Mathematical modeling of cell cycle regulation in response to DNA damage: Exploring mechanisms of cell-fate determination

The plk1 Gene Regulatory Network Modeling Identifies Three Circuits for plk1-mediated Genomic Instability Leading to Neoplastic Transformation

Genomic instability has been increasingly recognized over the past decade as a fundamental driver of cancer initiation and progression, largely owing to its association with specific genes and cellular mechanisms that offer therapeutic potential. However, a comprehensive molecular framework that captures the interconnected processes underlying this phenomenon remains elusive. In this study, we focused on polo-like kinase 1 (PLK1), a key cell cycle regulator frequently overexpressed in diverse human tumors, to reconstruct a regulatory network that consolidates pre-existing biological knowledge exclusively related to pathways involved in genome stability maintenance and cancer. The resulting model integrates nine biological processes, 1030 reactions, and 716 molecular species to form a literature-supported network in which PLK1 serves as a central regulatory node. However, rather than depicting an isolated PLK1-centric system, this network reflects a broader and more complex architecture of interrelated genomic instability mechanisms. As expected, the simulations reproduced known behaviors associated with PLK1 dysregulation, reinforcing the well-established role of the kinase in genome destabilization. Importantly, this model also enables the exploration of additional, less-characterized dynamics, including the potential involvement of genes such as kif2c, incenp, and other regulators of chromosomal segregation and DNA repair, which appear to contribute to instability events downstream of PLK1. While these findings are grounded in mechanistic simulations and require further experimental validation, gene expression and survival analyses across tumor types support their clinical relevance by linking them to poor prognosis in specific cancers. Overall, the model provides a systemic and adaptable foundation for studying PLK1-related genomic instability, enabling both the reinforcement of known mechanisms and discovery of candidate genes and circuits that may drive tumorigenesis through compromised genome integrity across distinct cancer contexts.

Curating models from BioModels: Developing a workflow for creating OMEX files

The reproducibility of computational biology models can be greatly facilitated by widely adopted standards and public repositories. We examined 50 models from the BioModels Database and attempted to validate the original curation and correct some of them if necessary. For each model, we reproduced these published results using Tellurium. Once reproduced we manually created a new set of files, with the model information stored by the Systems Biology Markup Language (SBML), and simulation instructions stored by the Simulation Experiment Description Markup Language (SED-ML), and everything included in an Open Modeling EXchange (OMEX) file, which could be used with a variety of simulators to reproduce the same results. On the one hand, the reproducibility procedure of 50 models developed a manual workflow that we would use to build an automatic platform to help users more easily curate and verify models in the future. On the other hand, these exercises allowed us to find the limitations and possible enhancement of the current curation and tooling to verify and curate models.

Curating models from BioModels: Developing a workflow for creating OMEX files

The reproducibility of computational biology models can be greatly facilitated by widely adopted standards and public repositories. We examined 50 models from the BioModels Database and attempted to validate the original curation and correct some of them if necessary. For each model, we reproduced these published results using Tellurium. Once reproduced we manually created a new set of files, with the model information stored by the Systems Biology Markup Language (SBML), and simulation instructions stored by the Simulation Experiment Description Markup Language (SED-ML), and everything included in an Open Modeling EXchange (OMEX) file, which could be used with a variety of simulators to reproduce the same results. On the one hand, the reproducibility procedure of 50 models developed a manual workflow that we would use to build an automatic platform to help users more easily curate and verify models in the future. On the other hand, these exercises allowed us to find the limitations and possible enhancement of the current curation and tooling to verify and curate models.

TOPAS-Tissue: A Framework for the Simulation of the Biological Response to Ionizing Radiation at the Multi-Cellular Level

This work aims to develop and validate a framework for the multiscale simulation of the biological response to ionizing radiation in a population of cells forming a tissue. We present TOPAS-Tissue, a framework to allow coupling two Monte Carlo (MC) codes: TOPAS with the TOPAS-nBio extension, capable of handling the track-structure simulation and subsequent chemistry, and CompuCell3D, an agent-based model simulator for biological and environmental behavior of a population of cells. We verified the implementation by simulating the experimental conditions for a clonogenic survival assay of a 2-D PC-3 cell culture model (10 cells in 10,000 µm2) irradiated by MV X-rays at several absorbed dose values from 0-8 Gy. The simulation considered cell growth and division, irradiation, DSB induction, DNA repair, and cellular response. The survival was obtained by counting the number of colonies, defined as a surviving primary (or seeded) cell with progeny, at 2.7 simulated days after irradiation. DNA repair was simulated with an MC implementation of the two-lesion kinetic model and the cell response with a p53 protein-pulse model. The simulated survival curve followed the theoretical linear-quadratic response with dose. The fitted coefficients α = 0.280 ± 0.025/Gy and β = 0.042 ± 0.006/Gy2 agreed with published experimental data within two standard deviations. TOPAS-Tissue extends previous works by simulating in an end-to-end way the effects of radiation in a cell population, from irradiation and DNA damage leading to the cell fate. In conclusion, TOPAS-Tissue offers an extensible all-in-one simulation framework that successfully couples Compucell3D and TOPAS for multiscale simulation of the biological response to radiation.

