Attila Csikász-Nagy

Irreversible cell-cycle transitions are due to systems-level feedback

The irreversibility of cell-cycle transitions is commonly thought to derive from the irreversible degradation of certain regulatory proteins. We argue that irreversible transitions in the cell cycle (or in any other molecular control system) cannot be attributed to a single molecule or reaction, but that they derive from feedback signals in reaction networks. This systems-level view of irreversibility is supported by many experimental observations.

Mathematical model of the fission yeast cell cycle with checkpoint controls at the G1/S, G2/M and metaphase/anaphase transitions

All events of the fission yeast cell cycle can be orchestrated by fluctuations of a single cyclin-dependent protein kinase, the Cdc13/Cdc2 heterodimer. The G1/S transition is controlled by interactions of Cdc13/Cdc2 and its stoichiometric inhibitor, Rum1. The G2/M transition is regulated by a kinase-phosphatase pair, Wee1 and Cdc25, which determine the phosphorylation state of the Tyr-15 residue of Cdc2. The meta/anaphase transition is controlled by interactions between Cdc13/Cdc2 and the anaphase promoting complex, which labels Cdc13 subunits for proteolysis. We construct a mathematical model of fission yeast growth and division that encompasses all three crucial checkpoint controls. By numerical simulations we show that the model is consistent with a broad selection of cell cycle mutants, and we predict the phenotypes of several multiple-mutant strains that have not yet been constructed.

The Cell Cycle Switch Computes Approximate Majority

Both computational and biological systems have to make decisions about switching from one state to another. The ‘Approximate Majority’ computational algorithm provides the asymptotically fastest way to reach a common decision by all members of a population between two possible outcomes, where the decision approximately matches the initial relative majority. The network that regulates the mitotic entry of the cell-cycle in eukaryotes also makes a decision before it induces early mitotic processes. Here we show that the switch from inactive to active forms of the mitosis promoting Cyclin Dependent Kinases is driven by a system that is related to both the structure and the dynamics of the Approximate Majority computation. We investigate the behavior of these two switches by deterministic, stochastic and probabilistic methods and show that the steady states and temporal dynamics of the two systems are similar and they are exchangeable as components of oscillatory networks.

The critical size is set at a single-cell level by growth rate to attain homeostasis and adaptation

Budding yeast cells are assumed to trigger Start and enter the cell cycle only after they attain a critical size set by external conditions. However, arguing against deterministic models of cell size control, cell volume at Start displays great individual variability even under constant conditions. Here we show that cell size at Start is robustly set at a single-cell level by the volume growth rate in G1, which explains the observed variability. We find that this growth-rate-dependent sizer is intimately hardwired into the Start network and the Ydj1 chaperone is key for setting cell size as a function of the individual growth rate. Mathematical modelling and experimental data indicate that a growth-rate-dependent sizer is sufficient to ensure size homeostasis and, as a remarkable advantage over a rigid sizer mechanism, it reduces noise in G1 length and provides an immediate solution for size adaptation to external conditions at a population level.

Computational systems biology of the cell cycle

One of the early success stories of computational systems biology was the work done on cell-cycle regulation. The earliest mathematical descriptions of cell-cycle control evolved into very complex, detailed computational models that describe the regulation of cell division in many different cell types. On the way these models predicted several dynamical properties and unknown components of the system that were later experimentally verified/identified. Still, research on this field is far from over. We need to understand how the core cell-cycle machinery is controlled by internal and external signals, also in yeast cells and in the more complex regulatory networks of higher eukaryotes. Furthermore, there are many computational challenges what we face as new types of data appear thanks to continuing advances in experimental techniques. We have to deal with cell-to-cell variations, revealed by single cell measurements, as well as the tremendous amount of data flowing from high throughput machines. We need new computational concepts and tools to handle these data and develop more detailed, more precise models of cell-cycle regulation in various organisms. Here we review past and present of computational modeling of cell-cycle regulation, and discuss possible future directions of the field.

Stochastic Petri Net extension of a yeast cell cycle model.

This paper presents the definition, solution and validation of a stochastic model of the budding yeast cell cycle, based on Stochastic Petri Nets (SPN). A specific family of SPNs is selected for building a stochastic version of a well-established deterministic model. We describe the procedure followed in defining the SPN model from the deterministic ODE model, a procedure that can be largely automated. The validation of the SPN model is conducted with respect to both the results provided by the deterministic one and the experimental results available from literature. The SPN model catches the behavior of the wild type budding yeast cells and a variety of mutants. We show that the stochastic model matches some characteristics of budding yeast cells that cannot be found with the deterministic model. The SPN model fine-tunes the simulation results, enriching the breadth and the quality of its outcome.

