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Evaporation-Induced Patterns from Droplets Containing Motile and Nonmotile Bacteria Tittu Thomas Nellimoottil,† Pinjala Nagaraju Rao,‡ Siddhartha Sankar Ghosh,*,†,§ and Arun Chattopadhyay*,§,| Department of Biotechnology, Department of Chemical Engineering, Centre for Nanotechnology, and Department of Chemistry, Indian Institute of Technology, Guwahati-781039, India ReceiVed March 4, 2007. In Final Form: May 30, 2007 In this letter, we report the observations of specific pattern formation from the evaporation of aqueous droplets containing motile and nonmotile bacteria. We found that when motile bacteria were present the droplet evaporated into disclike patterned deposits of bacteria. However, when the bacteria were made nonmotile by treatment with liquid nitrogen, the droplet evaporated into ringlike deposits. We also observed that bacteria with higher motility produced more uniformly deposited disclike patterns. Furthermore, we propose a model with numerical simulations to explain the mechanism of formation of these patterns. The model is based on the advective fluid flow from the center of the droplet toward the edge due to enhanced evaporation from the edge of the pinned droplet in comparison to that from the free surface. For the case of motile bacteria, we have added another velocity parameter toward the axis of the droplet and directed against the fluid flow in order to account for the disclike pattern formation. The numerical simulations match the experimental observations well. The present work, by qualitative and quantitative understanding of the evaporation of bacteria droplets, demonstrates that the inherent bacterial motility is primarily responsible for the formation of these differential patterns.
Introduction droplet1
A consummate understanding of an evaporating has important consequences in emerging technologies such as micro and nanoscale array fabrications,2 inkjet printing, paint technology, and protein crystallization.3 The formation of so-called “coffee rings”, in systems involving hydroxyapatite nanoparticles,4 coffee,1,5,6 and polystyrene latex microspheres,7 has been explained using the concept of contact-line “pinning” and enhanced evaporation from the edge of the droplet in comparison to its free surface. In addition, there are efforts in generating patterned deposition under different experimental conditions, such as constrained evaporation leading to concentric deposits of solute particles and evaporation in the presence of an electric field leading to guided patterns. However, recent experiments with respect to the evaporation of protein-containing aqueous droplets indicate that the proposed mechanism of evaporation may not necessarily be general in nature.7 Thus, a thorough understanding of the phenomenon under different evaporation conditions as well as involving the evaporation of different species is deemed essential in order to have more versatile applications of the phenomenon. It is interesting that the primary focus, with respect to the evaporation-induced pattern formation mentioned above, has been confined to understanding the pattern formation where the solute (dispersed) particles in question were inanimate * Corresponding authors. (A.C.) E-mail:
[email protected]. (S.S.G.) E-mail:
[email protected]. † Department of Biotechnology. ‡ Department of Chemical Engineering. § Centre for Nanotechnology. | Department of Chemistry. (1) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827-829. (2) Deng, Y.; Zhu, X. Y.; Kienlen, T.; Guo, A. J. Am. Chem. Soc. 2006, 128, 2768-2769. (3) Dimitrov, A. S.; Dushkin, C. D.; Yoshimura, H.; Nagayama, K. Langmuir 1994, 10, 432-440. (4) Sommer, A. P.; Rozlosnik, N. Cryst. Growth Des. 2005, 5, 551-557. (5) Deegan, R. D. Phys. ReV. E 2000, 61, 475-485. (6) Chopra, M.; Li, L.; Hu, H.; Burns, M. A.; Larson, R. G. J. Rheol. 2003, 47, 1111-1132. (7) Chang, S. T.; Velev, O. D. Langmuir 2006, 22, 1459-1468.
