Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes

Identifying Markov Chain Models from Time-to-Event Data: An Algebraic Approach

Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type distribution, can we identify the transition rate parameters of the underlying Markov chain? For a specific class of solvable Markov models, we show this problem has a unique solution up to finite symmetry transformations, and we outline a recursive method for computing symbolic solutions for these models across any number of states. Using the Thomas decomposition technique from computer algebra, we further provide symbolic solutions for any model. Interestingly, different models with the same state count but distinct transition graphs can yield identical phase-type distributions. To distinguish among these, we propose additional properties beyond just the time to the next event. We demonstrate the method's applicability by inferring transcriptional regulation models from single-cell transcription imaging data.

Sequestration of gene products by decoys enhances precision in the timing of intracellular events

Expressed gene products often interact ubiquitously with binding sites at nucleic acids and macromolecular complexes, known as decoys. The binding of transcription factors (TFs) to decoys can be crucial in controlling the stochastic dynamics of gene expression. Here, we explore the impact of decoys on the timing of intracellular events, as captured by the time taken for the levels of a given TF to reach a critical threshold level, known as the first passage time (FPT). Although nonlinearity introduced by binding makes exact mathematical analysis challenging, employing suitable approximations and reformulating FPT in terms of an alternative variable, we analytically assess the impact of decoys. The stability of the decoy-bound TFs against degradation impacts FPT statistics crucially. Decoys reduce noise in FPT, and stable decoy-bound TFs offer greater timing precision with less expression cost than their unstable counterparts. Interestingly, when both bound and free TFs decay at the same rate, decoy binding does not directly alter FPT noise. We verify these results by performing exact stochastic simulations. These results have important implications for the precise temporal scheduling of events involved in the functioning of biomolecular clocks, development processes, cell-cycle control, and cell-size homeostasis.

Temporal variability and cell mechanics control robustness in mammalian embryogenesis

How living systems achieve precision in form and function despite their intrinsic stochasticity is a fundamental yet ongoing question in biology. We generated morphomaps of preimplantation embryogenesis in mouse, rabbit, and monkey embryos, and these morphomaps revealed that although blastomere divisions desynchronized passively, 8-cell embryos converged toward robust three-dimensional shapes. Using topological analysis and genetic perturbations, we found that embryos progressively changed their cellular connectivity to a preferred topology, which could be predicted by a physical model in which actomyosin contractility and noise facilitate topological transitions, lowering surface energy. This mechanism favored regular embryo packing and promoted a higher number of inner cells in the 16-cell embryo. Synchronized division reduced embryo packing and generated substantially more misallocated cells and fewer inner-cell-mass cells. These findings suggest that stochasticity in division timing contributes to robust patterning.

Stochastic Gene Expression in Proliferating Cells: Differing Noise Intensity in Single-Cell and Population Perspectives

Random fluctuations (noise) in gene expression can be studied from two complementary perspectives: following expression in a single cell over time or comparing expression between cells in a proliferating population at a given time. Here, we systematically investigated scenarios where both perspectives lead to different levels of noise in a given gene product. We first consider a stable protein, whose concentration is diluted by cellular growth, and the protein inhibits growth at high concentrations, establishing a positive feedback loop. For a stochastic model with molecular bursting of gene products, we analytically predict and contrast the steady-state distributions of protein concentration in both frameworks. Although positive feedback amplifies the noise in expression, this amplification is much higher in the population framework compared to following a single cell over time. We also study other processes that lead to different noise levels even in the absence of such dilution-based feedback. When considering randomness in the partitioning of molecules between daughters during mitosis, we find that in the single-cell perspective, the noise in protein concentration is independent of noise in the cell cycle duration. In contrast, partitioning noise is amplified in the population perspective by increasing randomness in cell-cycle time. Overall, our results show that the commonly used single-cell framework that does not account for proliferating cells can, in some cases, underestimate the noise in gene product levels. These results have important implications for studying the inter-cellular variation of different stress-related expression programs across cell types that are known to inhibit cellular growth.

Phenotypic noise and plasticity in cancer evolution

Non-genetic alterations can produce changes in a cell's phenotype. In cancer, these phenomena can influence a cell's fitness by conferring access to heritable, beneficial phenotypes. Herein, we argue that current discussions of 'phenotypic plasticity' in cancer evolution ignore a salient feature of the original definition: namely, that it occurs in response to an environmental change. We suggest 'phenotypic noise' be used to distinguish non-genetic changes in phenotype that occur independently from the environment. We discuss the conceptual and methodological techniques used to identify these phenomena during cancer evolution. We propose that the distinction will guide efforts to define mechanisms of phenotype change, accelerate translational work to manipulate phenotypes through treatment, and, ultimately, improve patient outcomes.

Effects of mRNA conformational switching on translational noise in gene circuits

Intragenic translational heterogeneity describes the variation in translation at the level of transcripts for an individual gene. A factor that contributes to this source of variation is the mRNA structure. Both the composition of the thermodynamic ensemble, i.e., the stationary distribution of mRNA structures, and the switching dynamics between those play a role. The effect of the switching dynamics on intragenic translational heterogeneity remains poorly understood. We present a stochastic translation model that accounts for mRNA structure switching and is derived from a Markov model via approximate stochastic filtering. We assess the approximation on various timescales and provide a method to quantify how mRNA structure dynamics contributes to translational heterogeneity. With our approach, we allow quantitative information on mRNA switching from biophysical experiments or coarse-grain molecular dynamics simulations of mRNA structures to be included in gene regulatory chemical reaction network models without an increase in the number of species. Thereby, our model bridges a gap between mRNA structure kinetics and gene expression models, which we hope will further improve our understanding of gene regulatory networks and facilitate genetic circuit design.

Exact solution of a three-stage model of stochastic gene expression including cell-cycle dynamics

The classical three-stage model of stochastic gene expression predicts the statistics of single cell mRNA and protein number fluctuations as a function of the rates of promoter switching, transcription, translation, degradation and dilution. While this model is easily simulated, its analytical solution remains an unsolved problem. Here we modify this model to explicitly include cell-cycle dynamics and then derive an exact solution for the time-dependent joint distribution of mRNA and protein numbers. We show large differences between this model and the classical model which captures cell-cycle effects implicitly via effective first-order dilution reactions. In particular we find that the Fano factor of protein numbers calculated from a population snapshot measurement are underestimated by the classical model whereas the correlation between mRNA and protein can be either over- or underestimated, depending on the timescales of mRNA degradation and promoter switching relative to the mean cell-cycle duration time.

