1. INTRODUCTION

The rapid detection and analysis of bacteria and other pathogenic cells can be an effective way for an early diagnosis of infectious diseases and the development of adequate treatment. Conventional microbiological techniques are typically based on cell culturing and incubation in order to increase the probing volume and with this the detection sensitivity. This lab procedure, however, can require up to two to three days [1]. Multidrug-resistant pathogens and the resulting decreased curability and increased mortality [2] require quicker inspection approaches to switch from universal broad-spectrum antibiotics to more tailored ones.

The analysis of the angular light scattering distribution is an approach with the potential to achieve the desired compromise between the highest sensitivities and short characterization times. Scattering is caused by even small objects and fluctuations and can provide structural information about the cells [3–7]. Its high sensitivity makes it a promising tool for characterizing even very small sample volumes and the lowest cell concentrations. This may enable microbial observations on just a few available cells, particularly after significantly shorter cellular growth times.

The links between characteristic phenotypic cell properties and their influences on light scattering have been studied and utilized for several microbial and biomedical purposes. Angular scatter scans or spectra from bacterial suspensions [8–12], as well as individual cells [13–15], have been measured to retrieve information about the cell size, shape, or refractive index with the purpose of assessing pathogens or their state or condition (e.g., their current phase of growth [15]). It has also been shown that two-dimensional diffraction patterns from bacterial colonies can be used to classify and identify different pathogenic species with the help of a machine learning data analysis. Reasonable results could be achieved after only a few hours of cell culturing [16–18].

 

Fig. 1. Setup of the scatter sensor; scheme of the angular definitions; result of an ARS measurement on a blank PBS sample without bacterial cells.

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Besides the structural influences on the angular scatter distribution, there is a correlation between scattering and cell concentrations. This is indeed broadly utilized to quantify the latter, mainly indirectly, with the help of photometric methods such as turbidimetry and optical density (OD) measurements [19]. These measures hold important information for many biomedical experiments, for example, to monitor cellular growth or the lack of such when screening for antibiotics or when identifying pathogens with selective growth media [20]. The concentration estimation by direct scatter measurements has also been demonstrated [7,11,21]. This approach holds advantages, where photometric methods show limitations such as small sample volumes (short optical path lengths) and very low concentrations.

The purpose of this study is to evaluate if and how angle-resolved light scattering can be used for applications, even combining the challenges of small sample sizes and low cell concentrations. Here, accordingly, only very few cells for investigation are provided, which poses difficulty, for example, in the rapidly growing field of lab-on-a-chip technologies. Detection capabilities down to the single cell level could open the path to quick and sensitive screening and characterization of samples in the earliest stages, and thus speed up conventional microbial characterization techniques.

Other than studying either isolated cells or indefinitely dense cell suspensions, this work focuses on a range of sample dilutions with respect to both the cell structure and concentration. Beyond commonly discussed structural influences such as sizes and shapes, the paper additionally addresses the cellular aggregation. The propensity to form aggregates can also be very typical for specific bacterial types (e.g., separated cells, pairs, chains, or clusters) and reveal additional information about the state or condition of the cells. We believe considering them not only expands the pool of relevant sample information, but also brings the technique much closer to the application in microbial research. To the best of our knowledge, this is the first study to systematically investigate the impact of typical bacterial aggregation structures on angle-resolved light scattering.

2. DEFINITIONS AND THEORETICAL ASPECTS

A. Definitions

The scattered light can be described by the angle-resolved scattering (ARS) [22,23], which is defined as the power $\Delta {{\rm P}_s}$ scattered into a solid angle $\Delta {\Omega _s}$ and normalized to this solid angle and the incident power ${{\rm P}_i}$:

The directly transmitted part of the light, ${{\rm P}_T}$, which is not scattered or absorbed by the sample normalized to the incident light power, is defined as the transmittance, T. The transmittance correlates to the OD, which is often used to quantify the cell concentration (typically measured at a wavelength of 600 nm and an optical path length of 1 cm):

B. Light Scattering Theory and Scatter Models

The angular distribution of scattered light depends on the structural and optical properties of the illuminated object. For biological cells, this includes their phenotypic appearance with cell parameters such as their size, shape, and structure, as well as their refractive index relative to the surrounding medium.