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

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

Reusable rule-based cell cycle model explains compartment-resolved dynamics of 16 observables in RPE-1 cells

The mammalian cell cycle is regulated by a well-studied but complex biochemical reaction system. Computational models provide a particularly systematic and systemic description of the mechanisms governing mammalian cell cycle control. By combining both state-of-the-art multiplexed experimental methods and powerful computational tools, this work aims at improving on these models along four dimensions: model structure, validation data, validation methodology and model reusability. We developed a comprehensive model structure of the full cell cycle that qualitatively explains the behaviour of human retinal pigment epithelial-1 cells. To estimate the model parameters, time courses of eight cell cycle regulators in two compartments were reconstructed from single cell snapshot measurements. After optimisation with a parallel global optimisation metaheuristic we obtained excellent agreements between simulations and measurements. The PEtab specification of the optimisation problem facilitates reuse of model, data and/or optimisation results. Future perturbation experiments will improve parameter identifiability and allow for testing model predictive power. Such a predictive model may aid in drug discovery for cell cycle-related disorders.

Handling DNA malfunctions by unsupervised machine learning model

The cell cycle is a rich field for research, especially, the DNA damage. DNA damage, which happened naturally or as a result of environmental influences causes change in the chemical structure of DNA. The extent of DNA damage has a significant impact on the fate of the cell in later stages. In this paper, we introduced an Unsupervised Machine learning Model for DNA Damage Diagnosis and Analysis. Mainly, we employed K-means clustering unsupervised machine learning algorithms. Unsupervised algorithms commonly draw conclusions from datasets by solely utilizing input vectors, disregarding any known or labeled outcomes. The model provided deep insight about DNA damage and exposes the protein levels for proteins when work together in sub-network model to deal with DNA damage occurrence, the unsupervised artificial model explained the sub-network biological model activities in regard to the changing in their concentrations in several clusters, they have been grouped in such as (0 - no damage, 1 - low, 2 - medium, 3 - high, and 4 - excess) DNA damage clusters. The results provided a rational and persuasive explanation for numerous important phenomena, including the oscillation of the protein p53, in a clear and understandable manner. Which is encouraging since it demonstrates that the K-means clustering approach can be easily applied to many similar biological systems, which aids in better understanding the key dynamics of these systems.

An autonomous mathematical model for the mammalian cell cycle

A mathematical model for the mammalian cell cycle is developed as a system of 13 coupled nonlinear ordinary differential equations. The variables and interactions included in the model are based on detailed consideration of available experimental data. A novel feature of the model is inclusion of cycle tasks such as origin licensing and initiation, nuclear envelope breakdown and kinetochore attachment, and their interactions with controllers (molecular complexes involved in cycle control). Other key features are that the model is autonomous, except for a dependence on external growth factors; the variables are continuous in time, without instantaneous resets at phase boundaries; mechanisms to prevent rereplication are included; and cycle progression is independent of cell size. Eight variables represent cell cycle controllers: the Cyclin D1-Cdk4/6 complex, APC^Cdh1, SCF^βTrCP, Cdc25A, MPF, NuMA, the securin-separase complex, and separase. Five variables represent task completion, with four for the status of origins and one for kinetochore attachment. The model predicts distinct behaviors corresponding to the main phases of the cell cycle, showing that the principal features of the mammalian cell cycle, including restriction point behavior, can be accounted for in a quantitative mechanistic way based on known interactions among cycle controllers and their coupling to tasks. The model is robust to parameter changes, in that cycling is maintained over at least a five-fold range of each parameter when varied individually. The model is suitable for exploring how extracellular factors affect cell cycle progression, including responses to metabolic conditions and to anti-cancer therapies.

