Departamento de Biotecnología, Universidad Autónoma Metropolitana, Iztapalapa C.P. 09340, México, D.F. Mexico.
Biotechnol Bioeng. 1993 Jun 5;42(1):1-10. doi: 10.1002/bit.260420102.
A mathematical model, linking microscopic to macroscopic parameters of the kinetics of mycelial growth is presented. The model consists of two parts: (a) a microscopic description, based on the assumption that growth of a mycelium can be represented approximately by the growth of a symmetric binary tree, where the branching level (microscopic state variable) is logarithmically related to the number of tips and segments; and (b) a macroscopic description which makes use of the microscopic description in order to define the parameters related to the evolution of biomass (macroscopic state variable) as a function of time. The latter uses a distribution of arrested tips in a population of mycelia, in order to estimate the fraction of non-growing biomass in terms of a power law function with coefficient, n, of the biomass concentration. The microscopic description explains the fact that the germ tube specific growth rate of Aspergillus nidulans measured in a growth chamber, is about the double the specific growth rate of this organism, when measured in shake flasks. It predicts that the length of the hyphal growth unit of the mycelium of Geotrichum candidum would be approximately the double the germ tube length measured at the time just before the first branching event. It also allows the derivation of useful expressions for predicting macroscopic parameters, such as the maximal specific growth rate, the initial amount of biomass, and the amount of biomass before the branching process starts. Those estimates are done in terms of microscopic quantities, i.e., the amount of germinated spores, the diameters of the spores and hyphae, the average rate of tip extension, and the average internodal segment length. Estimation of coefficient n by fitting the macroscopic description to a growth curve of A. niger gives an indication on the degree of skewness of the distribution of arrested mycelia. Estimated macroscopic parameters are in relative good agreement with measured average segment length.
本文提出了一个将微观参数与丝状真菌生长动力学的宏观参数联系起来的数学模型。该模型由两部分组成：(a) 微观描述，基于假设丝状真菌的生长可以近似用对称二叉树的生长来表示，其中分支水平（微观状态变量）与尖端和片段的数量呈对数关系；(b) 宏观描述，利用微观描述来定义与生物量演变相关的参数（宏观状态变量）作为时间的函数。后者利用了菌丝体群体中被截留尖端的分布，以便根据幂律函数来估计非生长生物量的分数，该函数的系数 n 与生物量浓度有关。微观描述解释了这样一个事实，即在生长室中测量的 Aspergillus nidulans 的芽管比生长率大约是在摇瓶中测量时该生物的比生长率的两倍。它预测 Geotrichum candidum 菌丝体的菌丝生长单位的长度大约是在第一次分支事件之前测量的芽管长度的两倍。它还允许推导出有用的表达式来预测宏观参数，如最大比生长率、初始生物量和分支过程开始前的生物量。这些估计是根据微观量来进行的，即发芽孢子的数量、孢子和菌丝的直径、尖端延伸的平均速率和平均节间段长度。通过将宏观描述拟合到 A. niger 的生长曲线来估计系数 n，可以指示被截留菌丝体分布的偏斜程度。估计的宏观参数与测量的平均片段长度相对吻合。
