Facts and Figures about SARS-CoV-2 and other Viruses

By Dr. Lim Ju Boo  8^th March, 2021

 

This essay is dedicated to my close friend, Ir. TO Lau, a senior civil engineer-cum-newspaper columnist, and also to my long-time friends Ms. Chia Choon Lan and Ms. Chiew Mui Kheng both newspapers reporters who in the 1970s till 1980 always troubled and chased after me almost daily on stories concerning astronomy, eclipses, comets and events happening in the skies.

Now I need to write a different story for them.

The Size of SARS-CoV-2 Virus:

 

Over the last one night I was trying to figure out how effective is the face mask we are wearing as one of our preventive measures against the current Covid-19 pandemic. I have already written an article on this earlier comparing the sizes of pore in a face mask and the size of the virus here:

https://scientificlogic.blogspot.com/search?q=face+masks+does+not+protect

 

However, we would like to look at this problem from another angle by comparing the droplets or water vapour from the breath of a healthy individual and the size of a single water molecule with that of the SARS- Covid-2 virus and see how a mask can handle this.

 

First of all, let us search the literature to see if there was any work being done on the size of droplets exhaled in the breath.

 

There is at least a few papers published that gave only the diameter of the droplets from the breath but not their volume. We need to change that into volume by assuming most of the nasal droplets and viruses just like the SARS-Covid-2 virus are spherical in shape. In any case water droplets are all spherical, not liner or in other shapes. A sphere also has the smallest surface area for a volume.

 

Numerous papers published have given different but almost the same data on the size of the exhaled droplets.

 

For instance, in their paper by Rao S. Papineni and Frank Rosenthal they characterized the size distribution of droplets exhaled by healthy human subjects by performing four respiratory actions. i.e. mouth breathing, nose breathing, coughing and talking.

 

They measured their sizes by both an optical particle counter (OPC) and an analytical transmission electron microscope (AEM).

 

The OPC indicated a preponderance of particles less than 1 μm (1 micrometer) or 1x10^-6 or 0.000 001 metre although larger particles were also found. Measurements with the AEM confirmed the existence of larger sized droplets in the exhaled breath.

 

In general, coughing produced the largest droplet concentrations and nose breathing the least, although considerable inter subject variability was observed (1).

 

The Size and Concentration of Droplets Generated by Coughing in Human Subjects has also been studied by Shinhao Yang , Grace W.M. Lee , Cheng-Min Chen , Chih-Cheng Wu and  Kuo- Pin Yu (2).

 

The investigation on sizes of exhaled particles and small airways was also conducted by B. Bake, P. Larsson, G. Ljungkvist, E. Ljungström & A-C Olin (3).

 

Interestingly most of the findings on the size of droplets or breath vapour showed about the same results as wet stream, which has a diameter between 0.5 – 1.0 μm (0.0,000,005 m – 0.000,001 m) and we shall work on that assumption as the average size of droplets or water vapour from our breath.

 

We shall not go into all the numerous studies done as this is not a research paper, but is a simple article meant for the general non- technical readers to make it readable.

 

It suffices to say that most of the particle sizes of droplets exhaled from breath, water vapour, wet steam or mist do not vary very much in their sizes. Their sizes were between 0.5 to 1 μm (micrometre) in diameter whichever method was used in their measurements.

 

We shall use their diameter between 0.0,000,005 m – 0.000,001 m as our average for the sake of simplicity for our general readers, and we shall also assume out of simplicity that all droplets and viruses are spherical in shape since we are dealing with such tiny particles and that would not make much difference on their shapes.

 

The Sizes of Nasal Droplets and Water Vapour:

 

Since the volume (V) of a sphere is =4/3 π r³, the volume of breath droplets as water vapour is between 6.5x10^-20 – 5.2x10^-19 cubic metre, derived from the data from various papers published. (1 micrometre or micron (u) = 1x10^-6 m).

