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Proceedings of IMECE 2008 2008 ASME International Mechanical Engineering Congress and Exposition

October 31 – November 6, 2008, Boston, Massachusetts, USA

IMECE2008- 66436

TRACKING BACTERIA IN A MICROFLUIDIC CHEMOTAXIS ASSAY

Zhiyu Wang1 David M. Casale2 Gail Rosen1 Min Jun Kim2,*

1Department of Electrical & Computer Engineering Drexel University

Philadelphia, PA 19104 U.S.A

2Department of Mechanical & Mechanics Drexel University

Philadelphia, PA 19104 U.S.A

ABSTRACT In order to research the chemotaxis of Escherichia coli and

other bacteria, several methods and devices have been applied including capillary assays, parallel channel assays, etc. Existing methods provide only qualitative data by the way of cell counting. However, a microfluidic channel and microscope imaging system provide a quantitative measurement of individual E. coli’s chemotaxis under a controlled chemical environment. This paper presents such quantitative analysis system. First, a computer model is developed and analyzed. Secondly, we use the microfluidic channel to begin to collect experimental data for comparison. Through a phase contrast microscope and high-speed CCD camera, the E. coli (HCB-33, wide-type) movement is captured, analyzed, and several chemotactic parameters are gathered. This data will be used to compare the movement of E. coli under unbiased and biased environments. BACKGROUND OF CHEMOTAXIS

E. coli’s movement exhibits two types of motion: runs and tumbles. The track of an E. coli’s movement in the absence of a chemical gradient can be seen as a series of runs and tumbles, resembling a random walk [1]. There are several parameters used to assess the characteristics of the random walks of E. coli according to different cases. For example, in the case of assessing a single cell, motility can be interpreted in terms of its speed, tumbling frequency, the mean run duration, the turn angle between two successive runs and etc. While for the cell-population motility, the diffusion constant is used [2].

Chemotaxis is the response of a motile organism to a chemical gradient present in its surroundings. Organisms such as bacteria use various receptors throughout the cell to sense the chemical gradient, triggering a response that will create responding motion in a biased direction. This motion will be along the direction of either increasing or decreasing

concentration, dependent upon whether the chemical is a chemoattractant or chemorepellent [3].

Chemotaxis is achieved through the change of movement. Motility of E. coli is determined by the rotation mode of the flagellar filaments, each of which is driven by a reversible rotary motor located at the base of flagella. The movement can be determined by whether the flagella are moving clockwise (CW) or counterclockwise (CCW), where a CW relates to an unbundling motion of the flagella, hence a tumble, and CCW relates to bundling motion of the flagella, a straight run for the bacteria. The motion of flagella determines the helicity, for example run corresponds to the right-handed and tumble corresponds to left-handed. As a result the flagella provide a nearly constant propulsion and drive the cell in a smooth track. And then the helicity determines the mode of flagella’s move, in a bundle or respectively. In the end, all of these are responsible for the E. coli’s movement: run or tumble [1, 4-8].

Previous work has shown that E. coli will behave differently under chemotactic stimulus, yet none have successfully determined the quantitative change in tumbling angle and effective run time accurately [9]. The microfluidic device belongs to the assay in which a gradient of the stimulant is established by diffusion. The principle of this assay is the establishment of a stable gradient (linear or two-dimensional) of a stimulant between large reservoirs. The microfluidic device provides a controlled-chemical-gradient environment, where single E. coli bacterium experience chemotaxis. Moreover, because the gradient in this assay results from the stable diffusion, it could be seen as a constant and this could give us the quantitative insight about E. coli response to chemical gradient. Through image processing, the swimming speed, tumbling frequency, the mean run duration, the turn angle between two successive runs and other parameters can be measured and analyzed. We also use a random-variable modeling to simulate the E. coli random walk for different

* Corresponding author: mkim@coe.drexel.edu

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environmental cased, which is different from the reported simulation strategies [9-12]. BACKGROUND OF MICROFLUIDIC PDMS CHANNEL

