Dorina Lindemann‡
a,
Christoph Westerwalbesloh‡a,
Dietrich Kohlheyerab,
Alexander Grünbergerac and
Eric von Lieres*a
aInstitute of Bio- and Geosciences, IBG-1: Biotechnology, Forschungszentrum Jülich, Jülich 52425, Germany. E-mail: e.von.lieres@fz-juelich.de; Fax: +49-2461-61-3870; Tel: +49-2461-61-2168
bRWTH Aachen University, Aachener Verfahrenstechnik (AVT.MSB), Aachen, Germany
cMultiscale Bioengineering, Bielefeld University, Bielefeld, Germany
First published on 7th May 2019
Growth is one of the most fundamental characteristics of life, but detailed knowledge regarding growth at nutrient limiting conditions remains scarce. In recent years progress in microfluidic single-cell analysis and cultivation techniques has given insights into many fundamental growth characteristics such as growth homeostasis, aging and cell division of microbial cells. Using microfluidic single-cell cultivation technologies we examined how single-cell growth at defined carbon conditions, ranging from strongly limiting conditions (0.01 mmol L−1) to a carbon surplus (100 mmol L−1), influenced cell-to-cell variability. The experiments showed robust growth of populations at intermediate concentrations and cell-to-cell variability was higher at low and high carbon concentrations, among an isogenic population. Single-cell growth at extremely limiting conditions led not only to significant variability of division times, but also to an increased number of cells that did not pursue growth. Overall, the results demonstrate that cellular behaviour shows robust, Monod-like growth, with significant cell-to-cell heterogeneity at extreme limiting conditions, resembling natural habitats. Due to this significant influence of the environment on cellular physiology, more carefulness needs to be given future microfluidic single-cell experiments. Consequently, our results lay the foundation for the re-interpretation and design of workflows for future experiments aiming at an improved understanding of cell growth mechanisms.
Under constant environmental conditions the growth rate of a population will converge towards a value solely determined by the current environmental parameters, independent of the population's history. Generally only one of these parameters, for example nutrient concentration, temperature, pH or osmotic pressure, is limiting. The relationship between growth rate and the particular limiting parameter, acting as the growth-controlling factor, can be measured by systematically varying the limiting parameter. The result is a growth kinetic which stretches from no growth, usually close to or at the absence of the limiting component, across a range of linear dependence of growth on the nutrient concentration up to saturation and ends with inhibition or toxicity. The situation of a single substrate being growth limiting can be studied by using a single carbon source that is exclusively metabolized and thereby determines growth. Monod has provided a mathematical description of a growth kinetic, as long as only one parameter is limiting and no inhibitors are present.2 Depending on this carbon source, a bacterial culture will show a substrate-specific growth kinetic with a certain maximum growth rate (μmax) and substrate concentration (Ks) at which is reached. For a quantitative and meaningful analysis of μ several preconditions have to be fulfilled by the respective cultivation device and measurement technique. Firstly, the provision of a stable and simultaneously highly versatile and controllable environment over a wide range of nutrient concentrations, pH values or temperatures. Secondly, the maintenance of steady state growth over a longer period of time and thirdly, a coupled online measurement that records data in high-resolution, real-time and non-invasively.
Fig. 1 Applicability of cultivation devices for nutrient screenings and growth analysis in chemostat. Top: Mother machine (MM);22 middle: monolayer growth chamber (MGC) used in combination with the simulations of Hornung et al.;16 bottom: table-top fermenter. |
(1) Precisely controlled chemostat cultivation that minimizes the occurrence of concentration and temperature gradients due to fast transfer of mass and heat.
(2) Applicability of a wide range of media, pH, temperatures, etc.
(3) Automated, noninvasive and constant observation in high spatio-temporal resolution with time-lapse microscopy, which is robust against optical properties of medium components.
(4) A typically very high structure density with regard to cultivation sites, which can be utilized for high-throughput by/through parallelization of experiments with high cell densities.
(5) Laminar flow without turbulences, quantified by a low Reynolds number.
(6) Mixing of solutes dominated by diffusion.
