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

A generative benchmark for evaluating the performance of fluorescent cell image segmentation

Fluorescent cell imaging technology is fundamental in life science research, offering a rich source of image data crucial for understanding cell spatial positioning, differentiation, and decision-making mechanisms. As the volume of this data expands, precise image analysis becomes increasingly critical. Cell segmentation, a key analysis step, significantly influences quantitative analysis outcomes. However, selecting the most effective segmentation method is challenging, hindered by existing evaluation methods' inaccuracies, lack of graded evaluation, and narrow assessment scope. Addressing this, we developed a novel framework with two modules: StyleGAN2-based contour generation and Pix2PixHD-based image rendering, producing diverse, graded-density cell images. Using this dataset, we evaluated three leading cell segmentation methods: DeepCell, CellProfiler, and CellPose. Our comprehensive comparison revealed CellProfiler's superior accuracy in segmenting cytoplasm and nuclei. Our framework diversifies cell image data generation and systematically addresses evaluation challenges in cell segmentation technologies, establishing a solid foundation for advancing research and applications in cell image analysis.

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

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

A stochastic vs deterministic perspective on the timing of cellular events

Cells are the fundamental units of life, and like all life forms, they change over time. Changes in cell state are driven by molecular processes; of these many are initiated when molecule numbers reach and exceed specific thresholds, a characteristic that can be described as "digital cellular logic". Here we show how molecular and cellular noise profoundly influence the time to cross a critical threshold-the first-passage time-and map out scenarios in which stochastic dynamics result in shorter or longer average first-passage times compared to noise-less dynamics. We illustrate the dependence of the mean first-passage time on noise for a set of exemplar models of gene expression, auto-regulatory feedback control, and enzyme-mediated catalysis. Our theory provides intuitive insight into the origin of these effects and underscores two important insights: (i) deterministic predictions for cellular event timing can be highly inaccurate when molecule numbers are within the range known for many cells; (ii) molecular noise can significantly shift mean first-passage times, particularly within auto-regulatory genetic feedback circuits.

Advanced methods for gene network identification and noise decomposition from single-cell data

Central to analyzing noisy gene expression systems is solving the Chemical Master Equation (CME), which characterizes the probability evolution of the reacting species' copy numbers. Solving CMEs for high-dimensional systems suffers from the curse of dimensionality. Here, we propose a computational method for improved scalability through a divide-and-conquer strategy that optimally decomposes the whole system into a leader system and several conditionally independent follower subsystems. The CME is solved by combining Monte Carlo estimation for the leader system with stochastic filtering procedures for the follower subsystems. We demonstrate this method with high-dimensional numerical examples and apply it to identify a yeast transcription system at the single-cell resolution, leveraging mRNA time-course experimental data. The identification results enable an accurate examination of the heterogeneity in rate parameters among isogenic cells. To validate this result, we develop a noise decomposition technique exploiting time-course data but requiring no supplementary components, e.g., dual-reporters.

Feedback between stochastic gene networks and population dynamics enables cellular decision-making

Phenotypic selection occurs when genetically identical cells are subject to different reproductive abilities due to cellular noise. Such noise arises from fluctuations in reactions synthesizing proteins and plays a crucial role in how cells make decisions and respond to stress or drugs. We propose a general stochastic agent-based model for growing populations capturing the feedback between gene expression and cell division dynamics. We devise a finite state projection approach to analyze gene expression and division distributions and infer selection from single-cell data in mother machines and lineage trees. We use the theory to quantify selection in multi-stable gene expression networks and elucidate that the trade-off between phenotypic switching and selection enables robust decision-making essential for synthetic circuits and developmental lineage decisions. Using live-cell data, we demonstrate that combining theory and inference provides quantitative insights into bet-hedging-like response to DNA damage and adaptation during antibiotic exposure in Escherichia coli.

Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions

Many imaging techniques for biological systems-like fixation of cells coupled with fluorescence microscopy-provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

Chronic arsenic exposure induces malignant transformation of human HaCaT cells through both deterministic and stochastic changes in transcriptome expression

Biological processes are inherently stochastic, i.e., are partially driven by hard to predict random probabilistic processes. Carcinogenesis is driven both by stochastic and deterministic (predictable non-random) changes. However, very few studies systematically examine the contribution of stochastic events leading to cancer development. In differential gene expression studies, the established data analysis paradigms incentivize expression changes that are uniformly different across the experimental versus control groups, introducing preferential inclusion of deterministic changes at the expense of stochastic processes that might also play a crucial role in the process of carcinogenesis. In this study, we applied simple computational techniques to quantify: (i) The impact of chronic arsenic (iAs) exposure as well as passaging time on stochastic gene expression and (ii) Which genes were expressed deterministically and which were expressed stochastically at each of the three stages of cancer development. Using biological coefficient of variation as an empirical measure of stochasticity we demonstrate that chronic iAs exposure consistently suppressed passaging related stochastic gene expression at multiple time points tested, selecting for a homogenous cell population that undergo transformation. Employing multiple balanced removal of outlier data, we show that chronic iAs exposure induced deterministic and stochastic changes in the expression of unique set of genes, that populate largely unique biological pathways. Together, our data unequivocally demonstrate that both deterministic and stochastic changes in transcriptome-wide expression are critical in driving biological processes, pathways and networks towards clonal selection, carcinogenesis, and tumor heterogeneity.

