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 findin..., This dataset was collected using a custom-engineered viscometer designed to measure the kinematic viscosity of extracellular slime matrix (ECM) samples from Physarum polycephalum. The experimental setup involved precise mechanical control and sensor readouts (force, distance, temperature and humidity) to record how Physarum polycephalum responded to varying concentrations of magnesium chloride (MgCl2·6H2O). In parallel, growth measurements were recorded to study the organism's network expansion, while fractal dimension analysis was performed to assess network complexity.
Data Collection

Viscosity Data: Force and distance measurements were collected using load cells and distance sensors connected to a Raspberry Pi 4B. The data were processed with custom Python scripts. Measurements were taken across different concentrations of MgCl2·6H2O over time.

Growth Data: Network expansion was measured in mm² over time using time-lapse imaging and image analysis. Data were collected from multipl..., , # A mathematical model to predict network growth in *Physarum polycephalum* as a function of extracellular matrix viscosity, measured by a novel viscometer

## Project Overview

This repository contains the data, code and 3D models related to the research titled *\"A Mathematical Model to Predict Network Growth in Physarum polycephalum as a Function of Extracellular Matrix Viscosity, Measured by a Novel Viscometer\"*. The repository includes raw and processed data from viscosity measurements, fractal dimension analysis and growth data. It also includes 3D models, technical drawings and Python scripts required to operate and analyse the viscometer system.

DOI: [https://doi.org/10.5061/dryad.0k6djhb9m](https://doi.org/10.5061/dryad.0k6djhb9m)

## Data Directory Overview

The dataset is organised into several main directories containing different aspects of the experimental data and necessary files for processing and analysis. Below is a brief overview of each directory:

1. **GrowthFractal...