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.

Collective behavior and self-organization in neural rosette morphogenesis

Neural rosettes develop from the self-organization of differentiating human pluripotent stem cells. This process mimics the emergence of the embryonic central nervous system primordium, i.e., the neural tube, whose formation is under close investigation as errors during such process result in severe diseases like spina bifida and anencephaly. While neural tube formation is recognized as an example of self-organization, we still do not understand the fundamental mechanisms guiding the process. Here, we discuss the different theoretical frameworks that have been proposed to explain self-organization in morphogenesis. We show that an explanation based exclusively on stem cell differentiation cannot describe the emergence of spatial organization, and an explanation based on patterning models cannot explain how different groups of cells can collectively migrate and produce the mechanical transformations required to generate the neural tube. We conclude that neural rosette development is a relevant experimental 2D in-vitro model of morphogenesis because it is a multi-scale self-organization process that involves both cell differentiation and tissue development. Ultimately, to understand rosette formation, we first need to fully understand the complex interplay between growth, migration, cytoarchitecture organization, and cell type evolution.

Coupling gene expression dynamics to cell size dynamics and cell cycle events: Exact and approximate solutions of the extended telegraph model

The standard model describing the fluctuations of mRNA numbers in single cells is the telegraph model which includes synthesis and degradation of mRNA, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by the cell cycle phase, cellular growth and division, and other crucial aspects of cellular biology. Here, we derive the analytical time-dependent solution of an extended telegraph model that explicitly considers the doubling of gene copy numbers upon DNA replication, dependence of the mRNA synthesis rate on cellular volume, gene dosage compensation, partitioning of molecules during cell division, cell-cycle duration variability, and cell-size control strategies. Based on the time-dependent solution, we obtain the analytical distributions of transcript numbers for lineage and population measurements in steady-state growth and also find a linear relation between the Fano factor of mRNA fluctuations and cell volume fluctuations. We show that generally the lineage and population distributions in steady-state growth cannot be accurately approximated by the steady-state solution of extrinsic noise models, i.e. a telegraph model with parameters drawn from probability distributions. This is because the mRNA lifetime is often not small enough compared to the cell cycle duration to erase the memory of division and replication. Accurate approximations are possible when this memory is weak, e.g. for genes with bursty expression and for which there is sufficient gene dosage compensation when replication occurs.

Dimerization induces bimodality in protein number distributions

We examined gene expression with DNA switching between two states, active and inactive. Subpopulations emerge from mechanisms that do not arise from trivial transcriptional heterogeneity. Although the RNA demonstrates a unimodal distribution, dimerization intriguingly causes protein bimodality. No control loop or deterministic bistability are present. In such a situation, increasing the degradation rate of the protein does not lead to bimodality. The bimodality is achieved through the interplay between the protein monomer and the formation of protein dimer. We applied Stochastic Simulation Algorithm (SSA) and found that cells spontaneously change states at the protein level. While sweeping parameters, decreasing the rate constant of dimerization severely impairs the bimodality. We also examined the influence of DNA switching. To have bimodality, the system requires a proper ratio of DNA in the active state to the inactive state. In addition to bimodality of the monomer, tetramerization also causes the bimodality of the dimer.

Concentration fluctuations in growing and dividing cells: Insights into the emergence of concentration homeostasis

Intracellular reaction rates depend on concentrations and hence their levels are often regulated. However classical models of stochastic gene expression lack a cell size description and cannot be used to predict noise in concentrations. Here, we construct a model of gene product dynamics that includes a description of cell growth, cell division, size-dependent gene expression, gene dosage compensation, and size control mechanisms that can vary with the cell cycle phase. We obtain expressions for the approximate distributions and power spectra of concentration fluctuations which lead to insight into the emergence of concentration homeostasis. We find that (i) the conditions necessary to suppress cell division-induced concentration oscillations are difficult to achieve; (ii) mRNA concentration and number distributions can have different number of modes; (iii) two-layer size control strategies such as sizer-timer or adder-timer are ideal because they maintain constant mean concentrations whilst minimising concentration noise; (iv) accurate concentration homeostasis requires a fine tuning of dosage compensation, replication timing, and size-dependent gene expression; (v) deviations from perfect concentration homeostasis show up as deviations of the concentration distribution from a gamma distribution. Some of these predictions are confirmed using data for E. coli, fission yeast, and budding yeast.

A domestic plant differs from its wild relative along multiple axes of within-plant trait variability and diversity

For 10,000 years humans have altered plant traits through domestication and ongoing crop improvement, shaping plant form and function in agroecosystems. To date, studies have focused on how these processes shape whole-plant or average traits; however, plants also have characteristic levels of trait variability among their repeated parts, which can be heritable and mediate critical ecological interactions. Here, we examine an underappreciated scale of trait variation-among leaves, within plants-that may have changed through the process of domestication and improvement. Variability at this scale may itself be a target of selection, or be shaped as a by-product of the domestication process. We explore how levels of among-leaf trait variability differ between cultivars and wild relatives of alfalfa (Medicago sativa), a key forage crop with a 7,000-year domestication history. We grew individual plants from 30 wild populations and 30 cultivars, and quantified variability in a broad suite of physical, nutritive, and chemical leaf traits, including measures of chemical dissimilarity (beta diversity) among leaves within each plant. We find that trait variability has changed over the course of domestication, with effects often larger than changes in trait means. Domestic alfalfa had elevated among-leaf variability in SLA, trichomes, and C:N; increased diversity in defensive compounds; and reduced variability in phytochemical composition. We also elucidate fundamental relationships between trait means and variability, and between overall production of secondary metabolites and patterns of chemical diversity. We conclude that within-plant variability is an overlooked dimension of trait diversity in a globally critical agricultural crop. Trait variability is actually higher in cultivated plants compared to wild progenitors for multiple nutritive, physical, and chemical traits, highlighting a scale of variation that may mitigate loss of trait diversity at other scales in alfalfa agroecosystems, and in other crops with similar histories of domestication and improvement.