Using steady-state formula to estimate time-dependent parameters of stochastic gene transcription models

When studying stochastic gene transcription, it is important to understand how system parameters are temporally modulated in response to varying environments. Experimentally, the dynamic distribution data of RNA copy numbers measured at multiple time points are often fitted to stochastic transcription models to estimate time-dependent parameters. However, current methods require determining which parameters are time-dependent, as well as their analytical formulas, before the optimal fit. In this study, we developed a method to estimate time-dependent parameters in a classical two-state model without prior assumptions regarding the system parameters. At each measured time point, the method fitted the dynamic distribution data using a steady-state distribution formula, in which the estimated constant parameters were approximated as time-dependent parameter values at the measured time point. The accuracy of this method can be guaranteed for RNA molecules with relatively high degradation rates and genes with relatively slow responses to induction. We quantify the accuracy of the method and implemented this method on two sets of dynamic distribution data from prokaryotic and eukaryotic cells, and revealed the temporal modulation of transcription burst size in response to environmental changes.

Quantifying and correcting bias in transcriptional parameter inference from single-cell data

The snapshot distribution of mRNA counts per cell can be measured using single-molecule fluorescence in situ hybridization or single-cell RNA sequencing. These distributions are often fit to the steady-state distribution of the two-state telegraph model to estimate the three transcriptional parameters for a gene of interest: mRNA synthesis rate, the switching on rate (the on state being the active transcriptional state), and the switching off rate. This model assumes no extrinsic noise, i.e., parameters do not vary between cells, and thus estimated parameters are to be understood as approximating the average values in a population. The accuracy of this approximation is currently unclear. Here, we develop a theory that explains the size and sign of estimation bias when inferring parameters from single-cell data using the standard telegraph model. We find specific bias signatures depending on the source of extrinsic noise (which parameter is most variable across cells) and the mode of transcriptional activity. If gene expression is not bursty then the population averages of all three parameters are overestimated if extrinsic noise is in the synthesis rate; underestimation occurs if extrinsic noise is in the switching on rate; both underestimation and overestimation can occur if extrinsic noise is in the switching off rate. We find that some estimated parameters tend to infinity as the size of extrinsic noise approaches a critical threshold. In contrast when gene expression is bursty, we find that in all cases the mean burst size (ratio of the synthesis rate to the switching off rate) is overestimated while the mean burst frequency (the switching on rate) is underestimated. We estimate the size of extrinsic noise from the covariance matrix of sequencing data and use this together with our theory to correct published estimates of transcriptional parameters for mammalian genes.

Phase separation reduces cell-to-cell variability of transcriptional bursting

Gene expression is a stochastic and noisy process often occurring in "bursts". Experiments have shown that the compartmentalization of proteins by liquid-liquid phase separation is conducive to reducing the noise of gene expression. Therefore, an important goal is to explore the role of bursts in phase separation noise reduction processes. We propose a coupled model that includes phase separation and a two-state gene expression process. Using the timescale separation method, we obtain approximate solutions for the expectation, variance, and noise strength of the dilute phase. We find that a higher burst frequency weakens the ability of noise reduction by phase separation, but as the burst size increases, this ability first increases and then decreases. This study provides a deeper understanding of phase separation to reduce noise in the stochastic gene expression with burst kinetics.

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.

Inferring stochastic rates from heterogeneous snapshots of particle positions

Many imaging techniques for biological systems - like fixation of cells coupled with fluorescence microscopy - provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

Poisson representation: a bridge between discrete and continuous models of stochastic gene regulatory networks

Stochastic gene expression dynamics can be modelled either discretely or continuously. Previous studies have shown that the mRNA or protein number distributions of some simple discrete and continuous gene expression models are related by Gardiner's Poisson representation. Here, we systematically investigate the Poisson representation in complex stochastic gene regulatory networks. We show that when the gene of interest is unregulated, the discrete and continuous descriptions of stochastic gene expression are always related by the Poisson representation, no matter how complex the model is. This generalizes the results obtained in Dattani & Barahona (Dattani & Barahona 2017 J. R. Soc. Interface 14, 20160833 (doi:10.1098/rsif.2016.0833)). In addition, using a simple counter-example, we find that the Poisson representation in general fails to link the two descriptions when the gene is regulated. However, for a general stochastic gene regulatory network, we demonstrate that the discrete and continuous models are approximately related by the Poisson representation in the limit of large protein numbers. These theoretical results are further applied to analytically solve many complex gene expression models whose exact distributions are previously unknown.

Stochastic modeling of the mRNA life process: A generalized master equation

The mRNA life cycle is a complex biochemical process, involving transcription initiation, elongation, termination, splicing, and degradation. Each of these molecular events is multistep and can create a memory. The effect of this molecular memory on gene expression is not clear, although there are many related yet scattered experimental reports. To address this important issue, we develop a general theoretical framework formulated as a master equation in the sense of queue theory, which can reduce to multiple previously studied gene models in limiting cases. This framework allows us to interpret experimental observations, extract kinetic parameters from experimental data, and identify how the mRNA kinetics vary under regulatory influences. Notably, it allows us to evaluate the influences of elongation processes on mature RNA distribution; e.g., we find that the non-exponential elongation time can induce the bimodal mRNA expression and there is an optimal elongation noise intensity such that the mature RNA noise achieves the lowest level. In a word, our framework can not only provide insight into complex mRNA life processes but also bridge a dialogue between theoretical studies and experimental data.

