Ontogeny & Phylogeny: IV. Phage lambda again.

Xuhua Xia xia at cc.umanitoba.ca
Wed Apr 27 22:43:49 EST 1994

                   Ontogeny and Phylogeny IV:
                       Phage Lambda Again

In this posting we will begin to lay down the ontogenic chain of
the phage lambda. To do so, and for review purpose, let us first
have an analog.

When you are to write a complicated computer program, you first
draft a flowchart with physical loops, branches, and what not. Then
you write your program according to the flowchart. The finished
program is a linear array of computer codes, no longer containing
physical loops and branches. If someone else pirates the source
code of this program from you and wants to find out what the
program does, he will try to reconstruct the flowchart that
originally leads to the program. He can claim to understand the
program once the flowchart has been reconstructed.

Now a genetic program does not seem to be very different from a
computer program. It also is made of a linear array of genetic
codes, with no physical loops and branches. To understand how this
program will guide the development of an organism, we need to
"reconstruct" the underlying flowchart with loops and branches and
all that. In case you forget, such a flowchart is what we have
termed an ontogenic chain.

Obviously, such a reconstruction of a genetic flowchart is no easy
job, and it is for reducing our work load that I have deferred
discussion of the vertebrate head in favour of the phage lambda. I
have mentioned before that developmental biology deals with
differential expression of genes during ontogeny. Such differnetial
expression can occur both spatially and temporally. For example,
the sonic hedgehog gene is expressed only in the posterior of the
vertebrate limb but not in any other places in the limb. In
addition, its expression is hardly detectable before stage 17 in
the chick embryo, but the expression increases in latter stages and
eventually fades away again. If we indulged ourselves with the
development of multicellular organisms, we would have to deal with
something that changes both spatially and temporally. This implies
that we have to deal with frustrating, and often unsolvable,
partial differential equations.

For phage lambda, we will only concern ourselves only with the
temporal dimension. So ordinary differnetial equation will mostly
be sufficient for our purpose.

Let us now make an intelligent guess as to the beginning of the
genetic flowchart of phage lambda. What should the creature do
after its DNA has been injected into a host bacterium and takes up
its typical circular form?

The most obvious guess is that the phage DNA should replicate
itself because the fitness (i.e., the propensity of future
survival) of the phage ultimately depends on the number of copies
of packaged phage DNA.

Such a guess may be thought to be trivial, but it is not. There are
50 or so genes in the phage DNA, including a number of genes that
make the head proteins and a number of genes that make the tail
proteins. Why should not the genes for the head and tail proteins
be expressed first? It is optimality models that allow us to
predict, a priori, that head and tail proteins should not be made
before DNA replication because otherwise it would be like buying
many gift wrappers without buying any gift.

(I should memtion that Darwinian theory of evolution, with its
conclusion that all organisms in nature should evolve towards
maximizing fitness under natural selection, is essentially a
justification for the use of optimality models in biology. I have
heard molecular biologists claiming repeatedly that Darwin has no
place in molecular biology. Yet what explanatory power can
optimality models have without natural selection?)

It turns out that our first guess that phage DNA replication should
take place first is almost perfectly right. First, genes O, P and
cro are among the first phage genes to be transcribed. Second, a
small fragment of the lambda genome, carrying only O, P, the
replication origin region, the promoter pR (italic p with subscript
R), and the cro gene, replicates autonomously as a plasmid (from
Lambda II, p. 145).

(Here we see that the ontogenic chain of phage lambda is longer
than that of a plasmid, which gives us a hint that either phage
lambda has evolved from plasmid by true "terminal addition", or
plasmids have evolved from phages by terminal deletion.)

Now we see that the function of the first subprogram of the phage
genetic program is to make a duplicated copy of itself. It is like
a computer program that reads in the program file and write out an
identical copy. We can name this first subprogram of the phage
genetic program as "Replication Subprogram".

The rest of this posting deals only with this subprogram.

Now this Replication Subprogram is quite tricky. We learned that
there are two ways to replicate phage DNA: one employing the Cairns
(theta) form and the other using the rolling circle (sigma) form.
Now we have to find out the conditional branching in the phage
genetic subprogram. Under what condition should the theta form be
used and under what condition should the rolling circle form be

(If you are a serious reader, you should find out the difference
between replication by the theta form and replication by the
rolling circle form. There is no point for me to copy readily
available books and create traffic jam in the network.)

The replication by the theta form generates phage DNA that is
identical to its "parental" copy, i.e., a circle, which can
continue to replicate like its "parent". The rate of increase in
number (N) of the circular phage DNA, in its simpliest form, can be
written as

     -- = R1 * N                                  [1]

The replication by the rolling circle form generates cancatenated
phage DNA. The rate of increase in number of concatenated phage DNA
(Nc) is

     --- = N0 * R2                                [2]

where N0 is the number of circular phage DNA that begin to
replicate by rolling-circle form.

We see that N does not appear on the right side of Equation [2]
because the rolling-circle generates copies of concatenated phage
DNA which cannot become rolling circles themselves.

We can predict when the theta form should be used and when the
rolling circle should be used by the phage based on Equations [1]
and [2]. If R1 > R2, then the rolling circle should never be used
because R1 * N > N0 * R2. However, if R2 > R1, then replication by
the rolling circle form can be more efficient in a short period.
For example, when the number of phage DNA reached N(T) at time T
and all these N(T) copies switch to replication by the rolling
circle, then N0 in Equation [2] equals N(T). The instantaneous rate
of increase by rolling circle form would be N(T) * R2, which is
greater than N(T) * R1, given R2 > R1. The advantage for the
rollling circle form can last for only a short time because the
rate of increase in Equation [2] is fixed whereas the rate in
Equation [1] increases with N.

This short-term advantage is like the last sprint in a long-
distance race. Even without mathematics we can infer that the
rolling-circle can only be used during the last leg of DNA
replication. It turns out that our inference is correct. The phage
does replicate first with the theta form, and the rolling circle is
used during the late phage of DNA replication.

So far we have reasoned in a way that has been labelled as
adaptationist programme which was eloquently criticized by Stephen
Jay Gould and Richard Lewontin. Will such adaptationist thinking
carry us to something solid? Have we rationalized too prematurely
the observation "theta form first and rolling circle last"? Why
couldn't the rolling circle have evolved for purposes other than

Don't expect me for an answer, but we will find out as we go along.

(to be continued)

Xuhua Xia
University of Manitoba
xia at ccu.umanitoba.ca

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