The role of modelling in identifying drug targets for diseases of the cell cycle

The art of modeling gene regulatory circuits

The amazing complexity of gene regulatory circuits, and biological systems in general, makes mathematical modeling an essential tool to frame and develop our understanding of their properties. Here, we present some fundamental considerations to develop and analyze a model of a gene regulatory circuit of interest, either representing a natural, synthetic, or theoretical system. A mathematical model allows us to effectively evaluate the logical implications of our hypotheses. Using our models to systematically perform in silico experiments, we can then propose specific follow-up assessments of the biological system as well as to reformulate the original assumptions, enriching both our knowledge and our understanding of the system. We want to invite the community working on different aspects of gene regulatory circuits to explore the power and benefits of mathematical modeling in their system.

A dynamical systems approach for multiscale synthesis of Alzheimer's pathogenesis

Alzheimer's disease (AD) is a spatially dynamic pathology that implicates a growing volume of multiscale data spanning genetic, cellular, tissue, and organ levels of the organization. These data and bioinformatics analyses provide clear evidence for the interactions within and between these levels. The resulting heterarchy precludes a linear neuron-centric approach and necessitates that the numerous interactions are measured in a way that predicts their impact on the emergent dynamics of the disease. This level of complexity confounds intuition, and we propose a new methodology that uses non-linear dynamical systems modeling to augment intuition and that links with a community-wide participatory platform to co-create and test system-level hypotheses and interventions. In addition to enabling the integration of multiscale knowledge, key benefits include a more rapid innovation cycle and a rational process for prioritization of data campaigns. We argue that such an approach is essential to support the discovery of multilevel-coordinated polypharmaceutical interventions.

Proposal for a New Diagnostic Histopathological Approach in the Evaluation of Ki-67 in GEP-NETs

Introduction: Studies have shown that the Ki-67 index is a valuable biomarker for the diagnosis, and classification of gastro-entero-pancreatic neuroendocrine tumors (GEP-NETs). We re-evaluated the expression of Ki-67 based on the intensity of the stain, basing our hypothesis on the fact that the Ki-67 protein is continuously degraded. Background: The aim was to evaluate whether a new scoring method would be more effective in classifying NETs by reducing staining heterogeneity. Methods: Patients with GEP-NET (n = 87) were analyzed. The classification difference between the two methods was determined. Results: The classification changed significantly when the Ki-67 semiquantal index was used. The percentage of G1 patients increased from 18.4% to 60.9%, while the G2 patients decreased from 66.7% to 29.9% and the G3 patients also decreased from 14.9% to 9.2%. Moreover, it was found that the traditional Ki-67 was not significantly related to the overall survival (OS), whereas the semiquantal Ki-67 was significantly related to the OS. Conclusions: The new quantification was a better predictor of OS and of tumor classification. Therefore, it could be used both as a marker of proliferation and as a tool to map tumor dynamics that can influence the diagnosis and guide the choice of therapy.

A multi-scale agent-based model for avascular tumour growth

In this paper, we have developed a multi-scale, lattice-free, agent based model of avascular tumour growth in epithelial tissue. The model integrates different events to identify the underlying diversity within intracellular, cellular, and extracellular layer dynamics. The model considers every cell as an agent. A cellular agent may proliferate, spawns two identical daughter agents, or it may be transformed into other phenotypes during its life time depending on its internal proteins' activity as well as its external microenvironment. In this context, a simplified age-structured cell cycle model is adopted from the existing literature. The model considers that the intracellular events are regulated by p27 gene expression. In this model, p27 protein controls the overall tumour growth dynamics. Moreover, p27 is controlled by the external oxygen and nutrients that are modelled with the reaction-diffusion equations. The model also considers several biophysical forces which directly effect on the tumour growth dynamics. This modelling framework offers biologically realistic outcomes and also covers important criteria of the hallmarks of cancer which include oxygen and nutrient consumptions, micro-environmental heterogeneity, tumour cell proliferation by avoiding growth suppressor signals, replication of tumour cells at an abnormally faster rate, and resistance of apoptosis. The avascular tumour growth model is validated with immunohistochemistry and histopathology data. The outcome of the proposed model is very close to the range of the patient data, which concludes that the model is capable enough to mimic these complex biophysical phenomena.

