Computational systems biology of the cell cycle

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.

Modelling radiobiology

Radiotherapy has played an essential role in cancer treatment for over a century, and remains one of the best-studied methods of cancer treatment. Because of its close links with the physical sciences, it has been the subject of extensive quantitative mathematical modelling, but a complete understanding of the mechanisms of radiotherapy has remained elusive. In part this is because of the complexity and range of scales involved in radiotherapy-from physical radiation interactions occurring over nanometres to evolution of patient responses over months and years. This review presents the current status and ongoing research in modelling radiotherapy responses across these scales, including basic physical mechanisms of DNA damage, the immediate biological responses this triggers, and genetic- and patient-level determinants of response. Finally, some of the major challenges in this field and potential avenues for future improvements are also discussed.

Computational Biology Helps Understand How Polyploid Giant Cancer Cells Drive Tumor Success

Precision and organization govern the cell cycle, ensuring normal proliferation. However, some cells may undergo abnormal cell divisions (neosis) or variations of mitotic cycles (endopolyploidy). Consequently, the formation of polyploid giant cancer cells (PGCCs), critical for tumor survival, resistance, and immortalization, can occur. Newly formed cells end up accessing numerous multicellular and unicellular programs that enable metastasis, drug resistance, tumor recurrence, and self-renewal or diverse clone formation. An integrative literature review was carried out, searching articles in several sites, including: PUBMED, NCBI-PMC, and Google Academic, published in English, indexed in referenced databases and without a publication time filter, but prioritizing articles from the last 3 years, to answer the following questions: (i) "What is the current knowledge about polyploidy in tumors?"; (ii) "What are the applications of computational studies for the understanding of cancer polyploidy?"; and (iii) "How do PGCCs contribute to tumorigenesis?"

A biochemical necroptosis model explains cell-type-specific responses to cell death cues

Necroptosis is a form of regulated cell death associated with degenerative disorders, autoimmune and inflammatory diseases, and cancer. To better understand the biochemical mechanisms regulating necroptosis, we constructed a detailed computational model of tumor necrosis factor-induced necroptosis based on known molecular interactions from the literature. Intracellular protein levels, used as model inputs, were quantified using label-free mass spectrometry, and the model was calibrated using Bayesian parameter inference to experimental protein time course data from a well-established necroptosis-executing cell line. The calibrated model reproduced the dynamics of phosphorylated mixed lineage kinase domain-like protein, an established necroptosis reporter. A subsequent dynamical systems analysis identified four distinct modes of necroptosis signal execution, distinguished by rate constant values and the roles of the RIP1 deubiquitinating enzymes A20 and CYLD. In one case, A20 and CYLD both contribute to RIP1 deubiquitination, in another RIP1 deubiquitination is driven exclusively by CYLD, and in two modes either A20 or CYLD acts as the driver with the other enzyme, counterintuitively, inhibiting necroptosis. We also performed sensitivity analyses of initial protein concentrations and rate constants to identify potential targets for modulating necroptosis sensitivity within each mode. We conclude by associating numerous contrasting and, in some cases, counterintuitive experimental results reported in the literature with one or more of the model-predicted modes of necroptosis execution. In all, we demonstrate that a consensus pathway model of tumor necrosis factor-induced necroptosis can provide insights into unresolved controversies regarding the molecular mechanisms driving necroptosis execution in numerous cell types under different experimental conditions.

DNA-structured mathematical model of cell-cycle progression in cyclic hypoxia

New experimental data have shown how the periodic exposure of cells to low oxygen levels (i.e., cyclic hypoxia) impacts their progress through the cell-cycle. Cyclic hypoxia has been detected in tumours and linked to poor prognosis and treatment failure. While fluctuating oxygen environments can be reproduced in vitro, the range of oxygen cycles that can be tested is limited. By contrast, mathematical models can be used to predict the response to a wide range of cyclic dynamics. Accordingly, in this paper we develop a mechanistic model of the cell-cycle that can be combined with in vitro experiments, to better understand the link between cyclic hypoxia and cell-cycle dysregulation. A distinguishing feature of our model is the inclusion of impaired DNA synthesis and cell-cycle arrest due to periodic exposure to severely low oxygen levels. Our model decomposes the cell population into five compartments and a time-dependent delay accounts for the variability in the duration of the S phase which increases in severe hypoxia due to reduced rates of DNA synthesis. We calibrate our model against experimental data and show that it recapitulates the observed cell-cycle dynamics. We use the calibrated model to investigate the response of cells to oxygen cycles not yet tested experimentally. When the re-oxygenation phase is sufficiently long, our model predicts that cyclic hypoxia simply slows cell proliferation since cells spend more time in the S phase. On the contrary, cycles with short periods of re-oxygenation are predicted to lead to inhibition of proliferation, with cells arresting from the cell-cycle in the G2 phase. While model predictions on short time scales (about a day) are fairly accurate (i.e, confidence intervals are small), the predictions become more uncertain over longer periods. Hence, we use our model to inform experimental design that can lead to improved model parameter estimates and validate model predictions.

Periodicity in the embryo: Emergence of order in space, diffusion of order in time

Does embryonic development exhibit characteristic temporal features? This is apparent in evolution, where evolutionary change has been shown to occur in bursts of activity. Using two animal models (Nematode, Caenorhabditis elegans and Zebrafish, Danio rerio) and simulated data, we demonstrate that temporal heterogeneity exists in embryogenesis at the cellular level, and may have functional consequences. Cell proliferation and division from cell tracking data is subject to analysis to characterize specific features in each model species. Simulated data is then used to understand what role this variation might play in producing phenotypic variation in the adult phenotype. This goes beyond a molecular characterization of developmental regulation to provide a quantitative result at the phenotypic scale of complexity.

