To screen patients with cardiovascular diseases for their risk of cancer, our project aims to develop a LIRA-based system to target miRNA that are both highly expressed in CVD patients and capable of promoting cancer. LIRA is a designed RNA sequence with stem-loop structures, which could be activated by its target RNA to initiate the expression of reporter gene. To establish an ideal LIRA system, our modeling group mainly need to revolve the following four questions.

To answer , we applied differential analysis in GEO database to identify miRNA that are highly expressed in patients post myocardial infarction (MI) or with heart failure. After differential analysis of miRNA in cancer database from TCGA, we identified miR-142-3p and miR-210-3p as ideal targets, as they are both highly expressed in multiple types of cancer and in post MI patients. Additionally, we also verified that these two miRNAs could promote migration and invasion of cancer cells with wet lab experiments.

To address and , we designed single-arm LIRAs to target miR-142-3p or miR-210-3p initially. Next, we designed double-arm LIRAs to target miR-142-3p and miR-210-3p, which could only be activated in the presence of both miRNAs. To optimize the design of LIRA, we analyzed multiple indicators of LIRA, and used Multinomial Logistic Regression to evaluate the potential contribution of these indicators to the expected performance to LIRA. To improve model performance, we introduced Random Forest to identify key indicators that could influence the stability and functionality of LIRA.

To answer , we conducted kinetic modeling to simulate the reaction of LIRA-mediated expression of reporter gene to obtain predicted time and concentration curves of the reaction. Furthermore, using 3D curves, we simulated the reaction with miR-142-3p and miR-210-3p at different concentrations, and estimated suitable concentration of LIRA for detecting miRNAs at a variety of concentration.

In summary, our modeling work laid the ground for our wet lab experiments that generates the LIRA to target miR-142-3p and miR-210-3p, and paved the way for the future application of the LIRA in the screening of cancer risk in post-MI patients.

Epidemiology studies have revealed that patients with CVDs, such as myocardial infarction (MI), heart failure (HF) and atherosclerosis, have increased risk of getting cancer ^[1-4]. For instance, MI patients exhibit increased prevalence of a variety of cancers and elevated mortality that are caused by cancer ^[1]. HF patients also show higher cancer risk compared to healthy individuals ^[5]. Experiments using animal models reveal that MI enhances tumor progression through circulating factors and immune reprogramming ^[6,7]. Especially, MI leads to aberrant miRNA secretion from the inflicted heart into blood, which could circulate to distant organs and contribute to cancer progression at distant organs ^[8]. To find good targets for our cancer screening kit for CVD patients, we analyzed database of CVD, including MI and HF, and databases of multiple cancers, to identify miRNA that show increased expression in both CVD and cancer, and then verified the function of the identified miRNA on cancer progression.

The whole process of our analysis of MI and cancer database is shown in Figure 1. First, we searched Gene Expression Omnibus (GEO) database using myocardial infarction and miRNA as key words and collected 318 datasets. Since our aim is to identify highly expressed miRNA in the blood of MI patients, we manually excluded 305 irrelevant datasets based on the sample sources, species and disease descriptions. To the remaining 13 datasets, we calculated the log₂FC value of the miRNAs based on the ratio of the mean values of the patient samples and control and applied logarithmic transformation to the ratio ^[9]. We used Student's t-test to obtain P-values for each miRNA. Furthermore, to reduce the occurrence of false positives, we adjusted the P-values by comparing these P-values with the threshold selected for an acceptable false discovery rate (FDR) ^[10], and used adj.P value to refer FDR. We used the log₂FC > 1 and adj.P Value < 0.05 as our screening criteria ^[11], and got 9 datasets that contained significantly upregulated miRNA.