A novel evaluation method for Ki-67 immunostaining in paraffin-embedded tissues

The Ki-67 labeling index is traditionally used to investigate tumor aggressiveness. However, no diagnostic or prognostic value has been associated to the heterogeneous pattern of nuclear positivity. The aims of this study were to develop a classification for the patterns of Ki-67-positive nuclei; to search scientific evidence for the Ki-67 expression and location throughout the cell cycle; and to develop a protocol to apply the classification of patterns of Ki-67-positive nuclei in squamous epithelium with different proliferative activities. Based on empirical observation of paraffin sections submitted to immunohistochemistry for the determination of Ki-67 labeling index and literature review about Ki-67 expression, we created a classification of the patterns of nuclear positivity (NP1, NP2, NP3, NP4, and mitosis). A semi-automatic protocol was developed to identify and quantify the Ki-67 immunostaining patterns in target tissues. Two observers evaluated 7000 nuclei twice to test the intraobserver reliability, and six evaluated 1000 nuclei to the interobserver evaluation. The results showed that the immunohistochemical patterns of Ki-67 are similar in the tumoral and non-tumoral epithelium and were classified without difficulty. There was a high intraobserver reliability (Spearman correlation coefficient > 0.9) and moderate interobserver agreement (k = 0.523). Statistical analysis showed that non-malignant epithelial specimens presented a higher number of NP1 (geographic tongue = 83.8 ± 21.8; no lesion = 107.6 ± 52.7; and mild dysplasia = 86.6 ± 25.8) when compared to carcinoma in Situ (46.8 ± 34.8) and invasive carcinoma (72.6 ± 37.9). The statistical evaluation showed significant difference (p < 0.05). Thus, we propose a new way to evaluate Ki-67, where the pattern of its expression may be associated with the dynamics of the cell cycle. Future proof of this association will validate the use of the classification for its possible impact on cancer prognosis and guidance on personalized therapy.

Discovery and development of Seliciclib. How systems biology approaches can lead to better drug performance

Seliciclib (R-Roscovitine) was identified as an inhibitor of CDKs and has undergone drug development and clinical testing as an anticancer agent. In this review, the authors describe the discovery of Seliciclib and give a brief summary of the biology of the CDKs Seliciclib inhibits. An overview of the published in vitro and in vivo work supporting the development as an anti-cancer agent, from in vitro experiments to animal model studies ending with a summary of the clinical trial results and trials underway is presented. In addition some potential non-oncology applications are explored and the potential mode of action of Seliciclib in these areas is described. Finally the authors argue that optimisation of the therapeutic effects of kinase inhibitors such as Seliciclib could be enhanced using a systems biology approach involving mathematical modelling of the molecular pathways regulating cell growth and division.

Apigenin induces autophagic cell death in human papillary thyroid carcinoma BCPAP cells

Apigenin-induced autophagic cell death in human papillary thyroid carcinoma BCPAP cells is associated with ROS generation, DNA damage and cell cycle arrest.

Quantitative analysis of the effects of iododeoxyuridine and ionising radiation treatment on the cell cycle dynamics of DNA mismatch repair deficient human colorectal cancer cells

DNA mismatch repair (MMR) is involved in processing DNA damage following treatment with ionising radiation (IR) and various classes of chemotherapy drugs including iododeoxyuridine (IUdR), a known radiosensitiser. In this study, the authors have developed asynchronous probabilistic cell cycle models to assess the isolated effects of IUdR and IR and the combined effects of IUdR + IR treatments on MMR damage processing. The authors used both synchronous and asynchronous MMR-proficient/MMR-deficient cell populations and followed treated cells for up to two cell cycle times. They have observed and quantified differential cell cycle responses to MMR damage processing following IR and IUdR + IR treatments, principally in the duration of both G1 and G2/M cell cycle phases. The models presented in this work form the foundation for the development of an approach to maximise the therapeutic index for IR and IUdR + IR treatments in MMR-deficient (damage tolerant) cancers.

Pharmacological inhibition of ATM by KU55933 stimulates ATM transcription

Ataxia-telangiectasia mutated (ATM) kinase is a component of a signalling mechanism that determines the process of decision-making in response to DNA damage and involves the participation of multiple proteins. ATM is activated by DNA double-strand breaks (DSBs) through the Mre11–Rad50–Nbs1 (MRN) DNA repair complex, and orchestrates signalling cascades that initiate the DNA damage response. Cells lacking ATM are hypersensitive to insults, particularly genotoxic stress, induced through radiation or radiomimetic drugs. Here, we investigate the degree of ATM activation during time-dependent treatment with genotoxic agents and the effects of ATM on phospho-induction and localization of its downstream substrates. Additionally, we have demonstrated a new cell-cycle-independent mechanism of ATM gene regulation following ATM kinase inhibition with KU5593. Inhibition of ATM activity causes induction of ATM protein followed by oscillation and this mechanism is governed at the transcriptional level. Furthermore, this autoregulatory induction of ATM is also accompanied by a transient upregulation of p53, pATR and E2F1 levels. Since ATM inhibition is believed to sensitize cancer cells to genotoxic agents, this novel insight into the mechanism of ATM regulation might be useful for designing more precise strategies for modulation of ATM activity in cancer therapy.

