Design principles of the yeast G1/S switch

Initial nutrient condition determines the recovery speed of quiescent cells in fission yeast

Most of microbe cells spend the majority of their times in quiescence due to unfavorable environmental conditions. The study of this dominant state is crucial for understanding the basic cell physiology. Retained recovery ability is a critical property of quiescent cells, which consists of two features: how long the cells can survive (the survivability) and how fast they can recover (the recovery activity). While the survivability has been extensively studied under the background of chronological aging, how the recovery activity depends on the quiescent time and what factors influence its dynamics have not been addressed quantitatively. In this work, we systematically quantified both the survivability and the recovery activity of long-lived quiescent fission yeast cells at the single cell level under various nutrient conditions. It provides the most profound evolutionary dynamics of quiescent cell regeneration ability described to date. We found that the single cell recovery time linearly increased with the starvation time before the survivability significantly declined. This linearity was robust under various nutrient conditions and the recovery speed was predetermined by the initial nutrient condition. Transcriptome profiling further revealed that quiescence states under different nutrient conditions evolve in a common trajectory but with different speed. Our results demonstrated that cellular quiescence has a continuous spectrum of depths and its physiology is greatly influenced by environmental conditions.

Network regulation meets substrate modification chemistry

Biochemical networks are at the heart of cellular information processing. These networks contain distinct facets: (i) processing of information from the environment via cascades/pathways along with network regulation and (ii) modification of substrates in different ways, to confer protein functionality, stability and processing. While many studies focus on these factors individually, how they interact and the consequences for cellular systems behaviour are poorly understood. We develop a systems framework for this purpose by examining the interplay of network regulation (canonical feedback and feed-forward circuits) and multisite modification, as an exemplar of substrate modification. Using computational, analytical and semi-analytical approaches, we reveal distinct and unexpected ways in which the substrate modification and network levels combine and the emergent behaviour arising therefrom. This has important consequences for dissecting the behaviour of specific signalling networks, tracing the origins of systems behaviour, inference of networks from data, robustness/evolvability and multi-level engineering of biomolecular networks. Overall, we repeatedly demonstrate how focusing on only one level (say network regulation) can lead to profoundly misleading conclusions about all these aspects, and reveal a number of important consequences for experimental/theoretical/data-driven interrogations of cellular signalling systems.

The regulatory mechanism of the yeast osmoresponse under different glucose concentrations

Cells constantly respond to environmental changes by modulating gene expression programs. These responses may demand substantial costs and, thus, affect cell growth. Understanding the regulation of these processes represents a key question in biology and biotechnology. Here, we studied the responses to osmotic stress in glucose-limited environments. By analyzing seventeen osmotic stress-induced genes and stress-activated protein kinase Hog1, we found that cells exhibited stronger osmotic gene expression response and larger integral of Hog1 nuclear localization during adaptation to osmotic stress under glucose-limited conditions than under glucose-rich conditions. We proposed and verified that in glucose-limited environment, glycolysis intermediates (representing "reserve flux") were limited, which required cells to express more glycerol-production enzymes for stress adaptation. Consequently, the regulatory mechanism of osmoresponse was derived in the presence and absence of such reserve flux. Further experiments suggested that this reserve flux-dependent stress-defense strategy may be a general principle under nutrient-limited environments.

Synthetic biology tools for engineering Goodwin oscillation in Trypanosoma brucei brucei

Kinetoplastid protozoa possess properties that are highly divergent from the mammalian, yeast and bacterial cells more commonly used in synthetic biology and represent a tantalisingly untapped source of bioengineering potential. Trypanosoma brucei brucei (T. b. brucei), an established model organism for studying the Kinetoplastida, is non-pathogenic to humans and provides an interesting test case for establishing synthetic biology in this phylogenetic class. To demonstrate further the tractability of Kinetoplastida to synthetic biology, we sought to construct and demonstrate a Goodwin oscillator, the simplest oscillatory gene network, in T. b. brucei for the first time. We report one completed iteration of the archetypal synthetic biology Design-Build-Test-Learn (DBTL) cycle; firstly, using Ab initio mathematical modelling of the behaviour a theoretical, oscillatory, trypanosomal synthetic gene network (SGN) to inform the design of a plasmid encoding that network. Once assembled, the plasmid was then used to generate a stable transfectant T. b. brucei cell line. To test the performance of the oscillatory SGN, a novel experimental setup was established to capture images of the fluorescent signal from motion-restricted live cells. Data captured were consistent with oscillatory behaviour of the SGN, with cellular fluorescence observed to oscillate with a period of 50 min, with varying amplitude and linear growth trend. This first DBTL cycle establishes a foundation for future cycles in which the SGN design and experimental monitoring setup can be further refined.

Quantitative model of eukaryotic Cdk control through the Forkhead CONTROLLER

In budding yeast, synchronization of waves of mitotic cyclins that activate the Cdk1 kinase occur through Forkhead transcription factors. These molecules act as controllers of their sequential order and may account for the separation in time of incompatible processes. Here, a Forkhead-mediated design principle underlying the quantitative model of Cdk control is proposed for budding yeast. This design rationalizes timing of cell division, through progressive and coordinated cyclin/Cdk-mediated phosphorylation of Forkhead, and autonomous cyclin/Cdk oscillations. A "clock unit" incorporating this design that regulates timing of cell division is proposed for both yeast and mammals, and has a DRIVER operating the incompatible processes that is instructed by multiple CLOCKS. TIMERS determine whether the clocks are active, whereas CONTROLLERS determine how quickly the clocks shall function depending on external MODULATORS. This "clock unit" may coordinate temporal waves of cyclin/Cdk concentration/activity in the eukaryotic cell cycle making the driver operate the incompatible processes, at separate times.

