Overview


Introduction


Mathematical modeling is the representation of complex phenomena and processes in mathematical equations. Mathematical modeling is a very attractive tool in the interpretation and prediction of experimental results. In the DBTL cycle (Design, Build, Test, Learn), appropriate mathematical modeling can optimize Design, reduce the burden of Build and Test, deepen the knowledge in the Learn phase, and make this cycle more efficient.

"If all you have is a hammer, everything looks like a nail."

We were told the above saying on Human Practices with Dr. Sakuraba. This is the saying that describes how one's own preconceptions distort one's thinking and cause one to miss the essence of the issue at hand. The choice of which mathematical model to use in the Dry Lab is very important. If we stick to one method when making a choice, we may lose our objective. We have taken this saying that Dr. Sakuraba told us to keep in mind and carefully selected the best method for our purpose.

Model in Our Project


In our project, POIROT, we have developed a glaucoma detection device using miRNA biomarker in tear fluid. In the system we developed, the biomarkers are amplified as dsDNA through an isothermal amplification, and the amplified dsDNA is detected by lateral flow to determine positive or negative.

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Figure 1.

Modeling reduces experiments and accelerates the engineering cycle, and aids in the design as well as the further advancement of projects. Figure 1 outlines the role of the Model in our project. From here, we describe how our models have progressed along with the development of our project.

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Figure 2. Model in Our Project.

miRNA Selection

Bioinformatics analysis is often used for biomarker selection, using data from papers and databases. We also wanted to contribute to biomarker selection from the Dry Lab side. In the course of our literature review, we found that the research on biomarkers in tear fluid related to glaucoma had not progressed very far. Therefore, we asked Prof. Ochiya, who specializes in biomarker-based disease detection, if we could do a meta-analysis integrating data from a few papers to examine appropriate biomarkers. During Human Practices with Prof. Ochiya, he said that the current research on tear fluid biomarkers is a mixed bag and that it is technically very difficult to perform a meta-analysis and that it is not reliable. Therefore, Dry Lab decided not to use meta-analysis to select biomarkers. Instead, we selected miRNAs biomarkers for glaucoma from a highly reliable paper introduced to us by Prof. Ochiya 1.

In considering what the Dry Lab could contribute, we focused on the sequence specificity needed for the amplification system. It is predicted that there are approximately 1600 different types of miRNAs in tear fluid 2. Furthermore, miRNAs have subsets, and miRNAs belonging to the same subset have very similar sequences.

As described above, the sequence specificity of the amplification and detection system is very important when detecting miRNAs, which are expected to have many similar sequences. We decided to evaluate the sequence specificity needed for our amplification and detection system by detecting for the presence of similar sequences of the miRNAs we selected as biomarkers in the tear fluid. Our research revealed that miRNAs with sequences very similar to the miRNAs we selected as biomarkers are present in tear fluid.

These results indicate that Exponential amplification reaction (EXPAR), which was intended to be used as the amplification system, has insufficient sequence specificity. Dry Lab suggested that a more sequence-specific amplification method is necessary to ensure that only the target biomarker is amplified.

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Figure 3. Similar miRNA sequences found in similar sequence search of (a) hsa-miR-10b-5p and (b) hsa-miR-30d-5p, which we chose as biomarkers for glaucoma. Light green bases in similar sequences represent mismatches with the target sequence.

For more information, see:

TWJ Specificity

The suggestion in miRNA Selection showed that the amplification system requires an amplification method with high sequence specificity. Through our literature review, we chose Three-Way-Junction SDA (TWJ-SDA) as the amplification method with high sequence specificity. In the course of our research on TWJ-SDA, we realized that there is no solid theory as to why TWJ-SDA has high sequence specificity. Therefore, we theoretically identify the cause of the sequence specificity of TWJ-SDA.

