Overview

Mathematical modeling played an essential role in understanding and optimizing our project. It allowed us to investigate aspects of the project that could not be determined through experimentation, such as the volume of blood required for the microfluidic chip. Using variables for the unknown quantities, we could get an equation to calculate the volume of blood needed.

Modeling also allowed us to make predictions regarding the kinetics of the aptamer and cDNA binding using simple formulas. These predictions were cross-validated with our wet lab data.

Additionally, we analyzed the five putative biomarkers central to our project. We used Bayes’ Theorem to find the correlation factor between each biomarker and MDD, as well as other diseases where they show upregulation or downregulation. This analysis gave us a Bayesian network with probabilities.

We are developing additional models, such as a feasibility/reliability model, which strengthens our purpose of choosing five biomarkers instead of one.

Bayesian Network

Introduction

Being a heterogeneous disorder, MDD is influenced by a variety of factors. Therefore, a single biomarker may not be the only factor causing MDD or even provide us with an accurate indication of whether or not a person has MDD. So, to bring high sensitivity and reliability to MDD diagnosis, our microfluidic chip employs 5 different putative biomarkers. Thus, to understand the significance and relevance of our biomarkers to MDD and its correlation with other diseases and validate our choice, we use the Bayesian network for biomarker analysis.

Main goals

Extensive research studies to determine all the possible associations of our 5 different putative biomarkers to MDD and other diseases
To determine the extent to which the biomarkers for MDD and other disorders correlate. We utilize Bayesian probability to accomplish this.
Create a Bayesian network to visualize the connection.
Biomarker analysis from the Bayesian network.
To verify the reliability and validity of the biomarkers we chose.

The Network for Biomarker Analysis

All the values are represented in percentage.

Bayesian Analysis:

To prove that the biomarker level indicated MDD itself and not any other diseases, we did a Bayesian Analysis of all the diseases associated with each biomarker.
For this, we used Bayes’ theorem of conditional probability:

Where,
A_i =disease associated with the particular biomarker, B = varied regulation of the biomarker.
P(A_i|B) =probability of having disease when there is varied regulation of B biomarker.
P(B|A_i)= probability of finding varying levels of B biomarker when having A_i disease.
P(A_i), P(B)=independent probability of A_i and B
Doing the Bayesian Analysis for each biomarker, we can determine the probability that MDD is associated with the varied regulation of each biomarker. Combining the five probabilities, we can conclude that the disease diagnosed is MDD.
For the Bayesian Analysis, we assume that each disease is mutually independent and exhaustive. We also assume that the probability of having a varied regulation of the biomarker (P(B)) is 1 given that the kit only detects varied regulation. The independent probability of A_i would be the incidence rate of the disease.

Please click on the different buttons to get a Correlation factor tables for each biomarker

miRNA 132 miRNA124 GSalpha Cortisol Serotonin

Tabulated Bayesian probabilities value for miRNA 132

Diseases	Bayesian probability
MDD	3.384 ^[1]
Inflammatory Bowel Disease	0.1606 ^[2]
Osteoarthritis	2.624 ^[3]
Type 2 Diabetes	5 ^[4]
Hepatic steatosis	18.5 ^[5]
Aortic Atherosclerosis	6.57 ^[6]
Brain Ischeima	0.173 ^[7]
Periodontal disease	9.5 ^[8]
Alzheimer’s	0.5 ^[9]
Degenerative Disc Disease	15 ^[10]

Tabulated Bayesian probabilities value for miRNA 124

Diseases	Correlation factor
MDD	6.0 ^[11]
Parkinson's Disease	0.0335 ^[12]
Hepatic Cancer	0.00465 ^[13]
Rheumatoid Arthritis	0.12 ^[14]
Myocardial Infarction	3.325 ^[15]
Epilepsy	0.35 ^[16]
Glioblastoma Multiforme	0.0016 ^[17]
Huntington's	0.0065 ^[18]
Ovarian Cancer	0.006 ^[19]
Alzheimer’s	1.95 ^[20]

Correlation factor for GSalpha

Diseases	Correlation factor
MDD	4.0 ^[21]
Cushing syndrome	0.00045 ^[22]
Colorectal cancer	0.06321 ^[23]
McCune-Albright syndrome	0.0275 ^[24]
Fibrous dysplasia	0.64 ^[25]
Pseudo hypothyroidism	0.0000042 ^[26]
Hepatocellular Carcinoma	0.00608 ^[27]
Obesity	2.94 ^[28]

