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Malthusian Memes - An Exponentialist View
Viral Replicators - An Exponentialist View
Bacterial Replicators - An Exponentialist View
Cellular Replicators - An Exponentialist View
Rabbit Replicators - An Exponentialist View
Human Replicators - An Exponentialist View
Grey Goo - An Exponentialist View
Death By Replication
Exponential Assembly - An Exponentialist View

Population Doubling Mechanism

New Malthusian Scale

External Links:
Human Cell Reproduction 

Cells article on Wikipedia

Cellular Replicators - An Exponentialist View

(It is recommended that you also read Bacterial Replicators - An Exponentialist View)

Cell Division

Cells replicate through a process of cell division, and can form multi-cellular life-forms. Cell division is referred to in my Exponentialist web site as a replication event. The human body grows from a fertilised egg (zygote), and does so by cell division. Click on the image below for an example:

  

Final cell population after 4 generations is 16. 

Often, the description stops there, or else focuses on stages of embryonic development. All too often, the description of cell division is taken as a complete explanation, leading to a simplistic calculation of the number of cell generations that it takes to grow an individual. As Richard Dawkins states in "Climbing Mount Improbable" (Dawkins, 1996): 

"This way of calculating the number of cell generations is actually unrealistic because it only gives a minimum figure. It assumes that, after every cell generation, all cells do on to duplicate.  ...So a blue whale in fact consists of a number of cell lineages of different length, building different parts of the whale. Some of these lineages go on dividing for more than fifty-seven cell generations. Others stop dividing after fewer than fifty-seven cell generations."

Because this generational approach to calculating cell populations unrealistically assumes all cells are immortal he refers to this approach as naive (Dawkins, 1996). See Cell Replication section of Richard Dawkins - An Exponentialist View for more.

However, getting back to the image above, if only the pink cell in the third generation dies then the final population is only 14. Or, if only the yellow cell in the second generation dies, then the final population is 12.

If both the pink cell in the third generation and the yellow cell in the second generation die, then the final population is 10. 

Few people stop to think of cells in Malthusian terms, as a population with birth rates and death rates. That is the purpose of this article. 

Consider the following table, which uses my New Malthusian Scale to measure the cell population:

A-Pops 1 2 4 8 16 32   64 128 256 512 1024
B-Pops 1 2 4 8 16 32   64 128 256 512 1024
C-Pops 1 2 4 8 16 32   64 128 256 512 1024
D-Pops 1 2 4 8 16 32   64 128 256 512 1024
E-Pops 1 2 4 8 16 32 45.47 64 128 256 512 1024

Table A. Cell population doubling for a typical human

Note:  1A-pop = 1024 pops, 1B-pop = 1024 A-pops, 1 C-pop = 1024 B-pops etc. 

Note that the population doubling times are not constant, and yet exponential growth of the population occurs. I mention this because people often assume a constant rate of growth of required to produce true exponential growth. As the following table shows, such a belief is a fallacy:

Cell Population Doublings (Total) Cell Population Timeline Milestone
3 8 A-Pops 3 days Last time all cells are identical 
8 128 A Pops 6-7 days Blastocyst implantation 
30 1024 C-Pops 8 weeks In females, life-time egg supply now formed
41 2 E-Pops 9 months Birth
44 16 E-Pops 4-5 years Kindergarten
Between 45 & 46 45.47 E-Pops (50,000 billion cells) 18 years Adult 

Table B. Cell population milestones for a typical human

In Table B, I have distinguished foetal growth (yellow background) from postnatal growth (green background). Tanner neatly summarises the difference between foetal growth and postnatal growth (Tanner, 1978)

"Thus, postnatal growth, for most tissues, is chiefly a period of development and enlargement of existing cells, whereas early foetal life is a period of cell division and the addition of new cells."

Tanner describes the 3 main phases of human cell growth as:

Postnatal growth is therefore deemed to be largely a matter of adding cytoplasm to existing cells. Tanner explains the timeline for the cessation of cell division, which depends upon the tissue involved:

Tissue Milestones For Cell Division

Nerve

Neuron - stops 10 to 18 postmenstrual weeks

Neuroglia - stops before 2 years of age  

Muscle

Surge during adolescence (especially males), then stops.

