Team:GZHS-United/Model

Modeling of GZHS-United

Project design based on modeling

L-ascorbate peroxidase activity plays an important role in molecular function and biological process. Hydrogen peroxide is one of the direct signal molecule clusters that leading coral bleaching. L-ascorbate peroxidase coded by APX is one of the degradation of peroxide effect most prominent enzymes.

Fig1. L-ascorbate peroxidase activity plays an important role^[1]

Hence, we focus on the factors related to L-ascorbate peroxidase activity, and catalysis of the reaction: L-ascorbate + hydrogen peroxide = dehydroascorbate + 2 H2O

Collecting data under the direction of modeling will help us to detect the relationship between temperatures, illumination, pH and L-ascorbate peroxidase activity.

The Principles of Mathematics of modeling

Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a “smooth” function is constructed that approximately fits the data. ^[2]

A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data.

We know that one of the problems of linear regression is under fitting, which will not achieve a good prediction. Because it is an unbiased estimation with minimum mean square error. The way to solve this problem is to allow some deviation in the estimate. One of the most effective methods is locally weighted linear regression (LWLR).^[3]

1. Model

Same as the linear regression model, but for each prediction point, θ needs to be recalculated. It's not fixed.

2. Loss function

For the prediction point x, wi represents the distance between xi and x. If they are close, wi=1, if they are far away, wi=0.

K controls the attenuation speed of wi.

Therefore, the loss function can be understood as a linear regression operation for the sample points near the prediction point.

3. Algorithm

The local linear weighting algorithm needs to recalculate weights for each predicted sample point.

Our optimization goal is:

Therefore, the iterative formula is:

Where W is the skew symmetric matrix.

Assume that

Then

Project design based on modeling

We made an experimental design based on modeling, collecting data to detect the relationship between temperatures, illumination, pH and L-ascorbate peroxidase activity.

The reaction between AsA and H2O2 was catalyzed by APX to oxidize AsA to monodehydroascorbic acid (MDAsA). As AsA was oxidized, the absorbance was continuously decreased. The absorbance was measured and the enzyme activity of the enzyme liquid was calculated based on the change of absorbance.

Fig2. L-ascorbate peroxidase participates in this reaction. ^[4]

Referring to Dalton et al. 's method and Solarbio's ascorbic acid peroxidase activity detection kit, AsA colorimetry was used to start the reaction by adding AsA into the extracted sample enzyme solution, and the difference between OD290 at the 10th and 130th seconds was observed. Three parallel measurements were made for each sample.