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Mathematical Modeling of Intrusive Growth of Fusiform Initials in Relation to Radial Growth and Expanding Cambial Circumference in Pinus sylvestris L.

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Abstract

This study on the cambium of Pinus sylvestris L. examines the intrusive growth of fusiform cambial initials and its possible contribution to the tangential and radial expansions of the cambial cylinder. The location and extent of intrusive growth of the fusiform initials were determined by microscopic observations and by mathematical modeling. In order to meet the required circumferential expansion of the cambial cylinder, the fusiform initials grow in groups by means of a symplastic rather than intrusive growth, leaving no room for the assumption that intrusive growth of the initials takes place between radial walls and has a direct role in the increase of the cambial circumference. Therefore, it is postulated that the fusiform initials grow intrusively between the tangential walls of the neighboring initials and their immediate derivatives and not between the radial walls of the adjacent initials as per common belief.

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Abbreviations

N r :

Number of periclinal divisions

L :

Circumference of cambial cylinder

ΔL :

Increase in circumference of cambial cylinder

r :

Radius of cambial cylinder

Δr :

Increase in the cambial radius

l r :

Radial width of the fusiform initial

l c :

Tangential width of the fusiform initial

Δl r :

Increase in radial width of the fusiform initial

Δl c :

Increase in tangential width of the fusiform initial

u r :

Radial displacement of the initial cell

du r :

Changes in radial displacement

dr :

Radial width of the intrusively growing cell

dl :

Tangential width of the intrusively growing cell

ε r :

Strain in radial direction

ε l :

Strain in tangential direction

T :

Time span between two successive periclinal divisions

Δt :

Progress of time between two successive periclinal divisions

a :

Factor covering the phases of advancement towards a periclinal division and ranging in value from zero to one

t 0 − t 9 :

Ten consecutive time intervals during the growth of a fusiform initial

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Authors and Affiliations

  1. Department of Biophysics and Cell Biology, University of Silesia, ul. Jagiellońska 28, 40-032, Katowice, Poland

    D. Karczewska & J. Karczewski

  2. Department of Biosystematics, Opole University, Oleska 48, 45-052, Opole, Poland

    W. Włoch & P. Kojs

  3. Botanical Garden – Centre for Biological Diversity Conservation of the Polish Academy of Science, Prawdziwka 2, 02-973, Warszawa 76, Poland

    W. Włoch, J. Jura-Morawiec & P. Kojs

  4. Department of Botany, Jamia Hamdard (Hamdard University), Tughlaqabad, New Delhi, 110062, India

    M. Iqbal

  5. Department of Plant Production, College of Food and Agriculture Sciences, King Saud University, P.O. Box 2460, Riyadh, 11451, Kingdom of Saudi Arabia

    M. Iqbal

  6. Australian Dracaena Research Centre, P.O. Box 925, Williamstown, VIC, 3016, Australia

    J. Krawczyszyn

Authors
  1. D. Karczewska
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  2. J. Karczewski
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  3. W. Włoch
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  4. J. Jura-Morawiec
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  6. M. Iqbal
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  7. J. Krawczyszyn
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Correspondence to W. Włoch.

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Karczewska, D., Karczewski, J., Włoch, W. et al. Mathematical Modeling of Intrusive Growth of Fusiform Initials in Relation to Radial Growth and Expanding Cambial Circumference in Pinus sylvestris L.. Acta Biotheor 57, 331–348 (2009). https://doi.org/10.1007/s10441-009-9068-y

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