Abstract
Networks of interacting proteins orchestrate the responses of living cells to a variety of external stimuli1, but how sensitive is the functioning of these protein networks to variations in theirbiochemical parameters? One possibility is that to achieve appropriate function, the reaction rate constants and enzyme concentrations need to be adjusted in a precise manner, and any deviation from these 'fine-tuned' values ruins the network's performance. An alternative possibility is that key properties of biochemical networks are robust2; that is, they are insensitive to the precise values of the biochemical parameters. Here we address this issue in experiments using chemotaxis of Escherichia coli, one of the best-characterized sensory systems3,4. We focus on how response and adaptation to attractant signals vary with systematic changes in the intracellular concentration of the components of the chemotaxis network. We find that some properties, such as steady-state behaviour and adaptation time, show strong variations in response to varying protein concentrations. In contrast, the precision of adaptation is robust and does not vary with the protein concentrations. This is consistent with a recently proposed molecular mechanism for exact adaptation, where robustness is a direct consequence of the network's architecture2.
The E. coli chemotaxis system3,4 has emerged as a prototype for understanding how processes at the network level arise from interactions between individual components5,6. The protein network responsible for chemotaxis has been characterized in detail3,4 (Box 1). This sensory network governs the migration of bacteria towards chemical attractants and away from repellents by translating temporal changes in the level of chemical stimuli into a modulation of the cell's swimming direction. This is achieved bycontrolling the frequency of abrupt direction changes called tumbles. An important feature of chemotaxis is exact adaptation: achange in the concentration of a chemical stimulant induces a rapid change in the bacteria's tumbling frequency, which gradually adapts back precisely to its pre-stimulus value7,8.
Once the components of a biochemical network are isolated and their interactions characterized, the mechanisms of the network's functioning can be addressed. Here, we focus on a distinct, complementary aspect, namely the sensitivity of the network's functioning to variations in its biochemical parameters. Specifically, we ask how sensitive exact adaptation in chemotaxis is to variations in the concentration of proteins in the network. Several theoretical proposals for the molecular mechanism of adaptation5,9, 10, 11 required that the biochemical parameters of the chemotaxis network have to be fine-tuned to obtain exact adaptation. Deviations of the parameters from their fine-tuned values would result only in partial adaptation. In contrast, a recent analysis2, based on a two-state model of chemoreceptors3,12, proposed that exact adaptation is a robust property of chemotaxis. That is, the ability of the bacteria to adapt precisely would survive substantial variations in any of the biochemical parameters of the network.
To differentiate between the fine-tuned and robust scenarios, we systematically varied the concentrations of the chemotaxis-network proteins, and measured the resulting behaviour. Similar methods have been used in analyses of metabolic pathways13. The tumbling frequency, averaged over a population of swimming cells, was measured using a video microscopy image-analysis system14. Cells were stimulated by addition of a saturating amount of attractant (1 mM L-aspartate), and their behaviour was compared with that of unstimulated cells (Fig. 1). The cells responded to the attractant by suppressing tumbling. The tumbling frequency then increased as the cells adapted, with a characteristic adaptation time, reaching a new steady state. The adaptation precision, P, was defined as the ratio between the steady-state tumbling frequency of unstimulated and stimulated cells: wild-type cells showed exact adaptation7,8,15 (P = 0.98 
0.05, mean standard deviation (s.d.)). The same degree of adaptation precision was also found for other attractants and repellents (1 mM L-serine, 50 mM L-leucine, data not shown. Note, however, that a lower steady-state tumbling frequency was reported15 in the presence of L-serine than in its absence under different buffer conditions).
Figure 1: Tumbling frequency as a function of time for wild-type (RP437) cells.
Circles: cells stimulated at time t = 0 by mixing with saturating attractant (1 mM L-aspartate). Squares: unstimulated cells (mock-mixed with chemotaxis buffer). Tumbling frequency was determined using computerized video tracking14. Each point represents data from 10 s motion of 100–400 cells. The adaptation time wasdefined as the time where the tumbling frequency of stimulated cells rises to halfway between its earliest measured value and its steady-state value. Precision of adaptation was defined as the ratio between the steady-state tumbling frequency of unstimulated cells (full horizontal line) and stimulated cells (dashed horizontal line).