Uncovering the effect of RNA polymerase steric interactions on gene expression noise: Analytical distributions of nascent and mature RNA numbers

The telegraph model is the standard model of stochastic gene expression, which can be solved exactly to obtain the distribution of mature RNA numbers per cell. A modification of this model also leads to an analytical distribution of nascent RNA numbers. These solutions are routinely used for the analysis of single-cell data, including the inference of transcriptional parameters. However, these models neglect important mechanistic features of transcription elongation, such as the stochastic movement of RNA polymerases and their steric (excluded-volume) interactions. Here we construct a model of gene expression describing promoter switching between inactive and active states, binding of RNA polymerases in the active state, their stochastic movement including steric interactions along the gene, and their unbinding leading to a mature transcript that subsequently decays. We derive the steady-state distributions of the nascent and mature RNA numbers in two important limiting cases: constitutive expression and slow promoter switching. We show that RNA fluctuations are suppressed by steric interactions between RNA polymerases, and that this suppression can in some instances even lead to sub-Poissonian fluctuations; these effects are most pronounced for nascent RNA and less prominent for mature RNA, since the latter is not a direct sensor of transcription. We find a relationship between the parameters of our microscopic mechanistic model and those of the standard models that ensures excellent consistency in their prediction of the first and second RNA number moments over vast regions of parameter space, encompassing slow, intermediate, and rapid promoter switching, provided the RNA number distributions are Poissonian or super-Poissonian. Furthermore, we identify the limitations of inference from mature RNA data, specifically showing that it cannot differentiate between highly distinct RNA polymerase traffic patterns on a gene.

Single-cell transcriptional uncertainty landscape of cell differentiation

Background: Single-cell studies have demonstrated the presence of significant cell-to-cell heterogeneity in gene expression. Whether such heterogeneity is only a bystander or has a functional role in the cell differentiation process is still hotly debated. Methods: In this study, we quantified and followed single-cell transcriptional uncertainty - a measure of gene transcriptional stochasticity in single cells - in 10 cell differentiation systems of varying cell lineage progressions, from single to multi-branching trajectories, using the stochastic two-state gene transcription model. Results: By visualizing the transcriptional uncertainty as a landscape over a two-dimensional representation of the single-cell gene expression data, we observed universal features in the cell differentiation trajectories that include: (i) a peak in single-cell uncertainty during transition states, and in systems with bifurcating differentiation trajectories, each branching point represents a state of high transcriptional uncertainty; (ii) a positive correlation of transcriptional uncertainty with transcriptional burst size and frequency; (iii) an increase in RNA velocity preceding the increase in the cell transcriptional uncertainty. Conclusions: Our findings suggest a possible universal mechanism during the cell differentiation process, in which stem cells engage stochastic exploratory dynamics of gene expression at the start of the cell differentiation by increasing gene transcriptional bursts, and disengage such dynamics once cells have decided on a particular terminal cell identity. Notably, the peak of single-cell transcriptional uncertainty signifies the decision-making point in the cell differentiation process.

Stochastic switching of delayed feedback suppresses oscillations in genetic regulatory systems

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model where stochastic delays evolve by a continuous-time Markov chain, and between switching events, the system of interest evolves via a deterministic delay equation. Our main contribution is the calculation of an effective delay equation in the fast switching limit. This effective equation maintains the influence of all subsystem delays and cannot be replaced with a single effective delay. To illustrate the relevance of this calculation, we investigate a simple model of stochastically switching delayed feedback motivated by gene regulation. We show that sufficiently fast switching between two oscillatory subsystems can yield stable dynamics.

Analysis and design of single-cell experiments to harvest fluctuation information while rejecting measurement noise

Introduction: Despite continued technological improvements, measurement errors always reduce or distort the information that any real experiment can provide to quantify cellular dynamics. This problem is particularly serious for cell signaling studies to quantify heterogeneity in single-cell gene regulation, where important RNA and protein copy numbers are themselves subject to the inherently random fluctuations of biochemical reactions. Until now, it has not been clear how measurement noise should be managed in addition to other experiment design variables (e.g., sampling size, measurement times, or perturbation levels) to ensure that collected data will provide useful insights on signaling or gene expression mechanisms of interest. Methods: We propose a computational framework that takes explicit consideration of measurement errors to analyze single-cell observations, and we derive Fisher Information Matrix (FIM)-based criteria to quantify the information value of distorted experiments. Results and Discussion: We apply this framework to analyze multiple models in the context of simulated and experimental single-cell data for a reporter gene controlled by an HIV promoter. We show that the proposed approach quantitatively predicts how different types of measurement distortions affect the accuracy and precision of model identification, and we demonstrate that the effects of these distortions can be mitigated through explicit consideration during model inference. We conclude that this reformulation of the FIM could be used effectively to design single-cell experiments to optimally harvest fluctuation information while mitigating the effects of image distortion.

Theoretical investigation of functional responses of bio-molecular assembly networks

Cooperative protein-protein and protein-DNA interactions form programmable complex assemblies, often performing non-linear gene regulatory operations involved in signal transductions and cell fate determination. The apparent structure of those complex assemblies is very similar, but their functional response strongly depends on the topology of the protein-DNA interaction networks. Here, we demonstrate how the coordinated self-assembly creates gene regulatory network motifs that corroborate the existence of a precise functional response at the molecular level using thermodynamic and dynamic analyses. Our theoretical and Monte Carlo simulations show that a complex network of interactions can form a decision-making loop, such as feedback and feed-forward circuits, only by a few molecular mechanisms. We characterize each possible network of interactions by systematic variations of free energy parameters associated with the binding among biomolecules and DNA looping. We also find that the higher-order networks exhibit alternative steady states from the stochastic dynamics of each network. We capture this signature by calculating stochastic potentials and attributing their multi-stability features. We validate our findings against the Gal promoter system in yeast cells. Overall, we show that the network topology is vital in phenotype diversity in regulatory circuits.

