scholarly journals Modeling Bacterial Population Growth from Stochastic Single-Cell Dynamics

2014 ◽  
Vol 80 (17) ◽  
pp. 5241-5253 ◽  
Author(s):  
Antonio A. Alonso ◽  
Ignacio Molina ◽  
Constantinos Theodoropoulos
Keyword(s):  
Differential Equation ◽  
Population Growth ◽  
Single Cell ◽  
Bacterial Cells ◽  
Estimation Of Parameters ◽  
Deterministic Models ◽  
Cell Dynamics ◽  
Bacterial Populations ◽  
Content Type ◽  
Number Of Individuals

ABSTRACTA few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that they are capable of adapting and proliferating on a food matrix. This is why any quantitative health risk assessment policy must incorporate methods to accurately predict the growth of bacterial populations from a small number of pathogens. In this aim, mathematical models have become a powerful tool. Unfortunately, at low cell concentrations, standard deterministic models fail to predict the fate of the population, essentially because the heterogeneity between individuals becomes relevant. In this work, a stochastic differential equation (SDE) model is proposed to describe variability within single-cell growth and division and to simulate population growth from a given initial number of individuals. We provide evidence of the model ability to explain the observed distributions of times to division, including the lag time produced by the adaptation to the environment, by comparing model predictions with experiments from the literature forEscherichia coli,Listeria innocua, andSalmonella enterica. The model is shown to accurately predict experimental growth population dynamics for both small and large microbial populations. The use of stochastic models for the estimation of parameters to successfully fit experimental data is a particularly challenging problem. For instance, if Monte Carlo methods are employed to model the required distributions of times to division, the parameter estimation problem can become numerically intractable. We overcame this limitation by converting the stochastic description to a partial differential equation (backward Kolmogorov) instead, which relates to the distribution of division times. Contrary to previous stochastic formulations based on random parameters, the present model is capable of explaining the variability observed in populations that result from the growth of a small number of initial cells as well as the lack of it compared to populations initiated by a larger number of individuals, where the random effects become negligible.

scholarly journals Stochasticity in Colonial Growth Dynamics of Individual Bacterial Cells

2013 ◽  
Vol 79 (7) ◽  
pp. 2294-2301 ◽  
Author(s):  
Konstantinos P. Koutsoumanis ◽  
Alexandra Lianou
Keyword(s):  
Kinetic Parameters ◽  
Single Cells ◽  
Growth Curves ◽  
Growth Dynamics ◽  
Time Lapse ◽  
Initial Population ◽  
Bacterial Cells ◽  
Stochastic Growth ◽  
Bacterial Populations ◽  
Content Type

ABSTRACTConventional bacterial growth studies rely on large bacterial populations without considering the individual cells. Individual cells, however, can exhibit marked behavioral heterogeneity. Here, we present experimental observations on the colonial growth of 220 individual cells ofSalmonella entericaserotype Typhimurium using time-lapse microscopy videos. We found a highly heterogeneous behavior. Some cells did not grow, showing filamentation or lysis before division. Cells that were able to grow and form microcolonies showed highly diverse growth dynamics. The quality of the videos allowed for counting the cells over time and estimating the kinetic parameters lag time (λ) and maximum specific growth rate (μmax) for each microcolony originating from a single cell. To interpret the observations, the variability of the kinetic parameters was characterized using appropriate probability distributions and introduced to a stochastic model that allows for taking into account heterogeneity using Monte Carlo simulation. The model provides stochastic growth curves demonstrating that growth of single cells or small microbial populations is a pool of events each one of which has its own probability to occur. Simulations of the model illustrated how the apparent variability in population growth gradually decreases with increasing initial population size (N0). For bacterial populations withN0of >100 cells, the variability is almost eliminated and the system seems to behave deterministically, even though the underlying law is stochastic. We also used the model to demonstrate the effect of the presence and extent of a nongrowing population fraction on the stochastic growth of bacterial populations.

scholarly journals Prokaryotic Single-Cell RNA Sequencing by In Situ Combinatorial Indexing

