Measurement and modeling of transcriptional noise in the cell cycle regulatory network

Expression Dynamics and Genetic Compensation of Cell Cycle Paralogues in Saccharomyces cerevisiae

Cell cycle progression of the yeast Saccharomyces cerevisiae is largely driven by the expression of cyclins, which in turn bind the cyclin-dependent kinase CDK1 providing specificity. Due to the duplication of the yeast genome during evolution, most of the cyclins are present as a pair of paralogues, which are considered to have similar functions and periods of expression. Here, we use single molecule inexpensive fluorescence in situ hybridization (smiFISH) to measure the expression of five pairs of paralogous genes relevant for cell cycle progression (CLN1/CLN2, CLB5/CLB6, CLB3/CLB4, CLB1/CLB2 and ACE2/SWI5) in a large number of unsynchronized single cells representing all cell cycle phases. We systematically compare their expression patterns and strengths. In addition, we also analyze the effect of the knockout of one part of each pair on the expression of the other gene. In order to classify cells into specific cell cycle phases, we developed a convolutional neural network (CNN). We find that the expression levels of some cell-cycle related paralogues differ in their correlation, with CLN1 and CLN2 showing strong correlation and CLB3 and CLB4 showing weakest correlation. The temporal profiles of some pairs also differ. Upon deletion of their paralogue, CLB1 and CLB2 seem to compensate for the expression of the other gene, while this was not observed for ACE2/SWI5. Interestingly, CLB1 and CLB2 also seem to share work between mother and bud in the G2 phase, where CLB2 is primarily expressed in the bud and CLB1 in the mother. Taken together, our results suggest that paralogues related to yeast cell cycle progression should not be considered as the same but differ both in their expression strength and timing as well in their precise role in cell cycle regulation.

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

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

Genetic interactions derived from high-throughput phenotyping of 6589 yeast cell cycle mutants

Over the last 30 years, computational biologists have developed increasingly realistic mathematical models of the regulatory networks controlling the division of eukaryotic cells. These models capture data resulting from two complementary experimental approaches: low-throughput experiments aimed at extensively characterizing the functions of small numbers of genes, and large-scale genetic interaction screens that provide a systems-level perspective on the cell division process. The former is insufficient to capture the interconnectivity of the genetic control network, while the latter is fraught with irreproducibility issues. Here, we describe a hybrid approach in which the 630 genetic interactions between 36 cell-cycle genes are quantitatively estimated by high-throughput phenotyping with an unprecedented number of biological replicates. Using this approach, we identify a subset of high-confidence genetic interactions, which we use to refine a previously published mathematical model of the cell cycle. We also present a quantitative dataset of the growth rate of these mutants under six different media conditions in order to inform future cell cycle models.

Clb3-centered regulations are recurrent across distinct parameter regions in minimal autonomous cell cycle oscillator designs

Some biological networks exhibit oscillations in their components to convert stimuli to time-dependent responses. The eukaryotic cell cycle is such a case, being governed by waves of cyclin-dependent kinase (cyclin/Cdk) activities that rise and fall with specific timing and guarantee its timely occurrence. Disruption of cyclin/Cdk oscillations could result in dysfunction through reduced cell division. Therefore, it is of interest to capture properties of network designs that exhibit robust oscillations. Here we show that a minimal yeast cell cycle network is able to oscillate autonomously, and that cyclin/Cdk-mediated positive feedback loops (PFLs) and Clb3-centered regulations sustain cyclin/Cdk oscillations, in known and hypothetical network designs. We propose that Clb3-mediated coordination of cyclin/Cdk waves reconciles checkpoint and oscillatory cell cycle models. Considering the evolutionary conservation of the cyclin/Cdk network across eukaryotes, we hypothesize that functional ("healthy") phenotypes require the capacity to oscillate autonomously whereas dysfunctional (potentially "diseased") phenotypes may lack this capacity.

A hybrid stochastic model of the budding yeast cell cycle

The growth and division of eukaryotic cells are regulated by complex, multi-scale networks. In this process, the mechanism of controlling cell-cycle progression has to be robust against inherent noise in the system. In this paper, a hybrid stochastic model is developed to study the effects of noise on the control mechanism of the budding yeast cell cycle. The modeling approach leverages, in a single multi-scale model, the advantages of two regimes: (1) the computational efficiency of a deterministic approach, and (2) the accuracy of stochastic simulations. Our results show that this hybrid stochastic model achieves high computational efficiency while generating simulation results that match very well with published experimental measurements.

Mathematical Model Explaining the Role of CDC6 in the Diauxic Growth of CDK1 Activity during the M-Phase of the Cell Cycle

In this paper we propose a role for the CDC 6 protein in the entry of cells into mitosis. This has not been considered in the literature so far. Recent experiments suggest that CDC 6 , upon entry into mitosis, inhibits the appearance of active CDK 1 and cyclin B complexes. This paper proposes a mathematical model which incorporates the dynamics of kinase CDK 1 , its regulatory protein cyclin B, the regulatory phosphatase CDC 25 and the inhibitor CDC 6 known to be involved in the regulation of active CDK 1 and cyclin B complexes. The experimental data lead us to formulate a new hypothesis that CDC 6 slows down the activation of inactive complexes of CDK 1 and cyclin B upon mitotic entry. Our mathematical model, based on mass action kinetics, provides a possible explanation for the experimental data. We claim that the dynamics of active complexes CDK 1 and cyclin B have a similar nature to diauxic dynamics introduced by Monod in 1949. In mathematical terms we state it as the existence of more than one inflection point of the curve defining the dynamics of the complexes.