Comprehensive Analysis of G1 Cyclin Docking Motif Sequences that Control CDK Regulatory Potency In Vivo

Many protein-modifying enzymes recognize their substrates via docking motifs, but the range of functionally permissible motif sequences is often poorly defined. During eukaryotic cell division, cyclin-specific docking motifs help cyclin-dependent kinases (CDKs) phosphorylate different substrates at different stages, thus enforcing a temporally ordered series of events. In budding yeast, CDK substrates with Leu/Pro-rich (LP) docking motifs are recognized by Cln1/2 cyclins in late G1 phase, yet the key sequence features of these motifs were unknown. Here, we comprehensively analyze LP motif requirements in vivo by combining a competitive growth assay with deep mutational scanning. We quantified the effect of all single-residue replacements in five different LP motifs by using six distinct G1 cyclins from diverse fungi including medical and agricultural pathogens. The results uncover substantial tolerance for deviations from the consensus sequence, plus requirements at some positions that are contingent on the favorability of other motif residues. They also reveal the basis for variations in functional potency among wild-type motifs, and allow derivation of a quantitative matrix that predicts the strength of other candidate motif sequences. Finally, we find that variation in docking motif potency can advance or delay the time at which CDK substrate phosphorylation occurs, and thereby control the temporal ordering of cell cycle regulation. The overall results provide a general method for surveying viable docking motif sequences and quantifying their potency in vivo, and they reveal how variations in docking strength can tune the degree and timing of regulatory modifications.

Age-dependent decline in stress response capacity revealed by proteins dynamics analysis

The aging process is regarded as the progressive loss of physiological integrity, leading to impaired biological functions and the increased vulnerability to death. Among various biological functions, stress response capacity enables cells to alter gene expression patterns and survive when facing internal and external stresses. Here, we explored changes in stress response capacity during the replicative aging of Saccharomyces cerevisiae. To this end, we used a high-throughput microfluidic device to deliver intermittent pulses of osmotic stress and tracked the dynamic changes in the production of downstream stress-responsive proteins, in a large number of individual aging cells. Cells showed a gradual decline in stress response capacity of these osmotic-related downstream proteins during the aging process after the first 5 generations. Among the downstream stress-responsive genes and unrelated genes tested, the residual level of response capacity of Trehalose-6-Phosphate Synthase (TPS2) showed the best correlation with the cell remaining lifespan. By monitor dynamics of the upstream transcription factors and mRNA of Tps2, it was suggested that the decline in downstream stress response capacity was caused by the decline of translational rate of these proteins during aging.

Life span extension by glucose restriction is abrogated by methionine supplementation: Cross-talk between glucose and methionine and implication of methionine as a key regulator of life span

Caloric restriction (CR) is known to extend life span across species; however, the molecular mechanisms are not well understood. We investigate the mechanism by which glucose restriction (GR) extends yeast replicative life span, by combining ribosome profiling and RNA-seq with microfluidic-based single-cell analysis. We discovered a cross-talk between glucose sensing and the regulation of intracellular methionine: GR down-regulated the transcription and translation of methionine biosynthetic enzymes and transporters, leading to a decreased intracellular methionine concentration; external supplementation of methionine cancels the life span extension by GR. Furthermore, genetic perturbations that decrease methionine synthesis/uptake extend life span. These observations suggest that intracellular methionine mediates the life span effects of various nutrient and genetic perturbations, and that the glucose-methionine cross-talk is a general mechanism for coordinating the nutrient status and the translation/growth of a cell. Our work also implicates proteasome as a downstream effector of the life span extension by GR.

Critical slowing down and attractive manifold: A mechanism for dynamic robustness in the yeast cell-cycle process

Biological processes that execute complex multiple functions, such as the cell cycle, must ensure the order of sequential events and maintain dynamic robustness against various fluctuations. Here, we examine the mechanisms and fundamental structure that achieve these properties in the cell cycle of the budding yeast Saccharomyces cerevisiae. We show that this process behaves like an excitable system containing three well-decoupled saddle-node bifurcations to execute DNA replication and mitosis events. The yeast cell-cycle regulatory network can be divided into three modules-the G1/S phase, early M phase, and late M phase-wherein both positive feedback loops in each module and interactions among modules play important roles. Specifically, when the cell-cycle process operates near the critical points of the saddle-node bifurcations, a critical slowing down effect takes place. Such interregnum then allows for an attractive manifold and sufficient duration for cell-cycle events, within which to assess the completion of DNA replication and mitosis, e.g., spindle assembly. Moreover, such arrangement ensures that any fluctuation in an early module or event will not transmit to a later module or event. Thus, our results suggest a possible dynamical mechanism of the cell-cycle process to ensure event order and dynamic robustness and give insight into the evolution of eukaryotic cell-cycle processes.

