many microorganisms move around by swimming in liquid medium , and can modulate their swimming behavior in order to move up gradients of chemicals , temperature , or light . in liquid environments ,
escherichia coli swims in a random pattern composed of  runs  , in which the cell maintains an approximately constant direction , and  tumbles
 , in which it stops and randomly changes direction1 . runs and tumbles are generated by different states of the motors that rotate the bacterial flagella .
each cell has several flagellar motors that can rotate either clockwise ( cw ) or counterclockwise ( ccw ) .
when the motors turn ccw , the flagella rotate together in a bundle and push the cell forward .
when one or more of the motors turn cw , some flagella may break from the bundle and cause the cell to tumble and randomize its orientation . during chemotaxis , e. coli biases its  random walk  based on temporal changes in chemical concentration .
when the bacterium moves up a gradient of attractant it detects an increase in attractant concentration , and reduces its probability of tumbling .
the modulation of bacterial swimming serves as a model system for the way a living cell processes signals from its environment and changes its behavior based on those signals1,2 .
the first consists of observing freely swimming cells , typically in a flow - cell setup .
chemoeffector]variation is created in space or time35 , and the change in swimming behavior is then examined6,7
. the second type of assay uses cells that are tethered to a surface  usually a microscope slide  so that the rotation of an individual flagellar motor can be followed8,9 .
the approaches above have enabled the acquisition of large amounts of data that have yielded important insights into bacterial swimming and its modulation .
however , both assays are limited in their ability to quantify whole - cell swimming , as discussed in supplementary note 1 . in this paper
we describe the development of an optical - trap based assay to investigate cell motility .
this assay allowed us to quantify bacterial swimming in a well - controlled environment for durations up to 1 hour and at data acquisition rates that are faster than the ~100 hz flagellar rotation rates .
we were thus able to characterize the long - term statistics of the run - tumble time series in individual cells .
moreover , we were able to characterize higher - order features of bacterial swimming , such as changes in velocity and reversals of swimming direction .
our single - cell motility assay involves a custom - made instrument combining optical tweezers , light and fluorescence microscopy , and a microfluidic chamber ( fig . 1a ) .
the optical tweezers consist of two traps generated by two orthogonally polarized beams from a single 1064-nm diode - pumped solid - state laser10 .
the separation between the two traps is controlled by a piezo - actuated mirror stage . a custom flow - cell ( supplementary fig . 1 ; see also online methods ) serves as the experimental trap chamber , and can be displaced relative to the two traps in all directions by a three - axis translational stage . for measurements of bacterial motility ,
the chambers were filled with a tryptone broth - based  trapping medium  , though other buffers are also appropriate ( see online methods ) .
bacteria were injected into a top  antechamber  and flowed through a narrow inlet into the bottom channel , where they were captured by the traps . trapping a rod - shaped bacterium by each end with two optical traps11 allowed us to orient the cell at will in the plane of the chamber ( figure 1b ) .
trapped bacteria were visualized either by brightfield or epifluorescence microscopy ( fig . 1c ; see also online methods ) . [ despite immobilization by the optical traps , cells displayed motile behavior , evinced by flagellar bundle rotation and counter - rotation (  rolling  ) of the cell body12 .
this behavior was detected directly and sensitively by the optical traps themselves , by imaging light from both orthogonally polarized trapping beams onto two separate position - sensitive photodetectors ( psd ) .
consistent with previous reports on optically - trapped cells12,13 , power spectra from the psd outputs upon trapping of a swimming cell revealed two peaks with frequencies   100 and   10 hz ( fig .
these oscillatory signals correspond to flagellar bundle rotation and cell body counter - rotation or 
roll12,13 , respectively ( fig . 1b ) . our measured flagellar rotation (  ) and body - roll rates (  ) are consistent with those observed in experiments with freely swimming cells14 , demonstrating that the optical traps did not inhibit motility other than in fixing the cell s position .
although cell swimming was not observed directly , these oscillation frequencies provide information on the motile behavior of the cell ( see supplementary note 2 ) . in a typical experiment
, we trapped an e. coli cell ( strain rp437 , wild - type for chemotaxis15 ) horizontally , defined as x in fig .
