1. Introduction

Non-invasive biospeckle measurements are used extensively in different fields, such as in agriculture, for monitoring fruit ripening [1]; dentistry, for the early diagnosis of tooth erosion [2] or for monitoring the curing kinetics of dental cements [3]; oenology, for the characterization of the effects of grape variety, vintage and of different wine-making cellars on a wine’s viscosity [4]; or in microbiology, for the characterization of Bacillus thuringiensis crystals used as a biopesticide [5]. In a previous study, we showed that biospeckle is a reliable method for real-time monitoring of bacterial growth kinetics in liquid culture [6] using Bacillus thuringiensis as a model bacterium. B.thuringiensis is a Gram-positive, spore-forming bacterium that synthesizes parasporal crystalline inclusions [7]. Each B.thuringiensis strain produces specific insecticidal toxins within these crystals, which are known as δ-endotoxins and are widely used against lepidopteran, dipteran, and coleopteran pests [8,9]. The mode of action of this biopesticide is that, after being swallowed by the insect larvae, the crystal content is solubilized in the alkaline pH of the midgut, the protoxins are then activated and become capable of recognizing and binding to special receptors inducing the epithelium cell perforation and apoptosis signaling activation. This results in the insect starving to death [10].

The fermentation process of B.thuringiensis cells consists of the first two phases where the vegetative cells synthesize the enzymes and factors needed for cell division and population growth and start to consume the nutrients and multiply. This process therefore corresponds to the lag phase (which lasts for less than 2 hours, allowing the bacteria to adapt to the culture medium) and the exponential phase (where cell division occurs and the number of vegetative cells therefore increases). Nonetheless, when nutrients and oxygen become insufficient in the medium, the bacterium enters the stationary phase. Being in a stressful environment, the bacterium begins synthesizing a spore (containing its DNA) and a protein crystal. Hence, the cell membrane is destroyed, releasing the spore and the crystal, as well as cellular debris, into the medium. This last phase is called cell lysis [11]. From a scattering point of view, two of the four growth phases were distinguished: the exponential phase, where the number of the bacteria increases (hence the number of scatterers increases), and the stationary phase, where sporulation and cell lysis occur (meaning that the size of scatterers changes).

In a prior study, we proved that speckle grain size and spatial contrast are accurate tools for monitoring the fermentation process of B.thuringiensis cells. A high correlation between speckle parameters and the analytical methods used by microbiologists was also revealed [6]. In this new study, we simulate bacterial fermentation, using calibrated polystyrene microspheres with different sizes and at different concentrations. Our main purpose is to explain the ability of the speckle spatial analysis to recover characteristics of perfectly known scattering media. In section 2, we explain how we simulate the fermentation process by assimilating the bacteria as well as crystals and spores to different sizes and proportions of polystyrene microspheres. The speckle experimental setup and parameters are also described in this section. Section 3 presents the results, including our analysis of the speckle grain size dx curve. Finally, in section 4, we draw our conclusions.

2. Experimental study

2.1 Sample characterization and handling

We consider Lebanese Bacillus thuringiensis var. Kurstaki strain LIP^MKA [12] as our reference bacterium. In order to promote the sporulation of the B.thuringiensis cells, the LIP^MKA strain were cultivated in a T3 medium at 30°C, the pH was adjusted at 6.8 and the stirrer speed was set at 250 rpm (round per minute) [12]. The B.thuringiensis cells appear as rods measuring 3 to 5 µm long and about 1.0 µm wide, as largely documented in the literature [11,13,14]. The sizes of LIP^MKA spores and crystals were determined using scanning electron microscopy (SEM) (Hitachi S3200N) images [see left-hand parts of Figs. 1(a) and 1(b)] and ImageJ software for image analysis [15]. Crystal and spore size distributions were determined using the Rice rule for the number and width of bins [16] and are illustrated in the right-hand parts of Figs. 1(a) and 1(b) respectively, yielding bipyramidal crystals of a mean size equal to 1.55 ± 0.29 µm and spores of a mean size equal to 1.54 ± 0.27 µm. The same procedure was conducted twice to ensure reproducibility. The distinction between spores and crystals was made by the operator, based on a shape criterion [see Fig. 1(b)].

 

Fig. 1. (a) Left: SEM image representing LIP^MKA bipyramidal crystals. Right: Size distribution of LIP^MKA bipyramidal crystals. (b) Left: SEM image representing LIP^MKA spores and crystals. Right: Size distribution of LIP^MKA spores.

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To simulate bacterial fermentation growth in the speckle experiments, two different sizes of microspheres were chosen. Polystyrene microspheres (Polybead Microspheres from Polysciences, Inc) with a diameter size of 4.5 ± 0.315 µm and 1.5 ± 0.075 µm, having anisotropy factors (g) equal to 0.87981 and 0.92995, respectively, were suspended in deionized water and used as scattering particles to represent the bacteria on the one hand and the crystals and spores on the other. As shown by the scattering indicators shown in Fig. 2, most of the scattered light is in the forward direction for both cases.