Second, we summarized multiple epidemiology studies and identified 33 types of cancers showing faster progression or higher risk in CVD ^[12-16]. We conducted differential analysis of miRNA expression of these 33 types of cancer using the Cancer Genome Atlas Program (TCGA) database and obtained 22 cancer datasets that show significantly upregulated expression of miRNA using our screening criteria (log₂FC > 1 and FDR < 0.05). The names of these 22 types of cancers are listed in Table 1.

We compared the significantly upregulated miRNAs in MI and cancers to identify miRNAs that are significantly upregulated in both diseases and obtained 24 miRNAs. We think that two criteria are especially important for the potential effects on cancer promotion of these 24 miRNAs during CVD:

1. log₂FC values in MI. A high log₂FC value of the miRNA in MI demonstrates a large increased amount of this miRNA in the blood of MI patients, which indicates that a large amount of this miRNA is likely to reach distant organs through circulation system and exerts its potential cancer-promoting effects at distant organs.

2.Types of cancers that show significantly upregulated expression of these miRNAs. miRNAs that are highly expressed in multiple types of cancers could potentially influence the progression of multiple types of cancers. We would like to design a screening kit to identify MI patients with increased risk of getting of a variety of cancers, instead of a certain type of cancer.

We summarized these two key information of the 24 miRNAs in Table 2.

To further evaluate the log₂FC in MI and types of cancers of these 24 miRNAs, we applied a scatter dots graph to visualize these data (Figure 2). MiR-210-3p and miR-142-3p distinguish from other miRNAs in this graph, as they show both much higher log₂FC values in MI and much more types of cancers that showed significantly upregulated expression of them than other miRNAs.

As shown in Table 2, miR-210-3p ranks the highest in log₂FC value in MI (6.18), which demonstrate 73 folds of increased expression in MI patients, and show significantly upregulated expression in 13 types of cancers, with log₂FC values in cancer ranged from 1.02 to 5.04. The log₂FC values of miR-210-3p in 13 types of cancers are shown in Table 3.

miR-142-3p ranks the second highest in log₂FC value in MI (3.51), which demonstrated 11 folds of increased expression in MI patients, and show increased expression in 10 types of cancers, with a log₂FC values in cancers range from 1.04 to 6.61. The log₂FC values of miR-142-3p in 10 types of cancers are shown in Table 4.

To summarize, our analysis shows that miR-142-3p and miR-210-3p are the best target miRNAs to identify MI patients with high risk of getting cancers.

HF is a condition resulting from the impairment of cardiac contractility and/or diastolic function^[17].Current study also reveals that HF can promote cancer ^[6]. Hence we also analyzed miRNAs that are highly expressed in HF patients in GEO database. The analysis process is shown in the flowchart (Figure 3).

We collected 158 datasets from GEO database using heart failure and miRNA as key words. After we manually excluded 151 irrelevant datasets based on the sample sources, species and disease descriptions, we got 7 datasets to analyze miRNA expression. Using log₂FC > 1 and adj.P Value < 0.05 as screening criteria, we got 6 datasets that contain significantly upregulated miRNAs in HF. We compared the significantly upregulated miRNAs in HF with those in cancers, which was described in the previous section, we got 35 miRNAs that show significantly upregulated expression in both diseases. We summarized the log₂FC in HF and types of cancers that show significantly upregulated expression of these miRNAs in Table 5.

To further evaluate the log₂FC in HF and types of cancers of these 35 miRNAs, we applied a scatter dots graph to visualize these data (Figure 4). Unlike the results of analysis in MI, these miRNAs all clustered in the lower-left part of the graph, demonstrating that no miRNA showed superior performances on both log₂FC values in HF and types of cancers that showed significantly upregulated expression.

In summary, we did not identify ideal miRNAs as targets for cancer screening from our analysis of HF database.