Small reserve stem cell supply throughout adult life

Fat

Stops at puberty

Bone

Surge during adolescence (especially males), then stops. 

Small reserve stem cell supply throughout adult life

Table C. Cell population milestones for various human tissue types

Of course, in absolute terms, the last population doubling (by definition) increases the cell population by as much as all previous doublings. So, in absolute terms, it could be argued that as much growth occurs in the last population doubling as occurred in the all previous doublings. Given that the cell population of an adult human is generally taken to be 50,000 billion cells, this means that the total cell population of 25,000 billion cells (22.74 E-Pops) reached during early childhood is matched by an equal amount by adulthood. 

What is not clear from Tanner's explanation is whether new cells are "born" (through cell replication, known as mitosis) to replace any cells that might die. In other words, what is the birth rate and death rate for cells of different tissue types whilst cell division continues? However, the story does not stop there.

Postnatal Cell Production

Robert Wilson, in the BBC (1998) series "The Human Body", states we are "...constantly replacing cells from head to toe..." (parenthesised notes below are mine): 

The last episode of the series focuses on cancer, which is a type of disease which features runaway cell division. Such unrestrained exponential growth leads to death for the individual, and therefore death for the cancer, if not stopped.

Self-Repair

Lynn Margulis and Dorion Sagan make the following observations about the human body (Margulis, Sagan 1995, p.23)

"It continuously self-repairs. Every five days you get a new stomach lining. You get a new liver every two months. Your skin replaces itself every six weeks. Every year, ninety-eight percent of the atoms in your body are replaced."

So, we have two types of self-repair. We have bodily self-repair with "new cells for old" and we have cellular self-repair with "new atoms for old" through metabolism. It is interesting to note that they refer to atoms, and not to cell division. Margulis and Sagan have a curiously romantic and chauvinistic attitude towards cells (Margulis, Sagan 1995, p.24):

"The cell is the smallest unit of life."

I refer to this view as cellular chauvinism. See Viral Replicators - An Exponentialist View for my criticism of this view.

New Cells For Old?

With regard to our skins, most people are aware that household dust is largely composed of dead skin cells. I would venture to suggest, therefore, that most cell births and deaths in the adult human body occur in the skin. After all, our skin is our first line of defence against the hazards of our environment.  However, the lining of the gut, which I would guess to be smaller in surface area than the skin, is replaced more often. So perhaps our long-suffering gut cells have the highest rate of deaths and births in an adult human. Then, if you're a drinker, perhaps it's your liver that is driven to a greater numbers of deaths and births of cells.

To verify these statements it would be necessary to know the cell populations of an average human's skin, gut and liver. In an adult human, each discrete population of differentiated cells remains relatively stable. If not, your skin, gut or liver would increase or decrease in size! So, given that birth rate equals death rate for each (skin, gut, liver), a measurement of the number of dead cells would reveal the birth rate of new cells. So far, apart from Wilson's assertion regarding dead gut cells, I haven't come across this information.

Conclusion

It is strange to consider that Malthus' Principle Of Population applies at this reductionist level. I hope I have now shown that it is possible to simply, and meaningfully, model the growth of human cell populations in Malthusian terms. Even sub-populations of differentiated cells within a body can be modelled in this way. Of course, all eukaryote life-forms (which excludes bacteria and viruses) grow in the same way, through cell division to produce an adult form and ongoing metabolism. Hence, a similar exponentialist analysis of cell populations would apply to individuals of all species of fungus, plant, animal, or insect.  

Cell populations provide an interesting real-life example of the explosive power of exponential growth, together with an encouraging example of Zero Population Growth in adult individuals within defined limits to growth.

To your health, and a long life!

David Coutts

References

Dawkins, Richard, Climbing Mount Improbable. Penguin. 1996.

Margulis, Lynn; Sagan, Dorion, What Is Life? Simon & Schuster. 1995

Tanner, J.M., Foetus Into Man. 1978, 1989.

Wilson, Robert. The Human Body. 1998

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Send email to exponentialist@optusnet.com.au with questions or comments about this web site.
Copyright 2001 David A. Coutts
Last modified: 08 November, 2009