Proteins as fuzzy controllers: Auto tuning a biological fuzzy inference system to predict protein dynamics in complex biological networks

Biological systems such as mammalian cell cycle are complex systems consisting of a large number of molecular species interacting in ways that produce complex nonlinear systems dynamics. Discrete models such as Boolean models and continuous models such as Ordinary Differential Equations (ODEs) have been widely used to study these systems. Boolean models are simple and can capture qualitative systems behaviour, but they cannot capture the continuous trends of protein concentrations, while ODE models capture continuous trends but require kinetics parameters that are limited. Further, as systems get larger, complexity of these models becomes an issue for parameterization, analysis and interpretation. Also, molecular systems operate under the conditions of uncertainty and noise and our understanding of molecular processes in general is more at a qualitative level characterised by vagueness, imprecision and ambiguity. Hence, as more data are generated, there is a greater need for simpler data driven methods that can approximate continuous system behaviour while representing vagueness and ambiguity without requiring kinetic parameters. Fuzzy inferencing is one such promising method with the ability to work with qualitative vague/imprecise biological knowledge. In this study, we propose a fuzzy inference system for representing continuous behaviour of proteins and apply to some key proteins in the mammalian cell cycle system. The methods we introduced here is novel to protein interaction systems and cell cycle proteins. Our study proposes a three-stage approach to develop fuzzy protein controllers. In stage one, protein system is studied for interactions. We studied some significant core controllers of mammalian cell cycle and their producers and degraders as presented in a published ODE model. Based on the observations from a dataset generated from it, we developed Fuzzy inference systems (FIS) in the second stage, that involved deriving fuzzy IF-THEN rules and their processing, and manually tuned the FIS to predict the dynamics of individual proteins. In stage three, we employed Particle Swarm Optimisation (PSO) for optimising the FIS to further enhance prediction accuracy. Systems dynamics simulation results of the optimised FIS models were in close agreement with the benchmark ODE model results. The results show that the FIS models provide a close approximation to the comprehensive benchmark model in robustly representing continuous protein dynamics while representing the control of protein behavior in an intuitive and transparent format without requiring kinetic parameters. Therefore, FIS models can be an alternative to ODEs in network modelling. Further, FIS models can be assembled to develop large complex systems without losing information or accuracy.

Computational modeling of protracted HCMV replication using genome substrates and protein temporal profiles

Human cytomegalovirus (HCMV) is a major cause of illness in immunocompromised individuals. The HCMV lytic cycle contributes to the clinical manifestations of infection. The lytic cycle occurs over ∼96 h in diverse cell types and consists of viral DNA (vDNA) genome replication and temporally distinct expression of hundreds of viral proteins. Given its complexity, understanding this elaborate system can be facilitated by the introduction of mechanistic computational modeling of temporal relationships. Therefore, we developed a multiplicity of infection (MOI)-dependent mechanistic computational model that simulates vDNA kinetics and late lytic replication based on in-house experimental data. The predictive capabilities were established by comparison to post hoc experimental data. Computational analysis of combinatorial regulatory mechanisms suggests increasing rates of protein degradation in association with increasing vDNA levels. The model framework also allows expansion to account for additional mechanisms regulating the processes. Simulating vDNA kinetics and the late lytic cycle for a wide range of MOIs yielded several unique observations. These include the presence of saturation behavior at high MOIs, inefficient replication at low MOIs, and a precise range of MOIs in which virus is maximized within a cell type, being 0.382 IU to 0.688 IU per fibroblast. The predicted saturation kinetics at high MOIs are likely related to the physical limitations of cellular machinery, while inefficient replication at low MOIs may indicate a minimum input material required to facilitate infection. In summary, we have developed and demonstrated the utility of a data-driven and expandable computational model simulating lytic HCMV infection.

Crosstalk between Plk1, p53, cell cycle, and G2/M DNA damage checkpoint regulation in cancer: computational modeling and analysis

Different cancer cell lines can have varying responses to the same perturbations or stressful conditions. Cancer cells that have DNA damage checkpoint-related mutations are often more sensitive to gene perturbations including altered Plk1 and p53 activities than cancer cells without these mutations. The perturbations often induce a cell cycle arrest in the former cancer, whereas they only delay the cell cycle progression in the latter cancer. To study crosstalk between Plk1, p53, and G2/M DNA damage checkpoint leading to differential cell cycle regulations, we developed a computational model by extending our recently developed model of mitotic cell cycle and including these key interactions. We have used the model to analyze the cancer cell cycle progression under various gene perturbations including Plk1-depletion conditions. We also analyzed mutations and perturbations in approximately 1800 different cell lines available in the Cancer Dependency Map and grouped lines by genes that are represented in our model. Our model successfully explained phenotypes of various cancer cell lines under different gene perturbations. Several sensitivity analysis approaches were used to identify the range of key parameter values that lead to the cell cycle arrest in cancer cells. Our resulting model can be used to predict the effect of potential treatments targeting key mitotic and DNA damage checkpoint regulators on cell cycle progression of different types of cancer cells.

