Leaf math: how one unusual bush changed the equation of a plant growth model
We love the leaves for their shade, autumn colors, smell, and the arrangement of the leaves of a plant is a practical way to determine their species. However, the details of how plants control the location of their leaves, remained in botany an inexplicable riddle. One species of Japanese plants with an unusual pattern of leaf placement has recently allowed us to look at an unexpected angle at how almost all plants control this arrangement.
“We have developed a new model to explain one particular pattern of the arrangement of leaves (phyllotaxis). But in fact, it reflects more accurately not only the nature of this particular plant, but also the wide variety of almost all leaf patterns observed in nature, ”says Associate Professor of the Botanical Garden Koisikawa of Tokyo University Munetaka Sugiyama.
Leaves on O. japonica branch (top left) and schematic representation of orixate phyllotaxis (right). The orixate pattern demonstrates an unusual cycle of changing the angles of the leaves, consisting of four values ​​(from 180 degrees to 90 degrees, then to 180 degrees and to 270 degrees). The image from the scanning electron microscope (in the center and lower left) shows the winter bud of Orixa japonica, in which leaves begin to grow. Leaf buds are sequentially labeled from the oldest leaf (P8) to the youngest (P1). Point O marked the tip of the shoot.
To determine the placement of leaves, botanists measure the angles between the leaves, moving along the stem from the oldest to the youngest leaf.
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Standard patterns are symmetrical, the leaves are arranged at regular intervals of 90 degrees (basil or mint), 180 degrees (stem herbs, such as bamboo), or Fibonacci spirals with golden corners (for example, needles of some spherical cacti or succulent aloe multi-leaved).
An unusual pattern, studied by the research team of assistant professor Sugiyama, is named “orixate” in honor of Orixa japonica , a shrub native to Japan, China and the Korean Peninsula. Sometimes O. japonica is used as a hedge.
The angles between the leaves of O. Japonica are 180 degrees, 90 degrees, 180 degrees, 270 degrees, and then the next sheet “drops” the pattern back to 180 degrees.
“Our research gives the potential to fully understand the amazing patterns of nature,” says Sugiyama.
Sugiyama’s research team began its study with an exhaustive test of the mathematical equation used to model the placement of leaves.
Mathematically, the arrangement of leaves has been modeled since 1996 using an equation known as DC2 (Douady and Couder 2). The equation can generate many, but not all, patterns of leaf placement observed in nature, due to changes in various plant physiology variables, such as the relationship between different plant organs or the strength of chemical signals within the plant.
DC2 has two flaws that the researchers wanted to eliminate:
1) Whatever values ​​we put into the DC2 equation, some rare layout patterns cannot be calculated.
2) The Fibonacci spiral pattern (gold spiral) is the most common spiral pattern observed in nature, but it is only slightly more common than other spiral patterns calculated by the DC2 equation.
Orixate phyllotaxis simulation in accordance with Expanded Douady and Couder 2. Video by Takaki Yonekura, CC-BY-ND, originally published on PLOS Computational Biology DOI: 10.1371 / journal.pcbi.1007044
At least four unrelated plant species have an unusual orixate leaf pattern. Researchers suspect that it should be possible to create an orixate pattern using a fundamental genetic and cellular mechanic common to all plants, because the opposite possibility of individual evolutionary change that led to the same, very unusual pattern four or more times seems too improbable.
The DC2 equation uses one fundamental assumption that the leaves emit a constant signal to suppress the growth of other leaves near them, and with increasing distance this signal becomes weaker. Researchers suspect that this signal is most likely associated with the plant hormone auxin, but the specific physiology remains unknown.
“We abandoned this fundamental assumption, assuming that the power of repression is not really constant, but changes with age. We tested both increasing and decreasing strength with increasing age, and noticed that an unusual orixate pattern is calculated when the old leaves have a stronger suppressive effect, ”says Sugiyama.
This conjecture that the power of the overwhelming signal changes with age can be used for direct further studies of the genetics or physiology of plant development.
Researchers call this new version of the EDC2 equation (Expanded Douady and Couder 2).
The first author of a research article, a graduate student, Takaaki Youngakura, developed computer simulations to generate thousands of leaf placement patterns calculated by the EDC2 equation, as well as to calculate the generation frequency of identical patterns. More common patterns in nature were calculated by EDC2 more often, further reinforcing the accuracy of the ideas used to create the formula.
“There are other very unusual leaf pattern patterns that are still not explained by our new formula. Now we are trying to create a new concept that will be able to explain all the known patterns of the location of the leaves, but not almost everything , ”said Sugiyama.
