# Modeling Receptor Motility along Advecting Lipid Membranes

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## Abstract

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## 1. Introduction

## 2. Continuum Models of Receptor Motility

#### 2.1. Receptor–Ligand-Mediated Cell Adhesion

#### 2.2. Cell Contractility

#### 2.3. Protein Relocation on Advecting Membranes

#### 2.4. Receptor Mediated Endocytosis

#### 2.5. Protein Motility Miscellanea

## 3. Statistical Models of Receptor Motility

## 4. Discussion

#### 4.1. Modeling the Mass Flux of Receptors

#### 4.2. Evaluation of the Protein Diffusion Coefficient

#### 4.3. Modeling Receptor–Ligand Kinetics

## 5. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of an adherent cell onto an enriched ligands substrate, inspired by [25,26]. The image depicts the concept formulated within the adhesion traction model. Vectors ${\mathit{n}}_{\mathcal{S}}$ and ${\mathit{t}}_{\mathcal{S}}$ represent the normal and the tangent vector at a certain location on the cell membrane, respectively. Within the cutoff limit $\delta $, the tangential component $\mathit{t}cos\beta $ of the traction exerted by ligands (vertical traction $t$), attracts the receptors on the cell membrane, generating an additive flux term, ${\mathit{h}}_{\mathrm{R}}^{T}$, appearing in Equation (3). $\beta $ is the angle with respect to the vertical defined by $\mathit{t}$.

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**MDPI and ACS Style**

Arricca, M.; Salvadori, A.; Bonanno, C.; Serpelloni, M.
Modeling Receptor Motility along Advecting Lipid Membranes. *Membranes* **2022**, *12*, 652.
https://doi.org/10.3390/membranes12070652

**AMA Style**

Arricca M, Salvadori A, Bonanno C, Serpelloni M.
Modeling Receptor Motility along Advecting Lipid Membranes. *Membranes*. 2022; 12(7):652.
https://doi.org/10.3390/membranes12070652

**Chicago/Turabian Style**

Arricca, Matteo, Alberto Salvadori, Claudia Bonanno, and Mattia Serpelloni.
2022. "Modeling Receptor Motility along Advecting Lipid Membranes" *Membranes* 12, no. 7: 652.
https://doi.org/10.3390/membranes12070652