Scaling laws governing stochastic growth and division of single bacterial cells

A generalized adder for cell size homeostasis: Effects on stochastic clonal proliferation

Measurements of cell size dynamics have revealed phenomenological principles by which individual cells control their size across diverse organisms. One of the emerging paradigms of cell size homeostasis is the adder, where the cell cycle duration is established such that the cell size increase from birth to division is independent of the newborn cell size. We provide a mechanistic formulation of the adder, considering that cell size follows any arbitrary nonexponential growth law. Our results show that the main requirement to obtain an adder regardless of the growth law (the time derivative of cell size) is that cell cycle regulators are produced at a rate proportional to the growth law, and cell division is triggered when these molecules reach a prescribed threshold level. Among the implications of this generalized adder, we investigate fluctuations in the proliferation of single-cell-derived colonies. Considering exponential cell size growth, random fluctuations in clonal size show a transient increase and then eventually decay to zero over time (i.e., clonal populations become asymptotically more similar). In contrast, several forms of nonexponential cell size dynamics (with adder-based cell size control) yield qualitatively different results: clonal size fluctuations monotonically increase over time, reaching a nonzero value. These results characterize the interplay between cell size homeostasis at the single-cell level and clonal proliferation at the population level, explaining the broad fluctuations in clonal sizes seen in barcoded human cell lines.

Cell size and selection for stress-induced cell fusion in unicellular eukaryotes

In unicellular organisms, sexual reproduction typically begins with the fusion of two cells (plasmogamy) followed by the fusion of their two haploid nuclei (karyogamy) and finally meiosis. Most work on the evolution of sexual reproduction focuses on the benefits of the genetic recombination that takes place during meiosis. However, the selection pressures that may have driven the early evolution of binary cell fusion, which sets the stage for the evolution of karyogamy by bringing nuclei together in the same cell, have seen less attention. In this paper we develop a model for the coevolution of cell size and binary cell fusion rate. The model assumes that larger cells experience a survival advantage from their larger cytoplasmic volume. We find that under favourable environmental conditions, populations can evolve to produce larger cells that undergo obligate binary cell fission. However, under challenging environmental conditions, populations can evolve to subsequently produce smaller cells under binary cell fission that nevertheless retain a survival advantage by fusing with other cells. The model thus parsimoniously recaptures the empirical observation that sexual reproduction is typically triggered by adverse environmental conditions in many unicellular eukaryotes and draws conceptual links to the literature on the evolution of multicellularity.

Metabolic rearrangement enables adaptation of microbial growth rate to temperature shifts

Temperature is a key determinant of microbial behaviour and survival in the environment and within hosts. At intermediate temperatures, growth rate varies according to the Arrhenius law of thermodynamics, which describes the effect of temperature on the rate of a chemical reaction. However, the mechanistic basis for this behaviour remains unclear. Here we use single-cell microscopy to show that Escherichia coli exhibits a gradual response to temperature upshifts with a timescale of ~1.5 doublings at the higher temperature. The response was largely independent of initial or final temperature and nutrient source. Proteomic and genomic approaches demonstrated that adaptation to temperature is independent of transcriptional, translational or membrane fluidity changes. Instead, an autocatalytic enzyme network model incorporating temperature-sensitive Michaelis-Menten kinetics recapitulates all temperature-shift dynamics through metabolome rearrangement, resulting in a transient temperature memory. The model successfully predicts alterations in the temperature response across nutrient conditions, diverse E. coli strains from hosts with different body temperatures, soil-dwelling Bacillus subtilis and fission yeast. In sum, our model provides a mechanistic framework for Arrhenius-dependent growth.

Exact distributions of threshold crossing times of proteins under post-transcriptional regulation by small RNAs

The timings of several cellular events like cell lysis, cell division, or pore formation in endosomes are regulated by the time taken for the relevant proteins to cross a threshold in number or concentration. Since protein synthesis is stochastic, the threshold crossing time is a first passage problem. The exact distributions of these first passage processes have been obtained recently for unregulated and autoregulated genes. Many proteins are however regulated by post-transcriptional regulation, controlled by small noncoding RNAs (sRNAs). Certain mathematical models of gene expression with post-transcriptional sRNA regulation have been recently exactly mapped to models without sRNA regulation. Utilizing this mapping and the exact distributions, we calculate exact results on fluctuations (full distribution, all cumulants, and characteristic times) of protein threshold crossing times in the presence of sRNA regulation. We derive two interesting predictions from these exact results. We show that the size of the fluctuation of the threshold crossing times have a nonmonotonic U-shaped behavior as a function of the rates of binding and unbinding of the sRNA-mRNA complex. Thus there are optimal parameters that minimize noise. Furthermore, the fluctuations in models with sRNA regulation may be higher or lower compared to the model without regulation, depending on the mean protein burst size.

Single-cell imaging of the Mycobacterium tuberculosis cell cycle reveals linear and heterogenous growth

Difficulties in antibiotic treatment of Mycobacterium tuberculosis (Mtb) are partly thought to be due to heterogeneity in growth. Although the ability of bacterial pathogens to regulate growth is crucial to control homeostasis, virulence and drug responses, single-cell growth and cell cycle behaviours of Mtb are poorly characterized. Here we use time-lapse, single-cell imaging of Mtb coupled with mathematical modelling to observe asymmetric growth and heterogeneity in cell size, interdivision time and elongation speed. We find that, contrary to Mycobacterium smegmatis, Mtb initiates cell growth not only from the old pole but also from new poles or both poles. Whereas most organisms grow exponentially at the single-cell level, Mtb has a linear growth mode. Our data show that the growth behaviour of Mtb diverges from that of model bacteria, provide details into how Mtb grows and creates heterogeneity and suggest that growth regulation may also diverge from that in other bacteria.

Nature of barriers determines first passage times in heterogeneous media

Intuition suggests that passage times across a region increase with the number of barriers along the path. Can this fail depending on the nature of the barrier? To probe this fundamental question, we exactly solve for the first passage time in general d-dimensions for diffusive transport through a spatially patterned array of obstacles - either entropic or energetic, depending on the nature of the obstacles. For energetic barriers, we show that first passage times vary non-monotonically with the number of barriers, while for entropic barriers it increases monotonically. This non-monotonicity for energetic barriers is further reflected in the behaviour of effective diffusivity as well. We then design a simple experiment where a robotic bug navigates in a heterogeneous environment through a spatially patterned array of obstacles to validate our predictions. Finally, using numerical simulations, we show that this non-monotonic behaviour for energetic barriers is general and extends to even super-diffusive transport.