2019 ◽  
Author(s):  
Sydney B. Blattman ◽  
Wenyan Jiang ◽  
Panos Oikonomou ◽  
Saeed Tavazoie
Keyword(s):  
Single Cell ◽  
Rna Sequencing ◽  
Low Cost ◽  
Bacterial Cells ◽  
Single Experiment ◽  
Bacterial Populations ◽  
Single Cell Rna Sequencing ◽  
Gene Expression Heterogeneity ◽  
Mrna Polyadenylation

AbstractDespite longstanding appreciation of gene expression heterogeneity in isogenic bacterial populations, affordable and scalable technologies for studying single bacterial cells have been limited. While single-cell RNA sequencing (scRNA-seq) has revolutionized studies of transcriptional heterogeneity in diverse eukaryotic systems, application of scRNA-seq to prokaryotes has been hindered by their extremely low mRNA abundance, lack of mRNA polyadenylation, and thick cell walls. Here, we present Prokaryotic Expression-profiling by Tagging RNA In Situ and sequencing (PETRI-seq), a low-cost, high-throughput, prokaryotic scRNA-seq pipeline that overcomes these technical obstacles. PETRI-seq uses in situ combinatorial indexing to barcode transcripts from tens of thousands of cells in a single experiment. PETRI-seq captures single cell transcriptomes of Gram-negative and Gram-positive bacteria with high purity and low bias, with median capture rates >200 mRNAs/cell for exponentially growing E. coli. These characteristics enable robust discrimination of cell-states corresponding to different phases of growth. When applied to wild-type S. aureus, PETRI-seq revealed a rare sub-population of cells undergoing prophage induction. We anticipate broad utility of PETRI-seq in defining single-cell states and their dynamics in complex microbial communities.

scholarly journals Noise-driven growth rate gain in clonal cellular populations

2016 ◽  
Vol 113 (12) ◽  
pp. 3251-3256 ◽  
Author(s):  
Mikihiro Hashimoto ◽  
Takashi Nozoe ◽  
Hidenori Nakaoka ◽  
Reiko Okura ◽  
Sayo Akiyoshi ◽  
...  
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Single Cell ◽  
Single Cells ◽  
Population Level ◽  
Growth Conditions ◽  
Cell Dynamics ◽  
Generation Times ◽  
Complex Population ◽  
The Mean

Cellular populations in both nature and the laboratory are composed of phenotypically heterogeneous individuals that compete with each other resulting in complex population dynamics. Predicting population growth characteristics based on knowledge of heterogeneous single-cell dynamics remains challenging. By observing groups of cells for hundreds of generations at single-cell resolution, we reveal that growth noise causes clonal populations of Escherichia coli to double faster than the mean doubling time of their constituent single cells across a broad set of balanced-growth conditions. We show that the population-level growth rate gain as well as age structures of populations and of cell lineages in competition are predictable. Furthermore, we theoretically reveal that the growth rate gain can be linked with the relative entropy of lineage generation time distributions. Unexpectedly, we find an empirical linear relation between the means and the variances of generation times across conditions, which provides a general constraint on maximal growth rates. Together, these results demonstrate a fundamental benefit of noise for population growth, and identify a growth law that sets a “speed limit” for proliferation.

Solutions of ordinary differential equations as limits of pure jump markov processes

1970 ◽  
Vol 7 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Thomas G. Kurtz
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Population Growth ◽  
Ordinary Differential Equations ◽  
Markov Processes ◽  
Radioactive Decay ◽  
Dynamic Processes ◽  
Deterministic Models ◽  
Image Position ◽  
Jump Markov Processes

In a great variety of fields, e.g., biology, epidemic theory, physics, and chemistry, ordinary differential equations are used to give continuous deterministic models for dynamic processes which are actually discrete and random in their development. Perhaps the simplest example is the differential equation used to describe a number of processes including radioactive decay and population growth.

scholarly journals High-Content Imaging to Phenotype Antimicrobial Effects on Individual Bacteria at Scale

mSystems ◽  
2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Sushmita Sridhar ◽  
Sally Forrest ◽  
Ben Warne ◽  
Mailis Maes ◽  
Stephen Baker ◽  
...  
Keyword(s):  
Staphylococcus Aureus ◽  
High Resolution ◽  
Antimicrobial Resistance ◽  
Morphological Characteristics ◽  
Bacterial Cells ◽  
Bacterial Populations ◽  
Content Type ◽  
High Content Imaging ◽  
Serovar Typhimurium ◽  
Multiple Cells