The experimental device is a simple PDMS microchannel, shown in Figure 1. The two channels will contain different chemical solutions, one a chemical attractant such as aspartic acid, the other a standard solution of motility buffer, while the central chamber will be filled with a sparse concentration of bacteria. As syringe pumps drive the two solutions into the channels with the same flow rate, diffusion will take place between aspartic acid and the central well. Diffusion will also take place between the motility buffer and the central well. A steady state laminar flow regimen will also develop due to the channel dimensions, limiting convection as shown in Figure 2. Depending upon the diffusivity rates of these two solutions, a steady state gradient will eventually be achieved over the central chamber, shown in Figure 3. For steady state diffusion, it is acceptable to use Fick’s first law to describe a one-dimension system by

(1)

where J is the diffusion flux, D is the diffusion coefficient, Φ is the concentration of diffusing material, and x is the spatial coordinate. The microchannel will effectively control diffusion, to maintain a steady gradient of chemoattractant in the channel of interest. This steady state gradient is important to the analyze, as previous studies have shown that E. coli tends to adapt to the presence of chemicals over time, if they act as a step function [13, 14]. Certain transients in chemical concentration gradients have been seen to cause increased and reduced running distance in E. coli, so there is a need to have a steady state concentration gradient. The microchannel will effectively control diffusion, to maintain a steady gradient of chemoattractant in the channel of interest.

Figure 1. PDMS microchannel assay for bacterial chemotaxis.

Figure 2. Velocity Field in the PDMS Channel.

Figure 3. Diffusion in the central chamber.

SIMULATION AND EXPERIMENT RESULTS

According to the distributions of the parameters used to depict the E. coli motility, we developed a computer model based on the random variables to simulate the random walks of E. coli under unbiased and biased environment. For the unbiased random walk, we could use three random variables to simulate it: 1) The run distance is an exponentially distributed random variable; 2) The turn angle follows a uniform distribution between 0 and π (azimuthally symmetric about the initial direction); 3) When the cell selects an azimuthal angle, the decision of whether it moves upwards or downwards depends on a Bernoulli random variable with the probability for upward 1/2 and the probability for downward also 1/2 [15]. We summarize the simulation algorithm as follows: Step 1. Starting from a tumble, according to the probability

density function of the turn angle (a uniform distribution), E. coli selects a random value as the next running’s azimuthal angle.

Step 2. According to the probability density function of a Bernoulli distribution, E. coli selects a random value to

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decide whether the azimuthal angle is upward or downward. At this step, E. coli will eventually decide the direction of next run.

Step 3. According to the probability density function of the run distance (an exponential distribution), E. coli selects a random value as the run distance and together with the run direction updates the present position for the next tumble and run.

Step 4. E. coli moves according to a tumble + a run to update the new position based the last run position. For each turn angle, the final azimuthal angle is an accumulated value from the first tumble.

Run distance E(λ=1/0.5) Turn angle 1/2Sinθ, θ between [0, π] Direction of the run angle Bernoulli(p=1/2,q=1/2)

TABLE 1 Parameters for the simulation under unbiased environment.

Figure 4. Simulation of E. coli unbiased random walks. There are 500 runs and 500 tumbles. The starting point is (0, 0). Table 1 shows the parameters for the simulation and Fig. 4 shows the simulation result. In the species like E. coli, there will be a tendency of positive stimulation (an increasing chemoattractant gradient or a decreasing chemorepellent gradient) decreasing the probability of clockwise rotation and, therefore, the probability of tumbles. On the other hand, a tendency for the negative stimulation (a decreasing chemoattractant gradient or an increasing chemorepellent gradient) increases this probability. We could conclude that in this situation the runs in the “right” direction are prolonged, and the runs in the “wrong” direction are shortened. According to this, we change the simulation’s parameter and Table 2 shows that and Fig. 5 shows the simulation result. Run distance along the chemoattrator gradient

E(λ=1/0.6)

Run distance against the chemoattrator gradient

E(λ=1/0.4)

Turn angle 1/2Sinθ, θ between [0, π] Direction of the run angle Bernoulli(up=1/2,down=1/2) TABLE 2 Parameters for the simulation under biased environment.