Mathematical Modelling in Biomedicine: A Primer for the Curious and the Skeptic

In most disciplines of natural sciences and engineering, mathematical and computational modelling are mainstay methods which are usefulness beyond doubt. These disciplines would not have reached today's level of sophistication without an intensive use of mathematical and computational models together with quantitative data. This approach has not been followed in much of molecular biology and biomedicine, however, where qualitative descriptions are accepted as a satisfactory replacement for mathematical rigor and the use of computational models is seen by many as a fringe practice rather than as a powerful scientific method. This position disregards mathematical thinking as having contributed key discoveries in biology for more than a century, e.g., in the connection between genes, inheritance, and evolution or in the mechanisms of enzymatic catalysis. Here, we discuss the role of computational modelling in the arsenal of modern scientific methods in biomedicine. We list frequent misconceptions about mathematical modelling found among biomedical experimentalists and suggest some good practices that can help bridge the cognitive gap between modelers and experimental researchers in biomedicine. This manuscript was written with two readers in mind. Firstly, it is intended for mathematical modelers with a background in physics, mathematics, or engineering who want to jump into biomedicine. We provide them with ideas to motivate the use of mathematical modelling when discussing with experimental partners. Secondly, this is a text for biomedical researchers intrigued with utilizing mathematical modelling to investigate the pathophysiology of human diseases to improve their diagnostics and treatment.

Modeling the Control of Meiotic Cell Divisions: Entry, Progression, and Exit

Upon nitrogen starvation, Schizosaccharomyces pombe exit the mitotic cell cycle and become irreversibly committed to the completion of meiosis program. Meiotic cell divisions are coordinated with sporulation events to produce haploid spores. In the last few decades, experiments on fission yeast have revealed different molecular players involved in two meiotic cell divisions, meiosis I (MI) and meiosis II (MII). How the MI entry, MI-to-MII transition, and MII exit occur because of the dynamics of the regulatory network is not well understood. In this work, we developed a comprehensive mathematical model of the network that describes the temporal dynamics of meiotic progression. The model accounts for the phenotypes of several experimental data (single and multiple mutations). We demonstrate the control strategy involving multiple feedback loops to yield two successive division cycles. The differential regulation of anaphase-promoting complex/cyclosome (APC/C) coactivators and its inhibitors is crucial for the dynamics of both MI-to-MII transition and MII exit. This model generates mechanistic insights that help in further experiments and modeling.

Towards abstraction of computational modelling of mammalian cell cycle: Model reduction pipeline incorporating multi-level hybrid petri nets

Cell cycle is a large biochemical network and it is crucial to simplify it to gain a clearer understanding and insights into the cell cycle. This is also true for other biochemical networks. In this study, we present a model abstraction scheme/pipeline to create a minimal abstract model of the whole mammalian cell cycle system from a large Ordinary Differential Equation model of cell cycle we published previously (Abroudi et al., 2017). The abstract model is developed in a way that it captures the main characteristics (dynamics of key controllers), responses (G1-S and G2-M transitions and DNA damage) and the signalling subsystems (Growth Factor, G1-S and G2-M checkpoints, and DNA damage) of the original model (benchmark). Further, our model exploits: (i) separation of time scales (slow and fast reactions), (ii) separation of levels of complexity (high-level and low-level interactions), (iii) cell-cycle stages (temporality), (iv) functional subsystems (as mentioned above), and (v) represents the whole cell cycle - within a Multi-Level Hybrid Petri Net (MLHPN) framework. Although hybrid Petri Nets is not new, the abstraction of interactions and timing we introduced here is new to cell cycle and Petri Nets. Importantly, our models builds on the significant elements, representing the core cell cycle system, found through a novel Global Sensitivity Analysis on the benchmark model, using Self Organising Maps and Correlation Analysis that we introduced in (Abroudi et al., 2017). Taken the two aspects together, our study proposes a 2-stage model reduction pipeline for large systems and the main focus of this paper is on stage 2, Petri Net model, put in the context of the pipeline. With the MLHPN model, the benchmark model with 61 continuous variables (ODEs) and 148 parameters were reduced to 14 variables (4 continuous (Cyc_Cdks - the main controllers of cell cycle) and 10 discrete (regulators of Cyc_Cdks)) and 31 parameters. Additional 9 discrete elements represented the temporal progression of cell cycle. Systems dynamics simulation results of the MLHPN model were in close agreement with the benchmark model with respect to the crucial metrics selected for comparison: order and pattern of Cyc_Cdk activation, timing of G1-S and G2-M transitions with or without DNA damage, efficiency of the two cell cycle checkpoints in arresting damaged cells and passing healthy cells, and response to two types of global parameter perturbations. The results show that the MLHPN provides a close approximation to the comprehensive benchmark model in robustly representing systems dynamics and emergent properties while presenting the core cell cycle controller in an intuitive, transparent and subsystems format.

What Will B Will B: Identifying Molecular Determinants of Diverse B-Cell Fate Decisions Through Systems Biology

B-cells are the poster child for cellular diversity and heterogeneity. The diverse repertoire of B lymphocytes, each expressing unique antigen receptors, provides broad protection against pathogens. However, B-cell diversity goes beyond unique antigen receptors. Side-stepping B-cell receptor (BCR) diversity through BCR-independent stimuli or engineered organisms with monoclonal BCRs still results in seemingly identical B-cells reaching a wide variety of fates in response to the same challenge. Identifying to what extent the molecular state of a B-cell determines its fate is key to gaining a predictive understanding of B-cells and consequently the ability to control them with targeted therapies. Signals received by B-cells through transmembrane receptors converge on intracellular molecular signaling networks, which control whether each B-cell divides, dies, or differentiates into a number of antibody-secreting distinct B-cell subtypes. The signaling networks that interpret these signals are well known to be susceptible to molecular variability and noise, providing a potential source of diversity in cell fate decisions. Iterative mathematical modeling and experimental studies have provided quantitative insight into how B-cells achieve distinct fates in response to pathogenic stimuli. Here, we review how systems biology modeling of B-cells, and the molecular signaling networks controlling their fates, is revealing the key determinants of cell-to-cell variability in B-cell destiny.

