Diffusion in macromolecular solutions and networks is a topic of vast importance in many fields related to medical devices, biotechnology, tissue engineering, or drug delivery. Understanding diffusion in complex media is also essential for describing molecular transport through biological systems such as cells and tissues. Thus, scientific effort has been devoted to developing techniques for both measuring and predicting diffusion in macromolecular solutions and networks.
Here, we describe a model on the basis of the homogenization theory which was developed to enable diffusion predictions in macromolecular environments based on a set of key measurable system parameters. The two novel aspects of our work are: 1) the use of homogenization theory to describe mass transport in macromolecular solutions, and 2) the premise of the developed model which is based on conceptualizing a dimensionless parameter that is responsible for differences in diffusivity and which is composed solely of easily measurable or readily accessible system parameters. Here, we present measurements of probe diffusion, Ribonuclease A (RNase) in different polymeric solutions (Dextran and Ficoll) conducted by Fluorescence Correlation Spectroscopy (FCS). RNase was labeled with Atto488 NHS ester with 52% labeling efficiency following the manufacturer's procedures. Polymer solutions of desired final concentration were prepared by dissolution of the polymer in phosphate buffered saline (10 mM PBS, pH 7.4). Only polymer solutions in the dilute and semi-dilute regimes were used, i.e. below or equal to the polymer overlap concentration, c*.
This presentation focuses on the adaptation of the homogenization theory to predict diffusion of solutes in polymer solutions. We will specifically discuss the mathematical framework of the model, the assumptions, validation with other models and experimental data and future directions. Specifically, here we describe a simple 3D physical model as a proof of concept – a spherical solute subjected to a random walk motion which is physically obstructed by stationary spherical obstacles (polymer chains). Well-accepted Monte Carlo simulations validated the theory, while appropriately chosen experimental polymer-solute systems validated the model. Notably, the model only used physically meaningful and measurable system variables and not fitted parameters, which makes it broadly applicable to many systems as long as the basic model assumptions are partially satisfied. Furthermore, the diffusion trends predicted by the model conform to trends discussed in the literature where obstruction model for the description of diffusion has been applied. Our current work is focused on expanding the developed theoretical framework towards describing the diffusion in systems where interactions between solute-polymer-solvent contribute to hindered diffusivities.
In summary, we developed a novel computational framework based on the homogenization theory to describe solute diffusion in polymer solutions. To the best of our knowledge, homogenization theory has not been used previously to describe mass transfer in polymer solutions. Monte Carlo simulations confirmed the homogenization theory. An excellent agreement between the two simulation techniques as well as comparison to experimental data provided further evidence for the utility of the homogenization theory for predicting diffusion in macromolecular solutions.