1b . the motion of each trapped end in the orthogonal plane , along the vertical direction ( y ) and along the optical axis ( z ) ,
the y and z components of the low - frequency signal are 90 out of phase , indicating that the cell end moved in a circular trajectory perpendicular to its body axis ( fig .
the rotation is clockwise , as measured looking at the tail of the cell in the direction of swimming , consistent with the expected direction of body roll1 .
the higher - frequency oscillatory signal corresponding to flagellar bundle rotation also reveals a circular motion , in the counterclockwise direction , as expected ( fig .
the high photon - flux at near - infrared wavelengths generated by the optical traps has been shown to induce photodamage in cells16,17 .
as demonstrated previously16 , this damage can be largely mitigated by trapping cells under reduced oxygen conditions , for instance by use of an oxygen - scavenging system .
we optimized conditions to enhance cell viability in our trap ( online methods ) . under our tryptone
broth - based  trapping medium  ( with oxygen scavenger ) , we found that trapped e. coli cells displayed healthy behavior , growing and dividing at a rate comparable to standard values from the literature ( ~2 h generation time at room temperature18 ) ( supplementary figure 2 ) .
furthermore , swimming could be followed in individual cells for extended periods of time ( up to ~1 hour , data not shown ) .
our trapping protocol constitutes a substantial improvement over a previously reported trap - based study of bacterial swimming under oxygenated conditions19 , where cells could be monitored only for very short times ( < 10 s ) .
closer examination of swimming traces revealed regions of alternating oscillatory and non - oscillatory (  erratic  ) signals ( compare 11.5 s and 1.52 s regions in fig .
2b ; only the low - frequency component corresponding to body roll is shown for clarity . [ ) . by imaging the motion of a cy3-labeled cell using epifluorescence microscopy and simultaneously monitoring the trap signals
generated by this motion , we established that these oscillatory and erratic signals correspond to runs and tumbles of the cell , respectively . cell images taken during oscillatory periods ( 1.2 s , 2.2 s , 2.7 s , 3.2 s ) display a well - formed flagellar bundle extending from the tail of the cell as expected for a run , whereas those taken during erratic periods ( 1.7 s ) exhibit a disrupted bundle , indicative of a tumbling conformation20 ( figure 2a ) . to ascertain that the observed run - tumble behavior in trapped cells is physiologically relevant and rule out the possibility of an artifact induced by the optical traps , we performed two control experiments . in the first
, we examined the motility of two mutant strains : a chey deletion ( strain cr20 ; see supplementary table 1 for list of strains used in this study ) , which does not tumble , and a chez deletion ( strain cr33 ) , which mostly tumbles and does not run . as shown in figure 3a  c , data traces obtained from these mutants display the expected phenotypes : 
runners  generate prolonged oscillatory signals , whereas  tumblers  undergo continuous erratic motion . in the second control experiment
, we quantified the run - tumble behavior of strain ps2001-pms16421 , in which a permanently active cheyd13k mutant protein is expressed from an inducible promoter , under the control of isopropyl -d-1-thiogalactopyranoside ( iptg ) .
this strain allowed us to modulate run - tumble statistics and to compare them to those obtained with our wild - type strain . to quantify the swimming behavior of optically - trapped cells
, we developed an automated run - tumble detection routine using the continuous wavelet transform22 to discriminate regions of oscillatory and non - oscillatory behavior ( online methods and supplementary fig .
3 ) . for a data set of 43 wild - type cells constituting a total of 5,473 detected run events , our algorithm yielded an average run duration of 3.90  0.30 s ( mean  s.e.m . ,
n = 43 ) , within the range of previously reported values ( 0.84 s)7,21,23 .
analysis of 53 ps2001-pms164 mutant cells at various induction levels revealed that , as expected , run durations are longer than in wild - type cells at low ( 1 m ) iptg concentrations and shorter at high ( 100 m ) iptg concentrations .
as shown in figure 3d , the tumble bias b  defined as the fraction of time the cell spends tumbling , b = ttum/(ttum+trun)exhibits a sigmoidal response to iptg .
the midpoint of the response is at ~20 m and the enhancement in bias relative to wild - type cells is a factor of ~4 .
this behavior is in good agreement with the literature21 , further confirming our view that tumbles exhibited by trapped e. coli represent physiologically relevant events .
we note , however , that trapped cells exhibited longer tumble durations than observed in free swimming cells ( see supplementary note 3 ) . the ability to track an individual bacterium for an extended time period ( fig .
we determined the cumulative run duration distributions for 43 individual wild - type and 44 individual ps2001-pms164 cells at a range of induction levels ( figures 4b and 4c ; similar cumulative distributions for the tumble duration are shown in supplementary fig .
