Transient response to chemotactic stimuli in Escherichia coli (tethered bacteria/adaptation)

Proc. Nat. Acad. Sci. USA Vol. 72, No. 8, pp. 3235-3239, August 1975 Microbiology Transient response to chemotactic stimuli in Escherichia coli (tethered bacteria/adaptation) HOWARD C. BERG AND P. M. TEDESCO Department of Molecular, Cellular and Developmental Biology, University of Colorado, Boulder, Colo. 82 Communicated by Keith R. Porter, May 21, 1975 ABSTRACT We have followed by eye and with the tracking microscope the rotational behavior of E. coli tethered to coverslips by their flagella. The cells change their directions of rotation at random, on the average, about once a second. When an attractant is added or a repellent is subtracted, they spin clockwise (as viewed through the coverslip, i.e., along the flagellum toward the body) for many seconds, then counter-clockwise for many seconds, and then gradually resume their normal mode of behavior. The time interval between the onset of the stimulus and the clockwise to counter-clockwise transition is a linear function of the change in receptor occupancy. The cells adapt slowly at a constant rate to the addition of an attractant or the subtraction of a repellent. They adapt rapidly to the subtraction of an attractant or the addition of a repellent. Responses to mixed stimuli can be analyzed in terms of one equivalent stimulus. The swimming pattern of Escherichia coli resembles a three-dimensional random walk. A cell moves along a relatively straight path (runs), stops and jiggles about (twiddles), and then runs again (1). Twiddles occur at random, about once a second; they generate changes in direction which are nearly random (1, 2). The chemotactic behavior of a cell can be characterized in terms of a single parameter, the probability per unit time that a twiddle will occur. When the cell swims up a spatial gradient of an attractant, the probability that a twiddle will occur is somewhat smaller than it is in an isotropic solution; when it swims down the gradient, the probability is about the same as it is in an isotropic solution (1); thus, the cell drifts up the gradient by increasing the lengths of runs which are favorable. The same asymmetry is observed when cells are exposed to temporal gradients generated by the enzymatic synthesis or destruction of an attractant; as the concentration of the attractant increases, twiddles occur less frequently; as it decreases, they occur about as often as they do in the absence of a stimulus (3). When a large amount of attractant is suddenly added, the cells swim without twiddling for several minutes and then gradually resume their normal mode of behavior; when the attractant is diluted out, they twiddle more frequently, but only for a few seconds (4). Why is the response to the addition of attractant so persistent? It is useful for a bacterium to compare differences in concentration over a long time span, because such comparisons are less sensitive to local fluctuations in concentration (4). Too long a time span, however, is detrimental, because the signal inhibiting the twiddle will persist after a change in direction has occurred (5). E. coli cannot bias its random walk successfully if comparisons are made over a time span much Abbreviations: AIbu, a-amino isobutyric acid; CCW, counter-clockwise rotation of a cell when tethered to the coverslip; CW, clockwise rotation of a cell when tethered to the coverslip; MeAsp, a- methyl-dl-aspartic acid. 3235 longer than the mean run length (3). The mean run length must be shorter than a few seconds, or changes in direction will be dominated by rotational diffusion (1). The results described here suggest that E. coli has found the optimum solution. As the concentration of an attractant increases, the cell adapts slowly at a constant rate. As the concentration decreases, it adapts rapidly. The time spans over which comparisons are made differ depending on whether the bacterium is moving up or down the gradient. The measurements were made by exposing cells tethered to coverslips by their flagella (6) to varying concentrations of attractants and/or repellents (7) and by monitoring the changes in the direction of their rotation by eye or with the tracking microscope (8). MATERIALS AND METHODS Reagents. All solutions were prepared from reagent-grade chemicals and glass-distilled water. Rabbit anti-filament antibody (62 mg/ml) was the gift of Steven H. Larsen, who preadsorbed antisera against whole cells with a nonflagellated derivative of E. coli AW45 (M318) and purified the antibody by precipitation with ammonium sulfate (3-4%). Cells were exposed to the nonmetabolizable attractants (9) MeAsp (a-methyl-dl-aspartic acid, Sigma) and AIbu (aamino isobutyric acid, Calbiochem A grade) and the repellent (1) L-leucine (Calbiochem A grade) in a medium (tethering medium) containing.67 M sodium chloride,.1 M potassium phosphate (ph 7.), and 1-4 M EDTA. Tethered Cells. Wild-type E. coli strain AW45 (9) was grown in minimal salts medium on glucose, threonine, leucine, and histidine, and then harvested and washed in chemotaxis medium as described by Hazelbauer et al. (11). Cells grown in this fashion average 1.5 flagella per cell (7). They were tethered to glass by a method similar to that of Silverman and Simon (6). The cells were suspended in tethering medium at a concentration of about 3 X 18/ml. Anti-filament antibody was added at a final dilution of 1:5. The suspension was allowed to stand 1 hr at room temperature over coverslips (Corning no. 1) or windows made from such coverslips that had been cleaned with fuming nitric acid and rinsed with glass-distilled water. The coverslips (or windows) were inverted and sealed with Apiezon L to flow chambers filled with tethering medium. Measurement Procedures. The rotation was followed in the tracking microscope in a chamber with inlet and outlet pipes described previously (3). The medium was changed by inserting a tube connected to the inlet pipe into a vial containing the new solution and opening the valve on the vacuum line for 7 sec. The chamber and all solutions were maintained at 32.. The x- and y-velocities of the tracked bacte-

3236 Microbiology: Berg and Tedesco Table 1. Rotational behavior of E. coli AW45 (19 cells) measured with the tracking microscope Direction of rotation CW CCW Tracking time (min) 23.9 25. Rotation rate (rps)*t 12. ± 2.9 12.2 ± 2.5 Interval between reversals (sec)* 1.35 ±.82 1.24 ±.63 * The values are the means for the population A one standard deviation, calculated by weighting the means for each bacterium equally. t Data from 8 of the 19 bacteria. rium were recorded (8), together with an event marker indicating the direction of rotation. Measurements by eye were made with a stop watch and a phase-contrast microscope (4X) equipped with a flow chamber made by cementing pieces of coverslips to a slide with silicone rubber cement (GE RTV-12). The chamber was.4 mm deep, 6 mm wide, and 18 mm long. A 6 X 8 mm patch of the top window was exposed to the medium. Solutions were drawn through the chamber at a rate of about.1 ml/sec via inlet and outlet pipes connected to wells designed to ensure uniform flow from one side of the chamber to the other. A new solution reached the center of the chamber in.7 see and displaced about 96% of the old solution within 1.7 sec, more than 99% within 2.7 see (measurements made with tethering medium containing methylene blue by the optical absorption methods of ref. 12). In most experiments the valve on the vacuum line was opened 5-7 sec. One or more cells from the same culture were studied for as long as 3 hr. A number of such cells continued to spin for more than 3 days. RESULTS Behavior in the absence of chemotactic stimuli Larsen et al. (7) have shown that clockwise (CW) rotation of a cell tethered to a coverslip (counter-clockwise rotation when tethered to a slide) is equivalent to a run, in which a cell is pushed by the concerted action of left-handed helical flagella, whereas counter-clockwise (CCW) rotation is equivalent to a twiddle, in which the flagella cease to move in concert. The behavior of swimming cells can be inferred from measurements made on tethered cells. Tethered cells (AW45) repeatedly change their directions of rotation, on the average, about once a second. Some cells spend more time spinning CW, others CCW. CW and CCW intervals are distributed exponentially; CW and CCW intervals of different length occur at random; the lengths of successive CW and CCW intervals are uncorrelated. Thus, both CW-to-CCW reversals and CCW-to-CW reversals are random events (see ref. 2). They occur with probabilities that, for a particular cell, are constants. The aggregate data are summarized in Table 1. These results are consistent with those obtained earlier on swimming cells (1) with one exception: The probability in a tethered cell that a CCW to CW reversal will occur is much smaller than the probability in a swimming cell that a twiddle will end; the probability for the reversal varies from cell to cell (data not shown), whereas that for the twiddle does not. This implies that the twiddle in a swimming cell is ter- 5 11 Or- Proc. Nat. Acad. Sci. USA 72 (1975) IV 5 - _ - c E / 8 1 12 14 16 Time (sec) FIG. 1. The response of a tethered cell to a step change of - 1-3 M MeAsp. The addition