Protein concentration fluctuations in the high expression regime: Taylor's law and its mechanistic origin

Protein concentration in a living cell fluctuates over time due to noise in growth and division processes. In the high expression regime, variance of the protein concentration in a cell was found to scale with the square of the mean, which belongs to a general phenomenon called Taylor's law (TL). To understand the origin for these fluctuations, we measured protein concentration dynamics in single E. coli cells from a set of strains with a variable expression of fluorescent proteins. The protein expression is controlled by a set of constitutive promoters with different strength, which allows to change the expression level over 2 orders of magnitude without introducing noise from fluctuations in transcription regulators. Our data confirms the square TL, but the prefactor A has a cell-to-cell variation independent of the promoter strength. Distributions of the normalized protein concentration for different promoters are found to collapse onto the same curve. To explain these observations, we used a minimal mechanistic model to describe the stochastic growth and division processes in a single cell with a feedback mechanism for regulating cell division. In the high expression regime where extrinsic noise dominates, the model reproduces our experimental results quantitatively. By using a mean-field approximation in the minimal model, we showed that the stochastic dynamics of protein concentration is described by a Langevin equation with multiplicative noise. The Langevin equation has a scale invariance which is responsible for the square TL. By solving the Langevin equation, we obtained an analytical solution for the protein concentration distribution function that agrees with experiments. The solution shows explicitly how the prefactor A depends on strength of different noise sources, which explains its cell-to-cell variability. By using this approach to analyze our single-cell data, we found that the noise in production rate dominates the noise from cell division. The deviation from the square TL in the low expression regime can also be captured in our model by including intrinsic noise in the production rate.

Cell cycle progression and transmitotic apoptosis resistance promote escape from extrinsic apoptosis

Extrinsic apoptosis relies on TNF-family receptor activation by immune cells or receptor-activating drugs. Here, we monitored cell cycle progression at a resolution of minutes to relate apoptosis kinetics and cell-to-cell heterogeneities in death decisions to cell cycle phases. Interestingly, we found that cells in S phase delay TRAIL receptor-induced death in favour of mitosis, thereby passing on an apoptosis-primed state to their offspring. This translates into two distinct fates, apoptosis execution post mitosis or cell survival from inefficient apoptosis. Transmitotic resistance is linked to Mcl-1 upregulation and its increased accumulation at mitochondria from mid-S phase onwards, which allows cells to pass through mitosis with activated caspase-8, and with cells escaping apoptosis after mitosis sustaining sublethal DNA damage. Antagonizing Mcl-1 suppresses cell cycle-dependent delays in apoptosis, prevents apoptosis-resistant progression through mitosis and averts unwanted survival after apoptosis induction. Cell cycle progression therefore modulates signal transduction during extrinsic apoptosis, with Mcl-1 governing decision making between death, proliferation and survival. Cell cycle progression thus is a crucial process from which cell-to-cell heterogeneities in fates and treatment outcomes emerge in isogenic cell populations during extrinsic apoptosis. This article has an associated First Person interview with the first author of the paper.

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.

Mechanobiological conceptual framework for assessing stem cell bioprocess effectiveness

Fully realizing the enormous potential of stem cells requires developing efficient bioprocesses and optimizations founded in mechanobiological considerations. Here, we emphasize the importance of mechanotransduction as one of the governing principles of stem cell bioprocesses, underscoring the need to further explore the behavioral mechanisms involved in sensing mechanical cues and coordinating transcriptional responses. We identify the sources of intrinsic, extrinsic, and external noise in bioprocesses requiring further study, and discuss the criteria and indicators that may be used to assess and predict cell-to-cell variability resulting from environmental fluctuations. Specifically, we propose a conceptual framework to explain the impact of mechanical forces within the cellular environment, identify key cell state determinants in bioprocesses, and discuss downstream implementation challenges.

Noise suppression in stochastic genetic circuits using PID controllers

Inside individual cells, protein population counts are subject to molecular noise due to low copy numbers and the inherent probabilistic nature of biochemical processes. We investigate the effectiveness of proportional, integral and derivative (PID) based feedback controllers to suppress protein count fluctuations originating from two noise sources: bursty expression of the protein, and external disturbance in protein synthesis. Designs of biochemical reactions that function as PID controllers are discussed, with particular focus on individual controllers separately, and the corresponding closed-loop system is analyzed for stochastic controller realizations. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources, but this noise suppression comes at the cost of reduced static sensitivity of the output to the input signal. In contrast, integral feedback has no effect on the protein noise level from stochastic expression, but significantly minimizes the impact of external disturbances, particularly when the disturbance comes at low frequencies. Counter-intuitively, integral feedback is found to amplify external disturbances at intermediate frequencies. Next, we discuss the design of a coupled feedforward-feedback biochemical circuit that approximately functions as a derivate controller. Analysis using both analytical methods and Monte Carlo simulations reveals that this derivative controller effectively buffers output fluctuations from bursty stochastic expression, while maintaining the static input-output sensitivity of the open-loop system. In summary, this study provides a systematic stochastic analysis of biochemical controllers, and paves the way for their synthetic design and implementation to minimize deleterious fluctuations in gene product levels.

In the noisy cellular environment, biochemical species such as genes, RNAs and proteins that often occur at low molecular counts, are subject to considerable stochastic fluctuations in copy numbers over time. How cellular biochemical processes function reliably in the face of such randomness is an intriguing fundamental problem. Increasing evidence suggests that random fluctuations (noise) in protein copy numbers play important functional roles, such as driving genetically identical cells to different cell fates. Moreover, many disease states have been attributed to elevated noise levels in specific proteins. Here we systematically investigate design of biochemical systems that function as proportional, integral and derivative-based feedback controllers to suppress protein count fluctuations arising from bursty expression of the protein and external disturbance in protein synthesis. Our results show that different controllers are effective in buffering different noise components, and identify ranges of feedback gain for minimizing deleterious fluctuations in protein levels.

Computational methods for characterizing and learning from heterogeneous cell signaling data

Heterogeneity in cell signaling pathways is increasingly appreciated as a fundamental feature of cell biology and a driver of clinically relevant disease phenotypes. Understanding the causes of heterogeneity, the cellular mechanisms used to control heterogeneity, and the downstream effects of heterogeneity in single cells are all key obstacles for manipulating cellular populations and treating disease. Recent advances in genetic engineering, including multiplexed fluorescent reporters, have provided unprecedented measurements of signaling heterogeneity, but these vast data sets are often difficult to interpret, necessitating the use of computational techniques to extract meaning from the data. Here, we review recent advances in computational methods for extracting meaning from these novel data streams. In particular, we evaluate how machine learning methods related to dimensionality reduction and classification can identify structure in complex, dynamic datasets, simplifying interpretation. We also discuss how mechanistic models can be merged with heterogeneous data to understand the underlying differences between cells in a population. These methods are still being developed, but the work reviewed here offers useful applications of specific analysis techniques that could enable the translation of single-cell signaling data to actionable biological understanding.

Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations

The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise. We find that the solution of the chemical master equation-including static extrinsic noise-exactly agrees with the agent-based formulation when the network under study exhibits stochastic concentration homeostasis, a novel condition that generalizes concentration homeostasis in deterministic systems to higher order moments and distributions. We illustrate stochastic concentration homeostasis for a range of common gene expression networks. When this condition is not met, we demonstrate by extending the linear noise approximation to agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the chemical master equation. Surprisingly, the total noise of the agent-based approach can still be well approximated by extrinsic noise models.

Exponential trajectories, cell size fluctuations, and the adder property in bacteria follow from simple chemical dynamics and division control

Experiments on steady-state bacterial cultures have uncovered several quantitative regularities at the system level. These include, first, the exponential growth of cell size with time and the balanced growth of intracellular chemicals between cell birth and division, which are puzzling given the nonlinear and decentralized chemical dynamics in the cell. We model a cell as a set of chemical populations undergoing nonlinear mass action kinetics in a container whose volume is a linear function of the chemical populations. This turns out to be a special class of dynamical systems that generically has attractors in which all populations grow exponentially with time at the same rate. This explains exponential balanced growth of bacterial cells without invoking any regulatory mechanisms and suggests that this could be a robust property of protocells as well. Second, we consider the hypothesis that cells commit themselves to division when a certain internal chemical population reaches a threshold of N molecules. We show that this hypothesis leads to a simple explanation of some of the variability observed across cells in a bacterial culture. In particular, it reproduces the adder property of cell size fluctuations observed recently in E. coli; the observed correlations among interdivision time, birth volume, and added volume in a generation; and the observed scale of the fluctuations (CV ≈ 10-30%) when N is between 10 and 100. Third, upon including a suitable regulatory mechanism that optimizes the growth rate of the cell, the model reproduces the observed bacterial growth laws including the dependence of the growth rate and ribosomal protein fraction on the medium. Thus, the models provide a framework for unifying diverse aspects of bacterial growth physiology under one roof. They also suggest new questions for experimental and theoretical enquiry.

Antibiotic tolerance, persistence, and resistance of the evolved minimal cell, Mycoplasma mycoides JCVI-Syn3B

Antibiotic resistance is a growing problem, but bacteria can evade antibiotic treatment via tolerance and persistence. Antibiotic persisters are a small subpopulation of bacteria that tolerate antibiotics due to a physiologically dormant state. Hence, persistence is considered a major contributor to the evolution of antibiotic-resistant and relapsing infections. Here, we used the synthetically developed minimal cell Mycoplasma mycoides JCVI-Syn3B to examine essential mechanisms of antibiotic survival. The minimal cell contains only 473 genes, and most genes are essential. Its reduced complexity helps to reveal hidden phenomenon and fundamental biological principles can be explored because of less redundancy and feedback between systems compared to natural cells. We found that Syn3B evolves antibiotic resistance to different types of antibiotics expeditiously. The minimal cell also tolerates and persists against multiple antibiotics. It contains a few already identified persister-related genes, although lacking many systems previously linked to persistence (e.g. toxin-antitoxin systems, ribosome hibernation genes).

Thermodynamic uncertainty relation to assess biological processes

We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states and discuss how optimal these processes are in light of the universal bound set by the thermodynamic uncertainty relation (TUR). The values of the uncertainty product Q of TUR, which can be used as a measure of the precision of enzymatic processes realized for a given thermodynamic cost, are suboptimal when the substrate concentration is at the Michaelis constant, and some of the key biological processes are found to work around this condition. We illustrate the utility of Q in assessing how close the molecular motors and biomass producing machineries are to the TUR bound, and for the cases of biomass production (or biological copying processes), we discuss how their optimality quantified in terms of Q is balanced with the error rate in the information transfer process. We also touch upon the trade-offs in other error-minimizing processes in biology, such as gene regulation and chaperone-assisted protein folding. A spectrum of Q recapitulating the biological processes surveyed here provides glimpses into how biological systems are evolved to optimize and balance the conflicting functional requirements.

Molecular switch architecture determines response properties of signaling pathways

Many intracellular signaling pathways are composed of molecular switches, proteins that transition between two states-on and off Typically, signaling is initiated when an external stimulus activates its cognate receptor that, in turn, causes downstream switches to transition from off to on using one of the following mechanisms: activation, in which the transition rate from the off state to the on state increases; derepression, in which the transition rate from the on state to the off state decreases; and concerted, in which activation and derepression operate simultaneously. We use mathematical modeling to compare these signaling mechanisms in terms of their dose-response curves, response times, and abilities to process upstream fluctuations. Our analysis elucidates several operating principles for molecular switches. First, activation increases the sensitivity of the pathway, whereas derepression decreases sensitivity. Second, activation generates response times that decrease with signal strength, whereas derepression causes response times to increase with signal strength. These opposing features allow the concerted mechanism to not only show dose-response alignment, but also to decouple the response time from stimulus strength. However, these potentially beneficial properties come at the expense of increased susceptibility to upstream fluctuations. We demonstrate that these operating principles also hold when the models are extended to include additional features, such as receptor removal, kinetic proofreading, and cascades of switches. In total, we show how the architecture of molecular switches govern their response properties. We also discuss the biological implications of our findings.

The influence of methylation status on a stochastic model of MGMT dynamics in glioblastoma: Phenotypic selection can occur with and without a downshift in promoter methylation status

Glioblastoma originates in the brain and is one of the most aggressive cancer types. Glioblastoma represents 15% of all brain tumours, with a median survival of 15 months. Although the current standard of care for such a tumour (the Stupp protocol) has shown positive results for the prognosis of patients, O-6-methylguanine-DNA methyltransferase (MGMT) driven drug resistance has been an issue of increasing concern and hence requires innovative approaches. In addition to the well established drug resistance factors such as tumour location and blood brain barriers, it is also important to understand how the genetic and epigenetic dynamics of the glioblastoma cells can play a role. One important aspect of this is the study of methylation status of MGMT following administration of temozolomide. In this paper, we extend our previously published model that simulated MGMT expression in glioblastoma cells to incorporate the promoter methylation status of MGMT. This methylation status has clinical significance and is used as a marker for patient outcomes. Using this model, we investigate the causative relationship between temozolomide treatment and the methylation status of the MGMT promoter in a population of cells. In addition by constraining the model to relevant biological data using Approximate Bayesian Computation, we were able to identify parameter regimes that yield different possible modes of resistances, namely, phenotypic selection of MGMT, a downshift in the methylation status of the MGMT promoter or both simultaneously. We analysed each of the parameter sets associated with the different modes of resistance, presenting representative solutions as well as discovering some similarities between them as well as unique requirements for each of them. Finally, we used them to devise optimal strategies for inhibiting MGMT expression with the aim of minimising live glioblastoma cell numbers.

