Mathematical modeling the surface roughness distribution of artificial cell wall material

Abstract

The plant cell walls play an important role in defining the shape and size of the plant cell, matter flow regulation, mitigation of environmental influences and achievement of homeostasis, as well as in defense and protection against pathogens in plant tissues and organs. This paper presents an original approach to the establishment of the mathematical model based upon the former study dealing with the surface nano-roughness distribution of the model cell wall. The differential equation accompanied with the appropriate additional conditions, which describes such kind of distributions, has been formulated and presented. The developed model was tested using the already reported experimental data of an artificial cell wall, made of polysaccharides based on bacterial cellulose supplemented with xyloglucan and pectin (BCPX) that imitate properties of the natural cell wall. It has been demonstrated that proposed differential equation, has an analytical solution in the form of the normal Gaussian distribution, which describes the surface roughness of cell walls made of this material accurately.

Ćelijski zidovi biljaka imaju značajnu ulogu u definisanju oblika i veličina biljnih ćelija, kao i regulaciji razmene materija, zaštiti ćelijskih tkiva i organa od patogenih klica, ublažavanje nepovoljnih uticaja okoline itd. U ovom radu je prikazan originalni pristup formiranju matematičkog modela za opisivanje raspodele površinske nano-hrapavosti veštačkog modela ćelijskog zida. Formulisana je diferencijalna jednačina sa odgovarajućim dodatnim uslovima, koja opisuje raspodele navedenog tipa Razvijeni model je testiran koristeći postojeće (objavljene) eksperimentalne podatke merenja površinske hrapavosti veštačkih model-materijala ćelijskih zidova, izrađenih od polisaharida zasnovanih na bakterijskoj celulozi oplemenjenoj ksiloglukanom i pektinom (BCPX), koji imitira svojstva prirodnih ćelijskih zidova. Potvrđeno je da predložena diferencijalna jednačina ima analitičko rešenje u formi Gausove funkcije, koja precizno opisuje hrapavost ćelijskih zidova napravljenih od ovog materijala.