Difference between revisions of "Team:NUS Singapore-Sci/enzyme kinetics"
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$$\delta_{t}S = G_{s} - D_{s\cdot}S -k_{2}\cdot ER\cdot S +k{-2}\cdot ERS \quad \textrm{(Equation 1)}$$ <br> | $$\delta_{t}S = G_{s} - D_{s\cdot}S -k_{2}\cdot ER\cdot S +k{-2}\cdot ERS \quad \textrm{(Equation 1)}$$ <br> | ||
| − | $$\delta_{t}ER = k_{1}\cdot E\cdot R - k{-1}\cdot ER - k_{2}\cdot ERS +k_{-2}\cdot ERS \quad \ | + | $$\delta_{t}ER = k_{1}\cdot E\cdot R - k{-1}\cdot ER - k_{2}\cdot ERS +k_{-2}\cdot ERS \quad \textrm{(Equation 2)}$$ <br> |
| − | $$\delta_{t}ERS = k_{2}\cdot ER\cdot S - k_{3}\cdot ERS - k_{-2}\cdot ERS \quad \ | + | $$\delta_{t}ERS = k_{2}\cdot ER\cdot S - k_{3}\cdot ERS - k_{-2}\cdot ERS \quad \textrm{(Equation 3)} $$ <br> |
| − | $$\delta_{t}P = k_{3}\cdot ERS - D_{s}\cdot P \quad \ | + | $$\delta_{t}P = k_{3}\cdot ERS - D_{s}\cdot P \quad \textrm{(Equation 4)} $$ <br> |
| − | $$\delta_{t}F = k_{4}\cdot P - D_{f}\cdot F \quad \ | + | $$\delta_{t}F = k_{4}\cdot P - D_{f}\cdot F \quad \textrm{(Equation 5)} $$ <br><br> |
where Equation 4 assumes that ERS to ER + P is an non-energetically favourable step, and hence is unlikely to occur. | where Equation 4 assumes that ERS to ER + P is an non-energetically favourable step, and hence is unlikely to occur. | ||
</div> | </div> | ||
Revision as of 18:25, 17 October 2018
Enzyme
Kinetics
Enzyme Kinetics and Least Squares Regression
The efficiency of our RESCUE system is likely to be dependent on multiple factors such as mismatch distance, length of spacer regions as with ADAR-dCas13b constructs (Cox et al., 2016), as well as the relative concentrations of the substrates/enzymes. The concept of regression models can be utilized to identify and evaluate the significance of these factors from experimental results. As such, a early build of an enzyme kinetics regression model on dCas13b-APOBEC editing efficiency may help us to gain further insights of the RESCUE system.
Goal
- 1. Simulate the RESCUE system under different relative concentrations of substrates and enzymes to determine the concentrations that might yield maximum efficiency.
- 2. Determine the change in the binding and catalytic efficiency when spacer length and mismatch distance is varied, which will help in the design of gRNA for more efficient base editing.
Our assumptions of the model are as follows:
- 1. Association between dCas13b and gRNA is reversible and precedes enzyme-gRNA complex association with substrate mRNA. This is because dCas13b requires the gRNA to bind to the correct target sequence.
- 2. Once the Enzyme-gRNA-Substrate-mRNA trinity complex (ERS) is formed, the reaction will proceed in a single direction to produce the cleaved product.
First, we build upon a kinetics model for our fusion protein product.
Where:
Given the set of kinetic equation as defined above, the rate of change of each protein/RNA can then be described in the following differential equations as follow:
$$\delta_{t}S = G_{s} - D_{s\cdot}S -k_{2}\cdot ER\cdot S +k{-2}\cdot ERS \quad \textrm{(Equation 1)}$$
$$\delta_{t}ER = k_{1}\cdot E\cdot R - k{-1}\cdot ER - k_{2}\cdot ERS +k_{-2}\cdot ERS \quad \textrm{(Equation 2)}$$
$$\delta_{t}ERS = k_{2}\cdot ER\cdot S - k_{3}\cdot ERS - k_{-2}\cdot ERS \quad \textrm{(Equation 3)} $$
$$\delta_{t}P = k_{3}\cdot ERS - D_{s}\cdot P \quad \textrm{(Equation 4)} $$
$$\delta_{t}F = k_{4}\cdot P - D_{f}\cdot F \quad \textrm{(Equation 5)} $$
where Equation 4 assumes that ERS to ER + P is an non-energetically favourable step, and hence is unlikely to occur.
S - Unedited Substrate mRNA
R - Guide RNA
E - Enzyme for C to U editing
ER - Enzyme-gRNA complex
ERS - Enzyme-gRNA-Substrate complex
P - Edited Product mRNA
F - Green Fluorescent protein produced
Given the set of kinetic equation as defined above, the rate of change of each protein/RNA can then be described in the following differential equations as follow:
$$\delta_{t}S = G_{s} - D_{s\cdot}S -k_{2}\cdot ER\cdot S +k{-2}\cdot ERS \quad \textrm{(Equation 1)}$$
$$\delta_{t}ER = k_{1}\cdot E\cdot R - k{-1}\cdot ER - k_{2}\cdot ERS +k_{-2}\cdot ERS \quad \textrm{(Equation 2)}$$
$$\delta_{t}ERS = k_{2}\cdot ER\cdot S - k_{3}\cdot ERS - k_{-2}\cdot ERS \quad \textrm{(Equation 3)} $$
$$\delta_{t}P = k_{3}\cdot ERS - D_{s}\cdot P \quad \textrm{(Equation 4)} $$
$$\delta_{t}F = k_{4}\cdot P - D_{f}\cdot F \quad \textrm{(Equation 5)} $$
where Equation 4 assumes that ERS to ER + P is an non-energetically favourable step, and hence is unlikely to occur.