 

However because of their ranges in sizes, for simplicity sake we shall use only the largest exhaled volume, mainly water vapour from the breath of a healthy individual for all comparison. After all, we need to compare them with the size of a SARS-CoV-2 virus.

 

Let us now look at the size of SARS-CoV-2 virus for comparison. Again, various estimates of their diameter between 10^-7 to 5x10^-7 metres has been given. Hence their calculated volume is between 5.2x10^-22 cubic metre – 6.5x10^-20 cubic metre. 

 

Since the largest volume of droplets mainly water vapour from our breath exhaled by an healthy individual is 5.2x10^-19 cubic meter, and if we take the largest size of a SAR-CoV-2 virus as 6.5x10^-20 cubic metre, this implies the breath droplets from a healthy individual would be 8 times larger than the SAR-CoV-2 virus.

 

If a face mask is worn, the size in volume of the water vapour exhaled in our breath will between 8 - 10 times that of the SARS CoV-2 virus.

 

We can conclude if the breath vapour is 8 – 10 times larger than the virus, can escape through a face mask, there is no reason why a virus smaller cannot escape through the same mask. What’s more, we are assuming all the air inhaled or exhaled goes completely through the pores of the mask which in fact is not so.

 

Most of the wearers wear face masks loosely, and even when properly tied up, most of the air would take the path of least resistance, namely through the spaces between the mask and the cheeks.

 

Worse still, the breath enters and exhausts through the groove between the nose and the cheek especially for those with long and protruding noses.

 

Those large spaces along the contours of the cheeks and face are truly passages free for all, not just for viruses, but even for water vapour and nasal droplets to escape as all would the paths of least resistance.

 

However, it is most likely the exhaled air besides water vapour from the breath even in healthy individual also contain sticky mucus droplets that may get trapped onto the fabric of the mask, allowing only uncontaminated water vapour to escape.

 

This is one possibility we need to look at their usefulness especially if we are sick with an infective respiratory problem. 

Interestingly, when steam sprouts out from boiling water, the volume sizes of the steam droplets will vary greatly accordingly to the surrounding temperatures.

 

Once steam is visible like a mist, its particle size will be less than 50 microns (5x10^-5 m) in diameter. Its volume will be less than 6.5x10^-14 cubic metre.

 

This implies visible steam as in mist with a water vapour diameter between 50 – 100 microns (5x10^-5 to 10x10^-4 m) will have a volume between 6.5x10^-14 to 5.2x10^-13 cubic metres.

 

This puts visible steam and mist as breath condensed on a cold mirror between 1,000,000 to 8,000,000 times larger than the SARS-CoV-2 virus.

 

The Size of a Water Molecule:

 

But how does the size of this virus compare to the size of a single water molecule?

 

To answer that, we need to calculate out the volume of a water molecule.

 

The volume of a water molecule can be calculated out in this way:

 

The density of water is 10^3 kg/m³ and Avogadro’s number = 6x10^23

/mol (to be exact = 6.02214076×10^23 /mol).

Since the molecular mass of water is 18 g/mol (to be exact = 18.01528 g/mol),

Hence the number of molecules in 18 g (0.018 kg) of water = 6x10^23

The mass of a molecule of water is 0.018 / 6x10^23 = 3x10^-26 kg

Density = mass / volume

Hence volume = mass / density, the volume of a single water molecule is:

3 × 10^–26 /1000 = 3x10^-29 cubic metres.

 

This is 0.00 000 000 000 000 000 000 000 000 003 cubic metre.  

 

If we think there are far too many zeros – 28 zeros all in - after the decimal point in front, if we express volumes in the cubic metre as we scientists would normally do using the SI (International System of Units), when you may be more familiar with expressing volumes in millilitres as we do in analytical chemistry, then you may add another 6 zeros after the decimal point to give 34 zeros after the decimal point to express it in millilitres.

