Model
Optimizing Wetlab with Software Analysis
This year, Lambert iGEM simulated CRISPRi and Toehold reactions using MATLAB, and also optimized toeholds using machine learning.
Toeholds
Overview
Along with the CRISPRi system, our team developed a cell-free toehold biosensor to measure CRISPRi efficiency. Toeholds can be summarized by two major constructs we designed (see Toehold Design) (See Fig. 1):
The team also decided to make a deterministic ODE model to simulate the toehold reaction. Since the team is pioneering research for cell-free toehold expression, there is minimal data regarding our experimentation. To address this, Lambert iGEM developed a simulated graph using MATLAB, which serves as a guide for the toehold committee, creating a threshold for them to aim for. After the toehold committee completes their experimentation, we will use their results to better fit our parameters, creating a mutual transfer of data.
Development
To assist in interpreting and validating the toeholds reactions, Lambert iGEM incorporated a deterministic ordinary differential equations (ODE) model to simulate the reaction and correlate fluorescence caused by the downregulation of GFP from the toehold.
Signaling Pathway
We used MATLAB’s SimBiology software to diagram each reaction using the Law of Mass Action and Hill 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 (Park, 2022). In contrast, Hill equations are needed to properly diagram catalytic enzyme kinetics when utilizing multiple ligand areas (Zi, 2012). The pathway begins with the introduction of inhA DNA from cells into the system and ends with the expression of GFP (see Fig. 2).
Biochemical Reactions
The model contains a total of 4 biochemical reactions (see Fig. 2) for the toehold simulation as described below (see Table 1 & 2).
| Reaction | Description |
|---|---|
| Chi6 → inhA | Chi6 is used to protect linear DNA |
| inhA + RNAP → RNA | RNA polymerase binds to the inhA DNA to transcribe into RNA |
| RNA ↔ [S_on] | RNA binds to the toehold switch, activating the toehold switch |
| [S_on] → GFP | Activated Toehold Switch transcribes GFP |
There is one reaction simulating the leakage rate of the toehold switch, as described below.
| [S_off] → GFP | Off-state toehold switch could mistakenly transcribe GFP |
Initial Values of Species
In order to simulate our reactions, our team needed to input quantities to initialize each component in our model (see Table 3). The initial value of each species was obtained from the Toehold committee (see Experiments).
| Name | Initial Value | Units |
|---|---|---|
| Off State Toehold Switch | 1 | nanomoles |
| GFP | 0 | nanomoles |
| inhA | 15 | nanomoles |
| Activated Toehold Switch | 1 | nanomoles |
| RNAP | 0.1 | nanomoles |
| RNA | 5 | nanomoles |
| Chi6 | 2 | nanomoles |
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 (Table 4):
| Variable | Reaction | Estimated Value | Units |
|---|---|---|---|
| k1 | Reaction constant for off stage toehold switch mistakenly transcribing GFP | 0.0013 | nanomoles/second |
| k2 | Rate constant for GFP degradation | -.0025 | nanomoles/second |
| k3 | Rate constant for Chi6 protecting linearized inhA DNA | 1 | nanomoles/second |
| Vm_Trigger | Maximal rate of reaction needed for Michaelis-Menten enzyme kinetics for RNA trigger binding to off state toehold switch | 5 | nanomoles/second |
| n_Trigger | Hill kinetic coefficient for trigger binding to off state toehold switch | 2.78 | unitless |
| Kp_Trigger | Michaelis-Menten constant for trigger binding to off stage toehold switch | 30 | nanomoles |
| n_GFP | Hill kinetic coefficient for on state toehold switch transcribing GFP | 2 | unitless |
| Kp_GFP | Michaelis-Menten constant for on state toehold switch transcribing GFP | 0.8696 | nanomoles |
| Vm_GFP | Maximal rate of reaction needed for Michaelis-Menten enzyme kinetics for on state toehold switch transcribing GFP | 3 | nanomoles/second |
| Vm_RNAP | Maximal rate of reaction needed for Michaelis-Menten enzyme kinetics for inhA DNA getting transcribed into RNA | 3 | nanomoles/second |
| n_RNAP | Hill kinetic coefficient for inhA DNA getting transcribed into RNA | 4 | unitless |
| Kp_RNAP | Michaelis-Menten constant for inhA DNA getting transcribed into RNA | 1 | nanomoles |
Ordinary Differential Equations
As mentioned previously, Lambert iGEM incorporated the Mass Action Kinetic Laws and Hill Equations to represent the reactions for the Toehold model. Mass Action Kinetic Laws describe a biomolecular interaction; it states that the relationship between a reaction’s rate and its product of reactant concentrations is proportional. Hill equations are used to study the kinetics of reactions that behave sigmoidally. The Hill equation is a useful tool for analyzing the rate of numerous transporter-mediated processes and enzyme-catalyzed reactions (see Table 5).
| Number | ODE |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 |
Assumptions
This model is under the premise that all rate constants remain constant regardless of environmental factors. It also assumes that ribosomes utilize all types of amino acids at the same rate and that all cells get lysed into DNA at a constant proportion.
Results
Estimated GFP Expression for Toeholds
To assess the efficacy of our CRISPRi system, we engineered toehold switches as reporter mechanisms. Lambert iGEM utilized MATLAB to perform precise modeling of gene expression of inhA, a gene linked to the pathogenicity of M. tuberculosis (see Toeholds M.tb POC). We created a complete set of ODEs and used Simbiology’s Model Analyzer to simulate the concentration of GFP over 16 hours with 15 nanomoles of the inhA DNA initially. While producing GFP protein from the inhA target construct, the graph increases at first and then plateaus at around four hours (see Fig. 3).
Estimated unbounded inhA DNA
We also developed a curve that modeled unbounded inhA DNA over time, showing that as time goes on, the toehold is able to bind to all of the inhA DNA, and as the toehold switch reaches a certain saturation point, the graph goes towards an asymptote at 0 (see Fig. 4).
Bound inhA DNA vs GFP concentration
We then plotted inhA DNA concentrations with GFP expression, over a fixed time interval of 16 hours (see Fig. 5).
To evaluate the effectiveness of our toehold experimentation (see Experiments), we utilized the Lambert line-of-best-fit between GFP expression and fluorescence used to correlate CRISPRi, represented by the equation RFU = 6.1[GFP]. By converting our inhA DNA concentration to fluorescence, the similarity presented by our experimental results (see Fig. 6) and the logarithmic shape of our model (see Fig. 7) prove the accuracy of our wetlab. The minor discrepancies in the scales of the graphs could be attributed to potential pipetting errors or differences in the sensitivity or calibration of the plate readers we used.
While RFU values can vary across different plate readers due to the unique calibration, sensitivity, and gain settings in each one, our graphs serve as reference points for SHIELD, enabling researchers to confirm the shape of their graphs when testing their own effector genes.
Future Plans
In the future, in addition to the current models and equations created towards CRISPRi and toeholds, Lambert iGEM will continue to refine our parameters with our wet lab experimentation. The team hopes to develop Machine Learning (ML) models such as a Gradient Boosting model to combine previous models to create new models and fine-tune parameters. This will help increase the accuracy in the amount of fluorescence present, and assess the risk of antimicrobial resistance through different socioeconomic conditions. Additionally, the team plans to explore deep learning models to improve predictive analysis. These models will further incorporate additional features such as environmental factors and genetic variability to enhance the understanding of CRISPRi and toeholds.