From our analysis of MI database, we found miR-210-3p and miR-142-3p are two outstanding candidates targets to identify MI patients with high risk of cancer. We used an ROC curve to evaluate the diagnostic performance of miR-142-3p and miR-210-3p on our collected raw dataset samples from MI (Figure 5). We found that combined ROC curve of miR-210-3p and miR-142-3p (AUC=0.78) showed better results than ROC of miR-210-3p alone (AUC=0.66) and ROC of miR-142-3p alone (AUC=0.60), which demonstrates that using miR-210-3p and miR-142-3p as target miRNA simultaneously could decrease the probability of false discovery rate of detecting MI than using these 2 miRNAs as target miRNA separately.

We also revisited our HF screening dataset to specifically analyze miR-142-3p and miR-210-3p. MiR-142-3p was identified from our analysis of HF dataset with log₂FC value (2.13), which demonstrated a 5 folds increased expression (Figure 4). MiR-210-3p failed to be selected from our analysis of HF dataset due to the log₂FC value (0.67) did not pass our screening criteria.

From our analysis, we suggest using both miR-210-3p and miR-142-3p together as targets to screen MI patients to identify those with high risks of getting cancer.

Through bioinformatic analysis, we identified miR-210-3p and miR-142-3p as potential targets for screening cancer risk in MI patients. We did literature research of these two miRNA, and found that they are involved in the regulation of migration and invasion of cancer cells ^[18-21] .To verify whether miR-210-3p and miR-142-3p can promote migration and invasion of cancer cells, mimics and inhibitors of miR-210-3p or miR-142-3p were transfected into human renal clear cell carcinoma cell line 786-o cells, and the transfected cells were tested by Wound Healing and Transwell assays.

To verify the function of miR-210-3p in cancer cells, we did Transwell and Wound Healing assays with 786-o cells transfected with mimics of miR-210-3p (mimics) and inhibitor of miR-210-3p (inhibitor). In Wound Healing assay, we evaluated the relative migration levels through measuring the wound area of 786-o cells transfected with control, mimics and inhibitor of miR-210-3p. Statistical analysis of the Wound Healing assays shows that 786-o cells transfected with mimics of miR-210-3p migrated faster than control cells and 786-o cells transfected with inhibitor of miR-210-3p migrated slower than control cells (Figure 6). Next, we evaluate the invasion levels through counting the amounts of 786-o cells that colonized in the lower well of transwell assays. Statistical analysis demonstrated that 786-o cells transfected with mimics of miR-210-3p showed higher invasion capability than control cells and 786-o cells transfected with inhibitor of miR-210-3p showed lower invasion ability than control cells (Figure 7). To summarize, 786-o cells with overexpression of miR-210-3p have increased migration and invasion capabilities, demonstrating that miR-210-3p could promote the migration and invasion of cancer cells.

Similarly, to verify the function of miR-142-3p in cancer cells, we did Transwell and Wound Healing assays with 786-o cells transfected with mimics of miR-142-3p (mimics) and inhibitor of miR-142-3p (inhibitor). In Wound Healing assay, we evaluated the relative migration levels through measuring the wound area of 786-o cells transfected with control, mimics and inhibitor of miR-142-3p. Statistical analysis of the Wound Healing assays shows that 786-o cells transfected with mimics of miR-142-3p migrated faster than control cells and 786-o cells transfected with inhibitor of miR-142-3p migrated slower than control cells (Figure 8). Next, we evaluate the invasion levels through counting the amounts of 786-o cells that colonized in the lower well of Transwell assays. Statistical analysis demonstrated that 786-o cells transfected with mimics of miR-142-3p showed higher invasion capability than control cells and 786-o cells transfected with inhibitor of miR-142-3p showed lower invasion ability than control cells (Figure 9). In summary, 786-o cells with overexpression of miR-210-3p have increased migration and invasion capabilities, demonstrating that miR-210-3p could promote the migration and invasion of cancer cells.

Together, the results of transwell and Wound Healing assays indicated that increased expression of miR-210-3p and miR-142-3p in MI patients might enhance the invasion and migration of cancer cells, which supports our idea of developing a screening kit that targets miR-210-3p and miR-142-3p to MI patients with high risk of cancer.

