Complex Systems Biology Approach in Connecting PI3K-Akt and NF-κB Pathways in Prostate Cancer.

Phosphatidylinositol 3'-OH kinase (PI3K)-Akt and transcription factor NF-κB are important molecules involved in the regulation of cell proliferation, apoptosis, and oncogenesis. Both PI3K-Akt and Nuclear Factor-kappaB (NF-κB) are involved in the development and progression of prostate cancer, however, the crosstalk and molecules connecting these pathway remains unclear. A multilevel system representation of the PI3K-Akt and NF-κB pathways was constructed to determine which signaling components contribute to adaptive behavior and coordination. In silico experiments conducted using PI3K-Akt and NF-κB, mathematical models were modularized using biological functionality and were validated using a cell culture system. Our analysis demonstrates that a component representing the IκB kinase (IKK) complex can coordinate these two pathways. It is expected that interruption of this molecule could represent a potential therapeutic target for prostate cancer.

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

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

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

BACKGROUND: Cytometry of asynchronous proliferating cell populations produces data with an extractable time-based feature embedded in the frequency of clustered, correlated events. Here, we present a specific case of general methodology for calculating dynamic expression profiles of epitopes that oscillate during the cell cycle and conversion of these values to the same scale. METHODS: Samples of K562 cells from one population were labeled by direct and indirect antibody methods for cyclins A2 and B1 and phospho-S10-histone H3. The same indirect antibody was used for both cyclins. Directly stained samples were counter-stained with 4'6-diamidino-2-phenylindole and indirectly stained samples with propidium to label DNA. The S phase cyclin expressions from indirect assays were used to scale the expression of the cyclins of the multi-variate direct assay. Boolean gating and two dimensional, sequential regions set on bivariate displays of the directly conjugated sample data were used to untangle and isolate unique, unambiguous expression values of the cyclins along the four-dimensional data path through the cell cycle. The median values of cyclins A2 and B1 from each region were correlated with the frequency of events within each region. RESULTS: The sequential runs of data were plotted as continuous multi-line linear equations of the form y = [(y(i+1)-y(i))/(x(i+1)-x(i))]x + y(i)-[(y(i+1)-y(i))/(x(i+1)-x(i))]x(i) (line between points (x(i),y(i)) and (x(i+1), y(i+1))) to capture the dynamic expression profile of the two cyclins. CONCLUSIONS: This specific approach demonstrates the general methodology and provides a rule set from which the cell cycle expression of any other epitopes could be measured and calculated. These expression profiles are the "state variable" outputs, useful for calibrating mathematical cell cycle models.

Dynamic epitope expression from static cytometry data: principles and reproducibility.

BACKGROUND: An imprecise quantitative sense for the oscillating levels of proteins and their modifications, interactions, and translocations as a function of the cell cycle is fundamentally important for a cartoon/narrative understanding for how the cell cycle works. Mathematical modeling of the same cartoon/narrative models would be greatly enhanced by an open-ended methodology providing precise quantification of many proteins and their modifications, etc. Here we present methodology that fulfills these features. METHODOLOGY: Multiparametric flow cytometry was performed on Molt4 cells to measure cyclins A2 and B1, phospho-S10-histone H3, DNA content, and light scatter (cell size). The resulting 5 dimensional data were analyzed as a series of bivariate plots to isolate the data as segments of an N-dimensional "worm" through the data space. Sequential, unidirectional regions of the data were used to assemble expression profiles for each parameter as a function of cell frequency. RESULTS: Analysis of synthesized data in which the true values where known validated the approach. Triplicate experiments demonstrated exceptional reproducibility. Comparison of three triplicate experiments stained by two methods (single cyclin or dual cyclin measurements with common DNA and phospho-histone H3 measurements) supported the feasibility of combining an unlimited number of epitopes through this methodology. The sequential degradations of cyclin A2 followed by cyclin B1 followed by de-phosphorylation of histone H3 were precisely mapped. Finally, a two phase expression rate during interphase for each cyclin was robustly identified. CONCLUSIONS: Very precise, correlated expression profiles for important cell cycle regulating and regulated proteins and their modifications can be produced, limited only by the number of available high-quality antibodies. These profiles can be assembled into large information libraries for calibration and validation of mathematical models.

CytoSys: a tool for extracting cell-cycle-related expression dynamics from static data.

