Analysis of a detailed multi-stage model of stochastic gene expression using queueing theory and model reduction.

We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA into protein. The processes in sub-cellular compartments are described by an arbitrary number of processing stages, thus accounting for a significantly finer molecular description of gene expression than conventional models such as the telegraph, two-stage and three-stage models of gene expression. We use two distinct tools, queueing theory and model reduction using the slow-scale linear-noise approximation, to derive exact or approximate analytic expressions for the moments or distributions of nuclear mRNA, cytoplasmic mRNA and protein fluctuations, as well as lower bounds for their Fano factors in steady-state conditions. We use these to study the phase diagram of the stochastic model; in particular we derive parametric conditions determining three types of transitions in the properties of mRNA fluctuations: from sub-Poissonian to super-Poissonian noise, from high noise in the nucleus to high noise in the cytoplasm, and from a monotonic increase to a monotonic decrease of the Fano factor with the number of processing stages. In contrast, protein fluctuations are always super-Poissonian and show weak dependence on the number of mRNA processing stages. Our results delineate the region of parameter space where conventional models give qualitatively incorrect results and provide insight into how the number of processing stages, e.g. the number of rate-limiting steps in initiation, splicing and mRNA degradation, shape stochastic gene expression by modulation of molecular memory.

Mechanisms of cell size regulation in slow-growing Escherichia coli cells: discriminating models beyond the adder.

Under ideal conditions, Escherichia coli cells divide after adding a fixed cell size, a strategy known as the adder. This concept applies to various microbes and is often explained as the division that occurs after a certain number of stages, associated with the accumulation of precursor proteins at a rate proportional to cell size. However, under poor media conditions, E. coli cells exhibit a different size regulation. They are smaller and follow a sizer-like division strategy where the added size is inversely proportional to the size at birth. We explore three potential causes for this deviation: degradation of the precursor protein and two models where the propensity for accumulation depends on the cell size: a nonlinear accumulation rate, and accumulation starting at a threshold size termed the commitment size. These models fit the mean trends but predict different distributions given the birth size. To quantify the precision of the models to explain the data, we used the Akaike information criterion and compared them to open datasets of slow-growing E. coli cells in different media. We found that none of the models alone can consistently explain the data. However, the degradation model better explains the division strategy when cells are larger, whereas size-related models (power-law and commitment size) account for smaller cells. Our methodology proposes a data-based method in which different mechanisms can be tested systematically.

Unraveling IFN-I response dynamics and TNF crosstalk in the pathophysiology of systemic lupus erythematosus.

Introduction: The innate immune system serves the crucial first line of defense against a wide variety of potential threats, during which the production of pro-inflammatory cytokines IFN-I and TNFα are key. This astonishing power to fight invaders, however, comes at the cost of risking IFN-I-related pathologies, such as observed during autoimmune diseases, during which IFN-I and TNFα response dynamics are dysregulated. Therefore, these response dynamics must be tightly regulated, and precisely matched with the potential threat. This regulation is currently far from understood. Methods: Using droplet-based microfluidics and ODE modeling, we studied the fundamentals of single-cell decision-making upon TLR signaling in human primary immune cells (n = 23). Next, using biologicals used for treating autoimmune diseases [i.e., anti-TNFα, and JAK inhibitors], we unraveled the crosstalk between IFN-I and TNFα signaling dynamics. Finally, we studied primary immune cells isolated from SLE patients (n = 8) to provide insights into SLE pathophysiology. Results: single-cell IFN-I and TNFα response dynamics display remarkable differences, yet both being highly heterogeneous. Blocking TNFα signaling increases the percentage of IFN-I-producing cells, while blocking IFN-I signaling decreases the percentage of TNFα-producing cells. Single-cell decision-making in SLE patients is dysregulated, pointing towards a dysregulated crosstalk between IFN-I and TNFα response dynamics. Discussion: We provide a solid droplet-based microfluidic platform to study inherent immune secretory behaviors, substantiated by ODE modeling, which can challenge the conceptualization within and between different immune signaling systems. These insights will build towards an improved fundamental understanding on single-cell decision-making in health and disease.

Fundamental limits of parasitoid-driven host population suppression: Implications for biological control.

