# Study on the Attachment of Escherichia coli to Sediment Particles at a Single-Cell Level: The Effect of Particle Size

^{1}

^{2}

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^{†}

## Abstract

**:**

_{2}and are similar in density. Through a bacterial tracking method together with microfluidic techniques, the attachment of single Escherichia coli cells on the particles was observed. The results showed that only a small portion of the cells that approach the particles remain attached and that the attachment probability per approach increases with surface area for both sediment and glass particles within the size range (8–62 μm) examined in this study. Therefore, finer sediments with more surface area have a higher E. coli attachment capacity. The attachment probability is higher on sediment particles than on glass microspheres of equivalent size, indicating preferential attachment of E. coli to sediment particles. The partition coefficient of the commonly used linear partition model was calculated based on microscopic measurements and the obtained relation of the partition coefficient with attachment probability and particle size was validated with data from the published literature.

## 1. Introduction

_{s}= the concentration of particle-associated bacteria (the number of bacteria associated with particles per unit water volume), colony-forming units (cfu)/L; s = sediment concentration, g/L; k = the partition coefficient, L/g; C

_{w}= the concentration of planktonic bacteria, cfu/L. This linear model works reasonably well in groundwater with relatively low bacteria concentrations [19,20] and has been verified in surface water [19], although it is still an empirical formula and lacks a fundamental thermodynamic basis [21,22]. Equation (1) agrees with the aforementioned observations that the particle concentration has an impact on bacterial attachment, but it does not explain how factors such as particle size affect bacterial attachment, and the influencing factors of the partition coefficient k is still not clear.

^{5}(cfu)/L and the suspended sediment concentration, with a density of 2.6 g/cm

^{3}and diameter of 30 μm, is 1 g/L, the number of sediment particles is 272 times the number of bacteria. This finding is in agreement with Goulder’s (1977) observation that in an estuary, there were many particles on which no bacteria were attached [24]. Thus, very few particles have attached bacteria on their surface, which makes direct observation very difficult.

_{2}and are similar in density to the natural particles. We placed particles of different sizes in flow cells, through which we continuously streamed an E. coli suspension. Using microscopy, we chose a number of particles, estimated the number of bacteria coming into contact with them, and directly counted the number of bacteria that remained attached on them. From these data, the attachment probability, i.e., the number of bacteria attached to a particle versus the number ever approaching the particle, was calculated. Then, the relation between cell attachment probability and particle size was analyzed. The partition coefficient of the linear partition model was conceptualized based on the microscopic measurements and compared with the results from the literature.

## 2. Materials and Methods

#### 2.1. Bacterial Strain and Bacterial Suspension

_{600}~0.1 at room temperature and the concentration was assessed following membrane filtration procedures (USEPA method 1603). Ten-micromolar PBS (pH = 7.4) was used throughout the experiments. Before each experiment, bacteria were first grown on nutrient broth (NB) agar plates at 37 °C overnight. Monoclonal colonies were isolated and inoculated into culturing tubes containing 5 mL NB medium and then grown in an incubator shaken at 150 rpm at 37 °C. After 7 h, 1 mL of E. coli culture, which reached the exponential growth phase (OD

_{600}≈ 1.0), was further diluted 20-fold in 100 mL NB medium and grown again in the same incubator for 15 h. Subsequently, cells were harvested in the stationary phase by centrifugation at 12,000 rpm for 2 min, after which they were washed three times with sterile PBS.

#### 2.2. Particles

#### 2.3. Microfluidic Device and Microscope

#### 2.4. Experimental Procedure

#### 2.5. Counting of Attached Cells

_{a}= f

_{c}N

_{local}= DN

_{local}/H, where f

_{c}= the compensation factor; D = the median diameter of suspended sediment particles, μm; H = the height of the below-equator part of sediment particles that is used for counting E. coli, μm; N

_{local}= the local attachment number of cells on the below-equator part of sediment particles. It is found that the number of attached cells on the front surface of the particles is roughly the same as that on the rear surface, which suggests that the assumption of a roughly uniform distribution of attached cells on particles is reasonable.

#### 2.6. Estimating of Approaching Cells

_{ap}using Equation (2):

_{1}= the flux of E. coli at the adjacent area, count/(μm

^{2}·s); t = time period, s; S = the projected area of the adjacent area perpendicular to the flow direction, which was a circular ring, μm

^{2}; u

_{1}= the flow velocity at the adjacent area, μm/s; l = distance between the particle surface and the boundary of adjacent area, μm

^{;}R

_{0}= the radius of particle, μm; $\overline{{C}_{w}}$ = the average concentration of planktonic bacteria, cfu/L.

_{w}may not be constant throughout the channel due to ‘shear trapping’. Some motile cells, such as E. coli, tend to be depleted in the low-shear region and accumulate in the high-shear region due to the alignment of the swimming direction with fluid streamlines caused by shear forces [35].

_{1}can be expressed as Equation (3) according to the theoretical solution of Stokes flow:

_{0}= average velocity, μm/s.