A stochastic model of size control in the budding yeast cell cycle

BACKGROUND

Cell size is a key characteristic that significantly affects many aspects of cellular physiology. There are specific control mechanisms during cell cycle that maintain the cell size within a range from generation to generation. Such control mechanisms introduce substantial variabilities to important properties of the cell cycle such as growth and division. To quantitatively study the effect of such variability in progression through cell cycle, detailed stochastic models are required.

RESULTS

In this paper, a new hybrid stochastic model is proposed to study the effect of molecular noise and size control mechanism on the variabilities in cell cycle of the budding yeast Saccharomyces cerevisiae. The proposed model provides an accurate, yet computationally efficient approach for simulation of an intricate system by integrating the deterministic and stochastic simulation schemes. The developed hybrid stochastic model can successfully capture several key features of the cell cycle observed in experimental data. In particular, the proposed model: 1) confirms that the majority of noise in size control stems from low copy numbers of transcripts in the G1 phase, 2) identifies the size and time regulation modules in the size control mechanism, and 3) conforms with phenotypes of early G1 mutants in exquisite detail.

CONCLUSIONS

Hybrid stochastic modeling approach can be used to provide quantitative descriptions for stochastic properties of the cell cycle within a computationally efficient framework.

Modeling the dynamic behavior of biochemical regulatory networks

Strategies for modeling the complex dynamical behavior of gene/protein regulatory networks have evolved over the last 50 years as both the knowledge of these molecular control systems and the power of computing resources have increased. Here, we review a number of common modeling approaches, including Boolean (logical) models, systems of piecewise-linear or fully non-linear ordinary differential equations, and stochastic models (including hybrid deterministic/stochastic approaches). We discuss the pro's and con's of each approach, to help novice modelers choose a modeling strategy suitable to their problem, based on the type and bounty of available experimental information. We illustrate different modeling strategies in terms of some abstract network motifs, and in the specific context of cell cycle regulation.

Layers of regulation of cell-cycle gene expression in the budding yeast Saccharomyces cerevisiae

In the budding yeast Saccharomyces cerevisiae, transcription factors (TFs) regulate the periodic expression of many genes during the cell cycle, including gene products required for progression through cell-cycle events. Experimental evidence coupled with quantitative models suggests that a network of interconnected TFs is capable of regulating periodic genes over the cell cycle. Importantly, these dynamical models were built on transcriptomics data and assumed that TF protein levels and activity are directly correlated with mRNA abundance. To ask whether TF transcripts match protein expression levels as cells progress through the cell cycle, we applied a multiplexed targeted mass spectrometry approach (parallel reaction monitoring) to synchronized populations of cells. We found that protein expression of many TFs and cell-cycle regulators closely followed their respective mRNA transcript dynamics in cycling wild-type cells. Discordant mRNA/protein expression dynamics was also observed for a subset of cell-cycle TFs and for proteins targeted for degradation by E3 ubiquitin ligase complexes such as SCF (Skp1/Cul1/F-box) and APC/C (anaphase-promoting complex/cyclosome). We further profiled mutant cells lacking B-type cyclin/CDK activity ( clb1-6) where oscillations in ubiquitin ligase activity, cyclin/CDKs, and cell-cycle progression are halted. We found that a number of proteins were no longer periodically degraded in clb1-6 mutants compared with wild type, highlighting the importance of posttranscriptional regulation. Finally, the TF complexes responsible for activating G1/S transcription (SBF and MBF) were more constitutively expressed at the protein level than at periodic mRNA expression levels in both wild-type and mutant cells. This comprehensive investigation of cell-cycle regulators reveals that multiple layers of regulation (transcription, protein stability, and proteasome targeting) affect protein expression dynamics during the cell cycle.

Transcriptional timing and noise of yeast cell cycle regulators-a single cell and single molecule approach

Gene expression is a stochastic process and its appropriate regulation is critical for cell cycle progression. Cellular stress response necessitates expression reprogramming and cell cycle arrest. While previous studies are mostly based on bulk experiments influenced by synchronization effects or lack temporal distribution, time-resolved methods on single cells are needed to understand eukaryotic cell cycle in context of noisy gene expression and external perturbations. Using smFISH, microscopy and morphological markers, we monitored mRNA abundances over cell cycle phases and calculated transcriptional noise for SIC1, CLN2, and CLB5, the main G1/S transition regulators in budding yeast. We employed mathematical modeling for in silico synchronization and for derivation of time-courses from single cell data. This approach disclosed detailed quantitative insights into transcriptional regulation with and without stress, not available from bulk experiments before. First, besides the main peak in G1 we found an upshift of CLN2 and CLB5 expression in late mitosis. Second, all three genes showed basal expression throughout cell cycle enlightening that transcription is not divided in on and off but rather in high and low phases. Finally, exposing cells to osmotic stress revealed different periods of transcriptional inhibition for CLN2 and CLB5 and the impact of stress on cell cycle phase duration. Combining experimental and computational approaches allowed us to precisely assess cell cycle progression timing, as well as gene expression dynamics.

