Team:UC Davis/Modeling
CenozoicModeling Saturation Kinetics
Enzyme kinetics is the study of how fast reaction proceeds when influenced by a catalyst. Our project involves a single substrate mechanism where the chemical of concern (substrate) causes the stress pathways within the mammalian system to be activated. Via our stress promoter + eGFP plasmids [Promoter list], we are utilizing the activation of the stress pathways to also turn on eGFP expression.
In that way, we can use eGFP expression, measured by fluorescence, as a proxy for the level or “velocity” of stress in the cell. By exposing cells to different concentrations of chemicals of concern, we can assess the relative “stress” by measuring for eGFP expression.
A goal for our project is to build a device that is sensitive enough to detect levels of chemicals that are found in the environment.
In that way, we can use eGFP expression, measured by fluorescence, as a proxy for the level or “velocity” of stress in the cell. By exposing cells to different concentrations of chemicals of concern, we can assess the relative “stress” by measuring for eGFP expression.
A goal for our project is to build a device that is sensitive enough to detect levels of chemicals that are found in the environment.
Table 3. Chemicals of Concern
| Chemical name | Occupational limit | LD50 | Klamath Environmental concentration | Cytotoxicology(In micromoles per liter) |
|---|---|---|---|---|
| Hydrogen Peroxide | 75 mg/L | 2000 mg/kg | -- | Relevant dose is 60 uM |
| Warfarin | 0.1 ug/L | 374 mg/kgmice186 mg/kg rats | Qualitatively detected by Tom Young’s lab; unpublished data | Relevant dose is 0.0316 – 31.6 μM |
| 2,4-D | 10 ug/L | 2019 ppm (min)12979 ppm(max) | 0.424 - 7.49 ppm | - |
| Copper sulfate | 1 ppb by inhalation | 30 mg/kg | Copper measured at concentration of 19-67 ppm (112uM - 420uM) | Relevant dose is & lt;1.3ppm (6.25uM) |
| Metam Sodium | Limit of irritation 22 ug/L | 781 mg/kg (rat)1836 ppm (min) | 131309.21 kg | - |
Given these values we could achieve this goal if we were able to determine if our genetic devices are within or below these ranges.
What do the numbers mean?
The Michaelis Menten equation shown above, allows for the calculation of Km (the Michaelis-Menten constant) and Vm( maximum reaction velocity). Vm is the rate of product formation (in our case expression of eGFP) and Km is the ratio of the dissociation rate to the association rate. Km is also the corresponding substrate concentration at which the reaction velocity is one-half the maximum reaction velocity. Therefore, a smaller Km implies a greater reaction velocity and vice versa. Thus, Km informs us about the amount of substrate that stimulates eGFP allowing us to use this value to approximate sensitivity of our constructs to a specific chemical. Hence, we will reference Km as Kstim .
MATLAB code
To fit the Michaelis-Menten model to our data we used MATLAB. We took advantage of the NLINFIT function in order to extrapolate the values of the parameters Vm and Kstim as well as their 95% confidence intervals. The MATLAB code takes in the substrate concentration and fluorescence intensity data points and returns the Vm and Km values for the given input.