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.

Emergent statistical laws in single-cell transcriptomic data.

Large-scale data on single-cell gene expression have the potential to unravel the specific transcriptional programs of different cell types. The structure of these expression datasets suggests a similarity with several other complex systems that can be analogously described through the statistics of their basic building blocks. Transcriptomes of single cells are collections of messenger RNA abundances transcribed from a common set of genes just as books are different collections of words from a shared vocabulary, genomes of different species are specific compositions of genes belonging to evolutionary families, and ecological niches can be described by their species abundances. Following this analogy, we identify several emergent statistical laws in single-cell transcriptomic data closely similar to regularities found in linguistics, ecology, or genomics. A simple mathematical framework can be used to analyze the relations between different laws and the possible mechanisms behind their ubiquity. Importantly, treatable statistical models can be useful tools in transcriptomics to disentangle the actual biological variability from general statistical effects present in most component systems and from the consequences of the sampling process inherent to the experimental technique.

Protein degradation sets the fraction of active ribosomes at vanishing growth.

Growing cells adopt common basic strategies to achieve optimal resource allocation under limited resource availability. Our current understanding of such "growth laws" neglects degradation, assuming that it occurs slowly compared to the cell cycle duration. Here we argue that this assumption cannot hold at slow growth, leading to important consequences. We propose a simple framework showing that at slow growth protein degradation is balanced by a fraction of "maintenance" ribosomes. Consequently, active ribosomes do not drop to zero at vanishing growth, but as growth rate diminishes, an increasing fraction of active ribosomes performs maintenance. Through a detailed analysis of compiled data, we show that the predictions of this model agree with data from E. coli and S. cerevisiae. Intriguingly, we also find that protein degradation increases at slow growth, which we interpret as a consequence of active waste management and/or recycling. Our results highlight protein turnover as an underrated factor for our understanding of growth laws across kingdoms.

Multiomics Topic Modeling for Breast Cancer Classification.

The integration of transcriptional data with other layers of information, such as the post-transcriptional regulation mediated by microRNAs, can be crucial to identify the driver genes and the subtypes of complex and heterogeneous diseases such as cancer. This paper presents an approach based on topic modeling to accomplish this integration task. More specifically, we show how an algorithm based on a hierarchical version of stochastic block modeling can be naturally extended to integrate any combination of 'omics data. We test this approach on breast cancer samples from the TCGA database, integrating data on messenger RNA, microRNAs, and copy number variations. We show that the inclusion of the microRNA layer significantly improves the accuracy of subtype classification. Moreover, some of the hidden structures or "topics" that the algorithm extracts actually correspond to genes and microRNAs involved in breast cancer development and are associated to the survival probability.

A 3D transcriptomics atlas of the mouse nose sheds light on the anatomical logic of smell.

The sense of smell helps us navigate the environment, but its molecular architecture and underlying logic remain understudied. The spatial location of odorant receptor genes (Olfrs) in the nose is thought to be independent of the structural diversity of the odorants they detect. Using spatial transcriptomics, we create a genome-wide 3D atlas of the mouse olfactory mucosa (OM). Topographic maps of genes differentially expressed in space reveal that both Olfrs and non-Olfrs are distributed in a continuous and overlapping fashion over at least five broad zones in the OM. The spatial locations of Olfrs correlate with the mucus solubility of the odorants they recognize, providing direct evidence for the chromatographic theory of olfaction. This resource resolves the molecular architecture of the mouse OM and will inform future studies on mechanisms underlying Olfr gene choice, axonal pathfinding, patterning of the nervous system, and basic logic for the peripheral representation of smell.

The Dynamics of Aerotaxis in a Simple Eukaryotic Model.