Unicellular bacterial cells exist in a wide range of sizes and very different shapes; yet, the vast majority exhibit sizes of about 0.5–2 µm in diameter and two major shapes: (a) rod (bacillus) and (b) sphere (coccus). They are procaryotic cells without a nucleus. They can appear in different arrangements, predominantly, separated, in pairs (diplococci), groups of four (tetrads), chains (streptococci), or clusters (staphylococci). It should be noted that these phenotypic characteristics are neither entirely unique to the specific cell type nor always identical for different populations of the same species, as they also depend on the environmental and growing conditions. However, they are very typical and often used to help identify species, whereas the variations can indicate further information such as the current growth phase or cellular stresses [20].

Several scattering models (most importantly the Mie scattering theory for homogenous spherical particles) allow scattering from small particles such as bacterial cells to be predicted if the cell dimensions and refractive index are known [11,24]. Under consideration of certain approximations and corresponding ranges of validity, measured scattering distributions can be compared to the outcomes of a model in order to inversely obtain cellular parameters from the scattering. Due to the variety of these parameters and the complexity of the correlations, these methods rely on accurate assumptions and prior knowledge about the sample.

Scattering from multiple cells introduces additional challenges, because multiple scattering, as well as interferences between the waves scattered by the individual cells, must be considered. The first effect can be neglected in the case of small samples and low cell concentrations [25], as in this work. The latter strongly depends on the relative positions of the cells. Usually, it is assumed, that the number of cells is sufficiently large, and their separations and orientations are random, so that there are no systematic phase relations between the waves scattered by all the cells. In this case, the total scattered intensities are simply the sum of the intensities scattered by the individual cells [26], and analytical scatter models can be used. These conditions, however, do not apply for bacterial samples with occurring cell aggregates. It has been shown that the Mie theory does not agree with bacterial scattering in the case of cellular aggregation, especially at small polar angles ($\theta {\rm_s}\lt {20}^\circ$ with wavelengths in the visible spectral range) [11]. In such a case, simulations can be performed by means of numeric electromagnetic modeling, yet with tremendously increased computational effort or at the expense of accuracy. In this work, the impacts of the aggregating behavior on the scattering distribution are assessed using an experimental approach.

The complex correlations, as well as the diversity of scatter sources, can lead to a wide range of scatter patterns. This provides an ideal characterization signal to identify unique combinations of cell properties and to distinguish or identify cell types. The approach used in this work is an empirical model-based data analysis in order to derive such distinct scatter features representing various cell morphologies by utilizing the following fit function:

The parameters ${{\rm b}_0}$, L, and s are the three modeling coefficients. This model is also known as the Harvey–Shack scatter model and is commonly used to predict stray light in optical designs [27]. Here it is assessed to determine whether it can be used to adequately describe the scattering from bacterial cell suspensions.

3. LIGHT SCATTERING SENSOR FOR ANALYSIS OF BIOLOGICAL CELLS

The light scattering measurement concept is a variation of the sensor described in [28], which works in the forward (transmission) hemisphere. The reason for this is the stronger forward scattering distribution of bacteria, as predicted with the Mie scattering theory.