 

That is the volume of one molecule of water whichever way we like to express it.

 

This means the size of SARS-CoV-2 is between 17 million to 2166 million times larger than a molecule of water or a molecule of water is 6x10^-8 to 4.6x10^-10 (0.00,000,006 to 0.000 000 000 46) times smaller than a SARS- CoV-2 virus.

 

Viruses:

Let us now look a little bit about viruses in general, their sizes, and a little on their discovery.

 

Generally there are the smallest of infective agents. They vary in sizes. For instance one of the smallest viruses is one that causes yellow fever. Their diameter assuming it is spherical is only 0.02 micrometre (2x10^-8 m) across. Its volume is thus 4.2x10^-24 cubic metre.

 

2x10^-8 and 4.2x10^-24 written in the scientific nomenclature means 0.00 000 002, and 0.000 000 000 000 000 000 000 0042.

 

This puts the size of the virus that causes yellow fever just 0.2 times the diameter of the Covid-19 virus, and in terms of volume, it is just 8x10^-3 (0.008) times that of Covid-19 virus.

 

Another way of putting it is, the smallest Covid-19 virus is 124 times larger than virus that causes yellow fever.

 

A virus thrives totally on the enzyme machinery of the host cell. Some viruses especially the largest ones are affected by certain antibiotics, but generally they are not, only bacteria do.

 

History:

 

The history on the discovery of the virus is interesting. It was not discovered directly. The existence of viruses was suspected for a long time before they were seen.

 

For instance the French biologist, microbiologist, and chemist Louis Pasteur already suspected that may be germs too small to be seen. The story began with a Russian bacteriologist, Dmitri Iosifovich Ivanovski who in 1892 was looking at the tobacco-mosaic disease that caused the leaves of the tobacco plant to have a mottled appearance.

 

What he found was that the juice of an affected plant could affect the leaves of a healthy plant. He then tried to find out the agent that caused it by passing the juice through porcelain filters with holes so ultra fine that not even the smallest bacterium could pass through, and yet the juice that passed through could still infect the tobacco plants.

 

He then thought his filters could be defective to allow the bacteria to pass through.

 

Then in 1897 a Dutch bacteriologist, Martinus Willem Beijerinck repeated what Dmitri did, and he too found the same. He concluded the agent that caused the tobacco-mosaic disease was small enough to pass through even ultra-fine porcelain filters.

 

Since he could not see anything under the microscope in the clear infected fluid, and was unable to culture anything in a test tube, he thought perhaps the infected agent might have been some small molecules, maybe about the size of a sugar molecule.

 

Beijerinck decided to call the agent a filterable virus which in Latin means a poison. Then in 1897 a German bacteriologist by the name, Friedrich August Johannes Loffler passed the blood of an animal infected with foot and mouth disease through a fine porcelain filter. What he found was that the fluid could still cause the disease in healthy animals. So it was quite a mystery.

 

It was not until 1901 that Walter Reed found the agent that caused yellow fever was a filterable virus. This discovery was followed by a German bacteriologist Walther Kruse who showed that the common cold was caused by a virus.

 

By the early 1930’s more than 3 dozen diseases such as smallpox, chickenpox, hydrophobia, influenza, poliomyelitis, herpes, etc were actually found to be caused by viruses. Yet its mechanism of their infectivity was still inscrutable.

 

Then came along an English bacteriologist, William Joseph Elford who used finer and finer collodion membranes as filters to investigate.  It was he who finally managed to filter out the viruses as different particles that caused these diseases.

 

That gave him some clue how small the sizes of the viruses were that caused various diseases by knowing the fineness of the membrane he used. He found that even the smallest virus was still larger than most molecules as we calculated out earlier by comparing the size of the SARS-Covid-2 virus with the size of a water molecule.

 

For instance the volume of Covid-19 virus is between 5.2x10^-22 cubic metre – 6.5x10^-20 cubic metre.

