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Resolving the diffusion coefficient is a key element in many biological and engineering systems, including pharmacological drug transport and fluid mechanics analyses. Additionally, these systems often have spatial variation in the diffusion coefficient that must be determined, such as for injectable drug-eluting implants into heterogeneous tissues. Unfortunately, obtaining the diffusion coefficient from images in such cases is an inverse problem with only discrete data points. The development of a robust method that can work with such noisy and ill-posed datasets to accurately determine spatially varying diffusion coefficients is of great value across a large range of disciplines. Here, we developed an inverse solver that uses physics-informed neural networks (PINNs) to calculate spatially varying diffusion coefficients from numerical and experimental image data in varying biological and engineering applications. The residual of the transient diffusion equation for a concentration field is minimized to find the diffusion coefficient. The robustness of the method as an inverse solver was tested using both numerical and experimental datasets. The predictions show good agreement with both the numerical and experimental benchmarks; an error of less than 6.31% was obtained against all numerical benchmarks, while the diffusion coefficient calculated in experimental datasets matches the appropriate ranges of other reported literature values. Our work demonstrates the potential of using PINNs to resolve spatially varying diffusion coefficients, which may aid a wide-range of applications, such as enabling better-designed drug-eluting implants for regenerative medicine or oncology fields.
Resolving the diffusion coefficient is a key element in many biological and engineering systems, including pharmacological drug transport and fluid mechanics analyses. Additionally, these systems often have spatial variation in the diffusion coefficient that must be determined, such as for injectable drug-eluting implants into heterogeneous tissues. Unfortunately, obtaining the diffusion coefficient from images in such cases is an inverse problem with only discrete data points. The development of a robust method that can work with such noisy and ill-posed datasets to accurately determine spatially varying diffusion coefficients is of great value across a large range of disciplines. Here, we developed an inverse solver that uses physics-informed neural networks (PINNs) to calculate spatially varying diffusion coefficients from numerical and experimental image data in varying biological and engineering applications. The residual of the transient diffusion equation for a concentration field is minimized to find the diffusion coefficient. The robustness of the method as an inverse solver was tested using both numerical and experimental datasets. The predictions show good agreement with both the numerical and experimental benchmarks; an error of less than 6.31% was obtained against all numerical benchmarks, while the diffusion coefficient calculated in experimental datasets matches the appropriate ranges of other reported literature values. Our work demonstrates the potential of using PINNs to resolve spatially varying diffusion coefficients, which may aid a wide-range of applications, such as enabling better-designed drug-eluting implants for regenerative medicine or oncology fields.
Lipid rafts are known as highly ordered lipid domains that are enriched in saturated lipids such as the ganglioside GM1. While lipid rafts are believed to exist in cells and to serve as signaling platforms through their enrichment in signaling components, they have never been directly observed in the plasma membrane without treatments that artificially cluster GM1 into large lattices. Here we report that microscopic GM1-enriched domains can form, without lipid crosslinking, in the plasma membrane of live mammalian cells expressing the EphA2 receptor tyrosine kinase in response to its ligand ephrinA1-Fc. The GM1-enriched microdomains form concomitantly with EphA2-enriched microdomains, but only partially co-localize with them. To gain insight into how plasma membrane heterogeneity controls signaling, we quantify the degree of EphA2 segregation and study initial EphA2 signaling steps in both EphA2-enriched and EphA2-depleted domains. By measuring dissociation constants, we demonstrate that EphA2 oligomerization is the same in EphA2-enriched and -depleted domains. However, EphA2 interacts preferentially with its downstream effector SRC in EphA2-depleted domains. The ability to induce microscopic GM1-enriched domains in live cells using a ligand for a transmembrane receptor will give us unprecedented opportunities to study the biology of lipid rafts.
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