RCA Model
Overview
This year, Lambert iGEM is utilizing rolling circle amplification (RCA) with padlock probes as one of the methods to detect circulating microRNAs (miRNA) in blood in order to diagnose coronary artery disease (CAD).
This reaction can be summarized in 4 steps:
- Hybridization: miRNA binds to a padlock probe (Graugnard et al., 2010)
- Ligation: SplintR, an enzyme, circularizes the miRNA to the padlock probe (Jin et al., 2016; Lohman et al., 2013)
- Amplification: phi29 DNA polymerase uses the hybridized miRNA as a primer to begin amplification and create DNA rolling circle product (RCP) reporters (Esteban et al., 1993; Macdonald et al., 1994)
- Detection: We are testing two different reporting mechanisms for RCA
- Fluorophores and quenchers bind to the RCPs, decreasing fluorescence
- Lettuce aptamers bind to RCPs, causing fluorescence
Development
To assist in corroborating and interpreting RCA reactions, Lambert iGEM incorporated a deterministic ordinary differential equations (ODE) system to simulate the reaction process. Our model converted several reactions in the RCA system into ODEs to correlate fluorescence, caused by RCP-fluorophore-quencher or RCP-aptamer reactions, to the initial miRNA concentration. Lambert iGEM also reached out to Dr. Mark Styczynski from the Georgia Institute of Technology to aid in the identification of parameters and initial steps for creating our models. He recommended useful functionalities on MATLAB and research tools to find important rate constants.
Signaling Pathway
The team used MATLAB’s SimBiology software to diagram each reaction using the Law of Mass Action and Michaelis-Menten equations. The Mass Action equations are used to diagram the collision of reactants in a solution, which is needed for most reactants in our reaction pathways (Zi, 2012). On the other hand, when enzymes are utilized, Michaelis-Menten equations are needed to properly diagram catalytic enzyme kinetics (Park, 2022; Zi, 2012). The pathway begins with the introduction of miRNA into the system and ends with either RCP-quencher-fluorophore (RFQ) (see Fig. 1) or RCP-aptamer activity (see Fig. 2) as the final reporter.
Figure 1. RCA reaction pathway with an RCP-quencher-fluorophore reporter system in MATLAB Simbiology
Figure 2. RCA reaction pathway with an RCP-aptamer reporter system in MATLAB Simbiology
Biochemical Reactions
The model contains a total of 7 biochemical reactions (see Fig. 1) for the RCP-fluorophore-quencher reporting mechanism and 4 biochemical reactions (see Fig. 2) for the RCP-aptamer reporting mechanism. The first 3 reactions, shown below, are identical for both reporter mechanisms:
| Reactions | Description |
|---|---|
| \(M + P \xrightarrow{k}MP\) | Input miRNA (M) binds to the complementary arms of free padlock probes (P) to form miRNA-padlock probe complexes (MP) |
| \(MP + SplR \Longleftrightarrow MP_{circularized}\) | miRNA-padlock probe complexes (MP) are ligated by SplintR ligase (SplR) to circularized complexes (MP_circularized) |
| \(MP_{circularized} + phi29 \Longleftrightarrow R_{free}\) | Circularized miRNA-padlock probe complexes (MP_circularized) are extended by phi29 DNA polymerase (phi29) to create free DNA rolling circle products, or RCPs (R_free) |
RCA with RCP-fluorophore-quencher reporters includes an additional 4 reactions:
| Reactions | Description |
|---|---|
| Free RCPs (R_free) bind to free fluorophores (F_free) to form RCP-fluorophore complexes (RF) | |
| Free RCPs (R_free) bind to free quenchers (Q_free) to form RCP-quenchers complexes (RQ) | |
| RCP-fluorophore complexes (RF) bind to free quenchers (Q_free) to form RCP-quencher-fluorophore complexes (RFQ) | |
| RCP-quencher complexes (RQ) bind to free fluorophores (F_free) to form RCP-quencher-fluorophore complexes (RFQ) |
Alternatively, RCA with RCP-aptamer reporters includes 1 more reaction:
| Reactions | Description |
|---|---|
| \(R_{free} + apt \xrightarrow{k_{rcpapt}} RCPapt\) | Free RCPs (R_free) bind to free aptamers (apt) to form RCP-aptamer complexes (RCPapt) |
Initial Values of Species