objects and evaporation-induced pattern formation involving living beings has not been studied at all. Recent investigations of the patterning of biological entities such as bacteria, viruses,8,9 and arrays of single cells on substrate surfaces10 further underscore the need to understand the phenomenon in a larger context involving species other than inanimate objects. Herein, we report the results of investigations of the evaporation of sessile droplets containing bacteria that were either motile or nonmotile at the time of evaporation. The primary objective of the investigation was to understand the difference in the evaporation-induced pattern formation involving the above two systems. Our experimental observations indicate that the pattern formation was related to the bacteria being motile or nonmotile at the time of evaporation. The nonmotile bacteria containing aqueous droplets evaporated into commonly observed ring patterns, whereas the evaporation of motile bacteria containing droplets resulted in disclike patterns. Numerical simulations, based on the conventional model and using advective fluid flow toward the droplet edge with the incorporation of an additional velocity parameter for the motility of bacteria, could account for the disclike patterns in motile bacteria containing droplet vis-a`-vis ring formation for the nonmotile ones. Experimental Section Three bacteria strains, namely, Escherichia coli MTCC433, green fluorescence protein (GFP) expressing Escherichia coli DH5R, and Lactobacillus saliVarius subsp salivarius NRRL B 1949, were grown under their respective standard growth conditions. The cultures were then centrifuged and washed in two cycles, and the collected bacteria were suspended in sterile doubly distilled water. A 0.5 µL portion of each of the suspensions was immediately withdrawn by a micropipette and subsequently deposited onto alcohol-cleaned coverslips. In a parallel set of experiments, the diluted bacteria were made nonmotile by keeping them in liquid nitrogen (LN2) for 10 min, followed by immediate thawing to room temperature. Subsequently, (8) Razatos, A.; Ong, Y.; Sharma, M. M.; Georgiou, G. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 11059-11064. (9) Cheung, C. L.; Chung, S.; Chatterji, A.; Lin, T.; Johnson, J. E.; Hok, S.; Perkind, J.; Yoreo, J. J. D. J. Am. Chem. Soc. 2006, 128, 10801-10807. (10) Hui, E. E.; Bhatia, S. N. Langmuir 2007, 23, 4103-4107.
10.1021/la7006205 CCC: $37.00 © 2007 American Chemical Society Published on Web 07/12/2007
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R)
Figure 1. Schematic diagram of the droplet, where θ is the contact angle made by the drop with the substrate, h0 is the initial height of the drop, and J(r, t) is the rate at which fluid evaporation takes place. 0.5 µL portions of the cultures were similarly placed on cover slips for further evaporation. Drops of about 1.4 mm contact diameter were allowed to evaporate under ambient conditions, and the resultant patterns were probed using an optical microscope (AxioCam MRC Zeiss). The component images were integrated, using Macromedia Fireworks MX 2004, in order to have complete views of the whole patterns, which are reported herein.
Results and Discussion An evaporating droplet can be assumed to take the shape of a spherical cap at all evaporation times, with the radius remaining constant until the drop flattens to a film. The radius of the sphere (R) can be related to the height (h) and the base radius (r) of the droplet (eq 1).
r2 + h 2 2h
(1)
A schematic diagram of the droplet is shown in Figure 1. According to the conventional view, the extraordinary evaporation from the edge of the droplet in comparison to that from the free surface leads to an advective fluid flow toward the edge. The flowing fluid carries along with it the dispersed particles that are subsequently deposited at the pinned contact line. This process continues until the droplet completely evaporates. The result is the formation of a ringlike pattern upon evaporation of the droplet. The evaporation process leading to the deposition of particles at the edge can be modeled on the basis of instantaneous velocity components of particles in the r and z coordinates, ur and uz respectively. According to Hu and Larson,6,11 the velocity components can be written as
u˜ r ) u˜ z )
(
)
3 1 1 z˜2 2z˜ {(1 - r˜2) - (1 - r˜2)-λ(θ)} 2 8 1 - ˜t r˜ h˜ h˜
( (
)
(2)
z˜3 3 1 z˜2 [1 + λ(θ)(1 - r˜2)-λ(θ) - 1] 2 + 4 1 - ˜t 3h˜ h˜ z˜2 3 1 z˜3 {(1 - r˜2) - (1 - r˜2)-λ(θ)} 2 - 3 h˜ (0, t) (3) 2 1 - ˜t 2h˜ 3h˜
)
where r˜ ) r/R, z˜ ) z/h0; h˜ ) h/h0; ˜t ) t/tf; u˜ r ) urtf/R; u˜ z ) uztf/h0; and λ(θ) ) 0.5 - (θ/π). Here, tf is the total time for complete evaporation of the droplet, and h0 is the initial height of the droplet.