Microfluidic cultivation devices can be classified by the degree of freedom in which cells proliferate.8 In regard of environmental maintenance, experiment duration and the acquisition of growth rates, they exhibit certain differences.
The highest degree of isolation for single-cell analysis is achieved by negative dielectrophoresis.9 This technically rather demanding setup for non-contact cell traps is driven by an electric field in which a few cells can be held over several generations with exceptional environmental control, restricting the dimensions available for translational movement practically to zero. However, as side-effect the trap creates heat, potentially influencing cell physiology.10–12 It is also difficult and time consuming to collect data for large numbers of cells, since the number of trapped and thereby observable cells is comparably limited.
Monolayer growth chambers restrict cell growth to a single layer and enable monitoring of classical colony formation and expansion in two dimensions13,14 with growth rates often defined by area increase. This limits the experiment duration until chambers, often sized approx. 50 × 50 μm, are overgrown. Chambers with very wide entrances can be used to create stable conditions for long times, but nutrient gradients will form at low concentrations.15 Therefore Hornung et al. have used a model to describe the relationship between nutrient uptake, cell growth and movement and have been able to determine growth kinetics and uptake rates for C. glutamicum at limiting C-source concentrations.16 However, high nutrient concentrations lead to high growth rates and fast cell movement, which also creates significant challenges for the image analysis that is required to determine the desired growth rates. Therefore Fig. 1 indicates the combination of monolayer growth chambers and modeling to be best for low nutrient concentrations.
The present study deploys the microfluidic mother-machine (MM) design, which restricts cell division in a linear, one-dimensional manner. Excess cells are removed with the medium flow at the open ends of each growth channel (see Fig. 2). Thereby, experiment duration becomes theoretically infinite, enabling high resolution measurement of μmax while excluding effects of the preculture. In regard of data acquisition and analysis, cell tracking and lineage recreation are facilitated and more detailed compared to monolayer growth chambers.17–20 Until now the MM design has been used for studies concerning limited bacterial growth, physiology, dynamic gene regulation or cell-size control and homeostasis.17–19,21 With a growth channel length of 15 to 20 μm and a diameter of 1 μm, nutrient gradients only appear at very low concentrations. Under such conditions it becomes difficult to derive, calibrate and validate appropriate models, as it is possible for monolayer growth chambers.16 Investigations at very high nutrient concentrations on the other hand are very well possible, since the cells are caught within the growth channels and can not be flushed out even if they do not grow (see Fig. 1).
Fig. 2 Microfluidic single cell cultivation device and image analysis. (A) Schematic draft of medium flow, supply and growth channels. (B) Schematic cell proliferation in a growth channel over time. (C) Phase contrast images of growth channels shortly after cell seeding and after 2.6 h cultivation. (D) Image analysis: growth channels are automatically cut out (beige frames) and later sequentially arranged to form a kymograph. Manually detected cell division events (blue dots), connected by the lines representing cell life time, created using the ground truth mode of molyso.20 |
The choice of cultivation device potentially influences the measurement, for example via spatial restriction of cellular movement. However, Dusny et al.12 have compared different microfluidic cultivation devices with regard to the growth of C. glutamicum and while they have reported differences regarding the snapping motion connected to cell division they have found very similar growth rates for substantially different degrees of confinement. Therefore we expect our results to be valid across different cultivation devices and scales.
Heterogeneity in bacterial populations has so far consistently been observed in biofilms, pathogenic communities, natural environments and bio-processes.24–26 Especially under stressful conditions, sub-populations with different metabolic and phenotypic characteristics and abilities appear to be beneficial for the survival of a population.27–29 The resulting “noise” in bacterial populations has proven to be a major source of heterogeneity even in isogenic populations grown in the same environment.25,30 The particularly detailed representation of proliferation in microfluidic single-cell cultivation adds a great quality to growth kinetic analysis by including cell-to-cell heterogeneity.