 

Fig. 2. Logarithmic scale representation of the phase function (for a parallel polarization) for an anisotropy factor g equal to (a) 0.92995 for the 1.5-µm microspheres (b) 0.87981 for the 4.5-µm microspheres. Incident light comes from the left of the graph. The dashed line is a visual guide, indicating a 20° angle.

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The scattering coefficient µ_s of the aqueous microsphere suspensions was estimated using the experimental setup illustrated in Fig. 3. The setup includes a He-Ne laser with a wavelength of 632.8 nm, a half-wave plate (λ/2) and a polarizer for adjusting the incident intensity of the laser, the studied sample, a microscope objective is used to focus the transmitted photons from the sample on the diaphragm so that only the ballistic ones can pass and reach the photomultiplier tube (PMT). The total attenuation coefficient ${\mu _t}$ is determined using the Beer-Lambert's law:

 

Fig. 3. Experimental setup for the measurement of the total attenuation coefficient ${{\boldsymbol {\mu} }_{\boldsymbol{t}}}$.

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We also measured the optical density (OD) of each microsphere sample using a Cary 60 Varian flash spectrophotometer set at 600 nm [6]. Table 1 shows the optical characteristics of the microsphere suspensions used to model the two studied phases of fermentation. As previously mentioned, we divided the fermentation process into two main phases. Details of the samples relating to phase I (i.e., the exponential phase) are given in Table 1(a). Only the 4.5-µm polystyrene microspheres were used to simulate bacterial growth; corresponding samples were numbered 1 to 5. We varied their scattering coefficient ${\mu _s}$ and measured their optical density OD. Optical properties of phase II (i.e,. the stationary phase) sample details are given in Table 1(b). Here, we considered mixtures of 4.5- and 1.5-µm microspheres in order to recreate the phenomenon that occurred: each 4.5-µm microsphere [noted B for “bacterial” in Table 1(b)] was replaced by three 1.5-µm microspheres [noted C&S for “crystal and spores” in Table 1(b)] to reproduce the cell lysis phase where each bacterium bursts, liberating one crystal, one spore and cellular debris [11]. Corresponding samples were numbered 5 to 9. Sample 9 corresponds to an ideal case where at the end of the fermentation, bacteria in vegetative phase are completely neglected, and the culture medium contains only crystals, spores and cell debris of the same size (1.5 µm).

Table 1. Optical properties of microsphere suspensions that simulate bacterial suspensions during: (a) Phase I where there were only 4.5-µm polystyrene microspheres and (b) Phase II where mixtures of 4.5 and 1.5 µm microspheres were considered. The values of the optical density OD and the scattering coefficient µ_s correspond to the average of three measurements.

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2.2 Speckle experimental setup

The speckle experimental setup is illustrated in Fig. 4. A linearly polarized 15-mW He-Ne laser, with a wavelength $\lambda $ of 632.8 nm, illuminates a 10 mm × 10 mm × 45 mm quartz cell containing the polystyrene microspheres suspended in deionized water. The light beam passes through a polarizer before it reaches the sample. Transmitted scattered light is collected by a high-speed recording Complementary Metal Oxide Semiconductor CMOS camera (MotionBLITZ EoSens mini1, pixel size 14 µm × 14 µm). An analyzer was added in front of the camera in order to analyze the linear parallel polarized scattered light. The camera exposure time and framerate were set at 0.5 ms and 1950 fps, respectively. The time exposure value corresponds to a compromise between the signal-to-noise ratio in speckle patterns and the Brownian motion of the microspheres in the medium. The distance D between the sample and the camera was set at 20 cm. The angle θ between the optical axis and the collected scattered light was set at 20° (see dashed lines in Fig. 2) in order to avoid direct beam detection and to ensure that only scattered photons were detected.

 

Fig. 4. Speckle experimental setup.

