Circadian clock effects on cellular proliferation: Insights from theory and experiments

Oscillations of the cellular circadian clock have emerged as an important regulator of many physiological processes, both in health and in disease. One such process, cellular proliferation, is being increasingly recognized to be affected by the circadian clock. Here, we review how a combination of experimental and theoretical work has furthered our understanding of the way circadian clocks couple to the cell cycle and play a role in tissue homeostasis and cancer. Finally, we discuss recently introduced methods for modeling coupling of clocks based on techniques from survival analysis and machine learning and highlight their potential importance for future studies.     

Network Development in Biological Gels: Role in Lymphatic Vessel Development

In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the collagen volume fraction, and the evolution of the proton concentration in a collagen implant; as described in experiments of Boardman and Swartz (Circ. Res. 92, 801–808, 2003). Using linear stability analysis, we find that above a critical level of proton concentration, spatial patterns form due to small perturbations in the initially uniform steady state. Using a long wavelength reduction, we can reduce the two coupled partial differential equations to one fourth order equation that is very similar to the Cahn–Hilliard equation; however, it has more complex nonlinearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model. This work was supported by the Royal Society (London) by the award of a University Research Fellowship.     

The segmentation clock in mice: interaction between the Wnt and Notch signalling pathways

In the last few years, the efforts to elucidate the mechanisms underlying the segmentation clock in various vertebrate species have multiplied. Early evidence suggested that oscillations are caused by one of the genes under the Notch signalling pathway (like those of the her or Hes families). Recently, Aulehla et al. [Wnt3a plays a major role in the segmentation clock controlling somitogenesis. Dev. Cell 4, 395-406] discovered that Axin2 (a gene under the Wnt3a signalling pathway) also oscillates in the presomitic mesoderm (PSM) of mice embryos and proposed some mechanisms through which the Notch and Wnt3a pathways may interact. They further suggested that a decreasing concentration of Wnt3a along the PSM may be the gradient the segmentation clock interacts with to form somites. These results were reviewed by Rida et al. [A notch feeling of somite segmentation and beyond. Dev. Biol. 265, 2-22], who introduced a complex clockwork comprising genes Hes1, Lfng (under the Notch pathway), and Axin2, as well as their multiple interactions. In the present work we develop a mathematical model based on the Rida et al. review and use it to tackle some of the questions raided by the Aulehla et al. paper: can the Axin2 feedback loop constitute a clock? Could a decreasing Wnt3a signaling constitute the wavefront, where phase is recorded and the spatial pattern laid down? What is the master oscillator?     

Econometric models for biohydrogen development

Biohydrogen is considered as an attractive clean energy source due to its high energy content and environmental-friendly conversion. Analyzing various economic scenarios can help decision makers to optimize development strategies for the biohydrogen sector. This study surveys econometric models of biohydrogen development, including input-out models, life-cycle assessment approach, computable general equilibrium models, linear programming models and impact pathway approach. Fundamentals of each model were briefly reviewed to highlight their advantages and disadvantages. The input-output model and the simplified economic input-output life-cycle assessment model proved most suitable for economic analysis of biohydrogen energy development. A sample analysis using input-output model for forecasting biohydrogen development in the United States is given.     

From simple to detailed models for cell polarization

Many mathematical models have been proposed for the process of cell polarization. Some of these are ‘functional models’ that capture a class of dynamical behaviour, whereas others are derived from features of signalling molecules. Some mechanistic models are detailed, and therefore complex, whereas others are simplified. Each type contributes to our understanding of cell polarization. However, the huge variety at different levels of detail makes comparisons challenging. Here, we provide examples of both elementary and more detailed models for polarization. We also display how a recent mathematical method, local perturbation analysis, can provide an appropriate tool for such comparisons. This technique simplifies and speeds up the model development process by revealing the effect of model extensions, parameter variations and in silico manipulations such as knock-out or over-expression of key molecules. Finally, simulations in both one dimension and two dimensions, and particularly in deforming two-dimensional ‘cells’, can highlight behaviour not captured by traditional simulation methods.     