In order to simulate our reactions, our team needed to input quantities to initialize each component in our model. The initial value of each species was obtained from RCA wetlab protocols:
| Variable | Species | Initial Value | Units |
|---|---|---|---|
| M | miRNA | 0.5 | picomoles |
| P | padlock probes | 0.05 | picomoles |
| SplR | SplintR | 25 | molecules |
| phi29 | phi29 DNA polymerase | 12.5 | molecules |
| R_free | free RCP | 0 | molecules |
| F_free | free fluorophores | 180664245 | molecules |
| Q_free | free quenchers | 361328490 | molecules |
| RF | bound RCP-fluorophores | 0 | picomoles |
| RQ | bound RCP-quenchers | 0 | picomoles |
| RFQ | bound RCP-fluorophores-quenchers | 0 | picomoles |
| apt | free lettuce aptamers | 10 | micromoles |
| RCPapt | bound RCP-aptamers | 0 | picomoles |
Parameters
Rate constants and degradation rates are required to input into our Mass Action Laws and Michaelis-Menten equations. These values were derived from literature or estimated if the values could not be found. The value of each parameter is shown below:
| Variable | Reaction | Estimated Values | Units |
|---|---|---|---|
| Mdeg | rate constant for miRNA degradation | 0.000019254 | 1/second |
| k_padlock | rate constant for miRNA-padlock binding | 32000 | 1/(moles*second) |
| Vmcircular | maximal rate of reaction needed for Michaelis-Menten enzyme kinetics for MP-SplintR binding | 0.008 | moles/second |
| Kmcircular | Michaelis-Menten constant for MP-SplintR binding | 1 | moles |
| Vmphi29 | maximal rate of reaction needed for Michaelis-Menten enzyme kinetics for MP_circular-phi29 binding | 112 | moles/second |
| Kmphi29 | Michaelis-Menten constant for MP_circular-phi29 binding | 31 | moles |
| RCPdeg | rate constant for free RCP degradation | 0 | 1/second |
| k1 | forward reaction rate constant for free RCP and free fluorophore binding | 1e12 | 1/(moles*second) |
| k2 | backward reaction rate constant for free RCP and free fluorophore binding | 0 | 1/second |
| k3 | forward reaction rate constant for free RCP and free quencher binding | 1e12 | 1/(moles*second) |
| k4 | backward reaction rate constant for free RCP and free quencher binding | 0 | 1/second |
| k5 | forward reaction rate constant for bound RF and free quencher binding | 1e12 | 1/(moles*second) |
| k6 | backward reaction rate constant for bound RF and free quencher binding | 0 | 1/second |
| k7 | forward reaction rate constant for bound RQ and free fluorophore binding | 1e12 | 1/(moles*second) |
| k8 | backward reaction rate constant for bound RQ and free fluorophore binding | 0 | 1/second |
| k_rcpapt | rate constant for free RCP and free lettuce aptamer binding | 1e7 | 1/(moles*second) |
Ordinary Differential Equations
As mentioned previously, Lambert iGEM incorporated the Mass Action Kinetic Laws and Michaelis-Menten Equations to represent the reactions for the RCA model. We generated 12 ordinary differential equations for RCP-fluorophore-quencher reporters and 9 ODEs for RCP-aptamer reporters. The first six ODEs are identical for both reporting mechanisms, as shown below:
| Ordinary Differential Equations |
|---|
| \(\frac{d[M]}{dt} = -(k_{padlock}[M][P] - M_{deg}[M])\) |
| \(\frac{d[P]}{dt} = -k_{padlock}[M][P]\) |
| \(\frac{d[SplR]}{dt} = -\frac{V_{mcircular}[MP]}{K_{mcircular} + [MP]}\) |
| \(\frac{d[MP]}{dt} = k_{padlock}[M][P] - \frac{V_{mcircular}[MP]}{K_{mcircular} + [MP]}\) |
| \(\frac{d[MP_{circular}]}{dt} = \frac{V_{mcircular}[MP]}{K_{mcircular} + [MP]} - \frac{V_{mphi29}[MP_{circular}]}{K_{mphi29} + [MP_{circular}]}\) |
| \(\frac{d[phi29]}{dt} = - \frac{V_{mphi29}[MP_{circular}]}{K_{mphi29} + [MP_{circular}]}\) |
We designed 6 more equations to diagram the RCP-Fluorophore-Quencher reporting mechanism:
| Ordinary Differential Equations |
|---|
| \(\frac{d[R_{free}]}{dt} = \frac{V_{mphi29}[MP_{circular}]}{K_{mphi29} + [MP_{circular}]} -(RCP_{deg}[R_{free}]) - (k_1[R_{free}][F_{free}] - k_2[RF]) - (k_3[R_{free}][Q_{free}] - k_4[RQ])\) |
| \(\frac{d[F_{free}]}{dt} = -(k_1[R_{free}][F_{free}] - k_2[RF]) - (k_7[F_{free}][RQ] - k_8[RFQ])\) |
| \(\frac{d[Q_{free}]}{dt} = -(k_3[R_{free}][Q_{free}] - k_2[RQ]) - (k_5[Q_{free}][RF] - k_6[RFQ])\) |
