the discovery that in phyllotactic lattices dislocations occur [68–70]. Single dislocation often changes not only a quality of the pattern but, most importantly, the chirality of ontogenetic helix (**Figure 11**).

#### **3.7 Snail shell, narwhal tooth and ourselves**

Chirality of spiral snail shells has intrigued the scientists for centuries not less than the regularity of phyllotaxis. One of the memorable episodes from the Jules Verne's

#### **Figure 11.**

*Modeling clay replica of magnolia's reproductive shoot shows single dislocation (red lines) in the phyllotactic lattice. This developmental event changes here not only the phyllotactic pattern but also the chiral configuration of ontogenetic helix. Red dots label the same pattern element replicated twice on both sides of the unrolled surface of the shoot; it enables counting the numbers of parastichies in two opposite sets; the numbers change from 5:9 to 5:8.*

**175**

**4. Conclusion**

*Mirror Symmetry of Life*

*DOI: http://dx.doi.org/10.5772/intechopen.96507*

terns in wild type organisms and mutants [71, 72].

example of Darwinian selection!

famous novel *Twenty Thousand Leagues Under the Seas* tells the story of Professor Aronnaux finding the extreme rarity – lefthanded shell of the olive snail. It is known to malacologists that approximately 90% of all gastropods have their shells righthanded – of Z type. However, there are snails like *Amhidromus inversus* that have dextral and sinistral shells equally frequent, or like *Neptunea angulata* where the shells are exclusively sinistral. Notably the Z shell grows as the descending spiral, coiling from the top downward. Therefore moving downward the dextral spiral of the shell we execute CW motion not CCW as it would be in the case of ascending helices of plant structures. The direction of the shell coiling is initiated in the embryo by the spiral cell cleavage typical for lower Metazoa including snails. At this stage there is a possibility of altering the normal pattern and forcing experimentally the development of opposite chirality. The genetic mechanisms determining the chirality patterning in snails are slowly being unraveled through studying specific gene expression pat-

However, the reason for a change in a frequency of shell chiral configuration among individuals within a population sometimes can be truly surprising. It was found that among small, properly righthanded *Satsuma* snails the opposite, lefthanded individuals started growing in number. Thorough studies revealed that it was due to activity of predators [73]. The snakes *(Pareas iwasakii)* with their asymmetric jaws, preferably eating the righthanded snails, decimated their population. Through the selective elimination of these snails from the initial population, the snakes contributed to the prevalence of rare lefthanded snails. The divergence of the initial population led to development of a new species. What a wonderful

In contrast to the snails equipped with molecular mechanism allowing for development of S or Z shells another famous chiral structure in animal kingdom, the narwhal tusk exhibits always a lefthanded spiral (S). It is so even in a case of both tusks being fully developed in one individual, which is rare. The opposite spiral is perhaps also possible as shows the walking stick used by Darwin displayed in the collections of Science Museum, UK [74]. Either the material it is made of is not a narwhal tusk or Darwin, who was very interested in cases of mirror-symmetry in nature [61], consciously adopted and used this particular object being aware of its uniqueness. The third, least probable possibility is that the artist carved the right spiral from the polished left spiral of the narwhal tusk. The reason for the prevalence of one chiral configuration in spiraling of the narwhal tusks is unknown. L/R symmetry of our body is best illustrated by asymmetry of the internal organ positions like heart or liver. It is our hands, however, that are most frequently presented as an example of mirror symmetry. Less known aspect of the symmetry in a human body is the hair whorl resembling, with all due proportion, the twirling needles in coniferous shoot (**Figure 9**). There is a dispute over significance of the observation that the righthanded people have more frequently their hair twirling CW on the top of their heads. Half of the lefthanded people have in turn the CCW hair whorls. Until now the search for possible common, genetic etiology of these chiral phenomena has been unsuccessful [75]. There is also unknown whether the scalp hair whorl chirality is concordant or discordant with the smaller whorls of minute hair covering our whole body. These become visible, especially in children, when their skin is suntanned.

There is no one universal mechanism that stays behind the mirror symmetry of life. The frequency of both chiral configurations is not the same in different biological systems. However, as it has been discussed here, it was not always assessed

#### *Mirror Symmetry of Life DOI: http://dx.doi.org/10.5772/intechopen.96507*

*Current Topics in Chirality - From Chemistry to Biology*

the chiral configuration of ontogenetic helix.

**3.7 Snail shell, narwhal tooth and ourselves**

ontogenetic helix (**Figure 11**).

