Apparent scaling of virus surface roughness—An example from the pandemic SARS-nCoV

This paper investigates the scaling of the surface roughness of coronavirus, including the SARS-nCoV based on fractal and spectral analyses of their published electron microscopy images. The box-counting fractal dimensions obtained are subjected to ANOVA tests for statistical significance. Results show that the SARS-nCoV particles could not statistically be resolved by their shape on the basis of the fractal dimension values, but they could be distinguished from the earlier SARS-CoV particles. MANOVA test results require interaction of factors used for classifying virions into different types. The topological entropies, a measure of randomness in a system, measured for the images of varying size show correlation with the fractal dimensions. Spectral analyses of our data show a departure from power-law self-similarity, suggesting an apparent scaling of surface roughness over a band of maximum an order of magnitude. The spectral crossover that corresponds to characteristic length scale may represent average viral size. Our results may be useful in inferring the nature of surface-contact between the viral and human cell, causing infection and also in providing clues for new drugs, although it is too early to say. In addition, limitations of this study, including possible ways to avoid the bias in scaling exponents due to the use of different techniques are discussed.