Experimental testing of a new integrated model of the budding yeast Start transition

A perturbation approach for refining Boolean models of cell cycle regulation

Considerable effort is required to build mathematical models of large protein regulatory networks. Utilizing computational algorithms that guide model development can significantly streamline the process and enhance the reliability of the resulting models. In this article, we present a perturbation approach for developing data-centric Boolean models of cell cycle regulation. To evaluate networks, we assign a score based on their steady states and the dynamical trajectories corresponding to the initial conditions. Then, perturbation analysis is used to find new networks with lower scores, in which dynamical trajectories traverse through the correct cell cycle path with high frequency. We apply this method to refine Boolean models of cell cycle regulation in budding yeast and mammalian cells.

Modeling the START transition in the budding yeast cell cycle

Budding yeast, Saccharomyces cerevisiae, is widely used as a model organism to study the genetics underlying eukaryotic cellular processes and growth critical to cancer development, such as cell division and cell cycle progression. The budding yeast cell cycle is also one of the best-studied dynamical systems owing to its thoroughly resolved genetics. However, the dynamics underlying the crucial cell cycle decision point called the START transition, at which the cell commits to a new round of DNA replication and cell division, are under-studied. The START machinery involves a central cyclin-dependent kinase; cyclins responsible for starting the transition, bud formation, and initiating DNA synthesis; and their transcriptional regulators. However, evidence has shown that the mechanism is more complicated than a simple irreversible transition switch. Activating a key transcription regulator SBF requires the phosphorylation of its inhibitor, Whi5, or an SBF/MBF monomeric component, Swi6, but not necessarily both. Also, the timing and mechanism of the inhibitor Whi5's nuclear export, while important, are not critical for the timing and execution of START. Therefore, there is a need for a consolidated model for the budding yeast START transition, reconciling regulatory and spatial dynamics. We built a detailed mathematical model (START-BYCC) for the START transition in the budding yeast cell cycle based on established molecular interactions and experimental phenotypes. START-BYCC recapitulates the underlying dynamics and correctly emulates key phenotypic traits of ~150 known START mutants, including regulation of size control, localization of inhibitor/transcription factor complexes, and the nutritional effects on size control. Such a detailed mechanistic understanding of the underlying dynamics gets us closer towards deconvoluting the aberrant cellular development in cancer.

Mitigating transcription noise via protein sharing in syncytial cells

Bursty transcription allows nuclei to concentrate the work of transcribing mRNA into short, intermittent intervals, potentially reducing transcriptional interference. However, bursts of mRNA production can increase noise in protein abundances. Here, we formulate models for gene expression in syncytia, or multinucleate cells, showing that protein abundance noise may be mitigated locally via spatial averaging of diffuse proteins. Our modeling shows a universal reduction in protein noise, which increases with the average number of nuclei per cell and persists even when the number of nuclei is itself a random variable. Experimental data comparing distributions of a cyclin mRNA that is conserved between brewer's yeast and a closely related filamentous fungus Ashbya gossypii confirm that syncytism is permissive of greater levels of transcriptional noise. Our findings suggest that division of transcriptional labor between nuclei allows syncytia to sidestep tradeoffs between efficiency and precision of gene expression.

Influence of cell volume on the gene transcription rate

Cells vary in volume throughout their life cycle and in many other circumstances, while their genome remains identical. Hence, the RNA production factory must adapt to changing needs, while maintaining the same production lines. This paradox is resolved by different mechanisms in distinct cells and circumstances. RNA polymerases have evolved to cope with the particular circumstances of each case and the different characteristics of the several RNA molecule types, especially their stabilities. Here we review current knowledge on these issues. We focus on the yeast Saccharomyces cerevisiae, where many of the studies have been performed, although we compare and discuss the results obtained in other eukaryotes and propose several ideas and questions to be tested and solved in the future. TAKE AWAY.

Implications of differential size-scaling of cell-cycle regulators on cell size homeostasis

Accurate timing of division and size homeostasis is crucial for cells. A potential mechanism for cells to decide the timing of division is the differential scaling of regulatory protein copy numbers with cell size. However, it remains unclear whether such a mechanism can lead to robust growth and division, and how the scaling behaviors of regulatory proteins influence the cell size distribution. Here we study a mathematical model combining gene expression and cell growth, in which the cell-cycle activators scale superlinearly with cell size while the inhibitors scale sublinearly. The cell divides once the ratio of their concentrations reaches a threshold value. We find that the cell can robustly grow and divide within a finite range of the threshold value with the cell size proportional to the ploidy. In a stochastic version of the model, the cell size at division is uncorrelated with that at birth. Also, the more differential the cell-size scaling of the cell-cycle regulators is, the narrower the cell-size distribution is. Intriguingly, our model with multiple regulators rationalizes the observation that after the deletion of a single regulator, the coefficient of variation of cell size remains roughly the same though the average cell size changes significantly. Our work reveals that the differential scaling of cell-cycle regulators provides a robust mechanism of cell size control.