Coupling of cell growth modulation to asymmetric division and cell cycle regulation in Caulobacter crescentus

In proliferating bacteria, growth rate is often assumed to be similar between daughter cells. However, most of our knowledge of cell growth derives from studies on symmetrically dividing bacteria. In many α-proteobacteria, asymmetric division is a normal part of the life cycle, with each division producing daughter cells with different sizes and fates. Here, we demonstrate that the functionally distinct swarmer and stalked daughter cells produced by the model α-proteobacterium Caulobacter crescentus can have different average growth rates under nutrient-replete conditions despite sharing an identical genome and environment. The discrepancy in growth rate is due to a growth slowdown associated with the cell cycle stage preceding DNA replication (the G1 phase), which initiates in the late predivisional mother cell before daughter cell separation. Both progenies experience a G1-associated growth slowdown, but the effect is more severe in swarmer cells because they have a longer G1 phase. Activity of SpoT, which produces the (p)ppGpp alarmone and extends the G1 phase, accentuates the cell cycle-dependent growth slowdown. Collectively, our data identify a coupling between cell growth, the G1 phase, and asymmetric division that C. crescentus may exploit for environmental adaptation through SpoT activity. This coupling differentially modulates the growth rate of functionally distinct daughter cells, thereby altering the relative abundance of ecologically important G1-specific traits within the population.

A Generalized Adder mechanism for Cell Size Homeostasis: Implications for Stochastic Dynamics of Clonal Proliferation

Measurements of cell size dynamics have revealed phenomenological principles by which individual cells control their size across diverse organisms. One of the emerging paradigms of cell size homeostasis is the adder, where the cell cycle duration is established such that the cell size increase from birth to division is independent of the newborn cell size. We provide a mechanistic formulation of the adder considering that cell size follows any arbitrary non-exponential growth law. Our results show that the main requirement to obtain an adder regardless of the growth law (the time derivative of cell size) is that cell cycle regulators are produced at a rate proportional to the growth law and cell division is triggered when these molecules reach a prescribed threshold level. Among the implications of this generalized adder, we investigate fluctuations in the proliferation of single-cell derived colonies. Considering exponential cell size growth, random fluctuations in clonal size show a transient increase and then eventually decay to zero over time (i.e., clonal populations become asymptotically more similar). In contrast, several forms of non-exponential cell size dynamics (with adder-based cell size control) yield qualitatively different results: clonal size fluctuations monotonically increase over time reaching a non-zero value. These results characterize the interplay between cell size homeostasis at the single-cell level and clonal proliferation at the population level, explaining the broad fluctuations in clonal sizes seen in barcoded human cell lines.

Differential growth regulates asymmetric size partitioning in Caulobacter crescentus

Cell size regulation has been extensively studied in symmetrically dividing cells, but the mechanisms underlying the control of size asymmetry in asymmetrically dividing bacteria remain elusive. Here, we examine the control of asymmetric division in Caulobacter crescentus, a bacterium that produces daughter cells with distinct fates and morphologies upon division. Through comprehensive analysis of multi-generational growth and shape data, we uncover a tightly regulated cell size partitioning mechanism. We find that errors in division site positioning are promptly corrected early in the division cycle through differential growth. Our analysis reveals a negative feedback between the size of daughter cell compartments and their growth rates, wherein the larger compartment grows slower to achieve a homeostatic size partitioning ratio at division. To explain these observations, we propose a mechanistic model of differential growth, in which equal amounts of growth regulators are partitioned into daughter cell compartments of unequal sizes and maintained over time via size-independent synthesis.

Architectural underpinnings of stochastic intergenerational homeostasis

Living systems are naturally complex and adaptive and offer unique insights into the strategies for achieving and sustaining stochastic homeostasis in different conditions. Here we focus on homeostasis in the context of stochastic growth and division of individual bacterial cells. We take advantage of high-precision long-term dynamical data that have recently been used to extract emergent simplicities and to articulate empirical intra- and intergenerational scaling laws governing these stochastic dynamics. From these data, we identify the core motif in the mechanistic coupling between division and growth, which naturally yields these precise rules, thus also bridging the intra- and intergenerational phenomenologies. By developing and utilizing techniques for solving a broad class of first-passage processes, we derive the exact analytic necessary and sufficient condition for sustaining stochastic intergenerational cell-size homeostasis within this framework. Furthermore, we provide predictions for the precision kinematics of cell-size homeostasis and the shape of the interdivision time distribution, which are compellingly borne out by the high-precision data. Taken together, these results provide insights into the functional architecture of control systems that yield robust yet flexible stochastic homeostasis.

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Emergent Spatiotemporal Organization in Stochastic Intracellular Transport Dynamics

The interior of a living cell is an active, fluctuating, and crowded environment, yet it maintains a high level of coherent organization. This dichotomy is readily apparent in the intracellular transport system of the cell. Membrane-bound compartments called endosomes play a key role in carrying cargo, in conjunction with myriad components including cargo adaptor proteins, membrane sculptors, motor proteins, and the cytoskeleton. These components coordinate to effectively navigate the crowded cell interior and transport cargo to specific intracellular locations, even though the underlying protein interactions and enzymatic reactions exhibit stochastic behavior. A major challenge is to measure, analyze, and understand how, despite the inherent stochasticity of the constituent processes, the collective outcomes show an emergent spatiotemporal order that is precise and robust. This review focuses on this intriguing dichotomy, providing insights into the known mechanisms of noise suppression and noise utilization in intracellular transport processes, and also identifies opportunities for future inquiry.

Scaling of stochastic growth and division dynamics: A comparative study of individual rod-shaped cells in the Mother Machine and SChemostat platforms

Microfluidic platforms enable long-term quantification of stochastic behaviors of individual bacterial cells under precisely controlled growth conditions. Yet, quantitative comparisons of physiological parameters and cell behaviors of different microorganisms in different experimental and device modalities is not available due to experiment-specific details affecting cell physiology. To rigorously assess the effects of mechanical confinement, we designed, engineered, and performed side-by-side experiments under otherwise identical conditions in the Mother Machine (with confinement) and the SChemostat (without confinement), using the latter as the ideal comparator. We established a protocol to cultivate a suitably engineered rod-shaped mutant of Caulobacter crescentus in the Mother Machine and benchmarked the differences in stochastic growth and division dynamics with respect to the SChemostat. While the single-cell growth rate distributions are remarkably similar, the mechanically confined cells in the Mother Machine experience a substantial increase in interdivision times. However, we find that the division ratio distribution precisely compensates for this increase, which in turn reflects identical emergent simplicities governing stochastic intergenerational homeostasis of cell sizes across device and experimental configurations, provided the cell sizes are appropriately mean-rescaled in each condition. Our results provide insights into the nature of the robustness of the bacterial growth and division machinery.

Effects of Molecular Noise on Cell Size Control

Cells employ control strategies to maintain a stable size. Dividing at a target size (the "sizer" strategy) is thought to produce the tightest size distribution. However, this result follows from phenomenological models that ignore the molecular mechanisms required to implement the strategy. Here we investigate a simple mechanistic model for exponentially growing cells whose division is triggered at a molecular abundance threshold. We find that size noise inherits the molecular noise and is consequently minimized not by the sizer but by the "adder" strategy, where a cell divides after adding a target amount to its birth size. We derive a lower bound on size noise that agrees with publicly available data from six microfluidic studies on Escherichia coli bacteria.