Figure 2. (A) Pattern formed by GFP-expressed motile E. coli DH5R. (B) Pattern formed by GFP-expressed cold-treated (nonmotile) E. coli DH5R. (C and D) Radial profile of cell concentration by numerical simulations corresponding to images A and B, respectively. The scale bars is 0.2 mm.
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Figure 3. Bright-field images of evaporation patterns from droplets of a bacterial solution. (A) Motile E. coli MTCC443. (B) Motile E. coli DH5R. (C) Nonmotile L. saliVarius. (D) Nonmotile E. coli MTCC443. (E) Nonmotile E. coli DH5R. (F) Nonmotile L. SaliVarius NRRL B 1949. Bacteria in images D-F were treated with LN2 before evaporation of the droplet. The typical diameter of a droplet was about 1.5 mm.
The above model has been appropriately applied to the evaporation of droplets for inanimate objects such as coffee. However, when considering the evaporation of droplets consisting of motile bacteria one needs to consider the ability of the bacteria to swim away from the edge toward the axis. To account for the difference in experimental observations between the evaporationinduced pattern formations from motile and nonmotile bacteria, we have introduced additional velocity components for the motile bacteria while keeping the above expressions for nonmotile ones. The normal evaporation-induced flux would move the bacteria toward the edge of the droplet, thereby increasing their population at the edge. However, the inherent motility of the bacteria would induce a net movement toward the center, where the concentration is rather low. The bacterial motion can be described by introducing a velocity toward the center of the droplet.
Vb ) -D
∇c |∇c|
(4)
Here the concentration gradient of active bacteria,∇c, provides the direction of the driving force for the bacterial motion, and D is a phenomenological coefficient determining the diffusion of bacteria in the fluid. D depends on the activity of an individual motile bacterium and can be assumed to have a normal distribution over the population of motile bacteria.12 Hence the net velocity in the r and z directions (Supporting Information) can be modified for motile bacteria as in eq 5
uf ) u + Vb
(5)
Here, u represents the fluid velocity as given by Hu and Larson.11,13 (eqs 2 and 3). The details of calculation of uf are included in
Supporting Information (SI-I). Numerical simulations for the nonmotile bacteria have been performed using a system of 500 particles that were initially distributed randomly. The particle positions were dynamically updated on the basis of only the fluid velocity as proposed by Hu and Larson11,12 (SI-I). For numerical simulations involving motile bacteria, apart from the advective flow due to evaporation, the bacterial motion has also been considered, which predominantly drives these microorganisms to the central axis of the evaporating sessile droplet. The simulations were implemented using MATLAB 7.0, and the corresponding concentration profiles were generated. Figure 2A shows the fluorescence micrograph of the patterns from a droplet containing GFP expressed motile E. coli bacteria. The corresponding micrograph of the nonmotile bacteria is shown in Figure 2B. As evident from the Figure, the bacteria that were nonmotile at the time of evaporation produced circular ring patterns with very few bacteria present inside the ring. However, for the bacteria that were motile at the time of evaporation, a considerable number of bacteria were present in the intervening region, in addition to those in the perimeter. In other words, the motile bacteria upon evaporation produced disclike patterns, and the nonmotile ones produced only ring patterns. It is also interesting that the width of the ring corresponding to the nonmotile bacteria is larger in comparison to that of bacteria that are motile. The present observations indicate that during the evaporation of the droplet bacterial motion toward the center of the droplet is significant, in addition to the usual advective fluid flow toward the edge. The simulation results are shown in Figure (11) Hu, H.; Larson, R. G. Langmuir 2005, 21, 3963-3971. (12) Liu, Z.; Papadopoulos, K. D. Appl. EnViron. Microbiol. 1995, 35673572. (13) Hu, H.; Larson, R. G. J. Phys. Chem. B 2006, 110, 7090-7094