Figure 1 shows the overall sensor setup combined with an optical microscope channel (maximum of $12{\times}$ magnification) for monitoring the scatter measurement position. The sensor consists of a 660 nm diode laser source, beam preparation optics, including a spatial filter to form a clean, Gaussian beam, and focusing lens, that produces a 35 µm spot (at ${{1/e}^2}$ intensity) with a power of about 3 mW in the sample plane (incidence angle ${\theta _i} = {0}^\circ$). The sensor consists of a CMOS detector matrix for a 2D angular data acquisition in one single shot. The setup has been designed such that the required small spot size can be achieved with a divergence as small as possible (the divergence being inversely proportional to the spot size of the Gaussian beam) by still maintaining a compact sensor setup. The result leads to a specular transmitted beam with an extension of ${\theta _s} = \;\pm {4}^\circ$ on the matrix detector. The maximum detectable scattering angles given by the geometric dimensions and distance of the CMOS detector are $|{\theta _s}| = {35}^\circ$ (polar angles) and ${\varphi _s} = {\pm}{180}^\circ$. The CMOS is covered by an apodizing neutral density filter for an extended detector dynamic range, and beam dumps are used to suppress retroreflection of the directly transmitted light.

Sensor calibration is achieved with the help of a diffuser with a known ARS (characterized by a goniometer-based ARS measurement system [29]). The same diffuser is also used to calibrate the apodizing filter. The scattering sensor has a dynamic range of ${\gt}5.5$ orders of magnitude. The instrument signature is below ${\rm ARS} = {{10}^{- 4}}\;{{\rm sr}^{- 1}}$ for angles ${\theta _s} \gt {5}^\circ$ as can be seen in the measurement result of a blank sample without bacterial cells in Fig. 1. The measurement exposure times are between ${\sim}{0.5}$ and 500 ms.

4. EXPERIMENTAL

A. Analysis of Cell Concentrations and Bacterial Species

1. Bacterial Cell Suspensions and Microscopic Inspection

Four bacterial organisms in a similar size range (diameters about 1 µm), but with slightly different characteristic morphologies, were chosen: coccoid Micrococcus luteus HKI 183 (M. luteus), Kocuria varians IMET 11364 (K. varians), Lactococcus lactis IMET 10669 (L. lactis), and rod-shaped Escherichia coli RV 308 (E. coli). All strains were obtained from the Jena Microbial Resource Collection (JMRC). As outlined before, the actual cell properties of a sample can differ in certain ranges depending on external conditions. The most relevant properties of the cell samples as prepared for this study were assessed by light microscopy (see Fig. 2) and are summarized in Table 1. The cell sizes were thereby estimated with the help of the microscope software ZEN, Carl Zeiss Microscopy GmbH (length measurement, average of  ${\gt}5{-}10$ values per species).

 

Fig. 2. Light microscopy images (${50} \times$ objective) of different bacterial suspensions (upper row) and corresponding 2D light scattering patterns (lower rows) measured with the detector matrix-based scattering sensor. For each of the four organisms, the results of the concentration levels 2, 4, and 6 are shown. (The concentration levels decrease from the top to bottom rows.)

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Table 1. Summary of Scatter-Relevant Properties of the Investigated Cell Suspensions as Determined by Light Microscopy

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The final samples were obtained from culturing, followed by multiple steps of centrifugation and resuspension in phosphate-buffered saline (PBS). A dilution series with a comparable starting concentration of ${\rm OD} = {1}$ ($\lambda = {600}\;{\rm nm}$, ${\rm path}\;{\rm length} = {1}\;{\rm cm}$) was prepared for all four organisms (dilution 1:2, 8 concentration levels each). The corresponding cell numbers per milliliter were counted manually using a Neubauer counting chamber. (All cell counts were determined with a square-to-square standard deviation of ${\sim}{30}\%$.)

For the scatter measurements, the cell suspensions were encapsulated between two glass slides with a gap of about ${195}\;{\unicode{x00B5}{\rm m}}\;\pm {3}\%$. Considering the sensor spot size of 35 µm, this results in a detected sample volume of ${\sim}{190}\;{\rm pl}\;\pm {3}\%$ per measurement. The equivalent number of cells in the spot ranges from 100 to 300 for the samples with the highest concentration (level 1). They decrease by a dilution factor of 2 to each following level down to single cells for the lowest concentrations (level 8; see Table 1).

