Viruses are very small

The typical size of a virus is around 100 nanometres. One nanometre is 10⁻⁹ metres, a billionth of a metre. The wavelength oif light we can see is around 400-700 nanometres. Nanometres are good units for atomic scale. That excellent source Wikipedia tells me that the diameter of a helium atom, for example, is about 0.06 nm, and that of a ribosome is about 20 nm. The term nanoscale is used for things up to 100 nm, so many viruses are nanoscale. [1] If you still tend to confuse a bacterium with a virus, bacteria are 1-10 thousand nanometres across, so generally a bacterium are ten to a hundred times bigger than a virion (that's the right word for a single viral particle). The smallest bacteria are about the same size as the very largest virus particles.

There's a pig virus (PCV, porcine circovirus) that is 17nm across. It is icosahedral, as are many viruses.

Herpes simplex virus is around 125nm across, has at least 74 genes, its capsid is icosahedral . More. This is what causes cold sores (HSV-1) and common genital infections (HSV-2). HSV-1 has about 90 RNA strands around 155,000 base pairs (unit, kbp, kilo-base-pairs). I found varying numbers for this. Different more.

Influenza A has 7 genes, is roughly elliptical and 80-120 nm in diameter. the genome is 13588 bases long, on eight RNA segments that code for between 10 and 14 proteins. Read about it.

HIV is around 100nm across and is a different shape from other viruses; it has 9 genes, 15 viral proteins, 9749 nucleotides (is that the same as base pairs?)

Coronavirus is quite big, at 50-200nm 30,000 base pairs (30kbp)

There's a large virus called mimivirus, some 500nm across

There's a recently discovered (2013) giant virus called pandoravirus, 1000nm = 1 micrometre in diameter.  A typical virus contains 10 genes, a pandoravirus will have 1.5-2.5 thousand genes. Understandably, they were often mistaken for bacteria.

There are an awful lot more viruses than you might expect. I came across a new word, nonillion = 10³⁰, nine more sets of 000 after a million. the number of individual virus partcles, virions, on the planet is around 10³¹, so ten nonilllion. One way af checking this is to count them in a sample of seawater—I found various techniques for this, and quite a few studies. [6]. 

Some numbers: 

Prokaryotes are single celled organisms without a nucleus (that's a crude definition) and are divided into two sorts, archaea and bacteria. Eukaryota are a third domain which do have nuclei. These prokaryotes are abundant in the oceans and are attacked by viruses so that around 20-40% of prokaryotes are killed each day.

In the top 200m of the oceans, there are about 5x10⁵ prokaryotes per millitre of seawater, and 5x10⁴ below [7, 10], making for an estimate of around 10²⁹ cells at any moment in the oceans. The high turnover, of 1-3 weeks in the upper ocean, or 2½ years in the soil, suggests that estimates of carbon capture held in plants has been way too low. See [7] below. If you think 10²⁹ is a 'so what?' sort of number, the number of rice grains in another extension page stayed below 10²⁰; this is a billion times bigger. the number of observable stars in the universe is only an estimate, but the Milky Way has around 10¹¹ stars (that's the right number of zeroes only). It is thought there might be 10¹³ galaxies, so 10²⁴ stars (a European quadrillion, an American septillion). The number of prokaryotes is still 100,000 times bigger.

A gram of faeces (pause for school-age expressions of disgust and yes, I spelled it correctly) will typically have 10⁹ viral particles. The oceans have about 10³⁰ or 10³¹ virions and when we add in the land, we will reliably reach 10³¹. The number of perkaryotes (archaea and bacteria) is similar.

Question 1. If a virus particle was the size of a balloon (say a litre or two) and if you imagine filling a space with 10³¹ balloons, representing all the virions on earth, how would that compare with the size of the sun? The sun is 1.41x10¹⁸km³ in volume.

Question 2. A chosen example virus has particles whose diameter is about 125nm. So what is its volume in litres? You may express this to appropriate precision (not very many significant figures).

Question 3.  The space enclosed by a school desk is close to one cubic metre, which is 1000 litres. Compare the ratio of the volumes in litres of  desk/virus  to  Earth/desk. Earth is about 10¹² km³; use the virus in Q2. 

