Abstract
In this contribution we deal with a new mathematical description of the response of short-term coleoptile/hypocotyl expansion growth to temperature. Although the interest of both the bio-mechanical basis of elongation growth and temperature responses has been studied in plant biology and biophysics for a long time, yet the question of the mode of actions of temperature is very relevant and still open. Here we introduce a simple idea that the normal distribution, due to the central limit theorem (CLT), is able to report on temperature-dependent elongation growth. The numerical fittings for temperature affected growth are in good agreement with empirical data. We suggest that the observation concerning a crossover effect occurring in temperature driven elongation together with CLT leads to the formulation of a hypothesis about the possible universal character of such a description, supposedly for many plant species and families. We conclude with the statement that properly constructed equations of temperature affected growth, should possibly include a specific term proportional to exp[-((T-T0)/T0)<sup>2</sup>] with T0 corresponding to the temperature of the optimum growth.
Highlights
It has been a long search for an adequate description of the response of the short-term cell expansion growth to temperature and numerous mathematical models have been developed
A multi-linear model (Coelho and Dale 1980) as less rigid than the bilinear model used for crop system simulation packages (Hunt and Pararajasingham 1995) required, in turn, five or more parameters to describe the temperature response
More recent attempts were presented by Yan and Hunt (1999) where the temperature response of plant growth and development has been modelled by >-distribution
Summary
It has been a long search for an adequate description of the response of the short-term cell expansion growth to temperature and numerous mathematical models have been developed. The linear model was proposed by Summerfield and Roberts (1987) This model is only effective when the temperature does not approach the optimum whereas the conditions frequently exceed the optimum temperature and such linear description fails to account for the suppressed growth and development at high temperatures. To resolve this contradiction Olsen et al (1993) adopted a bilinear approach. A multi-linear model (Coelho and Dale 1980) as less rigid than the bilinear model used for crop system simulation packages (Hunt and Pararajasingham 1995) required, in turn, five or more parameters to describe the temperature response. Even though the authors stressed that the description employed only three cardinal numbers, no further link to biochemical basis has been given
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