Merkens et al. had already reported that PCA can be used as sole carbon source for C. glutamicum.38 Merkens et al. reached growth rates of 0.14 h−1 in microtiter plates and shaking flasks using CGXII as growth medium.38 They also discussed the importance of co-metabolization of both carbon sources in minimal media for C. glutamicum, usually PCA and glucose, and came to the conclusion that co-metabolization is likely.38 Subsequent experiments with CGXII but without glucose used varying levels of PCA as limiting carbon source in microfluidics.15,16
We expanded the use of an existing technology platform towards a new application, the easy and precise experimental acquisition of growth kinetics. The methods applied here serve as model for the investigation of the influence of media components on cellular physiology. The microfluidic single-cell cultivation system was taken to its operating limits and the range of available growth data for PCA as substrate was expanded significantly compared to earlier data from Hornung et al.16 For the first time the full concentration range including single-cell division age distributions was covered.
To exclude potential effects from the preculture, all data points of cell division events starting before 15 h after experiment start, tstart, were discarded. Experiments with less than 5 division events were marked as growth rate zero. Experiments with more than 5 and less than 50 events were ignored as the number of data points was considered too low to be representative of a population growth rate. The non-zero growth rates were fitted using eqn (1) for deriving colony growth rates from single-cell division time distributions:13,43
(1) |
(2) |
The correction factor scales the observed cell generation times so that if a long generation time τ1 and a short generation time τ2 have the same probability, we can also expect the same number of observed events for both generation times. Eqn (1) can be converted into a sum to approximate the probability distribution:
(3) |
(4) |
As the existing literature indicates several uptake systems working in parallel, we expanded the growth model by adding a second Michaelis–Menten term (see eqn (5)), which is equivalent to two kinetics working in parallel.44
(5) |
However, at concentrations of 0.01 mmol L−1 to 0.02 mmol L−1, spatial heterogeneity occurred along the growth channel (see also Fig. 4). Cells close to the channel opening proliferated, while cells located more centrally grew significantly slower or even stopped dividing. Based on the work of Hornung et al., the boundaries of the operating range of our system were assessed.16 Hornung et al. used a specific chamber geometry and a mass balance based approach to fit kinetic parameters of C. glutamicum to experimental data. They reported an uptake rate per single cell u∞ḡ:
(6) |
(7) |
Fig. 4 Spatial heterogeneity along a growth channel. (a) Kymograph of cell proliferation in 0.01 mmol L−1 PCA. (b) Schematic graph of doubling time distribution along the growth channel. |
This volume related uptake can be used to find the medium inlet concentration at which the cells in the center of the growth channel, open at both ends, would have only half of the medium inlet concentration (see also ESI†):
(8) |
As our growth channels have a length l of ca. 20 μm, we calculate a critical PCA concentration of . The predicted diffusive transport limitation presumably explains the observed spatial heterogeneity along the growth channel for concentrations below 0.05 mmol L−1. For some of the experiments at low concentration no division events at all were observed, further underscoring the heterogeneity of the phenotypic reaction to such challenging conditions.
At higher concentrations (20 and 30 mmol L−1), potential toxicity leads to a higher metabolic burden and thus to slower growth and death of the cells under investigation. Since the resulting long generation times were not fully covered by the experiment duration, the length of detectable doubling times was obviously limited and results may be shifted towards a lower mean value, marking the upper boundary of our technology. Similar to low concentrations the experimental results also varied strongly from experiment to experiment, some experiments without any growth at all, while few cells grew comparatively fast.
We also investigated the percentage of all channels with captured cells, that contained cells dividing within the first 15 h of the experiment (see Fig. 10, ESI†). Interestingly for all concentrations below 50 mmol L−1, between 80% and 100% of all channels showed cell divisions, while concentrations of 50 mmol L−1 and above led to inactivity. The ratio of channels containing dividing cells appeared to be independent of growth channel type and concentration (see also Fig. 11, ESI†). A possible interpretation is that for low concentrations cells are able to use stored nutrients from the preculture, but for high concentrations the bacteriostatic effect of PCA is too strong and effects all cells equally.
Fig. 5 shows the mean growth rates for different PCA concentrations on half-logarithmic scale. The means are the average of the biological replicates for each concentration, where the population growth rate for a single experiment was determined from the distribution of single-cell generation times as described in Section 2.5.
