Abstract
The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.
Highlights
The study of diffusion of solutes such as small molecules or globular proteins in aqueous macromolecular solutions is important in many biological, biomedical, and biopharmaceutical fields
The homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy
We develop a framework based on homogenization theory for the prediction of solute diffusivity in macromolecular environments and validate the theory with experimental data obtained by fluorescence correlation spectroscopy (FCS)
Summary
The study of diffusion of solutes such as small molecules or globular proteins in aqueous macromolecular solutions is important in many biological, biomedical, and biopharmaceutical fields. While great strides have been made, diffusion, being a dynamic process, is difficult to measure in real time [9, 10] and challenging to accurately predict a-priori [11, 12]. Underpinning their importance in multiple fields, many models have been developed for the prediction of diffusion in macromolecular systems [11, 13,14,15,16,17,18,19,20,21,22,23]. Models that utilize readily available or measurable system parameters would be of high utility to researchers in the field
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