single - cell distributions are predominantly exponential but also display significant cell - to - cell variability
. to determine more accurately the shape of the distributions , we normalized each curve by the individual - cell mean run duration ( as determined by an exponential fit ) along the time axis , maximizing the overlap of the individual distributions7 ( figures 4d and 4e ) . by pooling all the normalized data
average  single - cell run duration distribution ( solid black lines , fig . 4d and 4e ) . both wild - type and ps2001-pms164 strains
display exponential distributions at short times , but the former additionally exhibited a pronounced  heavy tail  corresponding to very long runs , which was much smaller in the mutant strain .
the curves for individual wild - type cells further indicate that very long runs are taken in the majority of cells , rather than in a few outliers .
interestingly , this behavior matches that previously reported in single - motor tethered cell studies24 and may similarly represent the inherent stochasticity in the chemotactic signaling pathway in wild - type cells .
such a degree of stochasticity is not present in the ps2001-pms164 strain , where the concentration of signaling protein cheyd13k is externally controlled .
the ability to collect sufficient statistics from individual trapped bacteria provides information not available in population distributions .
note that taking the population averages of the single - cell distributions in figures 4b prior to normalization does not give an accurate representation of the average distribution ( compare solid black lines in fig . 4b and 4d ) , emphasizing the importance of collecting single - cell statistics .
our preceding analysis of trapped cells characterized their motility in terms of the standard two - state ,  run - tumble  picture . yet , this abstraction of cell swimming is only a first approximation .
researchers in the field have already pointed to aspects of movement beyond this approximation , including changes in cell velocity after a tumble7 , reversal of swimming direction when the flagellar bundle changes its orientation25,26 and changes in motor and swimming velocity as a function of multiple physiological and mechanical factors6,13 .
most of these observations , however , were sporadic in nature , limited by the noise or short time duration of available techniques .
swimming traces collected by our technique also exhibited  higher order  swimming dynamics , in particular reversals in phase difference between y and z signals ( compare r1 and r2 in fig .
5a ) , indicating reversals in swimming direction ( as established in the fluorescence images of supplementary fig . 5 ) and
to fully analyze such higher - order behavioral patterns , we used the continuous wavelet transform to determine not only the body roll frequency  but also the phase difference  between y and z signals at every point in time ( supplementary fig .
two - dimensional histograms in  and  for two representative cells are shown in figures 5c and 5d .
the majority of trapped wild - type cells ( 42 of 43 cells ) exhibited reversals , illustrated by the two peaks along the horizontal  axis in the histograms .
reversals occurred frequently ( an average of 21 reversal events were detected per time trace ) and exclusively after the cell tumbles , on average one out of every 6 tumbles , or every 21.2  1.1 s ( mean  s.e.m . , n = 859 ) ( the distribution of inter - reversal durations for a typical cell is shown in fig .
reversals were also accompanied by an observable change in body - roll rate  ( fig .
5c ) , and thus presumably swimming speed . interestingly , a similar analysis on the flagellar bundle rotation signal indicated no corresponding changes in rotation rate  in the majority of cells ( data not shown ) .
these observations suggest that reversals may play an important role in the motility of cells .
7 ) . occasionally ( in 6 of 42 cells ) , cells exhibited noticeable , discrete changes in body roll rate with no corresponding change in swimming direction ( illustrated in the two peaks along the vertical  axis in the histograms , fig .
5d ) . changes in speed occurred both spontaneously , without tumbling ( 69.5% ) as shown in the time trace figure 5b , or following a tumble ( 30.5% ) .
furthermore , the flagellar bundle exhibited no corresponding changes in rotation rate  ( data not shown ) .
these observations suggest that speed changes may represent different conformational states of the flagellar bundle ( see supplementary note 5 ) .
in addition to these higher order features , many cells exhibited asymmetric  distributions ( fig . 5c and 5d ) , indicating a bias in swimming direction . while we found no preferred swimming direction in the cell population , reflecting the fact that our traps do not impose directionality , many individual bacteria do display a statistically significant bias ( see supplementary note 6 ) .
our single - cell motility assay involves a custom - made instrument combining optical tweezers , light and fluorescence microscopy , and a microfluidic chamber ( fig . 1a ) .
the optical tweezers consist of two traps generated by two orthogonally polarized beams from a single 1064-nm diode - pumped solid - state laser10 .