Estimates of differential toxin expression governing heterogeneous intracellular lifespans of Streptococcus pneumoniae

Following invasion of the host cell, pore-forming toxins secreted by pathogens compromise vacuole integrity and expose the microbe to diverse intracellular defence mechanisms. However, the quantitative correlation between toxin expression levels and consequent pore dynamics, fostering the intracellular life of pathogens, remains largely unexplored. In this study, using Streptococcus pneumoniae and its secreted pore-forming toxin pneumolysin (Ply) as a model system, we explored various facets of host-pathogen interactions in the host cytosol. Using time-lapse fluorescence imaging, we monitored pore formation dynamics and lifespans of different pneumococcal subpopulations inside host cells. Based on experimental histograms of various event timescales such as pore formation time, vacuolar death or cytosolic escape time and total degradation time, we developed a mathematical model based on first-passage processes that could correlate the event timescales to intravacuolar toxin accumulation. This allowed us to estimate Ply production rate, burst size and threshold Ply quantities that trigger these outcomes. Collectively, we present a general method that illustrates a correlation between toxin expression levels and pore dynamics, dictating intracellular lifespans of pathogens.

Enhancing circuit stability under growth feedback with supplementary repressive regulation

The field of synthetic biology and biosystems engineering increasingly acknowledges the need for a holistic design approach that incorporates circuit-host interactions into the design process. Engineered circuits are not isolated entities but inherently entwined with the dynamic host environment. One such circuit-host interaction, 'growth feedback', results when modifications in host growth patterns influence the operation of gene circuits. The growth-mediated effects can range from growth-dependent elevation in protein/mRNA dilution rate to changes in resource reallocation within the cell, which can lead to complete functional collapse in complex circuits. To achieve robust circuit performance, synthetic biologists employ a variety of control mechanisms to stabilize and insulate circuit behavior against growth changes. Here we propose a simple strategy by incorporating one repressive edge in a growth-sensitive bistable circuit. Through both simulation and in vitro experimentation, we demonstrate how this additional repressive node stabilizes protein levels and increases the robustness of a bistable circuit in response to growth feedback. We propose the incorporation of repressive links in gene circuits as a control strategy for desensitizing gene circuits against growth fluctuations.

How Plant Toxins Cause Early Larval Mortality in Herbivorous Insects: An Explanation by Modeling the Net Energy Curve

Plants store chemical defenses that act as toxins against herbivores, such as toxic isothiocyanates (ITCs) in Brassica plants, hydrolyzed from glucosinolate (GLS) precursors. The fitness of herbivorous larvae can be strongly affected by these toxins, causing immature death. We modeled this phenomenon using a set of ordinary differential equations and established a direct relationship between feeding, toxin exposure, and the net energy of a larva, where the fitness of an organism is proportional to its net energy according to optimal foraging theory. Optimal foraging theory is widely used in ecology to model the feeding and searching behavior of organisms. Although feeding provides energy gain, plant toxins and foraging cause energy loss for the larvae. Our equations explain that toxin exposure and foraging can sharply reduce larval net energy to zero at an instar. Since herbivory needs energy, the only choice left for a larva is to stop feeding at that time point. If that is significantly earlier than the end of the last instar stage, the larva dies without food. Thus, we show that plant toxins can cause immature death in larvae from the perspective of optimal foraging theory.

First-passage-time statistics of growing microbial populations carry an imprint of initial conditions

In exponential population growth, variability in the timing of individual division events and environmental factors (including stochastic inoculation) compound to produce variable growth trajectories. In several stochastic models of exponential growth we show power-law relationships that relate variability in the time required to reach a threshold population size to growth rate and inoculum size. Population-growth experiments in E. coli and S. aureus with inoculum sizes ranging between 1 and 100 are consistent with these relationships. We quantify how noise accumulates over time, finding that it encodes-and can be used to deduce-information about the early growth rate of a population.

The human cell count and size distribution

Cell size and cell count are adaptively regulated and intimately linked to growth and function. Yet, despite their widespread relevance, the relation between cell size and count has never been formally examined over the whole human body. Here, we compile a comprehensive dataset of cell size and count over all major cell types, with data drawn from >1,500 published sources. We consider the body of a representative male (70 kg), which allows further estimates of a female (60 kg) and 10-y-old child (32 kg). We build a hierarchical interface for the cellular organization of the body, giving easy access to data, methods, and sources (https://humancelltreemap.mis.mpg.de/). In total, we estimate total body counts of ≈36 trillion cells in the male, ≈28 trillion in the female, and ≈17 trillion in the child. These data reveal a surprising inverse relation between cell size and count, implying a trade-off between these variables, such that all cells within a given logarithmic size class contribute an equal fraction to the body's total cellular biomass. We also find that the coefficient of variation is approximately independent of mean cell size, implying the existence of cell-size regulation across cell types. Our data serve to establish a holistic quantitative framework for the cells of the human body, and highlight large-scale patterns in cell biology.

Bacterial cell-size changes resulting from altering the relative expression of Min proteins

The timing of cell division, and thus cell size in bacteria, is determined in part by the accumulation dynamics of the protein FtsZ, which forms the septal ring. FtsZ localization depends on membrane-associated Min proteins, which inhibit FtsZ binding to the cell pole membrane. Changes in the relative concentrations of Min proteins can disrupt FtsZ binding to the membrane, which in turn can delay cell division until a certain cell size is reached, in which the dynamics of Min proteins frees the cell membrane long enough to allow FtsZ ring formation. Here, we study the effect of Min proteins relative expression on the dynamics of FtsZ ring formation and cell size in individual Escherichia coli bacteria. Upon inducing overexpression of minE, cell size increases gradually to a new steady-state value. Concurrently, the time required to initiate FtsZ ring formation grows as the size approaches the new steady-state, at which point the ring formation initiates as early as before induction. These results highlight the contribution of Min proteins to cell size control, which may be partially responsible for the size fluctuations observed in bacterial populations, and may clarify how the size difference acquired during asymmetric cell division is offset.

Metabolomic rearrangement controls the intrinsic microbial response to temperature changes

Temperature is one of the key determinants of microbial behavior and survival, whose impact is typically studied under heat- or cold-shock conditions that elicit specific regulation to combat lethal stress. At intermediate temperatures, cellular growth rate varies according to the Arrhenius law of thermodynamics without stress responses, a behavior whose origins have not yet been elucidated. Using single-cell microscopy during temperature perturbations, we show that bacteria exhibit a highly conserved, gradual response to temperature upshifts with a time scale of ~1.5 doublings at the higher temperature, regardless of initial/final temperature or nutrient source. We find that this behavior is coupled to a temperature memory, which we rule out as being neither transcriptional, translational, nor membrane dependent. Instead, we demonstrate that an autocatalytic enzyme network incorporating temperature-sensitive Michaelis-Menten kinetics recapitulates all temperature-shift dynamics through metabolome rearrangement, which encodes a temperature memory and successfully predicts alterations in the upshift response observed under simple-sugar, low-nutrient conditions, and in fungi. This model also provides a mechanistic framework for both Arrhenius-dependent growth and the classical Monod Equation through temperature-dependent metabolite flux.