_{ap}can be calculated with Equation (4):

_{p}= U

_{0}·C

_{w}, the flux of non-particle-associated E. coli that is directly measured, count/(μm

^{2}·s).

#### 2.7. Attachment Probability Per Approach and Per Contact

_{a}is the number of cells that are ultimately attached to a particle, while N

_{ap}is the number of cells that have ever approached the particle.

_{c}. After approaching the particles, cells need to directly contact the surface to initiate attachment [33]. However, not every cell-particle contact can lead to attachment. E. coli in contact with particles can still escape from the near-surface regions of the particles. Tumbling, identified as rapid changes in swimming direction, is one of the influencing factors [36]. Therefore, p

_{c}reflects the influence of biological and chemical properties of cells and particles on attachment while excluding the effect of external hydrodynamic conditions. p

_{c}can be calculated as the attachment probability per approach, dividing the number of contacts by the number per approach. In the microfluidic experiment, i.e., under laminar flow, the larger the size of the particle, the longer distance cells would move to pass through the particle and thus lead to higher contact frequency. The contact number per approach is assumed to be proportional to the particle size. Thus, p

_{c}can be expressed as Equation (6):

## 3. Results and Discussion

#### 3.1. The Time Evolution of the Number of Attached Cells on Both Sediment and Glass Particles with Different Sizes

^{1}~10

^{5}cfu/L [5]. In a typical water environment [37], where the suspended sediment concentration is 0.5 g/L and the average equivalent diameter of suspended sediment is 30 μm, it can be calculated that the number density of suspended sediment is more than 10

^{7}L

^{−1}. Therefore, the number of suspended sediment particles is much larger than the number of E. coli cells, and only a minority of particles would have attached cells on them. In this case, the attached cells on particles are so sparse that they would not affect subsequent attachments.

#### 3.2. Attachment Probability of Cells and Its Relation with the Size of Particles

_{c}was obtained from time t via Equation (2) while $\overline{{C}_{w}}$ = 5.4 × 10

^{9}cfu/L. The result is also plotted in Figure 2. From the resulting curves of N

_{a}vs. N

_{ap}, by linearly fitting the early time part of the curves (i.e., before the curves reach a plateau), we can obtain the attachment probabilities, which are the slopes of the fitting lines. For 10 μm sediment, the data from the initial 10 h were used for the linear fitting, and for other particles, the data from the initial 15 h were used. The obtained attachment probabilities for sediment particles and glass microspheres with different sizes are shown in Figure 3.

_{c}for particles with different sizes. Thus, the attachment number is dependent on the total cell-particle contact number, and the influence of particle size on E. coli attachment is more likely reflected through an impact on hydrodynamic conditions than through an impact on surface properties. The results also verify Hispsey’s assumption (2008) that the attachment probability per unit surface area could be considered the same for sediments within the size range of 8–62 μm [39]. Although the attachment probability on sediment with different grain sizes could be considered the same from statistical perspectives, it is likely that there exists a preferred attachment surface in single sediment particles.

#### 3.3. Conceptualization of the Partition Coefficient and its Relation with the Attachment Probability Per Approach and the Particle Size

_{Ew}= the number of E. coli in the water column, cfu; r

_{a}= the attachment rate, s

^{−1}; N

_{Es}= the number of attached E. coli, cfu; r

_{d}= the detachment rate, s

^{−1}.

_{a}is proportional to the total cell-particle contact number and attachment probability per contact. It is reasonable to assume that the cell-particle contact number is proportional to the available area of the particle. A similar relationship was also used in an earlier work [39]. Then, r

_{a}can be expressed as r

_{a}∝ A

_{s}·p

_{c}, here A

_{s}is the total surface area provided by all particles per unit water volume, and A

_{s}= 6 s/(ρ

_{s}D) given ρ

_{s}= the density of suspended sediment particles.

_{a}can be expressed as:

_{ap}: k = λp

_{ap}/ρ

_{s}D

^{2}r

_{d}. The attachment rate coefficient λ is related to external hydrodynamic conditions. Bacterial detachment would occur most likely when the shear stress of flow exceeds a threshold. Of course, cell properties and factors influencing cell itself, such as EPS, matrix-degrading enzymes and nutrient levels, etc. may also affect bacterial detachment [40]. However, the detachment would be less affected by the particle size. Therefore, it is reasonable to treat the detachment rate r

_{d}as a constant when flow conditions are set. Then, the partition coefficient can be expressed as Equation (12).

_{a}= λ

_{a}/r

_{d}is independent of particle size. Combining Equations (7) and (12), the partition coefficient would have a negative correlation with D, and this agrees with previous literature reports [14,15].