the separation between the two traps is controlled by a piezo - actuated mirror stage . a custom flow - cell ( supplementary fig . 1 ; see also online methods ) serves as the experimental trap chamber , and can be displaced relative to the two traps in all directions by a three - axis translational stage . for measurements of bacterial motility ,
the chambers were filled with a tryptone broth - based  trapping medium  , though other buffers are also appropriate ( see online methods ) .
bacteria were injected into a top  antechamber  and flowed through a narrow inlet into the bottom channel , where they were captured by the traps . trapping a rod - shaped bacterium by each end with two optical traps11 allowed us to orient the cell at will in the plane of the chamber ( figure 1b ) .
trapped bacteria were visualized either by brightfield or epifluorescence microscopy ( fig . 1c ; see also online methods ) . [ despite immobilization by the optical traps , cells displayed motile behavior , evinced by flagellar bundle rotation and counter - rotation (  rolling  ) of the cell body12 .
this behavior was detected directly and sensitively by the optical traps themselves , by imaging light from both orthogonally polarized trapping beams onto two separate position - sensitive photodetectors ( psd ) .
consistent with previous reports on optically - trapped cells12,13 , power spectra from the psd outputs upon trapping of a swimming cell revealed two peaks with frequencies   100 and   10 hz ( fig .
these oscillatory signals correspond to flagellar bundle rotation and cell body counter - rotation or 
roll12,13 , respectively ( fig . 1b ) . our measured flagellar rotation (  ) and body - roll rates (  ) are consistent with those observed in experiments with freely swimming cells14 , demonstrating that the optical traps did not inhibit motility other than in fixing the cell s position .
although cell swimming was not observed directly , these oscillation frequencies provide information on the motile behavior of the cell ( see supplementary note 2 ) . in a typical experiment
, we trapped an e. coli cell ( strain rp437 , wild - type for chemotaxis15 ) horizontally , defined as x in fig .
1b . the motion of each trapped end in the orthogonal plane , along the vertical direction ( y ) and along the optical axis ( z ) ,
the y and z components of the low - frequency signal are 90 out of phase , indicating that the cell end moved in a circular trajectory perpendicular to its body axis ( fig .
the rotation is clockwise , as measured looking at the tail of the cell in the direction of swimming , consistent with the expected direction of body roll1 .
the higher - frequency oscillatory signal corresponding to flagellar bundle rotation also reveals a circular motion , in the counterclockwise direction , as expected ( fig .
the high photon - flux at near - infrared wavelengths generated by the optical traps has been shown to induce photodamage in cells16,17 .
as demonstrated previously16 , this damage can be largely mitigated by trapping cells under reduced oxygen conditions , for instance by use of an oxygen - scavenging system .
we optimized conditions to enhance cell viability in our trap ( online methods ) . under our tryptone
broth - based  trapping medium  ( with oxygen scavenger ) , we found that trapped e. coli cells displayed healthy behavior , growing and dividing at a rate comparable to standard values from the literature ( ~2 h generation time at room temperature18 ) ( supplementary figure 2 ) .
furthermore , swimming could be followed in individual cells for extended periods of time ( up to ~1 hour , data not shown ) .
our trapping protocol constitutes a substantial improvement over a previously reported trap - based study of bacterial swimming under oxygenated conditions19 , where cells could be monitored only for very short times ( < 10 s ) .
closer examination of swimming traces revealed regions of alternating oscillatory and non - oscillatory (  erratic  ) signals ( compare 11.5 s and 1.52 s regions in fig . 2b ; only the low - frequency component corresponding to body roll is shown for clarity .
[ ) . by imaging the motion of a cy3-labeled cell using epifluorescence microscopy and simultaneously monitoring the trap signals generated by this motion , we established that these oscillatory and erratic signals correspond to runs and tumbles of the cell , respectively . cell images taken during oscillatory periods ( 1.2 s , 2.2 s , 2.7 s , 3.2 s ) display a well - formed flagellar bundle extending from the tail of the cell as expected for a run , whereas those taken during erratic periods ( 1.7 s ) exhibit a disrupted bundle , indicative of a tumbling conformation20 ( figure 2a ) . to ascertain that the observed run - tumble behavior in trapped cells is physiologically relevant and rule out the possibility of an artifact induced by the optical traps , we performed two control experiments . in the first , we examined the motility of two mutant strains : a chey deletion ( strain cr20 ; see supplementary table 1 for list of strains used in this study ) , which does not tumble , and a chez deletion ( strain cr33 ) , which mostly tumbles and does not run . as shown in figure 3a  c , data traces obtained from these mutants display the expected phenotypes : 
, we quantified the run - tumble behavior of strain ps2001-pms16421 , in which a permanently active cheyd13k mutant protein is expressed from an inducible promoter , under the control of isopropyl -d-1-thiogalactopyranoside ( iptg ) .