We initially thought that Molecular Dynamics simulation (MD simulation) could be used to identify the cause of the sequence specificity. Therefore, we asked Dr. Sakuraba, who specialized in MD simulation. As a result of Human Practices with Dr. Sakuraba, we found that it is very difficult to identify the cause of the sequence specificity in MD simulation. We decided to use the ODE Model recommended by Dr. Sakuraba. The results of the analysis using the ODE Model revealed the reason why the amplification of TWJ-SDA is sequence-specific. TWJ-SDA keeps the association constant low by making the complex formation a multistep process. This is the reason for high sequence specificity. In the process of investigating the cause of the sequence specificity, we learned about the constraints of TWJ-SDA template and helper to have the sequence specificity.

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Figure 4. Schematic Diagram of TWJ Specificity

For more information, see:

Sequence Design

The TWJ Specificity section has helped us to understand the constraints of TWJ-SDA template and helper to have the sequence specificity. However, these constraints are not the only ones that are important when designing the template and helper. Another important factor in sequence design is the Signal to Noise ratio (S/N ratio), which is the ratio of amplified products in the presence and absence of the target miRNA. The reason why this S/N ratio is important is that in TWJ-SDA, if the template and helper are not designed well, the reaction of template and helper alone will produce the amplified product even if the target miRNA is not present. We focused on the S/N ratio and decided to seek conditions that would increase the S/N ratio.

While the focus of the TWJ Specificity section was the sequence specificity of TWJ-SDA, the S/N ratio is the focus of this section. We built an ODE model different from the one used in the TWJ Specificity section and tried to predict the S/N ratio for various conditions. Through comparison with experimental results and improvement of the model, we were able to create the model that predicted the S/N ratio in the experimental results to some extent.

We have integrated the predictive model for S/N ratio with the constraints for being sequence specific identified in the TWJ Specificity section. The integrated model allows us to design the template and helper that will enable TWJ-SDA with sequence specificity and high S/N ratio.

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Figure 5. Schematic Diagram of Sequence Design

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Figure 6. Comparison of predictions of S/N Ratio in simulation and experimental results. The horizontal axis shows the rank order of large and small S/N Ratio in the simulation and the vertical axis shows the rank order of large and small S/N Ratio in the experiment.

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Amplification Comparison

From the miRNA Selection section, it was found that tear fluid can contain miRNAs that have similar sequences of the biomarker miRNAs. In order to distinguish these similar sequences, TWJ-SDA should be used. Then, is TWJ-SDA alone sufficient for amplification? If not enough, what amplification methods would be appropriate to add to TWJ-SDA? The goal of this section is to suggest from the model what amplification methods would be best to use in the amplification system.

First, the simulation results showed that TWJ-SDA alone was not sufficient for amplification. Therefore, we had to select further amplification methods to use after TWJ-SDA. Based on the conditions required for the amplification system, literature review, 3and Human Practices, we narrowed down the candidate amplification methods after TWJ-SDA to three : Exponential amplification reaction (EXPAR), 2step-SDA, and 3step-SDA.

In order to select the best one among these amplification methods, we developed an ODE Model for each amplification method. We compared the amplification efficiency, Positive-to-Negative Ratio, and robustness to time and enzyme activity of the three options using the ODE Model. As a result, we proposed 3step-SDA as the amplification method after TWJ-SDA. We not only contributed to the selection of the amplification reaction, but also provided support for Wet Lab by predicting the amount of reactants that would increase the amplification efficiency and robustness.

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Figure 7. Amplification Comparison.

For more information, see:

CRISPR-Cas 3/12a MD Simulation

We decided to use CRISPR-Cas as a system to detect amplified dsDNA. There are several options for how many steps of SDA to connect to CRISPR-Cas in the signal amplification process. Although we suggested the appropriate amplification method in the Amplification Comparison section, as an alternative approach, we attempted to examine the most desirable number of n step-SDA steps using MD simulation. Based on the assumption that the higher the stability of the protein, crRNA, and DNA complexes, the better the detection ability, we evaluated the stability of each complex. As a result of MD simulation, we reached the conclusion that 3step-SDA was the most desirable amplification method after TWJ-SDA.The results in the Amplification Comparison section indicate that 3step-SDA is also expected to be superior in terms of amplification efficiency and robustness. Therefore, Dry Lab could confidently propose that 3step-SDA is the best amplification method after TWJ-SDA.