A processive phosphorylation circuit with multiple kinase inputs and mutually diversional routes controls G1/S decision

Studies on multisite phosphorylation networks of cyclin-dependent kinase (CDK) targets have opened a new level of signaling complexity by revealing signal processing routes encoded into disordered proteins. A model target, the CDK inhibitor Sic1, contains linear phosphorylation motifs, docking sites, and phosphodegrons to empower an N-to-C terminally directed phosphorylation process. Here, we uncover a signal processing mechanism involving multi-step competition between mutually diversional phosphorylation routes within the S-CDK-Sic1 inhibitory complex. Intracomplex phosphorylation plays a direct role in controlling Sic1 degradation, and provides a mechanism to sequentially integrate both the G1- and S-CDK activities while keeping S-CDK inhibited towards other targets. The competing phosphorylation routes prevent premature Sic1 degradation and demonstrate how integration of MAPK from the pheromone pathway allows one to tune the competition of alternative phosphorylation paths. The mutually diversional phosphorylation circuits may be a general way for processing multiple kinase signals to coordinate cellular decisions in eukaryotes.

The decision of whether and when a cell divides is tightly controlled. Here, the authors show in yeast that there is a multi-step competition between different phosphorylation states and sites in the S phase CDK-Sic1 complex, which controls Sic1 degradation and coordinates the precise timing of the G1/S transition.

Cell Cycle Inhibitor Whi5 Records Environmental Information to Coordinate Growth and Division in Yeast

Proliferating cells need to evaluate the environment to determine the optimal timing for cell cycle entry. However, how this is achieved is not well understood. Here, we show that, in budding yeast, the G1 inhibitor Whi5 is a key environmental indicator and plays a crucial role in coordinating cell growth and division. We found that, under a variety of nutrient and stress conditions, Whi5 amount in G1 is proportional to the cell's doubling time in the environment, which in turn influences the timing for the next cell cycle entry. In addition, the coordination between division and environment is further fine-tuned in G1 by environmentally dependent growth rate, G1 cyclin-Cdk1 contribution, and Whi5 threshold at the start. Our results show that the cell stores the past environmental information in Whi5, which works together with other mechanisms sensing the current environmental condition to achieve an adaptive cellular decision making process.

The Design Principles of Biochemical Timers: Circuits that Discriminate between Transient and Sustained Stimulation

Many cellular responses for which timing is critical display temporal filtering-the ability to suppress response until stimulated for longer than a given minimal time. To identify biochemical circuits capable of kinetic filtering, we comprehensively searched the space of three-node enzymatic networks. We define a metric of "temporal ultrasensitivity," the steepness of activation as a function of stimulus duration. We identified five classes of core network motifs capable of temporal filtering, each with distinct functional properties such as rejecting high-frequency noise, committing to response (bistability), and distinguishing between long stimuli. Combinations of the two most robust motifs, double inhibition (DI) and positive feedback with AND logic (PF_AND), underlie several natural timer circuits involved in processes such as cell cycle transitions, T cell activation, and departure from the pluripotent state. The biochemical network motifs described in this study form a basis for understanding common ways cells make dynamic decisions.

Multisite phosphorylation code of CDK

The quantitative model of cyclin-dependent kinase (CDK) function states that cyclins temporally order cell cycle events at different CDK activity levels, or thresholds. The model lacks a mechanistic explanation, as it is not understood how different thresholds are encoded into substrates. We show that a multisite phosphorylation code governs the phosphorylation of CDK targets and that phosphorylation clusters act as timing tags that trigger specific events at different CDK thresholds. Using phospho-degradable CDK threshold sensors with rationally encoded phosphorylation patterns, we were able to predictably program thresholds over the entire range of the Saccharomyces cerevisiae cell cycle. We defined three levels of CDK multisite phosphorylation encoding: (i) Ser-Thr swapping in phosphorylation sites, (ii) patterning of phosphorylation sites, and (iii) cyclin-specific docking combined with modulation of CDK activity. Thus, CDK can signal via hundreds of differentially encoded targets at precise times to provide a temporally ordered phosphorylation pattern required for cell division.

CDK and MAPK Synergistically Regulate Signaling Dynamics via a Shared Multi-site Phosphorylation Region on the Scaffold Protein Ste5

We report an unanticipated system of joint regulation by cyclin-dependent kinase (CDK) and mitogen-activated protein kinase (MAPK), involving collaborative multi-site phosphorylation of a single substrate. In budding yeast, the protein Ste5 controls signaling through a G1 arrest pathway. Upon cell-cycle entry, CDK inhibits Ste5 via multiple phosphorylation sites, disrupting its membrane association. Using quantitative time-lapse microscopy, we examined Ste5 membrane recruitment dynamics at different cell-cycle stages. Surprisingly, in S phase, where Ste5 recruitment should be blocked, we observed an initial recruitment followed by a steep drop-off. This delayed inhibition revealed a requirement for both CDK activity and negative feedback from the pathway MAPK Fus3. Mutagenesis, mass spectrometry, and electrophoretic analyses suggest that the CDK and MAPK modify shared sites, which are most extensively phosphorylated when both kinases are active and able to bind their docking sites on Ste5. Such collaborative phosphorylation can broaden regulatory inputs and diversify output dynamics of signaling pathways.