2. Angle-Resolved Light Scattering Measurements

The measured 2D scatter distributions show a huge variety of patterns, even among one sample type. In particular, low cell concentrations and the species with a tendency to form small aggregates or clusters (M. luteus, K. varians, L. lactis), where the actual number of cells in the spot varies most, show this behavior. A systematic data analysis is required in order to make reliable statements concerning certain sample and related scatter characteristics. Figure 2 summarizes exemplary ARS results for all four organisms at different concentration levels.

The scattering distributions allow separating the different cell concentrations, simply by the help of the overall scattering levels. To quantify these levels, for each measurement, integrated scattering values $S$ are calculated according to Eq. (2). In Fig. 3(a), these values are plotted as a function of the corresponding cell numbers. The averages show a linear correlation for all four cell types in the entire investigated concentration range. The variations within one sample are mainly related to the statistic fluctuations of actual cell numbers in the spot. As outlined before, especially the three cluster forming species and low concentration samples show noticeably large fluctuations, demonstrated by accordingly high standard deviations of their scattering values ${\sigma _S}$, for high-low concentrations: M. luteus (${\sigma _{S\:}}\sim{15}\% {-} {90}\%$), K. varians (${\sigma _S}\;\sim{45}\% {-} {110}\%$), and L. lactis (${\sigma _S}\;\sim{50}\% {-} {170}\%$) in contrast to the non-clustered E. coli cells (${\sigma _{S\:}}\sim{10}\% {-} {45}\%$).

 

Fig. 3. Data analysis of angle-resolved light scattering measurements on serial dilutions of different bacterial suspensions. (a) Correlation of integrated scatter values S with the cell concentration of the different investigated organisms (pastel shade marks: individual measurements, 10 measurements each; intense marks: average values). (b) Azimuthal averages of the measured ARS distributions, normalized to scatter values S (pastel shade curves: averages of individual concentration levels, eight levels each; intense curves: overall averages).

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Besides the overall scattering level, the combination of a small sample volume and coherent light illumination leads to interference patterns in the 2D-ARS (Fig. 2) that also change with the detected cell number. A dense cell suspension shows small random speckles, whereas the patterns become more geometric with decreasing cell numbers. Additionally, the scatter distributions become less isotropic, as non-spherical or irregular shapes of the individual cells or cell aggregates cause scattering in predominant directions.

Differences between the scatter patterns from the various cell types become readily apparent when comparing the measurements within the same concentration level. The first row in Fig. 2, for example (concentration level 2), shows a very homogeneous distribution for E. coli, whereas the others show clear parts of increased scattering in the center (near angle). L. lactis thereby stands out with a starlike pattern in contrast to more round ones. Similar characteristics can also be seen for the other concentration levels. However, the aforementioned effects related to the concentration, such as differences through speckles and anisotropy, also have to be considered.

Azimuthal averages of the measured 2D-ARS are calculated. In this way, the scattering distributions measured at all concentration levels can be compared in order to extract only cell-type characteristic scattering features. By normalizing this to the scatter value $S$, it is shown in Fig. 3(b) that these azimuthally averaged curves when determined from the same cell type (same colors) indeed generally match one another. For different cell types, the curves, however, are clearly distinguishable.

Thus, the measured scatter distributions are indeed characteristic for the individual cell types, independent of the sample concentration.

The curves can be described by the scatter model introduced in Section 2, Eq. (4). The parameter ${{\rm b}_0}$ is equal to the ARS at ${\theta _s} = {0}^\circ$ and thus correlates to the sample concentration. It is determined by a linear fit in the near-angular range. Parameters s and L correlate to the slope and curvature of the ARS, respectively, that appear to be descriptive for the determined bacterial scattering curves. The identification of the parameters by minimizing the merit function between measurements and the model thus allows the data to be reduced to two characteristic scattering features. Even though the resulting curves describe only rough fits to the measured data, the determined parameters are suitable to successfully separate different cell types, as demonstrated in Fig. 4.

 

Fig. 4. Scatter model parameter derived from measurements on different bacterial suspensions.

