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Network Modeling Analysis in Health Informatics and Bioinformatics

Erschienen in:

01.09.2012 | Original Article

Studying cancer-cell populations by programmable models of networks

verfasst von: Luca Bortolussi, Alberto Policriti

Erschienen in: Network Modeling Analysis in Health Informatics and Bioinformatics | Ausgabe 3/2012

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Abstract

We draw the basic lines for an approach to build mathematical and programmable network models, to be applied in the study of populations of cancer-cells at different stages of disease development. The methodology we propose uses a stochastic Concurrent Constraint Programming language, a flexible stochastic modelling language employed to code networks of agents. It is applied to (and partially motivated by) the study of differently characterized populations of prostate cancer cells. In particular, we prove how our method is suitable to systematically reconstruct and compare different mathematical models of prostate cancer growth—together with interactions with different kinds of hormone therapy—at different levels of refinement. Moreover, we show our technique at work in analysing the nature of noise and in the possible presence of competing mechanisms in the models proposed.

Vorheriger Artikel Merging network patterns: a general framework to summarize biomedical network data

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The constraints that can be used to update the constraint store are rather limited, as they simply add a constant to some stream variables. This restriction, however, allows to interpret sCCP-actions as continuous fluxes, a required condition to define the hybrid semantics (see also Sect. 2.4).

A software tool to model and analyse sCCP programs is under development. A preliminary version is available from the authors upon request.

Notation: the time derivative of X _j is denoted by \(\dot{X_j}, \) while the value of X _j after a change of mode is indicated by X _j′.

An alternative way to incorporate lack of knowledge is to use imprecise probabilities, like in Imprecise Markov Chains (Skulj 2009).

For instance, if an instantaneous transition η has a guard Time = t ₀, t ₀ constant, and the corresponding event e _η is activated at time t (this value is stored in the state \(s^{\prime}\)), then the associated CDF will be the Dirac delta \(F(\cdot,s',e_\eta)=\delta_{t_0-t}(\cdot). \) Note that conditions like Time = K, with K a variable that can be changed by other events, can be dealt with by introducing vanishing states in which the clock c _η gets reset.

Changing the value of the scaling factors can be seen as assuming a different granularity in counting. For instance, if we have N tumour cells, and we change the reference parameter N ₀ from 1 to 10, it means that we count how many groups of 10 cells are present in the system.

This is not so relevant for the work presented here, given that the stochastic and the ODE model are essentially indistinguishable and given that a comparison with experimental data has been carried out in (Ideta et al. 2008) for the ODE model.

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Titel: Studying cancer-cell populations by programmable models of networks
verfasst von: Luca Bortolussi
Alberto Policriti
Publikationsdatum: 01.09.2012
Verlag: Springer Vienna
Erschienen in: Network Modeling Analysis in Health Informatics and Bioinformatics / Ausgabe 3/2012
Print ISSN: 2192-6662
Elektronische ISSN: 2192-6670
DOI: https://doi.org/10.1007/s13721-012-0010-x

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