Part 1 Objective

1.1 Introduction

We find that in the existing literature, the effects of different proteins on Drosophila eyes are mostly determined by manual counting the numbers of healthy and diseased ommatidia in compound eyes. However, we consider the method as a relatively inefficient and labor-consuming process. Thus, we intend to deal image data with a more efficient computer program instead of manual counting. This is an attempt in the combination of biology and computer science. We hope that more researchers will conduct further studies to make contributions in this area and extend these methods to various biological explorations in the future.

1.2 Aim

The purpose of our mathematical modeling is to identify the health of Drosophila eyes by analyzing the distribution of Drosophila compound eyes. The model will help us count the number of micro eyes and their distributions. (It could get more efficient and accurate analysis and results when the image with high resolution.)

1.3 Problem We Face

To build a model, we need to first consider two questions:

1. How can human beings recognize an ommatidium in a picture?
2. How can human beings identify the regularity of a compound eye?

For question 1), we can infer different surface textures based on difference in brightness. To apply this in the program, our aim is to measure colors with digital analysis in RGB color mode.
For question 2), we can determine the regularity because we directly see and estimate if the 'lines' arranged ommatidia are 'straight'. That means, we need to introduce two measurements in our program: distance between ommatidia, and angle of deflection.

Part 2 Final Model

2.1 Procedure

Figure 1 The flow diagram of the program

Our program can be basically divided into two parts: dealing with one ommatidium and randomly selecting to find different ommatidia. (See Figure 1)

Step 1 :
Dealing with one ommatidium
In this step, we find some representative measurements for a single ommatidium. Find a square area in the compound eye.

Step 2 :
Find a brightest point in the compound eye area, which is an ommatidium. Because the round surface structure of the ommatidium, it looks normally brighter and has different color fluctuations than the surrounding area in the RGB image.

Step 3 :
In order to make it clear, we turn the brightest point into black in the example image. (See Figure 2)

Figure 2 To find an ommatidium

Figure 3 To find another 8 ommatidia

Step 4 :
Using the marked ommatidium in step 3 as a reference center, find another 8 ommatidia in two opposite directions. (See Figure 3) Take the measurements from the cross shape. Generally speaking, the angle formed by the intersection will not be less than 30°.

Step 5 :
Record the mean of the distance between the small points near the two regression lines and the angle between each small point and the regression line.

Step 6 :
In this step, we devise an approach to randomly find samples (ommatidia) in compound eyes. We break the picture into pieces and determine whether each region is within the compound eye.

Step 7 :
In this step, we identify whether the image piece includes compound eyes and repeat above steps each time.
If it is in compound eyes, execute the procedure in Step 1 and output the measurements into a file. (See Figure 4)

Figure 4 Part of data in the result

2.2 Application

The laboratory provides the pictures of Drosophila eyes. Input these pictures into the computer program and it can output some available data, which enables us to do further statistical analysis to determine if there is a significant difference among sets of data. From the results getting from the model, we find that there is no significant difference between group1 (the lacZ expressing eyes) and group2 (the CAHS3 expressing eyes), as well as group3 (the fly eyes with hTau and lacZ expressing) and group4 (the fly eyes with hTau and CAHS3 expressing), and there is a significant difference between group1 and group3, which conforms to the results getting from manual counting. Thus, we verify that the model is basically correct. (We assert that this method is efficient and useful because this automated process helps us save time and provide us with accurate, valid data.)

2.3 Results

Using the T-statistics we could obtain data into above tables.

From the table of Group1(the lacZ expressing eyes) & Group2(the CAHS3 expressing eyes), we can conclude that CAHS3 has no harmful effect on the Drosophila compound eyes.
From the table of Group3(the fly eyes with hTau and lacZ expressing) & Group4(the fly eyes with hTau and CAHS3 expressing), we can conclude that CAHS3 makes no significant treatment for the hTau Protein.
Table of Group1(the lacZ expressing eyes) & Group3(the fly eyes with hTau and lacZ expressing) illustrates that the harm done toxication of hTau protein is significant.
As a result, the protein CAHS3 extracted from tardworms has shown little therapeutic effect against the hTau protein.

Part 3 Future expectation

Our model is able to do part of the biological analysis; however, we suggest it as an attempt to process image automatically in science. We believe that it is just a start. In the future, with more scholars contributing to this study, the combination of computer programming and biological analysis will hopefully popularize and analyze results of different sorts of experiments. The computer analysis will hopefully be a efficient tool to help scientists to do their scientific studies. In the medical field, through the careful examination and judgment of computers models, we can identify the disease and health of patients more efficiently and accurately. The analysis of spectrum by computer analysis in the field of space, scientists could identify the cosmos more clearly and promote the progress of human society. In data science, it pushes the computational power of mathematics and provides a deep impetus for the development of data. With such methods, future iGEM teams could apply this model to show different kinds of counting of images with new perspective.

Part 4 Reference

Janani, Iyer, et al. Quantitative Assessment of Eye Phenotypes for Functional Genetic Studies Using Drosophila Melanogaster. 2016, May 1. https://doi.org/10.1534/g3- .116.027060.

Lee D, et al. Expression of mutant CHMP2B linked to neurodegeneration in humans disrupts circadian rhythms in Drosophila. FASEB Bioadv. 2019 Jul 11;1(8):511-520. doi: 10.1096/fba.2019-00042. PMID: 32123847; PMCID: PMC6996329.