Effects of delayed immune-response in tumor immune-system interplay

Giulio Caravagna
(Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi Milano-Bicocca, Viale Sarca 336, I-20126 Milan, Italy.)
Alex Graudenzi
(Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi Milano-Bicocca, Viale Sarca 336, I-20126 Milan, Italy.)
Marco Antoniotti
(Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi Milano-Bicocca, Viale Sarca 336, I-20126 Milan, Italy.)
Giancarlo Mauri
(Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi Milano-Bicocca, Viale Sarca 336, I-20126 Milan, Italy.)
Alberto d'Onofrio
(Department of Experimental Oncology, European Institute of Oncology, Via Ripamonti 435, 20141 Milan, Italy.)

Tumors constitute a wide family of diseases kinetically characterized by the co-presence of multiple spatio-temporal scales. So, tumor cells ecologically interplay with other kind of cells, e.g. endothelial cells or immune system effectors, producing and exchanging various chemical signals. As such, tumor growth is an ideal object of hybrid modeling where discrete stochastic processes model agents at low concentrations, and mean-field equations model chemical signals. In previous works we proposed a hybrid version of the well-known Panetta-Kirschner mean-field model of tumor cells, effector cells and Interleukin-2. Our hybrid model suggested -at variance of the inferences from its original formulation- that immune surveillance, i.e. tumor elimination by the immune system, may occur through a sort of side-effect of large stochastic oscillations. However, that model did not account that, due to both chemical transportation and cellular differentiation/division, the tumor-induced recruitment of immune effectors is not instantaneous but, instead, it exhibits a lag period. To capture this, we here integrate a mean-field equation for Interleukins-2 with a bi-dimensional delayed stochastic process describing such delayed interplay. An algorithm to realize trajectories of the underlying stochastic process is obtained by coupling the Piecewise Deterministic Markov process (for the hybrid part) with a Generalized Semi-Markovian clock structure (to account for delays). We (i) relate tumor mass growth with delays via simulations and via parametric sensitivity analysis techniques, (ii) we quantitatively determine probabilistic eradication times, and (iii) we prove, in the oscillatory regime, the existence of a heuristic stochastic bifurcation resulting in delay-induced tumor eradication, which is neither predicted by the mean-field nor by the hybrid non-delayed models.

In Ezio Bartocci and Luca Bortolussi: Proceedings First International Workshop on Hybrid Systems and Biology (HSB 2012), Newcastle Upon Tyne, 3rd September 2012, Electronic Proceedings in Theoretical Computer Science 92, pp. 106–121.
Published: 15th August 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.92.8 bibtex PDF
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