Number of equidistant spikes in a global spherical array?

Reimagining Coronavirus in 3D as a Metaphor of Global Society in Distress (Part #4)

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With the coronavirus as the point of departure, an initial challenge was to detect any indication from the research literature on the number of protein "spikes" -- bearing in mind that the different forms of the virus may have a different number and any given form might well adopt different configurations. Any reference to "spike" may indeed need to be understood dynamically (Fang Li, Structure, Function, and Evolution of Coronavirus Spike Proteins, Annual Review of Virology, 3, 2016, 1).

Use of "spike" is also confusing since it features in media reference to "spikes" in the number of cases and fatalities reported from coronavirus, as well as in the "spiking" in dynamic systems more generally (Andrés Aragoneses, et al, Unveiling the complex organization of recurrent patterns in spiking dynamical systems, Scientific Reports, 15 April 2014). The latter notes: that: Complex systems displaying recurrent spike patterns are ubiquitous in nature. Understanding the organization of these patterns is a challenging task.

The flu virus is understood to have some 450 protein spikes, whereas the HIV virus has from 10 to 20 spikes -- usefully contrasted with images of the dense pattern in the case of dengue fever (John Schiller, et al, Why HIV Virions Have Low Numbers of Envelope Spikes, PLoS Pathogens, 10, 2014, 8). The contrasts can also be seen with access to "protein spikes", and especially "coronavirus virions" in images via Google.

There is very little information on the number of protein spikes around the sphere of the coronavirus particle. One estimate found was an average of 74 by Benjamin W. Neuman, et al, (A structural analysis of M protein in coronavirus assembly and morphology Journal of Structural Biology, 174, 2011, 1):

To test the quality of this model, we counted the number of spikes on three-dimensional reconstructions of MHV particles. These particles showed an average of 74 spikes per particle, which gives an approximate inter-spike spacing of 17 nm. Our model predicts *90 spikes per particle.

Given that 74 is only an average, the focus in which follows will assume a pattern of 72 -- if only in a spirit of poetic licence. Again it should be emphasized that this is an exercise of the imagination, and the emphasis is metaphorical in a quest for memorable designs, as highlighted in a preceding discussion (Satellite Constellation and Crown Chakra as Complementary Global Metaphors? 2020). That exercise drew attention to a configuration of 72 for geometrical reasons, having various traditional symbolic connotations. Nevertheless, it is appropriate to recognize that the number of protein spikes may vary on a coronavirus for several reasons. Of potential relevance from this perspective is the most recent initiative (Jonathan Amos, OneWeb increases mega-constellation to 74 satellites, BBC News, 22 March 2020). Why 74? The completed network aims to achieve an orbital configuration of approximately 650 satellites,Â

The issue, as considered below, is then how to distribute "mushroom-spikes" evenly around a sphere -- with the primary focus on 72.

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