For more information, see

For the Future of Our System


"The model takes our project to the next level !"

POIROT was created for the detection of glaucoma. However, the system is highly flexible and can be applied to miRNA-based detection of a variety of diseases, not just glaucoma. Dry Lab focused on its applicability and wanted to help people to use our system with a minimum of required steps.

Similarity Sequence Search Software for miRNA

First, we developed software using the miRNA similarity search algorithm created in the miRNA Selection section. The software is designed to search not only for miRNAs in tear fluid, but also for similar sequences of miRNAs in blood plasma and leukocyte.

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Figure 8. Behavior of similar sequence search program.The program extracts sequences from the database and evaluates their similarity to the target sequence by checking for base matches.

For more information, see:

Sequence Design Software for TWJ-SDA

Using the integrated model created in the Sequence Design section, we have also created software that makes it easy to design templates and helpers that will enable TWJ-SDA with sequence specificity and high S/N ratio. This software makes it easy to know the optimal template and helper without conducting experiments. One of the hurdles in applying POIROT's system is the design of templates and helpers to be used in TWJ-SDA. Our software facilitates the application of POIROT's system to other disease biomarker miRNAs.

For more information, see:

Software derived from models will allow us to use our system easily once you select miRNA biomarkers. These software will increase the applicability of our system to other diseases.

Conclusion


Our Models accompanied and accelerated the progress of the project. In particular, the Models contributed to the selection of the amplification system, which is the most important part of our system. In addition, it was able to suggest the appropriate amount of reactants in the amplification system. In addition, the model has become the foundation of the software and has strongly contributed to expanding the applicability of our system!

Contribution


We have created a manual explaining how to use NUPACK Analysis, which we used for modeling, and a manual explaining how to perform MD simulation.
for more information, see

We have summarized the formulation methods necessary for modeling the Lateral Flow Assay, although we did not perform simulations.

Lateral Flow Assay Modeling as Proposal of a Versatile Method for Simulation Preparation.

Lateral Flow Assay (LFA) is a user-friendly disease testing tool, making it suitable as the quantitative component of a device designed for home-based glaucoma detection. This study introduces a comprehensive model for the Lateral Flow Assay (LFA) that focuses on time-dependent flow rates driven by capillary action, enhancing conventional approaches that combine the advection-diffusion equation with reaction equations. While traditional models often assume constant flow rates, leading to significant inaccuracies in reaction results on the assay strip, our approach effectively addresses these limitations. This enhancement provides a more accurate representation of reaction dynamics and underscores the necessity for improved modeling techniques in LFA. Additionally, we propose a discretization approach for simulating the model, employing appropriate approximation methods for the advection and diffusion terms. Future research directions include optimization of LFA system conditions for improved interpretation of positive and negative results.

For more information, see


Source Code


The code used in the Model simulation can be obtained at the following link: GitLab

References


  1. Cho, H.-k., Seong, H., Kee, C., Song, D. H., Kim, S. J., Seo, S. W., & Kang, S. S. (2022). MicroRNA profiles in aqueous humor between pseudoexfoliation glaucoma and normal tension glaucoma patients in a Korean population. Sci Rep, 12(1), 6217. https://doi.org/10.1038/s41598-022-09572-4

  2. Tanaka, Y., Tsuda, S., Kunikata, H. et al. (2014). Profiles of Extracellular MiRNAs in the Aqueous Humor of Glaucoma Patients Assessed with a Microarray System. Sci Rep, 4, 5089. https://doi.org/10.1038/srep05089

  3. Komiya, K., Noda, C., & Zamamura, M. (2024). Characterization of cascaded DNA generation reaction for amplifying DNA signal. New Generation Computing, 1-16. https://doi.org/10.1007/s00354-024-00249-2