Generalized phenomenological equation of plant growth

Enlargement is one of the most fundamental activities of plants, and there are many simultaneous processes involved. Several could be temperature-dependent, like metabolic processes and cell wall sensitivity. A description of plant cell elongation was elaborated by Lockhart in the mid-60's of the last century in the form of time-dependent differential equation. However, the main disadvantage of this approach was the missing environmental temperature at which growth takes place, as well as the lack of representation of environmental factors influencing growth, like growth stimulators/inhibitors, external pressure or light. This absence has been merely covered in the series of our recent papers. Consequently, this manuscript attempts to construct a fairly complete, all-encompassing set of mathematical relationships which describe the basic process of cell/organ extension and the effects of modifying environmental perturbations. The output is provided in a form of composite equation supported by mathematical derivations. Starting with the generalized time- and temperature-dependent growth equation, we involve the action of phytohormones and toxic compounds, and especially of light (photocontrol of plant growth) onto the growth processes. All these external factors (treated as perturbations) are mapped onto the proper terms of temperature modified equation of growth thus giving a new theoretical tool to verify, interpret and draw conclusions concerning data originating from various kinds of plant-physiological experiments. It seems that this novel approach can provide a starting point for further experimentation especially on the plastic and elastic components of the growth process.