Application of Parameter Optimization to Search for Oscillatory Mass-Action Networks Using Python

Biological systems can be described mathematically to model the dynamics of metabolic, protein, or gene-regulatory networks, but locating parameter regimes that induce a particular dynamic behavior can be challenging due to the vast parameter landscape, particularly in large models. In the current work, a Pythonic implementation of existing bifurcation objective functions, which reward systems that achieve a desired bifurcation behavior, is implemented to search for parameter regimes that permit oscillations or bistability. A differential evolution algorithm progressively approximates the specified bifurcation type while performing a global search of parameter space for a candidate with the best fitness. The user-friendly format facilitates integration with systems biology tools, as Python is a ubiquitous programming language. The bifurcation–evolution software is validated on published models from the BioModels Database and used to search populations of randomly-generated mass-action networks for oscillatory dynamics. Results of this search demonstrate the importance of reaction enrichment to provide flexibility and enable complex dynamic behaviors, and illustrate the role of negative feedback and time delays in generating oscillatory dynamics.

Parameter estimation in models of biological oscillators: an automated regularised estimation approach

BACKGROUND

Dynamic modelling is a core element in the systems biology approach to understanding complex biosystems. Here, we consider the problem of parameter estimation in models of biological oscillators described by deterministic nonlinear differential equations. These problems can be extremely challenging due to several common pitfalls: (i) a lack of prior knowledge about parameters (i.e. massive search spaces), (ii) convergence to local optima (due to multimodality of the cost function), (iii) overfitting (fitting the noise instead of the signal) and (iv) a lack of identifiability. As a consequence, the use of standard estimation methods (such as gradient-based local ones) will often result in wrong solutions. Overfitting can be particularly problematic, since it produces very good calibrations, giving the impression of an excellent result. However, overfitted models exhibit poor predictive power. Here, we present a novel automated approach to overcome these pitfalls. Its workflow makes use of two sequential optimisation steps incorporating three key algorithms: (1) sampling strategies to systematically tighten the parameter bounds reducing the search space, (2) efficient global optimisation to avoid convergence to local solutions, (3) an advanced regularisation technique to fight overfitting. In addition, this workflow incorporates tests for structural and practical identifiability.

RESULTS

We successfully evaluate this novel approach considering four difficult case studies regarding the calibration of well-known biological oscillators (Goodwin, FitzHugh-Nagumo, Repressilator and a metabolic oscillator). In contrast, we show how local gradient-based approaches, even if used in multi-start fashion, are unable to avoid the above-mentioned pitfalls.

CONCLUSIONS

Our approach results in more efficient estimations (thanks to the bounding strategy) which are able to escape convergence to local optima (thanks to the global optimisation approach). Further, the use of regularisation allows us to avoid overfitting, resulting in more generalisable calibrated models (i.e. models with greater predictive power).

Computational modelling of meiotic entry and commitment

In response to developmental and environmental conditions, cells exit the mitotic cell cycle and enter the meiosis program to generate haploid gametes from diploid germ cells. Once cells decide to enter the meiosis program they become irreversibly committed to the completion of meiosis irrespective of the presence of cue signals. How meiotic entry and commitment occur due to the dynamics of the regulatory network is not well understood. Therefore, we constructed a mathematical model of the regulatory network that controls the transition from mitosis to meiosis in Schizosaccharomyces pombe. Upon nitrogen starvation, yeast cells exit mitosis and undergo conjugation and meiotic entry. The model includes the regulation of Mei2, an RNA binding protein required for conjugation and meiotic entry, by multiple feedback loops involving Pat1, a kinase that keeps cells in mitosis, and Ste11, a transcription activator required for the sexual differentiation. The model accounts for various experimental observations and demonstrates that the activation of Mei2 is bistable, which ensures the irreversible commitment to meiosis. Further, we show by integrating the meiosis-specific regulation with a cell cycle model, the dynamics of cell cycle exit, G1 arrest and entry into meiosis under nitrogen starvation.

MAMMOTh: A new database for curated mathematical models of biomolecular systems

MOTIVATION

Living systems have a complex hierarchical organization that can be viewed as a set of dynamically interacting subsystems. Thus, to simulate the internal nature and dynamics of the entire biological system, we should use the iterative way for a model reconstruction, which is a consistent composition and combination of its elementary subsystems. In accordance with this bottom-up approach, we have developed the MAthematical Models of bioMOlecular sysTems (MAMMOTh) tool that consists of the database containing manually curated MAMMOTh fitted to the experimental data and a software tool that provides their further integration.

RESULTS

The MAMMOTh database entries are organized as building blocks in a way that the model parts can be used in different combinations to describe systems with higher organizational level (metabolic pathways and/or transcription regulatory networks). The tool supports export of a single model or their combinations in SBML or Mathematica standards. The database currently contains 110 mathematical sub-models for Escherichia coli elementary subsystems (enzymatic reactions and gene expression regulatory processes) that can be combined in at least 5100 complex/sophisticated models concerning more complex biological processes as de novo nucleotide biosynthesis, aerobic/anaerobic respiration and nitrate/nitrite utilization in E. coli. All models are functionally interconnected and sufficiently complement public model resources.

AVAILABILITY

http://mammoth.biomodelsgroup.ru.