this strain allowed us to modulate run - tumble statistics and to compare them to those obtained with our wild - type strain . to quantify the swimming behavior of optically - trapped cells
, we developed an automated run - tumble detection routine using the continuous wavelet transform22 to discriminate regions of oscillatory and non - oscillatory behavior ( online methods and supplementary fig .
3 ) . for a data set of 43 wild - type cells constituting a total of 5,473 detected run events , our algorithm yielded an average run duration of 3.90  0.30 s ( mean  s.e.m . ,
n = 43 ) , within the range of previously reported values ( 0.84 s)7,21,23 .
analysis of 53 ps2001-pms164 mutant cells at various induction levels revealed that , as expected , run durations are longer than in wild - type cells at low ( 1 m ) iptg concentrations and shorter at high ( 100 m ) iptg concentrations . as shown in figure 3d , the tumble bias b  defined as the fraction of time the cell spends tumbling , b = ttum/(ttum+trun)exhibits a sigmoidal response to iptg .
the midpoint of the response is at ~20 m and the enhancement in bias relative to wild - type cells is a factor of ~4 .
this behavior is in good agreement with the literature21 , further confirming our view that tumbles exhibited by trapped e. coli represent physiologically relevant events .
we note , however , that trapped cells exhibited longer tumble durations than observed in free swimming cells ( see supplementary note 3 ) .
we determined the cumulative run duration distributions for 43 individual wild - type and 44 individual ps2001-pms164 cells at a range of induction levels ( figures 4b and 4c ; similar cumulative distributions for the tumble duration are shown in supplementary fig .
single - cell distributions are predominantly exponential but also display significant cell - to - cell variability . to determine more accurately the shape of the distributions , we normalized each curve by the individual - cell mean run duration ( as determined by an exponential fit ) along the time axis , maximizing the overlap of the individual distributions7 ( figures 4d and 4e ) .
average  single - cell run duration distribution ( solid black lines , fig . 4d and 4e ) . both wild - type and ps2001-pms164 strains display exponential distributions at short times , but the former additionally exhibited a pronounced  heavy tail  corresponding to very long runs , which was much smaller in the mutant strain .
the curves for individual wild - type cells further indicate that very long runs are taken in the majority of cells , rather than in a few outliers .
interestingly , this behavior matches that previously reported in single - motor tethered cell studies24 and may similarly represent the inherent stochasticity in the chemotactic signaling pathway in wild - type cells .
such a degree of stochasticity is not present in the ps2001-pms164 strain , where the concentration of signaling protein cheyd13k is externally controlled .
the ability to collect sufficient statistics from individual trapped bacteria provides information not available in population distributions .
note that taking the population averages of the single - cell distributions in figures 4b prior to normalization does not give an accurate representation of the average distribution ( compare solid black lines in fig . 4b and 4d ) , emphasizing the importance of collecting single - cell statistics .
our preceding analysis of trapped cells characterized their motility in terms of the standard two - state ,  run - tumble  picture . yet , this abstraction of cell swimming is only a first approximation .
researchers in the field have already pointed to aspects of movement beyond this approximation , including changes in cell velocity after a tumble7 , reversal of swimming direction when the flagellar bundle changes its orientation25,26 and changes in motor and swimming velocity as a function of multiple physiological and mechanical factors6,13 .
most of these observations , however , were sporadic in nature , limited by the noise or short time duration of available techniques .
swimming traces collected by our technique also exhibited  higher order  swimming dynamics , in particular reversals in phase difference between y and z signals ( compare r1 and r2 in fig .
5a ) , indicating reversals in swimming direction ( as established in the fluorescence images of supplementary fig . 5 ) and
5b ) , corresponding to changes in swimming speed14,19 . to fully analyze such higher - order behavioral patterns
, we used the continuous wavelet transform to determine not only the body roll frequency  but also the phase difference  between y and z signals at every point in time ( supplementary fig .
two - dimensional histograms in  and  for two representative cells are shown in figures 5c and 5d .
the majority of trapped wild - type cells ( 42 of 43 cells ) exhibited reversals , illustrated by the two peaks along the horizontal  axis in the histograms .
reversals occurred frequently ( an average of 21 reversal events were detected per time trace ) and exclusively after the cell tumbles , on average one out of every 6 tumbles , or every 21.2  1.1 s ( mean  s.e.m .