In aerobic organisms, oxygen is essential for efficient energy production, and it acts as the last acceptor of the mitochondrial electron transport chain and as regulator of gene expression. However, excessive oxygen can lead to production of deleterious reactive oxygen species. Therefore, the directed migration of single cells or cell clumps from hypoxic areas toward a region of optimal oxygen concentration, named aerotaxis, can be considered an adaptive mechanism that plays a major role in biological and pathological processes. One relevant example is the development of O2 gradients when tumors grow beyond their vascular supply, leading frequently to metastasis. In higher eukaryotic organisms, aerotaxis has only recently begun to be explored, but genetically amenable model organisms suitable to dissect this process remain an unmet need. In this regard, we sought to assess whether Dictyostelium cells, which are an established model for chemotaxis and other motility processes, could sense oxygen gradients and move directionally in their response. By assessing different physical parameters, our findings indicate that both growing and starving Dictyostelium cells under hypoxic conditions migrate directionally toward regions of higher O2 concentration. This migration is characterized by a specific pattern of cell arrangement. A thickened circular front of high cell density (corona) forms in the cell cluster and persistently moves following the oxygen gradient. Cells in the colony center, where hypoxia is more severe, are less motile and display a rounded shape. Aggregation-competent cells forming streams by chemotaxis, when confined under hypoxic conditions, undergo stream or aggregate fragmentation, giving rise to multiple small loose aggregates that coordinately move toward regions of higher O2 concentration. By testing a panel of mutants defective in chemotactic signaling, and a catalase-deficient strain, we found that the latter and the pkbR1 null exhibited altered migration patterns. Our results suggest that in Dictyostelium, like in mammalian cells, an intracellular accumulation of hydrogen peroxide favors the migration toward optimal oxygen concentration. Furthermore, differently from chemotaxis, this oxygen-driven migration is a G protein-independent process.

The impact of whole genome duplications on the human gene regulatory networks.

This work studies the effects of the two rounds of Whole Genome Duplication (WGD) at the origin of the vertebrate lineage on the architecture of the human gene regulatory networks. We integrate information on transcriptional regulation, miRNA regulation, and protein-protein interactions to comparatively analyse the role of WGD and Small Scale Duplications (SSD) in the structural properties of the resulting multilayer network. We show that complex network motifs, such as combinations of feed-forward loops and bifan arrays, deriving from WGD events are specifically enriched in the network. Pairs of WGD-derived proteins display a strong tendency to interact both with each other and with common partners and WGD-derived transcription factors play a prominent role in the retention of a strong regulatory redundancy. Combinatorial regulation and synergy between different regulatory layers are in general enhanced by duplication events, but the two types of duplications contribute in different ways. Overall, our findings suggest that the two WGD events played a substantial role in increasing the multi-layer complexity of the vertebrate regulatory network by enhancing its combinatorial organization, with potential consequences on its overall robustness and ability to perform high-level functions like signal integration and noise control. Lastly, we discuss in detail the RAR/RXR pathway as an illustrative example of the evolutionary impact of WGD duplications in human.

Initial cell density encodes proliferative potential in cancer cell populations.

Individual cells exhibit specific proliferative responses to changes in microenvironmental conditions. Whether such potential is constrained by the cell density throughout the growth process is however unclear. Here, we identify a theoretical framework that captures how the information encoded in the initial density of cancer cell populations impacts their growth profile. By following the growth of hundreds of populations of cancer cells, we found that the time they need to adapt to the environment decreases as the initial cell density increases. Moreover, the population growth rate shows a maximum at intermediate initial densities. With the support of a mathematical model, we show that the observed interdependence of adaptation time and growth rate is significantly at odds both with standard logistic growth models and with the Monod-like function that governs the dependence of the growth rate on nutrient levels. Our results (i) uncover and quantify a previously unnoticed heterogeneity in the growth dynamics of cancer cell populations; (ii) unveil how population growth may be affected by single-cell adaptation times; (iii) contribute to our understanding of the clinically-observed dependence of the primary and metastatic tumor take rates on the initial density of implanted cancer cells.

A Topic Modeling Analysis of TCGA Breast and Lung Cancer Transcriptomic Data.