Figure 5. Simulation of E. coli biased random walks. There are 500 runs and 500 tumbles. The starting point is (0, 0). EXPERIMENT METHOD First, a wild type E. coli HCB-33, is cultured first. In order to make sure that the bacteria will not bind to other cells and have a complete mobility, the culture time and temperature are strictly controlled. Culture time will be also used to accurately control the population. Motility buffer is the ideal solution to promote bacteria motion, as it supplies everything necessary to the cell, with the addition of surfactants that act to prevent clumping. After culturing the E. coli, the solution is diluted by a motility buffer to ensure that the proper number of bacteria will appear within the center well. Upon completion of the combined bacteria and motility buffer solution, the solution will be pumped into PDMS micro-channels by syringe, filling all available space in all channels. It is essential to eliminate bubbles for the next experimental steps. The result is a sparse amount of bacteria within the inner chamber, allowing with enough room to run without obstruction. Once the PDMS micro-channels are filled with bacteria in solution, the whole assembly can be mounted on the inverted microscope. The left input port will supply aspartic acid, a chemo-attractant for E. coli, by means of a syringe pump. The right input port will supply pure motility buffer, the same solution that was used originally in the filling of the channels, also under the control of a syringe pump. The objective is to accurately control both flows, eliminating cross talk between the two exterior flow channels. Bacteria move at incredibly fast velocities for their scale. E. coli is no exception. The final portion of this experiment requires a CCD camera capable of frame rates >500fps. Videos

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can be taken of the bacteria motion as they move throughout the interior well, experiencing changes in chemical gradients depending upon their direction. This video will then be processed using Matlab code. This will provide normalized vector fields of the bacteria, depending upon the chemical gradient. EXPERIMENTAL RESULTS We also did some experiment about E. coli movement in the microfluidic channel. According the experiment method, we did a contrast experiment: E. coli random walk without chemoattractant gradient VS E. coli random walk with chemoattractant gradient. For the biased experiment, two solutions (motility buffer and aspartic acid) are pumped into the channel and the E. coli is observed to make a biased random walk in the central chamber where the chemoattractant gradient is developed by diffusion. When the E. coli is making their random walk in the focal plane, they are recorded. Figure 6 shows the tracking of two E. coli cells’ unbiased random walks, with the sampling rate 50 fps and the lens 40× (1 pixel = 0.375µm). From the track of E. coli 2 in Figure 6, we can clearly tell that there are three runs and two tumbles happing during the 113-frame video, but for E. coli 1 it is not very clear to tell which part of the track is a run or a tumble. Because there is no chemoattrator gradient in the central chamber, these two E. coli cells’ random walks are unbiased. If we can get enough long track of this unbiased random walk, we could compare it to the simulated walk and form the distributions of several parameters about the movement, which is one of our research goals.

Figure 6. The track of two E. coli’s unbiased movement (the black spots respond to the last positions of these two E. coli). The turn angle a is 154o and b is 123o. This figure is the result of a posterior image processing. In order to get a better illustration, we delete the background image. Figure 7 shows us the distribution of E. coli 2 (in Figure 6) moving speed. During the tumble the swimming speed first decreases to very low speed and then increases, so we could use this character to find the tumble positions. From Figure 7, we

find that between 0 to 2µm/s the frequency is 2 and this value corresponds to two tumbles during the video. The distribution of swimming speed under unbiased case is also used to compare with that under biased case.