Ensembles of signal transduction models using Pareto Optimal Ensemble Techniques (POETs)

Mathematical modeling of complex gene expression programs is an emerging tool for understanding disease mechanisms. However, identification of large models sometimes requires training using qualitative, conflicting or even contradictory data sets. One strategy to address this challenge is to estimate experimentally constrained model ensembles using multiobjective optimization. In this study, we used Pareto Optimal Ensemble Techniques (POETs) to identify a family of proof-of-concept signal transduction models. POETs integrate Simulated Annealing (SA) with Pareto optimality to identify models near the optimal tradeoff surface between competing training objectives. We modeled a prototypical-signaling network using mass-action kinetics within an ordinary differential equation (ODE) framework (64 ODEs in total). The true model was used to generate synthetic immunoblots from which the POET algorithm identified the 117 unknown model parameters. POET generated an ensemble of signaling models, which collectively exhibited population-like behavior. For example, scaled gene expression levels were approximately normally distributed over the ensemble following the addition of extracellular ligand. Also, the ensemble recovered robust and fragile features of the true model, despite significant parameter uncertainty. Taken together, these results suggest that experimentally constrained model ensembles could capture qualitatively important network features without exact parameter information.     

Mechanistic systems models of cell signaling networks: a case study of myocyte adrenergic regulation

Signal transduction networks coordinate a wide variety of cellular functions, including gene expression, metabolism, and cell fate processes. Understanding biological networks quantitatively is a major challenge to post-genomic biology, and mechanistic systems models will be crucial for this task. Here, we review approaches towards developing mechanistic systems models of established cell signaling networks. The ability of mechanistic system models to generate testable biological hypotheses and experimental strategies is discussed. As a case study of model development and analysis, we examined the functional roles of phospholamban, the L-type calcium channel, the ryanodine receptor, and troponin I phosphorylation upon β-adrenergic stimulation in the rat ventricular myocyte. Model analysis revealed that while protein kinase A-mediated phosphorylation of the ryanodine receptor greatly increases its calcium sensitivity, calcium autoregulation may adapt quickly by negating potential increases in contractility. Systematic combinations of in silico perturbations supported the conclusion that phospholamban phosphoregulation is the primary mechanism for increased sarcoplasmic reticulum load and calcium relaxation rate during β-adrenergic stimulation, while both phospholamban and the L-type calcium channel contribute to increased systolic calcium. Combined with detailed experimental studies, mechanistic systems models will be valuable for developing a quantitative understanding of cell signaling networks.     

Evolving cell models for systems and synthetic biology

This paper proposes a new methodology for the automated design of cell models for systems and synthetic biology. Our modelling framework is based on P systems, a discrete, stochastic and modular formal modelling language. The automated design of biological models comprising the optimization of the model structure and its stochastic kinetic constants is performed using an evolutionary algorithm. The evolutionary algorithm evolves model structures by combining different modules taken from a predefined module library and then it fine-tunes the associated stochastic kinetic constants. We investigate four alternative objective functions for the fitness calculation within the evolutionary algorithm: (1) equally weighted sum method, (2) normalization method, (3) randomly weighted sum method, and (4) equally weighted product method. The effectiveness of the methodology is tested on four case studies of increasing complexity including negative and positive autoregulation as well as two gene networks implementing a pulse generator and a bandwidth detector. We provide a systematic analysis of the evolutionary algorithm’s results as well as of the resulting evolved cell models.     