The Quantification of Bacterial Cell Size: Discrepancies Arise from Varied Quantification Methods

The robust regulation of the cell cycle is critical for the survival and proliferation of bacteria. To gain a comprehensive understanding of the mechanisms regulating the bacterial cell cycle, it is essential to accurately quantify cell-cycle-related parameters and to uncover quantitative relationships. In this paper, we demonstrate that the quantification of cell size parameters using microscopic images can be influenced by software and by the parameter settings used. Remarkably, even if the consistent use of a particular software and specific parameter settings is maintained throughout a study, the type of software and the parameter settings can significantly impact the validation of quantitative relationships, such as the constant-initiation-mass hypothesis. Given these inherent characteristics of microscopic image-based quantification methods, it is recommended that conclusions be cross-validated using independent methods, especially when the conclusions are associated with cell size parameters that were obtained under different conditions. To this end, we presented a flexible workflow for simultaneously quantifying multiple bacterial cell-cycle-related parameters using microscope-independent methods.

Mycobacterium tuberculosis grows linearly at the single-cell level with larger variability than model organisms

The ability of bacterial pathogens to regulate growth is crucial to control homeostasis, virulence, and drug response. Yet, we do not understand the growth and cell cycle behaviors of Mycobacterium tuberculosis (Mtb), a slow-growing pathogen, at the single-cell level. Here, we use time-lapse imaging and mathematical modeling to characterize these fundamental properties of Mtb. Whereas most organisms grow exponentially at the single-cell level, we find that Mtb exhibits a unique linear growth mode. Mtb growth characteristics are highly variable from cell-to-cell, notably in their growth speeds, cell cycle timing, and cell sizes. Together, our study demonstrates that growth behavior of Mtb diverges from what we have learned from model bacteria. Instead, Mtb generates a heterogeneous population while growing slowly and linearly. Our study provides a new level of detail into how Mtb grows and creates heterogeneity, and motivates more studies of growth behaviors in bacterial pathogens.

Super-exponential growth and stochastic size dynamics in rod-like bacteria

Proliferating bacterial cells exhibit stochastic growth and size dynamics, but the regulation of noise in bacterial growth and morphogenesis remains poorly understood. A quantitative understanding of morphogenetic noise control, and how it changes under different growth conditions, would provide better insights into cell-to-cell variability and intergenerational fluctuations in cell physiology. Using multigenerational growth and width data of single Escherichia coli and Caulobacter crescentus cells, we deduce the equations governing growth and size dynamics of rod-like bacterial cells. Interestingly, we find that both E. coli and C. crescentus cells deviate from exponential growth within the cell cycle. In particular, the exponential growth rate increases during the cell cycle irrespective of nutrient or temperature conditions. We propose a mechanistic model that explains the emergence of super-exponential growth from autocatalytic production of ribosomes coupled to the rate of cell elongation and surface area synthesis. Using this new model and statistical inference on large datasets, we construct the Langevin equations governing cell growth and size dynamics of E. coli cells in different nutrient conditions. The single-cell level model predicts how noise in intragenerational and intergenerational processes regulate variability in cell morphology and generation times, revealing quantitative strategies for cellular resource allocation and morphogenetic noise control in different growth conditions.

Mechanistic aspects of IPTG (isopropylthio-β-galactoside) transport across the cytoplasmic membrane of Escherichia coli-a rate limiting step in the induction of recombinant protein expression

Coupling transcription of a cloned gene to the lac operon with induction by isopropylthio-β-galactoside (IPTG) has been a favoured approach for recombinant protein expression using Escherichia coli as a heterologous host for more than six decades. Despite a wealth of experimental data gleaned over this period, a quantitative relationship between extracellular IPTG concentration and consequent levels of recombinant protein expression remains surprisingly elusive across a broad spectrum of experimental conditions. This is because gene expression under lac operon regulation is tightly correlated with intracellular IPTG concentration due to allosteric regulation of the lac repressor protein (lacY). An in-silico mathematical model established that uptake of IPTG across the cytoplasmic membrane of E. coli by simple diffusion was negligible. Conversely, lacY mediated active transport was a rapid process, taking only some seconds for internal and external IPTG concentrations to equalize. Optimizing kcat and KM parameters by targeted mutation of the galactoside binding site in lacY could be a future strategy to improve the performance of recombinant protein expression. For example, if kcat were reduced whilst KM was increased, active transport of IPTG across the cytoplasmic membrane would be reduced, thereby lessening the metabolic burden on the cell and expediating accumulation of recombinant protein. The computational model described herein is made freely available and is amenable to optimize recombinant protein expression in other heterologous hosts.

ONE-SENTENCE SUMMARY

A computational model made freely available to optimize recombinant protein expression in Escherichia coli other heterologous hosts.

Optimal control of bioproduction in the presence of population heterogeneity

Cell-to-cell variability, born of stochastic chemical kinetics, persists even in large isogenic populations. In the study of single-cell dynamics this is typically accounted for. However, on the population level this source of heterogeneity is often sidelined to avoid the inevitable complexity it introduces. The homogeneous models used instead are more tractable but risk disagreeing with their heterogeneous counterparts and may thus lead to severely suboptimal control of bioproduction. In this work, we introduce a comprehensive mathematical framework for solving bioproduction optimal control problems in the presence of heterogeneity. We study population-level models in which such heterogeneity is retained, and propose order-reduction approximation techniques. The reduced-order models take forms typical of homogeneous bioproduction models, making them a useful benchmark by which to study the importance of heterogeneity. Moreover, the derivation from the heterogeneous setting sheds light on parameter selection in ways a direct homogeneous outlook cannot, and reveals the source of approximation error. With view to optimally controlling bioproduction in microbial communities, we ask the question: when does optimising the reduced-order models produce strategies that work well in the presence of population heterogeneity? We show that, in some cases, homogeneous approximations provide remarkably accurate surrogate models. Nevertheless, we also demonstrate that this is not uniformly true: overlooking the heterogeneity can lead to significantly suboptimal control strategies. In these cases, the heterogeneous tools and perspective are crucial to optimise bioproduction.

Evolutionary scaling of maximum growth rate with organism size

Data from nearly 1000 species reveal the upper bound to rates of biomass production achievable by natural selection across the Tree of Life. For heterotrophs, maximum growth rates scale positively with organism size in bacteria but negatively in eukaryotes, whereas for phototrophs, the scaling is negligible for cyanobacteria and weakly negative for eukaryotes. These results have significant implications for understanding the bioenergetic consequences of the transition from prokaryotes to eukaryotes, and of the expansion of some groups of the latter into multicellularity. The magnitudes of the scaling coefficients for eukaryotes are significantly lower than expected under any proposed physical-constraint model. Supported by genomic, bioenergetic, and population-genetic data and theory, an alternative hypothesis for the observed negative scaling in eukaryotes postulates that growth-diminishing mutations with small effects passively accumulate with increasing organism size as a consequence of associated increases in the power of random genetic drift. In contrast, conditional on the structural and functional features of ribosomes, natural selection has been able to promote bacteria with the fastest possible growth rates, implying minimal conflicts with both bioenergetic constraints and random genetic drift. If this extension of the drift-barrier hypothesis is correct, the interpretations of comparative studies of biological traits that have traditionally ignored differences in population-genetic environments will require revisiting.

