Beta-Amyloid Degradation Model

Introduction

This is another degradation model we designed to help UCL 2013 iGEM team with their Beta-Amyloid Degradation Assays. Beta-Amyloid is known as the component of Amyloids Plaque in association with Alzheimer's disease (AD), in which the target of UCL iGEM this year. Matrix metallopeptidase 9 (MMP-9) was discovered to be able to degrade Beta-Amyloid that can be potentially used to cure Alzheimer's disease. The model provides information about how efficient is MMP-9 enzyme to degrade Beta-Amyloids base on the assays from UCL team.

Description

Objective

The Mathematical model is based on MATLAB extension Simbiology, it will predict how long will take to degrade a certain concentration of Beta-Amyloid by a given amount of MMP-9 enzyme. The simulation results can help UCL iGEM team to modify their assays in order to achieve better experimental results. The model can also be used to provide a preliminary prediction of degrading Amyloid Plaque in vivo.

Degradation Assays of UCL 2013 iGEM team

The details of the assays are here. There are three different substrates which are soluble aggregated β-amyloid (Aβ),aggregated β-amyloid (Aβ) fibrils 1-40 and aggregated β-amyloid (Aβ) fibrils 1-42. Here is the table that defines the initial concentrations of all substrates and the enzyme from the assays.

Species	Concentration	Units
soluble Aβ	25	uM
Aβ fibrils 1-40	200	uM
Aβ fibrils 1-42	100	uM
MMP-9	0.2	uM

Methods

The Model

Explanation

Equations

We choose simple Michalis-Menten mechanism for Beta-Amyloid degradation. The ODEs for all substrate are:

The Km values here are for each substrate correspondingly whereas Kcat values are for MMP-9 in each assay.

Assumption

Although Matrix metallopeptidase 9 (MMP-9) is a well characterised enzyme, there is no clear kinetic data for degrading soluble Beta-Amyloids and its fibrils.