Parasitoid wasps are increasingly being used to control insect pest populations, where the pest is the host species parasitized by the wasp. Here we use the discrete-time formalism of the Nicholson-Bailey model to investigate a fundamental question-are there limits to parasitoid-driven suppression of the host population density while still ensuring a stable coexistence of both species? Our model formulation imposes an intrinsic self-limitation in the host's growth resulting in a carrying capacity in the absence of the parasitoid. Different versions of the model are considered with parasitism occurring at a developmental stage that is before, during, or after the growth-limiting stage. For example, the host's growth limitation may occur at its larval stage due to intraspecific competition, while the wasps attack either the host egg, larval or pupal stage. For slow-growing hosts, models with parasitism occurring at different life stages are identical in terms of their host suppression dynamics but have contrasting differences for fast-growing hosts. In the latter case, our analysis reveals that wasp parasitism occurring after host growth limitation yields the lowest pest population density conditioned on stable host-parasitoid coexistence. For ecologically relevant parameter regimes we estimate this host suppression to be roughly 10-20% of the parasitoid-free carrying capacity. We further expand the models to consider a fraction of hosts protected from parasitism (i.e., a host refuge). Our results show that for a given host reproduction rate there exists a critical value of protected host fraction beyond which, the system dynamics are stable even for high levels of parasitism that drive the host to arbitrary low population densities. In summary, our systematic analysis sheds key insights into the combined effects of density-dependence in host growth and parasitism refuge in stabilizing the host-parasitoid population dynamics with important implications for biological control.

Development of adaptive anoikis resistance promotes metastasis that can be overcome by CDK8/19 Mediator kinase inhibition.

Anoikis resistance or evasion of cell death triggered by cell detachment into suspension is a hallmark of cancer that is concurrent with cell survival and metastasis. The effects of frequent matrix detachment encounters on the development of anoikis resistance in cancer remains poorly defined. Here we show using a panel of ovarian cancer models, that repeated exposure to suspension stress in vitro followed by attached recovery growth leads to the development of anoikis resistance paralleling in vivo development of anoikis resistance in ovarian cancer ascites. This resistance is concurrent with enhanced invasion, chemoresistance and the ability of anoikis adapted cells to metastasize to distant sites. Adapted anoikis resistant cells show a heightened dependency on oxidative phosphorylation and can also evade immune surveillance. We find that such acquired anoikis resistance is not genetic, as acquired resistance persists for a finite duration in the absence of suspension stress. Transcriptional reprogramming is however essential to this process, as acquisition of adaptive anoikis resistance in vitro and in vivo is exquisitely sensitive to inhibition of CDK8/19 Mediator kinase, a pleiotropic regulator of transcriptional reprogramming. Our data demonstrate that growth after recovery from repeated exposure to suspension stress is a direct contributor to metastasis and that inhibition of CDK8/19 Mediator kinase during such adaptation provides a therapeutic opportunity to prevent both local and distant metastasis in cancer.

A heritable iron memory enables decision-making in Escherichia coli.

The importance of memory in bacterial decision-making is relatively unexplored. We show here that a prior experience of swarming is remembered when Escherichia coli encounters a new surface, improving its future swarming efficiency. We conducted >10,000 single-cell swarm assays to discover that cells store memory in the form of cellular iron levels. This "iron" memory preexists in planktonic cells, but the act of swarming reinforces it. A cell with low iron initiates swarming early and is a better swarmer, while the opposite is true for a cell with high iron. The swarming potential of a mother cell, which tracks with its iron memory, is passed down to its fourth-generation daughter cells. This memory is naturally lost by the seventh generation, but artificially manipulating iron levels allows it to persist much longer. A mathematical model with a time-delay component faithfully recreates the observed dynamic interconversions between different swarming potentials. We demonstrate that cellular iron levels also track with biofilm formation and antibiotic tolerance, suggesting that iron memory may impact other physiologies.

Disrupting cellular memory to overcome drug resistance.

Gene expression states persist for varying lengths of time at the single-cell level, a phenomenon known as gene expression memory. When cells switch states, losing memory of their prior state, this transition can occur in the absence of genetic changes. However, we lack robust methods to find regulators of memory or track state switching. Here, we develop a lineage tracing-based technique to quantify memory and identify cells that switch states. Applied to melanoma cells without therapy, we quantify long-lived fluctuations in gene expression that are predictive of later resistance to targeted therapy. We also identify the PI3K and TGF-ß pathways as state switching modulators. We propose a pretreatment model, first applying a PI3K inhibitor to modulate gene expression states, then applying targeted therapy, which leads to less resistance than targeted therapy alone. Together, we present a method for finding modulators of gene expression memory and their associated cell fates.

A cell-based model for size control in the multiple fission alga Chlamydomonas reinhardtii.