Evaluation of multitype mathematical models for CFSE-labeling experiment data

Carboxy-fluorescein diacetate succinimidyl ester (CFSE) labeling is an important experimental tool for measuring cell responses to extracellular signals in biomedical research. However, changes of the cell cycle (e.g., time to division) corresponding to different stimulations cannot be directly characterized from data collected in CFSE-labeling experiments. A number of independent studies have developed mathematical models as well as parameter estimation methods to better understand cell cycle kinetics based on CFSE data. However, when applying different models to the same data set, notable discrepancies in parameter estimates based on different models has become an issue of great concern. It is therefore important to compare existing models and make recommendations for practical use. For this purpose, we derived the analytic form of an age-dependent multitype branching process model. We then compared the performance of different models, namely branching process, cyton, Smith-Martin, and a linear birth-death ordinary differential equation (ODE) model via simulation studies. For fairness of model comparison, simulated data sets were generated using an agent-based simulation tool which is independent of the four models that are compared. The simulation study results suggest that the branching process model significantly outperforms the other three models over a wide range of parameter values. This model was then employed to understand the proliferation pattern of CD4+ and CD8+ T cells under polyclonal stimulation.

Interoperability of time series cytometric data: a cross platform approach for modeling tumor heterogeneity

The cell cycle, with its highly conserved features, is a fundamental driver for the temporal control of cell proliferation-while abnormal control and modulation of the cell cycle are characteristic of tumor cells. The principal aim in cancer biology is to seek an understanding of the origin and nature of innate and acquired heterogeneity at the cellular level, driven principally by temporal and functional asynchrony. A major bottleneck when mathematically modeling these biological systems is the lack of interlinked structured experimental data. This often results in the in silico models failing to translate the specific hypothesis into parameterized terms that enable robust validation and hence would produce suitable prediction tools rather than just simulation tools. The focus has been on linking data originating from different cytometric platforms and cell-based event analysis to inform and constrain the input parameters of a compartmental cell cycle model, hence partly measuring and deconvolving cell cycle heterogeneity within a tumor population. Our work has addressed the concept that the interoperability of cytometric data, derived from different cytometry platforms, can complement as well as enhance cellular parameters space, thus providing a more broader and in-depth view of the cellular systems. The initial aim was to enable the cell cycle model to deliver an improved integrated simulation of the well-defined and constrained biological system. From a modeling perspective, such a cross platform approach has provided a paradigm shift from conventional cross-validation approaches, and from a bioinformatics perspective, novel computational methodology has been introduced for integrating and mapping continuous data with cross-sectional data. This establishes the foundation for developing predictive models and in silico tracking and prediction of tumor progression

Analysis of cell cycle dynamics using probabilistic cell cycle models

In this study, we develop asynchronous probabilistic cell cycle models to quantitatively assess the effect of ionizing radiation on a human colon cancer cell line. We use both synchronous and asynchronous cell populations and follow treated cells for up to 2 cell cycle times. The model outputs quantify the changes in cell cycle dynamics following ionizing radiation treatment, principally in the duration of both Gi and G(2)/M phases.

Integration of Principles of Systems Biology and Radiation Biology: Toward Development of in silico Models to Optimize IUdR-Mediated Radiosensitization of DNA Mismatch Repair Deficient (Damage Tolerant) Human Cancers

Over the last 7 years, we have focused our experimental and computational research efforts on improving our understanding of the biochemical, molecular, and cellular processing of iododeoxyuridine (IUdR) and ionizing radiation (IR) induced DNA base damage by DNA mismatch repair (MMR). These coordinated research efforts, sponsored by the National Cancer Institute Integrative Cancer Biology Program (ICBP), brought together system scientists with expertise in engineering, mathematics, and complex systems theory and translational cancer researchers with expertise in radiation biology. Our overall goal was to begin to develop computational models of IUdR- and/or IR-induced base damage processing by MMR that may provide new clinical strategies to optimize IUdR-mediated radiosensitization in MMR deficient (MMR⁻) “damage tolerant” human cancers. Using multiple scales of experimental testing, ranging from purified protein systems to in vitro (cellular) and to in vivo (human tumor xenografts in athymic mice) models, we have begun to integrate and interpolate these experimental data with hybrid stochastic biochemical models of MMR damage processing and probabilistic cell cycle regulation models through a systems biology approach. In this article, we highlight the results and current status of our integration of radiation biology approaches and computational modeling to enhance IUdR-mediated radiosensitization in MMR⁻ damage tolerant cancers.