Dynamic scaling of stochastic thermodynamic observables for chemical reactions at and away from equilibrium

Physical kinetic roughening processes are well-known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available synthetically and occurring naturally? Here, we formulate an approach to the dynamic scaling of stochastic fluctuations in thermodynamic observables at and away from equilibrium. Both analytical expressions and numerical simulations confirm our dynamic scaling ansatz with associated scaling exponents, function, and law. A survey of common chemical mechanisms reveals classes that organize according to the molecularity of the reactions involved, the nature of the reaction vessel and external reservoirs, (non)equilibrium conditions, and the extent of autocatalysis in the reaction network. Varying experimental parameters, such as temperature, can cause coupled reactions capable of chemical feedback to transition between these classes. While path observables, such as the dynamical activity, have scaling exponents that are time-independent, the variance in the entropy production and flow can have time-dependent scaling exponents and self-averaging properties as a result of temporal correlations that emerge during thermodynamically irreversible processes. Altogether, these results establish dynamic universality classes in the nonequilibrium fluctuations of thermodynamic observables for well-mixed chemical reactions.

High-throughput determination of dry mass of single bacterial cells by ultrathin membrane resonators

How bacteria are able to maintain their size remains an open question. Techniques that can measure the biomass (dry mass) of single cells with high precision and high-throughput are demanded to elucidate this question. Here, we present a technological approach that combines the transport, guiding and focusing of individual bacteria from solution to the surface of an ultrathin silicon nitride membrane resonator in vacuum. The resonance frequencies of the membrane undergo abrupt variations at the instants where single cells land on the membrane surface. The resonator design displays a quasi-symmetric rectangular shape with an extraordinary capture area of 0.14 mm², while maintaining a high mass resolution of 0.7 fg (1 fg = 10⁻¹⁵g) to precisely resolve the dry mass of single cells. The small rectangularity of the membrane provides unprecedented frequency density of vibration modes that enables to retrieve the mass of individual cells with high accuracy by specially developed inverse problem theory. We apply this approach for profiling the dry mass distribution in Staphylococcus epidermidis and Escherichia coli cells. The technique allows the determination of the dry mass of single bacterial cells with an accuracy of about 1% at an unparalleled throughput of 20 cells/min. Finally, we revisit Koch & Schaechter model developed during 60 s to assess the intrinsic sources of stochasticity that originate cell size heterogeneity in steady-state populations. The results reveal the importance of mass resolution to correctly describe these mechanisms.

A technological approach combines transport, guiding and focusing of individual bacteria from solution to ultrathin membrane resonators for dry mass determination of single cells with accuracy within 1% and throughput of 20 cells/min.

Nutrient availability as an arbiter of cell size

Pioneering work carried out over 60 years ago discovered that bacterial cell size is proportional to the growth rate set by nutrient availability. This relationship is traditionally referred to as the 'growth law'. Subsequent studies revealed the growth law to hold across all orders of life, a remarkable degree of conservation. However, recent work suggests the relationship between growth rate, nutrients, and cell size is far more complicated and less deterministic than originally thought. Focusing on bacteria and yeast, here we review efforts to understand the molecular mechanisms underlying the relationship between growth rate and cell size.

Feedback linking cell envelope stiffness, curvature, and synthesis enables robust rod-shaped bacterial growth

Bacterial growth is remarkably robust to environmental fluctuations, yet the mechanisms of growth-rate homeostasis are poorly understood. Here, we combine theory and experiment to infer mechanisms by which Escherichia coli adapts its growth rate in response to changes in osmolarity, a fundamental physicochemical property of the environment. The central tenet of our theoretical model is that cell-envelope expansion is only sensitive to local information, such as enzyme concentrations, cell-envelope curvature, and mechanical strain in the envelope. We constrained this model with quantitative measurements of the dynamics of E. coli elongation rate and cell width after hyperosmotic shock. Our analysis demonstrated that adaptive cell-envelope softening is a key process underlying growth-rate homeostasis. Furthermore, our model correctly predicted that softening does not occur above a critical hyperosmotic shock magnitude and precisely recapitulated the elongation-rate dynamics in response to shocks with magnitude larger than this threshold. Finally, we found that, to coordinately achieve growth-rate and cell-width homeostasis, cells employ direct feedback between cell-envelope curvature and envelope expansion. In sum, our analysis points to cellular mechanisms of bacterial growth-rate homeostasis and provides a practical theoretical framework for understanding this process.

Selection in a growing colony biases results of mutation accumulation experiments

Mutations provide the raw material for natural selection to act. Therefore, understanding the variety and relative frequency of different type of mutations is critical to understanding the nature of genetic diversity in a population. Mutation accumulation (MA) experiments have been used in this context to estimate parameters defining mutation rates, distribution of fitness effects (DFE), and spectrum of mutations. MA experiments can be performed with different effective population sizes. In MA experiments with bacteria, a single founder is grown to a size of a colony (~ 108). It is assumed that natural selection plays a minimal role in dictating the dynamics of colony growth. In this work, we simulate colony growth via a mathematical model, and use our model to mimic an MA experiment. We demonstrate that selection ensures that, in an MA experiment, fraction of all mutations that are beneficial is over-represented by a factor of almost two, and that the distribution of fitness effects of beneficial and deleterious mutations are inaccurately captured in an MA experiment. Given this, the estimate of mutation rates from MA experiments is non-trivial. We then perform an MA experiment with 160 lines of E. coli, and show that due to the effect of selection in a growing colony, the size and sector of a colony from which the experiment is propagated impacts the results. Overall, we demonstrate that the results of MA experiments need to be revisited taking into account the action of selection in a growing colony.

A Ratiometric Organic Fluorescent Nanogel Thermometer for Highly Sensitive Temperature Sensing

Sensing temperature in biological systems is of great importance, as it is constructive to understanding various physiological and pathological processes. However, the realization of highly sensitive temperature sensing with organic fluorescent nanothermometers remains challenging. In this study, we report a ratiometric fluorescent nanogel thermometer and study its application in the determination of bactericidal temperature. The nanogel is composed of a polarity-sensitive aggregation-induced emission luminogen with dual emissions, a thermoresponsive polymer with a phase transition function, and an ionic surface with net positive charges. During temperature-induced phase transition, the nanogel exhibits a reversible and sensitive spectral change between a red-emissive state and a blue-emissive state by responding to the hydrophilic-to-hydrophobic change in the local environment. The correlation between the emission intensity ratio of the two states and the external temperature is delicately established, and the maximum relative thermal sensitivities of the optimal nanogel are determined to be 128.42 and 68.39% °C⁻¹ in water and a simulated physiological environment, respectively. The nanogel is further applied to indicate the bactericidal temperature in both visual and ratiometric ways, holding great promise in the rapid prediction of photothermal antibacterial effects and other temperature-related biological events.