of the attractant began at time. Tracking started at about 1 sec. The strip-chart record was divided into 4-sec intervals. The figure shows the fraction of time that the cell rotated CW and the frequency of its reversals for each interval. The points are mean values obtained from data in three such experiments. In tethering medium, the cell rotated on the average.32 of the time CW and reversed.6 times per second; these values are indicated by the arrows at the right edge of the figure. We followed cells for much longer periods of time and found no evidence for damped oscillations. They appear to relax directly from the CCW mode to their normal mode of behavior; however, small oscillations could have been missed. minated by another process, probably one which involves interactions between two or more flagella (13). Basic response to abrupt changes in concentration When a tethered cell is suddenly exposed to an attractant, e.g., 1-3 M MeAsp, it spins in the run direction for many seconds (7), but it does not simply relax to its normal mode of behavior. Instead, it switches rapidly to the twiddle mode, remains there for some seconds, and then gradually relaxes to its normal mode of behavior (Fig. 1.) We call the interval of time between the onset of the stimulus and the CW to- CCW transition the "transition time". We refer to the subsequent rotation in the twiddle mode as the "overshoot". We have observed the overshoot on the addition of MeAsp or AIbu and on the subtraction of L-leucine. It has not been noted in measurements on populations of cells (4), because the transitions occur in different cells at widely different times (Table 2). Note, for example, that the standard deviation in the data for the step from to 1-3 M MeAsp (15 sec) is larger than the time scale on which the changes occur in Fig. 1. Overshoot phenomena of the kind shown in Fig. 1 also occur on the dilution of an attractant or on the addition of a repellent, but the effects are relatively short-lived. For example, a step from 1-3 to M MeAsp may cause a cell to spin CCW for about 15 sec. CW for another 15 sec. and then to relax gradually to its normal mode of behavior. A closer study of these responses will be made when a flow chamber is available in which the media can be changed more rapidly. We suspect that the overshoot is due to a process that is of marginal importance to twiddle regulation in E. coli. This belief is strengthened by results, described below, of studies of the functional dependence of the transition time on changes in the concentration of attractants and repellents. Cells sometimes spin CCW for a fraction of a revolution long before the actual transition begins, as judged from plots of the kind shown in Fig. 1. We ignore these early CCW events.

4 3 E 2 c 1 1-5 1-4 1-3 1-2 - Final Concentration of Attractant or Initial Concentration of Repellent (M) FIG. 2. A test of a model in which the transition time is proportional to the amount of attractant or repellent bound to chemoreceptors. () MeAsp, (o) AIbu, (A) L-leucine. The data for each bacterium were scaled, so that the transition time for -1-3 M MeAsp was 311 sec, that for -1-2 M-AIbu was 25 sec, and that for 1-2- M L-leucine was 89 sec (the mean values shown in Table 2). The means and standard deviations of the scaled data for other concentrations were plotted. The solid curves were derived from the law of mass action, given the dissociation constants shown in Table 2 and the constraints that they pass through the points (1-3 M, 311 sec), (1-2 M, 25 sec), and (1-2 M, 89 sec), respectively. Dependence of transition time on change in receptor occupancy We find, in agreement with Spudich and Koshland (14), that the data can be fit by a model in which the transition time (their recovery time) is proportional to the change in the amount of receptor bound. If attractants and repellents are in association-dissociation equilibrium with chemoreceptors, the dissociation constants can be computed from the law of mass action and ratios of transition times (Table 2). Data obtained over a wide range of concentrations can be fit by this model (Fig 2). The dissociation constant obtained for MeAsp is in agreement with that found by Mesibov et al. (15); the others have not been determined elsewhere..5 1. O 1..5 Microbiology: Berg and Tedesco 2 4 6 Time (min) FIG. 3. An experiment in which a cell was stimulated by the step addition and subtraction of MeAsp (-1-3-1-4 M, or -.86-.38 of the receptor bound, assuming a dissociation constant 1.6 X 1-4 M). The record has been divided into three parts and should be read from left to right and top down. A bar indicates that the cell was spinning