Understanding how population-size homeostasis emerges from stochastic individual cell behaviors remains a challenge in biology.1,2,3,4,5,6,7 The unicellular green alga Chlamydomonas reinhardtii (Chlamydomonas) proliferates using a multiple fission cell cycle, where a prolonged G1 phase is followed by n rounds of alternating division cycles (S/M) to produce 2n daughters. A "Commitment" sizer in mid-G1 phase ensures sufficient cell growth before completing the cell cycle. A mitotic sizer couples mother-cell size to division number (n) such that daughter size distributions are uniform regardless of mother size distributions. Although daughter size distributions were highly robust to altered growth conditions, ∼40% of daughter cells fell outside of the 2-fold range expected from a "perfect" multiple fission sizer.7,8 A simple intuitive power law model with stochastic noise failed to reproduce individual division behaviors of tracked single cells. Through additional iterative modeling, we identified an alternative modified threshold (MT) model, where cells need to cross a threshold greater than 2-fold their median starting size to become division-competent (i.e., Committed), after which their behaviors followed a power law model. The Commitment versus mitotic size threshold uncoupling in the MT model was likely a key pre-adaptation in the evolution of volvocine algal multicellularity. A similar experimental approach was used in size mutants mat3/rbr and dp1 that are, respectively, missing repressor or activator subunits of the retinoblastoma tumor suppressor complex (RBC). Both mutants showed altered relationships between Commitment and mitotic sizer, suggesting that RBC functions to decouple the two sizers.

Characterizing the role of autaptic feedback in enhancing precision of neuronal firing times.

In a chemical synapse, information flow occurs via the release of neurotransmitters from a presynaptic neuron that triggers an Action potential (AP) in the postsynaptic neuron. At its core, this occurs via the postsynaptic membrane potential integrating neurotransmitter-induced synaptic currents, and AP generation occurs when potential reaches a critical threshold. This manuscript investigates feedback implementation via an autapse, where the axon from the postsynaptic neuron forms an inhibitory synapse onto itself. Using a stochastic model of neuronal synaptic transmission, we formulate AP generation as a first-passage time problem and derive expressions for both the mean and noise of AP-firing times. Our analytical results supported by stochastic simulations identify parameter regimes where autaptic feedback transmission enhances the precision of AP firing times consistent with experimental data. These noise attenuating regimes are intuitively based on two orthogonal mechanisms - either expanding the time window to integrate noisy upstream signals; or by linearizing the mean voltage increase over time. Interestingly, we find regimes for noise amplification that specifically occur when the inhibitory synapse has a low probability of release for synaptic vesicles. In summary, this work explores feedback modulation of the stochastic dynamics of autaptic neurotransmission and reveals its function of creating more regular AP firing patterns.

Genome-wide screening reveals metabolic regulation of stop-codon readthrough by cyclic AMP.

Translational fidelity is critical for microbial fitness, survival and stress responses. Much remains unknown about the genetic and environmental control of translational fidelity and its single-cell heterogeneity. In this study, we used a high-throughput fluorescence-based assay to screen a knock-out library of Escherichia coli and identified over 20 genes critical for stop-codon readthrough. Most of these identified genes were not previously known to affect translational fidelity. Intriguingly, we show that several genes controlling metabolism, including cyaA and crp, enhance stop-codon readthrough. CyaA catalyzes the synthesis of cyclic adenosine monophosphate (cAMP). Combining RNA sequencing, metabolomics and biochemical analyses, we show that deleting cyaA impairs amino acid catabolism and production of ATP, thus repressing the transcription of rRNAs and tRNAs to decrease readthrough. Single-cell analyses further show that cAMP is a major driver of heterogeneity in stop-codon readthrough and rRNA expression. Our results highlight that carbon metabolism is tightly coupled with stop-codon readthrough.

Escherichia coli cells are primed for survival before lethal antibiotic stress.

