J. Paulsson et al., REQUIREMENTS FOR RAPID PLASMID COLE1 COPY NUMBER ADJUSTMENTS - A MATHEMATICAL-MODEL OF INHIBITION MODES AND RNA TURNOVER RATES, Plasmid, 39(3), 1998, pp. 215-234
The random distribution of ColE1 plasmids between the daughter cells a
t sell division introduces large copy number variations. Statistic var
iation associated with limited copy number in single cells also causes
fluctuations to emerge spontaneously during the cell cycle. Efficient
replication control out of steady state is therefore important to tam
e such stochastic effects of small numbers. In the present model, the
dynamic features of copy number control are divided into two parts: fi
rst, how sharply the replication frequency per plasmid responds to cha
nges in the concentration of the plasmid-coded inhibitor, RNA I, and s
econd, how tightly RNA I and plasmid concentrations are coupled. Singl
e (hyperbolic)- and multiple (exponential)-step inhibition mechanisms
are compared out of steady state and it is shown how the response in r
eplication frequency depends on the mode of inhibition. For both mecha
nisms, sensitivity of inhibition is ''bought'' at the expense of a rap
id turnover of a replication preprimer, RNA II. Conventional, single-s
tep, inhibition kinetics gives a sloppy replication control even at hi
gh RNA II turnover rates, whereas multiple-step inhibition has the pot
ential of working with unlimited precision. When plasmid concentration
changes rapidly, RNA I must be degraded rapidly to be ''up to date''
with the change. Adjustment to steady state is drastically impaired wh
en the turnover rate constants of RNA I decrease below certain thresho
lds, but is basically unaffected for a corresponding increase. Several
features of copy number control that are shown to be crucial for the
understanding of ColE1-type plasmids still remain to be experimentally
characterized. It is shown how steady-state properties reflect dynami
cs at the heart of regulation and therefore can be used to discriminat
e between fundamentally different copy number control mechanisms. The
experimental tests of the predictions made require carefully planned a
ssays, and some suggestions for suitable experiments arise naturally f
rom the present work. It is also discussed how the presence of the Rom
protein may affect dynamic dualities of copy number control. (C) 1998
Academic Press.