Modelling of the cancer cell cycle as a tool for rational drug development: A systems pharmacology approach to cyclotherapy

The dynamic of cancer is intimately linked to a dysregulation of the cell cycle and signalling pathways. It has been argued that selectivity of treatments could exploit loss of checkpoint function in cancer cells, a concept termed "cyclotherapy". Quantitative approaches that describe these dysregulations can provide guidance in the design of novel or existing cancer therapies. We describe and illustrate this strategy via a mathematical model of the cell cycle that includes descriptions of the G1-S checkpoint and the spindle assembly checkpoint (SAC), the EGF signalling pathway and apoptosis. We incorporated sites of action of four drugs (palbociclib, gemcitabine, paclitaxel and actinomycin D) to illustrate potential applications of this approach. We show how drug effects on multiple cell populations can be simulated, facilitating simultaneous prediction of effects on normal and transformed cells. The consequences of aberrant signalling pathways or of altered expression of pro- or anti-apoptotic proteins can thus be compared. We suggest that this approach, particularly if used in conjunction with pharmacokinetic modelling, could be used to predict effects of specific oncogene expression patterns on drug response. The strategy could be used to search for synthetic lethality and optimise combination protocol designs.

Molecular Network Dynamics of Cell Cycle Control: Periodicity of Start and Finish

The cell division cycle is controlled by a complex regulatory network which ensures that the phases of the cell cycle are executed in the right order. This regulatory network receives signals from the environment, monitors the state of the DNA, and decides timings of cell cycle events. The underlying transcriptional and post-translational regulatory interactions lead to complex dynamical responses, such as the oscillations in the levels of cell cycle proteins driven by intertwined biochemical reactions. A cell moves between different phases of its cycle similar to a dynamical system switching between its steady states. The complex molecular network driving these phases has been investigated in previous computational systems biology studies. Here, we review the critical physiological and molecular transitions that occur in the cell cycle and discuss the role of mathematical modeling in elucidating these transitions and understand cell cycle synchronization.

An Algorithm for Finding the Singleton Attractors and Pre-Images in Strong-Inhibition Boolean Networks

The detection of the singleton attractors is of great significance for the systematic study of genetic regulatory network. In this paper, we design an algorithm to compute the singleton attractors and pre-images of the strong-inhibition Boolean networks which is a biophysically plausible gene model. Our algorithm can not only identify accurately the singleton attractors, but also find easily the pre-images of the network. Based on extensive computational experiments, we show that the computational time of the algorithm is proportional to the number of the singleton attractors, which indicates the algorithm has much advantage in finding the singleton attractors for the networks with high average degree and less inhibitory interactions. Our algorithm may shed light on understanding the function and structure of the strong-inhibition Boolean networks.

T160‐phosphorylated CDK2 defines threshold for HGF dependent proliferation in primary hepatocytes

Liver regeneration is a tightly controlled process mainly achieved by proliferation of usually quiescent hepatocytes. The specific molecular mechanisms ensuring cell division only in response to proliferative signals such as hepatocyte growth factor (HGF) are not fully understood. Here, we combined quantitative time-resolved analysis of primary mouse hepatocyte proliferation at the single cell and at the population level with mathematical modeling. We showed that numerous G1/S transition components are activated upon hepatocyte isolation whereas DNA replication only occurs upon additional HGF stimulation. In response to HGF, Cyclin:CDK complex formation was increased, p21 rather than p27 was regulated, and Rb expression was enhanced. Quantification of protein levels at the restriction point showed an excess of CDK2 over CDK4 and limiting amounts of the transcription factor E2F-1. Analysis with our mathematical model revealed that T160 phosphorylation of CDK2 correlated best with growth factor-dependent proliferation, which we validated experimentally on both the population and the single cell level. In conclusion, we identified CDK2 phosphorylation as a gate-keeping mechanism to maintain hepatocyte quiescence in the absence of HGF.

Quantitative imaging with Fucci and mathematics to uncover temporal dynamics of cell cycle progression

Cell cycle progression is strictly coordinated to ensure proper tissue growth, development, and regeneration of multicellular organisms. Spatiotemporal visualization of cell cycle phases directly helps us to obtain a deeper understanding of controlled, multicellular, cell cycle progression. The fluorescent ubiquitination-based cell cycle indicator (Fucci) system allows us to monitor, in living cells, the G1 and the S/G2/M phases of the cell cycle in red and green fluorescent colors, respectively. Since the discovery of Fucci technology, it has found numerous applications in the characterization of the timing of cell cycle phase transitions under diverse conditions and various biological processes. However, due to the complexity of cell cycle dynamics, understanding of specific patterns of cell cycle progression is still far from complete. In order to tackle this issue, quantitative approaches combined with mathematical modeling seem to be essential. Here, we review several studies that attempted to integrate Fucci technology and mathematical models to obtain quantitative information regarding cell cycle regulatory patterns. Focusing on the technological development of utilizing mathematics to retrieve meaningful information from the Fucci producing data, we discuss how the combined methods advance a quantitative understanding of cell cycle regulation.

Validation of signalling pathways: Case study of the p16-mediated pathway

p16 is recognized as a tumor suppressor gene due to the prevalence of its genetic inactivation in all types of human cancers. Additionally, p16 gene plays a critical role in controlling aging, regulating cellular senescence, detection and maintenance of DNA damage. The molecular mechanism behind these events involves p16-mediated signaling pathway (or p16- Rb pathway), the focus of our study. Understanding functional dependence between dynamic behavior of biological components involved in the p16-mediated pathway and aforesaid molecular-level events might suggest possible implications in the diagnosis, prognosis and treatment of human cancer. In the present work, we employ reverse-engineering approach to construct the most detailed computational model of p16-mediated pathway in higher eukaryotes. We implement experimental data from the literature to validate the model, and under various assumptions predict the dynamic behavior of p16 and other biological components by interpreting the simulation results. The quantitative model of p16-mediated pathway is created in a systematic manner in terms of Petri net technologies.

