240
]. S. GRIFFITH
For purposes of exposition, it is convenient to consider such simple
mechanisms as these flip-flops. The actual controls involved in differentiation of mammalian cells may very well be much more complicated, but
certain general features should still be present. There should be a finite
number of stable states for the entire set of controls within the cell, which
means that there is this finite number of different kinds of differentiated cell
altogether in a particular animal. We shall call each of these kinds a "category"
[30], and can say that there are a finite number of categories of nerve cell
which may be enumerated as T 1 , T 2 • •• , Tn.
At this point it may be objected that we have ignored the possibility of
oscillatory solutions to the cellular control equations, and that the existence
of such solutions might invalidate the statement that there are only a finite
number of cell categories. This is true, but probably unimportant. It is
just possible that control systems leading to oscillations may be used by nerve
cells as internal clocks. For example, HORN [32] has found quite regularly
firing cells in cat visual cortex and suggested that this firing may be the
expression of some intrinsic biochemical process within each cell. However,
one would only expect a finite number of different stable oscillations, provided they are of the limit cycle type [39]. GOODWIN has argued that oscillations can occur which have indifferent stability, which would mean the
existence of an infinite number of different possible categories and hence
extra complexity. We shall not consider this possibility here, except to
remark that the equations on which he bases this conclusion are not entirely
satisfactory because they allow the concentrations of cellular constituents,
initially positive, to become sometimes negative [26].
There is a very superficial analogy between the existence of different
categories of nerve cell and the existence of different eigenstates for an
atom. True to this analogy, we can distinguish between spontaneous and
induced transitions between categories. The induced transition of a cell
between two categories, Ti and Tj say, could arise from the passage into
the cell of a suitable repressor. Spontaneous transition could occur if the
number of mRNA or repressor molecules, involved in a control situation,
is small. Random variations in these numbers could occasionally lead to
an "accidental" switching taking place. We would then have a set of
quantities pij (i =1=)), where pij is the probability per unit time that a cell
in category Ti is changed to one in category Tj • There is no reason to
assume that pij = hi'
Different categories would be expected to differ biochemically and also,
probably, morphologically. As I have discussed elsewhere [30], part at
least of the rules governing which pairs of neurons can synapse together
might be expected to depend upon which categories the pair of cells are in.
In this respect it is interesting to note the existence in invertebrates of cells,
identifiable from one individual to another, and having fixed relations of
]. S. GRIFFITH
For purposes of exposition, it is convenient to consider such simple
mechanisms as these flip-flops. The actual controls involved in differentiation of mammalian cells may very well be much more complicated, but
certain general features should still be present. There should be a finite
number of stable states for the entire set of controls within the cell, which
means that there is this finite number of different kinds of differentiated cell
altogether in a particular animal. We shall call each of these kinds a "category"
[30], and can say that there are a finite number of categories of nerve cell
which may be enumerated as T 1 , T 2 • •• , Tn.
At this point it may be objected that we have ignored the possibility of
oscillatory solutions to the cellular control equations, and that the existence
of such solutions might invalidate the statement that there are only a finite
number of cell categories. This is true, but probably unimportant. It is
just possible that control systems leading to oscillations may be used by nerve
cells as internal clocks. For example, HORN [32] has found quite regularly
firing cells in cat visual cortex and suggested that this firing may be the
expression of some intrinsic biochemical process within each cell. However,
one would only expect a finite number of different stable oscillations, provided they are of the limit cycle type [39]. GOODWIN has argued that oscillations can occur which have indifferent stability, which would mean the
existence of an infinite number of different possible categories and hence
extra complexity. We shall not consider this possibility here, except to
remark that the equations on which he bases this conclusion are not entirely
satisfactory because they allow the concentrations of cellular constituents,
initially positive, to become sometimes negative [26].
There is a very superficial analogy between the existence of different
categories of nerve cell and the existence of different eigenstates for an
atom. True to this analogy, we can distinguish between spontaneous and
induced transitions between categories. The induced transition of a cell
between two categories, Ti and Tj say, could arise from the passage into
the cell of a suitable repressor. Spontaneous transition could occur if the
number of mRNA or repressor molecules, involved in a control situation,
is small. Random variations in these numbers could occasionally lead to
an "accidental" switching taking place. We would then have a set of
quantities pij (i =1=)), where pij is the probability per unit time that a cell
in category Ti is changed to one in category Tj • There is no reason to
assume that pij = hi'
Different categories would be expected to differ biochemically and also,
probably, morphologically. As I have discussed elsewhere [30], part at
least of the rules governing which pairs of neurons can synapse together
might be expected to depend upon which categories the pair of cells are in.
In this respect it is interesting to note the existence in invertebrates of cells,
identifiable from one individual to another, and having fixed relations of