A new hierarchical approach to multi-level model abstraction for simplifying ODE models of biological networks and a case study: The G1/S Checkpoint/DNA damage signalling pathways of mammalian cell cycle

Model reduction is an important topic in studies of biological systems. By reducing the complexity of large models through multi-level models while keeping the essence (biological meaning) of the model, model reduction can help answer many important questions about these systems. In this paper, we present a new reduction method based on hierarchical representation and a lumping approach. We used G1/S checkpoint pathway represented in Ordinary Differential Equations (ODE) in Iwamoto et al. (2011) as a case study to present this reduction method. The approach consists of two parts; the first part represents the biological network as a hierarchy (multiple levels) based on protein binding relations, which allowed us to model the biological network at different levels of abstraction. The second part applies different levels (level 1, 2 and 3) of lumping the species together depending on the level of the hierarchy, resulting in a reduced and transformed model for each level. The model at each level is a representation of the whole system and can address questions pertinent to that level. We develop and simulate reduced models for levels-1, 2 and 3 of lumping for the G1/S checkpoint pathway and evaluate the biological plausibility of the proposed method by comparing the results with the original ODE model of Iwamoto et al. (2011). The results for continuous dynamics of the G1/S checkpoint pathway with or without DNA-damage for reduced models of level- 1, 2 and 3 of lumping are in very good agreement and consistent with the original model results and with biological findings. Therefore, the reduced models (level-1, 2 and 3) can be used to study cell cycle progression in G1 and the effects of DNA damage on it. It is suitable for reducing complex ODE biological network models while retaining accurate continuous dynamics of the system. The 3 levels of the reduced models respectively achieved 20%, 26% and 31% reduction of the base model. Moreover, the reduced model is more efficient to run (30%, 44% and 52% time reduction for the three levels) and generate solutions than the original ODE model. Simplification of complex mathematical models is possible and the proposed reduction method has the potential to make an impact across many fields of biomedical research.

Mathematical analysis-based feasibility study of pre-emptive medicine for Staphylococcus aureus infectious disease: Early detection and antibiotic-free maintenance therapy

Global efforts are being made to achieve the clinical implementation of pre-emptive medicine for Staphylococcus aureus (S. aureus) infectious disease, which will realize both early detection at the pre-symptom stage and bacteriostatic therapy by antibiotic-free medicine in a future. Several research groups proposed the intercellular signal transduction factor (auto-inducing peptide: AIP) antibody, the synthesised AIP analogues and a cyclic depsipeptide with high constitutional similarity to AIP as a candidate of the pre-emptive medicine for S. aureus infectious disease. In this paper, to evaluate a validity of them, we mathematically explored both a pre-symptom associated with the pathogenic expression process of S. aureus and several therapeutic targets that delay or suppress the appearance of the pre-symptom. The stochastic mathematical analysis identified a peak of fluctuation in intracellular AgrD concentration as the pre-symptom. Moreover, employing parameter sensitivity analysis, the enhancement of binding inhibition between AgrC receptor and AIP was identified as effective therapeutic target. Based on these findings, we evaluated a feasibility of above-mentioned candidates, and concluded that the continuous application of AgrC receptor antagonists, such as the synthesised AIP analogues and a cyclic depsipeptide with high constitutional similarity to AIP, is useful as pre-emptive medicine for S. aureus infectious disease.

Modeling Long ncRNA-Mediated Regulation in the Mammalian Cell Cycle

Long noncoding RNAs (lncRNAs) are transcripts longer than 200 nucleotides that are not translated into proteins. They have recently gained widespread attention due to the finding that tens of thousands of lncRNAs reside in the human genome, and due to an increasing number of lncRNAs that are found to be associated with disease. Some lncRNAs, including disease-associated ones, play different roles in regulating the cell cycle. Mathematical models of the cell cycle have been useful in better understanding this biological system, such as how it could be robust to some perturbations and how the cell cycle checkpoints could act as a switch. Here, we discuss mathematical modeling techniques for studying lncRNA regulation of the mammalian cell cycle. We present examples on how modeling via network analysis and differential equations can provide novel predictions toward understanding cell cycle regulation in response to perturbations such as DNA damage.

