Quantitative Resolution to some ”Absolute Discrepancies” in
Cancer Theories
a View from Phage lambda Genetic Switch
Ping Ao
Department of Mechanical Engineering and Department of Physics
University of Washington, Seattle, WA 98195, USA
(Dated: April 3 (2007))
Abstract
Is it possible to understand cancer? Or more specifically, is it possible to understand cancer
from genetic side? There already many answers in literature. The most optimistic one has claimed
that it is mission-possible. Duesberg and his colleagues reviewed the impressive amount of research
results on cancer accumulated over 100 years. It confirms the a general opinion that considering
all available experimental results and clinical observations there is no cancer theory without major
difficulties, including the prevailing gene-based cancer theories. They have then listed 9 ”absolute
discrepancies” for such cancer theory. In this letter the quantitative evidence against one of their
major reasons for dismissing mutation cancer theory, by both in vivo experiment and a first prin-
ciple computation, is explicitly pointed out.
To cite: P. Ao, 2007, Orders of magnitude change in phenotype rate caused by mutation,
Cellular Oncology 29: 67 - 69.
http://arxiv.org/abs/0704.0429v1
In a forceful article Duesberg and his colleagues (2005) reviewed the impressive amount
of research results on cancer accumulated over 100 years. It confirms the current conclu-
sion that considering all available experimental results and clinical observations there is no
cancer theory without major difficulties, including the prevailing gene-based cancer theories
(Hanahan and Weinberg 2000; Prehn 2002; Vogelstein and Kinzler 2004; Beckman and Loeb
2005). Phrasing differently, any known cancer theory is refutable to a substantial degree.
While the support for their own advocated chromosomal cancer theory appears strong, it
seems that their wholesale criticism on mutation cancer theory is premature. In this letter
the quantitative evidence against one of their major reasons for dismissing mutation cancer
theory, by both in vivo experiment and a first principle computation, is explicitly pointed
Duesberg et al (2005) listed 9 ”absolute discrepancies” or questions which they believe
the mutation cancer theory cannot answer:
”(1) How would non-mutagenic carcinogens cause cancer?
(2) What kind of mutation would cause cancer only after delays of several decades and many
cell generations?
(3) What kind of mutation would alter the phenotype of mutant cells perpetually, despite
the absence of further mutagens?
(4) What kind of mutation would be able to alter phenotypes at rates that exceed conven-
tional gene mutations 4-11 orders of magnitude?
(5) What kind of mutation would generate resistance against many more drugs than the one
used to select it?
(6) What kind of mutations would change the cellular and nuclear morphologies several-fold
within the same ”clonal” cancer?
(7) What kind of mutation would alter the expressions and metabolic activities of 1000s of
genes, which is the hallmark of cancer cells?
(8) What kind of mutation would consistently coincide with aneuploidy, although conven-
tional gene mutations generate infinite numbers of new phenotypes without altering the
karyotype?
(9) Why would cancer not be heritable via conventional mutations by conventional
Mendelian genetics?”
Evidently those important questions should be considered seriously by any cancer re-
searcher. There are, however, two general reasons that the temporally inability to address
them is not enough to dismiss mutation cancer theory. First, in many situations whether
the effects are the causes or the consequences, or mutual causes to each other, are still
poorly understood, though their associations with cancers may be obvious. The clarification
of such confusing requires further and more experimental and clinical studies. Such efforts
have been carrying out, for example, by Weiss et al (2004), Hermsen et al (2005), Weber et
al (2006); Bielas et al (2006), Levitus et al (2006), and Sjoblom et al (2006).
Second, the absence of an explanation or of a theory is not a proof that it would not
ever exist. If there were already enough amount of consistent experimental and clinical ob-
servations, the emergence of a theory would be simply a matter of time. It is a test to our
creativity and imagination. Therefore, those ”absolute discrepancies” are logically not nec-
essarily against the mutation cancer theory. Having given a ”dodged” defense, here I would
like to call the attention to one evidence specifically addressing above 4th discrepancy: ”(4)
What kind of mutation would be able to alter phenotypes at rates that exceed conventional
gene mutations 4-11 orders of magnitude?” The question (4) can be answered by mutation
cancer theory in a quantitative and first principle manner. The quantitative evidence also
suggests answers to questions (1) and (2) of Duesberg et al.