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The plot shows the fitting results of all measurements; the color saturation of the data points indicates the sample concentration. The “Lower concentration” thereby includes measurements on concentration levels 5-8, which corresponds to ${\lesssim }{15}$ cells in the characterization spot. Even at these very low cell numbers, first tendencies towards the cell type are visible. For higher cell numbers, the differentiation of cell types becomes even more distinctive. It is assumed that this mainly relates to the variation of cell and cluster sizes over the whole sample. Evidently, a larger sample can give a more inclusive overview, leading to a more precise “fingerprinting.”

B. Impact of Bacterial Cell Structures on Light Scattering Distribution

As discussed before, the determined scattering curves depend on the specific combination of phenotypic characteristics in a cell sample (size distribution, shapes, dielectric function, aggregation types). The classification of the samples is therefore based on various factors. Studying the impacts from individual factors might allow deducing further information and relating the observed scattering characteristics to possibly underlying cell properties.

We specifically looked at the influence from different cellular aggregations that are not considered by prevalent scatter models; yet, we expect significant impacts with regard to our experimental results. For scattering measurements on spherical polystyrene beads with sizes such as the bacterial cells but no occurring clustering, the curves are in good agreement with the Mie scattering theory over the full detected angular scattering range, as shown in Fig. 5. According to this model, the ARS curves of all coccoid cells should show very similar shapes. However, a comparison to the measurement results shown in the previous section [Fig. 3(b)] reveals strongly diverging curvatures. In particular, the sharp increase in the near-angular range (${\theta _s} \lt {10}^\circ$) of the measurements in Fig. 3(b) is in contrast to the Mie simulation. This leads to the assumption that this is mainly caused by larger structures such as the bacterial aggregations, because large scatterers predominantly scatter the light towards smaller scatter angles. In addition, the scattering curve of only singly occurring E. coli cells shows a much flatter slope in the near-angular range accordingly.

 

Fig. 5. Scatter measurement (azimuthal average) and Mie simulations of spherical polystyrene beads in water [30].

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In order to verify and further analyze this presumption, the impact of aggregate formation on the scattering distribution was investigated experimentally. Cellular structures were artificially generated by electron beam lithography. For this, ${\varnothing} = {1}\;{\unicode{x00B5}{\rm m}}$ holes were written in photoresist (substrate: chromium-coated glass wafer). The distribution of the holes was determined according to typically occurring bacterial patterns, as described in Section 2. Electron microscopic images of the equivalent structures are shown in Fig. 6. For each pattern, the same number of 50000 holes was distributed over a total area of ${3} \times {3}\;{{\rm mm}^2}$.

 

Fig. 6. Goniometric angle-resolved light scattering measurements on a coated and e-beam structured glass wafer (measurement parameter: $\lambda = {640}\;{\rm nm}$; ${\theta _i} = {0}^\circ$; s-pol), together with the corresponding SEM images of the structures (diameter of 15 µm in image sections) and scatter simulations [30] (diffraction model; minima are less distinct in the measurements because of addional scattering due to a higher order diffraction not being considered by the model, surface roughness, and fabrication tolerances) (a) Comparison of different cluster sizes (”small clusters”: 1–6 holes; “large clusters”: 1–40 holes). (b) Comparison of different arrangements (“chains”: 2–10 holes).

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The scatter measurements were performed with a goniometer-based scatterometer (wavelength of 640 nm, spot diameter of 1.5 mm), which allows measuring the ARS in an increased angular range, towards both very small and large scatter angles [29]. The angular scanning was thereby reduced to the polar direction, since isotropic scattering can be assumed for these cell configurations.