Computational models of biological processes are important building blocks in Systems Biology studies. Calibration and validation are two important steps for moving a mathematical model to a computational model. While calibration refers to finding numerical value of the coefficients such as rate constants in a mathematical model, validation refers to verifying that the calibrated model behaves the same as the biological system under previously unseen conditions such as environmental changes (e.g., drug treatment) or mutations. In lieu of direct measurements of rate constants, modeling of the molecular mechanisms that govern biological behaviors may be able to use dynamic expression profiles of reactant biomolecules for calibration. For validation, similar data, obtained under new conditions, are probably better than direct measurements of rate constants. In any case, direct measurement of rate constants is almost always impractical and difficult or impossible. Here, we show a computer-assisted methodology to extract embedded dynamic profiles of cell-cycle proteins from statically sampled, multivariate cytometry data guided by heuristics assembled from canonical cell-cycle knowledge. The methodology is implemented using standard "list mode" cytometry data-processing software followed by CytoSys - a software tool with an easy-to-use graphical interface. We demonstrate the use of CytoSys with a case study of exponentially growing, human erythroleukemia cells and extract the dynamic expression profiles of cyclin A for calibrating an existing deterministic mathematical model of the cell cycle.

Modelling the dynamics of signalling pathways.

In the present chapter we discuss methodologies for the modelling, calibration and validation of cellular signalling pathway dynamics. The discussion begins with the typical range of techniques for modelling that might be employed to go from the chemical kinetics to a mathematical model of biochemical pathways. In particular, we consider the decision-making processes involved in selecting the right mechanism and level of detail of representation of the biochemical interactions. These include the choice between (i) deterministic and stochastic chemical kinetics representations, (ii) discrete and continuous time models and (iii) representing continuous and discrete state processes. We then discuss the task of calibrating the models using information available in web-based databases. For situations in which the data are not available from existing sources we discuss model calibration based upon measured data and system identification methods. Such methods, together with mathematical modelling databases and computational tools, are often available in standard packages. We therefore make explicit mention of a range of popular and useful sites. As an example of the whole modelling and calibration process, we discuss a study of the cross-talk between the IL-1 (interleukin-1)-stimulated NF-kappaB (nuclear factor kappaB) pathway and the TGF-beta (transforming growth factor beta)-stimulated Smad2 pathway.

The role of dynamic stimulation pattern in the analysis of bistable intracellular networks.

Bistable systems play an important role in the functioning of living cells. Depending on the strength of the necessary positive feedback one can distinguish between (irreversible) "one-way switch" or (reversible) "toggle-switch" type behavior. Besides the well- established steady-state properties, some important characteristics of bistable systems arise from an analysis of their dynamics. We demonstrate that a supercritical stimulus amplitude is not sufficient to move the system from the lower (off-state) to the higher branch (on-state) for either a step or a pulse input. A switching surface is identified for the system as a function of the initial condition, input pulse amplitude and duration (a supercritical signal). We introduce the concept of bounded autonomy for single level systems with a pulse input. Towards this end, we investigate and characterize the role of the duration of the stimulus. Furthermore we show, that a minimal signal power is also necessary to change the steady state of the bistable system. This limiting signal power is independent of the applied stimulus and is determined only by systems parameters. These results are relevant for the design of experiments, where it is often difficult to create a defined pattern for the stimulus. Furthermore, intracellular processes, like receptor internalization, do manipulate the level of stimulus such that level and duration of the stimulus is conducive to characteristic behavior.

Complex systems biology approach to understanding coordination of JAK-STAT signaling.

In this work, we search for coordination as an organizing principle in a complex signaling system using a multilevel hierarchical paradigm. The objective is to explain the underlying mechanism of Interferon (IFN(gamma)) induced JAK-STAT (specifically JAK1/JAK2-STAT1) pathway behavior. Starting with a mathematical model of the pathway from the literature, we modularize the system using biological knowledge via principles of biochemical cohesion, biological significance, and functionality. The modularized system is then used as a basis for in silico inhibition, knockdown/deletion and perturbation experiments to discover a coordination mechanism. Our analysis shows that a module representing the SOCS1 complex can be identified as the coordinator. Analysis of the coordinator can then be used for the selection of biological experiments for the discovery of 'soft' molecular drug targets, that could lead to the development of improved therapeutics. The coordinator identified is also being investigated to determine its relationship to pathological conditions.