PCCP cover (26th of February 2012)

Last year I spent three months in Ljubljana, on the Faculty of mathematics and physics, collaborating with Rudi Podgornik and Anže Lošdorfer Božič on several projects, one of which just saw the light of the day. It is a semi-review paper >> "Energies and pressures in viruses: contribution of nonspecific electrostatic interactions" published in Physical Chemistry Chemical Physics (PCCP) journal.

This paper sums up my, Anže's and Rudi's contributions to the electrostatics of viruses and it also contains a cute analytical estimates of electrostatic energies and pressures in viruses obtained from the simplified models of electrostatic interactions in the mean-field approach (Poisson-Boltzmann). Anže contributed to the work also with some unpublished results which give an approximate estimate of the importance of multi-valent (counter)ions in an approach beyond the mean-field setting (so called strong coupling, dressed counterions approach).

The paper was chosen by the editors as the "cover paper", i.e. it was presented on the cover page of PCCP 14(11), and I made a special illustration for that purpose which is not contained in the paper (the image above).

It was an interesting illustration task because the virus ( >> cucumber mosaic virus) was made as a sort of an iso-surface based on the atomic (aminoacid) coordinates. That is where the "smoothness" of its surface comes from. I chose such sort of visualization because Anže calculated the coordinates of all the charges on the virus. If one understands this as a set of points in a three-dimensional space, it is immediately obvious that the visualization of such object will be problematic, especially because the set of points is of low density (they represent only aminoacids which carry charge in a solution of neutral pH). So, I needed to find a way to convert the set of points in an iso-surface, whose three-dimensional nature is much more evident, and to that aim I used the BLOB function in PovRay which belongs in a class of >> metaballs 3D objects invented and defined by James Blinn in the beginning of eighties (we cite Blinn in our paper). The procedure of making the blob iso-surface from the set of points is >> explained in our work in a huge footnote on page 3748.

An additional problem was to represent the virus so that one can equally clearly see its exterior and interior (without its RNA molecule), and that the shadows do not obscure the details of its 3D shape. That is why I calculated the image in three different lighting setups which I eventually "layered" appropriately in Adobe Photoshop. This was a really interesting undertaking and I concluded that the PovRay evangelists, who typically preach that all the lighting features should be calculated at once in PovRay, are wrong. Of course they are wrong, as are all the fanatics who cannot see good aspects of other worldviews and ways.

The calculation lasted for quite some time, also because the illustration needed to be made in high resolution. A detail of the illustration in real size is shown in the image above - note very "softened" transitions between light and dark areas of the shape. Note also that the image contains a >> geodesic dome of the same symmetry as the virus - I think that this helps to more clearly emphasize the regularity and mathematical nature of virus structure. Another geodesic dome, with a huge T-number, is shown as a subtle element of the background.

Blob method can be applied to any set of points. I applied it to the set of all aminoacids when I created the representation of the whole virus, and when I created the representation of the charge distribution, I applied it separately to negatively and positively charged aminoacids. A result of such a procedure is shown in the image above, again for CMV virus. Red and blue objects show the iso-surfaces of positive and negative charge (see >> the paper for details).

The image above shows the distribution of positive charge in a >> cowpea chlorotic mottle virus. This is a virus which infects >> black-eyed pea. This time, the virus is not shown in cross-sectional representation so that one can clearly see the distribution of charge on its outside. Here I also set up the ligthing in such a way that the shadows are clearly visible.

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Last updated on 26th of February 2012.