Studies of transcriptional state heterogeneity in sporulating cultures ofbacillus subtilis

Investigation of poly(γ-glutamic acid) production via online determination of viscosity and oxygen transfer rate in shake flasks

BACKGROUND

Poly(γ-glutamic acid) (γ-PGA) is a biopolymer with many useful properties making it applicable for instance in food and skin care industries, in wastewater treatment, in biodegradable plastics or in the pharmaceutical industry. γ-PGA is usually produced microbially by different Bacillus spp. The produced γ-PGA increases the viscosity of the fermentation broth. In case of shake flask fermentations, this results in an increase of the volumetric power input. The power input in shake flasks can be determined by measuring the torque of an orbitally rotating lab shaker. The online measurement of the volumetric power input enables to continuously monitor the formation or degradation of viscous products like γ-PGA. Combined with the online measurement of the oxygen transfer rate (OTR), the respiration activity of the organisms can be observed at the same time.

RESULTS

Two different Bacillus licheniformis strains and three medium compositions were investigated using online volumetric power input and OTR measurements as well as thorough offline analysis. The online volumetric power input measurement clearly depicted changes in γ-PGA formation due to different medium compositions as well as differences in the production behavior of the two investigated strains. A higher citric acid concentration and the addition of trace elements to the standard medium showed a positive influence on γ-PGA production. The online power input signal was used to derive an online viscosity signal which was validated with offline determined viscosity values. The online measurement of the OTR proved to be a valuable tool to follow the respiration activity of the cultivated strains and to determine its reproducibility under different cultivation conditions.

CONCLUSIONS

The combination of the volumetric power input and the OTR allows for an easy and reliable investigation of new strains, cultivation conditions and medium compositions for their potential in γ-PGA production. The power input signal and the derived online viscosity directly reflect changes in γ-PGA molecular weight and concentration, respectively, due to different cultivation conditions or production strains.

Effect of Intrinsic Noise on the Phenotype of Cell Populations Featuring Solution Multiplicity: An Artificial lac Operon Network Paradigm

Heterogeneity in cell populations originates from two fundamentally different sources: the uneven distribution of intracellular content during cell division, and the stochastic fluctuations of regulatory molecules existing in small amounts. Discrete stochastic models can incorporate both sources of cell heterogeneity with sufficient accuracy in the description of an isogenic cell population; however, they lack efficiency when a systems level analysis is required, due to substantial computational requirements. In this work, we study the effect of cell heterogeneity in the behaviour of isogenic cell populations carrying the genetic network of lac operon, which exhibits solution multiplicity over a wide range of extracellular conditions. For such systems, the strategy of performing solely direct temporal solutions is a prohibitive task, since a large ensemble of initial states needs to be tested in order to drive the system--through long time simulations--to possible co-existing steady state solutions. We implement a multiscale computational framework, the so-called "equation-free" methodology, which enables the performance of numerical tasks, such as the computation of coarse steady state solutions and coarse bifurcation analysis. Dynamically stable and unstable solutions are computed and the effect of intrinsic noise on the range of bistability is efficiently investigated. The results are compared with the homogeneous model, which neglects all sources of heterogeneity, with the deterministic cell population balance model, as well as with a stochastic model neglecting the heterogeneity originating from intrinsic noise effects. We show that when the effect of intrinsic source of heterogeneity is intensified, the bistability range shifts towards higher extracellular inducer concentration values.

Coarse-grained analysis of stochastically simulated cell populations with a positive feedback genetic network architecture

Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and efficient study of their long-time behaviour over a wide range of parameter values, the performance of solely direct temporal simulations requires significantly high computational time. In addition, when the dynamics of the cell populations exhibit non-trivial bistable behaviour, such an analysis becomes a prohibitive task, since a large ensemble of initial states need to be tested for the quest of possibly co-existing steady state solutions. In this work, we study cell populations which carry the lac operon network exhibiting solution multiplicity over a wide range of extracellular conditions (inducer concentration). By adopting ideas from the so-called "equation-free" methodology, we perform systems-level analysis, which includes numerical tasks such as the computation of coarse steady state solutions, coarse bifurcation analysis, as well as coarse stability analysis. Dynamically stable and unstable macroscopic (population level) steady state solutions are computed by means of bifurcation analysis utilising short bursts of fine-scale simulations, and the range of bistability is determined for different sizes of cell populations. The results are compared with the deterministic cell population balance model, which is valid for large populations, and we demonstrate the increased effect of stochasticity in small size populations with asymmetric partitioning mechanisms.