Time-averaging and nonergodicity of reset geometric Brownian motion with drift

How do near-bankruptcy events in the past affect the dynamics of stock-market prices in the future? Specifically, what are the long-time properties of a time-local exponential growth of stock-market prices under the influence of stochastically occurring economic crashes? Here, we derive the ensemble- and time-averaged properties of the respective "economic" or geometric Brownian motion (GBM) with a nonzero drift exposed to a Poissonian constant-rate price-restarting process of "resetting." We examine-based both on thorough analytical calculations and on findings from systematic stochastic computer simulations-the general situation of reset GBM with a nonzero [positive] drift and for all special cases emerging for varying parameters of drift, volatility, and reset rate in the model. We derive and summarize all short- and long-time dependencies for the mean-squared displacement (MSD), the variance, and the mean time-averaged MSD (TAMSD) of the process of Poisson-reset GBM under the conditions of both rare and frequent resetting. We consider three main regions of model parameters and categorize the crossovers between different functional behaviors of the statistical quantifiers of this process. The analytical relations are fully supported by the results of computer simulations. In particular, we obtain that Poisson-reset GBM is a nonergodic stochastic process, with generally MSD(Δ)≠TAMSD(Δ) and Variance(Δ)≠TAMSD(Δ) at short lag times Δ and for long trajectory lengths T. We investigate the behavior of the ergodicity-breaking parameter in each of the three regions of parameters and examine its dependence on the rate of reset at Δ/T≪1. Applications of these theoretical results to the analysis of prices of reset-containing options are pertinent.

Influence of homeostatic mechanisms of bacterial growth and division on structural properties of microcolonies: A computer simulation study

Bacterial growth and division generally occur by the process known as binary fission, in which the cells grow polarly until they divide into two daughter cells. Although this process is affected by factors that introduce stochastic variability in both growth rate and daughter cell length, the fact is that the size distribution in growing bacteria remains stable over time. This suggests the existence of homeostatic mechanisms that contribute to maintaining a stable size distribution. Those known as sizer and adder stand out among these mechanisms whose relevance is not entirely determined. In this work, computer simulations using an agent-based model are used to study the effect of these homeostatic mechanisms on the geometrical and structural properties of the developing microcolonies, focusing on the early stages of its development. Also, we examine the effect of linear or exponential dependence with the time of cellular growth on these properties. From our study, we deduce that these mechanisms do not have a noticeable impact on the properties studied, which could be due to the importance that stochastic factors play in the cell division and growth process. In addition, we discuss how competition between cell growth and diffusion is a key aspect in explaining the structure and geometry of developing bacterial microcolonies. The results of the study will help to clarify which processes and parameters should be considered relevant when designing simulation models.

Nanothermometer with Temperature Induced Reversible Emission for Evaluation of Intracellular Thermal Dynamics

Temperature dynamics reflect the physiological state of cells, and accurate measurement of intracellular temperature helps to understand the biological processes. Herein, we report a novel nanothermometer by conjugating a fluorescent probe 3-ethyl-2-[4-(1,2,2-triphenylvinyl)styryl]benzothiazol-3-ium iodide (TPEBT) with a thermoresponsive polymer poly(N-isopropylacrylamide-co-tetrabutylphosphonium styrenesulfonate) [P(NIPAM-co-TPSS)]. The derived nanoprobe TPEBT-P(NIPAM-co-TPSS) self-assembles into micelles with TPEBT as hydrophobic core and PNIPAM as hydrophilic shell. It exhibits aggregation-induced emission (AIE) at λ_ex/λ_em = 420/640 nm in aqueous medium with a quantum yield of Φ_F 11.9%. The rise in temperature transforms PNIPAM chains from linear to compact spheres to serve as the core of micelles, and meanwhile converts TPEBT from the state of aggregation to dispersion and redistributes in the micellar shell. Temperature-driven phase transition of P(NIPAM-co-TPSS) mediates the reversible aggregation and disaggregation of TPEBT and endows the nanothermometer with temperature-dependent AIE features and favorable sensitivity for temperature sensing in 32-40 °C. TPEBT-P(NIPAM-co-TPSS) is taken up by HeLa cells to distribute mainly in lysosomes. It enables quantitative visualization of in situ thermal dynamics in response to stimuli from carbonyl cyanide 4-(trifluoromethoxy)phenylhydrazone, oligomycin, genipin, and lipopolysaccharide. The real-time monitoring of photothermal-induced intracellular temperature variation is further conducted.

Methods to monitor bacterial growth and replicative rates at the single-cell level

The heterogeneity of bacterial growth and replicative rates within a population was proposed a century ago notably to explain the presence of bacterial persisters. The term "growth rate" at the single-cell level corresponds to the increase in size or mass of an individual bacterium while the "replicative rate" refers to its division capacity within a defined temporality. After a decades long hiatus, recent technical innovative approaches allow population growth and replicative rates heterogeneity monitoring at the single-cell level resuming in earnest. Among these techniques, the oldest and widely used is time-lapse microscopy, most recently combined with microfluidics. We also discuss recent fluorescence dilution methods informing only on replicative rates and best suited. Some new elegant single cell methods so far only sporadically used such as buoyant mass measurement and stable isotope probing have emerged. Overall, such tools are widely used to investigate and compare the growth and replicative rates of bacteria displaying drug-persistent behaviors to that of bacteria growing in specific ecological niches or collected from patients. In this review, we describe the current methods available, discussing both the type of queries these have been used to answer and the specific strengths and limitations of each method.

The Effects of Temperature on Cellular Physiology

Temperature impacts biological systems across all length and timescales. Cells and the enzymes that comprise them respond to temperature fluctuations on short timescales, and temperature can affect protein folding, the molecular composition of cells, and volume expansion. Entire ecosystems exhibit temperature-dependent behaviors, and global warming threatens to disrupt thermal homeostasis in microbes that are important for human and planetary health. Intriguingly, the growth rate of most species follows the Arrhenius law of equilibrium thermodynamics, with an activation energy similar to that of individual enzymes but with maximal growth rates and over temperature ranges that are species specific. In this review, we discuss how the temperature dependence of critical cellular processes, such as the central dogma and membrane fluidity, contributes to the temperature dependence of growth. We conclude with a discussion of adaptation to temperature shifts and the effects of temperature on evolution and on the properties of microbial ecosystems.

The possible modes of microbial reproduction are fundamentally restricted by distribution of mass between parent and offspring

Cells and simple cell colonies reproduce by fragmenting their bodies into pieces. Produced newborns need to grow before they can reproduce again. How big a cell or a cell colony should grow? How many offspring should be produced? Should they be of equal size or diverse? We show that the simple fact that the immediate mass of offspring cannot exceed the mass of parents restricts possible answers to these questions. For example, our theory states that, when mass is conserved in the course of fragmentation, the evolutionarily optimal reproduction mode is fragmentation into exactly two, typically equal, parts. Our theory also shows conditions which promote evolution of asymmetric division or fragmentation into multiple pieces.