Multiple Mechanisms Inactivate the LIN-41 RNA-Binding Protein To Ensure a Robust Oocyte-to-Embryo Transition in Caenorhabditis elegans

In the nematode Caenorhabditis elegans, the conserved LIN-41 RNA-binding protein is a translational repressor that coordinately controls oocyte growth and meiotic maturation. LIN-41 exerts these effects, at least in part, by preventing the premature activation of the cyclin-dependent kinase CDK-1 Here we investigate the mechanism by which LIN-41 is rapidly eliminated upon the onset of meiotic maturation. Elimination of LIN-41 requires the activities of CDK-1 and multiple SCF (Skp1, Cul1, and F-box protein)-type E3 ubiquitin ligase subunits, including the conserved substrate adaptor protein SEL-10/Fbw7/Cdc4, suggesting that LIN-41 is a target of ubiquitin-mediated protein degradation. Within the LIN-41 protein, two nonoverlapping regions, Deg-A and Deg-B, are individually necessary for LIN-41 degradation; both contain several potential phosphodegron sequences, and at least one of these sequences is required for LIN-41 degradation. Finally, Deg-A and Deg-B are sufficient, in combination, to mediate SEL-10-dependent degradation when transplanted into a different oocyte protein. Although LIN-41 is a potent inhibitor of protein translation and M phase entry, the failure to eliminate LIN-41 from early embryos does not result in the continued translational repression of LIN-41 oocyte messenger RNA targets. Based on these observations, we propose a model for the elimination of LIN-41 by the SEL-10 E3 ubiquitin ligase and suggest that LIN-41 is inactivated before it is degraded. Furthermore, we provide evidence that another RNA-binding protein, the GLD-1 tumor suppressor, is regulated similarly. Redundant mechanisms to extinguish translational repression by RNA-binding proteins may both control and provide robustness to irreversible developmental transitions, including meiotic maturation and the oocyte-to-embryo transition.

A systematic study of the determinants of protein abundance memory in cell lineage

Proteins are essential players of life activities. Intracellular protein levels directly affect cellular functions and cell fate. Upon cell division, the proteins in the mother cell are inherited by the daughters. However, what factors and by how much they affect this epigenetic inheritance of protein abundance remains unclear. Using both computational and experimental approaches, we systematically investigated this problem. We derived an analytical expression for the dependence of protein inheritance on various factors and showed that it agreed with numerical simulations of protein production and experimental results. Our work provides a framework for quantitative studies of protein inheritance and for the potential application of protein memory manipulation.

Determination of Cell Cycle Stage and Mitotic Exit Through the Quantification of the Protein Levels of Known Mitotic Regulators

There are multiple processes that occur at certain points during the cell cycle and that affect later steps. Impairment of such processes could cause delays or even completely abolish cell cycle progression. Therefore, it is extremely helpful in order to determine the potential consequences that interfering on a cellular process imposes on cell cycle progression to be able to precisely characterize the cell cycle stage by using molecular markers. Here, we describe the analysis of the protein levels of known mitotic regulators as molecular markers to monitor the progression of cells through the cell cycle by western blot in synchronized yeast cell cultures.

Parallel arrangements of positive feedback loops limit cell-to-cell variability in differentiation

Cellular differentiations are often regulated by bistable switches resulting from specific arrangements of multiple positive feedback loops (PFL) fused to one another. Although bistability generates digital responses at the cellular level, stochasticity in chemical reactions causes population heterogeneity in terms of its differentiated states. We hypothesized that the specific arrangements of PFLs may have evolved to minimize the cellular heterogeneity in differentiation. In order to test this we investigated variability in cellular differentiation controlled either by parallel or serial arrangements of multiple PFLs having similar average properties under extrinsic and intrinsic noises. We find that motifs with PFLs fused in parallel to one another around a central regulator are less susceptible to noise as compared to the motifs with PFLs arranged serially. Our calculations suggest that the increased resistance to noise in parallel motifs originate from the less sensitivity of bifurcation points to the extrinsic noise. Whereas estimation of mean residence times indicate that stable branches of bifurcations are robust to intrinsic noise in parallel motifs as compared to serial motifs. Model conclusions are consistent both in AND- and OR-gate input signal configurations and also with two different modeling strategies. Our investigations provide some insight into recent findings that differentiation of preadipocyte to mature adipocyte is controlled by network of parallel PFLs.

Design of Tunable Oscillatory Dynamics in a Synthetic NF-κB Signaling Circuit

Although oscillatory circuits are prevalent in transcriptional regulation, it is unclear how a circuit's structure and the specific parameters that describe its components determine the shape of its oscillations. Here, we engineer a minimal, inducible human nuclear factor κB (NF-κB)-based system that is composed of NF-κB (RelA) and degradable inhibitor of NF-κB (IκBα), into the yeast, Saccharomyces cerevisiae. We define an oscillation's waveform quantitatively as a function of signal amplitude, rest time, rise time, and decay time; by systematically tuning RelA concentration, the strength of negative feedback, and the degradation rate of IκBα, we demonstrate that peak shape and frequency of oscillations can be controlled in vivo and predicted mathematically. In addition, we show that nested negative feedback loops can be employed to specifically tune the frequency of oscillations while leaving their peak shape unchanged. In total, this work establishes design principles that enable function-guided design of oscillatory signaling controllers in diverse synthetic biology applications.