Understanding non-linear effects from Hill-type dynamics with application to decoding of p53 signaling

Analytical equations are derived depicting four possible scenarios resulting from pulsed signaling of a system subject to Hill-type dynamics. Pulsed Hill-type dynamics involves the binding of multiple signal molecules to a receptor and occurs e.g., when transcription factor p53 orchestrates cancer prevention, during calcium signaling, and during circadian rhythms. The scenarios involve: (i) enhancement of high-affinity binders compared to low-affinity ones, (ii) slowing reactions involving high-affinity binders, (iii) transfer of the clocking of low-affinity binders from the signal molecule to the products, and (iv) a unique clocking process that produces incremental increases in the activity of high-affinity binders with each signal pulse. In principle, these mostly non-linear effects could control cellular outcomes. An applications to p53 signaling is developed, with binding to most gene promoters identified as category (iii) responses. However, currently unexplained enhancement of high-affinity promoters such as CDKN1a (p21) by pulsed signaling could be an example of (i). In general, provision for all possible scenarios is required in the design of mathematical models incorporating pulsed Hill-type signaling as some aspect.

Steady-State-Preserving Simulation of Genetic Regulatory Systems

A novel family of exponential Runge-Kutta (expRK) methods are designed incorporating the stable steady-state structure of genetic regulatory systems. A natural and convenient approach to constructing new expRK methods on the base of traditional RK methods is provided. In the numerical integration of the one-gene, two-gene, and p53-mdm2 regulatory systems, the new expRK methods are shown to be more accurate than their prototype RK methods. Moreover, for nonstiff genetic regulatory systems, the expRK methods are more efficient than some traditional exponential RK integrators in the scientific literature.

A system of recurrent neural networks for modularising, parameterising and dynamic analysis of cell signalling networks

In this paper, we show how to extend our previously proposed novel continuous time Recurrent Neural Networks (RNN) approach that retains the advantage of continuous dynamics offered by Ordinary Differential Equations (ODE) while enabling parameter estimation through adaptation, to larger signalling networks using a modular approach. Specifically, the signalling network is decomposed into several sub-models based on important temporal events in the network. Each sub-model is represented by the proposed RNN and trained using data generated from the corresponding ODE model. Trained sub-models are assembled into a whole system RNN which is then subjected to systems dynamics and sensitivity analyses. The concept is illustrated by application to G1/S transition in cell cycle using Iwamoto et al. (2008) ODE model. We decomposed the G1/S network into 3 sub-models: (i) E2F transcription factor release; (ii) E2F and CycE positive feedback loop for elevating cyclin levels; and (iii) E2F and CycA negative feedback to degrade E2F. The trained sub-models accurately represented system dynamics and parameters were in good agreement with the ODE model. The whole system RNN however revealed couple of parameters contributing to compounding errors due to feedback and required refinement to sub-model 2. These related to the reversible reaction between CycE/CDK2 and p27, its inhibitor. The revised whole system RNN model very accurately matched dynamics of the ODE system. Local sensitivity analysis of the whole system model further revealed the most dominant influence of the above two parameters in perturbing G1/S transition, giving support to a recent hypothesis that the release of inhibitor p27 from Cyc/CDK complex triggers cell cycle stage transition. To make the model useful in a practical setting, we modified each RNN sub-model with a time relay switch to facilitate larger interval input data (≈20min) (original model used data for 30s or less) and retrained them that produced parameters and protein concentrations similar to the original RNN system. Results thus demonstrated the reliability of the proposed RNN method for modelling relatively large networks by modularisation for practical settings. Advantages of the method are its ability to represent accurate continuous system dynamics and ease of: parameter estimation through training with data from a practical setting, model analysis (40% faster than ODE), fine tuning parameters when more data are available, sub-model extension when new elements and/or interactions come to light and model expansion with addition of sub-models.

To senesce or not to senesce: how primary human fibroblasts decide their cell fate after DNA damage

Excessive DNA damage can induce an irreversible cell cycle arrest, called senescence, which is generally perceived as an important tumour-suppressor mechanism. However, it is unclear how cells decide whether to senesce or not after DNA damage. By combining experimental data with a parameterized mathematical model we elucidate this cell fate decision at the G1-S transition. Our model provides a quantitative and conceptually new understanding of how human fibroblasts decide whether DNA damage is beyond repair and senesce. Model and data imply that the G1-S transition is regulated by a bistable hysteresis switch with respect to Cdk2 activity, which in turn is controlled by the Cdk2/p21 ratio rather than cyclin abundance. We experimentally confirm the resulting predictions that to induce senescence i) in healthy cells both high initial and elevated background DNA damage are necessary and sufficient, and ii) in already damaged cells much lower additional DNA damage is sufficient. Our study provides a mechanistic explanation of a) how noise in protein abundances allows cells to overcome the G1-S arrest even with substantial DNA damage, potentially leading to neoplasia, and b) how accumulating DNA damage with age increasingly sensitizes cells for senescence.