Non-genetic factors can cause significant fluctuations in gene expression levels. Regardless of growing in a stable environment, this fluctuation leads to cell-to-cell variability in an isogenic population. This phenotypic heterogeneity allows a tiny subset of bacterial cells in a population called persister cells to tolerate long-term lethal antibiotic effects by entering into a non-dividing, metabolically repressed state. We occasionally noticed a high variation in persister levels, and to explore this, we tested clonal populations starting from a single cell using a modified Luria-Delbrück fluctuation test. Although we kept the conditions same, the diversity in persistence level among clones was relatively consistent: varying from ~60- to 100- and ~40- to 70-fold for ampicillin and apramycin, respectively. Then, we divided and diluted each clone to observe whether the same clone had comparable persister levels for more than one generation. Replicates had similar persister levels even when clones were divided, diluted by 1:20, and allowed to grow for approximately five generations. This result explicitly shows a cellular memory passed on for generations and eventually lost when cells are diluted to 1:100 and regrown (>seven generations). Our result demonstrates (1) the existence of a small population prepared for stress ("primed cells") resulting in higher persister numbers; (2) the primed memory state is reproducible and transient, passed down for generations but eventually lost; and (3) a heterogeneous persister population is a result of a transiently primed reversible cell state and not due to a pre-existing genetic mutation. IMPORTANCE Antibiotics have been highly effective in treating lethal infectious diseases for almost a century. However, the increasing threat of antibiotic resistance is again causing these diseases to become life-threatening. The longer a bacteria can survive antibiotics, the more likely it is to develop resistance. Complicating matters is that non-genetic factors can allow bacterial cells with identical DNA to gain transient resistance (also known as persistence). Here, we show that a small fraction of the bacterial population called primed cells can pass down non-genetic information ("memory") to their offspring, enabling them to survive lethal antibiotics for a long time. However, this memory is eventually lost. These results demonstrate how bacteria can leverage differences among genetically identical cells formed through non-genetic factors to form primed cells with a selective advantage to survive antibiotics.

Mechanisms of Cell Size Regulation in Slow-Growing Escherichia coli Cells: Discriminating Models Beyond the Adder.

Under ideal conditions, Escherichia coli cells divide after adding a fixed cell size, a strategy known as the adder. This concept applies to various microbes and is often explained as the division that occurs after a certain number of stages, associated with the accumulation of precursor proteins at a rate proportional to cell size. However, under poor media conditions, E. coli cells exhibit a different size regulation. They are smaller and follow a sizer-like division strategy where the added size is inversely proportional to the size at birth. We explore three potential causes for this deviation: precursor protein degradation, nonlinear accumulation rate, and a threshold size termed the commitment size. These models fit mean trends but predict different distributions given the birth size. To validate these models, we used the Akaike information criterion and compared them to open datasets of slow-growing E. coli cells in different media. the degradation model could explain the division strategy for media where cells are larger, while the commitment size model could account for smaller cells. The power-law model, finally, better fits the data at intermediate regimes.

Evaluating single-cell variability in proteasomal decay.

Gene expression is a stochastic process that leads to variability in mRNA and protein abundances even within an isogenic population of cells grown in the same environment. This variation, often called gene-expression noise, has typically been attributed to transcriptional and translational processes while ignoring the contributions of protein decay variability across cells. Here we estimate the single-cell protein decay rates of two degron GFPs in Saccharomyces cerevisiae using time-lapse microscopy. We find substantial cell-to-cell variability in the decay rates of the degron GFPs. We evaluate cellular features that explain the variability in the proteasomal decay and find that the amount of 20s catalytic beta subunit of the proteasome marginally explains the observed variability in the degron GFP half-lives. We propose alternate hypotheses that might explain the observed variability in the decay of the two degron GFPs. Overall, our study highlights the importance of studying the kinetics of the decay process at single-cell resolution and that decay rates vary at the single-cell level, and that the decay process is stochastic. A complex model of decay dynamics must be included when modeling stochastic gene expression to estimate gene expression noise.

Iron Memory in E. coli.

The importance of memory in bacterial decision-making is relatively unexplored. We show here that a prior experience of swarming is remembered when E. coli encounters a new surface, improving its future swarming efficiency. We conducted >10,000 single-cell swarm assays to discover that cells store memory in the form of cellular iron levels. This memory pre-exists in planktonic cells, but the act of swarming reinforces it. A cell with low iron initiates swarming early and is a better swarmer, while the opposite is true for a cell with high iron. The swarming potential of a mother cell, whether low or high, is passed down to its fourth-generation daughter cells. This memory is naturally lost by the seventh generation, but artificially manipulating iron levels allows it to persist much longer. A mathematical model with a time-delay component faithfully recreates the observed dynamic interconversions between different swarming potentials. We also demonstrate that iron memory can integrate multiple stimuli, impacting other bacterial behaviors such as biofilm formation and antibiotic tolerance.

The minimal intrinsic stochasticity of constitutively expressed eukaryotic genes is sub-Poissonian.

Gene expression inherently gives rise to stochastic variation ("noise") in the production of gene products. Minimizing noise is crucial for ensuring reliable cellular functions. However, noise cannot be suppressed below a certain intrinsic limit. For constitutively expressed genes, this limit is typically assumed to be Poissonian noise, wherein the variance in mRNA numbers is equal to their mean. Here, we demonstrate that several cell division genes in fission yeast exhibit mRNA variances significantly below this limit. The reduced variance can be explained by a gene expression model incorporating multiple transcription and mRNA degradation steps. Notably, in this sub-Poissonian regime, distinct from Poissonian or super-Poissonian regimes, cytoplasmic noise is effectively suppressed through a higher mRNA export rate. Our findings redefine the lower limit of eukaryotic gene expression noise and uncover molecular requirements for achieving ultralow noise, which is expected to be important for vital cellular functions.