**Figure 10.**

Asymmetry of phyllotactic lattice with regard to the shoot axis is most probably responsible for the peculiar twirling of needles frequently seen on the top of coniferous shoot (**Figure 9**). The chirality of these twirls results likely from the growing shoot torsion and is rather related to the orientation of vascular sympodia than to

*Shoot apical meristems isolated from winter buds of balsam fir (*Abies balsamea*) are truly green living crystals. The needle primordia are tightly packed on their lateral surface resembling crystal lattice. The unique case shown here illustrates the atavistic trait of dichotomy, rare in otherwise strictly monopodial conifer.*

Regularity of primordia initiation resembles crystal growth. The plant apical meristem where the primordia are tightly packed may be called by *licentia poetica*, a living crystal [69] (**Figure 10**). The similarity has been strengthened by the discovery that in phyllotactic lattices dislocations occur [68–70]. Single dislocation often changes not only a quality of the pattern but, most importantly, the chirality of

Chirality of spiral snail shells has intrigued the scientists for centuries not less than the regularity of phyllotaxis. One of the memorable episodes from the Jules Verne's

*Modeling clay replica of magnolia's reproductive shoot shows single dislocation (red lines) in the phyllotactic lattice. This developmental event changes here not only the phyllotactic pattern but also the chiral configuration of ontogenetic helix. Red dots label the same pattern element replicated twice on both sides of the unrolled surface of the shoot; it enables counting the numbers of parastichies in two opposite sets; the numbers change from 5:9 to 5:8.*

**174**

**Figure 11.**

famous novel *Twenty Thousand Leagues Under the Seas* tells the story of Professor Aronnaux finding the extreme rarity – lefthanded shell of the olive snail. It is known to malacologists that approximately 90% of all gastropods have their shells righthanded – of Z type. However, there are snails like *Amhidromus inversus* that have dextral and sinistral shells equally frequent, or like *Neptunea angulata* where the shells are exclusively sinistral. Notably the Z shell grows as the descending spiral, coiling from the top downward. Therefore moving downward the dextral spiral of the shell we execute CW motion not CCW as it would be in the case of ascending helices of plant structures.

The direction of the shell coiling is initiated in the embryo by the spiral cell cleavage typical for lower Metazoa including snails. At this stage there is a possibility of altering the normal pattern and forcing experimentally the development of opposite chirality. The genetic mechanisms determining the chirality patterning in snails are slowly being unraveled through studying specific gene expression patterns in wild type organisms and mutants [71, 72].

However, the reason for a change in a frequency of shell chiral configuration among individuals within a population sometimes can be truly surprising. It was found that among small, properly righthanded *Satsuma* snails the opposite, lefthanded individuals started growing in number. Thorough studies revealed that it was due to activity of predators [73]. The snakes *(Pareas iwasakii)* with their asymmetric jaws, preferably eating the righthanded snails, decimated their population. Through the selective elimination of these snails from the initial population, the snakes contributed to the prevalence of rare lefthanded snails. The divergence of the initial population led to development of a new species. What a wonderful example of Darwinian selection!

In contrast to the snails equipped with molecular mechanism allowing for development of S or Z shells another famous chiral structure in animal kingdom, the narwhal tusk exhibits always a lefthanded spiral (S). It is so even in a case of both tusks being fully developed in one individual, which is rare. The opposite spiral is perhaps also possible as shows the walking stick used by Darwin displayed in the collections of Science Museum, UK [74]. Either the material it is made of is not a narwhal tusk or Darwin, who was very interested in cases of mirror-symmetry in nature [61], consciously adopted and used this particular object being aware of its uniqueness. The third, least probable possibility is that the artist carved the right spiral from the polished left spiral of the narwhal tusk. The reason for the prevalence of one chiral configuration in spiraling of the narwhal tusks is unknown.

L/R symmetry of our body is best illustrated by asymmetry of the internal organ positions like heart or liver. It is our hands, however, that are most frequently presented as an example of mirror symmetry. Less known aspect of the symmetry in a human body is the hair whorl resembling, with all due proportion, the twirling needles in coniferous shoot (**Figure 9**). There is a dispute over significance of the observation that the righthanded people have more frequently their hair twirling CW on the top of their heads. Half of the lefthanded people have in turn the CCW hair whorls. Until now the search for possible common, genetic etiology of these chiral phenomena has been unsuccessful [75]. There is also unknown whether the scalp hair whorl chirality is concordant or discordant with the smaller whorls of minute hair covering our whole body. These become visible, especially in children, when their skin is suntanned.

#### **4. Conclusion**

There is no one universal mechanism that stays behind the mirror symmetry of life. The frequency of both chiral configurations is not the same in different biological systems. However, as it has been discussed here, it was not always assessed

carefully enough by investigators. *Spirogyra* case is uncertain. The narwhal tusks are probably always S-helical. On the contrary the shell coiling in most of the snails is of Z type. In many systems the chiral configuration of structures or processes is strictly controlled, in many others the control is loose or absent, which results in equal frequency of both S and Z forms.