Multiple modes of asexual reproduction are observed among microbial organisms in natural populations. These modes are not only subject to evolution, but may drive evolutionary competition directly through their impact on population growth rates. The most prominent transition between two such modes is the one from unicellularity to multicellularity. We present a model of the evolution of reproduction modes, where a parent organism fragments into smaller parts. While the size of an organism at fragmentation, the number of offspring, and their sizes may vary a lot, the combined mass of fragments is limited by the mass of the parent organism. We found that mass conservation can fundamentally limit the number of possible reproduction modes. This has important direct implications for microbial life: For unicellular species, the interplay between cell shape and kinetics of the cell growth implies that the largest and the smallest possible cells should be rod shaped rather than spherical. For primitive multicellular species, these considerations can explain why rosette cell colonies evolved a mechanistically complex binary split reproduction. Finally, we show that the loss of organism mass during sporulation can explain the macroscopic sizes of the formally unicellular microorganism Myxomycetes plasmodium. Our findings demonstrate that a number of seemingly unconnected phenomena observed in unrelated species may be different manifestations of the same underlying process.

Characterizing non-exponential growth and bimodal cell size distributions in fission yeast: An analytical approach

Unlike many single-celled organisms, the growth of fission yeast cells within a cell cycle is not exponential. It is rather characterized by three distinct phases (elongation, septation, and reshaping), each with a different growth rate. Experiments also showed that the distribution of cell size in a lineage can be bimodal, unlike the unimodal distributions measured for the bacterium Escherichia coli. Here we construct a detailed stochastic model of cell size dynamics in fission yeast. The theory leads to analytic expressions for the cell size and the birth size distributions, and explains the origin of bimodality seen in experiments. In particular, our theory shows that the left peak in the bimodal distribution is associated with cells in the elongation phase, while the right peak is due to cells in the septation and reshaping phases. We show that the size control strategy, the variability in the added size during a cell cycle, and the fraction of time spent in each of the three cell growth phases have a strong bearing on the shape of the cell size distribution. Furthermore, we infer all the parameters of our model by matching the theoretical cell size and birth size distributions to those from experimental single-cell time-course data for seven different growth conditions. Our method provides a much more accurate means of determining the size control strategy (timer, adder or sizer) than the standard method based on the slope of the best linear fit between the birth and division sizes. We also show that the variability in added size and the strength of size control in fission yeast depend weakly on the temperature but strongly on the culture medium. More importantly, we find that stronger size homeostasis and larger added size variability are required for fission yeast to adapt to unfavorable environmental conditions.

Advances in microscopy enable us to follow single cells over long timescales from which we can understand how their size varies with time and the nature of innate strategies developed to control cell size. These data show that in many cell types, growth is exponential and the distribution of cell size has one peak, namely there is a single characteristic cell size. However data for fission yeast show remarkable differences: growth is non-exponential and the distribution of cell sizes has two peaks, corresponding to different growth phases. Here we construct a detailed stochastic mathematical model of this organism; by solving the model analytically, we show that it is able to predict the two peaked distributions of cell size seen in data and provide an explanation for each peak in terms of various growth phases of the single-celled organism. Furthermore, by fitting the model to the data, we infer values for the rates of all microscopic processes in our model. This method is shown to provide a much more reliable inference than current methods and shed light on how the strategy used by fission yeast cells to control their size varies with external conditions.

Membrane rigidity regulates E. coli proliferation rates

Combining single cell experiments, population dynamics and theoretical methods of membrane mechanics, we put forward that the rate of cell proliferation in E. coli colonies can be regulated by modifiers of the mechanical properties of the bacterial membrane. Bacterial proliferation was modelled as mediated by cell division through a membrane constriction divisome based on FtsZ, a mechanically competent protein at elastic interaction against membrane rigidity. Using membrane fluctuation spectroscopy in the single cells, we revealed either membrane stiffening when considering hydrophobic long chain fatty substances, or membrane softening if short-chained hydrophilic molecules are used. Membrane stiffeners caused hindered growth under normal division in the microbial cultures, as expected for membrane rigidification. Membrane softeners, however, altered regular cell division causing persistent microbes that abnormally grow as long filamentous cells proliferating apparently faster. We invoke the concept of effective growth rate under the assumption of a heterogeneous population structure composed by distinguishable individuals with different FtsZ-content leading the possible forms of cell proliferation, from regular division in two normal daughters to continuous growing filamentation and budding. The results settle altogether into a master plot that captures a universal scaling between membrane rigidity and the divisional instability mediated by FtsZ at the onset of membrane constriction.

Distinguishing different modes of growth using single-cell data

Collection of high-throughput data has become prevalent in biology. Large datasets allow the use of statistical constructs such as binning and linear regression to quantify relationships between variables and hypothesize underlying biological mechanisms based on it. We discuss several such examples in relation to single-cell data and cellular growth. In particular, we show instances where what appears to be ordinary use of these statistical methods leads to incorrect conclusions such as growth being non-exponential as opposed to exponential and vice versa. We propose that the data analysis and its interpretation should be done in the context of a generative model, if possible. In this way, the statistical methods can be validated either analytically or against synthetic data generated via the use of the model, leading to a consistent method for inferring biological mechanisms from data. On applying the validated methods of data analysis to infer cellular growth on our experimental data, we find the growth of length in E. coli to be non-exponential. Our analysis shows that in the later stages of the cell cycle the growth rate is faster than exponential.

Quantitative Examination of Five Stochastic Cell-Cycle and Cell-Size Control Models for Escherichia coli and Bacillus subtilis

We examine five quantitative models of the cell-cycle and cell-size control in Escherichia coli and Bacillus subtilis that have been proposed over the last decade to explain single-cell experimental data generated with high-throughput methods. After presenting the statistical properties of these models, we test their predictions against experimental data. Based on simple calculations of the defining correlations in each model, we first dismiss the stochastic Helmstetter-Cooper model and the Initiation Adder model, and show that both the Replication Double Adder (RDA) and the Independent Double Adder (IDA) model are more consistent with the data than the other models. We then apply a recently proposed statistical analysis method and obtain that the IDA model is the most likely model of the cell cycle. By showing that the RDA model is fundamentally inconsistent with size convergence by the adder principle, we conclude that the IDA model is most consistent with the data and the biology of bacterial cell-cycle and cell-size control. Mechanistically, the Independent Adder Model is equivalent to two biological principles: (i) balanced biosynthesis of the cell-cycle proteins, and (ii) their accumulation to a respective threshold number to trigger initiation and division.

Continuous rate modeling of bacterial stochastic size dynamics

Bacterial division is an inherently stochastic process with effects on fluctuations of protein concentration and phenotype variability. Current modeling tools for the stochastic short-term cell-size dynamics are scarce and mainly phenomenological. Here we present a general theoretical approach based on the Chapman-Kolmogorov equation incorporating continuous growth and division events as jump processes. This approach allows us to include different division strategies, noisy growth, and noisy cell splitting. Considering bacteria synchronized from their last division, we predict oscillations in both the central moments of the size distribution and its autocorrelation function. These oscillations, barely discussed in past studies, can arise as a consequence of the discrete time displacement invariance of the system with a period of one doubling time, and they do not disappear when including stochasticity on either division times or size heterogeneity on the starting population but only after inclusion of noise in either growth rate or septum position. This result illustrates the usefulness of having a solid mathematical description that explicitly incorporates the inherent stochasticity in various biological processes, both to understand the process in detail and to evaluate the effect of various sources of variability when creating simplified descriptions.