The fission yeast cell size control system integrates pathways measuring cell surface area, volume, and time.

Eukaryotic cells tightly control their size, but the relevant aspect of size is unknown in most cases. Fission yeast divide at a threshold cell surface area (SA) due, in part, to the protein kinase Cdr2. We find that fission yeast cells only divide by SA under a size threshold. Mutants that divide at a larger size shift to volume-based divisions. Diploid cells divide at a larger size than haploid cells do, but they maintain SA-based divisions, and this indicates that the size threshold for changing from surface-area-based to volume-based control is set by ploidy. Within this size control system, we found that the mitotic activator Cdc25 accumulates like a volume-based sizer molecule, whereas the mitotic cyclin Cdc13 accumulates in the nucleus as a timer. We propose an integrated model for cell size control based on multiple signaling pathways that report on distinct aspects of cell size and growth, including cell SA (Cdr2), cell volume (Cdc25), and time (Cdc13). Combined modeling and experiments show how this system can generate both sizer- and adder-like properties.

Out-of-equilibrium gene expression fluctuations in the presence of extrinsic noise.

Cell-to-cell variability in protein concentrations is strongly affected by extrinsic noise, especially for highly expressed genes. Extrinsic noise can be due to fluctuations of several possible cellular factors connected to cell physiology and to the level of key enzymes in the expression process. However, how to identify the predominant sources of extrinsic noise in a biological system is still an open question. This work considers a general stochastic model of gene expression with extrinsic noise represented as fluctuations of the different model rates, and focuses on the out-of-equilibrium expression dynamics. Combining analytical calculations with stochastic simulations, we characterize how extrinsic noise shapes the protein variability during gene activation or inactivation, depending on the prevailing source of extrinsic variability, on its intensity and timescale. In particular, we show that qualitatively different noise profiles can be identified depending on which are the fluctuating parameters. This indicates an experimentally accessible way to pinpoint the dominant sources of extrinsic noise using time-coarse experiments.

Transcriptional regulation of Sis1 promotes fitness but not feedback in the heat shock response.

The heat shock response (HSR) controls expression of molecular chaperones to maintain protein homeostasis. Previously, we proposed a feedback loop model of the HSR in which heat-denatured proteins sequester the chaperone Hsp70 to activate the HSR, and subsequent induction of Hsp70 deactivates the HSR (Krakowiak et al., 2018; Zheng et al., 2016). However, recent work has implicated newly synthesized proteins (NSPs) - rather than unfolded mature proteins - and the Hsp70 co-chaperone Sis1 in HSR regulation, yet their contributions to HSR dynamics have not been determined. Here, we generate a new mathematical model that incorporates NSPs and Sis1 into the HSR activation mechanism, and we perform genetic decoupling and pulse-labeling experiments to demonstrate that Sis1 induction is dispensable for HSR deactivation. Rather than providing negative feedback to the HSR, transcriptional regulation of Sis1 by Hsf1 promotes fitness by coordinating stress granules and carbon metabolism. These results support an overall model in which NSPs signal the HSR by sequestering Sis1 and Hsp70, while induction of Hsp70 - but not Sis1 - attenuates the response.

PyEcoLib: a python library for simulating stochastic cell size dynamics.

Recently, there has been an increasing need for tools to simulate cell size regulation due to important applications in cell proliferation and gene expression. However, implementing the simulation usually presents some difficulties, as the division has a cycle-dependent occurrence rate. In this article, we gather a recent theoretical framework inPyEcoLib, a python-based library to simulate the stochastic dynamics of the size of bacterial cells. This library can simulate cell size trajectories with an arbitrarily small sampling period. In addition, this simulator can include stochastic variables, such as the cell size at the beginning of the experiment, the cycle duration timing, the growth rate, and the splitting position. Furthermore, from a population perspective, the user can choose between tracking a single lineage or all cells in a colony. They can also simulate the most common division strategies (adder, timer, and sizer) using the division rate formalism and numerical methods. As an example of PyecoLib applications, we explain how to couple size dynamics with gene expression predicting, from simulations, how the noise in protein levels increases by increasing the noise in division timing, the noise in growth rate and the noise in cell splitting position. The simplicity of this library and its transparency about the underlying theoretical framework yield the inclusion of cell size stochasticity in complex models of gene expression.