Mechanistic systems biology of inflammatory gene expression in airway smooth muscle as tool for asthma drug development

There is compelling evidence that airway smooth muscle cells may function as inflammatory cells in the airway system by producing multiple inflammatory cytokines in response to a large array of external stimuli such as acetylcholine, bradykinin, inflammatory cytokines, and toll-like receptor activators. However, how multiple extracellular stimuli interact in the regulation of inflammatory gene expression in an airway smooth muscle cell remains poorly understood. This review addresses the mechanistic systems biology of inflammatory gene expression in airway smooth muscle by discussing: a) redundancy underlying multiple stimulus-product relations in receptor-mediated inflammatory gene expression, and their regulation by convergent activation of Erk1/2 mitogen-activated protein kinase (MAPK), b) Erk1/2 MAPK-dependent induction of phosphatase expression as a negative feedback mechanism in the robust maintenance of inflammatory gene expression, and c) cyclooxygenase 2-dependent regulation of the differential temporal dynamics of early and late inflammatory gene expression. It is becoming recognized that a single-target approach is unlikely to be effective for the treatment of inflammatory airway diseases because airway inflammation is a result of complex interactions among multiple inflammatory mediators and cells types in the airway system. Understanding the mechanistic systems biology of inflammatory gene expression in airway smooth muscle and other cell types in the airway system may lead to the development of multi-target drug regimens for the treatment of inflammatory airway diseases such as asthma.

Probabilistic modeling of DNA mismatch repair effects on cell cycle dynamics and iododeoxyuridine-DNA incorporation

Previous studies in our laboratory have described increased and preferential radiosensitization of mismatch repair-deficient (MMR(-)) HCT116 colon cancer cells with 5-iododeoxyuridine (IUdR). Indeed, our studies showed that MMR is involved in the repair (removal) of IUdR-DNA, principally the G:IU mispair. Consequently, we have shown that MMR(-) cells incorporate 25% to 42% more IUdR than MMR(+) cells, and that IUdR and ionizing radiation (IR) interact to produce up to 3-fold greater cytotoxicity in MMR(-) cells. The present study uses the integration of probabilistic mathematical models and experimental data on MMR(-) versus MMR(+) cells to describe the effects of IUdR incorporation upon the cell cycle for the purpose of increasing IUdR-mediated radiosensitivity in MMR(-) cells. Two computational models have been developed. The first is a stochastic model of the progression of cell cycle states, which is applied to experimental data for two synchronized isogenic MMR(+) and MMR(-) colon cancer cell lines treated with and without IUdR. The second model defines the relation between the percentage of cells in the different cell cycle states and the corresponding IUdR-DNA incorporation at a particular time point. These models can be combined to predict IUdR-DNA incorporation at any time in the cell cycle. These mathematical models will be modified and used to maximize therapeutic gain in MMR(-) tumors versus MMR(+) normal tissues by predicting the optimal dose of IUdR and optimal timing for IR treatment to increase the synergistic action using xenograft models and, later, in clinical trials.

Modeling T cell proliferation and death in vitro based on labeling data: generalizations of the Smith-Martin cell cycle model

The fluorescent dye carboxyfluorescein diacetate succinimidyl ester (CFSE) classifies proliferating cell populations into groups according to the number of divisions each cell has undergone (i.e., its division class). The pulse labeling of cells with radioactive thymidine provides a means to determine the distribution of times of entry into the first cell division. We derive in analytic form the number of cells in each division class as a function of time based on the distribution of times to the first division. Choosing the distribution of time to the first division to fit thymidine labeling data for T cells stimulated in vitro under different concentrations of IL-2, we fit CFSE data to determine the dependence of T cell kinetic parameters on the concentration of IL-2. As the concentration of IL-2 increases, the average cell cycle time is shortened, the death rate of cells is decreased, and a higher fraction of cells is recruited into division. We also find that if the average cell cycle time increases with division class then the qualify of our fit to the data improves.