| \(\frac{d[RF]}{dt} = -(k_1[R_{free}][F_{free}] - k_2[RF]) - (k_5[Q_{free}][RF] - k_6[RFQ])\) |
| \(\frac{d[RQ]}{dt} = -(k_3[R_{free}][Q_{free}] - k_4[RQ]) - (k_7[F_{free}][RQ] - k_8[RFQ])\) |
| \(\frac{d[RFQ]}{dt} = -(k_7[F_{free}][RQ] - k_8[RFQ]) + (k_5[Q_{free}][RF] - k_6[RFQ])\) |
We also designed 3 additional equations to account for the RCP-aptamer reporting mechanism:
| Ordinary Differential Equations |
|---|
| \(\frac{d[R_{free}]}{dt} = \frac{V_{mphi29}[MP_{circular}]}{K_{mphi29}+MP_{circular}} - RCPdeg[R_{free}] - k_{rcpapt}[R_{free}][apt]\) |
| \(\frac{d[apt]}{dt} = -k_{rcpapt}[R_{free}][apt]\) |
| \(\frac{d[RCPapt]}{dt} = k_{rcpapt}[R_{free}][apt]\) |
Assumptions
Our RCA ODE model assumes all rate constants remain constant due to a lack of external environmental factors. Thus, this model replicates only the miRNA-padlock probe binding process to simulate RCP production and RCP-quencher-fluorophore/RCP-aptamer binding. The model also assumes the total quantity of padlock probes, SplintR ligase, phi29 DNA polymerase, fluorophores, and quenchers is known initially and remain constant over time. Finally, DNA polymerase activity is expected to remain the same regardless of the primer, miRNA, or dNTP concentration.
Results
After developing a complete set of ODEs, we utilized Simbiology’s Model Analyzer to simulate the quantity of bound RCP-quencher-fluorophore (RFQ) complexes (see Fig. 3) and bound RCP-aptamers (see Fig. 4) over 60 minutes with 0.5 picomoles of miRNA initially. As bound RFQ increases, the amount of free RCP decreases, dimming the fluorescence of the system. Alternatively, as bound RCP-aptamers increase, the system increases in fluorescence.
Initially, the bound RCP-fluorophore-quencher complexes are produced at a relatively quick exponential increase. Over time, the RFQ binding rate slows as the graph reaches an asymptote at .0001 picomoles of bound RFQ (see Fig. 3). On the other hand, bound RCP-aptamer is initially produced slowly, but the binding rate eventually becomes constant, allowing the graph to become linear over time (see Fig. 4). To help our hardware team interpret fluorescence measurements back to miRNA quantities, we plotted various initial miRNA concentrations to free fluorophores (see Fig. 5) and bound RCP-aptamers (see Fig. 6), which are analogues to free fluorophores, after a fixed time of 60 minutes and found the curve of best fit for each.
Our hardware team characterized our frugal hardware, Micro-Q, with varying concentrations of fluorophores, and they determined a curve of best-fit to relate fluorophore concentration to relative fluorescence units (RFUs). Thus, our modeling team connected miRNA concentration to fluorophore concentration (see Fig. 5 and 6), while our hardware team correlated fluorophore concentrations to fluorescence in RFUs. Together, our modeling simulations and hardware graphs enable CADlock to accurately calculate miRNA concentrations by quantifying the fluorescence with Micro-Q.
To experimentally assess the effectiveness of the RFQ reporting system, our wetlab team measured the fluorescence of varying linear probe complements, which are produced as rolling circle products in RCA, with constant quantities of quenchers and fluorophores. Our hardware team experimentally tested differing fluorophore concentrations on our plate reader, and we found a line of best fit between fluorophore concentration and RFUs: \(RFU = .908[fluorophores]\), where fluorophores were measured in micromolar concentrations (µM). Using this regression line, we derived a conversion rate between fluorophores concentration and fluorescence. Then, we modeled only the RFQ reporting system section of our overall model with different initial RCP concentrations to see how bound RFQ and free fluorophores changed, and we related initial RCP concentrations to fluorescence in RFUs (see Fig. 7). The negative logarithmic shape of our model is almost identical to our wetlab results, corroborating our experimentation (see Fig. 8 & 9). The variation in the scales of the two graphs can be attributed to micropipetting errors or differences in the plate reader used.