The microprotein Nrs1 rewires the G1/S transcriptional machinery during nitrogen limitation in budding yeast

Commitment to cell division at the end of G1 phase, termed Start in the budding yeast Saccharomyces cerevisiae, is strongly influenced by nutrient availability. To identify new dominant activators of Start that might operate under different nutrient conditions, we screened a genome-wide ORF overexpression library for genes that bypass a Start arrest caused by absence of the G1 cyclin Cln3 and the transcriptional activator Bck2. We recovered a hypothetical gene YLR053c, renamed NRS1 for Nitrogen-Responsive Start regulator 1, which encodes a poorly characterized 108 amino acid microprotein. Endogenous Nrs1 was nuclear-localized, restricted to poor nitrogen conditions, induced upon TORC1 inhibition, and cell cycle-regulated with a peak at Start. NRS1 interacted genetically with SWI4 and SWI6, which encode subunits of the main G1/S transcription factor complex SBF. Correspondingly, Nrs1 physically interacted with Swi4 and Swi6 and was localized to G1/S promoter DNA. Nrs1 exhibited inherent transactivation activity, and fusion of Nrs1 to the SBF inhibitor Whi5 was sufficient to suppress other Start defects. Nrs1 appears to be a recently evolved microprotein that rewires the G1/S transcriptional machinery under poor nitrogen conditions.

Commitment to cell division at the end of G1 phase in the budding yeast Saccharomyces cerevisiae is strongly influenced by nutrient availability. This study identifies a micro-protein that promotes G1/S transcription activation and cell cycle entry in yeast under nitrogen-limited conditions.

The CWI Pathway: A Versatile Toolbox to Arrest Cell-Cycle Progression

Cell-signaling pathways are essential for cells to respond and adapt to changes in their environmental conditions. The cell-wall integrity (CWI) pathway of Saccharomyces cerevisiae is activated by environmental stresses, compounds, and morphogenetic processes that compromise the cell wall, orchestrating the appropriate cellular response to cope with these adverse conditions. During cell-cycle progression, the CWI pathway is activated in periods of polarized growth, such as budding or cytokinesis, regulating cell-wall biosynthesis and the actin cytoskeleton. Importantly, accumulated evidence has indicated a reciprocal regulation of the cell-cycle regulatory system by the CWI pathway. In this paper, we describe how the CWI pathway regulates the main cell-cycle transitions in response to cell-surface perturbance to delay cell-cycle progression. In particular, it affects the Start transcriptional program and the initiation of DNA replication at the G1/S transition, and entry and progression through mitosis. We also describe the involvement of the CWI pathway in the response to genotoxic stress and its connection with the DNA integrity checkpoint, the mechanism that ensures the correct transmission of genetic material and cell survival. Thus, the CWI pathway emerges as a master brake that stops cell-cycle progression when cells are coping with distinct unfavorable conditions.

Mechanistic Inferences From Analysis of Measurements of Protein Phase Transitions in Live Cells

The combination of phase separation and disorder-to-order transitions can give rise to ordered, semi-crystalline fibrillar assemblies that underlie prion phenomena namely, the non-Mendelian transfer of information across cells. Recently, a method known as Distributed Amphifluoric Förster Resonance Energy Transfer (DAmFRET) was developed to study the convolution of phase separation and disorder-to-order transitions in live cells. In this assay, a protein of interest is expressed to a broad range of concentrations and the acquisition of local density and order, measured by changes in FRET, is used to map phase transitions for different proteins. The high-throughput nature of this assay affords the promise of uncovering sequence-to-phase behavior relationships in live cells. Here, we report the development of a supervised method to obtain automated and accurate classifications of phase transitions quantified using the DAmFRET assay. Systems that we classify as undergoing two-state discontinuous transitions are consistent with prion-like behaviors, although the converse is not always true. We uncover well-established and surprising new sequence features that contribute to two-state phase behavior of prion-like domains. Additionally, our method enables quantitative, comparative assessments of sequence-specific driving forces for phase transitions in live cells. Finally, we demonstrate that a modest augmentation of DAmFRET measurements, specifically time-dependent protein expression profiles, can allow one to apply classical nucleation theory to extract sequence-specific lower bounds on the probability of nucleating ordered assemblies. Taken together, our approaches lead to a useful analysis pipeline that enables the extraction of mechanistic inferences regarding phase transitions in live cells.