To design a screening kit that can target miR-210-3p and miR-142-3p, we adapted from an innovative approach named Loop-Initiated RNA Activator (LIRA) that was used to detect viral RNA^[18]. As shown in Figure 10, LIRA forms a stem-loop structure that mainly contains a recognition region, a ribosome binding sequence (RBS) and a start codon AUG. Without interaction with target RNA, the RBS and start codon in LIRA are kept in a close status in the stem structure, making them impossible to initiate translation of downstream reporter gene. The recognition region is a 31 nucleotides (nt) sequence that is reverse complimentary to the target RNA of LIRA. While 21 nt of the reverse complimentary sequence is designed to locate in the loop structure of LIRA, which is named as a*, 10 nt of the reverse complimentary sequence is designed to locate in the stem structure of LIRA, which is named as b*. As a result, the target RNA of LIRA can bind to both a* and b*, and the binding of the target RNA to b* destabilize the stem structure that locks RBS and start codon, which makes them to be exposed in an open status for the translation initiation of downstream reporter gene. Due to the complexity of secondary structure and complicated hybridization process of RNA, we used NUPACK software to design and analyze LIRA sequences in the subsequent study.

To design LIRA sequences that target miR-210-3p and miR-142-3p separately, we first determined the composition and structure of each part of LIRA, and replaced the recognition region with reverse complementary sequence of miR-210-3p and miR-142-3p. We used the design function of NUPACK to design the rest of LIRA sequences. Next, we used the analysis function of NUPACK to simulate the hybridization process of LIRA, and the nucleotide bases in the mismatch region of the LIRA with abnormal structure were modified to achieve our design expectation, which keep RBS and AUG at a closed status in a stem region without interactions with target miRNA and release RBS and AUG to an open status in a single strand RNA with interactions with target miRNA. The procedure of our LIRA designing is listed below.

During the process of designing, we found that our situation differed from the case reported in the literature in that the target RNA used in the literature was 31nt, while the target miRNAs used by our team were 22nt and 23nt respectively^[18]. Due to the difference in the length of the target RNA, we were unable to use the way of LIRA design reported in the literature directly. To determine the distribution of the recognition region on our LIRA, we defined a concept of stem-loop ratio: the ratio of the number of nucleotides of recognition region in the stem structure to the number of nucleotides of recognition region in the loop structure. We tried to design LIRA structure using different stem-loop ratios. We found that when the number of nucleotides of the recognition region in the stem is too large, it will partially overlap with the complementary sequence of RBS, which will lead to the exposure of the RBS sequence. Therefore, we designed LIRA to miR-210-3p with the stem-loop ratios from 0/22 to 13/9 and LIRA to miR-142-3p from 0/23 to 13/10. The hybridization of LIRA to their target miRNAs was also analyzed with NUPACK. The pairing results and related data are shown in Table 6 and Table 7.

We think that the greater the free energy of a LIRA, the easier it is for LIRA structures to be paired with miRNAs for translation; the smaller the free energy of a LIRA, the more stable the structure of LIRA is. Therefore, we chose free energy as an important index to analyze the hybridization of LIRAs to their target miRNAs. We calculated the changes of free energies of the LIRA before and after hybridization and fitted the changes of free energy to stem-loop ratio. From the fitting curve, it seems that there is no regularity between the changes of free energy and stem-loop ratio (Figure 11 and Figure 12).

Since the LIRA sequence designed by NUPACK algorithm in the unrestricted region is random, which causes large variations among these designed LIRA. Therefore, we designed 10 sequences for each stem-loop ratio and averaged the free energy values of these LIRA. A new fitting was performed with the averaged free energy and stem-loop ratio (Figure 13 and Figure 14). The new fitting curve demonstrates that there is no linear relationship between LIRA free energy and stem-loop ratio, indicating that LIRA would not become more or less stable as stem-loop ratio increase or decrease.