Modeling Cellular Noise Underlying Heterogeneous Cell Responses in the Epidermal Growth Factor Signaling Pathway

Cellular heterogeneity, which plays an essential role in biological phenomena, such as drug resistance and migration, is considered to arise from intrinsic (i.e., reaction kinetics) and extrinsic (i.e., protein variability) noise in the cell. However, the mechanistic effects of these types of noise to determine the heterogeneity of signal responses have not been elucidated. Here, we report that the output of epidermal growth factor (EGF) signaling activity is modulated by cellular noise, particularly by extrinsic noise of particular signaling components in the pathway. We developed a mathematical model of the EGF signaling pathway incorporating regulation between extracellular signal-regulated kinase (ERK) and nuclear pore complex (NPC), which is necessary for switch-like activation of the nuclear ERK response. As the threshold of switch-like behavior is more sensitive to perturbations than the graded response, the effect of biological noise is potentially critical for cell fate decision. Our simulation analysis indicated that extrinsic noise, but not intrinsic noise, contributes to cell-to-cell heterogeneity of nuclear ERK. In addition, we accurately estimated variations in abundance of the signal proteins between individual cells by direct comparison of experimental data with simulation results using Apparent Measurement Error (AME). AME was constant regardless of whether the protein levels varied in a correlated manner, while covariation among proteins influenced cell-to-cell heterogeneity of nuclear ERK, suppressing the variation. Simulations using the estimated protein abundances showed that each protein species has different effects on cell-to-cell variation in the nuclear ERK response. In particular, variability of EGF receptor, Ras, Raf, and MEK strongly influenced cellular heterogeneity, while others did not. Overall, our results indicated that cellular heterogeneity in response to EGF is strongly driven by extrinsic noise, and that such heterogeneity results from variability of particular protein species that function as sensitive nodes, which may contribute to the pathogenesis of human diseases.

Individual cell behaviors are controlled by a variety of noise, such as fluctuations in biochemical reactions, protein variability, molecular diffusion, transcriptional noise, cell-to-cell contact, temperature, and pH. Such cellular noise often interferes with signal responses from external stimuli, and such heterogeneity functions in induction of drug resistance, survival, and migration of cells. Thus, heterogeneous cellular responses have positive and negative roles. However, the regulatory mechanisms that produce cellular heterogeneity are unclear. By mathematical modeling and simulations, we investigated how heterogeneous signaling responses are evoked in the EGF signaling pathway and influence the switch-like activation of nuclear ERK. This study demonstrated that cellular heterogeneity of the EGF signaling response is evoked by cell-to-cell variation of particular signaling proteins, such as EGFR, Ras, Raf, and MEK, which act as sensitive nodes in the pathway. These results suggest that signaling responses in individual cells can be predicted from the levels of proteins of sensitive nodes. This study also suggested that proteins of sensitive nodes may serve as cell survival mechanisms.

Kinetic aspects of enzyme-mediated repair of DNA single-strand breaks

In cells and bacteria, DNA can be damaged in different ways. The efficient damage repair, mediated by various enzymes, is crucial for their survival. Most frequently, the damage is reduced to single-strand breaks. In human cells, according to the experiments, the repair of such breaks can mechanistically be divided into four steps including (i) the break detection, (ii) processing of damaged ends, (iii) gap filling, and (iv) ligation of unbound ends of the broken strand. The first and second steps run in parallel while the third and fourth steps are sequential. The author proposes a kinetic model describing these steps. It allows one to understand the likely dependence of the number of breaks in different states on enzyme concentrations. The dependence of these concentrations on the rate of the formation of breaks can be understood as well. In addition, the likely role of unzipping and zipping of the fragments of broken ends of the strand in the ligation step has been scrutinized taking the specifics of binding of DNA stands into account.

Mammalian synthetic biology: emerging medical applications

In this review, we discuss new emerging medical applications of the rapidly evolving field of mammalian synthetic biology. We start with simple mammalian synthetic biological components and move towards more complex and therapy-oriented gene circuits. A comprehensive list of ON-OFF switches, categorized into transcriptional, post-transcriptional, translational and post-translational, is presented in the first sections. Subsequently, Boolean logic gates, synthetic mammalian oscillators and toggle switches will be described. Several synthetic gene networks are further reviewed in the medical applications section, including cancer therapy gene circuits, immuno-regulatory networks, among others. The final sections focus on the applicability of synthetic gene networks to drug discovery, drug delivery, receptor-activating gene circuits and mammalian biomanufacturing processes.