This turns out to be 124 times to 15,500 times larger than the virus that causes the tobacco mosaic virus.

 

In contrast, the average size of a virus is only 0.001 the size of an average bacterium.

 

By then scientists knew that the largest viruses are the Bodo saltans virus, Megavirus chilensis, Acanthamoeba polyphaga mimvirus and ricketsia virus.

 

Living or Non-Living:

For many years after, scientists argued whether viruses are living or non-living? Their capability of multiplying to cause and transmit diseases suggests they were alive like bacteria. However an experiment conducted in 1935 by an American biochemist Wendell Meredith Stanley didn’t show otherwise.

 

What Stanley did was he macerated up tobacco leaves that were heavily infected by the tobacco mosaic virus, and started to isolate or purify the virus in pure and concentrated form using a protein-separation procedure. What Stanley found to his surprise the virus turned out as crystalline or crystallized form.

 

Still, when Stanley dissolved the crystals in liquid it could still infect the tobacco plant as before. For this discovery, Stanley shared the Nobel Prize in chemistry in 1946 with Summer and Northrop on the crystallizers of enzymes.

 

However, for some twenty years after Stanley made his Nobel Prize discovery, scientists found only viruses that affected plant diseases could be crystallized out. But it was not until 1955 that the first “animal virus” that caused poliomyelitis could be crystallized. This was demonstrated by Carlton E.Schwerdt and Frederick L. Schaffer.

 

This seems to suggest to many scientists, including Stanley and others that viruses are just molecules of proteins that are non-living.

 

Until today no living organisms including bacteria could be made into crystals. All living things must comply with the definition of life which itself has more than 100 definitions, yet none of these definitions are satisfactory and accepted.

 

Life and Crystals are Entirely Different:

 

Life as given by various definitions must comply with many characteristics such as its ability to feed, grow, and reproduce, respond to stimuli among others. 

But crystals are entirely a different entity. They are unable to do show any of the “living” characteristics. They are dead substance, unable to move on their own without an external force. They only have fixed structures. 

 

But then we can argue viruses remain infective, and are able to grow and multiply just as if they were living even after being crystallized, except they need a living host to do this. On their own they are fixed and immovable. 

 

Then came another debate in 1936 when two British scientists Frederick Charles Bawden together with Norman Wingate Pirie made a very interesting discovery.  

 

They found the tobacco mosaic virus actually contain ribonucleic acid even though its main composition was 94 % protein with the remaining 6 % made of RNA which of course is a nucleoprotein. But this is the chemical characteristic and composition of life.  

 

Ever since it was demonstrated that all other viruses too have RNA or DNA or both which is the common denominator of all living organisms.

 

Back to Square One:

So we are back to square one as to whether viruses are living or non-living? I think the debate still goes on.

 

But personally I think viruses are pre-life molecules that requires some kind of “life force” unknown to science for them to trigger into something that is living that can fit into the many criteria and definition of life.

 

Unfortunately, for that we need to bring in something else – An Intelligent Designer which I am afraid may not be acceptable to science, maybe to some scientists except myself.

 

But I think we will never be able to settle this question whether or not a virus is alive until we try to understand how life actually originated and what makes RNA and DNA tick into life, a question I feared most scientists today try to avoid answering. 

 

Even though viruses are made up of RNA or DNA, scientists admit neither RNA nor DNA by themselves is living. They are just the chemical footprints from something living, close to life, but not life itself. 

 

I am also afraid the difference between a nucleoprotein and proteins, the former closer to something living and the latter something non-living is as much as comparing a piece of beef hanging dead onto the hook of a butcher’s shop, with a living cow moving and feeding on living grass in a field – a life giving life to another.

 

See here:

https://scientificlogic.blogspot.com/2010/09/mystery-of-life-unmeasurable-vital.html

 

The Code of Life: 

However, viruses turn out to have also genes, and these are codes that make life essential. There again we are back to square one. Are viruses living or non-living? I am afraid we will never be able to answer.   