Cell-cycle transitions: a common role for stoichiometric inhibitors

The abrupt and irreversible transitions that drive cells through the DNA replication-division cycle are governed by molecular mechanisms that function as bistable “toggle” switches. A common theme of these switches is a network motif consisting of a “beleaguered” enzyme and its “domineering” substrate, locked in a feedback amplification loop.

The cell division cycle is the process by which eukaryotic cells replicate their chromosomes and partition them to two daughter cells. To maintain the integrity of the genome, proliferating cells must be able to block progression through the division cycle at key transition points (called “checkpoints”) if there have been problems in the replication of the chromosomes or their biorientation on the mitotic spindle. These checkpoints are governed by protein-interaction networks, composed of phase-specific cell-cycle activators and inhibitors. Examples include Cdk1:Clb5 and its inhibitor Sic1 at the G1/S checkpoint in budding yeast, APC:Cdc20 and its inhibitor MCC at the mitotic checkpoint, and PP2A:B55 and its inhibitor, alpha-endosulfine, at the mitotic-exit checkpoint. Each of these inhibitors is a substrate as well as a stoichiometric inhibitor of the cell-cycle activator. Because the production of each inhibitor is promoted by a regulatory protein that is itself inhibited by the cell-cycle activator, their interaction network presents a regulatory motif characteristic of a “feedback-amplified domineering substrate” (FADS). We describe how the FADS motif responds to signals in the manner of a bistable toggle switch, and then we discuss how this toggle switch accounts for the abrupt and irreversible nature of three specific cell-cycle checkpoints.

Firing of Replication Origins Frees Dbf4-Cdc7 to Target Eco1 for Destruction

Robust progression through the cell-division cycle depends on the precisely ordered phosphorylation of hundreds of different proteins by cyclin-dependent kinases (CDKs) and other kinases. The order of CDK substrate phosphorylation depends on rising CDK activity, coupled with variations in substrate affinities for different CDK-cyclin complexes and the opposing phosphatases [1-4]. Here, we address the ordering of substrate phosphorylation by a second major cell-cycle kinase, Cdc7-Dbf4 or Dbf4-dependent kinase (DDK). The primary function of DDK is to initiate DNA replication by phosphorylating the Mcm2-7 replicative helicase [5-7]. DDK also phosphorylates the cohesin acetyltransferase Eco1 [8]. Sequential phosphorylations of Eco1 by CDK, DDK, and Mck1 create a phosphodegron that is recognized by the ubiquitin ligase SCF^Cdc4. DDK, despite being activated in early S phase, does not phosphorylate Eco1 to trigger its degradation until late S phase [8]. DDK associates with docking sites on loaded Mcm double hexamers at unfired replication origins [9, 10]. We hypothesized that these docking interactions sequester limiting amounts of DDK, delaying Eco1 phosphorylation by DDK until replication is complete. Consistent with this hypothesis, we find that overproduction of DDK leads to premature Eco1 degradation. Eco1 degradation also occurs prematurely if Mcm complex loading at origins is prevented by depletion of Cdc6, and Eco1 is stabilized if loaded Mcm complexes are prevented from firing by a Cdc45 mutant. We propose that the timing of Eco1 phosphorylation, and potentially that of other DDK substrates, is determined in part by sequestration of DDK at unfired replication origins during S phase.

Using Microfluidic Devices to Measure Lifespan and Cellular Phenotypes in Single Budding Yeast Cells

Budding yeast Saccharomyces cerevisiae is an important model organism in aging research. Genetic studies have revealed many genes with conserved effects on the lifespan across species. However, the molecular causes of aging and death remain elusive. To gain a systematic understanding of the molecular mechanisms underlying yeast aging, we need high-throughput methods to measure lifespan and to quantify various cellular and molecular phenotypes in single cells. Previously, we developed microfluidic devices to track budding yeast mother cells throughout their lifespan while flushing away newborn daughter cells. This article presents a method for preparing microfluidic chips and for setting up microfluidic experiments. Multiple channels can be used to simultaneously track cells under different conditions or from different yeast strains. A typical setup can track hundreds of cells per channel and allow for high-resolution microscope imaging throughout the lifespan of the cells. Our method also allows detailed characterization of the lifespan, molecular markers, cell morphology, and the cell cycle dynamics of single cells. In addition, our microfluidic device is able to trap a significant amount of fresh mother cells that can be identified by downstream image analysis, making it possible to measure the lifespan with higher accuracy.

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.

Noise Decomposition Principle in a Coherent Feed-Forward Transcriptional Regulatory Loop

Coherent feed-forward loops exist extensively in realistic biological regulatory systems, and are common signaling motifs. Here, we study the characteristics and the propagation mechanism of the output noise in a coherent feed-forward transcriptional regulatory loop that can be divided into a main road and branch. Using the linear noise approximation, we derive analytical formulae for the total noise of the full loop, the noise of the branch, and the noise of the main road, which are verified by the Gillespie algorithm. Importantly, we find that (i) compared with the branch motif or the main road motif, the full motif can effectively attenuate the output noise level; (ii) there is a transition point of system state such that the noise of the main road is dominated when the underlying system is below this point, whereas the noise of the branch is dominated when the system is beyond the point. The entire analysis reveals the mechanism of how the noise is generated and propagated in a simple yet representative signaling module.

