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A developmental basis for stochasticity in floral organ numbers.

Kitazawa MS, Fujimoto K - Front Plant Sci (2014)

Bottom Line: Such morphological stochasticity is found in foral organ numbers.The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa.We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Theoretical Biology, Department of Biological Sciences, Osaka University Toyonaka, Osaka, Japan ; Research Fellow of the Japan Society for the Promotion of Science, Osaka University Toyonaka, Osaka, Japan.

ABSTRACT
Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers. Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 50 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type) organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning.

No MeSH data available.


The five statistics used to fit the variation in the floral organ number. (A) Gaussian distribution (Equation 4). (B) Log-normal distribution (Equation 5). (C) Gamma distribution (Equation 8). (D) Beta distribution (Equation 8). (E) Schematic diagram of the developmental model for the Poisson distribution. There are five candidate sites for sepal development. Increasing variation: usually, all sites have one sepal, making the number of sepals five; some of the sites stochastically have two sepals (shown in blue), making the total number of sepals six; if two sites produce two sepals each, the total number of sepals is seven. Decreasing variation: some sites stochastically fail to develop a sepal (shown in black), causing the total number of sepals to decrease. (F) Poisson distribution (Equation 10). Different lines in (A–D,F) represent different parameter values.
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Figure 2: The five statistics used to fit the variation in the floral organ number. (A) Gaussian distribution (Equation 4). (B) Log-normal distribution (Equation 5). (C) Gamma distribution (Equation 8). (D) Beta distribution (Equation 8). (E) Schematic diagram of the developmental model for the Poisson distribution. There are five candidate sites for sepal development. Increasing variation: usually, all sites have one sepal, making the number of sepals five; some of the sites stochastically have two sepals (shown in blue), making the total number of sepals six; if two sites produce two sepals each, the total number of sepals is seven. Decreasing variation: some sites stochastically fail to develop a sepal (shown in black), causing the total number of sepals to decrease. (F) Poisson distribution (Equation 10). Different lines in (A–D,F) represent different parameter values.

Mentions: This function exhibits a bell-shaped curve that is symmetric to the mean μ with standard deviation σ (Figure 2A). Although the values of the probability variable X are continuous, we assume that they represent the organ number.


A developmental basis for stochasticity in floral organ numbers.

Kitazawa MS, Fujimoto K - Front Plant Sci (2014)

The five statistics used to fit the variation in the floral organ number. (A) Gaussian distribution (Equation 4). (B) Log-normal distribution (Equation 5). (C) Gamma distribution (Equation 8). (D) Beta distribution (Equation 8). (E) Schematic diagram of the developmental model for the Poisson distribution. There are five candidate sites for sepal development. Increasing variation: usually, all sites have one sepal, making the number of sepals five; some of the sites stochastically have two sepals (shown in blue), making the total number of sepals six; if two sites produce two sepals each, the total number of sepals is seven. Decreasing variation: some sites stochastically fail to develop a sepal (shown in black), causing the total number of sepals to decrease. (F) Poisson distribution (Equation 10). Different lines in (A–D,F) represent different parameter values.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4217355&req=5

Figure 2: The five statistics used to fit the variation in the floral organ number. (A) Gaussian distribution (Equation 4). (B) Log-normal distribution (Equation 5). (C) Gamma distribution (Equation 8). (D) Beta distribution (Equation 8). (E) Schematic diagram of the developmental model for the Poisson distribution. There are five candidate sites for sepal development. Increasing variation: usually, all sites have one sepal, making the number of sepals five; some of the sites stochastically have two sepals (shown in blue), making the total number of sepals six; if two sites produce two sepals each, the total number of sepals is seven. Decreasing variation: some sites stochastically fail to develop a sepal (shown in black), causing the total number of sepals to decrease. (F) Poisson distribution (Equation 10). Different lines in (A–D,F) represent different parameter values.
Mentions: This function exhibits a bell-shaped curve that is symmetric to the mean μ with standard deviation σ (Figure 2A). Although the values of the probability variable X are continuous, we assume that they represent the organ number.

Bottom Line: Such morphological stochasticity is found in foral organ numbers.The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa.We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Theoretical Biology, Department of Biological Sciences, Osaka University Toyonaka, Osaka, Japan ; Research Fellow of the Japan Society for the Promotion of Science, Osaka University Toyonaka, Osaka, Japan.

ABSTRACT
Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers. Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 50 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type) organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning.

No MeSH data available.