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Description : The spike protein sequences of coronaviruses were obtained from the GenBank and GISAID database, including the coronaviruses from pangolin, bat, canine, porcine (three variations), feline, tiger, SARS-CoV-1, MERS, and SARS-CoV-2 (Wuhan, Beijing, New York, German and UK) were used as the representative examples in this study. By examining the values above and below the average/mean based on the positive and negative charge patterns of the amino acid residues of the spike proteins from coronaviruses, the proposed algorithm provides deep insights into the nonlinear evolving trends of spike proteins for understanding the viral gene sequence evolution and identifying the protein characteristics associated with viral fatality. SARS-CoV-1 is negative charged, SARS-CoV-2 is 10 times more positive charged. UK version 20% more charging!

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Published on : Jul 02, 2021 | Views : 1927 | Downloads : 1

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Semi-covariance coefficient analysis of spike proteins from SARS-CoV-2 and other coronaviruses for viral evolution and characteristics associated with fatality By Jun Huang, Jiamin Huang, Wandong Zhang December 25 2020 – January 25 2021 Data Processing Training for 401 Lab
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Agenda Introduction Materials and Methods Results and Conclusion 401 Lab 2020 Math Training
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1. Introduction 401 Lab 2020 Math Training Complex modeling has received significant attention in recent years and is increasingly used to explain the statistical phenomenon with increasing and decreasing fluctuations such as the similarity or difference of spike protein charge patterns of coronaviruses. Different from the existing covariance or correlation coefficient methods in traditional integer dimension construction, this study proposes a simplified novel fractional dimension derivation with the exact Excel tool algorithm. It involves the fractional center moment extension to covariance, which ends up as a complex covariance coefficient that is better than the Pearson correlation coefficient, in the sense that the nonlinearity relationship can be further depicted.
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Positive or Negative Charge 401 Lab 2020 Math Training The spike protein sequences of coronaviruses were obtained from the GenBank and GISAID database, including the coronaviruses from pangolin, bat, canine, porcine (three variations), feline, tiger, SARS-CoV-1, MERS, and SARS-CoV-2 (Wuhan, Beijing, New York, German and UK) were used as the representative examples in this study. By examining the values above and below the average/mean based on the positive and negative charge patterns of the amino acid residues of the spike proteins from coronaviruses, the proposed algorithm provides deep insights into the nonlinear evolving trends of spike proteins for understanding the viral gene sequence evolution and identifying the protein characteristics associated with viral fatality. SARS-CoV-1 is negative charged, SARS-CoV-2 is 10 times more positive charged. UK version 20% more charging!
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Viability 401 Lab 2020 Math Training The calculation results demonstrate that the complex covariance coefficient analyzed by this algorithm is capable of distinguishing the subtle nonlinear differences in the spike protein charge patterns with reference to the Wuhan SARS-CoV-2 for which the Pearson correlation coefficient may overlook. Our analysis reveals the unique convergent (positive correlative) to divergent (negative correlative) domain center positions of each virus. The convergent or conserved region may be critical to the viral evolution stability or viability; while the divergent region is highly variable between coronaviruses suggesting high frequency of mutations in this region.
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Residues 401 Lab 2020 Math Training The analysis shows that the conserved center region of SARS-CoV-1 spike protein is located at amino acid residues 900, but shifted to the amino acid residues 700 in MERS spike protein, and then to amino acid residues 600 in SARS-CoV-2 spike protein, indicating the evolvement of the coronaviruses. Another important characteristic our study reveals that the distance between the divergent mean and the maximal divergent point in each of the viruses (MERS>SARS-CoV-1>SARS-CoV-2) is proportional to viral fatality rate. This algorithm may help to understand and analyze the evolving trends and critical characteristics of other coronaviral proteins and viruses.
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2. Materials and Methods 401 Lab 2020 Math Training The coronavirus spike protein sequences used in this study were obtained from the NCBI GenBank and the GISAID database, including SARS-CoV-2 (the sequences isolated in Wuhan, Beijing Xinfadi wholesale market, Germany, New York, UK and New York Zoo tiger), SARS-CoV-1, Middle East respiratory syndrome (MERS), bat coronavirus (RaTG13), pangolin coronavirus, feline coronavirus, canine coronavirus, and swine coronaviruses [Swine Transmissible gastroenteritis virus (Swine-stomach), swine enteric coronavirus (Swine-Ent), and porcine respiratory coronavirus (Swine-Res)]. The sequence ID from the GenBank and GISAID database are listed in Table 1.