Inference on autoregulation in gene expression with variance-to-mean ratio

Some genes can promote or repress their own expressions, which is called autoregulation. Although gene regulation is a central topic in biology, autoregulation is much less studied. In general, it is extremely difficult to determine the existence of autoregulation with direct biochemical approaches. Nevertheless, some papers have observed that certain types of autoregulations are linked to noise levels in gene expression. We generalize these results by two propositions on discrete-state continuous-time Markov chains. These two propositions form a simple but robust method to infer the existence of autoregulation from gene expression data. This method only needs to compare the mean and variance of the gene expression level. Compared to other methods for inferring autoregulation, our method only requires non-interventional one-time data, and does not need to estimate parameters. Besides, our method has few restrictions on the model. We apply this method to four groups of experimental data and find some genes that might have autoregulation. Some inferred autoregulations have been verified by experiments or other theoretical works.

Biophysical modeling with variational autoencoders for bimodal, single-cell RNA sequencing data

We motivate and present biVI, which combines the variational autoencoder framework of scVI with biophysically motivated, bivariate models for nascent and mature RNA distributions. While previous approaches to integrate bimodal data via the variational autoencoder framework ignore the causal relationship between measurements, biVI models the biophysical processes that give rise to observations. We demonstrate through simulated benchmarking that biVI captures cell type structure in a low-dimensional space and accurately recapitulates parameter values and copy number distributions. On biological data, biVI provides a scalable route for identifying the biophysical mechanisms underlying gene expression. This analytical approach outlines a generalizable strategy for treating multimodal datasets generated by high-throughput, single-cell genomic assays.

A Markovian arrival stream approach to stochastic gene expression in cells

We analyse a generalisation of the stochastic gene expression model studied recently in Fromion et al. (SIAM J Appl Math 73:195-211, 2013) and Robert (Probab Surv 16:277-332, 2019) that keeps track of the production of both mRNA and protein molecules, using techniques from the theory of point processes, as well as ideas from the theory of matrix-analytic methods. Here, both the activity of a gene and the creation of mRNA are modelled with an arbitrary Markovian Arrival Process governed by finitely many phases, and each mRNA molecule during its lifetime gives rise to protein molecules in accordance with a Poisson process. This modification is important, as Markovian Arrival Processes can be used to approximate many types of point processes on the nonnegative real line, meaning this framework allows us to further relax our assumptions on the overall process of transcription.

Using Fano factors to determine certain types of gene autoregulation

The expression of one gene might be regulated by its corresponding protein, which is called autoregulation. Although gene regulation is a central topic in biology, autoregulation is much less studied. In general, it is extremely difficult to determine the existence of autoregulation with direct biochemical approaches. Nevertheless, some papers have observed that certain types of autoregulations are linked to noise levels in gene expression. We generalize these results by two propositions on discrete-state continuous-time Markov chains. These two propositions form a simple but robust method to infer the existence of autoregulation in certain scenarios from gene expression data. This method only depends on the Fano factor, namely the ratio of variance and mean of the gene expression level. Compared to other methods for inferring autoregulation, our method only requires non-interventional one-time data, and does not need to estimate parameters. Besides, our method has few restrictions on the model. We apply this method to four groups of experimental data and find some genes that might have autoregulation. Some inferred autoregulations have been verified by experiments or other theoretical works.

Leveraging transcriptomics for precision diagnosis: Lessons learned from cancer and sepsis

Diagnostics require precision and predictive ability to be clinically useful. Integration of multi-omic with clinical data is crucial to our understanding of disease pathogenesis and diagnosis. However, interpretation of overwhelming amounts of information at the individual level requires sophisticated computational tools for extraction of clinically meaningful outputs. Moreover, evolution of technical and analytical methods often outpaces standardisation strategies. RNA is the most dynamic component of all -omics technologies carrying an abundance of regulatory information that is least harnessed for use in clinical diagnostics. Gene expression-based tests capture genetic and non-genetic heterogeneity and have been implemented in certain diseases. For example patients with early breast cancer are spared toxic unnecessary treatments with scores based on the expression of a set of genes (e.g., Oncotype DX). The ability of transcriptomics to portray the transcriptional status at a moment in time has also been used in diagnosis of dynamic diseases such as sepsis. Gene expression profiles identify endotypes in sepsis patients with prognostic value and a potential to discriminate between viral and bacterial infection. The application of transcriptomics for patient stratification in clinical environments and clinical trials thus holds promise. In this review, we discuss the current clinical application in the fields of cancer and infection. We use these paradigms to highlight the impediments in identifying useful diagnostic and prognostic biomarkers and propose approaches to overcome them and aid efforts towards clinical implementation.