Next, we calculated the changes of free energy as the differences of free energy of LIRA before and after hybridization with its target miRNA, and analyzed the relation between LIRA free energy and the changes of free energy. We observed that the data had a clear linear relationship, so we linearly fitted it. The fitting results are shown in Figure 15 and Figure 16. The slope of the fitted curve is approximately equal to -1, which indicates that the free energy of LIRA after hybridization with its target miRNA is stable at a constant value. The free energy of LIRA hybridized with miR-210-3p is around -54 kcal/mol, and the free energy of LIRA hybridized with miR-142-3p is around -44 kcal/mol. These results show that free energy of LIRA before hybridization might be a more important indicator to determine the quality of a LIRA.

Furthermore, we averaged 10 LIRA free energies at the same stem-loop ratio, which could represent the LIRA free energy and hybridization free energy at certain stem-loop ratio. Subsequently, we performed a clustering with these 28 points, and observed a linear relationship between LIRA free energy and the averaged changes of free energy (Figure 17 and Figure 18).

From our analysis of LIRA to miR-210-3p and miR-142-3p, we concluded that stem-loop ratio has little effect on the free energy of LIRA. For our subsequent wet lab experiments, we chose 3 LIRA sequences for miR-210-3p with stem-loop ratios of 2/20, 7/15, and 10/12, and 3 LIRA sequences for miR-142-3p with stem-loop ratios of 3/20, 8/15, and 11/12. We selected these 6 LIRA sequences to verify whether stem-loop ratio indeed had no effect on the performance of LIRA with wet lab experiments. Meanwhile, since the free energies of these 6 LIRAs are very different, the influence of the LIRA free energy on the functions of LIRA can also be investigated (Table 8). In this regard, we expect that a stable LIRA structure is often accompanied by a lower free energy.

To target miR-210-3p and miR-142-3p simultaneously, we designed LIRAs with double-arm structure that can target two target RNA^[22]. As shown in Figure 19, double-arm LIRA has two recognition regions, A* and B*. While A* is located on the short arm of the double-arm structure, B* is located on the long arm of the double-arm structure, which is connected to RBS and AUG. We think that putting one miRNA reverse complimentary sequence in A* and the other miRNA reverse complimentary sequence in B* would make our LIRA targeting two miRNA. Our expectation is that only when the LIRA binds to the target miRNA A and then bind to the target miRNA B would expose the RBS and AUG in an open status to initiate the translation of the downstream reporter gene, and otherwise the RBS and AUG would be locked to at a closed status in stem region.

We identified the composition of each part of double-arm LIRA and replaced the recognition region with sequences that were reverse complimentary to miR-210-3p and miR-142-3p. Utilizing the design function of NUPACK, we designed a primary double-arm LIRA structure and obtained the sequence. The following is the design procedures of LIRA sequences to detect miR210-3p and miR142-3p in NUPACK.

During the process of simulation, we utilized NUPACK to generate 100 double-arm LIRAs. First, we hybridized each double-arm LIRA to both miR-142-3p and miR-210-3p, and found that 32 double-arm LIRAs could only hybridize to a single miRNA. We analyzed the results of the remaining 68 LIRA that could hybridize to both miRNAs, and 21 LIRAs did not form a correct base-pairing structure between RBS and AUG. We then modified the bases between RBS and AUG in these 21 LIRAs according to the hybridization results to ensure that RBS and AUG could be successfully exposed after hybridization. Finally, we analyzed the sequences at other regions of these 21 LIRAs, and found that 15 of them would destabilize AUG and RBS when LIRA interacts with miR-210-3p alone. We finally get 6 ideal double-arm LIRA that meet the design expectation, e.g., the RBS and AUG remain in a close status without interaction with miR-210-3p and miR-142-3p, and keep in an open status with interactions with miR-210-3p and miR-142-3p. The simulation results of these 6 LIRAs are shown in Table 9.