Fig. 5 Different kinetics fitted to experimental results. Results found in microfluidic experiments by Hornung et al. have also been included.16 Error bars depict the standard deviation of population growth rates of biological replicates where more than two were evaluated (PCA concentrations over 0.05 mmol L−1). |
The supply of PCA as sole carbon source and the subsequent observation of growth during microfluidic single-cell cultivation verified the reported findings that C. glutamicum is indeed capable of actively metabolizing PCA for its carbon demand. So far, PCA has been added to the nutrient medium as an iron chelator with a concentration of 0.195 mmol L−1. We could confirm earlier findings that 0.02 mmol L−1 PCA as sole carbon source leads to μ around 0.2 h−1 already.37 The maximum growth rate was observed at 6 mmol L−1 with a value of 0.4 ± 0.04 h−1 showing that the potential influence of PCA on growth is significant.
For PCA concentrations from 0.01 mmol L−1 to 0.05 mmol L−1, the cells showed very heterogeneous and slow growth, relatively independent of the applied concentration. As mentioned previously, heterogeneity was found along the length of the growth channels, expected to be caused by concentration gradients. Furthermore, slow growth and limited experiment time of 40 h resulted in an overall lower sample size compared to higher concentrations. Furthermore, for some experiments we did not find any division events at all, resulting in growth rates of 0.
A growth rate increase approximately proportional to the logarithm of the applied PCA concentration of 0.1 mmol L−1 to 0.4 mmol L−1 could be observed. Compared to 0.05 mmol L−1, nutrient supply seemed to exceed requirements for maintenance and more energy was put into proliferation and growth. This can be compared to results from earlier experiments by Hornung et al.16 They have investigated growth rates based on particle image velocity (PIV) and developed a simple analytic model to describe steady-state growth of cells in monolayer growth chambers. With the data from this study, we tried to corroborate and extend the existing growth model to higher concentration regimes.
The growth rates increased roughly as expected until 6 mmol L−1, where a maximum growth rate of (0.40 ± 0.04) h−1 was observed. Afterwards, growth rates in 20 mmol L−1, 30 mmol L−1, 50 mmol L−1 and 100 mmol L−1 PCA decreased in comparison to the observed μmax at 6 mmol L−1, pointing towards an inhibitory effect of high PCA concentrations. For 30 mmol L−1 the results were very heterogeneous: for two experiments we observed comparatively fast growth around 0.3 h−1, while three other experiments with the same conditions did not yield any growth at all. Concentrations above 30 mmol L−1 PCA indicated bacteriostatic conditions due to toxicity of the nutrient itself or osmotic pressure. Haußmann and Poetsch elucidated the proteome response of C. glutamicum in modified MMES medium (sulfur-free minimal medium) with a PCA content of 100 mmol L−1 as sole carbon source.49 They found that the metabolization of such aromatic compounds was challenging due to their physico-chemical properties and toxicity in general. In more detail, reduction equivalents like ATP were rare, demanding the TCA cycle and oxidative phosphorylation to be activated for energy generation, marking PCA as a gluconeogenic carbon source. Additionally, growth on PCA seemed to reduce amino acid biosynthesis leading to carbon-starvation responses, an up-regulation of respiratory chain proteins, and significant alterations in cell wall biosynthesis.49
For a more comprehensive analysis, two different models have been introduced in Section 2.5, which were fitted to the experimental data to provide a mathematical description of the observed results. The experiments at very low concentrations, apart from experiments at 0 mmol L−1, were taken into account although we observed spatial heterogeneity. Both equations are based on a Monod-equation and assume PCA as sole growth limiting factor. To account for the observed growth stop at high concentrations the equations contain an inhibition term. Eqn (4) is a Monod-kinetic multiplied with the inhibition term, which can be interpreted as one limiting enzyme and an inhibitory effect of the substrate. Eqn (5) is based on the idea of two enzymes or pathways working in parallel, so that two Monod-type kinetics are added and then multiplied with the inhibition term. This is based on the understanding of PCA metabolism as reported so far: transport of PCA into the cell can take place passively, mediated by porins, or actively via transporters like PcaK, whereupon the PCA is degraded via the β-ketoadipate pathway.49 Transport efficiency of the PcaK transporter was so far only investigated in model systems of E. coli where a saturation appeared at 5 nmol mg−1 PcaK protein.50 If one assumes that the intracellular supply of PCA is ensured, another reason for stagnating growth may be the degrading pathway itself. Zhao et al. performed comprehensive studies on regulating mechanisms of the β-ketoadipate pathway, responsible for PCA degradation.51 In the course of their work, the authors found the positive regulatory protein PcaO, which responded to the presence of PCA by activating its degrading branch of the β-ketoadipate pathway. They further reported that PCA reduced the effect of PcaO in low concentrations (0.2 mmol L−1 and 0.5 mmol L−1) and supported its effect in higher concentrations (1 mmol L−1 and 2 mmol L−1).