Topic modeling is a widely used technique to extract relevant information from large arrays of data. The problem of finding a topic structure in a dataset was recently recognized to be analogous to the community detection problem in network theory. Leveraging on this analogy, a new class of topic modeling strategies has been introduced to overcome some of the limitations of classical methods. This paper applies these recent ideas to TCGA transcriptomic data on breast and lung cancer. The established cancer subtype organization is well reconstructed in the inferred latent topic structure. Moreover, we identify specific topics that are enriched in genes known to play a role in the corresponding disease and are strongly related to the survival probability of patients. Finally, we show that a simple neural network classifier operating in the low dimensional topic space is able to predict with high accuracy the cancer subtype of a test expression sample.

A Model-Driven Quantitative Analysis of Retrotransposon Distributions in the Human Genome.

Retrotransposons, DNA sequences capable of creating copies of themselves, compose about half of the human genome and played a central role in the evolution of mammals. Their current position in the host genome is the result of the retrotranscription process and of the following host genome evolution. We apply a model from statistical physics to show that the genomic distribution of the two most populated classes of retrotransposons in human deviates from random placement, and that this deviation increases with time. The time dependence suggests a major role of the host genome dynamics in shaping the current retrotransposon distributions. Focusing on a neutral scenario, we show that a simple model based on random placement followed by genome expansion and sequence duplications can reproduce the empirical retrotransposon distributions, even though more complex and possibly selective mechanisms can have contributed. Besides the inherent interest in understanding the origin of current retrotransposon distributions, this work sets a general analytical framework to analyze quantitatively the effects of genome evolutionary dynamics on the distribution of genomic elements.

Investigating the epi-miRNome: identification of epi-miRNAs using transfection experiments.

Aim: Growing evidence shows a strong interplay between post-transcriptional regulation, mediated by miRNAs (miRs) and epigenetic regulation. Nevertheless, the number of experimentally validated miRs (called epi-miRs) involved in these regulatory circuitries is still very small. Material & methods: We propose a pipeline to prioritize candidate epi-miRs and to identify potential epigenetic interactors of any given miR starting from miR transfection experiment datasets. Results & conclusion: We identified 34 candidate epi-miRs: 19 of them are known epi-miRs, while 15 are new. Moreover, using an in-house generated gene expression dataset, we experimentally proved that a component of the polycomb-repressive complex 2, the histone methyltransferase enhancer of zeste homolog 2 (EZH2), interacts with miR-214, a well-known prometastatic miR in melanoma and breast cancer, highlighting a miR-214-EZH2 regulatory axis potentially relevant in tumor progression.

Concurrent processes set E. coli cell division.

A cell can divide only upon completion of chromosome segregation; otherwise, its daughters would lose genetic material. However, we do not know whether the partitioning of chromosomes is the key event for the decision to divide. We show how key trends in single-cell data reject the classic idea of replication-segregation as the rate-limiting process for cell division. Instead, the data agree with a model where two concurrent processes (setting replication initiation and interdivision time) set cell division on competing time scales. During each cell cycle, division is set by the slowest process (an "AND" gate). The concept of transitions between cell cycle stages as decisional processes integrating multiple inputs instead of cascading from orchestrated steps can affect the way we think of the cell cycle in general.

Dissecting the Control Mechanisms for DNA Replication and Cell Division in E. coli.

Understanding the classic problem of how single E. coli cells coordinate cell division with genome replication would open the way to addressing cell-cycle progression at the single-cell level. Recent studies produced new data, but the contrast in their conclusions and proposed mechanisms makes the emerging picture fragmented and unclear. Here, we re-evaluate available data and models, including generalizations based on the same assumptions. We show that although they provide useful insights, none of the proposed models captures all correlation patterns observed in data. We conclude that the assumption that replication is the bottleneck process for cell division is too restrictive. Instead, we propose that two concurrent cycles responsible for division and initiation of DNA replication set the time of cell division. This framework allows us to select a nearly constant added size per origin between subsequent initiations as the most likely mechanism setting initiation of replication.