ABSTRACT High-content imaging (HCI) is a technique for screening multiple cells in high resolution to detect subtle morphological and phenotypic variation. The method has been commonly deployed on model eukaryotic cellular systems, often for screening new drugs and targets. HCI is not commonly utilized for studying bacterial populations but may be a powerful tool in understanding and combatting antimicrobial resistance. Consequently, we developed a high-throughput method for phenotyping bacteria under antimicrobial exposure at the scale of individual bacterial cells. Imaging conditions were optimized on an Opera Phenix confocal microscope (Perkin Elmer), and novel analysis pipelines were established for both Gram-negative bacilli and Gram-positive cocci. The potential of this approach was illustrated using isolates of Klebsiella pneumoniae, Salmonella enterica serovar Typhimurium, and Staphylococcus aureus. HCI enabled the detection and assessment of subtle morphological characteristics, undetectable through conventional phenotypical methods, that could reproducibly distinguish between bacteria exposed to different classes of antimicrobials with distinct modes of action (MOAs). In addition, distinctive responses were observed between susceptible and resistant isolates. By phenotyping single bacterial cells, we observed intrapopulation differences, which may be critical in identifying persistence or emerging resistance during antimicrobial treatment. The work presented here outlines a comprehensive method for investigating morphological changes at scale in bacterial populations under specific perturbation. IMPORTANCE High-content imaging (HCI) is a microscopy technique that permits the screening of multiple cells simultaneously in high resolution to detect subtle morphological and phenotypic variation. The power of this methodology is that it can generate large data sets comprised of multiple parameters taken from individual cells subjected to a range of different conditions. We aimed to develop novel methods for using HCI to study bacterial cells exposed to a range of different antibiotic classes. Using an Opera Phenix confocal microscope (Perkin Elmer) and novel analysis pipelines, we created a method to study the morphological characteristics of Klebsiella pneumoniae, Salmonella enterica serovar Typhimurium, and Staphylococcus aureus when exposed to antibacterial drugs with differing modes of action. By imaging individual bacterial cells at high resolution and scale, we observed intrapopulation differences associated with different antibiotics. The outlined methods are highly relevant for how we begin to better understand and combat antimicrobial resistance.

scholarly journals A Single-Cell Genome for Thiovulum sp.

2012 ◽  
Vol 78 (24) ◽  
pp. 8555-8563 ◽  
Author(s):  
Ian P. G. Marshall ◽  
Paul C. Blainey ◽  
Alfred M. Spormann ◽  
Stephen R. Quake
Keyword(s):  
Single Cell ◽  
Multiple Displacement Amplification ◽  
Bacterial Cells ◽  
Content Type ◽  
Swimming Motility ◽  
Elkhorn Slough ◽  
Naturally Occurring ◽  
Wide Range ◽  
Cell Genome ◽  
Single Cell Genome

ABSTRACTWe determined a significant fraction of the genome sequence of a representative ofThiovulum, the uncultivated genus of colorless sulfurEpsilonproteobacteria, by analyzing the genome sequences of four individual cells collected from phototrophic mats from Elkhorn Slough, California. These cells were isolated utilizing a microfluidic laser-tweezing system, and their genomes were amplified by multiple-displacement amplification prior to sequencing.Thiovulumis a gradient bacterium found at oxic-anoxic marine interfaces and noted for its distinctive morphology and rapid swimming motility. The genomic sequences of the four individual cells were assembled into a composite genome consisting of 221 contigs covering 2.083 Mb including 2,162 genes. This single-cell genome represents a genomic view of the physiological capabilities of isolatedThiovulumcells.Thiovulumis the second-fastest bacterium ever observed, swimming at 615 μm/s, and this genome shows that this rapid swimming motility is a result of a standard flagellar machinery that has been extensively characterized in other bacteria. This suggests that standard flagella are capable of propelling bacterial cells at speeds much faster than typically thought. Analysis of the genome suggests that naturally occurringThiovulumpopulations are more diverse than previously recognized and that studies performed in the past probably address a wide range of unrecognized genotypic and phenotypic diversities ofThiovulum. The genome presented in this article provides a basis for future isolation-independent studies ofThiovulum, where single-cell and metagenomic tools can be used to differentiate between differentThiovulumgenotypes.