Identification of under-detected periodicity in time-series microarray data by using empirical mode decomposition

Detecting periodicity signals from time-series microarray data is commonly used to facilitate the understanding of the critical roles and underlying mechanisms of regulatory transcriptomes. However, time-series microarray data are noisy. How the temporal data structure affects the performance of periodicity detection has remained elusive. We present a novel method based on empirical mode decomposition (EMD) to examine this effect. We applied EMD to a yeast microarray dataset and extracted a series of intrinsic mode function (IMF) oscillations from the time-series data. Our analysis indicated that many periodically expressed genes might have been under-detected in the original analysis because of interference between decomposed IMF oscillations. By validating a protein complex coexpression analysis, we revealed that 56 genes were newly determined as periodic. We demonstrated that EMD can be used incorporating with existing periodicity detection methods to improve their performance. This approach can be applied to other time-series microarray studies.

A data-driven, mathematical model of mammalian cell cycle regulation

Few of >150 published cell cycle modeling efforts use significant levels of data for tuning and validation. This reflects the difficultly to generate correlated quantitative data, and it points out a critical uncertainty in modeling efforts. To develop a data-driven model of cell cycle regulation, we used contiguous, dynamic measurements over two time scales (minutes and hours) calculated from static multiparametric cytometry data. The approach provided expression profiles of cyclin A2, cyclin B1, and phospho-S10-histone H3. The model was built by integrating and modifying two previously published models such that the model outputs for cyclins A and B fit cyclin expression measurements and the activation of B cyclin/Cdk1 coincided with phosphorylation of histone H3. The model depends on Cdh1-regulated cyclin degradation during G1, regulation of B cyclin/Cdk1 activity by cyclin A/Cdk via Wee1, and transcriptional control of the mitotic cyclins that reflects some of the current literature. We introduced autocatalytic transcription of E2F, E2F regulated transcription of cyclin B, Cdc20/Cdh1 mediated E2F degradation, enhanced transcription of mitotic cyclins during late S/early G2 phase, and the sustained synthesis of cyclin B during mitosis. These features produced a model with good correlation between state variable output and real measurements. Since the method of data generation is extensible, this model can be continually modified based on new correlated, quantitative data.

Introductory review of computational cell cycle modeling

Recent advances in the modeling of the cell cycle through computer simulation demonstrate the power of systems biology. By definition, systems biology has the goal to connect a parts list, prioritized through experimental observation or high-throughput screens, by the topology of interactions defining intracellular networks to predict system function. Computer modeling of biological systems is often compared to a process of reverse engineering. Indeed, designed or engineered technical systems share many systems-level properties with biological systems; thus studying biological systems within an engineering framework has proven successful. Here we review some aspects of this process as it pertains to cell cycle modeling.

A mathematical model of HiF-1α-mediated response to hypoxia on the G1/S transition

Hypoxia is known to influence the cell cycle by increasing the G1 phase duration or by inducing a quiescent state (arrest of cell proliferation). This entry into quiescence is a mean for the cell to escape from hypoxia-induced apoptosis. It is suggested that some cancer cells have gain the advantage over normal cells to easily enter into quiescence when environmental conditions, such as oxygen pressure, are unfavorable [43,1]. This ability contributes in the appearance of highly resistant and aggressive tumor phenotypes [2]. The HiF-1α factor is the key actor of the intracellular hypoxia pathway. As tumor cells undergo chronic hypoxic conditions, HiF-1α is present in higher level in cancer than in normal cells. Besides, it was shown that genetic mutations promoting overstabilization of HiF-1α are a feature of various types of cancers [7]. Finally, it is suggested that the intracellular level of HiF-1α can be related to the aggressiveness of the tumors [53,24,4,10]. However, up to now, mathematical models describing the G1/S transition under hypoxia, did not take into account the HiF-1α factor in the hypoxia pathway. Therefore, we propose a mathematical model of the G1/S transition under hypoxia, which explicitly integrates the HiF-1α pathway. The model reproduces the slowing down of G1 phase under moderate hypoxia, and the entry into quiescence of proliferating cells under severe hypoxia. We show how the inhibition of cyclin D by HiF-1α can induce quiescence; this result provides a theoretical explanation to the experimental observations of Wen et al. (2010) [50]. Thus, our model confirms that hypoxia-induced chemoresistance can be linked, for a part, to the negative regulation of cyclin D by HiF-1α.

Boolean network model predicts knockout mutant phenotypes of fission yeast

Boolean networks (or: networks of switches) are extremely simple mathematical models of biochemical signaling networks. Under certain circumstances, Boolean networks, despite their simplicity, are capable of predicting dynamical activation patterns of gene regulatory networks in living cells. For example, the temporal sequence of cell cycle activation patterns in yeasts S. pombe and S. cerevisiae are faithfully reproduced by Boolean network models. An interesting question is whether this simple model class could also predict a more complex cellular phenomenology as, for example, the cell cycle dynamics under various knockout mutants instead of the wild type dynamics, only. Here we show that a Boolean network model for the cell cycle control network of yeast S. pombe correctly predicts viability of a large number of known mutants. So far this had been left to the more detailed differential equation models of the biochemical kinetics of the yeast cell cycle network and was commonly thought to be out of reach for models as simplistic as Boolean networks. The new results support our vision that Boolean networks may complement other mathematical models in systems biology to a larger extent than expected so far, and may fill a gap where simplicity of the model and a preference for an overall dynamical blueprint of cellular regulation, instead of biochemical details, are in the focus.