, n = 859 ) ( the distribution of inter - reversal durations for a typical cell is shown in fig .
, reversals were also accompanied by an observable change in body - roll rate  ( fig .
5c ) , and thus presumably swimming speed . interestingly , a similar analysis on the flagellar bundle rotation signal indicated no corresponding changes in rotation rate  in the majority of cells ( data not shown ) .
these observations suggest that reversals may play an important role in the motility of cells .
occasionally ( in 6 of 42 cells ) , cells exhibited noticeable , discrete changes in body roll rate with no corresponding change in swimming direction ( illustrated in the two peaks along the vertical  axis in the histograms , fig .
5d ) . changes in speed occurred both spontaneously , without tumbling ( 69.5% ) as shown in the time trace figure 5b , or following a tumble ( 30.5% ) .
furthermore , the flagellar bundle exhibited no corresponding changes in rotation rate  ( data not shown ) .
these observations suggest that speed changes may represent different conformational states of the flagellar bundle ( see supplementary note 5 ) .
in addition to these higher order features , many cells exhibited asymmetric  distributions ( fig . 5c and 5d ) , indicating a bias in swimming direction . while we found no preferred swimming direction in the cell population , reflecting the fact that our traps do not impose directionality , many individual bacteria do display a statistically significant bias ( see supplementary note 6 ) .
over the last half century , tremendous progress has been made towards understanding bacterial motility and chemotaxis .
this progress has been achieved by a combination of traditional biological tools such as genetics and biochemistry and quantitative methods from the physical sciences , both experimental7,2729 and theoretical30 . despite these advances ,
measurement techniques have so far exhibited a limited ability to probe and collect statistics on bacterial swimming at the level of the whole cell . here , our optical - trap assay offers a measurement tool for quantifying the long - term behavior of individual swimming cells . by limiting the physical translocation of the bacterial cell
while at the same time allowing high - accuracy measurement of its rotational motion , we were able to follow bacterial swimming for long periods of time with high temporal resolution .
the extensive run - tumble statistics thus collected from individual cells expand the range of measured distributions by over an order of magnitude over previous studies7 . as an example of the consequences of this advance , our wild - type cell run distributions now reveal , for the first time , a pronounced tail similar to that observed in individual flagellar motors24 .
these findings suggest that stochastic variation in the levels of chemotactic proteins is manifested in the long - term run - tumble behavior of swimming cells . with our technique
we investigated cell swimming beyond the classical , binary run - tumble picture , and quantified the statistics of cell reversals , changes in swimming speed , and direction bias . while these features are unique to the swimming behavior of the whole cell ( not revealed at the single flagellar motor level ) , they may also provide insight into the relationship of individual flagella and whole cell swimming phenotypes .
for example , cell reversals may reflect tumbling states in which multiple flagella rotate cw and disrupt the flagellar bundle .
tumbles involving a single flagellum are unlikely to induce reversals , as a partial bundle is likely to persist and bias the cell s direction during such tumbles14 .
changes in swimming speed and bias in swimming direction may similarly reflect different states or spatial arrangements of the flagella
a critical requirement for a quantitative characterization of cell chemotactic response is the ability to create an arbitrary stimulus , in the form of spatiotemporally varying chemoeffector concentrations , and to follow the response of the cell in terms of its swimming behavior as well as changes in intracellular parameters such as gene expression .
these advances will enable the development of an integrated device to quantify whole - cell swimming and chemotactic response .
 we present a single - cell motility assay , which allows the quantification of bacterial swimming in a well - controlled environment , for durations of up to an hour and with a temporal resolution higher than the flagellar rotation rates of ~100 hz . the assay is based on an instrument combining optical tweezers , light and fluorescence microscopy , and a microfluidic chamber . using this device 
 we characterized the long - term statistics of the run - tumble time series in individual escherichia coli cells . 
 we also quantified higher - order features of bacterial swimming , such as changes in velocity and reversals of swimming direction . 
INTRODUCTION
RESULTS
Experimental setup
Observation of single-cell run-tumble behavior
Single-cell statistics of motility parameters
Higher-order features in cell motility
DISCUSSION
Supplementary Material