Figure 7. The distribution of E. coli 2 (in Fig 6) moving speed. The mean of these speed samples is 20.17µm/s and the standard deviation is 9.3µm/s. The x axis corresponds to the value of E. coli moving speed and the y axis corresponds to the frequency of different speed sections. Figure 8 shows the track of the two E. coli cells’ biased random walk (there is an increasing chemoattractor gradient downwards) under the same experimental instrument. From the track of E. coli 2 in Figure 6, we can clearly tell that there are three runs and two tumbles happing during the 100-frame video, but for E. coli 1 because the few track in this video, it is impossible to analyze. Because there is a constant chemoattrator gradient in the central chamber resulting from the diffusion, these two E. coli cells’ random walks are biased. From the track of E. coli 2, we can find the length of the second running is obviously longer that those in Figure 6, and this is because positive stimulation (an increasing chemoattractant gradient or a decreasing chemorepellent gradient) decrease the probability of clockwise rotation and, therefore, the probability of tumbles and thus increase the length of the running along the gradient. If we can get enough long track of this biased random walk, we could compare it to the simulated walk and form the distributions of several parameters about the movement, which is one of our research goals.

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Figure 8. The track of two E. coli’s biased movement (the black spots respond to the last positions of these two E. coli) and the turn angle a is 165o and b is 15o. This figure is the result of a posterior image processing. In order to get a better illustration, we delete the background image. Figure 9 shows us the distribution of E. coli 1 (in Figure 8) moving speed. According to the character of swimming speed and tumble position, from Figure 7, we find that between 0 to 2µm/s the frequency is 3 and this value is so near to the two tumbles we analyze from the video. Several reasons will result to this inconsistency, for example there is another tumble with a large turn angle (this is a little difficult to analyze), and during a tumble the lowest speed last a little longer with 2 speed samples. The distribution of swimming speed under unbiased case is also used to compare with that under biased case.

Figure 9. The distribution of E. coli 1(in Figure 8) moving speed. The mean of these speed samples is 26.29µm/s and the standard deviation is 11.91µm/s. The x axis corresponds to the value of E. coli moving speed and the y axis corresponds to the frequency of different speed sections. CONCLUSIONS

The paper is presenting such a quantitative analysis system that the microfluidic channel could provide us a quantitative measurement of individual E. coli’s chemotaxis under a control envrionment. Through an inverted microscope and CCD camera, the E. coli HCB-33 motion is acquired, analyzed, and several movement parameters are gathered. This data is to be used to compare the movement of E.coli under unbiased and biased environments. From the Figure 7 and 9, we could find that there is a switch for the peak of the distribution of swimming speed for the biased case. The random motions of bacteria have been tracked successfully using the algorithm, and they behaved as expect. Based on the data of different parameters, we could conclude that the based environment (positive chemoattarctor gradient) result in a bigger mean of swimming speed and a bigger standard variance of swimming speed. In the near future work will be completed to bring quantitative results of this assay’s use with bacteria, and hopefully eukaryotic cells as well.

This assay is superior to other chemotactic models because it has the ability to be applied to control scenarios in engineering and micro-assembly. For example, we could control the chemoattractor gradient by pumping different-concentration solution into the channel. This research can also be built upon in a way that would enable others to successfully incorporate several protocols to successfully gather quantitative data on chemotaxis for other organisms, such as tetrahymena, which has significant implications on chemotaxis of other eukaryotic cells.

Now we are only able to measure several samples of these different parameters. We plan to optimize the software and try to measure a series of these different parameters and find their distributions, from which we could get another insight of the chemotaxis. Moreover, it is not enough to only calculate these different parameters about the movement for studying their chemotatic behavior stastistically and we will develop different models for this purpose. ACKONWLEDGE

The authors acknowledge the invaluable contributions of Howard Berg for access to his bacteria strains, expertise, and experience in culturing and handling E. coli (HCB 33). Special thanks go to Ed Steager for his useful conversations. This work was supported by NSF CAREER Award No. CMMI-0745019.

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