Sree N. Sreenath

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.

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 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.

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  =  [(yi+1−yi)/(xi+1−xi)]x + yi−[(yi+1−yi)/(xi+1−xi)]xi (line between points (xi,yi) and (xi+1, yi+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.

The Nile River Problematique: An Integrated Look at the Future of Egypt and Ethiopia

Abstract Globally and regionally a realization is setting in that the constraint of freshwater resources availability and their sharing could be a major impediment to security and subsequently to sustainable development of developing countries. This aspect of sustainability referred to as the “Problematique” requires a long-term perspective and explicit recognition of a plethora of dimensions of development that need to be considered independently and simultaneously. In this paper, we discuss the Nile River Problematique as a hypothetical situation, using a methodology to study the policy formulation between the years 2000 and 2050 for development of Egypt and the upstream country of Ethiopia as constrained by the growing population, increased global pressure for economic development, and the shared, annually finite water resource—the Nile. First, policy objectives are formulated. Central to our approach is the use of a decision (goal) seeking paradigm for the human dimension of global change referred to as the cybernetic paradigm. This requires the use of multilevel architecture of models to deal with complexity and the human/machine interactive process to deal with uncertainty. A computer-based reasoning support system is used. Different policy targets are examined. The approach yields not only which combination of policy options will work, but the level and extent the policies must be applied. How such policy measures are to be enforced is not discussed. Policy implications are presented quantitatively using a “foresight” or scenario approach. The formulated policies here are not prescriptive; however practitioners have tested the methodology in a workshop.

From Networks to Systems to Complex Systems: A Signaling Pathway Coordination Case Study

Networks of Signaling pathways provide a robust mechanism for cells to respond to various biological stimuli. In this paper we demonstrate cell adaptation through the viewpoint of an organizing principle between two interconnected pathways- MAPK and PKC. We use a multi-layered system representation of the pathways to determine the pathway components contributing to the adaptive behavior and coordination. The adaptation can be thought of as being manifested by a change in parameters of the coordinator. In silico experiments are conducted using MAPK/PKC mathematical model in literature to investigate the role of PLA2as a coordinator is reported here. Our results show that varying parameters of the coordinator not only activates the network of pathways where otherwise the pathway activity is very low, but also reveal the ability of the system to activate itself in the absence of the input, indicating relevance of the principle of bounded autonomy.

Cohesiveness: general systems and contra-reductionism revolution

Identification of functional modules in complex systems is becoming an important challenge in many scientific disciplines from biology to social sciences. Here we introduce the concept of cohesion as a guide for modularization. General systems treatment of the problem is necessary because in many real-life situations there is not enough information and data to model the systems in conventional mathematical terms. Principal results are derived in mathematical systems theory and an application to signaling pathways is presented.

A systems approach to validating the water vision of the Aral Sea basin

Abstract: The governments of the Aral Sea Basin countries, in cooperation with international organizations (UNESCO and World Bank) came up with a “water vision “for the region until 2025. The landlocked Aral Sea has been suffering from an imbalance in water evaporation, and, water inflow from its two main sources — Amu Darya and Syr Darya rivers, when the planners in the former Soviet Union from the 1960s diverted the river waters for irrigation. The irrigated area has increased from the 1960s by two‐thirds to 7 million hectares and the population by three‐fold to 50 million in the basin countries. Consequently the inflow to the Aral Sea from these two rivers decreased from 55 km3 in 1960 to a few km3 during the 1980s and 1990s. This has resulted in one of the worst man‐made ecological disasters of the century. In this paper, we examine different scenarios to achieve the vision goals and whether it is indeed feasible. Using IWMI basin‐oriented water accounting principles, we have shown that significant amount of water is being wasted in the region. Our analysis concludes that though not all the vision goals are likely to be met over the next 25 years, the inflow into the Aral Sea can be increased to over 20 km3 through better management and use of water resources.