 

What is even more interesting, some large viruses seem to have some loosely-packed chromosomes, with some of them packing as much as seventy-five or more genes, with each controlling their structures and function separately.

 

Most of these genes take over the functions of cellular machineries of a host cell they invade and their chemistry. A virus by itself is almost devoid of any metabolic chemistry which again fails itself against the definition of something living. 

 

What’s more fascinating, they can even mutate by replacing their own genes or a number of them and pass these own to their generations. This of course is awesome for something that is non-living. 

 

Just like bacteria that are able to pick up stray and dead DNA from the environment, and incorporate them into their DNA to make them hardier and more resilient as part of evolution, so too are viruses capable of picking up DNA from bacterial cells they infect and transmit them to another cell they next infect.

 

This observable fact among the viruses is called “transduction” a term given by Lederberg who discovered this phenomenon in 1952.

 

Viruses Seen by an Optical Microscope:

Actually some viruses can still be seen under an optical microscope as most people including bacteriologists did not know. 

 

It was a Scottish physician by the name of John Brown who in 1887 reported he could just make out some tiny particles or dots when he took some fluids from cowpox blisters and examined them under an optical microscope. This seemed quite an interesting observation. However this could be possible because we know that the virus that is responsible for cowpox is one of the largest known viruses.

 

Electron Microscope: 

But it was not until the invention of the electron microscope by Max Knoll and Ernst Ruska at the Berlin Technische Hochschule in 1931 that could magnify as high as 100,000 times instead of just 2,000 times with an optical microscope that made viruses clearly visible.

 

The electron microscope resolves objects as small as just 0.001 micrometre in diameter. But there was some drawbacks with the earlier models of the electron microscope since the samples had to be placed in a vacuum, and that changed the morphology and shape of a biological specimen due to dehydration in a vacuum.

 

This is the same principle used in vacuum evaporation during food processing. Besides this drawback, the tissues containing the cells have to be sliced ultra thin.

 

But we shall not go into electron microscopy for the time being as this essay is originally about the size of the SARS-Covid -2 virus compared to the size of water vapour and the size of a water molecule exhaled and expelled by a person to determine the effectiveness of wearing a face mask against SARS-Covid-2 virus.

We need to stop here after more than 7 hours of non-stop calculations and typing, else we would be tempted to continue typing and typing for many hours more into weeks and weeks, into months, and months leading into other similar issues on immunology, vaccinations, molecular biology, evolutionary biology then into genetics and other issues connected to the present Covid-19 pandemic.

 

Hence we need to stop.

 

Summary:

 

Viruses including SARS-Covid-2 virus are far too small to be filtered out by any thin face masks, not even by thick ultra-fine porcelain filters as first demonstrated by Dmitri Iosifovich Ivanovski in 1892.

Face masks may be useful to trap nasal droplets where viruses are stuck along with the sticky mucus discharge, and hence may give some protection to others nearby, but they cannot filter out any viruses for reasons already explained at length, or give significant protection to a normal individual wearer against the virus floating in the air.

 

References:

 

1. Papineni RS, Rosenthal FS. The size distribution of droplets in the exhaled breath of healthy human subjects.

 

2. The Size and Concentration of Droplets Generated by Coughing in Human Subjects

Shinhao Yang , Grace W.M. Lee , Cheng-Min Chen , Chih-Cheng Wu and  Kuo-Pin Yu

https://www.liebertpub.com/doi/10.1089/jam.2007.0610

 

3. Exhaled particles and small airways, B. Bake, P. Larsson, G. Ljungkvist, E. Ljungström & A-C Olin 

https://respiratory-research.biomedcentral.com/articles/10.1186/s12931-019-0970-9#:~:text=When%20exhaled%2C%20these%20particles%20have,of%200.7%20to%201.0%20%CE%BCm