CW; its length equals the transition time. The step addition of MeAsp (-1-3 M) gave a transition time of 3.7 min (not shown). In the first five trials the step from 1-4 to M was made after the transition had occurred. In the last trial the transition occurred in response to the step from 1-3 to 1-4 M. See the text. Table 2. Proc. Nat. Acad. Sci. USA 72 (1975) 3237 Transition times for the addition of attractant or the subtraction of repellent Attractants Repellent MeAsp AIbu L-Leucine No. of cells studied 17 26 5 Transition time (sec) for concentration jumps (M):* -1-4 139 ± 54-1-3 311 ± 15 65 ± 21 _1-2 25 ± 78 1-2_ 89 ± 15 1-l- 158 ± 19 Transitiontime ratios Whole populationt 2.24 ± 1.38 3.16 ± 1.57 1.78 ±.37 Individual cellst 2.22 ±.32 3.14 ±.68 1.8 ±.21 Dissociation constant (1.6 ±.5) (3.1 ± 1.3) (.98 ±.28) (M) X 1-4 X 1-3 X 1-2 * The mean i one standard deviation, each cell weighted equally. The stop watch was started as the concentration was changed and stopped when the cell completed at least one turn CCW. When possible, measurements on an individual cell were repeated several times, and the results were averaged. t The ratio of the transition times shown in the same column 4 one standard deviation. $ The mean 4 one standard deviation, obtained by computing the ratios for each cell individually and then pooling the data. Computed from the ratio given in the previous row on the assumption that the transition time for the concentration jump to C is proportional to C/(CD + C), where KD is the dissociation constant. The spread in the data obtained from different cells may be due to the fact that different cells have different numbers of each receptor. The ratios in the transition times for jumps of different concentration are more nearly the same from cell to cell than are the transition times themselves; compare the two transition time ratios given in Table 2. A cell that is highly sensitive to MeAsp may or may not be highly sensitive to AIbu, which uses a different chemoreceptor (data not shown). Additivity of transition times If the transition time for addition of attractant (or subtraction of repellent) is a linear function of the change in receptor occupancy, as implied by the results of Fig. 2, then the responses to consecutive increments (or decrements) in concentration should be additive. Spudich and Koshland (14) found this to be true for recovery times measured on addition of serine. We find it to be true under a variety of conditions, in particular, in stepping upwards in all possible ways between concentrations of MeAsp or AIbu which saturate none, 'A, 2A, or nearly all the chemoreeeptors. The second step can be made immediately after the occurrence of the transition due to the first, or minutes later; the results are the same.

3238 Microbiology: Berg and Tedesco Adaptation to addition of attractant or subtraction of repellent One way to explain the linear dependence of transition time on receptor occupancy is to suppose that a bacterium adapts to changes in occupancy (positive for attractants, negative for repellents) at a constant rate. If so, once the addition of attractant begins, variations in its concentration should not matter, provided that the occupancy of the receptor remains above the level to which the cell already has adapted; only the net change in the concentration is important. We find this to be the case, both for the addition of attractants and the subtraction of repellents. A particularly dramatic example is shown in Fig. 3. Note that the transition time is that for a step from to 1-4 M MeAsp, even though the concentration was raised initially to 1-3 M and held there for varying lengths of time. When this time exceeded the transition time for a step from to 1-4 M MeAsp, reversals appeared as soon as the concentration was dropped to a lower value. The observation by Spudich and Koshland (14) that recovery times for serine are the same for mixing times of 1-15 sec provides another example. Adaptation to subtraction of attractant or addition of repellent Adaptation in this direction is very rapid. One of the. easiest ways of showing this is to add a sizeable amount of attractant, e.g., 1-3 M MeAsp, to wait until the transition is about to occur, and then to remove the attractant briefly and add it back again. When this is done, the transition occurs about the same number of seconds after the second addition as it would have after the first. It does not matter when the subtraction is made; the result is always the same. If the concentration is pulsed to an intermediate level, one below that to which the cell already has adapted, the result is the same as if the cell had been