Fig 7.1

Fig 7.2

The bacteria flagella motor [source: Berg HC, Ann. Rev. Biochem 2003]Fig 7.3

Motors turn CCW

Run Tumble

Motor turns CW

When tethered to a surfacethe entire cell rotates, andIndividual motors show two-state behavior

time

CCW

CW

Fig 7.4 Bacterial runs and tumbles are related to the rotation direction of theflagella motors. When all motors are CCW, the flagella turn in a bundle and cell is propelled. When one or more turn CW, the cell tumbles. Switching Dynamics of a single motor can be seen by tethering a cell to a surface byMeans of its flagellum, so that the motor turns the entire cell body (at frequencies of a few hertz due to the large viscous drag of the body).

10 sec

Tumblingfrequency

1/sec

Time [min]

0 5 10 15 20 250

0.5

1

1.5

Fig 7.5 : Tumbling-frequency of a population of cells exposed at time t= 5to a step addition of saturating attractant (such as L-aspartate). Aftert=5, attractant is uniformly present at constant concentration. Exactadaptation means that the steady-state tumbling-frequency in the presence of attractant Is equal to that in its absence.

Fig 7.6[Alon et al Nature 1999]

Fig 6.7

0 1 2 3 4 5 6 7 8 9 100

5

10

15

0 1 2 3 4 5 6 7 8 9 100

5

10

15

Figure 7.8: Activity dynamics in the fine-tuned model inresponse to a step addition of saturating attractantAt time t=2 (dimensionless units throughout). A) Fine-tuned model showsexact adaptation with a tuned parameter set/ B) Dynamics when CheR levelIs lowered by 20% with respect to fine-tuned parameter set.

A

time

A

time

a( b(

Fig 7.9 Robust mechanism for exact adaptation. Un-methylated receptors are methylated by CheR at a constant rate. Methylated receptors (marked with CH3 groups) transit rapidly between active and inactive states (the former marked with a star). Attractant binding increases the rate to become inactive, whereas repellents increase the rate to become active. De-mthylation is due to CheB, which acts only on the active methylated receptors. The active receptors catalyze the phosphorylation of CheY, leading to tumbles.

0 1 2 3 4 5 6 7 8 9 100

5

10

15

0 1 2 3 4 5 6 7 8 9 100

5

10

15

Fig 7.10: Activity dynamics in the robust model in response to addition of saturating attractant at time t=2. a) model parameters K=10, VR R =1, VB B=2. b) sameparameters with R reduced by 20%. Exact adaptation is preserved,Steady-state tumbling frequency is fine-tuned.

A Aa( b(

time time

Fig 7.11. Experimental test of robustness in chemotaxis. The protein CheR was Expressed at different levels. Adaptation time and steady-state tumbling frequency varied with CheR, whereas adaptation remained exact. Adaptation precision is the ratio of tumbling frequency before and after saturating attractant (1mM aspartate). Wild-type tumbling frequency in this experiment is about 0.4/sec(black dot in b). Source: Alon, Barkai, Surette, Leibler, Nature 1999.