High resolution image and legend (34K)One of the key proteins in the adaptation mechanism3,4 is CheR, which is responsible for chemoreceptor methylation (Box 1). A strain deleted for cheR did not tumble and could not adapt (Fig.2). Tumbling was restored by CheR expression under a lac promoter from a low-copy plasmid. Intracellular CheR concentrations were varied, over a range of 
100-fold, by induction with different amounts of isopropyl-
-D-thiogalactoside (IPTG), and the average CheR concentration was quantitated by immunoblots. The initial smooth swimming response of the cells to attractant (<0.05 tumbles per s) was followed by adaptation. As CheR was varied between 0.4 and 6 times wild-type concentration, the adaptation time, 
, varied more than 20-fold, from 23 2 min to 1 min (Fig.2b). Similarly, the steady-state tumbling frequency, f, increased by about threefold. This is consistent qualitatively with model predictions2 where 1/[CheR] and f increases with the intracellular CheR concentration [CheR]. The tumbling frequency saturated at about 0.75 tumbles per s at the highest concentration of CheR attained (about 50 times the wild-type concentration). Throughout these variations, adaptation remained precise to within experimental error (Fig. 2a).
Figure 2: Chemotaxis behaviour of cells with varying intracellular concentration of the protein CheR.
CheR was expressed from the plasmid pUA4 with varying levels of IPTG induction in a strain deleted for cheR (RP4968). a, Precision of adaptation, defined as the ratio between the steady-state tumbling frequency of unstimulated cells and cells stimulated with 1 mM L-aspartate. A precision of 1.0 corresponds to exact adaptation. Cells lacking CheR (RP4968 with the control vector pHSG575, triangle) did not respond to attractants, but showed a persistent response of about 0.6 tumbles per s to repellent (50 mM L-leucine). b, Average steady-state tumbling frequency of unstimulated cells (open squares, right scale), and average adaptation time to a step-like stimulation with 1 mM L-aspartate (open circles, left scale). Solid circle, wild-type strain (RP437 + pHSG575). Triangle, tumbling frequency of RP4968 + pHSG575. Lines are guides to the eye. Relative CheR expression was measured by immunoblots. 'Wild-type' CheR concentration was defined as the induction level where the adaptation time was equal to that of RP437 + pHSG575. Immunoblots also showed that the level of other chemotaxis proteins (CheB and CheY) did not vary measurably with CheR expression. Errors in relative CheR level are estimated to be under 30%. Mean and standard deviation of triplicate experiments are shown.
High resolution image and legend (31K)Similar results were obtained when the concentrations of the other proteins in the network were varied (Table 1). The steady-state tumbling frequency was affected by changes in concentration of these proteins, in qualitative agreement with previous studies16, 17, 18, 19. For instance, an increase in the concentration of CheB, the receptor-demethylating enzyme (Box 1), caused a decrease in tumbling frequency and an increase in adaptation time. Loss of CheZ resulted in increased tumbling frequency, and the initial response to stimulation was a reduction in the tumbling frequency to about half of its adapted value, rather than to <0.05 tumbles per s as in the wild-type strain. This can be explained by the greatly reduced rate of CheY dephosphorylation in the absence of CheZ. Both tumbling frequency and adaptation time were modified upon simultaneous overexpression of the entire meche operon (encoding Tar, Tap, CheR, CheB, CheY and CheZ) from a plasmid. Strikingly, exact adaptation was observed for all of these perturbed networks (Table1), which is consistent with the predictions of the robust-adaptation model2.
To probe the mechanism for exact adaptation further, we used anactivated mutant of CheB, CheBc, which can demethylate the receptors but lacks the domain phosphorylated by CheA20,21. This mutant lacks the feedback loop that was often thought to be responsible for exact adaptation4,10,11. In this feedback loop, the receptor-controlled kinase, CheA, phosphorylates CheB, increasing the demethylation of the receptors and thereby downregulating its own activity (Box 1). We find that cells deleted for CheB on the chromosome, but which express CheBc, show response and exact adaptation to attractant stimuli (Table 1). This seems to exclude CheB phosphorylation as the mechanism of exact adaptation, although it may be important in other aspects of chemotaxis19,20. In this context, the postulated molecular mechanism that leads to robust exact adaptation, analysed in ref. 2, is not based on the phosphorylation feedback loop. The crux of this mechanism is a different type of feedback in which CheB demethylates receptors only when they are in their active conformation2,3,12.