Single-cell behavior and population heterogeneity: solving an inverse problem to compute the intrinsic physiological state functions

The dynamics of isogenic cell populations can be described by cell population balance models that account for phenotypic heterogeneity. To utilize the predictive power of these models, however, we must know the rates of single-cell reaction and division and the bivariate partition probability density function. These three intrinsic physiological state (IPS) functions can be obtained by solving an inverse problem that requires knowledge of the phenotypic distributions for the overall cell population, the dividing cell subpopulation and the newborn cell subpopulation. We present here a robust computational procedure that can accurately estimate the IPS functions for heterogeneous cell populations. A detailed parametric analysis shows how the accuracy of the inverse solution is affected by discretization parameters, the type of non-parametric estimators used, the qualitative characteristics of phenotypic distributions and the unknown partitioning probability density function. The effect of finite sampling and measurement errors on the accuracy of the recovered IPS functions is also assessed. Finally, we apply the procedure to estimate the IPS functions of an E. coli population carrying an IPTG-inducible genetic toggle network. This study completes the development of an integrated experimental and computational framework that can become a powerful tool for quantifying single-cell behavior using measurements from heterogeneous cell populations.

A mathematical and computational approach for integrating the major sources of cell population heterogeneity

Several approaches have been used in the past to model heterogeneity in bacterial cell populations, with each approach focusing on different source(s) of heterogeneity. However, a holistic approach that integrates all the major sources into a comprehensive framework applicable to cell populations is still lacking. In this work we present the mathematical formulation of a cell population master equation (CPME) that describes cell population dynamics and takes into account the major sources of heterogeneity, namely stochasticity in reaction, DNA-duplication, and division, as well as the random partitioning of species contents into the two daughter cells. The formulation also takes into account cell growth and respects the discrete nature of the molecular contents and cell numbers. We further develop a Monte Carlo algorithm for the simulation of the stochastic processes considered here. To benchmark our new framework, we first use it to quantify the effect of each source of heterogeneity on the intrinsic and the extrinsic phenotypic variability for the well-known two-promoter system used experimentally by Elowitz et al. (2002). We finally apply our framework to a more complicated system and demonstrate how the interplay between noisy gene expression and growth inhibition due to protein accumulation at the single cell level can result in complex behavior at the cell population level. The generality of our framework makes it suitable for studying a vast array of artificial and natural genetic networks. Using our Monte Carlo algorithm, cell population distributions can be predicted for the genetic architecture of interest, thereby quantifying the effect of stochasticity in intracellular reactions or the variability in the rate of physiological processes such as growth and division. Such in silico experiments can give insight into the behavior of cell populations and reveal the major sources contributing to cell population heterogeneity.

Environmentally-modulated changes in fluorescence distribution in cells with oscillatory genetic network dynamics