Adaptation through proportion

Adaptation is a ubiquitous feature in biological sensory and signaling networks. It has been suggested that adaptive systems may follow certain simple design principles across diverse organisms, cells and pathways. One class of networks that can achieve adaptation utilizes an incoherent feedforward control, in which two parallel signaling branches exert opposite but proportional effects on the output at steady state. In this paper, we generalize this adaptation mechanism by establishing a steady-state proportionality relationship among a subset of nodes in a network. Adaptation can be achieved by using any two nodes in the sub-network to respectively regulate the output node positively and negatively. We focus on enzyme networks and first identify basic regulation motifs consisting of two and three nodes that can be used to build small networks with proportional relationships. Larger proportional networks can then be constructed modularly similar to LEGOs. Our method provides a general framework to construct and analyze a class of proportional and/or adaptation networks with arbitrary size, flexibility and versatile functional features.

Switch-like Transitions Insulate Network Motifs to Modularize Biological Networks

Cellular decisions are made by complex networks that are difficult to analyze. Although it is common to analyze smaller sub-networks known as network motifs, it is unclear whether this is valid, because these motifs are embedded in complex larger networks. Here, we address the general question of modularity by examining the S. cerevisiae pheromone response. We demonstrate that the feedforward motif controlling the cell-cycle inhibitor Far1 is insulated from cell-cycle dynamics by the positive feedback switch that drives reentry to the cell cycle. Before cells switch on positive feedback, the feedforward motif model predicts the behavior of the larger network. Conversely, after the switch, the feedforward motif is dismantled and has no discernable effect on the cell cycle. When insulation is broken, the feedforward motif no longer predicts network behavior. This work illustrates how, despite the interconnectivity of networks, the activity of motifs can be insulated by switches that generate well-defined cellular states.

Cell-Size Control

Cells of a given type maintain a characteristic cell size to function efficiently in their ecological or organismal context. They achieve this through the regulation of growth rates or by actively sensing size and coupling this signal to cell division. We focus this review on potential size-sensing mechanisms, including geometric, external cue, and titration mechanisms. Mechanisms that titrate proteins against DNA are of particular interest because they are consistent with the robust correlation of DNA content and cell size. We review the literature, which suggests that titration mechanisms may underlie cell-size sensing in Xenopus embryos, budding yeast, and Escherichia coli, whereas alternative mechanisms may function in fission yeast.

The MYpop toolbox: Putting yeast stress responses in cellular context on single cell and population scales

Systems biology holds the promise to integrate multiple sources of information in order to build ever more complete models of cellular function. To do this, the field must overcome two significant challenges. First, the current strategy to model average cells must be replaced with population based models accounting for cell-to-cell variability. Second, models must be integrated with each other and with basic cellular function. This requires a core model of cellular physiology as well as a multiscale simulation platform to support large-scale simulation of culture or tissues from single cells. Here, we present such a simulation platform with a core model of yeast physiology as scaffold to integrate and simulate SBML models. The software automates this integration helping users simulate their model of choice in context of the cell division cycle. We benchmark model merging, simulation and analysis by integrating a minimal model of osmotic stress into the core model and analyzing it. We characterize the effect of single cell differences on the dynamics of osmoadaptation, estimating when normal cell growth is resumed and obtaining an explanation for experimentally observed glycerol dynamics based on population dynamics. Hence, the platform can be used to reconcile single cell and population level data.

Noise Reduction in Complex Biological Switches

Cells operate in noisy molecular environments via complex regulatory networks. It is possible to understand how molecular counts are related to noise in specific networks, but it is not generally clear how noise relates to network complexity, because different levels of complexity also imply different overall number of molecules. For a fixed function, does increased network complexity reduce noise, beyond the mere increase of overall molecular counts? If so, complexity could provide an advantage counteracting the costs involved in maintaining larger networks. For that purpose, we investigate how noise affects multistable systems, where a small amount of noise could lead to very different outcomes; thus we turn to biochemical switches. Our method for comparing networks of different structure and complexity is to place them in conditions where they produce exactly the same deterministic function. We are then in a good position to compare their noise characteristics relatively to their identical deterministic traces. We show that more complex networks are better at coping with both intrinsic and extrinsic noise. Intrinsic noise tends to decrease with complexity, and extrinsic noise tends to have less impact. Our findings suggest a new role for increased complexity in biological networks, at parity of function.

A Dynamical Framework for the All-or-None G1/S Transition

The transition from G1 into DNA replication (S phase) is an emergent behavior resulting from dynamic and complex interactions between cyclin-dependent kinases (Cdks), Cdk inhibitors (CKIs), and the anaphase-promoting complex/cyclosome (APC/C). Understanding the cellular decision to commit to S phase requires a quantitative description of these interactions. We apply quantitative imaging of single human cells to track the expression of G1/S regulators and use these data to parametrize a stochastic mathematical model of the G1/S transition. We show that a rapid, proteolytic, double-negative feedback loop between Cdk2:Cyclin and the Cdk inhibitor p27(Kip1) drives a switch-like entry into S phase. Furthermore, our model predicts that increasing Emi1 levels throughout S phase are critical in maintaining irreversibility of the G1/S transition, which we validate using Emi1 knockdown and live imaging of G1/S reporters. This work provides insight into the general design principles of the signaling networks governing the temporally abrupt transitions between cell-cycle phases.