Disentangling Intrinsic and Extrinsic Gene Expression Noise in Growing Cells

Gene expression is a stochastic process. Despite the increase of protein numbers in growing cells, the protein concentrations are often found to be confined within small ranges throughout the cell cycle. Generally, the noise in protein concentration can be decomposed into an intrinsic and an extrinsic component, where the former vanishes for high expression levels. Considering the time trajectory of protein concentration as a random walker in the concentration space, an effective restoring force (with a corresponding "spring constant") must exist to prevent the divergence of concentration due to random fluctuations. In this work, we prove that the magnitude of the effective spring constant is directly related to the fraction of intrinsic noise in the total protein concentration noise. We show that one can infer the magnitude of intrinsic, extrinsic, and measurement noises of gene expression solely based on time-resolved data of protein concentration, without any a priori knowledge of the underlying gene expression dynamics. We apply this method to experimental data of single-cell bacterial gene expression. The results allow us to estimate the average copy numbers and the translation burst parameters of the studied proteins.

3 '-5 ' crosstalk contributes to transcriptional bursting

BACKGROUND

Transcription in mammalian cells is a complex stochastic process involving shuttling of polymerase between genes and phase-separated liquid condensates. It occurs in bursts, which results in vastly different numbers of an mRNA species in isogenic cell populations. Several factors contributing to transcriptional bursting have been identified, usually classified as intrinsic, in other words local to single genes, or extrinsic, relating to the macroscopic state of the cell. However, some possible contributors have not been explored yet. Here, we focus on processes at the 3 ' and 5 ' ends of a gene that enable reinitiation of transcription upon termination.

RESULTS

Using Bayesian methodology, we measure the transcriptional bursting in inducible transgenes, showing that perturbation of polymerase shuttling typically reduces burst size, increases burst frequency, and thus limits transcriptional noise. Analysis based on paired-end tag sequencing (PolII ChIA-PET) suggests that this effect is genome wide. The observed noise patterns are also reproduced by a generative model that captures major characteristics of the polymerase flux between the ends of a gene and a phase-separated compartment.

CONCLUSIONS

Interactions between the 3 ' and 5 ' ends of a gene, which facilitate polymerase recycling, are major contributors to transcriptional noise.

Mathematical Modeling of Plasticity and Heterogeneity in EMT

The epithelial-mesenchymal transition (EMT) and the corresponding reverse process, mesenchymal-epithelial transition (MET), are dynamic and reversible cellular programs orchestrated by many changes at both biochemical and morphological levels. A recent surge in identifying the molecular mechanisms underlying EMT/MET has led to the development of various mathematical models that have contributed to our improved understanding of dynamics at single-cell and population levels: (a) multi-stability-how many phenotypes can cells attain during an EMT/MET?, (b) reversibility/irreversibility-what time and/or concentration of an EMT inducer marks the "tipping point" when cells induced to undergo EMT cannot revert?, (c) symmetry in EMT/MET-do cells take the same path when reverting as they took during the induction of EMT?, and (d) non-cell autonomous mechanisms-how does a cell undergoing EMT alter the tendency of its neighbors to undergo EMT? These dynamical traits may facilitate a heterogenous response within a cell population undergoing EMT/MET. Here, we present a few examples of designing different mathematical models that can contribute to decoding EMT/MET dynamics.

Identifiability analysis for stochastic differential equation models in systems biology

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.

Asymmetry of nanoparticle inheritance upon cell division: Effect on the coefficient of variation

Several previous studies have shown that when a cell that has taken up nanoparticles divides, the nanoparticles are inherited by the two daughter cells in an asymmetrical fashion, with one daughter cell receiving more nanoparticles than the other. This interesting observation is typically demonstrated either indirectly using mathematical modelling of high-throughput experimental data or more directly by imaging individual cells as they divide. Here we suggest that measurements of the coefficient of variation (standard deviation over mean) of the number of nanoparticles per cell over the cell population is another means of assessing the degree of asymmetry. Using simulations of an evolving cell population, we show that the coefficient of variation is sensitive to the degree of asymmetry and note its characteristic evolution in time. As the coefficient of variation is readily measurable using high-throughput techniques, this should allow a more rapid experimental assessment of the degree of asymmetry.

Identification of Differential Gene Groups From Single-Cell Transcriptomes Using Network Entropy

A complex tissue contains a variety of cells with distinct molecular signatures. Single-cell RNA sequencing has characterized the transcriptomes of different cell types and enables researchers to discover the underlying mechanisms of cellular heterogeneity. A critical task in single-cell transcriptome studies is to uncover transcriptional differences among specific cell types. However, the intercellular transcriptional variation is usually confounded with high level of technical noise, which masks the important biological signals. Here, we propose a new computational method DiffGE for differential analysis, adopting network entropy to measure the expression dynamics of gene groups among different cell types and to identify the highly differential gene groups. To evaluate the effectiveness of our proposed method, DiffGE is applied to three independent single-cell RNA-seq datasets and to identify the highly dynamic gene groups that exhibit distinctive expression patterns in different cell types. We compare the results of our method with those of three widely applied algorithms. Further, the gene function analysis indicates that these detected differential gene groups are significantly related to cellular regulation processes. The results demonstrate the power of our method in evaluating the transcriptional dynamics and identifying highly differential gene groups among different cell types.