Since the core of our project is to use LIRA to detect miR-142-3p and miR-210-3p, a comprehensive and detailed understanding of the LIRA-mediated reaction is essential for the success of our project. Through simulation of the process and analysis of the kinetics of the LIRA-mediated reaction, we can get crucial information of this reaction, such as the trend of changes of substrates and peak time of the expression of the reporter gene, which could provide critical information for designing and optimizing of our project.

We simulated reactions mediated by the single-arm and the double-arm LIRA under both intracellular and extracellular conditions, and our simulation includes the following steps:

The interactions between LIRA and its target RNA could change the conformation of LIRA, and initiate translation of downstream reporter gene. Since the reaction between single-arm LIRA and miR-142-3p has the same reaction process and parameters as the reaction between single-arm LIRA and miR-210-3p, we think that these two reactions have the same concentration-time curve and peak time of expression of reporter gene. Without loss of generality, we take miR-210-3p as an example for kinetic simulation below.

Schematic presentation of the intracellular reaction mediated by single-arm LIRA is shown in Figure 23

Reaction process of single-arm LIRA is listed in Figure 24

Since the transition from 210-CSIL to OSIL is rapid, we treated the product of the combination of CSIL210 and miR210 as OSIL210. Therefore, we carried out a reasonable simplification of the simulation, and the simplified reaction is shown in Figure 25.

Based on the chemical reaction described above, the equations of ordinary differential equations with specific parameter values are listed in Figure 26.

In the simulation, we set the initial concentration of PLMg and PLM210 as 0.01mol/L, and other substances as 0. We use MATLAB and ode45 function to get the numerical solution. As shown in Figure 27, the concentration of EGFP reaches the maximum value at 83 minutes and 1/2 of the maximum value at 11.5 minutes. The concentration of OSIL210 increases rapidly and reaches the maximum value of 0.00054mol/L at 160s. Due to the low transcription rate of PLMg and PLM210 plasmids, and the high reaction rate of OSIL210 to EGFP, the concentration of OSIL210 gradually decreases after 160s.

Next, we simulated the intracellular reaction mediated by double-arm LIRA, and the schematic presentation of this simulated reaction is shown in Figure 28.

For the reactions with double-arm LIRA, we assume that miR-210 cannot bind to CTIL when miR-142 is not present. According to these reaction processes, we can list the reaction equation of the two-arm LIRA, as shown in Figure 29.

According to the chemical reaction described above, the equations of ordinary differential equations with specific parameter values are listed below in Figure 30.

In the simulation, we set the initial concentration of PLMag, PLM210 and PLM142 as 0.01mol/L, and other substances as 0. Similarly, we use MATLAB and ode45 function to get the numerical solution. As shown in Figure 31, the concentration of EGFP reaches the maximum value of 0.00118mol/L at 3 minutes. The concentration of OTIL210 increases and reaches a maximum value of 0.00064mol/L at 95s. Due the low transcription rate of PLMg and PLM210 plasmids and the high reaction rate of OTIL210 to EGFP, the concentration of OTIL210 gradually decreases after 95s.

Compared to the intracellular kinetic simulation, the extracellular reaction process does not have the step of transcription of miR-142-3p and miR-210-3p from plasmids. Since the intracellular and extracellular conditions are different, the modeling parameters are altered accordingly. The reaction between single-arm LIRA and miR-142-3p has the same reaction process and parameters as the reaction between single-arm LIRA and miR-210-3p, these two reactions have the same concentration-time curve and the same peak time. Without loss of generality, we take miR210-3p as an example for kinetic simulation below.

Schematic presentation of extracellular reaction mediated by single-arm LIRA is shown in Figure 32.

Reaction process of single-arm LIRA are listed in Figure 33

Since the transition from 210-CSIL to OSIL is rapid, we treat the product of the combination of CSIL210 and miR210 as OSIL210. Therefore, we carry out a reasonable simplification of this simulation, and the simplified reaction is shown in Figure 34.