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2C,D with insets consisting of expanded views of part of the distribution of bacteria for each case. As is clear from the Figure, the distribution of bacteria from the nonmotile ones is primarily at the edge of the droplet, whereas a significant number of bacteria are present in the intervening region, in addition to those in the perimeter, for the motile ones. Also clear from the Figure (Figure 2C,D) is the result that the number of bacteria present in the perimeter for motile ones is less than the number present in the case of nonmotile ones. One may ask a question about the deposition of motile bacteria at the edge at all. This can be understood from the point of view that not all of the bacteria are always alive (i.e., there are nonmotile bacteria present even in the motile ones); the motility of individual bacteria may be different and may even be sufficiently low to be unable to overcome the advective flow-induced forces toward the perimeter, and thus they get deposited at the contact line. Even then, the qualitative comparison of pattern formation of GFP-expressed E. coli DH5R (motile and nonmotile) and the corresponding results from numerical simulations clearly indicates the role of the motility of bacteria in pattern formation. To further understand the role of bacteria motility in pattern formation, we pursued evaporation studies with three kinds of bacteria; two of them (from different strains) were of different motilities (E. coli MTCC443, E. coli DH5R), and the third one was naturally nonmotile (L. saliVarius). One set of droplets containing each of the three strains was evaporated as described above. Furthermore, another set of these bacterial strains was treated with LN2 in order to render each strain nonmotile, which was followed by thawing and evaporation of droplets of these bacteria. Results of the evaporation of all three types of bacteria are shown in Figure 3. It may be noted that when the bacteria were motile the droplets produced disclike patterns (Figure 3A,B). Also, more motile bacteria lead to more bacterial deposition within the ring (Figure 3A), whereas bacteria with lesser motility produced sharper rings with less bacteria present in the intervening region (Figure 3B). However, for the case of nonmotile bacteria (L. saliVarius), the droplets produced ringlike patterns instead of discs (Figure 3C) even though they were not treated with LN2. In other words, the evaporation of nonmotile bacteria produced ring patterns, just as that of inanimate objects did. Furthermore, whether the bacteria were naturally motile or not, the LN2-treated
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bacteria produced ringlike patterns in all three cases (Figure 3D-F). These observations clearly demonstrate that motile bacterial solution upon evaporation produced patterns (disclike) that are different from those of nonmotile bacteria (ringlike). An evaporative liquid droplet is usually pinned at the contact line between the liquid, air, and substrate interfaces. Subsequently enhanced evaporation from the edge of the droplet in comparison to that from the free surface leads to an advective fluid flow toward the pinned contact line. Solute particles that are carried by this flowing fluid are preferentially deposited at the edge, giving rise to the ringlike patterns. This is especially true when the droplet is small, where the gravitational force and Marangoni effects are negligible and no other force toward the center of the droplet is present. In the present set of experiments with nonmotile bacteria, we have observed ringlike patterns that have been accounted for by the established hydrodynamic models. However, when the bacteria were motile the evaporation-induced patterns were more like disclike than ringlike. This is possible if there is substantial movement of the bacteria toward the axis against the capillary force acting toward the edge of the droplet. We have successfully incorporated the migration of motile bacteria into the existing hydrodynamic models of evaporating sessile drops by using the bioconvective component, Vb, coupled with the fluid velocity, u. The theoretical understanding, substantiated by numerical simulation, of the mechanism of pattern formation from motile and nonmotile bacteria presented here holds potential for applications in biocarpets,14 biosensors, and other bionano devices. Acknowledgment. We thank the Department of Science and Technology, India (nos. SR/S5/NM-01/2005, DST/TSG/ME/ 2003/83, and 2/2/2005-S.F.) and the Council of Scientific and Industrial Research, India (no. 37 91258/06/EMRII) for funds and Dr. A. Ramesh, Department of Biotechnology, IIT Guwahati, for help. Supporting Information Available: Discussion of numerical simulations. Materials and methods. Simulation videos. This material is available free of charge via the Internet at http://pubs.acs.org. LA7006205 (14) Darnton, N.; Turner, L.; Breuer, K.; Berg, H. C. Biophys. J. 2004, 86, 1863-1870.