The effect of microRNA on protein variability and gene expression fidelity

Small regulatory RNA molecules such as microRNA modulate gene expression through inhibiting the translation of messenger RNA (mRNA). Such posttranscriptional regulation has been recently hypothesized to reduce the stochastic variability of gene expression around average levels. Here, we quantify noise in stochastic gene expression models with and without such regulation. Our results suggest that silencing mRNA posttranscriptionally will always increase, rather than decrease, gene expression noise when the silencing of mRNA also increases its degradation, as is expected for microRNA interactions with mRNA. In that regime, we also find that silencing mRNA generally reduces the fidelity of signal transmission from deterministically varying upstream factors to protein levels. These findings suggest that microRNA binding to mRNA does not generically confer precision to protein expression.

Gene expression model inference from snapshot RNA data using Bayesian non-parametrics

Gene expression models, which are key towards understanding cellular regulatory response, underlie observations of single-cell transcriptional dynamics. Although RNA expression data encode information on gene expression models, existing computational frameworks do not perform simultaneous Bayesian inference of gene expression models and parameters from such data. Rather, gene expression models-composed of gene states, their connectivities and associated parameters-are currently deduced by pre-specifying gene state numbers and connectivity before learning associated rate parameters. Here we propose a method to learn full distributions over gene states, state connectivities and associated rate parameters, simultaneously and self-consistently from single-molecule RNA counts. We propagate noise from fluctuating RNA counts over models by treating models themselves as random variables. We achieve this within a Bayesian non-parametric paradigm. We demonstrate our method on the Escherichia coli lacZ pathway and the Saccharomyces cerevisiae STL1 pathway, and verify its robustness on synthetic data.

A dynamical stochastic model of yeast translation across the cell cycle

Translation is a central step in gene expression, however its quantitative and time-resolved regulation is poorly understood. We developed a discrete, stochastic model for protein translation in S. cerevisiae in a whole-transcriptome, single-cell context. A "base case" scenario representing an average cell highlights translation initiation rates as the main co-translational regulatory parameters. Codon usage bias emerges as a secondary regulatory mechanism through ribosome stalling. Demand for anticodons with low abundancy is shown to cause above-average ribosome dwelling times. Codon usage bias correlates strongly both with protein synthesis rates and elongation rates. Applying the model to a time-resolved transcriptome estimated by combining data from FISH and RNA-Seq experiments, it could be shown that increased total transcript abundance during the cell cycle decreases translation efficiency at single transcript level. Translation efficiency grouped by gene function shows highest values for ribosomal and glycolytic genes. Ribosomal proteins peak in S phase while glycolytic proteins rank highest in later cell cycle phases.

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.

Genome-wide inference reveals that feedback regulations constrain promoter-dependent transcriptional burst kinetics

Gene expression in mammalian cells is highly variable and episodic, resulting in a series of discontinuous bursts of mRNAs. A challenge is to understand how static promoter architecture and dynamic feedback regulations dictate bursting on a genome-wide scale. Although single-cell RNA sequencing (scRNA-seq) provides an opportunity to address this challenge, effective analytical methods are scarce. We developed an interpretable and scalable inference framework, which combined experimental data with a mechanistic model to infer transcriptional burst kinetics (sizes and frequencies) and feedback regulations. Applying this framework to scRNA-seq data generated from embryonic mouse fibroblast cells, we found Simpson's paradoxes, i.e. genome-wide burst kinetics exhibit different characteristics in two cases without and with distinguishing feedback regulations. We also showed that feedbacks differently modulate burst frequencies and sizes and conceal the effects of transcription start site distributions on burst kinetics. Notably, only in the presence of positive feedback, TATA genes are expressed with high burst frequencies and enhancer-promoter interactions mainly modulate burst frequencies. The developed inference method provided a flexible and efficient way to investigate transcriptional burst kinetics and the obtained results would be helpful for understanding cell development and fate decision.

Interplay of Cellular mRNA, miRNA and Viral miRNA during Infection of a Cell

The understanding of the kinetics of gene expression in cells infected by viruses is currently limited. As a rule, the corresponding models do not take viral microRNAs (miRNAs) into account. Such RNAs are, however, operative during the replication of some viruses, including, e.g., herpesvirus. To clarify the kinetics of this category (with emphasis on the information available for herpesvirus), I introduce a generic model describing the transient interplay of cellular mRNA, protein, miRNA and viral miRNA. In the absence of viral miRNA, the cellular miRNA is considered to suppress the populations of mRNA and protein due to association with mRNA and subsequent degradation. During infection, the viral miRNA suppresses the population of cellular miRNA and via this pathway makes the mRNA and protein populations larger. This effect becomes appreciable with the progress of intracellular viral replication. Using biologically reasonable parameters, I investigate the corresponding mean-field kinetics and show the scale of the effect of viral miRNAs on cellular miRNA and mRNA. The scale of fluctuations of the populations of these species is illustrated as well by employing Monte Carlo simulations.

Interpretable and tractable models of transcriptional noise for the rational design of single-molecule quantification experiments

The question of how cell-to-cell differences in transcription rate affect RNA count distributions is fundamental for understanding biological processes underlying transcription. Answering this question requires quantitative models that are both interpretable (describing concrete biophysical phenomena) and tractable (amenable to mathematical analysis). This enables the identification of experiments which best discriminate between competing hypotheses. As a proof of principle, we introduce a simple but flexible class of models involving a continuous stochastic transcription rate driving a discrete RNA transcription and splicing process, and compare and contrast two biologically plausible hypotheses about transcription rate variation. One assumes variation is due to DNA experiencing mechanical strain, while the other assumes it is due to regulator number fluctuations. We introduce a framework for numerically and analytically studying such models, and apply Bayesian model selection to identify candidate genes that show signatures of each model in single-cell transcriptomic data from mouse glutamatergic neurons.