After relating complement concentrations to fluorescence, we applied the same conversion rate to ultimately correlate initial miRNA concentrations to fluorescence in RFUs on our plate reader depending on whether we use RFQ reporters (see Fig. 10) or RCP-aptamer reporters (see Fig. 11). As seen by the wetlab experimentation, the concentration of miRNA versus fluorescence follows a negative logarithmic trend when RFQs are utilized (see Fig. 12), exactly as predicted by the model (see Fig. 10). Thus, our model strongly validates our RCA wetlab experimentation with RFQ reporters.
Although every plate reader will input different RFU values relative to the blank, sensitivity, and gain of the machinery, these charts can help CADlock users confirm the shape of their graphs when they test their own miRNAs in laboratories.
RCT Model
Overview
Along with the rolling circle amplification (RCA) mechanism, our team utilizes rolling circle transcription (RCT) to detect circulating microRNAs (miRNAs) in blood. This reaction follows 4 main steps:
- Hybridization: miRNA binds to a padlock probe (Graugnard et al., 2010)
- Ligation: SplintR circularizes the miRNA to the padlock probe (Jin et al., 2016; Lohman et al., 2013)
- Amplification: T7 RNA polymerase uses the hybridized miRNA as a primer to begin amplification and create RNA Broccoli aptamer reporters (Esteban et al., 1993; Macdonald et al., 1994)
- Detection: The Broccoli aptamers bind to fluorophores, inducing fluorescence (Chandler et al., 2018)
Development
RCA and RCT follow the same pathway until the padlock probe amplification: RCA requires phi29 DNA polymerase to produce DNA rolling circle products (RCP), whereas RCT employs T7 RNA polymerase to create RNA Broccoli aptamers (Chandler et al., 2018). To accommodate this change, we applied the same ODE equations as were applied in RCA but modified the rate constant values. Since RCT utilizes RNA aptamers as a reporting mechanism rather than DNA RCP, we used the Gibbs free energy equation to derive the aptamer binding affinity from rate constants found in existing literature (see Fig. 14) (Thevendran et al., 2020).
Figure 13. Deriving the aptamer binding affinity using the Gibbs free energy equation
The RCT model serves the same purpose as the RCA model, which is to assist our team in interpreting and designing our RCT experimentation. Using Dr. Styczynski’s advice, we incorporated deterministic ODE equations to model the reactions throughout the pathway. With an initial miRNA concentration input, our model predicts the final RNA and aptamer-fluorophore complex concentrations, which should support our future experimental data.
Signaling Pathway
Like RCA, the team utilized MATLAB’s SimBiology software to diagram each reaction in the RCT reaction and aptamer-fluorophore binding using the Law of Mass Action and Michaelis-Menten Equations (Zi, 2012). The pathway begins with the introduction of miRNA into the system and ends with the final aptamer-fluorophore complex activity (see Fig. 13).
Biochemical Reactions
The model contained a total of 4 biochemical reactions (see Fig. 14), described below:
| Reactions | Description |
|---|---|
| \(M + P \xrightarrow{k} MP\) | Input miRNA (M) binds to the complementary arms of free padlock probes (P) to form miRNA-padlock probe complexes (MP) |
| \(MP + SplR \Longleftrightarrow MP_{circularized}\) | miRNA-padlock probe complexes (MP) are ligated by SplintR ligase (SplR) to circularized complexes (MP_circularized) |
| \(MP_{circularized} + T7_{poly} \Longleftrightarrow aptamer\) | Circularized miRNA-padlock probe complexes (MP_circularized) are extended by T7 RNA polymerase (T7poly) to create a Lettuce aptamer (aptamer) |
| \(aptamer + fluorophore \xrightarrow{k_{apt}} aptfluorophore\) | The aptamers (aptamer) bind to free fluorophores (fluorophore) to form aptamer-fluorophore complexes (aptfluorophore) |
Initial Values of Species
In order to simulate our reactions, our team needed to input values to initialize each component in our model. The initial quantity of each species was obtained from RCT wetlab protocols:
| Variable | Species | Initial Value | Units |
|---|---|---|---|
| M | miRNA | 0.5 | picomoles |
| P | padlock probes | 0.05 | picomoles |
| SplR | SplintR | 25 | molecules |
| T7poly | T7 RNA polymerase | 40 | molecules |
| aptamer | broccoli aptamer | 0 | molecules |
| fluorophore | free fluorophores | 180664245 | molecules |
