Single particle tracking of correlated bacterial dynamics

ABSTRACT Pattern formation in 3D random media has been a topic of interest in soft matter and biological systems. However, the onset of long-range microscopic ordering has not been explored in randomly moving self-propelled particles due to a lack of model systems as well as local probe techniques. In this article, we report on a novel experiment, using motile Escherichia coli bacteria as a model system, to study the onset of dynamic correlation and collective movement in three-- dimension. We use fluctuation of an optically trapped micron-size bead as a detector of correlated bacterial motion, and further study this behavior by analyzing the motility of fluorescent bacteria in a confocal volume. We find evidence of dynamic correlation at very low volume fractions (0.01). We show that the magnitude of this correlation strongly depends on the interbacterial distances and their coupling modes. This opens up possibilities to probe long-range pattern formation in actively propelled cells or organisms coupled through hydrodynamics and/or chemical signaling.

INTRODUCTION

Cell movement is ubiquitous in nature. A variety of interand intracellular signaling mechanisms underlie collective cell movement, which is a topic of intense current interest (Bray, 2002). The physical origins of fluid dynamics and chemical coupling between actively moving cells are poorly understood. This is a generic problem of active motion leading to long-range ordering, for example, birds in flight, a swarm of fish, or bacterial cells swimming together (Pedley and Kessler, 1992). Theoretical approaches for long-range ordering have also been explored (Berg, 2000; Gregoire et al., 2001; Jeremy et al., 1996; Nasseri and Phan-Thien, 1997; Toner and Tu, 1998). The motility and the chemotactic signaling mechanism of bacteria have been well characterized and serve as a good model system to address aspects of long-range ordering (Berg, 2000). A typical Escherichia coli bacterial cell is - 1(mu)m in diameter and 3 (mu)m in length, and has a mass of - 1 pg. Viscous forces dominate the motion of bacteria due to its very low Reynolds number of 0lo 10^sup -4^ (Purcell, 1977). Bacterial dynamics are characterized as tumbling and running. Under homogenous external chemical signal concentration, bacteria run with a mean velocity of 20 (mu)m/s, with exponentially distributed run lengths and mean time of 1-s runtime. They change direction randomly by tumbling, which has a mean duration of 0.1 s (Berg, 1996; Berg, 2000). In an interesting recent experiment, Wu and Libchaber (2000) analyzed active bacterial motion in quasi two-dimension and observed an anomalous diffusion, which they attributed to the collective dynamics of bacteria.

In this article, we probe these active processes using an optically localized bead (Ashkin, 1997) and measure the local ordering in the bacterial bath at different percentage volume fraction (0) 0.1, 0.01, and 0.001 corresponding to mean interbacterial spacing of 10, 21, and 46 (mu)m respectively. This allows us to measure the onset of correlation in bacterial dynamics in three dimensions. The above cooperative dynamics was further studied using confocal fluorescence detection (Webb et al., 2001). In particular, we present experiments as shown in Fig. 1, on 1), single particle tracking of an optically trapped polystyrene 3-(mu)m diameter bead in the presence of active (motile) bacteria at various concentrations, and 2), observing single fluorescent bacterial motion, at various volume fractions, through a 3.12-(mu)m diameter confocal excitation volume, which is much smaller than the mean run length. In the above experiments, we analyze the time series of Brownian fluctuations of the trapped bead and fluorescence intensity fluctuations with and without bacteria. From these experiments we are able to distinguish the subtle differences between thermal and active processes leading to correlated bacterial dynamics and the role of chemical signaling.