The Empirical Fluctuation Pattern of E. coli Division Control.

In physics, it is customary to represent the fluctuations of a stochastic system at steady state in terms of linear response to small random perturbations. Previous work has shown that the same framework describes effectively the trade-off between cell-to-cell variability and correction in the control of cell division of single E. coli cells. However, previous analyses were motivated by specific models and limited to a subset of the measured variables. For example, most analyses neglected the role of growth rate variability. Here, we take a comprehensive approach and consider several sets of available data from both microcolonies and microfluidic devices in different growth conditions. We evaluate all the coupling coefficients between the three main measured variables (interdivision times, cell sizes and individual-cell growth rates). The linear-response framework correctly predicts consistency relations between a priori independent experimental measurements, which confirms its validity. Additionally, the couplings between the cell-specific growth rate and the other variables are typically non zero. Finally, we use the framework to detect signatures of mechanisms in experimental data involving growth rate fluctuations, finding that (1) noise-generating coupling between size and growth rate is a consequence of inter-generation growth rate correlations and (2) the correlation patterns agree with a near-adder model where the added size has a dependence on the single-cell growth rate. Our findings define relevant constraints that any theoretical description should reproduce, and will help future studies aiming to falsify some of the competing models of the cell cycle existing today in the literature.

Zipf and Heaps laws from dependency structures in component systems.

Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes or texts as sets of words. On one hand, the joint occurrence of components emerges from architectural and specific constraints in such systems. On the other hand, general regularities may unify different systems, such as the broadly studied Zipf and Heaps laws, respectively concerning the distribution of component frequencies and their number as a function of system size. Dependency structures (i.e., directed networks encoding the dependency relations between the components in a system) were proposed recently as a possible organizing principles underlying some of the regularities observed. However, the consequences of this assumption were explored only in binary component systems, where solely the presence or absence of components is considered, and multiple copies of the same component are not allowed. Here we consider a simple model that generates, from a given ensemble of dependency structures, a statistical ensemble of sets of components, allowing for components to appear with any multiplicity. Our model is a minimal extension that is memoryless and therefore accessible to analytical calculations. A mean-field analytical approach (analogous to the "Zipfian ensemble" in the linguistics literature) captures the relevant laws describing the component statistics as we show by comparison with numerical computations. In particular, we recover a power-law Zipf rank plot, with a set of core components, and a Heaps law displaying three consecutive regimes (linear, sublinear, and saturating) that we characterize quantitatively.

Modelling the evolution of transcription factor binding preferences in complex eukaryotes.

Transcription factors (TFs) exert their regulatory action by binding to DNA with specific sequence preferences. However, different TFs can partially share their binding sequences due to their common evolutionary origin. This "redundancy" of binding defines a way of organizing TFs in "motif families" by grouping TFs with similar binding preferences. Since these ultimately define the TF target genes, the motif family organization entails information about the structure of transcriptional regulation as it has been shaped by evolution. Focusing on the human TF repertoire, we show that a one-parameter evolutionary model of the Birth-Death-Innovation type can explain the TF empirical repartition in motif families, and allows to highlight the relevant evolutionary forces at the origin of this organization. Moreover, the model allows to pinpoint few deviations from the neutral scenario it assumes: three over-expanded families (including HOX and FOX genes), a set of "singleton" TFs for which duplication seems to be selected against, and a higher-than-average rate of diversification of the binding preferences of TFs with a Zinc Finger DNA binding domain. Finally, a comparison of the TF motif family organization in different eukaryotic species suggests an increase of redundancy of binding with organism complexity.

Relevant parameters in models of cell division control.