According to the chemical reaction described above, the equations of ordinary differential equations with specific parameter values are listed below.

In the simulation, we set the initial concentration of PLMg, PLM210 and PLM142 as 0.01mol/L, and other substances as 0. Similarly, we use MATLAB and ode45 function to get the numerical solution. As shown in Figure 36, the concentration of fluorescent protein EGFP reaches the maximum value of 0.0083mol/L at 30 minutes and 1/2 of the maximum value at 9 minutes. The concentration of OSIL210 increases rapidly and reached a maximum value of 0.00054mol/L at 160s. The concentration of OSIL210 gradually decreases after 160s.

Next, we simulated the extracellular reaction mediated by double-arm LIRA, and the schematic presentation of this simulated reaction is shown in Figure 37.

The process of reaction mediated by single-arm LIRA is listed in Figure 38

According to the chemical reaction expression above, the equations of ordinary differential equations with specific parameter values are listed below.

In the simulation, we set the initial concentration of PLMag, miR210-3p and miR142-3p as 0.01mol/L, and other substances as 0. Similarly, we use MATLAB and ode45 function to get the numerical solution. As shown in Figure 40, the concentration of EGFP reaches the maximum value of 0.0083mol/L at 30 minutes and 1/2 of the maximum value at 9 minutes. The concentration of OTIL210 increases rapidly and reaches a maximum value of 0.00054mol/L at 160s. The concentration of OTIL210 gradually decreases after 160s.

After conducting kinetic analysis of the reactions mediated by our double-armed LIRA, we started to think how to apply LIRA as a testing kit in practical situations. We encountered an issue which is that the concentrations of the two highly expressed target miRNAs in patient blood often vary, whereas in our kinetic simulation, we assumed the concentrations for both target miRNAs are equal. Consequently, it is questionable to simply take the kinetic simulation results as our reference for LIRA's application in real-world situation. To address this issue, we aim to introduce different concentrations of our target miRNAs in our LIRA reaction system to observe the corresponding dynamic changes in EGFP expression.

Firstly, we set the concentrations of miR-210-3p and miR-142-3p. We selected concentrations of 0.0025, 0.005, 0.01, 0.02, and 0.04 mol/L for our 2 target miRNAs, while keeping the LIRA concentration at 0.01 mol/L. Subsequently, we simulate the reactions between 2 miRNA and LIRA based on our extracellular kinetic model of reaction mediated by double-armed LIRA. From our simulation of extracellular reaction in Figure 40, we can see that the value of EGFP reaches its maximum in our reaction at approximately 30 minutes. Hence, we collected the EGFP values at 40 minutes in our reaction after changing the concentrations of our target miRNA and presented the results as scatter points in three-dimensional space, as shown in Figure 41.

From Figure 41, we can see that the EGFP expression increases to high values as the concentrations of miR-210-3p and miR-142-3p increase. Additionally, the scatter points in the graph tend to cluster more densely at lower concentrations of miR-210-3p and miR-142-3p. To better understand the relationship between the concentrations of miR-210-3p and miR-142-3p and their corresponding EGFP values, we attempted to fit these scatter points.

A Quadratic Regression is commonly used for surface fitting models ^[23]. Therefore, we employed the fitting function as Z = a + bX + cY + dX² + eY² + fXY, where Z represents the dependent variable (EGFP), and X and Y are the independent variables (X: [miR-210-3p], Y: [miR-142-3p]). By substituting the data into this equation, we can obtain the values of each parameter. The specific parameter interpretations and results are presented in Table 23 below.