In vivo and in silico analysis of PCNA ubiquitylation in the activation of the Post Replication Repair pathway in S. cerevisiae

BACKGROUND

The genome of living organisms is constantly exposed to several damaging agents that induce different types of DNA lesions, leading to cellular malfunctioning and onset of many diseases. To maintain genome stability, cells developed various repair and tolerance systems to counteract the effects of DNA damage. Here we focus on Post Replication Repair (PRR), the pathway involved in the bypass of DNA lesions induced by sunlight exposure and UV radiation. PRR acts through two different mechanisms, activated by mono- and poly-ubiquitylation of the DNA sliding clamp, called Proliferating Cell Nuclear Antigen (PCNA).

RESULTS

We developed a novel protocol to measure the time-course ratios between mono-, di- and tri-ubiquitylated PCNA isoforms on a single western blot, which were used as the wet readout for PRR events in wild type and mutant S. cerevisiae cells exposed to acute UV radiation doses. Stochastic simulations of PCNA ubiquitylation dynamics, performed by exploiting a novel mechanistic model of PRR, well fitted the experimental data at low UV doses, but evidenced divergent behaviors at high UV doses, thus driving the design of further experiments to verify new hypothesis on the functioning of PRR. The model predicted the existence of a UV dose threshold for the proper functioning of the PRR model, and highlighted an overlapping effect of Nucleotide Excision Repair (the pathway effectively responsible to clean the genome from UV lesions) on the dynamics of PCNA ubiquitylation in different phases of the cell cycle. In addition, we showed that ubiquitin concentration can affect the rate of PCNA ubiquitylation in PRR, offering a possible explanation to the DNA damage sensitivity of yeast strains lacking deubiquitylating enzymes.

CONCLUSIONS

We exploited an in vivo and in silico combinational approach to analyze for the first time in a Systems Biology context the events of PCNA ubiquitylation occurring in PRR in budding yeast cells. Our findings highlighted an intricate functional crosstalk between PRR and other events controlling genome stability, and evidenced that PRR is more complicated and still far less characterized than previously thought.

Mathematical modeling of fission yeast Schizosaccharomyces pombe cell cycle: exploring the role of multiple phosphatases

Cell cycle is the central process that regulates growth and division in all eukaryotes. Based on the environmental condition sensed, the cell lies in a resting phase G0 or proceeds through the cyclic cell division process (G1→S→G2→M). These series of events and phase transitions are governed mainly by the highly conserved Cyclin dependent kinases (Cdks) and its positive and negative regulators. The cell cycle regulation of fission yeast Schizosaccharomyces pombe is modeled in this study. The study exploits a detailed molecular interaction map compiled based on the published model and experimental data. There are accumulating evidences about the prominent regulatory role of specific phosphatases in cell cycle regulations. The current study emphasizes the possible role of multiple phosphatases that governs the cell cycle regulation in fission yeast S. pombe. The ability of the model to reproduce the reported regulatory profile for the wild-type and various mutants was verified though simulations.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11693-011-9090-7) contains supplementary material, which is available to authorized users.

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.

Dynamic expression profiles from static cytometry data: component fitting and conversion to relative, "same scale" values

Background

Cytometry of asynchronous proliferating cell populations produces data with an extractable time-based feature embedded in the frequency of clustered, correlated events. Here, we present a specific case of general methodology for calculating dynamic expression profiles of epitopes that oscillate during the cell cycle and conversion of these values to the same scale.

Methods

Samples of K562 cells from one population were labeled by direct and indirect antibody methods for cyclins A2 and B1 and phospho-S10-histone H3. The same indirect antibody was used for both cyclins. Directly stained samples were counter-stained with 4′6-diamidino-2-phenylindole and indirectly stained samples with propidium to label DNA. The S phase cyclin expressions from indirect assays were used to scale the expression of the cyclins of the multi-variate direct assay. Boolean gating and two dimensional, sequential regions set on bivariate displays of the directly conjugated sample data were used to untangle and isolate unique, unambiguous expression values of the cyclins along the four-dimensional data path through the cell cycle. The median values of cyclins A2 and B1 from each region were correlated with the frequency of events within each region.

Results

The sequential runs of data were plotted as continuous multi-line linear equations of the form y  =  [(y_i+1−y_i)/(x_i+1−x_i)]x + y_i−[(y_i+1−y_i)/(x_i+1−x_i)]x_i (line between points (x_i,y_i) and (x_i+1, y_i+1)) to capture the dynamic expression profile of the two cyclins.

Conclusions

This specific approach demonstrates the general methodology and provides a rule set from which the cell cycle expression of any other epitopes could be measured and calculated. These expression profiles are the “state variable” outputs, useful for calibrating mathematical cell cycle models.

State of the art in silico tools for the study of signaling pathways in cancer

In the last several years, researchers have exhibited an intense interest in the evolutionarily conserved signaling pathways that have crucial roles during embryonic development. Interestingly, the malfunctioning of these signaling pathways leads to several human diseases, including cancer. The chemical and biophysical events that occur during cellular signaling, as well as the number of interactions within a signaling pathway, make these systems complex to study. In silico resources are tools used to aid the understanding of cellular signaling pathways. Systems approaches have provided a deeper knowledge of diverse biochemical processes, including individual metabolic pathways, signaling networks and genome-scale metabolic networks. In the future, these tools will be enormously valuable, if they continue to be developed in parallel with growing biological knowledge. In this study, an overview of the bioinformatics resources that are currently available for the analysis of biological networks is provided.

