Difference between revisions of "Team:SBS SH 112144/Model"
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Revision as of 18:31, 15 October 2018
Overview
Modeling, which involve rigorous data processing and complex mathematical computation, is often crucial for the discoveries in the realm of science. Our models mainly provide a solid foundation upon which we could design our device and build its prototype. Through background research, we have discovered four significant variables for the successful operation of the device and its potential commercial use. Therefore, we developed mathematical models to explore the optimal combination of four variables and to guide the experiments in wet lab.
One key problem in our wet lab is the difficulty precise data. How we give the data enough validity to support the work afterwards is worth discussing about. Another difficulty lies in the complexity of the optimal combination of four dimensional variables. Will we be able to obtain this combination to satisfy our needs? Our models gave a positive answer!
Model
A. Intro to variables
To achieve our goal of optimizing the setting of our device, we need to determine the parameters we are interested in. According to some background research[1], we plan to focus on pH, temperature, protein concentration and reaction time.
1. pH and temperature: because enzyme’s catalytic function is hugely dependent on the pH and temperature of the surrounding environment, and even a slight deviation from the optimal parameter might denature some of the enzyme, we wish to figure out the optimal pH and temperature in the reaction that could best ”bring out” the lysozyme’s potential.
2. Protein concentration: the production and purification of this protein require a decent cost of material and manpower. Plus, methods to immobilize enzymes such as entrapment and cross-linkage are not easy to achieve. It would be cost-effective to identify the appropriate concentration of the enzyme required for the reaction thus prevent waste.
3. Reaction time: the concern about time is due to two reasons. First of all, time is directly related to efficiency of the facility, and a commercial company always prefer the more efficient option. Most importantly, since the end goal of our device is to be able to provide the different metabolites and component of cyanobacteria for medical/ scientific research, biofuel manufacturing and agricultural production, we would like to maintain the activity and completeness of those parts as intact as possible. Our device the cyanobacteria is in a dynamic state, thus overtime reaction might cause damage to crucial components such as chlorophylls, and not to mention all those chemicals such as bugbuster mixed in the reaction system. To summarize, we want the reaction time to be both enough for the cleavage and minimizing the damage to the cyanobacterial components.
B. Optimized Sparse Matrix
In the field of quantitative biology, free-form surfaces need to be constructed from discretely observed shape points. Since the properties of biological data are difficult to express with a mathematical function, it is necessary to first establish a regular grid and then perform interpolation calculation on the basis of the grid.
Our model implements two-dimensional spline interpolation of the Green function around the nearest neighbor points of the interpolation point[2,3]. By doing this we could reduce the calculation time; by using the nearest neighbors around the interpolation point to move the interpolation, changing the equilibrium of the distribution of the value points sequentially helps to improve the stability of the interpolation results.
As we know, the surface s(x) can be expressed as:
$$ s(x) = T(x) + \sum w_jg(x,x_j) $$