Differentiation resistance through altered retinoblastoma protein function in acute lymphoblastic leukemia: in silico modeling of the deregulations in the G1/S restriction point pathway

BACKGROUND

As in many cancer types, the G1/S restriction point (RP) is deregulated in Acute Lymphoblastic Leukemia (ALL). Hyper-phosphorylated retinoblastoma protein (hyper-pRb) is found in high levels in ALL cells. Nevertheless, the ALL lymphocyte proliferation rate for the average patient is surprisingly low compared to its normal counterpart of the same maturation level. Additionally, as stated in literature, ALL cells possibly reside at or beyond the RP which is located in the late-G1 phase. This state may favor their differentiation resistant phenotype. A major phenomenon contributing to this fact is thought to be the observed limited redundancy in the phosphorylation of retinoblastoma protein (pRb) by the various Cyclin Dependent Kinases (Cdks). The latter may result in partial loss of pRb functions despite hyper-phosphorylation.

RESULTS

To test this hypothesis, an in silico model aiming at simulating the biochemical regulation of the RP in ALL is introduced. By exploiting experimental findings derived from leukemic cells and following a semi-quantitative calibration procedure, the model has been shown to satisfactorily reproduce such a behavior for the RP pathway. At the same time, the calibrated model has been proved to be in agreement with the observed variation in the ALL cell cycle duration.

CONCLUSIONS

The proposed model aims to contribute to a better understanding of the complex phenomena governing the leukemic cell cycle. At the same time it constitutes a significant first step in the creation of a personalized proliferation rate predictor that can be used in the context of multiscale cancer modeling. Such an approach is expected to play an important role in the refinement and the advancement of mechanistic modeling of ALL in the context of the emergent and promising scientific domains of In Silico Oncology and more generally In Silico Medicine.

Role of Computational Modeling in Understanding Cell Cycle Oscillators

The periodic oscillations in the activity of the cell cycle regulatory program, drives the timely activation of key cell cycle events. Interesting dynamical systems, such as oscillators, have been investigated by various theoretical and computational modeling methods. Thanks to the insights achieved by these modeling efforts we have gained considerable insights about the underlying molecular regulatory networks that can drive cell cycle oscillations. Here we review the basic features and characteristics of biological oscillators, discussing from a computational modeling point of view their specific architectures and the current knowledge about the dynamics that the life evolution selected to drive cell cycle oscillations.

Bifurcation in Cell Cycle Dynamics Regulated by p53

We study the regulating mechanism of p53 on the properties of cell cycle dynamics in the light of the proposed model of interacting p53 and cell cycle networks via p53. Irradiation (IR) introduce to p53 compel p53 dynamics to suffer different phases, namely oscillating and oscillation death (stabilized) phases. The IR induced p53 dynamics undergo collapse of oscillation with collapse time Δt which depends on IR strength. The stress p53 via IR drive cell cycle molecular species MPF and cyclin dynamics to different states, namely, oscillation death, oscillations of periods, chaotic and sustain oscillation in their bifurcation diagram. We predict that there could be a critical Δtc induced by p53 via IRc, where, if Δt〈Δtc the cell cycle may come back to normal state, otherwise it will go to cell cycle arrest (apoptosis).

Modelling the onset of senescence at the G1/S cell cycle checkpoint

BACKGROUND

DNA damage (single or double-strand breaks) triggers adapted cellular responses. These responses are elicited through signalling pathways, which activate cell cycle checkpoints and basically lead to three cellular fates: cycle arrest promoting DNA repair, senescence (permanent arrest) or cell death. Cellular senescence is known for having a tumour-suppressive function and its regulation arouses a growing scientific interest. Here, we advance a qualitative model covering DNA damage response pathways, focusing on G1/S checkpoint enforcement, supposedly more sensitive to arrest than G2/M checkpoint.

RESULTS

We define a discrete, logical model encompassing ATM (ataxia telangiectasia mutated) and ATR (ATM and Rad3-related) pathways activation upon DNA damage, as well as G1/S checkpoint main components. It also includes the stress responsive protein p38MAPK (mitogen-activated protein kinase 14) known to be involved in the regulation of senescence. The model has four outcomes that convey alternative cell fates: proliferation, (transient) cell cycle arrest, apoptosis and senescence. Different levels of DNA damage are considered, defined by distinct combinations of single and double-strand breaks. Each leads to a single stable state denoting the cell fate adopted upon this specific damage. A range of model perturbations corresponding to gene loss-of-function or gain-of-function is compared to experimental mutations.

