A mathematical model to predict network growth in physarum polycephalum as a function of extracellular matrix viscosity, measured by a novel viscometer

Physarum polycephalum is a slime mould that forms complex networks, making
it an ideal model organism for studying network formation and adaptation.
We introduce a novel viscometer capable of accurately measuring
extracellular matrix ECM viscosity in small biological samples, overcoming
the limitations of conventional instruments. Using this device, we
measured the relative kinematic viscosity and developed continuous models
to predict network size over time as a function of ECM viscosity and
network complexity. Our results show that increased ECM viscosity, driven
by higher salt (MgCl2·6H2O) concentrations, significantly slows network
expansion but does not affect the final network complexity. Fractal
Dimension (FD) analysis revealed that network complexity converged to a
similar value across all viscosity conditions during the equilibrium
stage. The models demonstrated strong predictive power, with a Mean
Squared Error below 0.4 %, closely aligning with experimental data. These
findings highlight the critical role of ECM viscosity in influencing
network expansion while demonstrating that complexity remains stable
across varying conditions. This study advances our understanding of the
physical parameters shaping P. polycephalum networks and provides a
foundation for exploring network dynamics in other adaptive systems. These
insights offer new tools for research in biological systems where sample
material is limited.