Team:Tec-Chihuahua/Model
From the first moment we made this our project, we repeatedly heard the same question: “how can you make sure AMPs get to bee larvae?” This is a valid and central concern. One of the key elements to our project’s success is that the antimicrobial peptides encapsulated within PLGA nanoparticles reach the bee larvae with enough peptide concentration to inhibit pathogenic bacteria.
In order to measure the final amount of AMPs that will be delivered to each larva, we model the amount of peptide released from the nanoparticles in their path through the insides of the nurse bee and into the jelly fed to larvae.
The model will help us to determine the initial dosage of AMPs necessary to reach their final destination with high enough concentration.
The polylactic-co-glycolic acid (PLGA) is a biodegradable and biocompatible polymer that is used for the fabrication of drug delivery devices. PLGA could be used to transport proteins, peptides and macromolecules such as DNA and RNA.
PLGA is ideal for drug delivery because its degradation can be used to control the drug’s release profile by manipulating the factors involved in it. Some relevant parameters that influence the release are the polymer molecular weight, the ratio of the particle and the drug concentration.
The release behavior of PLGA is given by its degradation which occurs by hydrolysis. The degradation profile is through bulk degradation as a consequence of the water penetration into the particle and the polymer degradation. However, the degradation by water penetrations is way faster than the PLGA degradation.
The release behavior of PLGA is given by its degradation which occurs by hydrolysis. The degradation profile is through bulk degradation as a consequence of the water penetration into the particle and the polymer degradation. However, the degradation by water penetrations is way faster than the PLGA degradation.
The process can be divided into two phases
- The initial burst where there is a quantity of drug released at time zero related to the drug type, drug concentration, and polymer hydrophobicity.
- The progressive drug liberation through the weakened PLGA layer. The water hydrolyzes the polymer and creates a channel for where the drug can be released by diffusion and erosion until the complete polymer degradation1.
The model is based on the diffusion from the antimicrobial peptide in the interior of the PLGA nanoparticle to the exterior of it. Since out peptides will be delivered through PLGA 50:50 nanoencapsulation, we decided to use a simple Frickian diffusion model suggested by previous research2, 3, 4 . The diffusion equation can be seen here:
Where:
| Symbol | Variable | Unit |
|---|---|---|
| Mt | Drug released in time t | Same as M∞ |
| M∞ | Total amount of nano encapsulated drug | Same as Mt |
| T | Time | Seconds |
| D | Diffusion coefficient, dependent on the drug-polymer interations | Centimeter squared per second |
| R | Radius | Centimeter |
| ⍺ | The initial burst, which is a normal behavior of PLGA-drug release systems where quantity of initial drug is released independently of time. |
A fraction, in relation to the total amount of drug |
It was first necessary to define the appropriate boundary conditions for the equation. Before receiving the data for the radii range in our nanoparticles, we picked boundary conditions based on a wide range of pre-reported2 diffusion coefficients and radii, as well as time (from 0 to 35 days, far beyond what we need).
| Time (s) | diffusion coefficient (cm2/s) | Radius (cm) | Significant upper bound (n at which the summation term is smaller than 0.00001) |
|---|---|---|---|
| t= 3, 024, 000 s | D= 5x10-19 | R= 2.2x10-5 | 1 |
| R= 0.00013 | 4 | ||
| D= 4x10-16 | R= 2.2x10-5 | 15 | |
| R= 0.00013 | 62 | ||
| t= 0 s | Any value | 317 | |
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