A recent burst of dynamic single-cell data makes it possible to characterize the stochastic dynamics of cell division control in bacteria. Different models were used to propose specific mechanisms, but the links between them are poorly explored. The lack of comparative studies makes it difficult to appreciate how well any particular mechanism is supported by the data. Here, we describe a simple and generic framework in which two common formalisms can be used interchangeably: (i) a continuous-time division process described by a hazard function and (ii) a discrete-time equation describing cell size across generations (where the unit of time is a cell cycle). In our framework, this second process is a discrete-time Langevin equation with simple physical analogues. By perturbative expansion around the mean initial size (or interdivision time), we show how this framework describes a wide range of division control mechanisms, including combinations of time and size control, as well as the constant added size mechanism recently found to capture several aspects of the cell division behavior of different bacteria. As we show by analytical estimates and numerical simulations, the available data are described precisely by the first-order approximation of this expansion, i.e., by a "linear response" regime for the correction of size fluctuations. Hence, a single dimensionless parameter defines the strength and action of the division control against cell-to-cell variability (quantified by a single "noise" parameter). However, the same strength of linear response may emerge from several mechanisms, which are distinguished only by higher-order terms in the perturbative expansion. Our analytical estimate of the sample size needed to distinguish between second-order effects shows that this value is close to but larger than the values of the current datasets. These results provide a unified framework for future studies and clarify the relevant parameters at play in the control of cell division.

Stochastic timing in gene expression for simple regulatory strategies.

Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to reach in a precise time a threshold level of expression that triggers a specific downstream process. However, gene expression is subject to stochastic fluctuations, naturally inducing an uncertainty in this threshold-crossing time with potential consequences on biological functions and phenotypes. Here, we consider such 'timing fluctuations' and we ask how they can be controlled. Our analytical estimates and simulations show that, for an induced gene, timing variability is minimal if the threshold level of expression is approximately half of the steady-state level. Timing fluctuations can be reduced by increasing the transcription rate, while they are insensitive to the translation rate. In presence of self-regulatory strategies, we show that self-repression reduces timing noise for threshold levels that have to be reached quickly, while self-activation is optimal at long times. These results lay a framework for understanding stochasticity of endogenous systems such as the cell cycle, as well as for the design of synthetic trigger circuits.

Step by Step, Cell by Cell: Quantification of the Bacterial Cell Cycle.

The Escherichia coli cell cycle is a classic, but we are still missing some of its essential aspects. The reason is that our knowledge is mostly based on population data, and our grasp of the behavior of single cells is still very limited. Today, new dynamic single-cell data promise to overcome this barrier. Existing data from single cells have already led to findings and hypotheses that challenge standard views, and have raised new questions. Here, we review these recent developments and propose that a systematic exploration of the correlation patterns between 'cell-cycle intervals' defined by key molecular events measured in many single cells could lead to a quantitative characterization of the cell cycle in terms of inherent stochasticity and homeostatic controls.

Individuality and universality in the growth-division laws of single E. coli cells.

The mean size of exponentially dividing Escherichia coli cells in different nutrient conditions is known to depend on the mean growth rate only. However, the joint fluctuations relating cell size, doubling time, and individual growth rate are only starting to be characterized. Recent studies in bacteria reported a universal trend where the spread in both size and doubling times is a linear function of the population means of these variables. Here we combine experiments and theory and use scaling concepts to elucidate the constraints posed by the second observation on the division control mechanism and on the joint fluctuations of sizes and doubling times. We found that scaling relations based on the means collapse both size and doubling-time distributions across different conditions and explain how the shape of their joint fluctuations deviates from the means. Our data on these joint fluctuations highlight the importance of cell individuality: Single cells do not follow the dependence observed for the means between size and either growth rate or inverse doubling time. Our calculations show that these results emerge from a broad class of division control mechanisms requiring a certain scaling form of the "division hazard rate function," which defines the probability rate of dividing as a function of measurable parameters. This "model free" approach gives a rationale for the universal body-size distributions observed in microbial ecosystems across many microbial species, presumably dividing with multiple mechanisms. Additionally, our experiments show a crossover between fast and slow growth in the relation between individual-cell growth rate and division time, which can be understood in terms of different regimes of genome replication control.