An integrative model links multiple inputs and signaling pathways to the onset of DNA synthesis in hepatocytes

During liver regeneration, quiescent hepatocytes re-enter the cell cycle to proliferate and compensate for lost tissue. Multiple signals including hepatocyte growth factor, epidermal growth factor, tumor necrosis factor α, interleukin-6, insulin and transforming growth factor β orchestrate these responses and are integrated during the G₁ phase of the cell cycle. To investigate how these inputs influence DNA synthesis as a measure for proliferation, we established a large-scale integrated logical model connecting multiple signaling pathways and the cell cycle. We constructed our model based upon established literature knowledge, and successively improved and validated its structure using hepatocyte-specific literature as well as experimental DNA synthesis data. Model analyses showed that activation of the mitogen-activated protein kinase and phosphatidylinositol 3-kinase pathways was sufficient and necessary for triggering DNA synthesis. In addition, we identified key species in these pathways that mediate DNA replication. Our model predicted oncogenic mutations that were compared with the COSMIC database, and proposed intervention targets to block hepatocyte growth factor-induced DNA synthesis, which we validated experimentally. Our integrative approach demonstrates that, despite the complexity and size of the underlying interlaced network, logical modeling enables an integrative understanding of signaling-controlled proliferation at the cellular level, and thus can provide intervention strategies for distinct perturbation scenarios at various regulatory levels.

Genes adopt non-optimal codon usage to generate cell cycle-dependent oscillations in protein levels

Most cell cycle-regulated genes adopt non-optimal codon usage, namely, their translation involves wobbly matching codons. Here, the authors show that tRNA expression is cyclic and that codon usage, therefore, can give rise to cell-cycle regulation of proteins.

Most cell cycle-regulated genes adopt non-optimal codon usage.

Non-optimal codon usage can give rise to cell-cycle dynamics at the protein level.

The high expression of transfer RNAs (tRNAs) observed in G2 phase enables cell cycle-regulated genes to adopt non-optimal codon usage, and conversely the lower expression of tRNAs at the end of G1 phase is associated with optimal codon usage.

The protein levels of aminoacyl-tRNA synthetases oscillate, peaking in G2/M phase, consistent with the observed cyclic expression of tRNAs.

The cell cycle is a temporal program that regulates DNA synthesis and cell division. When we compared the codon usage of cell cycle-regulated genes with that of other genes, we discovered that there is a significant preference for non-optimal codons. Moreover, genes encoding proteins that cycle at the protein level exhibit non-optimal codon preferences. Remarkably, cell cycle-regulated genes expressed in different phases display different codon preferences. Here, we show empirically that transfer RNA (tRNA) expression is indeed highest in the G2 phase of the cell cycle, consistent with the non-optimal codon usage of genes expressed at this time, and lowest toward the end of G1, reflecting the optimal codon usage of G1 genes. Accordingly, protein levels of human glycyl-, threonyl-, and glutamyl-prolyl tRNA synthetases were found to oscillate, peaking in G2/M phase. In light of our findings, we propose that non-optimal (wobbly) matching codons influence protein synthesis during the cell cycle. We describe a new mathematical model that shows how codon usage can give rise to cell-cycle regulation. In summary, our data indicate that cells exploit wobbling to generate cell cycle-dependent dynamics of proteins.

Transcriptional regulation is a major controller of cell cycle transition dynamics

DNA replication, mitosis and mitotic exit are critical transitions of the cell cycle which normally occur only once per cycle. A universal control mechanism was proposed for the regulation of mitotic entry in which Cdk helps its own activation through two positive feedback loops. Recent discoveries in various organisms showed the importance of positive feedbacks in other transitions as well. Here we investigate if a universal control system with transcriptional regulation(s) and post-translational positive feedback(s) can be proposed for the regulation of all cell cycle transitions. Through computational modeling, we analyze the transition dynamics in all possible combinations of transcriptional and post-translational regulations. We find that some combinations lead to ‘sloppy’ transitions, while others give very precise control. The periodic transcriptional regulation through the activator or the inhibitor leads to radically different dynamics. Experimental evidence shows that in cell cycle transitions of organisms investigated for cell cycle dependent periodic transcription, only the inhibitor OR the activator is under cyclic control and never both of them. Based on these observations, we propose two transcriptional control modes of cell cycle regulation that either STOP or let the cycle GO in case of a transcriptional failure. We discuss the biological relevance of such differences.

Applications and trends in systems biology in biochemistry

Systems biology has received an ever increasing interest during the last decade. A large amount of third-party funding is spent on this topic, which involves quantitative experimentation integrated with computational modeling. Industrial companies are also starting to use this approach more and more often, especially in pharmaceutical research and biotechnology. This leads to the question of whether such interest is wisely invested and whether there are success stories to be told for basic science and/or technology/biomedicine. In this review, we focus on the application of systems biology approaches that have been employed to shed light on both biochemical functions and previously unknown mechanisms. We point out which computational and experimental methods are employed most frequently and which trends in systems biology research can be observed. Finally, we discuss some problems that we have encountered in publications in the field.

Simulation of the Ras/cAMP/PKA pathway in budding yeast highlights the establishment of stable oscillatory states

In the yeast Saccharomyces cerevisiae, the Ras/cAMP/PKA pathway plays a major role in the regulation of metabolism, stress resistance and cell cycle progression. We extend here a mechanistic model of the Ras/cAMP/PKA pathway that we previously defined by describing the molecular interactions and post-translational modifications of proteins, and perform a computational analysis to investigate the dynamical behaviors of the components of this pathway, regulated by different control mechanisms. We carry out stochastic simulations to consider, in particular, the effect of the negative feedback loops on the activity of both Ira2 (a Ras-GAP) and Cdc25 (a Ras-GEF) proteins. Our results show that stable oscillatory regimes for the dynamics of cAMP can be obtained only through the activation of these feedback mechanisms, and when the amount of Cdc25 is within a specific range. In addition, we highlight that the levels of guanine nucleotides pools are able to regulate the pathway, by influencing the transition between stable steady states and oscillatory regimes.