The present results show that exact adaptation is maintained despite substantial variations in the network-protein concentrations. Why is adaptation precision a robust property, whereas properties such as adaptation time and steady-state behaviour are sensitive to variations in biochemical parameters? It is tempting to argue that properties that are critical to the functioning of the network are selected to be robust so that they can withstand natural variations. There is indeed some evidence that exact adaptation is important in the sensory process. It allows the system to compensate for the presence of continued stimulation, and to be ready to respond to further stimuli. Mutant bacteria that show only partial adaptation (strains deleted for both cheR and cheB22, 23, 24) are severely deficient in chemotaxis, as assayed by their net motion in attractant gradients24,25, despite the fact that their steady-state tumbling frequency is close to that of the wild-type strain. In contrast, strains that have normal adaptation, but tumbling frequencies different from wild type, show chemotaxis ability that is comparable to the wild-type strain26. We confirmed this result using the present strains with varying CheR concentrations (data not shown). Furthermore, exact adaptation is found in other bacteria such as Bacillus subtilis27 and Rhodobacter sphaeroides28. These results suggest that exact adaptation is critical for chemotaxis, whereas chemotaxis ability is not dependent on the precise value of the steady-state tumbling frequency and the adaptation time. Exact adaptation might also be a 'side effect' of the mechanism for a different, critical aspect of chemotaxis (for example, the amplification or gain of the system6,22), and as such could be selected as a robust property.
The experimental approach presented here can be generalized to other biochemical or genetic networks. For a given network, those functional properties that are robust, and those that are sensitive with respect to parameter variations could be classified. It would then be interesting to see whether any 'design principles' connected with robustness, perhaps analogous to those used in engineering, emerge from such systematic studies.
Methods
Bacterial strains and plasmids. All strains were derivatives of E. coli K12 strain RP437 [thr leu his metF eda rpsL thi ara lacY xyl tonA tsx], which is wild type for chemotaxis16. pUA4 was constructed by subcloning an XbaI–HindIII fragment of pME1 (ref. 29) containing cheR from S. typhimurium and the EcoRI-SbaI fragment of pUC054 (ref. 30) containing lacIq into the low-copy vector pHSG575 (ref. 14). An EcoRI–HindIII fragment of pME30 (ref. 29) containing cheB from S. typhimurium was subcloned into pBAD18 (ref. 14) to yield pUA3. Similar results were obtained with cells expressing E. coli CheR and CheB from the plasmids p43:cheR (ref. 18) and p43:cheB (ref. 18). Other plasmids are listed in Table 1.
Behavioural assays. Cultures, grown overnight at 30 °C in Tryptone broth14 with selective antibiotics, were diluted 1:50 into 20 ml Tryptone broth in 125-ml flasks, shaken at 200 r.p.m. at 30 °C, induced after 2 h and collected at A600 = 0.5 (5 
108 cells ml-1). Cells were washed twice at 800g into chemotaxis buffer14 (7.6 mM (NH4)2, 2 mM MgSO4, 20 
M FeSO4, 0.1 mM EDTA, 0.1 mM L-methionine, 60 mM potassium phosphate, pH 6.8), and incubated for 15 min at room temperature. A sample (10 l) of cell suspension was stimulated by mixing with 10 l of 2 mM L-aspartate in chemotaxis buffer, or mock stimulated by mixing with 10 l chemotaxis buffer. Cells (0.5 l) were then placed in the centre of a circle inscribed with a china marker on a vinyl slide and covered by a vinyl coverslip (Fisher), creating a several-micron-thick fluid layer. To prevent cell adhesion to the surfaces, slides and coverslips were precoated by dipping in a solution of 0.1% bovine serum albumin (BSA) (>99% purity; Sigma) in chemotaxis buffer followed by a brief wash in distilled water. Bacteria were observed with dark-field video microscopy (Nikon Optiphot-2; field of view spanned 220 m), and average tumbling frequency was determined by computerized image analysis as previously described14. The behaviour with 1 mM L-aspartate stimuli was indistinguishable from that observed in control experiments with 0.5 mM or 10 mM L-aspartate stimuli. Chemotaxis ability was assayed on soft agar plates (Tryptone broth + 0.3% agar) at 30 °C17.
Protein quantitation. Cultures, grown as for the behavioural assays, were subjected to SDS–polyacrylamide gel electrophoresis and western blot analysis as described14. To determine relative expression in strains A and B, where B has a higher copy number per cell of the protein assayed, lysates of strain B were diluted with various amounts of PS2002 (ref. 14) lysate (an RP437 derivative deleted for Tar, Tap and all of the che genes) and compared with standards of strain A (equal total protein in each lane). The diluted strain intensities bracketed the standard intensity.
-helical coiled-coil interactions in receptor dimerization, signaling and adaptation during bacterial chemotaxis. J. Biol. Chem. 271, 17966–17973 (1996). |