Physical Constraints in Molecular Communication: 2D Diffusion in Stiff and Crowded Hydrogels

Diffusion is a fundamental process that governs molecular transport in biological systems and is influenced by the physical and chemical properties of the surrounding environment, including matrix stiffness and molecular crowding. In this study, we developed a two-dimensional hydrogel-based model to investigate how these factors modulate diffusion. Two concentrations of agarose gels (\(1\%\) w/v and \(2\%\) w/v) were taken to represent differences in matrix stiffness, while \(10\%\) w/v sucrose was introduced to create a crowding effect in respective conditions. In our setup, four experimental conditions were designed and analysed, i.e. baseline condition A (\(1\%\) w/v agarose), condition B (\(1\%\) w/v agarose with \(10\%\) w/v sucrose), condition C (\(2\%\) w/v agarose), and condition D (\(2\%\) w/v agarose with \(10\%\) w/v sucrose). Diffusion of methylene blue in four hydrogel conditions was monitored for over 24 hours, and radial spread of dye was quantified by image analysis using ImageJ. The mean squared radius (\(r^2\)) followed a linear relationship with time across all conditions in agreement with Fickian diffusion. However, effective diffusion was progressively reduced from baseline to respective conditions (A \(>\) B \(>\) C \(>\) D), with a percentage reduction of \(6.9\%\) on introducing crowding in condition B, \(14.5\%\) under stiffness alone in condition C and \(21.8\%\) under combined constraints in condition D at a significance level of \(p < 0.05\). These observations and results indicate that stiffness and crowding have an independent and additive effect on restricting molecular transport. This model provides a simple framework for understanding how physical limitations can influence diffusion-driven processes in complex biological environments.