We investigated the distribution of green fluorescent protein (GFP) expression levels in a population of E. coli cells expressing an artificial genetic regulatory network, known as the "repressilator". This network originally constructed by Elowitz and Leibler in 2000 consists of three cyclically-inhibiting promoter-repressor pairs. It is because of this architecture that the network has been known to oscillate at the single-cell level under certain conditions. A series of shake flask experiments were performed and analyzed using flow cytometry to test how cell populations carrying this system could be controlled extracellularly using the inducers anhydrotetracycline (aTc) and isopropyl-beta-d-thiogalactopyranoside (IPTG). With variation of [aTc], it exhibits a novel bi-threshold behavior, such that the entire culture reaches one of three steady states at a quasi-time-invariant "reference state." Also, there is significant hysteresis. Transiently, the middle state shows damping oscillations, while the low and high states show a stable steady state. The addition of IPTG serves to fine-tune the characteristics of the aTc-only expression, lowering the average and coefficient of variation (CV) of the distributions, and possibly perturbing the network to a different state. However, in modeling this system, the multiplicity and bi-threshold behavior are not theoretically possible according to the designed interactions. In order to explain this discrepancy, we hypothesize that one or more of the repressors have a significant nonspecific interaction with a promoter that does not contain its operator site. The new modeling results incorporating these extra interactions qualitatively match our experimental findings. After constructing plasmids to test these hypotheses, we discover that at least four of these interactions exist, which can create the low and high states and multiplicity seen experimentally. This genetic architecture has flexibility in its behavior that has not been demonstrated before, and the combination of experiment and modeling enlightened our understanding of the molecular interactions driving the network's behavior, leading us to discover the significance of nonspecific interactions.

A novel assay based on fluorescence microscopy and image processing for determining phenotypic distributions of rod-shaped bacteria

Cell population balance (CPB) models can account for the phenotypic heterogeneity that characterizes isogenic cell populations. To utilize the predictive power of these models, however, we must determine the single-cell reaction and division rates as well as the partition probability density function of the cell population. These functions can be obtained through the Collins-Richmond inverse CPB modeling methodology, if we know the phenotypic distributions of (a) the overall cell population, (b) the dividing cell subpopulation, and (c) the newborn cell subpopulation. This study presents the development of a novel assay that combines fluorescence microscopy and image processing to determine these distributions. The method is generally applicable to rod-shaped cells dividing through the formation of a characteristic constriction. Morphological criteria were developed for the automatic identification of dividing cells and validated through direct comparison with manually obtained measurements. The newborn cell subpopulation was obtained from the corresponding dividing cell subpopulation by collecting information from the two compartments separated by the constriction. The method was applied to E. coli cells carrying the genetic toggle network with a green fluorescent marker. Our measurements for the overall cell population were in excellent agreement with the distributions obtained via flow cytometry. The new assay constitutes a powerful tool that can be used in conjunction with inverse CPB modeling to rigorously quantify single-cell behavior from data collected from highly heterogeneous cell populations.

From single-cell genetic architecture to cell population dynamics: quantitatively decomposing the effects of different population heterogeneity sources for a genetic network with positive feedback architecture

Phenotypic cell-to-cell variability or cell population heterogeneity originates from two fundamentally different sources: unequal partitioning of cellular material at cell division and stochastic fluctuations associated with intracellular reactions. We developed a mathematical and computational framework that can quantitatively isolate both heterogeneity sources and applied it to a genetic network with positive feedback architecture. The framework consists of three vastly different mathematical formulations: a), a continuum model, which completely neglects population heterogeneity; b), a deterministic cell population balance model, which accounts for population heterogeneity originating only from unequal partitioning at cell division; and c), a fully stochastic model accommodating both sources of population heterogeneity. The framework enables the quantitative decomposition of the effects of the different population heterogeneity sources on system behavior. Our results indicate the importance of cell population heterogeneity in accurately predicting even average population properties. Moreover, we find that unequal partitioning at cell division and sharp division rates shrink the region of the parameter space where the population exhibits bistable behavior, a characteristic feature of networks with positive feedback architecture. In addition, intrinsic noise at the single-cell level due to slow operator fluctuations and small numbers of molecules further contributes toward the shrinkage of the bistability regime at the cell population level. Finally, the effect of intrinsic noise at the cell population level was found to be markedly different than at the single-cell level, emphasizing the importance of simulating entire cell populations and not just individual cells to understand the complex interplay between single-cell genetic architecture and behavior at the cell population level.