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.

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.

RNA velocity unraveled

We perform a thorough analysis of RNA velocity methods, with a view towards understanding the suitability of the various assumptions underlying popular implementations. In addition to providing a self-contained exposition of the underlying mathematics, we undertake simulations and perform controlled experiments on biological datasets to assess workflow sensitivity to parameter choices and underlying biology. Finally, we argue for a more rigorous approach to RNA velocity, and present a framework for Markovian analysis that points to directions for improvement and mitigation of current problems.

Single-cell sequencing data are snapshots of biological processes, making it challenging to infer dynamic relationships between cell types. RNA velocity attempts to bypass this challenge by treating the unspliced RNA content as a proxy for spliced RNA content in the near future, and using this “extrapolation” to build directional relationships. However, the method, as implemented in several software packages, is not yet reliable enough to be actionable, in part due to the large number of arbitrary, user-set hyperparameters, as well as fundamental incompatibilities between the biophysics of transcription in the living cell and the models used throughout the velocity workflows. In this study, we review these issues, and use existing results from the fields of stochastic modeling and fluorescence transcriptomics to develop an alternative theoretical framework. We show that our framework can facilitate the development and inference of physically consistent models for sequencing data, as well as the unification of single-cell analyses to self-consistently treat variation due to cell type dynamics and identities, the stochasticity inherent to single-molecule processes, and the uncertainty introduced by sequencing experiments.

Inference and uncertainty quantification of stochastic gene expression via synthetic models

Estimating uncertainty in model predictions is a central task in quantitative biology. Biological models at the single-cell level are intrinsically stochastic and nonlinear, creating formidable challenges for their statistical estimation which inevitably has to rely on approximations that trade accuracy for tractability. Despite intensive interest, a sweet spot in this trade-off has not been found yet. We propose a flexible procedure for uncertainty quantification in a wide class of reaction networks describing stochastic gene expression including those with feedback. The method is based on creating a tractable coarse-graining of the model that is learned from simulations, a synthetic model, to approximate the likelihood function. We demonstrate that synthetic models can substantially outperform state-of-the-art approaches on a number of non-trivial systems and datasets, yielding an accurate and computationally viable solution to uncertainty quantification in stochastic models of gene expression.

Data-based stochastic modeling reveals sources of activity bursts in single-cell TGF-β signaling

Cells sense their surrounding by employing intracellular signaling pathways that transmit hormonal signals from the cell membrane to the nucleus. TGF-β/SMAD signaling encodes various cell fates, controls tissue homeostasis and is deregulated in diseases such as cancer. The pathway shows strong heterogeneity at the single-cell level, but quantitative insights into mechanisms underlying fluctuations at various time scales are still missing, partly due to inefficiency in the calibration of stochastic models that mechanistically describe signaling processes. In this work we analyze single-cell TGF-β/SMAD signaling and show that it exhibits temporal stochastic bursts which are dose-dependent and whose number and magnitude correlate with cell migration. We propose a stochastic modeling approach to mechanistically describe these pathway fluctuations with high computational efficiency. Employing high-order numerical integration and fitting to burst statistics we enable efficient quantitative parameter estimation and discriminate models that assume noise in different reactions at the receptor level. This modeling approach suggests that stochasticity in the internalization of TGF-β receptors into endosomes plays a key role in the observed temporal bursting. Further, the model predicts the single-cell dynamics of TGF-β/SMAD signaling in untested conditions, e.g., successfully reflects memory effects of signaling noise and cellular sensitivity towards repeated stimulation. Taken together, our computational framework based on burst analysis, noise modeling and path computation scheme is a suitable tool for the data-based modeling of complex signaling pathways, capable of identifying the source of temporal noise.

Fluctuations in molecular networks give rise to heterogeneity in cellular behavior and therefore promote the diversification of tissues. For a better understanding of cellular decision making, it is important to identify sources of molecular fluctuations and to quantitatively describe them by predictive mathematical models. In this work, we focused on temporal fluctuations of the TGF-β signaling pathway that is important for controlling cell division and migration.

We characterized a single-cell dataset comprising hundreds of cells using time series analysis and a large-scale stochastic model. By fitting several model variants to the data, we identified the stochastic internalization of cell surface receptors into endosomes as a main source of temporal fluctuations (’bursts’) in the signaling pathway. The corresponding model accurately predicted novel experimental data, and provided insights into the long-term memory of signaling fluctuations. In summary, we propose a modeling approach to quantitatively describe heterogeneous behavior in large-scale single-cell datasets and to identify the underlying biological mechanisms.

Stochastic Transcription with Alterable Synthesis Rates

Background: Gene transcription is a random bursting process that leads to large variability in mRNA numbers in single cells. The main cause is largely attributed to random switching between periods of active and inactive gene transcription. In some experiments, it has been observed that variation in the number of active transcription sites causes the initiation rate to vary during elongation. Results: We established a mathematical model based on the molecular reaction mechanism in single cells and studied a stochastic transcription system consisting of two active states and one inactive state, in which mRNA molecules are produced with two different synthesis rates. Conclusions: By calculation, we obtained the average mRNA expression level, the noise strength, and the skewness of transcripts. We gave a necessary and sufficient condition that causes the average mRNA level to peak at a limited time. The model could help us to distinguish an appropriate mechanism that may be employed by cells to transcribe mRNA molecules. Our simulations were in agreement with some experimental data and showed that the skewness can measure the deviation of the distribution of transcripts from the mean value. Especially for mature mRNAs, their distributions were almost able to be determined by the mean, the noise (or the noise strength), and the skewness.