equilibrated at the lower level and a step to the higher level was made. Similar results are obtained on subtracting L-leucine, then adding it back and subtracting it again. We established an upper limit on this adaptation time by switching from a solution containing attractant (3 X 1-4 M MeAsp) to tethering medium and back again. Adaptation to the tethering medium was complete for a 4-sec pulse, nearly complete for a 3-sec pulse, and partially complete for a 2-sec pulse. Given the results of the measurements of the displacement rates (see Materials and Methods) and the time required for the attractant to diffuse away from cells tethered at the wall, this is what we would expect if adaptation to an instantaneous step could occur in a few seconds or less. Equivalence of attractants and repellents The transition times, measured in experiments involving two attractants or an attractant and a repellent (16, 17) are the times expected if (i) the absolute value of the signal generated by a given set of chemoreceptors is proportional to the change in receptor occupancy, (ii) the signals add, and (iii) the signals for attractants and repellents have the opposite sign. We would predict from Fig. 2, for example, that a step from tethering medium to tethering medium containing 1-4 M MeAsp and 1-2 M L-leucine would give a transition time of about 5 sec; this is observed. We also would predict that a step from tethering medium to tethering medium containing 1-4 M MeAsp and 1-3 M AIbu would give a transition time of about 2 sec; this is observed. The predictions are approximate, because of variations in the response :3 c O ṫ- Co Lo a1) C, W' a).11 I-r.5 1.1.5 Proc. Nat. Acad. Sci. USA 72 (1975) ---L o LUI 2 4 Time (min) FIG. 4. An experiment in which a cell was stimulated by the step addition and subtraction of MeAsp (-) and AIbu (---) at 3 X 1-4 M (.65 of the receptor bound) and 6 X 1-3 M (.66 of the receptor bound), respectively. The bar indicates that the cell was spinning CW; its length is equal to the transition time. The transition time for a step of -3 X 1-4 M MeAsp was 2.87 min, for -6 X 1-3 M AIbu 1.95 min, and for to both simultaneously 4.93 min. The MeAsp step is.6 times and the AIbu step.4 times as effective as both simultaneously; the signals from the two sets of receptors add to give the relative effective signal shown in the lower graph. The transition time for the stimulus shown in the figure was 4.98 min, as expected if both attractants had been added at time. from cell to cell. However, if the measurements are made on the same cell, first with the chemicals separately and then with the chemicals together, the agreement is excellent. A variation on the experiment of Fig. 3 was performed by displacing the MeAsp (3 X 1-4 M) with a solution containing a less effective concentration of AIbu (6 X 1-3 M). The results were similar; the transition occurred as if the AIbu had been added initially. Cells also were exposed to MeAsp for several minutes (until adapted), to AIbu at an equally effective concentration for a few seconds, and then to the MeAsp once again. The pulse of AIbu was ignored. We found the results of experiments of this kind bewildering until we realized that a mixed stimulus could always be described in terms of one equivalent signal. An example of this kind of analysis is shown in Fig. 4. DISCUSSION The linear dependence of the transition time on changes in receptor occupancy indicates the involvement of a process that occurs at a constant rate. The difference in the rates of adaptation to positive and negative changes in receptor occupancy implicates a second process that occurs at a more rapid rate. The equivalence of signals generated by two attractants or an attractant and a repellent suggests that these A model that processes are triggered by a common signal. incorporates these features is shown in Fig. 5. When the level in the signal reservoir, S, rises above that in the adaptation reservoir, A, the adaptation reservoir fills slowly at a constant rate, and the cells spin CW. When S drops below A, the adaptation reservoir empties rapidly, and the cells spin CCW. The gates are closed and the cells exhibit their normal behavior when A equals S. If the gating is such that when S rises slowly, A lags behind, the cells will tend to spin CW (to run). If when S drops slowly A follows closely, there will be little change in motile behavior. This is the asymmetry observed when cells swim in spatial gradients of an attractant (1, 2) or are exposed to an attractant as it is generated or destroyed enzymatically (3). The adaptation is incomplete as S increases but essentially complete as S decreases.