Correlation factor for Cortisol

Diseases	Correlation factor
MDD	0.4296 ^[29]
Metabolic Syndrome	0.4545 ^[30]
Addison’s Disease	0.9375 ^[31]
Anxiety	0.5034 ^[32]
Bipolar disorder	0.5 ^[33]
Psychosis	0.5 ^[34]
Schizophrenia	0.5 ^[35]
Cushing syndrome	0.598 ^[36]

Correlation factor for Serotonin

Diseases	Correlation factor
MDD	0.02772 ^[37]
Obesity	0.165 ^[38]
OCD	0.02 ^[39]
Metabolic Diseases	0.08 ^[40]
Hypertension	0.312 ^[41]
Eating Disorders	0.0324 ^[42]
Parkinson's	0.00001 ^[43]

Conclusion

Using the study of the Bayesian network and the correlation factor, we were able to choose the most suitable set of biomarkers for the diagnosis of MDD. Despite the fact that several biomarkers are linked to various forms of disease, our extensive literature review suggests that people with MDD are most impacted by the overexpression of miRNA 124, 132, cortisol and the downregulation of serotonin and gs alpha protein. This supported our prediction that all five biomarkers together impacted patients with MDD and the bayesian network was crucial in the selection of these biomarkers.

Kinetics

We are interested in two reactions that are taking place in our wet lab: one with FRET aptamer + cDNA and then the Aptasensor with the Biomarker. So here we have a model showing the chemical kinetics for those two reactions and verifying the results that we are getting from Wetlab.

1) Aptamer + cDNA → Aptasensor

2) Aptasensor + Target → Quantifier + cDNA

From the second reaction, we will get our cDNA back with the quantifier. From the chemical kinetics, we can module the reaction.

If we consider simple reactions like,

The initial concentration of this reaction is,

This will give us a plot of C vs time and an exponential one.

Assumption
For instance like the value (C0-A0) is always less than 0, since wet lab also uses more aptamer concentration than cDNA, we also took the value of k such that the denominator part can be neglected. Thus, we get a perfect exponential plot similar to the one from plotting the graph for time vs absorbance over time from the wet lab flourolog data.

Blood Volume Analysis

Introduction

OASYS being a diagnostic aid for MDD, works by utilizing a small sample of blood to detect biomarker levels. Since iGEM protocols do not allow conducting experiments with living samples, we performed calculations to quantify the minimum blood amount required by our tool for testing.

We have used variables in place of quantities that are not yet known or established. Later when accurate values are available, we can put them in place of the variables to obtain objective results. Below, we have attempted to explain these calculations using flowcharts and mathematical equations.

Flowchart

Calculations

The variables we have considered are as follows-:

Below are the calculations we did for finding the range of blood volume that will be required by our tool-:

Result and Conclusion

Through the above shown calculations we got the following expression-:

This gives us an approximate range of the amount of blood that our chip will require for testing. Due to the necessary restrictions of iGEM, we could not do real-world testing using blood samples. Once we have the needful permissions and licenses to perform trials, we can get accurate values to be put in this equation. That would ultimately give us tangible results for the minimum amount of blood required by the kit.

Future of the models

Our project involves a system comprising five different components working in parallel to quantify biomarkers for diagnosing clinical depression and assessing its severity.
The precision of the Bayesian model can be improved further when we get the correlation factors between the biomarkers and respective diseases.
Also by getting threshold values for our chosen biomarkers, we can accurately predict the blood volume sample required for testing.

Basically, our system can be considered as a structure, with each biomarker-quantifier complex serving as a separate component. To assess the reliability of our system, we can leverage the functioning probability of each individual component. These values can be incorporated into the following equation which will give an idea of the authenticity of our model.

Where h(p) is the feasibility function, and p represents the probability of each biomarker being connected to a disease.

In the case where each component has a functioning probability of 0.5 (50%), our system reliability would be approximately 96.875%. This equation remains flexible to accommodate real probabilities for each component.

Finally, Please refer our PI page for more information on the future implementation of our project .

References

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For Kinetics

1. Ultrasensitive fluorescence detection of Fe3+ ions using fluorescein isothiocyanate functionalized Ag/SiO2/SiO2 core–shell nanocomposites - Journal of Materials Science: Materials in Electronics Rajbongshi et al.
https://link.springer.com/article/10.1007/s10854-019-00852-w#Abs1

2. Isothermal real time DNA amplification instrument Terrijärvi
https://lutpub.lut.fi/handle/10024/159386