Tuesday, May 5, 2020

The beautiful mathematics and physics of virions

Next Monday I am giving a seminar, ``The mathematics and physics of virions", for the virtual Pandemic Seminar of the UQ School of Mathematics and Physics. Most of the talks so far have been about modeling the spread of the virus and the effect of social distancing measures. In contrast, I will look at phenomena at a much smaller scale.

The past month I have taken a crash course in what is known about the structure and properties of virions (single virus nanoparticles). There is some fascinating and beautiful mathematics and condensed matter physics involved. A nice place to start is this short animation video that shows how the Dengue fever virus replicates itself.



Three important questions for any virus are the following.

1. What is the structure of the virion?
In particular, what is the structure of the viral capsid, i.e. the protein shells that encapsulate the genome of the virus?

2. How does the capsid self assemble?

3. How is the genetic material packaged inside the capsid?

Handwashing with sanitiser works because hydrophobic interactions cause the breakup of the membrane that encases the virion. This is the same soft matter physics as when soap removes dirt.

The role of anti-viral drugs is to interrupt/sabotage any of the steps in the multi-step process of the action or duplication of the virion. Thus, finding answers to any of the three questions above may facilitate the development of anti-viral drugs or vaccines.

Here are a few of the articles I have found fascinating and helpful.

Geometry as a Weapon in the Fight Against Viruses
Reidun Twarock

On Virus Growth and Form 
Roya Zandi, Bogdan Dragnea, Alex Travesset, Rudolf Podgornik

TRIM5α self-assembly and compartmentalization of the HIV-1 viral capsid 
Alvin Yu, Katarzyna A. Skorupka, Alexander J. Pak, Barbie K. Ganser-Pornillos, Owen Pornillos, Gregory A. Voth

The figure below (taken from the second article above) shows the structure of the capsid of five different virions. The number of proteins in all of them is an integer multiple of 60.


Left to right: Satellite Tobacco Mosaic virus (composed of 60 proteins); L-A virus (120 proteins); Dengue virus (180 proteins); Chlorosome Vigna virus (180 proteins); Sindbis virus (240 proteins).

In the next post, I will explain the geometric origin of this quantisation.

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