Quantifying biochemical reaction rates from static population variability within incompletely observed complex networks

Quantifying biochemical reaction rates within complex cellular processes remains a key challenge of systems biology even as high-throughput single-cell data have become available to characterize snapshots of population variability. That is because complex systems with stochastic and non-linear interactions are difficult to analyze when not all components can be observed simultaneously and systems cannot be followed over time. Instead of using descriptive statistical models, we show that incompletely specified mechanistic models can be used to translate qualitative knowledge of interactions into reaction rate functions from covariability data between pairs of components. This promises to turn a globally intractable problem into a sequence of solvable inference problems to quantify complex interaction networks from incomplete snapshots of their stochastic fluctuations.

Learning of Iterative Learning Control for Flexible Manufacturing of Batch Processes

Flexible manufacturing as an essential component of smart manufacturing implements the customized production mode, thereby requesting fast controller adaptation for producing different goods but still with high precision. This problem becomes even more acute for batch processes. Here we present a solution called learning of iterative learning control (ILC) based on neural networks. It is able to recommend control parameters for ILC controllers accordingly, so as to yield fast tracking error convergence and smaller steady-state error for disparate set-point profiles, which is deemed an abstraction of different production needs. The method substantially outperforms a benchmark ILC on a variety of systems and cases, thereby showing its potential for deployment in the industrial Internet of Things.

Equivalence framework for an age-structured multistage representation of the cell cycle

We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an age-structured multistage Markov process for approximating cell cycle time distributions. We further demonstrate that the resulting mean behavior is equivalent, over large timescales, to the classical McKendrick-von Foerster integropartial differential equation. We conclude by extending this framework to a spatial context, facilitating the modeling of traveling wave phenomena and cell-mediated pattern formation. More generally, this methodology may be extended to myriad reaction-diffusion processes for which the age of individuals is relevant to the dynamics.

A Novel Dynamical Regulation of mRNA Distribution by Cross-Talking Pathways

In this paper, we use a similar approach to the one proposed by Chen and Jiao to calculate the mathematical formulas of the generating function V(z,t) and the mass function Pm(t) of a cross-talking pathways model in large parameter regions. Together with kinetic rates from yeast and mouse genes, our numerical examples reveal novel bimodal mRNA distributions for intermediate times, whereby the mode of distribution Pm(t) displays unimodality with the peak at m=0 for initial and long times, which has not been obtained in previous works. Such regulation of mRNA distribution exactly matches the transcriptional dynamics for the osmosensitive genes in Saccharomyces cerevisiae, which has not been generated by those models with one single pathway or feedback loops. This paper may provide us with a novel observation on transcriptional distribution dynamics regulated by multiple signaling pathways in response to environmental changes and genetic perturbations.

Quantification of transcription noise’s impact on cell fate commitment with digital resolutions

Motivation

Gene transcription is a random and noisy process. Tremendous efforts in single cell studies have been mapping transcription noises to phenotypic variabilities between isogenic cells. However, the exact role of the noise in cell fate commitment remains largely descriptive or even controversial.

Results

For a specified cell fate, we define the jumping digit I of a critical gene as a statistical threshold that a single cell has approximately an equal chance to commit the fate as to have at least I transcripts of the gene. When the transcription is perturbed by a noise enhancer without changing the basal transcription level E  0, we find a crossing digit k such that the noise catalyzes cell fate change when I > k while stabilizes the current state when I < k; k remains stable against enormous variations of kinetic rates. We further test the reactivation of latent HIV in 22 integration sites by noise enhancers paired with transcriptional activators. Strong synergistic actions are observed when the activators increase transcription burst frequency, whereas no synergism, but antagonism, is often observed if activators increase burst size. The synergistic efficiency can be predicted accurately by the ratio I / E0. When the noise enhancers double the noise, the activators double the burst frequency, and I / E0 ≥ 7, their combination is 10 times more effective than their additive effects across all 22 sites.

Availability and implementation

The jumping digit I may provide a novel probe to explore the phenotypic consequences of transcription noise in cell functions. Code is freely available at http://cam.gzhu.edu.cn/info/1014/1223.htm.

Supplementary information

Supplementary data are available at Bioinformatics online.

Systematic inference identifies a major source of heterogeneity in cell signaling dynamics: The rate-limiting step number

Identifying the sources of cell-to-cell variability in signaling dynamics is essential to understand drug response variability and develop effective therapeutics. However, it is challenging because not all signaling intermediate reactions can be experimentally measured simultaneously. This can be overcome by replacing them with a single random time delay, but the resulting process is non-Markovian, making it difficult to infer cell-to-cell heterogeneity in reaction rates and time delays. To address this, we developed an efficient and scalable moment-based Bayesian inference method (MBI) with a user-friendly computational package that infers cell-to-cell heterogeneity in the non-Markovian signaling process. We applied MBI to single-cell expression profiles from promoters responding to antibiotics and discovered a major source of cell-to-cell variability in antibiotic stress response: the number of rate-limiting steps in signaling cascades. This knowledge can help identify effective therapies that destroy all pathogenic or cancer cells, and the approach can be applied to precision medicine.

