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Analysis of Molecule Harvesting by Heterogeneous Receptors on MC Transmitters

Xinyu Huang, Yu Huang, Miaowen Wen, Nan Yang, Robert Schober

TL;DR

This paper designs a molecule harvesting transmitter (TX) model, where the surface of a spherical TX is covered by heterogeneous receptors with different sizes and arbitrary locations, and derives the molecule release rate and the fraction of molecules absorbed by the TX as well as the received signal at the RX.

Abstract

This paper designs a molecule harvesting transmitter (TX) model, where the surface of a spherical TX is covered by heterogeneous receptors with different sizes and arbitrary locations. If molecules hit any receptor, they are absorbed by the TX immediately. Within the TX, molecules are stored in vesicles that are continuously generated and released by the TX via the membrane fusion process. Considering a transparent receiver (RX) and molecular degradation during the propagation from the TX to the RX, we derive the molecule release rate and the fraction of molecules absorbed by the TX as well as the received signal at the RX. Notably, this analytical result is applicable for different numbers, sizes, and locations of receptors, and its accuracy is verified via particle-based simulations. Numerical results show that different vesicle generation rates result in the same number of molecules absorbed by the TX, but different peak received signals at the RX.

Analysis of Molecule Harvesting by Heterogeneous Receptors on MC Transmitters

TL;DR

This paper designs a molecule harvesting transmitter (TX) model, where the surface of a spherical TX is covered by heterogeneous receptors with different sizes and arbitrary locations, and derives the molecule release rate and the fraction of molecules absorbed by the TX as well as the received signal at the RX.

Abstract

This paper designs a molecule harvesting transmitter (TX) model, where the surface of a spherical TX is covered by heterogeneous receptors with different sizes and arbitrary locations. If molecules hit any receptor, they are absorbed by the TX immediately. Within the TX, molecules are stored in vesicles that are continuously generated and released by the TX via the membrane fusion process. Considering a transparent receiver (RX) and molecular degradation during the propagation from the TX to the RX, we derive the molecule release rate and the fraction of molecules absorbed by the TX as well as the received signal at the RX. Notably, this analytical result is applicable for different numbers, sizes, and locations of receptors, and its accuracy is verified via particle-based simulations. Numerical results show that different vesicle generation rates result in the same number of molecules absorbed by the TX, but different peak received signals at the RX.
Paper Structure (17 sections, 6 theorems, 17 equations, 4 figures, 1 table)

This paper contains 17 sections, 6 theorems, 17 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. TX Model
  4. Vesicle Generation
  5. Transportation of Molecules
  6. Receptors on the TX Membrane
  7. Propagation Environment and RX Model
  8. Analysis of Release and Harvest of Molecules at TX
  9. Molecule Release Rate from TX Membrane
  10. Molecule Harvesting at TX
  11. Analysis of Received Signal at RX
  12. Problem Formulation
  13. Derivation of Received Signal
  14. Numerical Results
  15. Conclusion
  16. ...and 2 more sections

Key Result

Theorem 1

The molecule release rate from the TX membrane at time $t$, when vesicles are continuously generated starting at time $t=0$, is given by where and In fc and fc2, $j_0(\cdot)$ is the zeroth order spherical Bessel function of the first kind olver1960bessel and $\lambda_n$ is obtained by solving $D_\mathrm{v}\lambda_nj_0'\left(\lambda_nr_{ \textnormal{T}}\right)=k_\mathrm{f}j_0\left(\lambda_nr_{ \

Figures (4)

  • Figure 1: Illustration of the MC system model where a spherical TX covered by heterogeneous receptors communicates with a transparent RX. Paths 1, 2, and 3 represent all possible diffusion paths of molecules after their release from the TX membrane.
  • Figure 2: Molecule release rate from the TX versus time $t$ for different values of $\mu$.
  • Figure 3: Number of molecules absorbed by the TX until time $t$ versus time $t$ for different distributions of receptors and different $\mu$, where $N_\mathrm{r}=11$.
  • Figure 4: Number of observed molecules within the RX at time $t$ versus time $t$ for different distributions of receptors and $\mu$, where $N_\mathrm{r}=11$.

Theorems & Definitions (6)

  • Theorem 1
  • Lemma 1
  • Theorem 2
  • Lemma 2
  • Lemma 3
  • Theorem 3