The budding yeast Start repressor Whi7 differs in regulation from Whi5, emerging as a major cell cycle brake in response to stress

Start is the main decision point in the eukaryotic cell cycle at which cells commit to a new round of cell division. It involves the irreversible activation of a transcriptional programme through the inactivation of Start transcriptional repressors: the retinoblastoma family in mammals, or Whi5 and its recently identified paralogue Whi7 (also known as Srl3) in budding yeast. Here, we provide a comprehensive comparison of Whi5 and Whi7 that reveals significant qualitative differences. Indeed, the expression, subcellular localization and functionality of Whi7 and Whi5 are differentially regulated. Importantly, Whi7 shows specific properties in its association with promoters not shared by Whi5, and for the first time, we demonstrate that Whi7, and not Whi5, can be the main contributor to Start inhibition such as it occurs in the response to cell wall stress. Our results help to improve understanding of the interplay between multiple differentially regulated Start repressors in order to face specific cellular conditions.

Highlighted Article: Cells can use the interplay between functionally redundant but differentially regulated cell-cycle repressors in order to confer new repression capabilities and to respond to specific cellular conditions.

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.

Bayesian inference using qualitative observations of underlying continuous variables

MOTIVATION

Recent work has demonstrated the feasibility of using non-numerical, qualitative data to parameterize mathematical models. However, uncertainty quantification (UQ) of such parameterized models has remained challenging because of a lack of a statistical interpretation of the objective functions used in optimization.

RESULTS

We formulated likelihood functions suitable for performing Bayesian UQ using qualitative observations of underlying continuous variables or a combination of qualitative and quantitative data. To demonstrate the resulting UQ capabilities, we analyzed a published model for immunoglobulin E (IgE) receptor signaling using synthetic qualitative and quantitative datasets. Remarkably, estimates of parameter values derived from the qualitative data were nearly as consistent with the assumed ground-truth parameter values as estimates derived from the lower throughput quantitative data. These results provide further motivation for leveraging qualitative data in biological modeling.

AVAILABILITY AND IMPLEMENTATION

The likelihood functions presented here are implemented in a new release of PyBioNetFit, an open-source application for analyzing Systems Biology Markup Language- and BioNetGen Language-formatted models, available online at www.github.com/lanl/PyBNF.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Differential Scaling of Gene Expression with Cell Size May Explain Size Control in Budding Yeast

Yeast cells must grow to a critical size before committing to division. It is unknown how size is measured. We find that as cells grow, mRNAs for some cell-cycle activators scale faster than size, increasing in concentration, while mRNAs for some inhibitors scale slower than size, decreasing in concentration. Size-scaled gene expression could cause an increasing ratio of activators to inhibitors with size, triggering cell-cycle entry. Consistent with this, expression of the CLN2 activator from the promoter of the WHI5 inhibitor, or vice versa, interfered with cell size homeostasis, yielding a broader distribution of cell sizes. We suggest that size homeostasis comes from differential scaling of gene expression with size. Differential regulation of gene expression as a function of cell size could affect many cellular processes.

Quantifying Nucleation In Vivo Reveals the Physical Basis of Prion-like Phase Behavior

Protein self-assemblies modulate protein activities over biological timescales that can exceed the lifetimes of the proteins or even the cells that harbor them. We hypothesized that these timescales relate to kinetic barriers inherent to the nucleation of ordered phases. To investigate nucleation barriers in living cells, we developed distributed amphifluoric FRET (DAmFRET). DAmFRET exploits a photoconvertible fluorophore, heterogeneous expression, and large cell numbers to quantify via flow cytometry the extent of a protein's self-assembly as a function of cellular concentration. We show that kinetic barriers limit the nucleation of ordered self-assemblies and that the persistence of the barriers with respect to concentration relates to structure. Supersaturation resulting from sequence-encoded nucleation barriers gave rise to prion behavior and enabled a prion-forming protein, Sup35 PrD, to partition into dynamic intracellular condensates or to form toxic aggregates. Our results suggest that nucleation barriers govern cytoplasmic inheritance, subcellular organization, and proteotoxicity.

Advances and challenges in logical modeling of cell cycle regulation: perspective for multi-scale, integrative yeast cell models

The eukaryotic cell cycle is robustly designed, with interacting molecules organized within a definite topology that ensures temporal precision of its phase transitions. Its underlying dynamics are regulated by molecular switches, for which remarkable insights have been provided by genetic and molecular biology efforts. In a number of cases, this information has been made predictive, through computational models. These models have allowed for the identification of novel molecular mechanisms, later validated experimentally. Logical modeling represents one of the youngest approaches to address cell cycle regulation. We summarize the advances that this type of modeling has achieved to reproduce and predict cell cycle dynamics. Furthermore, we present the challenge that this type of modeling is now ready to tackle: its integration with intracellular networks, and its formalisms, to understand crosstalks underlying systems level properties, ultimate aim of multi-scale models. Specifically, we discuss and illustrate how such an integration may be realized, by integrating a minimal logical model of the cell cycle with a metabolic network.