Question 4.  Divide the volume of the planet by the volume of the virion to have the ratio of their volume.  Take the diameter of planet is 12500km in diameter (it's 12742km). Working in metres, compare the planetary diameter with the diameter of a virion (100nm) to have the length ration of the two.  Show (harder) that this is length ratio is consistent with your volume ratio.

 The genome of a virus is made up of base pairs from the purines Adenine and Guanine, and the pyrimdines Cytosine  and Thymine (DNA)). The nucleotides are always in pairs AT and CG, so we just might view this as binary combinations. A virus has very small strands of this RNA or DNA (I think if the strands are RNA, then Thymine is replaced by Uracil). So imagine we could code such strands ourselves. An influenza-sized virion is the size we have been considering and has 14kbp. [I thought about using herpes, at 155kbp more than ten times as succesful at packing information.] So a single virion has about an equivalent of 14kilobits, or a little under 2 kilobytes. A typical novel is 400kb (kilobytes); my longer ebooks are 800kb. So a novel could conceivably fit into 2-4 hundred virions.

Question 5.  Suppose we could code AT and CG any way we liked and that we could group virions together in hundreds. How many novels of 400kb would fit into a milliliter? Let's assume our manufactured virions are still 125nm diameter, so we've built quite a few inefficiencies into our model, and we haven't looked at all about how we reference, order or even find the particles.

Just imagine 'catching" a book, pronounced 'buk' to approximate to both bug and book. If you caught a buk really badly you'd have to go to bed. I've no idea how the 'reading process' would work; I have only looked at the tiny volumes we could be considering if we were able to generate code on demand—instead of as now, where we can read it (the genetic code of a virus), given enough copies. Consider the way coronovirus changes as it is passed from person to person; this might be like editions of a newspaper story. The information content is similar, at 2kilobytes of text; a tweet of 140 characters might be about 300 bytes by the time you added overhead like metadata; the new definition of tweet length is double that. If you used a reduced character set (8 bits to a byte, one byte per character), you could easily halve this and have, as when stored on my computer, about a page per virion. Of course, you can imagine the attraction to advertisers, not so much catching a buk as catching a whole campaign.

Remember, viruses are very very small. If coding was no problem at all then the strands of code could be much longer —coronavirus is 30kpb, but a bacterium typically has a single DNA molecule of several million base pairs (my source). E coli for example has around 4000 kbp, which would make around 500 kilobytes, which would exceed many typical books. Just imagine complaining of a tummy buk, because your latest Parry Hotter has multiplied accidentally.


DJS 20200618


[1] https://en.wikipedia.org/wiki/Virus

[2] https://www.sciencelearn.org.nz/resources/1651-nanometres-and-nanoscale

[3] http://book.bionumbers.org/how-big-are-viruses/

[4] https://www.nature.com/articles/ncomms6980

[5] https://www.nationalgeographic.co.uk/science-and-technology/2020/04/there-are-more-viruses-stars-universe-why-do-only-some-infect-us

[6] https://www.virology.ws/2009/03/20/the-abundant-and-diverse-viruses-of-the-seas/

[7] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC33863/                         (superscripts fixed below; do read the original)

The number of prokaryotes and the total amount of their cellular carbon on earth are estimated to be 4–6 × 10³⁰ cells and 350–550 Pg of C (1 Pg = 10¹ g), respectively. Thus, the total amount of prokaryotic carbon is 60–100% of the estimated total carbon in plants, and inclusion of prokaryotic carbon in global models will almost double estimates of the amount of carbon stored in living organisms. In addition, the earth’s prokaryotes contain 85–130 Pg of N and 9–14 Pg of P, or about 10-fold more of these nutrients than do plants, and represent the largest pool of these nutrients in living organisms. Most of the earth’s prokaryotes occur in the open ocean, in soil, and in oceanic and terrestrial subsurfaces, where the numbers of cells are 1.2 × 10²⁹, 2.6 × 10²⁹, 3.5 × 110³⁰, and 0.25–2.5 × 10³⁰  respectively. The numbers of heterotrophic prokaryotes in the upper 200 m of the open ocean, the ocean below 200 m, and soil are consistent with average turnover times of 6–25 days, 0.8 yr, and 2.5 yr, respectively. Although subject to a great deal of uncertainty, the estimate for the average turnover time of prokaryotes in the subsurface is on the order of 1–2 × 10³ yr. The cellular production rate for all prokaryotes on earth is estimated at 1.7 × 10³⁰ cells/yr and is highest in the open ocean. The large population size and rapid growth of prokaryotes provides an enormous capacity for genetic diversity.