However, both the single-step as well as the two-step kinetic are able to reproduce equally well the measured data, so that the parallel activity of two regulatory mechanisms could not be confirmed in this study. Furthermore, both differ from the results by Hornung et al.16 The reasons for this could be attributed to the very different experimental setup and the fact that our study did not account for spatial heterogeneity at low concentrations. Table 1 shows the estimated kinetic parameters for our study and the results by Hornung et al.16
A common method to display heterogeneity in growth is to plot the variance against the respective mean generation time, Fig. 7 (see also Fig. 18, ESI† for the coefficient of variation). The results indicate that for C. glutamicum the population-wide generation time is positively correlated with the variance of the generation time distribution, implying an increase in heterogeneity and noise in low growth rates.
Various authors have reported similar observations for other organisms in varying environmental conditions and have proposed different explanations. Hashimoto et al. have reported a linear dependency for E. coli and found an x-intercept of this linear relation close to the minimum generation time within rich medium.13 De Martino et al. have developed a model employing entropy, which associates μmax and the “inverse temperature” as variables for a fixed mean growth rate, showing the trade-off between dynamically favoured, fast phenotypes and entropically favoured, slow growing ones.52 Schreiber et al. have hypothesized an evolutionary advantage of heterogeneity in challenging environments by the simultaneous presence of various capabilities as phenotypes. They predicted an increase of phenotypic heterogeneity in microbial metabolism under nutrient-limited, dynamic habitats compared to nutrient-saturated, stable habitats.28 Even though these studies are based on other organisms, the observation of heterogeneous generation time distributions under low nutrient supply, comparable to C. glutamicum, hint towards similar underlying mechanisms. Furthermore, the present data reflect a re-occurrence of the phenomenon in PCA concentrations above 10 mmol L−1. The causing circumstances might be the challenging conditions due to osmotic pressure or toxicity, but this requires further work to be understood in greater detail.
The presented data is able to resolve a growth kinetic with a saturation-like behaviour and shows how the growth dependence on nutrient availability can be described well by classic Monod-type kinetics although the regulatory mechanism for PCA metabolism is quite complex. However, the single-cell resolution reveals an increasing cell-to-cell heterogeneity, as the cells “struggle for life” under inhibiting or very low concentrations.
Studies within microfluidic devices become more common, and the used media are usually identical to those employed in macroscopic cultivations. The example of the defined CGXII medium shows how differences in the cultivation method can magnify effects by medium components not relevant at the macro-scale. This is caused by the change from batch-like conditions with higher cell densities within shake-flasks or similar devices to the microfluidic environment with conditions equivalent to a chemostat operating at very low cell densities. When the CGXII medium was used in the microfluidic environment it was found that PCA raised the growth of C. glutamicum by ca. 0.2 h−1, which is a half of the maximally observed rate of 0.4 h−1 for this medium in shake flasks or micro-well plate cultivations.37 In macroscopic experiments this growth supporting effect has not been detected. For a correct interpretation of results it will be important to ensure all medium components do not elicit similarly strong biological responses as PCA does in CGXII when a medium is transferred from macroscopic experiments.
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9ra02454a |
‡ These authors contributed equally to this work. |
This journal is © The Royal Society of Chemistry 2019 |