line with direct experimental comparison of AcrB-GFP levels pre- and postdivision in mothers and
daughters (Fig. 1E). In contrast, cytosolic mCherry
expressed in the same cells (fig. S19) and AcrB-GFP in DtolC cells were very close to q = 0.5.
This simple model captured two experimentally
determined long–time scale features of AcrB-GFP
data: the steady-state level and the time scale of
accumulation in the mother cell (Fig. 4, C and D).
Furthermore, our model made a parameter-free
prediction for the AcrB-GFP decay time scale in
the pulse-chase experiment in agreement with data
(Fig. 4E). For random partition, the steady-state
distribution of AcrAB-TolC across an exponential-
ly growing population would be approximately
Gaussian (Fig. 4F). As partitioning bias q increases,
the distribution widens and develops a rightward
skew with a growing overrepresentation of cells
with high-efflux capacities (e.g., in our data, we
expect about a sixfold enrichment of cells with
efflux levels in the top 1% class relative to the un-
biased partition expectation). This increase in pop-
ulation heterogeneity due to enrichment in extreme
phenotypes is the first generic consequence of
biased partitioning predicted by our model. The
second consequence is the emergence of a new
time scale exceeding the generation time [by a
factor of log(0.5)/log(q*) 1.4 here] (Fig. 4, C and
E) on which multidrug efflux phenotypes form,
persist, and change. Importantly, biased partition-
ing generates long-lived heterogeneity without
specialized regulatory mechanisms (19, 20).
Our experiments at subinhibitory antibiotic
concentrations uncovered long-lived single-cell
growth phenotypes that arise by biased parti-
tioning of AcrAB-TolC. Recent work suggests
that at low antibiotic concentrations, de novo
resistance mutations can readily emerge on short
time scales (18). Because selection can act on in-
dividual cell lineages in bacterial populations (21),
small-effect mutations such as gene amplifica-
tions (22) might be specifically selected for in
fast-growing lineages. Selection might be par-
ticularly strong in environments with low or
fluctuating antibiotic concentrations, which in-
creasingly occur in natural habitats as a result of
human activity (23) and within patients during
drug treatment (24). Notably, the acrAB locus
was found to be amplified in low or intermediate
antibiotic selection regimes (25), leading to high
levels of efflux-based antibiotic resistance. Multi-
drug efflux-mediated growth heterogeneity could
serve as a stepping-stone on the path of bacterial
populations toward antibiotic resistance.
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314 21 APRIL 2017 • VOL 356 ISSUE 6335 sciencemag.org SCIENCE
Fig. 4. Model of biased partitioning predicts long accumulation time
scale and large population heterogeneity. (A) Model schematic: average
fluorescence in generation (g + 1), fg+1, is given by biased binomial partition (with
bias q) of fluorescence in generation g, fg, and symmetric partition of newly expressed protein, expressed at rate 2l. (B) Bias q for individual lineages (dots) in
AcrB-GFP and DtolC. Line and envelope, mean ± SD over lineages. (C) Average
AcrB-GFP fluorescence in mother cells (blue line, mean; envelope, mean ± 1 SE).
Red, model prediction with q* from (B); light red, hypothetical prediction for larger
bias, q = 0.7; dark red, prediction for symmetric partition, q = 0.5. (D) Measured
versus predicted steady-state AcrB-GFP fluorescence for individual lineages
(dots), using q values from (B). (E) Decay of fluorescence in pulse-chase ex-
periment from start of “chase” to dashed line of Fig. 1F (solid blue, ArcB-GFP;
empty blue, cytosolic GFP) and parameter-free predictions using q* for AcrB-
GFP and q = 0.5 for cytosolic GFP. Inset shows the match between the
measured and predicted ratio of decay to generation time scale [tg = T/log(2)],
with T the mean doubling time). (F) Predicted steady-state distributions of
efflux phenotypes in growing populations for three values of bias q; increase in
q beyond unbiased partition (q = 0.5) leads to rightward skew.