Analytics and visualization tools to characterize single-cell stochasticity using bacterial single-cell movie cytometry data

Background

Time-lapse microscopy live-cell imaging is essential for studying the evolution of bacterial communities at single-cell resolution. It allows capturing detailed information about the morphology, gene expression, and spatial characteristics of individual cells at every time instance of the imaging experiment. The image analysis of bacterial "single-cell movies" (videos) generates big data in the form of multidimensional time series of measured bacterial attributes. If properly analyzed, these datasets can help us decipher the bacterial communities' growth dynamics and identify the sources and potential functional role of intra- and inter-subpopulation heterogeneity. Recent research has highlighted the importance of investigating the role of biological "noise" in gene regulation, cell growth, cell division, etc. Single-cell analytics of complex single-cell movie datasets, capturing the interaction of multiple micro-colonies with thousands of cells, can shed light on essential phenomena for human health, such as the competition of pathogens and benign microbiome cells, the emergence of dormant cells (“persisters”), the formation of biofilms under different stress conditions, etc. However, highly accurate and automated bacterial bioimage analysis and single-cell analytics methods remain elusive, even though they are required before we can routinely exploit the plethora of data that single-cell movies generate.

Results

We present visualization and single-cell analytics using R (ViSCAR), a set of methods and corresponding functions, to visually explore and correlate single-cell attributes generated from the image processing of complex bacterial single-cell movies. They can be used to model and visualize the spatiotemporal evolution of attributes at different levels of the microbial community organization (i.e., cell population, colony, generation, etc.), to discover possible epigenetic information transfer across cell generations, infer mathematical and statistical models describing various stochastic phenomena (e.g., cell growth, cell division), and even identify and auto-correct errors introduced unavoidably during the bioimage analysis of a dense movie with thousands of overcrowded cells in the microscope's field of view.

Conclusions

ViSCAR empowers researchers to capture and characterize the stochasticity, uncover the mechanisms leading to cellular phenotypes of interest, and decipher a large heterogeneous microbial communities' dynamic behavior. ViSCAR source code is available from GitLab at https://gitlab.com/ManolakosLab/viscar.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04409-9.

Single-cell growth inference of Corynebacterium glutamicum reveals asymptotically linear growth

Regulation of growth and cell size is crucial for the optimization of bacterial cellular function. So far, single bacterial cells have been found to grow predominantly exponentially, which implies the need for tight regulation to maintain cell size homeostasis. Here, we characterize the growth behavior of the apically growing bacterium Corynebacterium glutamicum using a novel broadly applicable inference method for single-cell growth dynamics. Using this approach, we find that C. glutamicum exhibits asymptotically linear single-cell growth. To explain this growth mode, we model elongation as being rate-limited by the apical growth mechanism. Our model accurately reproduces the inferred cell growth dynamics and is validated with elongation measurements on a transglycosylase deficient ΔrodA mutant. Finally, with simulations we show that the distribution of cell lengths is narrower for linear than exponential growth, suggesting that this asymptotically linear growth mode can act as a substitute for tight division length and division symmetry regulation.

Cell Growth Model with Stochastic Gene Expression Helps Understand the Growth Advantage of Metabolic Exchange and Auxotrophy

During cooperative growth, microbes often experience higher fitness by sharing resources via metabolite exchange. How competitive species evolve to cooperate is, however, not known. Moreover, existing models (based on optimization of steady-state resources or fluxes) are often unable to explain the growth advantage for the cooperating species, even for simple reciprocally cross-feeding auxotrophic pairs. We present here an abstract model of cell growth that considers the stochastic burst-like gene expression of biosynthetic pathways of limiting biomass precursor metabolites and directly connect the amount of metabolite produced to cell growth and division, using a "metabolic sizer/adder" rule. Our model recapitulates Monod's law and yields the experimentally observed right-skewed long-tailed distribution of cell doubling times. The model further predicts the growth effect of secretion and uptake of metabolites by linking it to changes in the internal metabolite levels. The model also explains why auxotrophs may grow faster when supplied with the metabolite they cannot produce and why two reciprocally cross-feeding auxotrophs can grow faster than prototrophs. Overall, our framework allows us to predict the growth effect of metabolic interactions in independent microbes and microbial communities, setting up the stage to study the evolution of these interactions. IMPORTANCE Cooperative behaviors are highly prevalent in the wild, but their evolution is not understood. Metabolic flux models can demonstrate the viability of metabolic exchange as cooperative interactions, but steady-state growth models cannot explain why cooperators grow faster. We present a stochastic model that connects growth to the cell's internal metabolite levels and quantifies the growth effect of metabolite exchange and auxotrophy. We show that a reduction in gene expression noise can explain why cells that import metabolites or become auxotrophs can grow faster and why reciprocal cross-feeding of metabolites between complementary auxotrophs allows them to grow faster. Furthermore, our framework can simulate the growth of interacting cells, which will enable us to understand the possible trajectories of the evolution of cooperation in silico.

Towards a synthetic cell cycle

Recent developments in synthetic biology may bring the bottom-up generation of a synthetic cell within reach. A key feature of a living synthetic cell is a functional cell cycle, in which DNA replication and segregation as well as cell growth and division are well integrated. Here, we describe different approaches to recreate these processes in a synthetic cell, based on natural systems and/or synthetic alternatives. Although some individual machineries have recently been established, their integration and control in a synthetic cell cycle remain to be addressed. In this Perspective, we discuss potential paths towards an integrated synthetic cell cycle.

A Sensitive and Reliable Organic Fluorescent Nanothermometer for Noninvasive Temperature Sensing

Sensing temperature at the subcellular level is of great importance for the understanding of miscellaneous biological processes. However, the development of sensitive and reliable organic fluorescent nanothermometers remains challenging. In this study, we report the fabrication of a novel organic fluorescent nanothermometer and study its application in temperature sensing. First of all, we synthesize a dual-responsive organic luminogen that can respond to the molecular state of aggregation and environmental polarity. Next, natural saturated fatty acids with sharp melting points as well as reversible and rapid phase transition are employed as the encapsulation matrix to correlate external heat information with the fluorescence properties of the luminogen. To apply the composite materials for biological application, we formulate them into colloidally dispersed nanoparticles by a technique that combines in situ surface polymerization and nanoprecipitation. As anticipated, the resultant zwitterionic nanothermometer exhibits sensitive, reversible, reliable, and multiparametric responses to temperature variation within a narrow range around the physiological temperature (i.e., 37 °C). Taking spectral position, fluorescence intensity, and fluorescence lifetime as the correlation parameters, the maximum relative thermal sensitivities are determined to be 2.15% °C^-1, 17.06% °C^-1, and 17.72% °C^-1, respectively, which are much higher than most fluorescent nanothermometers. Furthermore, we achieve the multimodal temperature sensing of bacterial biofilms using these three complementary fluorescence parameters. Besides, we also fabricate a cationic form of the nanothermometer to facilitate efficient cellular uptake, holding great promise for studying thermal behaviors in biological systems.