scholarly journals RadD Contributes to R-Loop Avoidance in Sub-MIC Tobramycin

mBio ◽  
2019 ◽  
Vol 10 (4) ◽  
Author(s):  
Veronica Negro ◽  
Evelyne Krin ◽  
Sebastian Aguilar Pierlé ◽  
Thibault Chaze ◽  
Quentin Giai Gianetto ◽  
...  
Keyword(s):  
Molecular Mechanisms ◽  
Coupling Factor ◽  
Resistant Bacteria ◽  
Bacterial Cells ◽  
Dna Breaks ◽  
Bacterial Populations ◽  
Content Type ◽  
Double Strand Dna Breaks ◽  
Translation Coupling ◽  
Recombination Pathway

ABSTRACTWe have previously identifiedVibrio choleraemutants in which the stress response to subinhibitory concentrations of aminoglycoside is altered. One gene identified, VC1636, encodes a putative DNA/RNA helicase, recently named RadD inEscherichia coli. Here we combined extensive genetic characterization and high-throughput approaches in order to identify partners and molecular mechanisms involving RadD. We show that double-strand DNA breaks (DSBs) are formed upon subinhibitory tobramycin treatment in the absence ofradDandrecBCDand that formation of these DSBs can be overcome by RNase H1 overexpression. Loss of RNase H1, or of the transcription-translation coupling factor EF-P, is lethal in theradDdeletion mutant. We propose that R-loops are formed upon sublethal aminoglycoside treatment, leading to the formation of DSBs that can be repaired by the RecBCD homologous recombination pathway, and that RadD counteracts such R-loop accumulation. We discuss how R-loops that can occur upon translation-transcription uncoupling could be the link between tobramycin treatment and DNA break formation.IMPORTANCEBacteria frequently encounter low concentrations of antibiotics. Active antibiotics are commonly detected in soil and water at concentrations much below lethal concentration. Although sub-MICs of antibiotics do not kill bacteria, they can have a major impact on bacterial populations by contributing to the development of antibiotic resistance through mutations in originally sensitive bacteria or acquisition of DNA from resistant bacteria. It was shown that concentrations as low as 100-fold below the MIC can actually lead to the selection of antibiotic-resistant cells. We seek to understand how bacterial cells react to such antibiotic concentrations usingE. coli, the Gram-negative bacterial paradigm, andV. cholerae, the causative agent of cholera. Our findings shed light on the processes triggered at the DNA level by antibiotics targeting translation, how damage occurs, and what the bacterial strategies are to respond to such DNA damage.

scholarly journals Effects of PslG on the Surface Movement of Pseudomonas aeruginosa

2018 ◽  
Vol 84 (13) ◽  
Author(s):  
Jingchao Zhang ◽  
Jing He ◽  
Chunhui Zhai ◽  
Luyan Z. Ma ◽  
Lichuan Gu ◽  
...  
Keyword(s):  
Pseudomonas Aeruginosa ◽  
Single Cell ◽  
Human Society ◽  
Bacterial Cells ◽  
Content Type ◽  
Surface Movement ◽  
Bacterial Surface ◽  
Biofilm Control ◽  
Preferred Direction ◽  
Biofilm Development

ABSTRACT PslG attracted a lot of attention recently due to its great potential abilities in inhibiting biofilms of Pseudomonas aeruginosa . However, how PslG affects biofilm development still remains largely unexplored. Here, we focused on the surface motility of bacterial cells, which is critical for biofilm development. We studied the effects of PslG on bacterial surface movement in early biofilm development at a single-cell resolution by using a high-throughput bacterial tracking technique. The results showed that compared with no exogenous PslG addition, when PslG was added to the medium, bacterial surface movement was significantly (4 to 5 times) faster and proceeded in a more random way with no clear preferred direction. A further study revealed that the fraction of walking mode increased when PslG was added, which then resulted in an elevated average speed. The differences of motility due to PslG addition led to a clear distinction in patterns of bacterial surface movement and retarded microcolony formation greatly. Our results provide insight into developing new PslG-based biofilm control techniques. IMPORTANCE Biofilms of Pseudomonas aeruginosa are a major cause for hospital-acquired infections. They are notoriously difficult to eradicate and pose serious health hazards to human society. So, finding new ways to control biofilms is urgently needed. Recent work on PslG showed that PslG might be a good candidate for inhibiting/disassembling biofilms of Pseudomonas aeruginosa through Psl-based regulation. However, to fully explore PslG functions in biofilm control, a better understanding of PslG-Psl interactions is needed. Toward this end, we examined the effects of PslG on the surface movement of Pseudomonas aeruginosa in this work. The significance of our work is in greatly enhancing our understanding of the inhibiting mechanism of PslG on biofilms by providing a detailed picture of bacterial surface movement at a single-cell level, which will allow a full understanding of PslG abilities in biofilm control and thus present potential applications in biomedical fields.

