Rate of cancer occurrence with age

R. M. C rmc at netcom.com
Fri Jun 24 17:11:39 EST 1994

Cathy Woodgold (woodgold at seismo.emr.ca) wrote:
: In article 3so at nwfocus.wa.com, venezia at zgi.com (Domenick Venezia) writes:
: >... Bruce Ames says that cancer goes up with the fifth power of
: > age.  Bottom line: if you live long enough cancer will get you.  But I am
: > not sure that it follows that if we extend life through telomeric extension,
: > i.e., the suppression of cellular senescence, that the occurrance of cancer 
: > would follow the same power function.  We need to think about why cancer
: > increases with age.  Is it that we are generating more replication errors
: > with age?  ...
: > What does TISSATAAFL stand for or mean?

: From this discussion, and from thinking about it, I've gotten a better
: understanding, I think, of what cancer is and of why we die of old age.
: Although I still intend to live as long as I can, these thoughts have
: made me more accepting of my own eventual death.  My father once said
: to me that having children was nature's way of getting a fresh start with
: healthy organs and now I'm thinking along those lines.  Of course, it's still
: a good idea to try NOT to die.

: Anyway, this is the way I think cancer works.  In order for a cell to become
: cancerous, it must overcome about five hurdles.  These include:  beginning
: to produce the substance that induces blood vessels to grow into a tumour;
: producing a substance that dissolves the intercellular substance, allowing
: the cells room to grow; producing telomerase so growth is no longer limited
: by the length of the telomeres; and other things, I suppose.  Each of these
: hurdles can be overcome by turning on (or off) certain genes that we already
: have in each of our cells.  These genes are needed at certain times for
: normal development, or are needed by specific kinds of cells in the body,
: so they're part of the human genome.  Accidentally turning on a gene is
: relatively easy to do ... a lot easier than spontaneously mutating a
: gene into something new and useful, for example.  However, it's not terribly
: easy;  the vast majority of our cells don't become cancerous.  There are
: controls that normally prevent a gene from accidentally turning on.

: I call a cell precancerous if it's overcome one or more of the hurdles, other
: than correctly using the genes during normal development.

: Lemma 1.  Everybody has lots of precancerous cells.  Evidence:  In Cancer
: and Vitamin C, the authors mention some autopsies that were done on people
: who died of things other than cancer, and said that it was very common for
: people to have cancers they didn't know about while they were alive.
: These cancers didn't seem to bother them.  So lots of people have full-fledged
: or almost full-fledged cancer;  there must be a much greater number of
: people who have cells that have overcome at least one of the hurdles.
: A bit of math makes this clear.  Maybe I'll explain further down.

: Lemma 2.  A fertilized egg that's going to develop into a live baby is
: neither cancerous nor precancerous.  Argument:  In order to develop into a
: live baby, the fetus must develop fairly normally ... have a heart that
: really beats, etc.  In order to develop fairly normally, each of the
: "hurdles" to cancer is used individually in various ways.  For example, blood
: vessels must be induced to grow a certain amount but not too much.
: For example, if all the embryo's cells were busy dissolving the intercellular
: substance, a normal fetus would not take shape.   Another argument:
: the fertilized egg is a totally undifferentiated cell.  Perhaps this
: means all its genes are turned on.  As it develops into a fetus,
: various cells have some genes turned on or off as appropriate, by some
: mechanism(s).  So almost by definition, the fertilized egg can't have
: genes that are inappropriately turned on.  Perhaps as the embryo 
: develops, cells with certain genes turned on simply gravitate towards
: the part of the body where such genes are appropriate.

: Lemma 3.  Cancer occurs with a rate of about the fifth power of age.
: Argument:  Suppose that "mistakes" that accidentally turn on genes that
: overcome the "hurdles" to cancer occur at a constant rate.

: N1 = R1 * NB * t

: N1  number of cells that have overcome hurdle 1
: R1  rate at which hurdle 1 occurs
: NB  number of cells in body
: t   time (i.e. age of individual, from conception)

: Suppose the "mistakes" occur randomly.  That is, a cell that has overcome
: one hurdle is neither more nor less likely to overcome another hurdle than
: a normal cell.

: N12 = (N1 * N2) / NB

: N12  number of cells that have overcome both hurdle 1 and hurdle 2
: N2   number of cells that have overcome hurdle 2

: N12345 = (N1 * N2 * N3 * N4 * N5) / NB ** 4

: N12345  estimated number of cells that have overcome all 5 hurdles
: **      exponentiation

: Substituting,

: N12345 = (R1*NB*t) * (R2*NB*t) * (R3*NB*t) * (R4*NB*t) * (R5*NB*t)/NB ** 4

:        = (R1 * R2 * R3 * R4 * R5) * NB * (t ** 5)

: When N12345 is a lot less than 1, one assumes the person doesn't have
: cancer.  When it's 1 or more, there's probably a cancerous cell, which
: will then begin dividing and the number of cancerous cells will increase
: rapidly, no longer constrained by the above equation.
:     This shows that cancer goes up with the fifth power of age;  that it goes
: up linearly with the number of cells in the body;  and that it depends, of
: course, on the rates of various cells overcoming various hurdles.  Was Bruce
: Ames' statment about the fifth power of age based on a similar argument,
: or was it backed up with experimental evidence?
:      We can reduce our cancer rate by reducing the rates of cells overcoming
: the various hurdles.  We can do this by:  avoiding radiation;  avoiding
: pollution or dangerous chemicals;  reducing pollution in the environment
: and in our food;  taking antioxidants.  Women can reduce their rate of
: breast cancer by:  not taking birth control pills;  not having abortions;
: and breastfeeding their children, if they have any.  (There are natural
: birth control methods now with lower pregnancy rates than the Pill.)
:    In all this, I've totally ignored the role of the immune system in
: controlling cancer.  It's extremely important;  lots and lots of cancerous
: cells are destroyed by the immune system.  I don't know why it fails sometimes.
: Perhaps the main mechanism of vitamin C in controlling cancer is by
: allowing the immune system to work.  Perhaps one of the "hurdles" that
: cancer overcomes is developing a way to dodge the immune system.

: Cathy             TISSATAAFL

How about the gene repair mechanisms, which should be taken into 
account.  Look at unicellular organisms such as chlorella and yeasts.  
They have lived for billions of years and are ageless.  May be we should 
start with simple models such as these.

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