Microbiology: Berg and Tedesco FIG. 5. A model for the chemoreception machinery of E. coli. Receptor signals are added to or subtracted from the signal reservoir in proportion to the change in receptor occupancy. The signals are positive for positive increments in the amount of attractant bound, negative for positive increments in the amount of repellent bound. The signaling is rapid; the attractants or repellents and their receptors remain in association-dissociation equilibrium. The level in the signal reservoir, S, is compared to the level in the adaptation reservoir, A. If S is greater than A, the comparator instructs the gate to fill the adaptation reservoir slowly at a constant rate and the motor to turn CW. If S is less than A, the comparator instructs a second gate to empty the adaptation reservoir rapidly and the motor to turn CCW. The receptors use a common signal, but it need not be the same as that used in the adaptation reservoir. This model incorporates fast and slow component responses, S and A, which reflect the present and past values of the status of the receptors, noted as essential by Macnab and Koshland (4), but it does not involve transient changes in the rate of formation or destruction of a tumble regulator, which occur at a time experimentally equivalent to t = (14). Proc. Nat. Acad. Sci. USA 72 (1975) 3239 If we are to make a quantitative fit of the model to the data in the small-signal domain, however, we need to know the functional dependence on S minus A of the probabilities that CW-to-CCW and CCW-to-CW reversals will occur. If there were no overshoot (Fig. 1), we could obtain this information (on the assumption that A approaches S linearly) by studying the way in which the cells relax to their normal behavior. The overshoot is not accounted for by the model. It may be due to another adaptive process, at the level of the motor, to large outputs from the comparator. It is not a simple matter of A rising above S and then falling slowly back again. If it were, a small increment in S soon after the cells spin CCW would abolish the overshoot. It does not. A positive change of less than 2% in the receptor occupancy causes such a cell to spin CW for a few seconds and then to relapse into a CCW phase as prolonged as before. Clearly, the matter deserves further study. The adaptation model was inspired by Edward Purcell. Discussions with Ken Foster and Bob Smyth have been helpful. This work was supported by grants from the National Science Foundation (GB-3337, BMS75-5848). 1. Berg, H. C. & Brown, D. A. (1972) Nature 239,5-54. 2. Berg, H. C. & Brown, D. A. (1974) Antibot. Chemother. (Basel) 19, 55-78. 3. Brown, D. A. & Berg, H. C. (1974) Proc. Nat. Acad. Sci. USA 71, 1388-1392. 4. Macnab, R. M. & Koshland, D. E., Jr. (1972) Proc. Nat. Acad. Sci. USA 69,259-2512. 5. Koshland, D. E., Jr. (1974) FEBS Lett. 4, S3-S9. 6. Silverman, M. & Simon, M. (1974) Nature 249,73-74. 7. Larsen, S. H., Reader, R. W., Kort, E. N., Tso, W.-W. & Adler, J. (1974) Nature 249, 74-77. 8. Berg, H. C. (1974) Nature 249,77-79. 9. Mesibov, R. & Adler, J. (1972) J. Bacteriol. 112,315-326. 1. Tso, W.-W. & Adler, J. (1974) J. Bacteriol. 118, 56-576. 11. Hazelbauer, G. L., Mesibov, R. F. & Adler, J. (1969) Proc. Nat. Acad. Sci. USA 64,13-137. 12. Futrelle, R. P. & Berg, H. C. (1972) Nature 239,517-518. 13. Berg, H. C. (1975) Nature 254,389-392. 14. Spudich, J. L. & Koshland, D. E., Jr. (1975) Proc. Nat. Acad. Sci. USA 72,71-713. 15. Mesibov, R., Ordal, G. W. & Adler, J. (1973) J. Gen. Physiol. 62,23-223. 16. Tsang, N., Macnab, R. & Koshland, D. E., Jr. (1973) Science 181,6-63. 17. Adler, J. & Tso, W.-W. (1974) Science 184, 1292-1294.