Each video below shows a top view of the patterns of the location of the leaves in the formation of new leaves (red semicircles) from the top of the shoot (black circle in the center) and their growth outwards. The suppression field is represented as a contour map, in which the highest suppression force is red, and the lowest is shown in blue.
Simulation of opposite (two-way, distichous) phyllotaxis by the equation Expanded Douady and Couder 2. Video Takaaki Yonekura, CC-BY-ND
Expanded Douady and Couder 2: Golden Helix Fillotaxis Simulation Video Takaaki Yonekura, CC-BY-ND
Cross-pair simulation (decussate) of phyllotaxis by the equation Expanded Douady and Couder 2. Video Takaaki Youngakura, CC-BY-ND
Simulation of a tripartite (tricussate) phyllotaxis Expanded Douady and Couder 2. Video Takaaki Youkura, CC-BY-ND
To determine the pattern of arrangement of leaves (phyllotaxis), experts recommend studying the group with respect to new leaves. (In ancient Greek, phyllon (phillon) means “leaf.”) Older leaves can change their direction (due to wind or exposure to the sun), which can make it difficult to determine their true angle of attachment to the stem.
Imagine a stem in the form of a circle and begin to carefully observe where the oldest and next oldest leaves are attached to the circle. The angle between these two leaves will be the first "angle of divergence." Continue to fix the angles of divergence between the ever younger leaves on the stem. The pattern of angles of divergence is a pattern of the location of the leaves.
The most common leaf patterns are opposite (regular with an angle of 180 degrees, bamboo), Fibonacci spiral (regular with an angle of 137.5 degrees, succulent Graptopetalum paraguayense ), cross-paired (regular with an angle of 90 degrees, basil) and triangular (regular with 60 degree angle, Nerium oleander ).
The arrangement of leaves with one leaf per node is called alternate phyllotaxis, and the arrangement of two or more leaves per node is called whorled. The common types of alternate phyllotaxis are opposite (distichous) (bamboo) and spiral (aloe succulent multivalent), and the common mute species are cross-paired (decussate) (basil and mint) and triangular (tricussate) ( Nerium oleander ). Image of Takaaki Youngakura, CC-BY-ND
Takaaki Yonekura, Akitoshi Iwamoto, Hironori Fujita, Munetaka Sugiyama, " PLOS Computational Biology : June 6, 2019, doi: 10.1371 / journal.pcbi.1007044.
Link ( Publication )
“We have developed a new model to explain one particular pattern of the arrangement of leaves (phyllotaxis). But in fact, it reflects more accurately not only the nature of this particular plant, but also the wide variety of almost all leaf patterns observed in nature, ”says Associate Professor of the Botanical Garden Koisikawa of Tokyo University Munetaka Sugiyama.
It's all about the corners
Leaves on O. japonica branch (top left) and schematic representation of orixate phyllotaxis (right). The orixate pattern demonstrates an unusual cycle of changing the angles of the leaves, consisting of four values ​​(from 180 degrees to 90 degrees, then to 180 degrees and to 270 degrees). The image from the scanning electron microscope (in the center and lower left) shows the winter bud of Orixa japonica, in which leaves begin to grow. Leaf buds are sequentially labeled from the oldest leaf (P8) to the youngest (P1). Point O marked the tip of the shoot.
To determine the placement of leaves, botanists measure the angles between the leaves, moving along the stem from the oldest to the youngest leaf.
')
Standard patterns are symmetrical, the leaves are arranged at regular intervals of 90 degrees (basil or mint), 180 degrees (stem herbs, such as bamboo), or Fibonacci spirals with golden corners (for example, needles of some spherical cacti or succulent aloe multi-leaved).
An unusual pattern, studied by the research team of assistant professor Sugiyama, is named “orixate” in honor of Orixa japonica , a shrub native to Japan, China and the Korean Peninsula. Sometimes O. japonica is used as a hedge.
The angles between the leaves of O. Japonica are 180 degrees, 90 degrees, 180 degrees, 270 degrees, and then the next sheet “drops” the pattern back to 180 degrees.
“Our research gives the potential to fully understand the amazing patterns of nature,” says Sugiyama.
Plant math
Sugiyama’s research team began its study with an exhaustive test of the mathematical equation used to model the placement of leaves.
Mathematically, the arrangement of leaves has been modeled since 1996 using an equation known as DC2 (Douady and Couder 2). The equation can generate many, but not all, patterns of leaf placement observed in nature, due to changes in various plant physiology variables, such as the relationship between different plant organs or the strength of chemical signals within the plant.
