Figure 1.
Illustration of the multiscale architecture of our unified model.
Environmental signals are sensed by the transmembrane receptor-kinase complexes which controls the level of the intracellular response regulator (CheY-P). The response regulator controls the rotational direction of flagellar motors and the bacterial tumble frequency. Some environmental factors (such as temperature) can also affect bacterial swimming speed and motor switching dynamics. The population distribution of cells is finally shaped by the alternating tumble and swim behaviors.
Figure 2.
The cell density distributions for bacterial chemotaxis.
Different density profiles correspond to different gradients of varying steepness . Symbols represent the experimental data from Ref. [32], whereas lines denote the fitting of our Eq. (7) to the data. We used
,
for MeAsp here.
Figure 3.
Tunability and accuracy of bacterial pH taxis.
(A) The preferred pH versus the logarithm of the Tar/Tsr ratio to base
for three representative parameter regimes:
,
, and
. The red symbols represent the experimental data from Ref. [8] and seem to coincide with the model curve for
. (B) The standard deviations of the cell distributions as a function of
for the three representative parameter regimes:
,
, and
. In the above numerical examples, we have fixed
,
and
.
Figure 4.
Inverted response to temperature changes and bacterial thermotaxis.
(A) The steady-state methylation level subtract the critical methylation level, , and the receptor response to temperature changes,
, as a function of temperature. The critical temperature
is determined by the crossing point where
(or equivalently
). Tar acts as a warm sensor for
and a cold sensor for
, which drives the cells towards
from both sides. (B) The steady-state cell distribution,
, as a function of temperature. For illustrative purposes, we assume that the swimming speed,
, increases linearly with temperature and that the motor dissociation constant is
, with a constant parameter
. Three cases are considered. The red solid line corresponds the case where both
and
are constant; the blue dot-dashed lines is for the case of constant
(i.e.
) and
; the green dashed line is generated by using
and
. Evidently, the steady-state cell distribution can be changed by the temperature dependence of the speed
, but it is insensitive to the temperature dependence of motor sensitivity
. Here, we fix
in all numerical examples. Other parameters used include:
,
,
,
,
,
,
,
,
, and
.
Figure 5.
Comparison between model results and experimental data for E. coli thermotaxis.
The blue symbols represent the cell density data obtained in Ref. [37] at min after applying a shallow temperature gradient
. The black dashed line is the inverse speed profile,
where
is a quadratic fitting to the measured swimming speed in Ref. [37]. The red solid line corresponds to model Eq. (13) with
and
. Other parameters used are the same to those in Fig. 4B.
Figure 6.
The cell density profiles under two opposing chemical and thermal gradients.
The temperature gradient used here is from to
in a channel of length
. Different density profiles correspond to different attractant (MesAsp) gradients
0.0, 3.0, 5.0, and 6.0
but the same concentration at the middle point:
. Other parameters used are the same to those in Fig. 4B.
Figure 7.
Schematic illustration of the effective potential for chemotaxis, pH taxis, and thermotaxis.
In the case of chemotaxis, decreases monotonically as the chemoattractant concentration
increases. For pH taxis,
decreases with pH for Tsr-only mutant cells and increase with pH for Tar-only mutant. Based on the push-pull mechanism,
for the wild-type E. coli represents the balancing effect between Tar and Tsr, leading to a local minimum in the effective potential. In the case of thermotaxis,
can be shifted by the effect of temperature-dependent swimming speed
. It is, however, insensitive to other temperature effects such as the temperature dependence of motor response,
, parameterized by
.