[8] https://bionumbers.hms.harvard.edu/bionumber.aspx?s=n&v=5&id=110706

"There are an estimated 10³¹ viral particles on earth, and human feces contain at least 10⁹ virus-like particles per gram (primary sources). Many of these are identifiable as viruses that infect bacteria (bacteriophages), but the great majority remains unidentified." See Lošdorfer Božič A et al., 2013 PMID 23860870 p.2 top line: "Viruses are the most abundant source of DNA and proteins in Earth’s oceans that contain on the order of 10³⁰ virions [ref 1, C. Suttle, Nat. Rev. Microbiol. 5, 801 (2007)]."

[9] https://jb.asm.org/content/202/9/e00052-20  I can only see the synopsis.

The number of virus particles on Earth is frequently reported in the scientific literature and in general-interest publications as being on the order of 10³¹ , with some confusion about whether this is a high or low estimate. This number is often given without a source, though it should be attributed a papers by Roger Hendrix published in 1999. As with any oft-repeated statistic, it is informative to know how it has been derived and whether it may have to be revised in the light of new evidence. I review the history of the 10 ³¹ estimate and use more recent assessments of the number of bacterial and viral particles in various habitats to conclude that the best estimate of the number of virus particles on Earth (“The Hendrix Product”) remains close to 10³¹ , and is unlikely to be either much less, or much more than that.

[10] https://books.google.co.uk/books? id=BwRSn2ikJW4C&pg=PA25&lpg=PA25&dq=Prokaryotes+per+cubic+metre+in+seawater&source=bl&ots=xFIx5nEsmh&sig=ACfU3U36dxCckU1odOcN1lY8LBI5y33RjQ&hl=en&sa=X&ved=2ahUKEwiMqeLbzKvqAhXyURUIHdhjCV0Q6AEwC3oECAsQAQ#v=onepage&q=Prokaryotes%20per%20cubic%20metre%20in%20seawater&f=false

Bacteria are prokaryotes in the range of 1 µm in size...[they] range from 10⁵ to 10⁷ cells per cubic centimeter (millilitre) of seawater.

1.  Volume of the sun is 1.41x10¹⁸km³ = 1.41x10²⁷m³ = 1.4x10³⁰ litres, so about the same as the balloon collection.

2.  125nm diameter =>62.5nm radius, which is 6.25x10⁻⁸m. 4/3 π r³ => a volume of 1.02x10⁻²¹m³, 1x10⁻¹⁸litres. 

3. desk / virus = 1000 /  10⁻¹⁸ litres = 10²¹.   The planet is  10¹²km³ = 10²¹m³ = 10²⁴ litres.  Planet / desk =  10²⁴ / 10³ litres = 10²¹.    Planet / virus = 10⁴².  So if the virus was the size of a desk, the desk would be the size of the planet. 

4.  The ratio of planet to virion is 12500km/125nm = 10¹⁴ in length. Considerations of volume would cube that, 10⁴².     Volume of planet / volume of virion = 10²⁴ / x10⁻¹⁸ = 10⁴².

5. Volume of virion 1x10⁻¹⁸ litres from Q2. Virions per millilitre = 10⁻³ / 10⁻¹⁸ = 10¹⁵.  A 400kb book requires 200 virions, so 'Books' per milliltre is 10¹⁵ / 200 = 5x10¹². The number of books in the world (source) is 1.3x10⁸. We don't need a millilitre; a microlitre would be plenty big enough. This makes you wonder how little space we would need for the sort of additional personal memory (in your head, injected, whatever) that science fiction writers have dreamed about since the mid-60s.



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