In the phage lambda system, a bio-system arguably started the modern molecular biology
(Cairns et al 1992), extensive and quantitative experiments have demonstrated that simple
mutations can cause the change in phenotypes over many orders of magnitude (Ptashne
2004; Oppenheim et al 2005). The phenotype easily accessible to experimental study is the
switching between lysogenic and lytic states. It is generally known that a mutation in the
DNA binding sites can cause more than 100 and more folds change in the switching rate,
controlled by a few base pairs in the genomic sequences (Revet et al 1999; Little et al 1999;
Dodd et al 2005). Systematic study showed that at least over 8 orders of magnitude change
can be observed among mutants. A quantitative study is summarized in Table I.
Phage lambda genotype λ+ (λ+OR321, wild) λ
OR3’23’ λ
OR121 λ
OR323 λ
OR123
Switching rate (exper) 2× 10−9 5× 10−7 3× 10−6 2× 10−5 ∞
Switching rate (theor) 1× 10−9 1× 10−7 3× 10−6 7× 10−5 ∞
Table I: This table is based on Zhu et al (2004, 2006). There are 5 different phage lambda
phenotypes, including the ”wild type”, which have been systematic studied experimentally
(Little et al 1999). The switching rate is the probability to switch from lysogenic to lytic
states per minute under normal lab condition. The symbol ? indicates that there is no
stable lysogenic state, that is, the phage lambda would immediately switch to lytic state.
The switching rate is then ”infinite”.
Quantitative answer to ”absolute discrepancy” 4:
The point should be emphasized is that the mathematical calculation is based on first prin-
ciple modelling without ”free” parameters. What the ”first principle” means is that the
interaction between involved proteins and the protein-DNA binding are based on carefully
reasoned physical, chemical and biological principles during past 40 years. What the ”pa-
rameter free” means is that all the kinetic parameters needed for the mathematical modelling
have been fixed by other experiments. Thus, the remarkable consistency over at least 8 or-
ders of magnitude between the experimental data and mathematical calculation shows that
it is unlikely due to artifacts in experiment and/or in modelling. Because such effect can
occur in phage lambda, there is no reason that same thing cannot occur in higher organisms
(Ptashne and Gann, 2002): Numerous gene regulatory sites similar to that of phage lambda
exist in our human genome and wrong switching in gene regulatory network is generally
believed to contribute to cancer. Therefore, the answer to the question (4) of Duesberg et
al based on mutation cancer theory is already positive.
Quantitative answer to ”absolute discrepancy” 2:
The viability of various mutants, some can live up to thousands of generations before going to
lytic state to kill its host E. coli, suggests that there can be a long delay in the manifestation
in phenotypes after a mutation. Such a gene regulatory example hence directly answers the
question (2) of Duesberg et al.
Quantitative answer to ”absolute discrepancy” 1:
In addition, it is known that the stability of lambda genetic switch can be influenced both
chemically and physically, without any mutagenic effect (Ptashne 2004; Zhu et al 2004),
that is, non-mutagenic agents can cause the switch from lysogenic to lytic states, therefore
changes the an otherwise robust phenotype. This fact suggests itself as an answer to the
question (1) of Duesberg et al.
To summarize, though whether chromosomal or mutation cancer theory, or both , are
the candidates for the cancer theory is too early to call, Duesberg et al is premature to
write out the mutation cancer theory. Even if neither were the final cancer theory, both
already appear clinically relevant (Meijer, 2005) and should be studied thoroughly. Finally,
I would like to venture a challenge to my fellow quantitative modelers: Is it possible to
address all those ”absolute discrepancy” quantitatively? I believe you can do better than
what presented here.
I thank R. Prehn and L. Loeb for stimulating discussions. This work was supported in
part by US National Institutes of Health under grant number HG002894.
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	References

  Is it possible to understand cancer? Or more specifically, is it possible to
understand cancer from genetic side? There already many answers in literature.
The most optimistic one has claimed that it is mission-possible. Duesberg and
his colleagues reviewed the impressive amount of research results on cancer
accumulated over 100 years. It confirms the a general opinion that considering
all available experimental results and clinical observations there is no cancer
theory without major difficulties, including the prevailing gene-based cancer
theories. They have then listed 9 "absolute discrepancies" for such cancer
theory. In this letter the quantitative evidence against one of their major
reasons for dismissing mutation cancer theory, by both in vivo experiment and a
first principle computation, is explicitly pointed out.

Introduction to Systems Biology (Humana Press, 2007).
( http://arxiv.org/ftp/q-bio/papers/0512/0512007.pdf )
http://arxiv.org/ftp/q-bio/papers/0512/0512007.pdf
[22] Ao P, 2007, Orders of magnitude change in phenotype rate caused by mutation, Cellular
Oncology 29: 67 - 69
	References