Model-based definition of population heterogeneity and its effects on metabolism in sporulating Bacillus subtilis

The soil bacterium Bacillus subtilis forms dormant, robust spores as a tactic to ensure survival under conditions of starvation. However, the sporulating culture includes sporulating and non-sporulating cells, because a portion of the cell population initiates sporulation in wild-type strain. We anticipated that the population effect must be considered carefully to analyse samples yielding population heterogeneity. We first built a mathematical model and simulated for signal transduction of the sporulation cue to see what mechanisms are responsible for generating the heterogeneity. The simulated results were confirmed experimentally, where heterogeneity is primarily modulated by negative feedback circuits, resulting in generation of a bistable response within the sporulating culture. We also confirmed that mutants relevant to negative feedback yield either sporulating or non-sporulating subpopulations. To see the effect of molecular mechanism between sporulating and non-sporulating cells in distinct manner, metabolome analysis was conducted using the above mutants. The metabolic profiles exhibited distinct characteristics with time regardless of whether sporulation was initiated or not. In addition, several distinct characteristics of metabolites were observed between strains, which was inconsistent with previously reported data. The results imply that careful consideration must be made in the interpretation of data obtained from cells yielding population heterogeneity.

Stochastic and deterministic simulations of heterogeneous cell population dynamics

A Monte Carlo algorithm, which can accurately simulate the dynamics of entire heterogeneous cell populations, was developed. The algorithm takes into account the random nature of cell division as well as unequal partitioning of cellular material at cell division. Moreover, it is general in the sense that it can accommodate a variety of single-cell, deterministic reaction kinetics as well as various stochastic division and partitioning mechanisms. The validity of the algorithm was assessed through comparison of its results with those of the corresponding deterministic cell population balance model in cases where stochastic behavior is expected to be quantitatively negligible. Both algorithms were applied to study: (a) linear intracellular kinetics and (b) the expression dynamics of a genetic network with positive feedback architecture, such as the lac operon. The effects of stochastic division as well as those of different division and partitioning mechanisms were assessed in these systems, while the comparison of the stochastic model with a continuum model elucidated the significance of cell population heterogeneity even in cases where only the prediction of average properties is of primary interest.

Monitoring population dynamics of the thermophilic Bacillus licheniformis CCMI 1034 in batch and continuous cultures using multi-parameter flow cytometry

Multi-parameter flow cytometry was used to monitor the population dynamics of Bacillus licheniformis continuous cultivations and the physiological responses to a starvation period and a glucose pulse. Using a mixture of two specific fluorescent stains, DiOC6(3) (3,3'-dihexylocarbocyanine iodide), and PI (propidium iodide), flow cytometric analysis revealed cell physiological heterogeneity. Four sub-populations of cells could be easily identified based on their differential fluorescent staining, these correspond to healthy cells (A) stained with DiOC6(3); cells or spores with a depolarised cytoplasmic membrane (B), no staining; cells with a permeabilised depolarised cytoplasmic membrane (C), stained with PI; and permeablised cells with a disrupted cytoplasmic membrane 'ghost cells' (D), stained with both DiOC6(3) and PI. Transmission electron micrographs of cells starved of energy showed different cell lysis process stages, highlighting 'ghost cells' which were associated with the double stained sub-population. It was shown, at the individual cell level, that there was a progressive inherent fluctuation in physiological heterogeneity in response to changing environmental conditions. All four sub-populations were shown to be present during glucose-limited continuous cultures, revealing a higher physiological stress level when compared with a glucose pulsed batch. A starvation period (batch without additional nutrients) increased the number of cells in certain sub-populations (cells with depolarised cytoplasmic membranes and cells with permeabilised depolarised cytoplasmic membranes), indicating that such stress may be caused by glucose limitation. Such information could be used to enhance process efficiency.

Cytometric monitoring of growth, sporogenesis and spore cell sorting in Paenibacillus polymyxa (formerly Bacillus polymyxa)

AIMS

Formation of bacterial endospores is a basic process in Gram-positive bacteria and has implications for health, industry and the environment. Flow cytometry offers a practical alternative for the rapid detection, enumeration and characterization of bacterial endospores.