Stochastic Petri Net extension of a yeast cell cycle model

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

Investigating the link between epithelial-mesenchymal transition and the cancer stem cell phenotype: A mathematical approach

Under the cancer stem cell (CSC) hypothesis, sustained metastatic growth requires the dissemination of a CSC from the primary tumour followed by its re-establishment in a secondary site. The epithelial-mesenchymal transition (EMT), a differentiation process crucial to normal development, has been implicated in conferring metastatic ability on carcinomas. Balancing these two concepts has led researchers to investigate a possible link between EMT and the CSC phenotype—indeed, recent evidence indicates that, following induction of EMT in human breast cancer and related cell lines, stem cell activity increased, as judged by the presence of cells displaying the CD44^high/CD24^low phenotype and an increase in the ability of cells to form mammospheres. We mathematically investigate the nature of this increase in stem cell activity. A stochastic model is used when small number of cells are under consideration, namely in simulating the mammosphere assay, while a related continuous model is used to probe the dynamics of larger cell populations. Two scenarios of EMT-mediated CSC enrichment are considered. In the first, differentiated cells re-acquire a CSC phenotype—this model implicates fully mature cells as key subjects of de-differentiation and entails a delay period of several days before de-differentiation occurs. In the second, pre-existing CSCs experience accelerated division and increased proportion of self-renewing divisions; a lack of perfect CSC biomarkers and cell sorting techniques requires that this model be considered, further emphasizing the need for better characterization of the mammary (cancer) stem cell hierarchy. Additionally, we suggest the utility of comparing mammosphere data to computational mammosphere simulations in elucidating the growth characteristics of mammary (cancer) stem cells.     

A logical analysis of the process of T cell activation: different consequences depending on the state of CD28 engagement

The adaptive immune system is a complex organized action of several immune cell types like, T cells, B cells, dendritic cells, mast cells, and their ability to recognize self and foreign molecular information. Based on logical analysis, a model has been developed that describes TCR-ligand association coupled to intracellular signaling events that result in a proliferation signal. The model demonstrates that after TCR-ligand binding, the activation of tyrosine kinases in one of the paths leads to oscillations between the subsequent states of activation and deactivation of Ca(2+) initiation. In our studies the effect of costimulation on the primary signal has also been explored. Analysis reveals that costimulation increases by more than 2.5 fold the number of paths rendering a cell proliferation signal compared to the outcome when costimulation is blocked. Traversal of 97% of these paths attains a costimulation threshold of activation. We also examined a hypothesis that couples the primary signal and costimulation by modeling costimulation to act as an inhibitor on the Inhibitor proteins. Using this hypothesis our analysis showed a 25% increase in the number of paths leading to cell proliferation in comparison to when costimulation is blocked. Our model also reveals that this hypothesis actually decrease by approximately 50% the number of paths attaining cell proliferation compared to the number of available paths leading to cell proliferation when costimulation does not act as an inhibitor on Inhibitor proteins. This suggests that costimulation influences cell proliferation by providing a greater diversity of paths that converge to this state. However, costimulation should be thought independent of its regulatory interaction with the inhibitor proteins.     

MS-BID: a Java package for label-free LC-MS-based comparative proteomic analysis

MS-BID (MS Biomarker Discovery Platform) is an integrative computational pipeline for biomarker discovery using LC-MS-based comparative proteomic analysis. This platform consists of several computational tools for: (i) detecting peptides in the collected patterns; (ii) matching detected peptides across a number of LC-MS datasets and (iii) selecting discriminatory peptides between classes of samples. AVAILABILITY: MS-BID source codes, binaries and documentations are freely available under LGPL from http://tools.proteomecenter.org/msBID.php.     

Parametric sensitivity analysis and reduction of a detailed nutritional model of plant cell cultures

A kinetic model of plant nutrition described by Cloutier et al. (Cloutier et al., 2008. Biotechnol Bioeng 99:189-200) is progressively simplified so as to obtain a predictive model that describes the evolution of the biomass and the extracellular and intracellular concentrations of three determining nutrients, that is, free intracellular nitrogen, phosphate, and carbohydrate compounds. Three techniques of global sensitivity analysis are successively applied to assess the model parameter influence and potential correlation. The resulting dynamic model is able to predict plant growth for the two most encountered plant bioprocesses, namely suspension cells and hairy roots.     