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Hypo, Hyper or Gauss Variances and Covariance 401 Lab 2020 Math Training
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3. Results and Conclusion To compare and prove the usefulness of the simplified complex variances, we compare the correlation of SARS-CoV-2 viral spike protein sequence with other coronavirus spike protein sequences. Since Excel is not capable of handling the imaginary number, we simplify the calculation with integer power, but separate the positive and negative covariance signs. Because coronaviruses spike proteins have different electrical charge levels, we normalize the covariance by the variance respectively just as the Pearson calculation does. 401 Lab 2020 Math Training
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Figures and Tables Figures 1-6 are the calculation results from our algorithm of semi-covariance coefficient for spike protein Wuhan SARS-CoV-2 in comparison with spike proteins of other coronaviruses listed in Table 1. Figure 7-9 are a combination of linear and nonlinear relationships baselined on Wuhan. Figure 10-15 are nonlinear relationships baselined on Wuhan. Figure 16-19 are linear relationships baselined on Wuhan. Figure 20 is a combination of linear and nonlinear relationships again. Nonlinear relationship is piece wised linear, that means only partial proteins are related. It is evident that the fatality rate caused by the virus is highly related to the distance between the divergent center (mean) and the maximal divergent point (Table 2). 401 Lab 2020 Math Training
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Scatter Plot A scatter graph (also called a scatter plot, scatter chart or scatter diagram) is a type of plot or mathematical diagram using Cartesian coordinates (with 4 quadrants) to display values for two variables for a set of data. The data are displayed as a collection of points, each having the value of one variable (charge value from Wuhan sequence) determining the position on the horizontal axis (for Wuhan) and the value of the other variable (charge value from others like Pangolin etc) determining the position on the vertical axis (for other). A scatter plot can suggest various kinds of correlations between variables with a certain linear or nonlinear pattern. Correlations may be positive (rising), negative (falling), or neither (uncorrelated). If the pattern of dots slopes from lower left to upper right, it indicates a positive correlation between the variables being studied. If the pattern of dots slopes from upper left to lower right, it indicates a negative correlation. 401 Lab 2020 Math Training
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Linear vs Nonlinear If the dots are continuously connected one after another, we have a simple linear relationship. If the dots form a few islands, we have the nonlinear pattern. If both patterns are there, we have the mixed of linear and nonlinear. If within the islands, it is linear, we can call it local linear, globally nonlinear, or piece wised linear. It means only a particular charged piece of the entire sequence is linear correlated within that piece. If we view the island as a super dot, and super dots forming a linear relationship, we call it global linear, locally nonlinear. It means the specially charged pieces of the entire sequence are linear correlated among the pieces. Each piece has its unique electro-biological functions. The 1st and 3rd quadrants are pieces where Wuhan sequence have the same charge as the Pangolin's. The 2nd and 4th quadrants are pieces where Wuhan sequence have the opposite charge as the Pangolin's. 401 Lab 2020 Math Training
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Conclusion We have analyzed spike protein charge patterns of coronaviruses by using our algorithm of semi-covariance (nonlinear) coefficient as compared to Pearson (linear) correlation. The analysis reveals additional performance index over Pearson analysis, such as both positive- and negative-correlative centers/regions in the spike proteins. The analysis provides in-depth understanding for the nonlinear viral evolution pattern and identifies the protein characteristics associated with viral fatality. The example code is available from the Excel file on the github server (https://github.com/steedhuang/covid-19-gene-convertor). Our future work will pay more attention on the relationship between positive charges to infectivity. As UK version has 20% more positive charges! 401 Lab 2020 Math Training
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Acknowledgement The work in Dr. Zhang’s lab is supported by a team grant on the Rapid Research Response to COVID-19 Outbreak awarded from the Canadian Institute of Health Research (CIHR) and by funding from the National Research Council of Canada. Thanks go to Lishen Wang from Jiangsu University for writing Python code to covert sequences into charges. Thanks also go to Rebecca Spencer and Mei Huang from Ottawa U and Hospital COVID-19 patient unit for proof reading and editing the final version. 401 Lab 2020 Math Training

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