Based on the calculations above, we obtained the regression equation: Z = -0.000118 + 0.3505X + 0.3288Y + 3.76XY - 7.42X² - 6.84Y². To understand the performance of our fitted equation, we conducted an Analysis of Variance (ANOVA) at a 95% confidence level (α = 0.05) for the terms in our regression. This analysis could assess the significance of our model terms and determine the terms that have statistically significant impacts on EGFP value. Tables 25 and 26 present the results of this analysis.

Based on the results of the ANOVA, we can observe that the R² value is high, indicating a good fit of the model. Additionally, the coefficients for the constant term, the interaction term ([miR-210-3p] * [142-3p]), the two linear terms ([miR-210-3p] and [miR-142-3p]), and the two quadratic terms ([miR-210-3p] * [miR-210-3p] and [miR-142-3p] * [miR-142-3p]) are all statistically significant. This suggests, in our quadratic regression equation, the terms are not redundant or causing interference in the regression results. Finally, we simulate the surface fitting based on our equation and the result is visualized in Figure 42.

From Figure 42 we can see that, as the concentrations of the two miRNAs continue to increase, the reaction rate accelerates, and the observed EGFP levels also rise continuously. When the concentration of one miRNA remains constant, as the concentration of the other miRNA increases, the EGFP value first rise and then decline. To have a more detailed observation of the changes of EGFP value in specific concentration ranges, we have plotted a contour map as shown in Figure 43.

Figure 43 is a contour plot of EGFP levels at 30 minutes for the reaction between LIRA and two target miRNAs. The color intensity in the figure represents different numerical ranges of EGFP. Specifically, the gradient from light green to dark green indicates an increasing trend of the EGFP variable from low to high. It can be observed that there is a distinct high-value region in the upper right corner of the plot. In contrast, as we move towards the lower left corner, the EGFP levels continuously decrease, and a low-value region appears. This may be attributed to the incomplete reaction of LIRA due to lower concentrations of miRNAs, resulting in lower EGFP value. Furthermore, we can observe in the plot that the EGFP value lies within the range of 0.008-0.01 when miR-210-3p is within 0.025-0.04 mol/L and miR-142-3p is within 0.0275-0.04 mol/L.

We can apply this conclusion into practical scenarios. Assuming the LIRA testing kit we use has a LIRA concentration of 0.01 mol/L, and only as the EGFP value reaches between 0.008 and 0.01 will it be considered as positive and identified by colors. We can simulate two scenarios:

First, we can use LIRA to detect unknown concentrations of miRNA in blood samples. When the concentrations of miR-210-3p and miR-142-3p in the blood sample we are testing fall within the ranges of 0.025-0.04 mol/Land 0.0275-0.04 mol/L respectively, the LIRA testing kit will successfully show colors and indicating after 30 minutes.

Second, we can use miRNA with known concentrations to validate the quality of the LIRA testing kit. Suppose we have miR-210-3p and miR-142-3p with concentrations as a mol/L and b mol/L, respectively, and both a and b are within the concentration range of 0-0.04 mol/L. Given the regression equation above, we can get Z = -0.000118 + 0.3505X + 0.3288Y + 3.76XY - 7.42X² - 6.84Y².When we add both a and b to the LIRA testing kit and allow the reaction to proceed for 30 minutes, the EGFP value that are detected should be close to the value of -0.000118 + 0.3505a + 0.3288b + 3.76ab - 7.42a² - 6.84b².With the premises of disregarding error interference, If there is a significant deviation between the two results, it indicates that there may be an quality issue with the LIRA testing kit.

In summary, in the future application of LIRA detection, it is necessary to take whether the concentration of LIRA and the concentrations of miRNA are falling in matching ranges as considerations and adjusting the LIRA concentration based on the concentration of miRNA in actual blood samples. Due to the limitation of lacking the information on the concentration of miRNA in blood samples, we can not adjust the concentration of our LIRA in our test kit. However, we believe that along with the advancement of miRNA detection technology and through continuous adjustment and optimization of our LIRA, we can finally obtain an ideal screening kit to detect expression of miRNA in real samples.