Quantitative framework for ordered degradation of APC/C substrates

Background

During cell-cycle progression, substrates of a single master regulatory enzyme can be modified in a specific order. Here, we used experimental and computational approaches to dissect the quantitative mechanisms underlying the ordered degradation of the substrates of the ubiquitin ligase APC/C^Cdc20, a key regulator of chromosome segregation in mitosis.

Results

We show experimentally that the rate of catalysis varies with different substrates of APC/C^Cdc20. Using a computational model based on multi-step ubiquitination, we then show how changes in the interaction between a single substrate and APC/C^Cdc20 can alter the timing of degradation onset relative to APC/C^Cdc20 activation, while ensuring a fast degradation rate. Degradation timing and dynamics depend on substrate affinity for the enzyme as well as the catalytic rate at which the substrate is modified. When two substrates share the same pool of APC/C^Cdc20, their relative enzyme affinities and rates of catalysis influence the partitioning of APC/C^Cdc20 among substrates, resulting in substrate competition. Depending on how APC/C^Cdc20 is partitioned among its substrates, competition can have minor or major effects on the degradation of certain substrates. We show experimentally that increased expression of the early APC/C^Cdc20 substrate Clb5 does not delay the degradation of the later substrate securin, arguing against a role for competition with Clb5 in establishing securin degradation timing.

Conclusions

The degradation timing of APC/C^Cdc20 substrates depends on the multi-step nature of ubiquitination, differences in substrate-APC/C^Cdc20 interactions, and competition among substrates. Our studies provide a conceptual framework for understanding how ordered modification can be established among substrates of the same regulatory enzyme, and facilitate our understanding of how precise temporal control is achieved by a small number of master regulators to ensure a successful cell division cycle.

Electronic supplementary material

The online version of this article (doi:10.1186/s12915-015-0205-6) contains supplementary material, which is available to authorized users.

Bud-Localization of CLB2 mRNA Can Constitute a Growth Rate Dependent Daughter Sizer

Maintenance of cellular size is a fundamental systems level process that requires balancing of cell growth with proliferation. This is achieved via the cell division cycle, which is driven by the sequential accumulation and destruction of cyclins. The regulatory network around these cyclins, particularly in G1, has been interpreted as a size control network in budding yeast, and cell size as being decisive for the START transition. However, it is not clear why disruptions in the G1 network may lead to altered size rather than loss of size control, or why the S-G2-M duration also depends on nutrients. With a mathematical population model comprised of individually growing cells, we show that cyclin translation would suffice to explain the observed growth rate dependence of cell volume at START. Moreover, we assess the impact of the observed bud-localisation of the G2 cyclin CLB2 mRNA, and find that localised cyclin translation could provide an efficient mechanism for measuring the biosynthetic capacity in specific compartments: The mother in G1, and the growing bud in G2. Hence, iteration of the same principle can ensure that the mother cell is strong enough to grow a bud, and that the bud is strong enough for independent life. Cell sizes emerge in the model, which predicts that a single CDK-cyclin pair per growth phase suffices for size control in budding yeast, despite the necessity of the cell cycle network around the cyclins to integrate other cues. Size control seems to be exerted twice, where the G2/M control affects bud size through bud-localized translation of CLB2 mRNA, explaining the dependence of the S-G2-M duration on nutrients. Taken together, our findings suggest that cell size is an emergent rather than a regulatory property of the network linking growth and proliferation.

Hog1 targets Whi5 and Msa1 transcription factors to downregulate cyclin expression upon stress

Yeast cells have developed complex mechanisms to cope with extracellular insults. An increase in external osmolarity leads to activation of the stress-activated protein kinase Hog1, which is the main regulator of adaptive responses, such as gene expression and cell cycle progression, that are essential for cellular survival. Upon osmostress, the G1-to-S transition is regulated by Hog1 through stabilization of the cyclin-dependent kinase inhibitor Sic1 and the downregulation of G1 cyclin expression by an unclear mechanism. Here, we show that Hog1 interacts with and phosphorylates components of the core cell cycle transcriptional machinery such as Whi5 and the coregulator Msa1. Phosphorylation of these two transcriptional regulators by Hog1 is essential for inhibition of G1 cyclin expression, for control of cell morphogenesis, and for maximal cell survival upon stress. The control of both Whi5 and Msa1 by Hog1 also revealed the necessity for proper coordination of budding and DNA replication. Thus, Hog1 regulates G1 cyclin transcription upon osmostress to ensure coherent passage through Start.

A docking interface in the cyclin Cln2 promotes multi-site phosphorylation of substrates and timely cell-cycle entry

BACKGROUND

Eukaryotic cell division is driven by cyclin-dependent kinases (CDKs). Distinct cyclin-CDK complexes are specialized to drive different cell-cycle events, though the molecular foundations for these specializations are only partly understood. In budding yeast, the decision to begin a new cell cycle is regulated by three G1 cyclins (Cln1-Cln3). Recent studies revealed that some CDK substrates contain a novel docking motif that is specifically recognized by Cln1 and Cln2, and not by Cln3 or later S- or M-phase cyclins, but the responsible cyclin interface was unknown.

RESULTS

Here, to explore the role of this new docking mechanism in the cell cycle, we first show that it is conserved in a distinct cyclin subtype (Ccn1). Then, we exploit phylogenetic variation to identify cyclin mutations that disrupt docking. These mutations disrupt binding to multiple substrates as well as the ability to use docking sites to promote efficient, multi-site phosphorylation of substrates in vitro. In cells where the Cln2 docking function is blocked, we observed reductions in the polarized morphogenesis of daughter buds and reduced ability to fully phosphorylate the G1/S transcriptional repressor Whi5. Furthermore, disruption of Cln2 docking perturbs the coordination between cell size and division, such that the G1/S transition is delayed.