METHODS AND RESULTS

Paenibacillus polymyxa was chosen for this study because its spores cause sporangium deformation and have thick walls with a star-shaped section. Sporulating populations were analysed with a particle analyser and a flow cytometer after labelling with propidium iodide and Syto-13. Flow cytometric detection of single spores was confirmed by optical and scanning electron microscopy after cell sorting. Four cell sub-populations were cytometrically detected in P. polymyxa cultures grown in liquid sporulation medium. Two sub-populations consisted of vegetative cells differing in both morphology and viability; the other two sub-populations consisted of spores differing in their viability.

CONCLUSIONS

This work has shown that flow cytometry is a simple and fast method (less than 15 minutes for sample preparation and analysis) for the study of the sporulation in P. polymyxa. The use of this technique allowed both detection and quantification of sporulation inside a culture, and distinguished cells that differed in viability despite being morphologically identical under microscopic observation.

SIGNIFICANCE AND IMPACT OF THE STUDY

Flow cytometry has been proved to be a valuable tool for the analysis of sporulation in P. polymyxa cultures, with the unique capacity of distinguishing between endospores and vegetative cells, and between live and dead cells, in the same analysis. An important percentage of non-viable endospores has been found in aged cultures using this method.

Heterogeneous distribution of lysine 6-aminotransferase during cephamycin C biosynthesis in Streptomyces clavuligerus demonstrated using green fluorescent protein as a reporter

The cellular distribution of the cephamycin biosynthetic enzyme lysine 6-aminotransferase (LAT) has been studied in Streptomyces clavuligerus hyphae by confocal microscopy using the S65T mutant of green fluorescent protein (GFP) as a reporter. LAT mediates the first committed step in the biosynthesis of the secondary metabolite cephamycin C by S. clavuligerus. The enzymic activity of LAT varies with time during the growth of S. clavuligerus in liquid medium. To investigate if this temporal variation occurs uniformly amongst all hyphae, S. clavuligerus was transformed with a plasmid containing the LAT-encoding gene translationally fused to the GFP-encoding gene. The LAT-GFP fusion product displayed fluorescence spectral characteristics of GFP, and showed similar temporal characteristics of LAT activity compared to the wild-type strain of S. clavuligerus. The transformed strain exhibited a heterogeneous distribution of fluorescence in mycelia grown in liquid cultures. This distribution varied significantly as the batch progressed: only a fraction of the mycelia fluoresced in the early growth phase, whereas nearly all hyphae fluoresced by the late growth phase. Thereafter, a non-uniform distribution of fluorescence was again observed in the declining growth phase. A large fraction of the non-fluorescent cells in the declining growth phase were found to be non-viable. Observations of S. clavuligerus colonies grown on solid agar also showed variation of LAT-GFP expression at different stages of growth. These observations in the solid phase can be explained in terms of nutrient deprivation and signalling molecules. The results suggest that physiological differentiation of S. clavuligerus mycelia leading to cephamycin C biosynthesis is both temporally and spatially distributed. The findings also revealed that the observed heterogeneity was independent of the position of individual cell compartments within the hypha. The potential of GFP as a reporter for the quantitative study of cephamycin biosynthesis at the cellular level has also been demonstrated.

Non-genetic population heterogeneity studied by in situ polymerase chain reaction

Expression of a lac operon in Salmonella typhimurium single cells was monitored using lac mRNA targeting in situ reverse transcription-polymerase chain reaction (RT-PCR). It is demonstrated that suboptimal induction of the lac operon in a culture of S. typhimuriuml/F'lac+ cells generates a subpopulation in which transcription of the lac operon occurs and another subpopulation in which transcription of the lac operon is repressed, whereas suboptimal induction of the lac operon in a culture of S. typhimuriuml/F'lacY cells generates a population with uniform levels of lac mRNA. The outcome of the single-cell lac mRNA detection assay was compared with the outcome of a single-cell beta-galactosidase assay. In cultures grown under different suboptimal lac induction conditions, the fraction of cells in which transcription of the lac operon occurred was concurrent with the fraction of cells showing beta-galactosidase activity. Besides supporting the hypothesis that the lactose permease has a role in generating non-genetic heterogeneity in suboptimally induced cultures of Lac+ cells, these results demonstrate the usefulness of in situ RT-PCR for the study of non-genetic population heterogeneities.