| aptfluorophore | bound aptamer-fluorophores | 0 | molecules |
Parameters
Rate constants and degradation rates are required to input into our Mass Action Laws and Michaelis-Menten equations. These values were derived from literature or estimated if the values could not be found. The value of each parameter is shown below:
| Variable | Reaction | Estimated Values | Units |
|---|---|---|---|
| Mdeg | rate constant for miRNA degradation | 0.000019254 | 1/second |
| k_padlock | rate constant for miRNA-padlock binding | 32000 | 1/(moles*second) |
| Vmcircular | maximal rate of reaction needed for Michaelis-Menten enzyme kinetics for MP-SplintR binding | 0.008 | moles/second |
| Kmcircular | Michaelis-Menten constant for MP-SplintR binding | 1 | mole |
| VmT7 | maximal rate of reaction needed for Michaelis-Menten enzyme kinetics for MP_circular-T7 binding | 14 | mole/minute |
| KmT7 | Michaelis-Menten constant for MP_circular-T7 binding | 1.8 | mole |
| aptdeg | rate constant for aptamer degradation | 0.004111193242 | 1/second |
| k_apt | rate constant for the binding affinity of broccoli aptamers | 89.92 | 1/mole*nanosecond |
Ordinary Differential Equations
Lambert iGEM incorporated the Mass Action Kinetic Laws and Michaelis-Menten Equations to represent the reactions for the RCT model and generated 9 ODEs, as shown below:
| Ordinary Differential Equations |
|---|
| \(\frac{d[M]}{dt} = -(k_{padlock}[M][P]) - (M_{deg}[M])\) |
| \(\frac{d[P]}{dt} = -(k_{padlock}[M][P])\) |
| \(\frac{d[SplR]}{dt} = -\frac{V_{mcircular}[MP]}{K_{mcircular}+[MP]}\) |
| \(\frac{d[MP]}{dt} = (k_{padlock}[M][P]) - (\frac{V_{m circular}[MP]}{K_{m circular}+[MP]})\) |
| \(\frac{d[MP_{circular}]}{dt} = (\frac{(V_{m circular}[MP]}{K_{m circular}+[MP])}-\frac{(V_{mT7}[MP_{circular}]}{K_{mT7}[MP_{circular}]})\) |
| \(\frac{d[T7_{poly}]}{dt} = -(\frac{V_{mT7}[MP_{circular}]}{K_{mT7}+[MP_{circular}]})\) |
| \(\frac{d[aptamer]}{dt} = -(apt_{deg}[aptamer])-(k_{fluorophore}[aptamer][fluorophore])+(\frac{V_{mT7}[MP_{circular}]}{K_{mT7}+[MP_{circular}]})\) |
| \(\frac{d[{aptfluorophore}]}{dt} = (k_{fluorophore}[aptamer][fluorophore])\) |
| \(\frac{d[fluorophore]}{dt} = -(k_{fluorophore}[aptamer][fluorophore])\) |
Assumptions
All rate constants remain constant regardless of external environmental factors. Thus, this model simulates only the miRNA-padlock binding process to estimate aptamer production and aptamer-fluorophore binding. The total quantity of padlock probes, SplintR ligase, T7 RNA polymerase, and fluorophores is known and does not change over time. RNA polymerase activity also remains constant regardless of primers, miRNA, or NTP concentration.
Results
After developing a set of ODE equations, we utilized SimBiology’s Model Analyzer to simulate the number of bound aptamer-fluorophore complexes over 60 minutes with 0.5 picomoles of miRNA initially (see Fig. 15).
Initially, the concentration of aptamer-fluorophore complexes is relatively low. However, as the reaction progresses, the rate of aptamer-fluorophore production steadily increases and reaches a constant rate. Hypothetically, as the quantity of bound aptamer-fluorophore increases, the entire system dims increasingly, showing an inverse relationship. We currently lack adequate wetlab results for RCT to validate, adjust, and improve our model, but we will be able to use our ODE system to drive future experimentation with RCT.
Future Plans
In the future, we hope to gather further data to calibrate our parameters and fit our experimentation better. Furthermore, Lambert iGEM is currently planning to continue research next year. To prepare for future models, our team is planning to submit to an Institutional Review Board (IRB) to access deidentified data related to microRNAs (miRNAs) and coronary artery disease (CAD). An IRB will allow our team to legally handle and use data that would otherwise be protected information. By submitting an IRB application, a review board will look over the purpose and use of the data we are requesting and determine whether our project threatens the protection of the patients. We expect IRB approval since we seek deidentified data and our work does not threaten the privacy of human subjects. After clearance, our team hopes to develop a random-forest supervised machine learning model to assess the risk of patients for CAD based on medical, geographic, and socioeconomic parameters.