_{ap}/D

^{2}. To test this relation, we applied it to data from the published literature and examined its validity. First, for different sized particles used in the literature data, we calculated p

_{ap}/D

^{2}using the regression function in Equation (7). Then, the measured values of k in the literature were plotted against the calculated p

_{ap}/D

^{2}as shown in Figure 4. All the data can be well fitted linearly. The slope, which equals λ

_{a}/ρ

_{s}in Equation (12), varies because λ

_{a}is related to system-dependent external hydrodynamic conditions and thus is different for different works [1,14,15,41]. The good results of linear fitting suggest the validity of the linear relation between k and p

_{ap}/D

^{2}. Moreover, considering that those previous results were measured by different groups at the macro level, Equation (12) is derived from a microscopic picture of bacterial attachment, so the agreement between earlier reported experimental results and Equation (12) indicates a generality of the obtained linear relation between k and p

_{ap}/D

^{2}. However, due to the limited size range that the data covered, to what extent Equation (12) can be effectively used needs to be further studied.

## 4. Conclusions

_{ap}/D

^{2}, which is quantitatively verified using data from the published literature. The work herein introduces a new way to study attachment and distribution of indicator bacteria to sediments at a single-cell resolution by combining bacterial tracking methods and microfluidic devices. Both physical and biochemical processes influence bacterial attachment to sediments. However, as shown in this work, we can separate and study the factors influencing the different stages of bacterial attachment individually. We hope this study will inspire additional work in the future to provide further details at the microscopic level for cell-particle interactions and to develop a comprehensive ecological model that could account for both attachment and detachment of E. coli on sediments, which will help to improve control over the contamination level of surface waters.

## Supplementary Materials

**a**) Picked positions for measuring E. coli flux in the cross-section of the channel. (

**b**) The cumulative average of E. coli flux at selected positions, Figure S2: Scanning electron microscope (SEM) micrographs of glass microspheres. (

**a**) 10 μm microspheres at low magnification (× 10k); (

**b**) 10 μm microspheres at high magnification (× 30k); (

**c**) 20 μm microspheres at low magnification (× 10k); (

**d**) 20 μm microspheres at high magnification (× 30k); (

**e**) 50 μm microspheres at low magnification (× 3.6k); (

**f**) 50 μm microspheres at high magnification (× 20k), Figure S3: SEM micrographs of sediment particles. (

**a**) 10 μm sediment particles at low magnification (× 10k); (

**b**) 10 μm sediment particles at high magnification (× 30k); (

**c**) 20 μm sediment particles at low magnification (× 3k); (

**d**) 20 μm sediment particles at high magnification (× 10k); (

**e**) 50 μm sediment particles at low magnification (× 3k); (

**f**) 50 μm sediment particles at high magnification (× 10k).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic of a microfluidic system and a flow-cell channel. (

**a**) Schematic of a microfluidic system: 1, syringe pump; 2, syringe; 3, flow cell; 4, inverted microscope; 5, waste container. (

**b**) The definitions of the x-, y-, and z-axes in one channel of the flow cell: Z = 0 at the bottom of the channel. (

**c**) E. coli attachment on a 50 μm sediment particle (

**left**) and a 50 μm glass microsphere (

**right**).

**Figure 2.**Time evolution of bacterial attachment to particles of different sizes. (

**a**,

**c**,

**e**) are for 10 μm, 20 μm, and 50 μm sediment particles, respectively; (

**b**,

**d**,

**f**) are for 10 μm, 20 μm, and 50 μm glass microspheres, respectively. The results were obtained by averaging 30 samples for each type of particle. Red arrows show the final measured numbers of attachments.

**Figure 3.**The relation between attachment probability and the diameter of particles for both sediment particles and glass microspheres. (

**a**) The relation between p

_{ap}and D. Lines are linear fittings of the corresponding data. (

**b**) The relation between relative p

_{c}and D. The base p

_{c}was for 20 μm sediments.

**Figure 4.**The relation between the calculated p

_{ap}/D

^{2}from Equation (9) and the measured k. Measured data were obtained from literature [1,14,15,41] and the corresponding partition coefficient was calculated for different particle sizes from 8 μm to 62 μm. Lines are linear fittings of the corresponding data.

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**MDPI and ACS Style**

Wu, T.; Zhai, C.; Zhang, J.; Zhu, D.; Zhao, K.; Chen, Y.
Study on the Attachment of *Escherichia coli* to Sediment Particles at a Single-Cell Level: The Effect of Particle Size. *Water* **2019**, *11*, 819.
https://doi.org/10.3390/w11040819

**AMA Style**

Wu T, Zhai C, Zhang J, Zhu D, Zhao K, Chen Y.
Study on the Attachment of *Escherichia coli* to Sediment Particles at a Single-Cell Level: The Effect of Particle Size. *Water*. 2019; 11(4):819.
https://doi.org/10.3390/w11040819

**Chicago/Turabian Style**

Wu, Tao, Chunhui Zhai, Jingchao Zhang, Dejun Zhu, Kun Zhao, and Yongcan Chen.
2019. "Study on the Attachment of *Escherichia coli* to Sediment Particles at a Single-Cell Level: The Effect of Particle Size" *Water* 11, no. 4: 819.
https://doi.org/10.3390/w11040819