152
B. M. SHAFFER
especially in the latent period before it begins, that they are effectively
asynchronous. But would such cells be in equilibrium?
Consider a single source of an unstable attractor and a stable or relatively stable repellent. The relative concentration gradient of the attractor (its absolute gradient at any point divided by the concentration)
will be greater than that of the repellent at all distances from the source,
and the ratio of the relative gradients will increase with distance. Even
if there is no difference in stability, the same relation will hold if there
is a high background level of repellent, but not of attractor, because of
prior and continuing secretion throughout the culture; for the background will decrease the relative gradient of repellent at all distances,
but its effect will be proportionately smaller nearer the source. If we
make the not too improbable assumptions that attractor and repellent
affect different elements of the surface and may be judged independently,
that the percentage concentration difference of one of them that will
balance any given difference of the other will be related in some measure
to the threshold differences detectable when each of them is experienced
separately at the same concentrations, that these thresholds approach
minimum values as concentration rises, and that during early aggregation the cells are less sensitive to the attractor, then a source making
sufficient attractor and repellent will be surrounded by an inner zone
of repulsion, an outer zone of attraction, and a narrow intermediate
zone in which the gradients are balanced. (If too little attractor is
secreted, there will be only repulsion.) And a cloud of such sources responding to one another will be in dynamic equilibrium following lines
of gradient equivalence, or rather, because of their own finite size and
limited accuracy of orientation, oscillating about these lines. An increase
in acrasin sensitivity, and also to some extent secretion, as the clouds
age, will shift the balance between attraction and repulsion in favour of
the former, and the zones of equivalence will collapse on to the cells.
The marked slowing down that a cell undergoes as it enters a cloud
—in purpureum phasic differences are superimposed—must be due to a
diffusible factor. Possibly this is the repellent itself, for on the simplest
hypothesis, a substance inhibiting cytoplasmic outflow should lower
cell speed if it does directly influence it. If the magnitude of the effect is
determined by concentration rather than gradient, as already suggested
for the attractor, there might be a very complex balance between these
substances; for if the ratio of the relative gradient of attractor to that of
repellent increases with distance from a source of both of them, the ratio
of their concentrations must fall; in addition multiple sources may influence one another's secretion. Against this, Samuel (1961) found that
the repellent apparently did not slow the cells down, although he was
not testing this hypothesis, and the conditions were quite different.
B. M. SHAFFER
especially in the latent period before it begins, that they are effectively
asynchronous. But would such cells be in equilibrium?
Consider a single source of an unstable attractor and a stable or relatively stable repellent. The relative concentration gradient of the attractor (its absolute gradient at any point divided by the concentration)
will be greater than that of the repellent at all distances from the source,
and the ratio of the relative gradients will increase with distance. Even
if there is no difference in stability, the same relation will hold if there
is a high background level of repellent, but not of attractor, because of
prior and continuing secretion throughout the culture; for the background will decrease the relative gradient of repellent at all distances,
but its effect will be proportionately smaller nearer the source. If we
make the not too improbable assumptions that attractor and repellent
affect different elements of the surface and may be judged independently,
that the percentage concentration difference of one of them that will
balance any given difference of the other will be related in some measure
to the threshold differences detectable when each of them is experienced
separately at the same concentrations, that these thresholds approach
minimum values as concentration rises, and that during early aggregation the cells are less sensitive to the attractor, then a source making
sufficient attractor and repellent will be surrounded by an inner zone
of repulsion, an outer zone of attraction, and a narrow intermediate
zone in which the gradients are balanced. (If too little attractor is
secreted, there will be only repulsion.) And a cloud of such sources responding to one another will be in dynamic equilibrium following lines
of gradient equivalence, or rather, because of their own finite size and
limited accuracy of orientation, oscillating about these lines. An increase
in acrasin sensitivity, and also to some extent secretion, as the clouds
age, will shift the balance between attraction and repulsion in favour of
the former, and the zones of equivalence will collapse on to the cells.
The marked slowing down that a cell undergoes as it enters a cloud
—in purpureum phasic differences are superimposed—must be due to a
diffusible factor. Possibly this is the repellent itself, for on the simplest
hypothesis, a substance inhibiting cytoplasmic outflow should lower
cell speed if it does directly influence it. If the magnitude of the effect is
determined by concentration rather than gradient, as already suggested
for the attractor, there might be a very complex balance between these
substances; for if the ratio of the relative gradient of attractor to that of
repellent increases with distance from a source of both of them, the ratio
of their concentrations must fall; in addition multiple sources may influence one another's secretion. Against this, Samuel (1961) found that
the repellent apparently did not slow the cells down, although he was
not testing this hypothesis, and the conditions were quite different.