CONCLUSIONS

As a step towards an integrative model of DNA-damage response pathways to better cover the onset of senescence, our model focuses on G1/S checkpoint enforcement. This model qualitatively agrees with most experimental observations, including experiments involving mutations. Furthermore, it provides some predictions.

A plausible model for bimodal p53 switch in DNA damage response

p53 is a tumor suppressor and the p53 dynamics displays stimulus dependent patterns. Recent evidence suggests a bimodal p53 switch in cell fate decision. However, no theoretical studies have been proposed to investigate bimodal p53 induction. Here we constructed a model and showed that MDM2-p53 mRNA binding might contribute to bimodal p53 switch through an intrinsic positive feedback loop. Lower damage favored pulsing while monotonic increasing was generated with higher damage. Bimodal p53 dynamics was largely influenced by cellular MDM2 and elevated p53/MDM2 ratios with increasing etoposide favor mono-ubiquitination. Our model replicated recent experiments and provided potential insights into dynamic mechanisms of bimodal switch.

Mechanisms that enhance sustainability of p53 pulses

The tumor suppressor p53 protein shows various dynamic responses depending on the types and extent of cellular stresses. In particular, in response to DNA damage induced by γ-irradiation, cells generate a series of p53 pulses. Recent research has shown the importance of sustaining repeated p53 pulses for recovery from DNA damage. However, far too little attention has been paid to understanding how cells can sustain p53 pulses given the complexities of genetic heterogeneity and intrinsic noise. Here, we explore potential molecular mechanisms that enhance the sustainability of p53 pulses by developing a new mathematical model of the p53 regulatory system. This model can reproduce many experimental results that describe the dynamics of p53 pulses. By simulating the model both deterministically and stochastically, we found three potential mechanisms that improve the sustainability of p53 pulses: 1) the recently identified positive feedback loop between p53 and Rorα allows cells to sustain p53 pulses with high amplitude over a wide range of conditions, 2) intrinsic noise can often prevent the dampening of p53 pulses even after mutations, and 3) coupling of p53 pulses in neighboring cells via cytochrome-c significantly reduces the chance of failure in sustaining p53 pulses in the presence of heterogeneity among cells. Finally, in light of these results, we propose testable experiments that can reveal important mechanisms underlying p53 dynamics.

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.

Transition probability in cell proliferation, stochasticity in cell differentiation, and the restriction point of the cell cycle in one package

Clonal cells are known to display stochastically varying interdivision times (IMT) and stochastic choices of cell fates. These features are suggested in the present paper to stem from discrete transitions of genes between different modes of their engagement in transcription. These transitions are explained by stochastic events of assembly/disassembly of huge ensembles of transcription factors needed to built-up gene-specific transcription preinitiation complexes (PIC). The time required to assemble a PIC at a gene promoter by random collisions of numerous proteins may be long enough to be comparable with the cell cycle. Independently published findings are reviewed to show that active genes may display discontinuous patterns of transcriptional output consistent with stochastically varying periods of PIC presence or absence at their promoters, and that these periods may reach several hours. This timescale matches the time needed for synchronised clonal cells to pass the restriction point (RP) of the cell cycle. RP is suggested to correspond to cell state where cell fate is determined by competing discrete transcriptional events. Cell fate choice depends on the event that, by chance, has outpaced other events able to commit the cell to alternative fates. Simple modelling based on these premises is consistent with general features of cell kinetics, including RP passage dependance on mitogenic stimulation, IMT distributions conformance to exponentially modified Gaussian, the limited proliferative potential of untransformed cells, relationships between changes in cell proliferation and differentiation, and bimodal distributions of cells over expression levels of genes involved in stem cell differentiation.

Rigor of cell fate decision by variable p53 pulses and roles of cooperative gene expression by p53

Upon DNA damage, the cell fate decision between survival and apoptosis is largely regulated by p53-related networks. Recent experiments found a series of discrete p53 pulses in individual cells, which led to the hypothesis that the cell fate decision upon DNA damage is controlled by counting the number of p53 pulses. Under this hypothesis, Sun et al. (2009) modeled the Bax activation switch in the apoptosis signal transduction pathway that can rigorously "count" the number of uniform p53 pulses. Based on experimental evidence, here we use variable p53 pulses with Sun et al.'s model to investigate how the variability in p53 pulses affects the rigor of the cell fate decision by the pulse number. Our calculations showed that the experimentally anticipated variability in the pulse sizes reduces the rigor of the cell fate decision. In addition, we tested the roles of the cooperativity in PUMA expression by p53, finding that lower cooperativity is plausible for more rigorous cell fate decision. This is because the variability in the p53 pulse height is more amplified in PUMA expressions with more cooperative cases.