DC2 has two flaws that the researchers wanted to eliminate:
1) Whatever values ​​we put into the DC2 equation, some rare layout patterns cannot be calculated.
2) The Fibonacci spiral pattern (gold spiral) is the most common spiral pattern observed in nature, but it is only slightly more common than other spiral patterns calculated by the DC2 equation.
Unusual pattern
Orixate phyllotaxis simulation in accordance with Expanded Douady and Couder 2. Video by Takaki Yonekura, CC-BY-ND, originally published on PLOS Computational Biology DOI: 10.1371 / journal.pcbi.1007044
At least four unrelated plant species have an unusual orixate leaf pattern. Researchers suspect that it should be possible to create an orixate pattern using a fundamental genetic and cellular mechanic common to all plants, because the opposite possibility of individual evolutionary change that led to the same, very unusual pattern four or more times seems too improbable.
The DC2 equation uses one fundamental assumption that the leaves emit a constant signal to suppress the growth of other leaves near them, and with increasing distance this signal becomes weaker. Researchers suspect that this signal is most likely associated with the plant hormone auxin, but the specific physiology remains unknown.
Rare patterns and standard rules
“We abandoned this fundamental assumption, assuming that the power of repression is not really constant, but changes with age. We tested both increasing and decreasing strength with increasing age, and noticed that an unusual orixate pattern is calculated when the old leaves have a stronger suppressive effect, ”says Sugiyama.
This conjecture that the power of the overwhelming signal changes with age can be used for direct further studies of the genetics or physiology of plant development.
Researchers call this new version of the EDC2 equation (Expanded Douady and Couder 2).
The first author of a research article, a graduate student, Takaaki Youngakura, developed computer simulations to generate thousands of leaf placement patterns calculated by the EDC2 equation, as well as to calculate the generation frequency of identical patterns. More common patterns in nature were calculated by EDC2 more often, further reinforcing the accuracy of the ideas used to create the formula.
“There are other very unusual leaf pattern patterns that are still not explained by our new formula. Now we are trying to create a new concept that will be able to explain all the known patterns of the location of the leaves, but not almost everything , ”said Sugiyama.
Each video below shows a top view of the patterns of the location of the leaves in the formation of new leaves (red semicircles) from the top of the shoot (black circle in the center) and their growth outwards. The suppression field is represented as a contour map, in which the highest suppression force is red, and the lowest is shown in blue.
Simulation of opposite (two-way, distichous) phyllotaxis by the equation Expanded Douady and Couder 2. Video Takaaki Yonekura, CC-BY-ND
Expanded Douady and Couder 2: Golden Helix Fillotaxis Simulation Video Takaaki Yonekura, CC-BY-ND
Cross-pair simulation (decussate) of phyllotaxis by the equation Expanded Douady and Couder 2. Video Takaaki Youngakura, CC-BY-ND
Simulation of a tripartite (tricussate) phyllotaxis Expanded Douady and Couder 2. Video Takaaki Youkura, CC-BY-ND
Do it yourself: identify the pattern
To determine the pattern of arrangement of leaves (phyllotaxis), experts recommend studying the group with respect to new leaves. (In ancient Greek, phyllon (phillon) means “leaf.”) Older leaves can change their direction (due to wind or exposure to the sun), which can make it difficult to determine their true angle of attachment to the stem.
Imagine a stem in the form of a circle and begin to carefully observe where the oldest and next oldest leaves are attached to the circle. The angle between these two leaves will be the first "angle of divergence." Continue to fix the angles of divergence between the ever younger leaves on the stem. The pattern of angles of divergence is a pattern of the location of the leaves.
The most common leaf patterns are opposite (regular with an angle of 180 degrees, bamboo), Fibonacci spiral (regular with an angle of 137.5 degrees, succulent Graptopetalum paraguayense ), cross-paired (regular with an angle of 90 degrees, basil) and triangular (regular with 60 degree angle, Nerium oleander ).
The arrangement of leaves with one leaf per node is called alternate phyllotaxis, and the arrangement of two or more leaves per node is called whorled. The common types of alternate phyllotaxis are opposite (distichous) (bamboo) and spiral (aloe succulent multivalent), and the common mute species are cross-paired (decussate) (basil and mint) and triangular (tricussate) ( Nerium oleander ). Image of Takaaki Youngakura, CC-BY-ND
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Takaaki Yonekura, Akitoshi Iwamoto, Hironori Fujita, Munetaka Sugiyama, " PLOS Computational Biology : June 6, 2019, doi: 10.1371 / journal.pcbi.1007044.
Link ( Publication )
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Source: https://habr.com/ru/post/457470/
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