MATERIAL AND METHODS

Sample preparation

The motile strain of E. coli RP437 was transformed (insertion of plasmid DNA, with gene of interest, into the bacteria) with a plasmid having enhanced green fluorescent protein (EGFP) gene driven by lac promoter (pUC origin, ampicillin resistance), for fluorescence measurements and imaging. Cells taken from plates were grown in 120-ml LB media for 18 It at 25 deg C. Cells were visually checked for their motile behavior, centrifuged at 5500 rpm for 20 min at 4 deg C and resuspended in motility buffer (MB, 10 mM KH2PO4, 67 mM NaCI, 0.1 mM EDTA and 0.1%Io glycerol) to the required concentration. Cells were incubated, at room temperature, in the motility buffer for 30 min before the experiments. Measurements were carried out at room temperature, at three different bacterial concentrations 10^sup 7^, 10^sup 8^, and 10^sup 9^ cells/ml. Sample cell volume was confined to - 120 (mu)l in a circular well of depth 1.5 mm made of neoprene O-rings between two cover slips. Both the optical trap and the fluorescence correlation spectroscopy (FCS) experiments were carried on the same batch of samples and at 5 (mu)m above the cover slip. The concentration of the Verapimil drug in our experiment, used to inhibit bacterial chemotaxis and motility, was based on the values reported in the literature (Tisa et al., 2000).

Experimental setup and data acquisition

The schematic of the experimental setup is shown in Fig. 1. The optical tweezer was set up by focusing an infrared laser (Nd-Yag, 1064 nm, 200 mW from Coherent, Santa Clara, CA) beam to a diffraction-limited focus using an objective lens (100X, N.A 1.4, Olympus, Japan). A red diode laser (5 mW, 635 nm, Thorlabs, Newton, NJ) was aligned coaxial to infrared for tracking the bead in the trap using back-scattered light collected on a quadrant detector (Shivashankar et. al., 1998). In confocal fluorescence measurements, a 488-nm laser (Ar-Ion, 50 mW from Spectra Physics, Mountain View, CA) was used to excite the fluorescent bacterial cells, and their emission signal was detected in a confocal arrangement (3.12-(mu)m diameter detection volume, characterized by measuring the diffusion constant of 1-(mu)m fluorescent bead). An avalanche photo detector (EG&G, Gaithersburg, MD) and a photon counter (SR400, Stanford Research Systems, Sunnyvale, CA) were used for photodetection. The time series of the trapped bead fluctuations and intensity fluctuations in the confocal volume was obtained using onboard DAQ (data acquisition card AT-MIO16EX10) and Labview software (National Instruments, Austin, TX). Each measurement of autocorrelation function (ACF) constitutes an average of 10 independent runs repeated on the same sample and more than five sets of experiments were performed on samples drawn from independent cultures. The statistical autocorrelation of the time series give values between + 1 and -1. In confocal fluorescence experiments, the intensity fluctuation time series was recorded with a 1-ms bin time for 50 s. Each experiment lasted for -2 h from the time of resuspension of cells in motility buffer. The motility buffer does not favor bacterial growth and thus the cell number remains unchanged. We have also confirmed, by microscopy, that the morphology is not changed during the experiment.

INSTRUMENTATION AND CALIBRATION

Optical trap characterization

CONCLUSIONS

In conclusion, we have directly measured the onset of dynamic correlation in randomly moving self-propelled particles. Using single particle tracking methods and tuning the mean interbacterial distance, comparable to their mean run lengths, we measured the correlation time scales. The magnitude of the dynamic viscosity in the bacterial bath was determined by separating the thermal and active correlation timescales in the trapped bead fluctuations. We propose that long-ranged pattern formation in chemotactic and motile bacterial bath may be strongly modulated by chemical signaling in addition to hydrodynamic coupling. Our results have implications in understanding localized microscopic ordering mechanisms in self-propelled organisms involving chemical signaling and hydrodynamic coupling modes.

We thank A. Libchaber and S. Rarnaswamy for useful discussions and John S. Parkinson, University of Utah, Salt Lake City, Utah USA for providing us with the bacterial strains.

[Reference]

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[Author Affiliation]

G. V. Soni,* B. M. Jaffar Ali,* Y. Hatwalne,^ and G. V. Shivashankar*^

[Author Affiliation]

*National Center for Biological Sciences, Tata Institute of Fundamental Research, GKVK Campus, Bangalore-560065, India; and ^Raman Research Institute, Bangalore, India

[Author Affiliation]

Submitted August 26, 2002, and accepted for publication October 31, 2002.

Address reprint requests to G. V. Shivashankar, E-mail: shiva@ncbs.res.in.