scholarly journals Contributions ofCandida albicansDimorphism, Adhesive Interactions, and Extracellular Matrix to the Formation of Dual-Species Biofilms withStreptococcus gordonii

mBio ◽  
2019 ◽  
Vol 10 (3) ◽  
Author(s):  
Daniel Montelongo-Jauregui ◽  
Stephen P. Saville ◽  
Jose L. Lopez-Ribot
Keyword(s):  
Extracellular Matrix ◽  
Oral Cavity ◽  
Bacterial Species ◽  
Fungal Species ◽  
Bacterial Cells ◽  
Mixed Species ◽  
Bacterial Populations ◽  
Content Type ◽  
Mutant Strains ◽  
Adhesive Interactions

ABSTRACTFungal and bacterial populations coexist in the oral cavity, frequently forming mixed-species biofilms that complicate treatment against polymicrobial infections. However, despite relevance to oral health, the bidirectional interactions between these microbial populations are poorly understood. In this study, we aimed to elucidate the mechanisms underlying the interactions between the fungal speciesCandida albicansand the bacterial speciesStreptococcus gordoniias they coexist in mixed-species biofilms. Specifically, the interactions of differentC. albicansmutant strains deficient in filamentation (efg1Δ/Δ andbrg1Δ/Δ), adhesive interactions (als3Δ/Δ andbcr1Δ/Δ), and production of matrix exopolymeric substances (EPS) (kre5Δ/Δ, mnn9Δ/Δ,rlm1Δ/Δ, andzap1Δ/Δ) were evaluated withS. gordoniiunder different conditions mimicking the environment in the oral cavity. Interestingly, our results revealed that growth of the biofilm-deficientC. albicansals3Δ/Δandbcr1Δ/Δmutant strains in synthetic saliva or withS. gordoniirestored their biofilm-forming ability. Moreover, challenging previous observations indicating an important role of morphogenetic conversions in the interactions between these two species, our results indicated a highly synergistic interaction betweenS. gordoniiand theC. albicansfilamentation-deficientefg1Δ/Δandbrg1Δ/Δdeletion mutants, which was particularly noticeable when the mixed biofilms were grown in synthetic saliva. Importantly, dual-species biofilms were found to exhibit increase in antimicrobial resistance, indicating that components of the fungal exopolymeric material confer protection to streptococcal cells against antibacterial treatment. Collectively, these findings unravel a high degree of complexity in the interactions betweenC. albicansandS. gordoniiin mixed-species biofilms, which may impact homeostasis in the oral cavity.IMPORTANCEMicrobial communities have a great impact in health and disease.C. albicansinteracts with multiple microorganisms in the oral cavity, frequently forming polymicrobial biofilms. We report on the synergistic interactions betweenC. albicansand the Gram-positive bacteriumS. gordonii, for which we have examined the different contributions of adhesive interactions, filamentation, and the extracellular matrix to the formation of dual-species biofilms. Our results demonstrate that growth in the presence of the bacterium can restore the biofilm-forming ability of differentC. albicansmutant strains with defects in adhesion and filamentation. The mixed-species biofilms also show high levels of resistance to antibacterial and antifungal antibiotics, and our results indicate that the fungal biofilm matrix protects bacterial cells within these mixed-species biofilms. Our observations add to a growing body of evidence indicating a high level of complexity in the reciprocal interactions and consortial behavior of fungal/bacterial biofilms.

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