The results of the scattering measurements plotted in Fig. 6 demonstrate how the different feature arrangements can indeed strongly modify the shape of the scattering curve. Only the “separated” artificial cell pattern scatters primarily as predicted by the diffraction model. (The diffraction is assumed to be the dominant scatter mechanism in this case; the less distinct minimum compared to the simulation can be explained by additional scattering due to a higher order diffraction not considered by the model, surface roughness, and fabrication tolerances.) In contrast, all other curves show clear deviations: the larger the clusters, the higher the ARS in the very near-angular scattering range (polar scattering angles ${\lesssim }{10}^\circ$), which again influences the overall curvature of the curves [Fig. 6(a)].

The ARS curves of the ”chains” and “tetrads” pattern in Fig. 6(b) illustrate the scattering sensitivity to the variety of possible arrangements and the resulting spectra of structure dimensions within the sample. The “chains” with dimensions ranging from 1 to 10 holes show a smooth curvature over the entire detected angular range, whereas the “tetrads” with a common diameter of about two holes form a minimum at a polar scattering angle of ${\approx} {20}^\circ$. The angular position of this minimum matches that of the modeled diffraction at equivalent ${\varnothing} = \;{2.3}\;{\unicode{x00B5}{\rm m}}$ structures. However, this model shows further minima whereas, at larger scatter angles, (${\gtrsim} {40}^\circ$) the measured scattering curve of the “tetrads” mostly follows that of the “separated” pattern. This behavior is also apparent for all the other “aggregated” patterns, which demonstrates that in this angular range the scattering is mainly defined by the individual ${\varnothing}= {1}\;{\unicode{x00B5}{\rm m}}$ holes. Therefore, it is possible to deduce information about cell sizes, despite the presence of cell aggregates when focusing on larger scatter angles, as shown in [11]. On the other hand, the smaller angles hold additional information about the aggregates and their dimensions.

Naturally, a mixture of certain types of aggregates occurs in one cell sample leading to the accordingly superimposed scatter distributions. In bacterial suspensions, the orientations and arrangements of the aggregates in three dimensions must further be taken into account. Some impacts caused by prevailing forms, however, can be noticed for the bacterial scattering curves measured in this work [Fig. 3(b)] when comparing them to the scattering of the artificial structures in Fig. 6. For example, for L. lactis, the sharply increasing slope towards the smallest scatter angles can also be observed for the artificial chain structures. Relatedly, the 2D scatter distributions of L. lactis (Fig. 2) imply that there are mainly chain structures or clusters with predominant structural directions in the sample by showing much more azimuthally inhomogeneous (starlike) patterns than all the other samples. Additionally, for K. varians, the occurring dip in the ARS curve at just below ${\theta _s} = {20}^\circ$ can be associated with the equivalent minimum caused by the high amount of tetrads in the sample.

Due to the numerous possibilities and complex correlations, it is not straightforward, or even possible, without further knowledge about the sample to fully reconstruct the composition of occurring aggregation forms (inverse scattering problem). The proposed method of data analysis, however, provides an alternative to successfully evaluate and discriminate the samples based on resulting characteristic scatter patterns. All in all, the results confirm the suspicion that, besides the influences of the cell sizes and shapes, these scattering patterns of the bacterial cell suspensions are to a great extent determined by the occurring forms of cellular aggregates.

5. SUMMARY

The experiments proved the high sensitivity and applicability of the angle-resolved light scattering approach for analyzing bacteria in small characterization volumes of ${\lt} 200 \;{\rm pl}$ with even few available cells per measurement. Different cell types and morphologies could be distinguished and assessed, together with the cell concentration. Besides commonly discussed influences such as cell sizes and shapes, we found that the scattering distribution was very sensitive to typical cellular aggregation forms. The impacts correlate to the arrangements and resultant aggregate dimensions. With the proposed characterization setup, it is possible to detect resulting scatter differences among cell types to utilize it for sample distinction and evaluation.

These results suggest a promising potential for an application in microbial research with regard to significantly shortened incubation times in comparison to conventional methods. This addresses challenges such as the detection of morphological changes or bacterial growth at the earliest stages. The feasibility of assessing the smallest sample volumes and the quick data acquisition might be attractive for lab-on-a-chip technologies.