Modeling bursty transcription and splicing with the chemical master equation

Splicing cascades that alter gene products posttranscriptionally also affect expression dynamics. We study a class of processes and associated distributions that emerge from models of bursty promoters coupled to directed acyclic graphs of splicing. These solutions provide full time-dependent joint distributions for an arbitrary number of species with general noise behaviors and transient phenomena, offering qualitative and quantitative insights about how splicing can regulate expression dynamics. Finally, we derive a set of quantitative constraints on the minimum complexity necessary to reproduce gene coexpression patterns using synchronized burst models. We validate these findings by analyzing long-read sequencing data, where we find evidence of expression patterns largely consistent with these constraints.

Lentiviral Nef Proteins Differentially Govern the Establishment of Viral Latency

Despite the clinical importance of latent human immunodeficiency virus type 1 (HIV-1) infection, our understanding of the biomolecular processes involved in HIV-1 latency control is still limited. This study was designed to address whether interactions between viral proteins, specifically HIV Nef, and the host cell could affect latency establishment. The study was driven by three reported observations. First, early reports suggested that human immunodeficiency virus type 2 (HIV-2) infection in patients produces a lower viral RNA/DNA ratio than HIV-1 infection, potentially indicating an increased propensity of HIV-2 to produce latent infection. Second, Nef, an early viral gene product, has been shown to alter the activation state of infected cells in a lentiviral lineage-dependent manner. Third, it has been demonstrated that the ability of HIV-1 to establish latent infection is a function of the activation state of the host cell at the time of infection. Based on these observations, we reasoned that HIV-2 Nef may have the ability to promote latency establishment. We demonstrate that HIV-1 latency establishment in T cell lines and primary T cells is indeed differentially modulated by Nef proteins. In the context of an HIV-1 backbone, HIV-1 Nef promoted active HIV-1 infection, while HIV-2 Nef strongly promoted latency establishment. Given that Nef represents the only difference in these HIV-1 vectors and is known to interact with numerous cellular factors, these data add support to the idea that latency establishment is a host cell-virus interaction phenomenon, but they also suggest that the HIV-1 lineage may have evolved mechanisms to counteract host cell suppression. IMPORTANCE Therapeutic attempts to eliminate the latent HIV-1 reservoir have failed, at least in part due to our incomplete biomolecular understanding of how latent HIV-1 infection is established and maintained. We here address the fundamental question of whether all lentiviruses actually possess a similar capacity to establish latent infections or whether there are differences between the lentiviral lineages driving differential latency establishment that could be exploited to develop improved latency reversal agents. Research investigating the viral RNA/DNA ratio in HIV-1 and HIV-2 patients could suggest that HIV-2 indeed has a much higher propensity to establish latent infections, a trait that we found, at least in part, to be attributable to the HIV-2 Nef protein. Reported Nef-mediated effects on host cell activation thus also affect latency establishment, and HIV-1 vectors that carry different lentiviral nef genes should become key tools to develop a better understanding of the biomolecular basis of HIV-1 latency establishment.

Using average transcription level to understand the regulation of stochastic gene activation

Gene activation is a random process, modelled as a framework of multiple rate-limiting steps listed sequentially, in parallel or in combination. Together with suitably assumed processes of gene inactivation, transcript birth and death, the step numbers and parameters in activation frameworks can be estimated by fitting single-cell transcription data. However, current algorithms require computing master equations that are tightly correlated with prior hypothetical frameworks of gene activation. We found that prior estimation of the framework can be facilitated by the traditional dynamical data of mRNA average level M(t), presenting discriminated dynamical features. Rigorous theory regarding M(t) profiles allows to confidently rule out the frameworks that fail to capture M(t) features and to test potential competent frameworks by fitting M(t) data. We implemented this procedure for a large number of mouse fibroblast genes under tumour necrosis factor induction and determined exactly the 'cross-talking n-state' framework; the cross-talk between the signalling and basal pathways is crucial to trigger the first peak of M(t), while the following damped gentle M(t) oscillation is regulated by the multi-step basal pathway. This framework can be used to fit sophisticated single-cell data and may facilitate a more accurate understanding of stochastic activation of mouse fibroblast genes.

The correlation between cell and nucleus size is explained by an eukaryotic cell growth model

In eukaryotes, the cell volume is observed to be strongly correlated with the nuclear volume. The slope of this correlation depends on the cell type, growth condition, and the physical environment of the cell. We develop a computational model of cell growth and proteome increase, incorporating the kinetics of amino acid import, protein/ribosome synthesis and degradation, and active transport of proteins between the cytoplasm and the nucleoplasm. We also include a simple model of ribosome biogenesis and assembly. Results show that the cell volume is tightly correlated with the nuclear volume, and the cytoplasm-nucleoplasm transport rates strongly influence the cell growth rate as well as the cell/nucleus volume ratio (C/N ratio). Ribosome assembly and the ratio of ribosomal proteins to mature ribosomes also influence the cell volume and the cell growth rate. We find that in order to regulate the cell growth rate and the cell/nucleus volume ratio, the cell must optimally control groups of kinetic and transport parameters together, which could explain the quantitative roles of canonical growth pathways. Finally, although not explicitly demonstrated in this work, we point out that it is possible to construct a detailed proteome distribution using our model and RNAseq data, provided that a quantitative cell division mechanism is known.