A general framework for modeling growth and division of mammalian cells

BACKGROUND

Modeling the cell-division cycle has been practiced for many years. As time has progressed, this work has gone from understanding the basic principles to addressing distinct biological problems, e.g., the nature of the restriction point, how checkpoints operate, the nonlinear dynamics of the cell cycle, the effect of localization, etc. Most models consist of coupled ordinary differential equations developed by the researchers, restricted to deal with the interactions of a limited number of molecules. In the future, cell-cycle modeling--and indeed all modeling of complex biologic processes--will increase in scope and detail.

RESULTS

A framework for modeling complex cell-biologic processes is proposed here. The framework is based on two constructs: one describing the entire lifecycle of a molecule and the second describing the basic cellular machinery. Use of these constructs allows complex models to be built in a straightforward manner that fosters rigor and completeness. To demonstrate the framework, an example model of the mammalian cell cycle is presented that consists of several hundred differential equations of simple mass action kinetics. The model calculates energy usage, amino acid and nucleotide usage, membrane transport, RNA synthesis and destruction, and protein synthesis and destruction for 33 proteins to give an in-depth look at the cell cycle.

CONCLUSIONS

The framework presented here addresses how to develop increasingly descriptive models of complex cell-biologic processes. The example model of cellular growth and division constructed with the framework demonstrates that large structured models can be created with the framework, and these models can generate non-trivial descriptions of cellular processes. Predictions from the example model include those at both the molecular level--e.g., Wee1 spontaneously reactivates--and at the system level--e.g., pathways for timing-critical processes must shut down redundant pathways. A future effort is to automatically estimate parameter values that are insensitive to changes.

Integrated computational model of cell cycle and checkpoint reveals different essential roles of Aurora-A and Plk1 in mitotic entry

Understanding the regulation of mitotic entry is one of the most important goals of modern cell biology, and computational modeling of mitotic entry has been a subject of several recent studies. However, there are still many regulation mechanisms that remain poorly characterized. Two crucial aspects are how mitotic entry is controlled by its upstream regulators Aurora-A and Plk1, and how mitotic entry is coordinated with other biological events, especially G2/M checkpoint. In this context, we reconstructed a comprehensive computational model that integrates the mitotic entry network and the G2/M checkpoint system. Computational simulation of this model and subsequent experimental verification revealed that Aurora-A and Plk1 are redundant to the activation of cyclin B/Cdk1 during normal mitotic entry, but become especially important for cyclin B/Cdk1 activation during G2/M checkpoint recovery. Further analysis indicated that, in response to DNA damage, Chk1-mediated network rewiring makes cyclin B/Cdk1 more sensitive to the down-regulation of Aurora-A and Plk1. In addition, we demonstrated that concurrently targeting Aurora-A and Plk1 during G2/M checkpoint recovery achieves a synergistic effect, which suggests the combinational use of Aurora-A and Plk1 inhibitors after chemotherapy or radiotherapy. Thus, the results presented here provide novel insights into the regulation mechanism of mitotic entry and have potential value in cancer therapy.

Molecular network dynamics of cell cycle control: transitions to start and finish

The cell cycle is controlled by complex regulatory network to ensure that the phases of the cell cycle happen in the right order and transitions between phases happen only if the earlier phase is properly finished. This regulatory network receives signals from the environment, monitors the state of the DNA, and decides when the cell can proceed in its cycle. The transcriptional and post-translational regulatory interactions in this network can lead to complex dynamical responses. The cell cycle dependent oscillations in protein activities are driven by these interactions as the regulatory system moves between steady states that correspond to different phases of the cell cycle. The analysis of such complex molecular network behavior can be investigated with the tools of computational systems biology. Here we review the basic physiological and molecular transitions in the cell cycle and present how the system-level emergent properties were found by the help of mathematical/computational modeling.

Towards a unifying, systems biology understanding of large-scale cellular death and destruction caused by poorly liganded iron: Parkinson's, Huntington's, Alzheimer's, prions, bactericides, chemical toxicology and others as examples

Exposure to a variety of toxins and/or infectious agents leads to disease, degeneration and death, often characterised by circumstances in which cells or tissues do not merely die and cease to function but may be more or less entirely obliterated. It is then legitimate to ask the question as to whether, despite the many kinds of agent involved, there may be at least some unifying mechanisms of such cell death and destruction. I summarise the evidence that in a great many cases, one underlying mechanism, providing major stresses of this type, entails continuing and autocatalytic production (based on positive feedback mechanisms) of hydroxyl radicals via Fenton chemistry involving poorly liganded iron, leading to cell death via apoptosis (probably including via pathways induced by changes in the NF-κB system). While every pathway is in some sense connected to every other one, I highlight the literature evidence suggesting that the degenerative effects of many diseases and toxicological insults converge on iron dysregulation. This highlights specifically the role of iron metabolism, and the detailed speciation of iron, in chemical and other toxicology, and has significant implications for the use of iron chelating substances (probably in partnership with appropriate anti-oxidants) as nutritional or therapeutic agents in inhibiting both the progression of these mainly degenerative diseases and the sequelae of both chronic and acute toxin exposure. The complexity of biochemical networks, especially those involving autocatalytic behaviour and positive feedbacks, means that multiple interventions (e.g. of iron chelators plus antioxidants) are likely to prove most effective. A variety of systems biology approaches, that I summarise, can predict both the mechanisms involved in these cell death pathways and the optimal sites of action for nutritional or pharmacological interventions.