In light of the newly discovered intrinsic cell chirality in animal cells we have now a great perspective of disentangling the ultracellular and molecular basis for the dynamic wavy and spiral patterns developing in cambia of trees - one of the most intriguing and least known biological rhythms. Discovered and thoroughly characterized by Hejnowicz and his followers in the last decades of past century it still remains a great mystery. Neither the nature of specific positional signals coming from the dynamic morphogenetic field to the cambial stem cells nor the mechanism of their response i.e. S or Z oriented cell divisions on the cylindrical surface of this embryonic tissue, have been elucidated. The tissue is also intriguing because of its structure. It may be compared to that of the liquid crystals – the elongated cambial stem cells may be aligned in the regular horizontal tiers, like the molecules in the smectic phase of the liquid crystal, or irregularly but parallel to the vertical axis, like in the nematic phase. The oscillating cambial cells taken together with their derivatives, continuously rotated in the successive wood layers, resemble the third, cholesteric phase of the liquid crystal [76].

Biomechanics of structures based on the possibility of changing chiral configurations, clearly the adaptive trait, cannot be underestimated. The resulting interlocked systems provide high resistance to mechanical stress. Interlocked are the cellulose microfibrils in the successive layers of the secondary cell wall in a single cell and, on the macroscale, the oppositely oriented wood fibers in the packets of consecutive wood increments of such giants as mahogany or camphor trees. Also the system of cortical resin canals in the young coniferous shoots, which runs oppositely to oriented vascular sympodia strengthens the axis mechanically.

These examples together with the crystalline character of phyllotactic patterns and cambial cells arrangements bring us back to already mentioned, at the beginning of this chapter, universality of some solutions based last but not least on the presence of mirror symmetry of life.

## **Acknowledgements**

The author expresses sincere thanks to her long life associates in the Department of Plant Developmental Biology at the University of Wroclaw, Poland for their continuous inspiration and support; especially to Dr. Katarzyna Sokołowska, who helped here with **Figure 5**, Dr. Alicja Banasiak, expert on plant cell walls and polar auxin transport and to Magdalena Turzańska (MSc), an excellent bryologist, for our endless discussions on the hidden beauty of a small world she immortalizes on her artistic microphotographs.

**177**

**Author details**

Beata Zagórska-Marek

University of Wrocław, Wrocław, Poland

provided the original work is properly cited.

\*Address all correspondence to: beata.zagorska-marek@uwr.edu.pl

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

*Mirror Symmetry of Life*

*DOI: http://dx.doi.org/10.5772/intechopen.96507*

*Mirror Symmetry of Life DOI: http://dx.doi.org/10.5772/intechopen.96507*

*Current Topics in Chirality - From Chemistry to Biology*

equal frequency of both S and Z forms.

cholesteric phase of the liquid crystal [76].

presence of mirror symmetry of life.

**Acknowledgements**

artistic microphotographs.

carefully enough by investigators. *Spirogyra* case is uncertain. The narwhal tusks are probably always S-helical. On the contrary the shell coiling in most of the snails is of Z type. In many systems the chiral configuration of structures or processes is strictly controlled, in many others the control is loose or absent, which results in

In light of the newly discovered intrinsic cell chirality in animal cells we have now a great perspective of disentangling the ultracellular and molecular basis for the dynamic wavy and spiral patterns developing in cambia of trees - one of the most intriguing and least known biological rhythms. Discovered and thoroughly characterized by Hejnowicz and his followers in the last decades of past century it still remains a great mystery. Neither the nature of specific positional signals coming from the dynamic morphogenetic field to the cambial stem cells nor the mechanism of their response i.e. S or Z oriented cell divisions on the cylindrical surface of this embryonic tissue, have been elucidated. The tissue is also intriguing because of its structure. It may be compared to that of the liquid crystals – the elongated cambial stem cells may be aligned in the regular horizontal tiers, like the molecules in the smectic phase of the liquid crystal, or irregularly but parallel to the vertical axis, like in the nematic phase. The oscillating cambial cells taken together with their derivatives, continuously rotated in the successive wood layers, resemble the third,

Biomechanics of structures based on the possibility of changing chiral configurations, clearly the adaptive trait, cannot be underestimated. The resulting interlocked systems provide high resistance to mechanical stress. Interlocked are the cellulose microfibrils in the successive layers of the secondary cell wall in a single cell and, on the macroscale, the oppositely oriented wood fibers in the packets of consecutive wood increments of such giants as mahogany or camphor trees. Also the system of cortical resin canals in the young coniferous shoots, which runs oppositely to oriented vascular sympodia strengthens the axis mechanically.

These examples together with the crystalline character of phyllotactic patterns and cambial cells arrangements bring us back to already mentioned, at the beginning of this chapter, universality of some solutions based last but not least on the

The author expresses sincere thanks to her long life associates in the Department

of Plant Developmental Biology at the University of Wroclaw, Poland for their continuous inspiration and support; especially to Dr. Katarzyna Sokołowska, who helped here with **Figure 5**, Dr. Alicja Banasiak, expert on plant cell walls and polar auxin transport and to Magdalena Turzańska (MSc), an excellent bryologist, for our endless discussions on the hidden beauty of a small world she immortalizes on her

**176**