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2.3 Speckle grain size dx

The speckle grain size dx was obtained by exploiting the speckle images. This grain size is calculated based on the Wiener-Khintchine theorem [17]. The normalized auto-covariance function ${c_I}({x,y} )$ of the speckle intensity pattern $I({x,y} )$ is shown in Eq. (2):

3. Results and discussion

Figures 5(a) and 5(b) show the variation of the speckle grain size dx for the LIP^MKA strain and polystyrene microsphere suspensions. A slight increase in the dx curves for the two samples is noticed when the diffuser concentration is low. Then, as the number of diffusers increases, the speckle grain size decreases. According to Li and Chiang [19], an increase in the scattering coefficient ${\mu _s}$ (i.e., the number of microspheres increases) leads to an increase in the size of the diffusion spot ${D_e}$ and hence a decrease in the speckle grain size dx [see Eq. (3)]. When large scatterers of different sizes (4.5 µm and 1.5 µm) are mixed in the same suspension, a plateau is observed, indicating the stationary phase in the fermentation process of the bacteria. Thus, the dx curve allows one to distinguish the different phases of bacterial growth. The two curves obtained here can be seen to have similar trends [Figs. 5(a) and 5(b)], meaning that the simulation done with the microspheres matches the biological process that occurs during the growth and sporulation of B.thuringiensis. Finally, for samples 8 and 9 we notice an increase in speckle grain size values. This is due to the fact that microspheres samples 8 and 9 correspond to an ideal case where all the bacteria initially present in the medium undergo fermentation process, explode, and liberate each their crystals and spores (see values in Table 1).

 

Fig. 5. Variation of the speckle grain size dx for (a) Bacillus thuringiensis strain LIP^MKA growth as a function of fermentation time and (b) suspensions of polystyrene microspheres as a function of the microsphere sample number, defined in Table 1. Error bars correspond to the standard deviation resulting from three measurements. The angle θ between the optical axis and the collected scattered light was set at 20°.

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Looking closer at Fig. 5(a), slight increase can be seen in both curves at the beginning of the fermentation [between 0 and 2 hours in graph (a) and sample numbers 1 and 2 in graph (b)], then both curves start decreasing as previously mentioned. To better understand the shape of the dx curves and the presence of a local maximum, we further sampled phase I microsphere suspensions. We considered the 4.5-µm microspheres with a scattering coefficient ${\mu _s}$ in the range [0 ; 9] cm^-1 in order to explore the transition between simple and multiple scattering regimes. Since the microsphere diameter 4.5 µm is larger than the optical wavelength, a Mie scattering regime occurs, favoring forward scattering [20]. Using a simple calculation based on Mie theory [21], we found that the light collected by the CMOS camera when θ (the angle between the optical axis and the collected diffused light) is set at 20°, lies within the side lobes of the scattering indicators as shown in Fig. 2(b). The next part of the study required a change in the geometry of the experimental setup, by varying the angle θ from 20° to 10° and then to 7.5°, allowing the detection of light from the primary lobe without any ballistic photons.

Figures 6(a) and 6(b) show the variation in speckle grain size dx as a function of the scattering coefficient ${\mu _s}$for the 4.5-µm microspheres, corresponding to the three values of θ. At 10° and 7.5°, the dx curves decrease continuously without showing any peaks at low ${\mu _s}$values unlike the dx curve at 20°. At low values of ${\mu _s}$, a simple scattering regime occurs. When ${\mu _s}$increases, the number of scatterers increases and a switch to a multi-scattering regime happens. When collecting diffused photons from the primary lobe, photons can be detected even if they encounter few interactions with the scatterers in the medium. Thus, for low values of${\mu _s}$, the scattered photons can be detected by the camera. However, when collecting diffused photons from the scattering side lobes, a relatively high rate of scatterers is required on the camera. Situated in the side lobes of the scattering indicator, the geometrical configuration at 20° is sensitive to the multi-scattering regime. Based on this angular study, the peaks in the curves of Figs. 5(a) and 5(b) and Fig. 6(b) illustrate the transition from simple to multi-scattering regime. Thus, while following the kinetic growth of the bacteria [6], the observed peaks mark the beginning of the fermentation and show that the bacteria have adapted to the culture medium and found it suitable for their proliferation.

 

Fig. 6. Variation of the speckle grain size dx as a function of the scattering coefficient ${\mu _s}$for the three positions of the camera, with θ set at (a) 7.5°, 10°, and (b) 20°. The dx curve corresponding to θ = 20° is displayed separately in order to highlight the presence of the local maximum.

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4. Conclusion

The aim of this work was to simulate the fermentation growth of the Bacillus thuringiensis bacterium using calibrated polystyrene microspheres and to improve our understanding of the variation of the speckle parameters during fermentation monitoring. Using different sizes and mixtures of microspheres, we recreated the fermentation process of bacterial growth, obtaining similar speckle grain size dx curves. We showed that dx decreases with the increase of the scattering coefficient ${\mu _s}$ showing the two essential phases of the bacterial growth: the exponential phase where the number of bacteria increases and thus dx decreases, and the stationary phase where the bacteria sporulate and burst, liberating their crystals and spores and where a “plateau” in the dx curves occurs. Furthermore, a peak in the dx curves at the beginning of the fermentation is observed indicating, from an optical point of view, a transition from a simple to a multi-scattering regime and, from a microbiological point of view, the beginning of the fermentation process.