  We present a minimal driven lattice gas model which generates the
morphological characteristics associated with single colony mycelium arising
from the growth and branching process of fungal hyphae, which is fed by a
single source of nutrients. We first analyze the growth and transport process
in the primary hypha modeled as a growing 1-d lattice, which is subject to
particle (vesicle) loss due to presence of dynamically created branching sites.
We show that the spatial profile of vesicles along the growing lattice is an
exponential distribution, while the length grows logarithmically with time. We
also find that the probability distribution of length of the hypha tends to a
Gaussian distribution function at late times. In contrast, the probability
distribution function of the time required for growth to a specific length
tends to a broad log-normal distribution. We simulate the resultant 2-d
morphology generated by the growing primary hypha, quantifying the motility
behavior and morphological characteristics of the colony. Analysis of the
temporal behavior and morphological characteristics of the resultant 2-d
morphology reveals a wide variability of these characteristics which depend on
the input parameters which characterize the branching and elongation dynamics
of the hyphae. By calibrating the input parameters for our model, we make some
quantitative comparison of the predictions of our model with the observed
experimental growth characteristics of fungal hyphae and the morphological
characteristics of single colony fungal mycelium.