Comparison of electrophysiological models for human ventricular cells and tissues

In this paper we briefly review currently published models for human ventricular cells and tissues. We discuss the Priebe–Beuckelmann (PB) model and the reduced version of this model constructed by Bernus et al. (redPB), the Ten Tusscher–Noble–Noble–Panfilov (TNNP) model and the Iyer–Mazhari–Winslow (IMW) model. We compare several characteristics of these models such as: sources of experimental data the models are based on, action potential morphology, action potential duration (APD) and conduction velocity (CV) restitution and computational efficiency. Finally, we discuss the application of a subset of these models—the redPB and the TNNP model—to study simulated spiral wave dynamics in 2D tissue sheets and in the human ventricles. We discuss the suitability of the different models for particular research questions and their limitations.     

A systems biology view of cancer

In order to understand how a cancer cell is functionally different from a normal cell it is necessary to assess the complex network of pathways involving gene regulation, signaling, and cell metabolism, and the alterations in its dynamics caused by the several different types of mutations leading to malignancy. Since the network is typically complex, with multiple connections between pathways and important feedback loops, it is crucial to represent it in the form of a computational model that can be used for a rigorous analysis. This is the approach of systems biology, made possible by new -omics data generation technologies. The goal of this review is to illustrate this approach and its utility for our understanding of cancer. After a discussion of recent progress using a network-centric approach, three case studies related to diagnostics, therapy, and drug development are presented in detail. They focus on breast cancer, B-cell lymphomas, and colorectal cancer. The discussion is centered on key mathematical and computational tools common to a systems biology approach.     

Optimal control for selected cancer chemotherapy ODE models: a view on the potential of optimal schedules and choice of objective function

In this article, four different mathematical models of chemotherapy from the literature are investigated with respect to optimal control of drug treatment schedules. The various models are based on two different sets of ordinary differential equations and contain either chemotherapy, immunotherapy, anti-angiogenic therapy or combinations of these. Optimal control problem formulations based on these models are proposed, discussed and compared. For different parameter sets, scenarios, and objective functions optimal control problems are solved numerically with Bock’s direct multiple shooting method.In particular, we show that an optimally controlled therapy can be the reason for the difference between a growing and a totally vanishing tumor in comparison to standard treatment schemes and untreated or wrongly treated tumors. Furthermore, we compare different objective functions. Eventually, we propose an optimization-driven indicator for the potential gain of optimal controls. Based on this indicator, we show that there is a high potential for optimization of chemotherapy schedules, although the currently available models are not yet appropriate for transferring the optimal therapies into medical practice due to patient-, cancer-, and therapy-specific components.     

Extracellular regulation of VEGF: Isoforms,proteolysis, and vascular patterning

The regulation of vascular endothelial growth factor A (VEGF) is critical to neovascularization in numerous tissues under physiological and pathological conditions. VEGF has multiple isoforms, created by alternative splicing or proteolytic cleavage, and characterized by different receptor-binding and matrix-binding properties. These isoforms are known to give rise to a spectrum of angiogenesis patterns marked by differences in branching, which has functional implications for tissues. In this review, we detail the extensive extracellular regulation of VEGF and the ability of VEGF to dictate the vascular phenotype. We explore the role of VEGF-releasing proteases and soluble carrier molecules on VEGF activity. While proteases such as MMP9 can ‘release’ matrix-bound VEGF and promote angiogenesis, for example as a key step in carcinogenesis, proteases can also suppress VEGF's angiogenic effects. We explore what dictates pro- or anti-angiogenic behavior. We also seek to understand the phenomenon of VEGF gradient formation. Strong VEGF gradients are thought to be due to decreased rates of diffusion from reversible matrix binding, however theoretical studies show that this scenario cannot give rise to lasting VEGF gradients in vivo. We propose that gradients are formed through degradation of sequestered VEGF. Finally, we review how different aspects of the VEGF signal, such as its concentration, gradient, matrix-binding, and NRP1-binding can differentially affect angiogenesis. We explore how this allows VEGF to regulate the formation of vascular networks across a spectrum of high to low branching densities, and from normal to pathological angiogenesis. A better understanding of the control of angiogenesis is necessary to improve upon limitations of current angiogenic therapies.