CONCLUSIONS

The findings point to a novel substrate interaction interface on cyclins, with patterns of conservation and divergence that relate to functional distinctions among cyclin subtypes. Furthermore, this docking function helps ensure full phosphorylation of substrates with multiple phosphorylation sites, and this contributes to punctual cell-cycle entry.

Reliable cell cycle commitment in budding yeast is ensured by signal integration

Cell fate decisions are critical for life, yet little is known about how their reliability is achieved when signals are noisy and fluctuating with time. In this study, we show that in budding yeast, the decision of cell cycle commitment (Start) is determined by the time integration of its triggering signal Cln3. We further identify the Start repressor, Whi5, as the integrator. The instantaneous kinase activity of Cln3-Cdk1 is recorded over time on the phosphorylated Whi5, and the decision is made only when phosphorylated Whi5 reaches a threshold. Cells adjust the threshold by modulating Whi5 concentration in different nutrient conditions to coordinate growth and division. Our work shows that the strategy of signal integration, which was previously found in decision-making behaviors of animals, is adopted at the cellular level to reduce noise and minimize uncertainty.

Multiple mechanisms determine the order of APC/C substrate degradation in mitosis

To ensure proper mitotic progression, robust ordering of the destruction of APC/C^Cdc20 substrates is driven by the integration of molecular mechanisms ranging from phosphorylation-dependent interaction with substrates to sensing of the status of the spindle assembly checkpoint.

The ubiquitin protein ligase anaphase-promoting complex or cyclosome (APC/C) controls mitosis by promoting ordered degradation of securin, cyclins, and other proteins. The mechanisms underlying the timing of APC/C substrate degradation are poorly understood. We explored these mechanisms using quantitative fluorescence microscopy of GFP-tagged APC/C^Cdc20 substrates in living budding yeast cells. Degradation of the S cyclin, Clb5, begins early in mitosis, followed 6 min later by the degradation of securin and Dbf4. Anaphase begins when less than half of securin is degraded. The spindle assembly checkpoint delays the onset of Clb5 degradation but does not influence securin degradation. Early Clb5 degradation depends on its interaction with the Cdk1–Cks1 complex and the presence of a Cdc20-binding “ABBA motif” in its N-terminal region. The degradation of securin and Dbf4 is delayed by Cdk1-dependent phosphorylation near their Cdc20-binding sites. Thus, a remarkably diverse array of mechanisms generates robust ordering of APC/C^Cdc20 substrate destruction.

Division of labour between Myc and G1 cyclins in cell cycle commitment and pace control

A body of evidence has shown that the control of E2F transcription factor activity is critical for determining cell cycle entry and cell proliferation. However, an understanding of the precise determinants of this control, including the role of other cell-cycle regulatory activities, has not been clearly defined. Here, recognizing that the contributions of individual regulatory components could be masked by heterogeneity in populations of cells, we model the potential roles of individual components together with the use of an integrated system to follow E2F dynamics at the single-cell level and in real time. These analyses reveal that crossing a threshold amplitude of E2F accumulation determines cell cycle commitment. Importantly, we find that Myc is critical in modulating the amplitude, whereas cyclin D/E activities have little effect on amplitude but do contribute to the modulation of duration of E2F activation, thereby affecting the pace of cell cycle progression.

Morphisms of reaction networks that couple structure to function

BACKGROUND

The mechanisms underlying complex biological systems are routinely represented as networks. Network kinetics is widely studied, and so is the connection between network structure and behavior. However, similarity of mechanism is better revealed by relationships between network structures.

RESULTS

We define morphisms (mappings) between reaction networks that establish structural connections between them. Some morphisms imply kinetic similarity, and yet their properties can be checked statically on the structure of the networks. In particular we can determine statically that a complex network will emulate a simpler network: it will reproduce its kinetics for all corresponding choices of reaction rates and initial conditions. We use this property to relate the kinetics of many common biological networks of different sizes, also relating them to a fundamental population algorithm.

CONCLUSIONS

Structural similarity between reaction networks can be revealed by network morphisms, elucidating mechanistic and functional aspects of complex networks in terms of simpler networks.

Advantages of proteins being disordered

The past decade has witnessed great advances in our understanding of protein structure-function relationships in terms of the ubiquitous existence of intrinsically disordered proteins (IDPs) and intrinsically disordered regions (IDRs). The structural disorder of IDPs/IDRs enables them to play essential functions that are complementary to those of ordered proteins. In addition, IDPs/IDRs are persistent in evolution. Therefore, they are expected to possess some advantages over ordered proteins. In this review, we summarize and survey nine possible advantages of IDPs/IDRs: economizing genome/protein resources, overcoming steric restrictions in binding, achieving high specificity with low affinity, increasing binding rate, facilitating posttranslational modifications, enabling flexible linkers, preventing aggregation, providing resistance to non-native conditions, and allowing compatibility with more available sequences. Some potential advantages of IDPs/IDRs are not well understood and require both experimental and theoretical approaches to decipher. The connection with protein design is also briefly discussed.