Modeling homeostasis mechanisms that set the target cell size

How organisms maintain cell size homeostasis is a long-standing problem that remains unresolved, especially in multicellular organisms. Recent experiments in diverse animal cell types demonstrate that within a cell population, cellular proliferation is low for small and large cells, but high at intermediate sizes. Here we use mathematical models to explore size-control strategies that drive such a non-monotonic profile resulting in the proliferation capacity being maximized at a target cell size. Our analysis reveals that most models of size control yield proliferation capacities that vary monotonically with cell size, and non-monotonicity requires two key mechanisms: (1) the growth rate decreases with increasing size for excessively large cells; and (2) cell division occurs as per the Adder model (division is triggered upon adding a fixed size from birth), or a Sizer-Adder combination. Consistent with theory, Jurkat T cell growth rates increase with size for small cells, but decrease with size for large cells. In summary, our models show that regulation of both growth and cell-division timing is necessary for size control in animal cells, and this joint mechanism leads to a target cell size where cellular proliferation capacity is maximized.

Extended Robust Boolean Network of Budding Yeast Cell Cycle

Background:

How to explore the dynamics of transition probabilities between phases of budding yeast cell cycle (BYCC) network based on the dynamics of protein activities that control this network? How to identify the robust structure of protein interactions of BYCC Boolean network (BN)? Budding yeast allows scientists to put experiments into effect in order to discover the intracellular cell cycle regulating structures which are well simulated by mathematical modeling.

Methods:

We extended an available deterministic BN of proteins responsible for the cell cycle to a Markov chain model containing apoptosis besides G1, S, G2, M, and stationary G1. Using genetic algorithm (GA), we estimated the kinetic parameters of the extended BN model so that the subsequent transition probabilities derived using Markov chain model of cell states as normal cell cycle becomes the maximum while the structure of chemical interactions of extended BN of cell cycle becomes more stable.

Results:

Using kinetic parameters optimized by GA, the probability of the subsequent transitions between cell cycle phases is maximized. The relative basin size of stationary G1 increased from 86% to 96.48% while the number of attractors decreased from 7 in the original model to 5 in the extended one. Hence, an increase in the robustness of the system has been achieved.

Conclusion:

The structure of interacting proteins in cell cycle network affects its robustness and probabilities of transitions between different cell cycle phases. Markov chain and BN are good approaches to study the stability and dynamics of the cell cycle network.

Sarcoplasmic Hypertrophy in Skeletal Muscle: A Scientific "Unicorn" or Resistance Training Adaptation?

Skeletal muscle fibers are multinucleated cells that contain mostly myofibrils suspended in an aqueous media termed the sarcoplasm. Select evidence suggests sarcoplasmic hypertrophy, or a disproportionate expansion of the sarcoplasm relative to myofibril protein accretion, coincides with muscle fiber or tissue growth during resistance training. There is also evidence to support other modes of hypertrophy occur during periods of resistance training including a proportional accretion of myofibril protein with fiber or tissue growth (i.e., conventional hypertrophy), or myofibril protein accretion preceding fiber or tissue growth (i.e., myofibril packing). In this review, we discuss methods that have been used to investigate these modes of hypertrophy. Particular attention is given to sarcoplasmic hypertrophy throughout. Thus, descriptions depicting this process as well as the broader implications of this phenomenon will be posited. Finally, we propose future human and rodent research that can further our understanding in this area of muscle physiology.

Epigenetic feedback and stochastic partitioning during cell division can drive resistance to EMT

Epithelial-mesenchymal transition (EMT) and its reverse process mesenchymal-epithelial transition (MET) are central to metastatic aggressiveness and therapy resistance in solid tumors. While molecular determinants of both processes have been extensively characterized, the heterogeneity in the response of tumor cells to EMT and MET inducers has come into focus recently, and has been implicated in the failure of anti-cancer therapies. Recent experimental studies have shown that some cells can undergo an irreversible EMT depending on the duration of exposure to EMT-inducing signals. While the irreversibility of MET, or equivalently, resistance to EMT, has not been studied in as much detail, evidence supporting such behavior is slowly emerging. Here, we identify two possible mechanisms that can underlie resistance of cells to undergo EMT: epigenetic feedback in ZEB1/GRHL2 feedback loop and stochastic partitioning of biomolecules during cell division. Identifying the ZEB1/GRHL2 axis as a key determinant of epithelial-mesenchymal plasticity across many cancer types, we use mechanistic mathematical models to show how GRHL2 can be involved in both the abovementioned processes, thus driving an irreversible MET. Our study highlights how an isogenic population may contain subpopulation with varying degrees of susceptibility or resistance to EMT, and proposes a next set of questions for detailed experimental studies characterizing the irreversibility of MET/resistance to EMT.

Effects of cell cycle variability on lineage and population measurements of messenger RNA abundance

Many models of gene expression do not explicitly incorporate a cell cycle description. Here, we derive a theory describing how messenger RNA (mRNA) fluctuations for constitutive and bursty gene expression are influenced by stochasticity in the duration of the cell cycle and the timing of DNA replication. Analytical expressions for the moments show that omitting cell cycle duration introduces an error in the predicted mean number of mRNAs that is a monotonically decreasing function of η, which is proportional to the ratio of the mean cell cycle duration and the mRNA lifetime. By contrast, the error in the variance of the mRNA distribution is highest for intermediate values of η consistent with genome-wide measurements in many organisms. Using eukaryotic cell data, we estimate the errors in the mean and variance to be at most 3% and 25%, respectively. Furthermore, we derive an accurate negative binomial mixture approximation to the mRNA distribution. This indicates that stochasticity in the cell cycle can introduce fluctuations in mRNA numbers that are similar to the effect of bursty transcription. Finally, we show that for real experimental data, disregarding cell cycle stochasticity can introduce errors in the inference of transcription rates larger than 10%.

Mixture distributions in a stochastic gene expression model with delayed feedback: a WKB approximation approach

Noise in gene expression can be substantively affected by the presence of production delay. Here we consider a mathematical model with bursty production of protein, a one-step production delay (the passage of which activates the protein), and feedback in the frequency of bursts. We specifically focus on examining the steady-state behaviour of the model in the slow-activation (i.e. large-delay) regime. Using a formal asymptotic approach, we derive an autonomous ordinary differential equation for the inactive protein that applies in the slow-activation regime. If the differential equation is monostable, the steady-state distribution of the inactive (active) protein is approximated by a single Gaussian (Poisson) mode located at the globally stable fixed point of the differential equation. If the differential equation is bistable (due to cooperative positive feedback), the steady-state distribution of the inactive (active) protein is approximated by a mixture of Gaussian (Poisson) modes located at the stable fixed points; the weights of the modes are determined from a WKB approximation to the stationary distribution. The asymptotic results are compared to numerical solutions of the chemical master equation.