A Stochastic Model of the Yeast Cell Cycle Reveals Roles for Feedback Regulation in Limiting Cellular Variability

The cell division cycle of eukaryotes is governed by a complex network of cyclin-dependent protein kinases (CDKs) and auxiliary proteins that govern CDK activities. The control system must function reliably in the context of molecular noise that is inevitable in tiny yeast cells, because mistakes in sequencing cell cycle events are detrimental or fatal to the cell or its progeny. To assess the effects of noise on cell cycle progression requires not only extensive, quantitative, experimental measurements of cellular heterogeneity but also comprehensive, accurate, mathematical models of stochastic fluctuations in the CDK control system. In this paper we provide a stochastic model of the budding yeast cell cycle that accurately accounts for the variable phenotypes of wild-type cells and more than 20 mutant yeast strains simulated in different growth conditions. We specifically tested the role of feedback regulations mediated by G1- and SG2M-phase cyclins to minimize the noise in cell cycle progression. Details of the model are informed and tested by quantitative measurements (by fluorescence in situ hybridization) of the joint distributions of mRNA populations in yeast cells. We use the model to predict the phenotypes of ~30 mutant yeast strains that have not yet been characterized experimentally.

The cell division cycle—the process by which a living cell makes a new replica of itself—is fundamental to all aspects of biological growth, development and reproduction. If cells make mistakes in cell cycle progression, they may die or give birth to aberrant progeny. Such mistakes are the root cause of serious human diseases such as cancer. Hence, we would like to understand how cells control cell cycle events and correct mistakes before they do serious damage. Yeast cells are especially suited to studying cell cycle progression because so much is known about the underlying molecular control system, and because yeast cells—being so small—are especially vulnerable to random fluctuations in molecular regulators of the cell cycle. Experimental studies have identified feedback signals in the regulatory network that appear to keep these fluctuations within manageable limits. To place these proposals in a rigorous theoretical framework, we present a stochastic model of the major feedback controls in the yeast cell cycle. Our model accounts accurately for a range of observations about cell cycle variability in wild-type and mutant cells, and makes a host of verifiable predictions about mutant strains that are seriously compromised in cell cycle progression.

A Model of Yeast Cell-Cycle Regulation Based on a Standard Component Modeling Strategy for Protein Regulatory Networks

To understand the molecular mechanisms that regulate cell cycle progression in eukaryotes, a variety of mathematical modeling approaches have been employed, ranging from Boolean networks and differential equations to stochastic simulations. Each approach has its own characteristic strengths and weaknesses. In this paper, we propose a “standard component” modeling strategy that combines advantageous features of Boolean networks, differential equations and stochastic simulations in a framework that acknowledges the typical sorts of reactions found in protein regulatory networks. Applying this strategy to a comprehensive mechanism of the budding yeast cell cycle, we illustrate the potential value of standard component modeling. The deterministic version of our model reproduces the phenotypic properties of wild-type cells and of 125 mutant strains. The stochastic version of our model reproduces the cell-to-cell variability of wild-type cells and the partial viability of the CLB2-dbΔ clb5Δ mutant strain. Our simulations show that mathematical modeling with “standard components” can capture in quantitative detail many essential properties of cell cycle control in budding yeast.

A model for aryl hydrocarbon receptor-activated gene expression shows potency and efficacy changes and predicts squelching due to competition for transcription co-activators

A stochastic model of nuclear receptor-mediated transcription was developed based on activation of the aryl hydrocarbon receptor (AHR) by 2,3,7,8-tetrachlorodibenzodioxin (TCDD) and subsequent binding the activated AHR to xenobiotic response elements (XREs) on DNA. The model was based on effects observed in cells lines commonly used as in vitro experimental systems. Following ligand binding, the AHR moves into the cell nucleus and forms a heterodimer with the aryl hydrocarbon nuclear translocator (ARNT). In the model, a requirement for binding to DNA is that a generic coregulatory protein is subsequently bound to the AHR-ARNT dimer. Varying the amount of coregulator available within the nucleus altered both the potency and efficacy of TCDD for inducing for transcription of CYP1A1 mRNA, a commonly used marker for activation of the AHR. Lowering the amount of available cofactor slightly increased the EC50 for the transcriptional response without changing the efficacy or maximal response. Further reduction in the amount of cofactor reduced the efficacy and produced non-monotonic dose-response curves (NMDRCs) at higher ligand concentrations. The shapes of these NMDRCs were reminiscent of the phenomenon of squelching. Resource limitations for transcriptional machinery are becoming apparent in eukaryotic cells. Within single cells, nuclear receptor-mediated gene expression appears to be a stochastic process; however, intercellular communication and other aspects of tissue coordination may represent a compensatory process to maintain an organism’s ability to respond on a phenotypic level to various stimuli within an inconstant environment.