Abstract
Practical imaging strategies are presented to investigate
cell or structural systems which resemble
Sierpinski carpet morphologies in biology. This
class of patterns can be quantitatively measured
with a Fractal Dimension to index structural complexity
and scale-invariant system properties. Filamentous
fungal colonies grow by repeated
branching from the hyphal tips which develop into
an interconnected (mycelial) network. This cell
distribution is non-random and stochastically fractal.
We investigate the regulation of hyphal branching
by measuring the positional distribution of acid
phosphatase, which is a marker enzyme for intracellular
regions strongly implicated in coordinated
regulation of the branching response. A nonequilibrium
experimental growth environment acts
to induce an adaptive response, and it is shown that
the spatial distribution of this enzyme can be understood
in terms of the Sierpinski fractal or a Percolation
cluster. Percolation measures the ability of
a fluid (e.g. enzyme) to spread or diffuse continuously.
Image-analysis and data interpretation
routines are developed to measure percolation
properties arid this is related to cell morphology at
different resolution scales to explore realistic cell
development strategies.
