Model
Theoretical Approach
Modeling in biology refers to the use of mathematical, computational, or simulation models to understand and predict the behavior of biological systems.
This process requires the creation of a model that represents the fundamental characteristics and behavior of the experiment. The experiment to be modeled involves the isolation of the tachyplesin protein from the E. Coli bacterium.
With an understanding of the experiment's objectives and having collected our data, we proceed to construct and execute the model, making comparisons with observations from the real experiment. Depending on the resulting values and whether they approximate the desired outcomes, we adjust the model accordingly.
Process flow model
To begin with, we will use a process flow model that analyzes the steps of the experiment.
The first step is the cultivation of E. coli bacteria. In practice, this involves placing a culture of E. Coli in a nutrient medium where it grows at an appropriate temperature. As the input parameters of the experiment, we have the time and the temperature of the culture. The process begins with the execution of the culture using the initial quantity of E. Coli, and in the output field, we have the new quantity of E. Coli.
Next in line is the collection of bacteria. When the culture reaches an appropriate quantity, we collect the E. coli bacteria. This is achieved by performing PCR to increase the quantity.
The third step is the lysis of the bacteria. In the input field, we have the PCR products obtained in the previous step. We perform electrophoresis to separate the bacteria and release cellular material.
The next step involves the extraction which includes the processes of ligation, golden gate, and transformation. In the output field, we have the transformed bacteria, which will be used as the input in the final step, the protein purification. In the protein purification step, we have the isolated protein as the output.
Mathematical model
We rely on a simplified kinetic equation that describes the developmental duration of each step in the process.
Basic Assumptions:
• Initial quantity of E. coli bacteria(No)
• Each step of the process takes a specific time duration, ti, and results in a quantity of product, Ni.
• The growth rate (μ) expresses how quickly the quantity of the product increases. It can also be the isolation rate for the corresponding step.
We use the general growth equation (using exponential growth) for each step:
First Step
For cultivation :
Second step
For PCR:
Third step
For electrophoresis:
Fourth step
For ligation and Golden Gate:
Fifth step
For transformation:
Sixth step
For protein isolation:
Conclusions
The use of experimental data in the equations leads to certain conclusions and more accurate estimates regarding the process. These conclusions will be approximate since the model is simpler than the actual process.
Specifically, based on the model, we can predict possible behavior in various areas that affect the performance of our experiment and, accordingly, improve them. Some of them are:
Growth and Yield: We predict the exponential growth of the product as it moves through each step of the process. Not all steps have the same effect on increasing the quantity of the product.
Loses: Some losses occur at each step. We can estimate the amount of material remaining after each step.
Timeframes: The model will provide information about the expected duration of each step and, therefore, the total time required to achieve the desired quantity.
Total Product Quantity: We calculate the total quantity of the isolated product at the end of the process, taking into account yield and losses.
Estimated Parameters: We can estimate the parameters necessary for optimizing the process.
According to the results, we approach the optimization of the processes, particularly the isolation process. We explore possible ways to increase yield, reduce losses, or accelerate the process.
Simultaneously, the need for experimental data to estimate model parameters and accurately model the process is emphasized. Finally, we have an approximate picture of the expected performance of the process, i.e., the final quantity of isolated Tachyplesin protein.