Abstract
Complex modeling has received significant attention in recent years and is increasingly used to explain statistical phenomena 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 results in a complex covariance coefficient that is better than the Pearson correlation coefficient, in the sense that the nonlinearity relationship can be further depicted. The spike protein sequences of coronaviruses were obtained from the GenBank and GISAID databases, including the coronaviruses from pangolin, bat, canine, swine (three variants), feline, tiger, SARS-CoV-1, MERS, and SARS-CoV-2 (including the strains from Wuhan, Beijing, New York, German, and the UK variant B.1.1.7) which 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 evolution and identifying the protein characteristics associated with viral fatality. 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 Wuhan strain SARS-CoV-2, 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 stability or viability; while the divergent region is highly variable between coronaviruses, suggesting high frequency of mutations in this region. The analyses show 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 evolution of the coronaviruses. Interestingly, the conserved center region of the spike protein in SARS-COV-2 variant B.1.1.7 shifted back to amino acid residues 700, suggesting this variant is more virulent than the original SARS-COV-2 strain. Another important characteristic our study reveals is 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 SARS-COV-2 variants, other coronaviral proteins and viruses.
Highlights
Complex algorithms are used to analyze real-world implementations, i.e., it comes as the trusted analytic solution, but typically tends to have challenges in software implementation complexity requiring simpler software solution by using complex theory
The coronavirus spike protein sequences used in this study were obtained from the NCBI GenBank and the GISAID databases, including SARS-CoV-2
We found that the distance between divergent center and the maximal divergent point is associated with viral fatality
Summary
Complex algorithms are used to analyze real-world implementations, i.e., it comes as the trusted analytic solution, but typically tends to have challenges in software implementation complexity requiring simpler software solution by using complex theory. The arithmetic data from the DNA sequences by counting the number of intervening bases from a specific base (A) to the one, etc. Being different from the traditional DNA hypothesis, RNA and protein analysis is based on fragment length between the domains with electrical charges. It emphasizes the influences on the behaviors of charges caused by the difference of information reception and lengths of expression or neighbor status observing the existence of fractal structure in stable DNA [6]. We wish to further examine the similar electrical charge specific (+1 for positive amino acid, −1 for negative counterpart, 0 for neutral one, Inter-event data) relationship among the coronaviruses. The SARS-CoV-2 virus is among the longest positive single-stranded
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