DERIVATION OF FORMULA OF APPROXIMATE IDEALIZED HYPHAL CONTOUR AS BUILT-IN HYPHAL FITTING PROFILE

Abstract

Hypha consists of two regions; cap (apex) and cylindrical shaft (subapex and mature combined). The hyphal-cap is the most critical part due to its dominant role in the hyphal-wall growth and mor- phogenesis. Just how the hyphal-wall growth is regulated in order to maintain its tubular shape has been the subject of much research for over 100 years. Here, we derived a formula of approximate idealized hyphal-contour based on gradients of secant lines joining a fixed coor- dinate at the starting hyphal-shaft to any coordinates on the contour. The formula is capable of being a control for experimental analysis in which it is not limited to one specific shape of the hyphal-like cell. Also, it potentially can play a role as built-in or ready-made hyphal-fitting profile that “best fits” microscopic images of various actual hyphal- like cells. In other words, given a microscopic image of hyphal-like cell, mycologists and microbiologists would not have to wonder about mathematical representation of its contour since the formula has pre- pared for it.