Bacterial metabolic heterogeneity: origins and applications in engineering and infectious disease

Bacteria within an isoclonal population display significant heterogeneity in metabolism, even under tightly controlled environmental conditions. Metabolic heterogeneity enables influential functions not possible or measurable at the ensemble scale. Several molecular and cellular mechanisms are likely to give rise to metabolic heterogeneity including molecular noise in metabolic enzyme expression, positive feedback loops, and asymmetric partitioning of cellular components during cell division. Dissection of the mechanistic origins of metabolic heterogeneity has been enabled by recent developments in single-cell analytical tools. Finally, we provide a discussion of recent studies examining the importance of metabolic heterogeneity in applied settings such as infectious disease and metabolic engineering.

Enhancement of gene expression noise from transcription factor binding to genomic decoy sites

The genome contains several high-affinity non-functional binding sites for transcription factors (TFs) creating a hidden and unexplored layer of gene regulation. We investigate the role of such “decoy sites” in controlling noise (random fluctuations) in the level of a TF that is synthesized in stochastic bursts. Prior studies have assumed that decoy-bound TFs are protected from degradation, and in this case decoys function to buffer noise. Relaxing this assumption to consider arbitrary degradation rates for both bound/unbound TF states, we find rich noise behaviors. For low-affinity decoys, noise in the level of unbound TF always monotonically decreases to the Poisson limit with increasing decoy numbers. In contrast, for high-affinity decoys, noise levels first increase with increasing decoy numbers, before decreasing back to the Poisson limit. Interestingly, while protection of bound TFs from degradation slows the time-scale of fluctuations in the unbound TF levels, the decay of bound TFs leads to faster fluctuations and smaller noise propagation to downstream target proteins. In summary, our analysis reveals stochastic dynamics emerging from nonspecific binding of TFs and highlights the dual role of decoys as attenuators or amplifiers of gene expression noise depending on their binding affinity and stability of the bound TF.

Correlation between protein concentration and bacterial cell size can reveal mechanisms of gene expression

Classically, gene expression is modeled as a chemical process with reaction rates dependent on the concentration of the reactants (typically, DNA loci, plasmids, RNA, enzymes, etc). Other variables like cell size are in general ignored. Size dynamics can become an important variable due to the low number of many of these reactants, imperfectly symmetric cell partitioning and molecule segregation. In this work we measure the correlation between size and protein concentration by observing the gene expression of the RpOD gene from a low-copy plasmid in Escherichia coli during balanced growth in different media. A positive correlation was found, and we used it to examine possible models of cell size dynamics and plasmid replication. We implemented a previously developed model describing the full gene expression process including transcription, translation, loci replication, cell division and molecule segregation. By comparing with the observed correlation, we determine that the transcription rate must be proportional to the size times the number of plasmids. We discuss how fluctuations in plasmid segregation, due to the low copy number, can impose limits in this correlation.

Skeletal Muscle Protein Composition Adaptations to 10 Weeks of High-Load Resistance Training in Previously-Trained Males

While high-load resistance training increases muscle hypertrophy, the intramuscular protein responses to this form of training remains largely unknown. In the current study, recreationally resistance-trained college-aged males (N = 15; mean ± SD: 23 ± 3 years old, 6 ± 5 years training) performed full-body, low-volume, high-load [68–90% of one repetition maximum (1RM)] resistance training over 10 weeks. Back squat strength testing, body composition testing, and a vastus lateralis biopsy were performed before (PRE) and 72 h after the 10-week training program (POST). Fiber type-specific cross-sectional area (fCSA), myofibrillar protein concentrations, sarcoplasmic protein concentrations, myosin heavy chain and actin protein abundances, and muscle tissue percent fluid were analyzed. The abundances of individual sarcoplasmic proteins in 10 of the 15 participants were also assessed using proteomics. Significant increases (p < 0.05) in type II fCSA and back squat strength occurred with training, although whole-body fat-free mass paradoxically decreased (p = 0.026). No changes in sarcoplasmic protein concentrations or muscle tissue percent fluid were observed. Myosin heavy chain protein abundance trended downward (−2.9 ± 5.8%, p = 0.069) and actin protein abundance decreased (−3.2 ± 5.3%, p = 0.034) with training. Proteomics indicated only 13 sarcoplasmic proteins were altered with training (12 up-regulated, 1 down-regulated, p < 0.05). Bioinformatics indicated no signaling pathways were affected, and proteins involved with metabolism (e.g., ATP-PCr, glycolysis, TCA cycle, or beta-oxidation) were not affected. These data comprehensively describe intramuscular protein adaptations that occur following 10 weeks of high-load resistance training. Although previous data from our laboratory suggests high-volume resistance training enhances the ATP-PCr and glycolytic pathways, we observed different changes in metabolism-related proteins in the current study with high-load training.

Order Through Disorder: The Characteristic Variability of Systems

Randomness characterizes many processes in nature, and therefore its importance cannot be overstated. In the present study, we investigate examples of randomness found in various fields, to underlie its fundamental processes. The fields we address include physics, chemistry, biology (biological systems from genes to whole organs), medicine, and environmental science. Through the chosen examples, we explore the seemingly paradoxical nature of life and demonstrate that randomness is preferred under specific conditions. Furthermore, under certain conditions, promoting or making use of variability-associated parameters may be necessary for improving the function of processes and systems.

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterizing stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealizations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time-course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with Matlab^® implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community.

Exact solution of stochastic gene expression models with bursting, cell cycle and replication dynamics

The bulk of stochastic gene expression models in the literature do not have an explicit description of the age of a cell within a generation and hence they cannot capture events such as cell division and DNA replication. Instead, many models incorporate the cell cycle implicitly by assuming that dilution due to cell division can be described by an effective decay reaction with first-order kinetics. If it is further assumed that protein production occurs in bursts, then the stationary protein distribution is a negative binomial. Here we seek to understand how accurate these implicit models are when compared with more detailed models of stochastic gene expression. We derive the exact stationary solution of the chemical master equation describing bursty protein dynamics, binomial partitioning at mitosis, age-dependent transcription dynamics including replication, and random interdivision times sampled from Erlang or more general distributions; the solution is different for single lineage and population snapshot settings. We show that protein distributions are well approximated by the solution of implicit models (a negative binomial) when the mean number of mRNAs produced per cycle is low and the cell cycle length variability is large. When these conditions are not met, the distributions are either almost bimodal or else display very flat regions near the mode and cannot be described by implicit models. We also show that for genes with low transcription rates, the size of protein noise has a strong dependence on the replication time, it is almost independent of cell cycle variability for lineage measurements, and increases with cell cycle variability for population snapshot measurements. In contrast for large transcription rates, the size of protein noise is independent of replication time and increases with cell cycle variability for both lineage and population measurements.