Restriction point control of the mammalian cell cycle via the cyclin E/Cdk2:p27 complex

Numerous top‐down kinetic models have been constructed to describe the cell cycle. These models have typically been constructed, validated and analyzed using model species (molecular intermediates and proteins) and phenotypic observations, and therefore do not focus on the individual model processes (reaction steps). We have developed a method to: (a) quantify the importance of each of the reaction steps in a kinetic model for the positioning of a switch point [i.e. the restriction point (RP)]; (b) relate this control of reaction steps to their effects on molecular species, using sensitivity and co‐control analysis; and thereby (c) go beyond a correlation towards a causal relationship between molecular species and effects. The method is generic and can be applied to responses of any type, but is most useful for the analysis of dynamic and emergent responses such as switch points in the cell cycle. The strength of the analysis is illustrated for an existing mammalian cell cycle model focusing on the RP [Novak B, Tyson J (2004) J Theor Biol230, 563–579]. The reactions in the model with the highest RP control were those involved in: (a) the interplay between retinoblastoma protein and E2F transcription factor; (b) those synthesizing the delayed response genes and cyclin D/Cdk4 in response to growth signals; (c) the E2F‐dependent cyclin E/Cdk2 synthesis reaction; as well as (d) p27 formation reactions. Nine of the 23 intermediates were shown to have a good correlation between their concentration control and RP control. Sensitivity and co‐control analysis indicated that the strongest control of the RP is mediated via the cyclin E/Cdk2:p27 complex concentration. Any perturbation of the RP could be related to a change in the concentration of this complex; apparent effects of other molecular species were indirect and always worked through cyclin E/Cdk2:p27, indicating a causal relationship between this complex and the positioning of the RP.

Cell cycle regulation by feed‐forward loops coupling transcription and phosphorylation

The eukaryotic cell cycle requires precise temporal coordination of the activities of hundreds of ‘executor’ proteins (EPs) involved in cell growth and division. Cyclin‐dependent protein kinases (Cdks) play central roles in regulating the production, activation, inactivation and destruction of these EPs. From genome‐scale data sets of budding yeast, we identify 126 EPs that are regulated by Cdk1 both through direct phosphorylation of the EP and through phosphorylation of the transcription factors that control expression of the EP, so that each of these EPs is regulated by a feed‐forward loop (FFL) from Cdk1. By mathematical modelling, we show that such FFLs can activate EPs at different phases of the cell cycle depending of the effective signs (+ or −) of the regulatory steps of the FFL. We provide several case studies of EPs that are controlled by FFLs exactly as our models predict. The signal‐transduction properties of FFLs allow one (or a few) Cdk signal(s) to drive a host of cell cycle responses in correct temporal sequence.

Circadian rhythms synchronize mitosis in Neurospora crassa

Significance Circadian rhythms provide temporal information to other cellular processes, such as metabolism. We investigate the coupling between the cell cycle and the circadian clock using mathematical modeling and experimentally validate model-driven predictions with a model filamentous fungus, Neurospora crassa. We demonstrate a conserved coupling mechanism between the cell cycle and the circadian clock in Neurospora as in mammals, which results in circadian clock-gated mitotic cycles. Furthermore, we observe circadian clock-dependent phase shifts of G1 and G2 cyclins, which may alter the timing of divisions. Our work has large implications for the general understanding of the connection between the cell cycle and the circadian clock. The cell cycle and the circadian clock communicate with each other, resulting in circadian-gated cell division cycles. Alterations in this network may lead to diseases such as cancer. Therefore, it is critical to identify molecular components that connect these two oscillators. However, molecular mechanisms between the clock and the cell cycle remain largely unknown. A model filamentous fungus, Neurospora crassa, is a multinucleate system used to elucidate molecular mechanisms of circadian rhythms, but not used to investigate the molecular coupling between these two oscillators. In this report, we show that a conserved coupling between the circadian clock and the cell cycle exists via serine/threonine protein kinase-29 (STK-29), the Neurospora homolog of mammalian WEE1 kinase. Based on this finding, we established a mathematical model that predicts circadian oscillations of cell cycle components and circadian clock-dependent synchronized nuclear divisions. We experimentally demonstrate that G1 and G2 cyclins, CLN-1 and CLB-1, respectively, oscillate in a circadian manner with bioluminescence reporters. The oscillations of clb-1 and stk-29 gene expression are abolished in a circadian arrhythmic frqko mutant. Additionally, we show the light-induced phase shifts of a core circadian component, frq, as well as the gene expression of the cell cycle components clb-1 and stk-29, which may alter the timing of divisions. We then used a histone hH1-GFP reporter to observe nuclear divisions over time, and show that a large number of nuclear divisions occur in the evening. Our findings demonstrate the circadian clock-dependent molecular dynamics of cell cycle components that result in synchronized nuclear divisions in Neurospora.

An insulin-to-insulin regulatory network orchestrates phenotypic specificity in development and physiology

Insulin-like peptides (ILPs) play highly conserved roles in development and physiology. Most animal genomes encode multiple ILPs. Here we identify mechanisms for how the forty Caenorhabditis elegans ILPs coordinate diverse processes, including development, reproduction, longevity and several specific stress responses. Our systematic studies identify an ILP-based combinatorial code for these phenotypes characterized by substantial functional specificity and diversity rather than global redundancy. Notably, we show that ILPs regulate each other transcriptionally, uncovering an ILP-to-ILP regulatory network that underlies the combinatorial phenotypic coding by the ILP family. Extensive analyses of genetic interactions among ILPs reveal how their signals are integrated. A combined analysis of these functional and regulatory ILP interactions identifies local genetic circuits that act in parallel and interact by crosstalk, feedback and compensation. This organization provides emergent mechanisms for phenotypic specificity and graded regulation for the combinatorial phenotypic coding we observe. Our findings also provide insights into how large hormonal networks regulate diverse traits.