Analytical distributions for detailed models of stochastic gene expression in eukaryotic cells

The stochasticity of gene expression presents significant challenges to the modeling of genetic networks. A two-state model describing promoter switching, transcription, and messenger RNA (mRNA) decay is the standard model of stochastic mRNA dynamics in eukaryotic cells. Here, we extend this model to include mRNA maturation, cell division, gene replication, dosage compensation, and growth-dependent transcription. We derive expressions for the time-dependent distributions of nascent mRNA and mature mRNA numbers, provided two assumptions hold: 1) nascent mRNA dynamics are much faster than those of mature mRNA; and 2) gene-inactivation events occur far more frequently than gene-activation events. We confirm that thousands of eukaryotic genes satisfy these assumptions by using data from yeast, mouse, and human cells. We use the expressions to perform a sensitivity analysis of the coefficient of variation of mRNA fluctuations averaged over the cell cycle, for a large number of genes in mouse embryonic stem cells, identifying degradation and gene-activation rates as the most sensitive parameters. Furthermore, it is shown that, despite the model's complexity, the time-dependent distributions predicted by our model are generally well approximated by the negative binomial distribution. Finally, we extend our model to include translation, protein decay, and auto-regulatory feedback, and derive expressions for the approximate time-dependent protein-number distributions, assuming slow protein decay. Our expressions enable us to study how complex biological processes contribute to the fluctuations of gene products in eukaryotic cells, as well as allowing a detailed quantitative comparison with experimental data via maximum-likelihood methods.

A mechanism for epithelial-mesenchymal heterogeneity in a population of cancer cells

Epithelial-mesenchymal heterogeneity implies that cells within the same tumor can exhibit different phenotypes-epithelial, mesenchymal, or one or more hybrid epithelial-mesenchymal phenotypes. This behavior has been reported across cancer types, both in vitro and in vivo, and implicated in multiple processes associated with metastatic aggressiveness including immune evasion, collective dissemination of tumor cells, and emergence of cancer cell subpopulations with stem cell-like properties. However, the ability of a population of cancer cells to generate, maintain, and propagate this heterogeneity has remained a mystifying feature. Here, we used a computational modeling approach to show that epithelial-mesenchymal heterogeneity can emerge from the noise in the partitioning of biomolecules (such as RNAs and proteins) among daughter cells during the division of a cancer cell. Our model captures the experimentally observed temporal changes in the fractions of different phenotypes in a population of murine prostate cancer cells, and describes the hysteresis in the population-level dynamics of epithelial-mesenchymal plasticity. The model is further able to predict how factors known to promote a hybrid epithelial-mesenchymal phenotype can alter the phenotypic composition of a population. Finally, we used the model to probe the implications of phenotypic heterogeneity and plasticity for different therapeutic regimens and found that co-targeting of epithelial and mesenchymal cells is likely to be the most effective strategy for restricting tumor growth. By connecting the dynamics of an intracellular circuit to the phenotypic composition of a population, our study serves as a first step towards understanding the generation and maintenance of non-genetic heterogeneity in a population of cancer cells, and towards the therapeutic targeting of phenotypic heterogeneity and plasticity in cancer cell populations.

Models of protein production along the cell cycle: An investigation of possible sources of noise

In this article, we quantitatively study, through stochastic models, the effects of several intracellular phenomena, such as cell volume growth, cell division, gene replication as well as fluctuations of available RNA polymerases and ribosomes. These phenomena are indeed rarely considered in classic models of protein production and no relative quantitative comparison among them has been performed. The parameters for a large and representative class of proteins are determined using experimental measures. The main important and surprising conclusion of our study is to show that despite the significant fluctuations of free RNA polymerases and free ribosomes, they bring little variability to protein production contrary to what has been previously proposed in the literature. After verifying the robustness of this quite counter-intuitive result, we discuss its possible origin from a theoretical view, and interpret it as the result of a mean-field effect.

Terminal Schwann cell and vacant site mediated synapse elimination at developing neuromuscular junctions

Synapses undergo transition from polyinnervation by multiple axons to single innervation a few weeks after birth. Synaptic activity of axons and interaxonal competition are thought to drive this developmental synapse elimination and tested as key parameters in quantitative models for further understanding. Recent studies of muscle synapses (endplates) show that there are also terminal Schwann cells (tSCs), glial cells associated with motor neurons and their functions, and vacant sites (or vacancies) devoid of tSCs and axons proposing tSCs as key effectors of synapse elimination. However, there is no quantitative model that considers roles of tSCs including vacancies. Here we develop a stochastic model of tSC and vacancy mediated synapse elimination. It employs their areas on individual endplates quantified by electron microscopy-based analyses assuming that vacancies form randomly and are taken over by adjacent axons or tSCs. The model reliably reproduced synapse elimination whereas equal or random probability models, similar to classical interaxonal competition models, did not. Furthermore, the model showed that synapse elimination is accelerated by enhanced synaptic activity of one axon and also by increased areas of vacancies and tSCs suggesting that the areas are important structural correlates of the rate of synapse elimination.

Predicting cancer cell invasion by single-cell physical phenotyping

The physical properties of cells are promising biomarkers for cancer diagnosis and prognosis. Here we determine the physical phenotypes that best distinguish human cancer cell lines, and their relationship to cell invasion. We use the high throughput, single-cell microfluidic method, quantitative deformability cytometry (q-DC), to measure six physical phenotypes including elastic modulus, cell fluidity, transit time, entry time, cell size, and maximum strain at rates of 102 cells per second. By training a k-nearest neighbor machine learning algorithm, we demonstrate that multiparameter analysis of physical phenotypes enhances the accuracy of classifying cancer cell lines compared to single parameters alone. We also discover a set of four physical phenotypes that predict invasion; using these four parameters, we generate the physical phenotype model of invasion by training a multiple linear regression model with experimental data from a set of human ovarian cancer cells that overexpress a panel of tumor suppressor microRNAs. We validate the model by predicting invasion based on measured physical phenotypes of breast and ovarian human cancer cell lines that are subject to genetic or pharmacologic perturbations. Taken together, our results highlight how physical phenotypes of single cells provide a biomarker to predict the invasion of cancer cells.