J. G. Albeck, J. M. Burke, S. L. Spencer, D. A. Lauffenburger, and P. K. Sorger, Modeling a snap-action, variable-delay switch controlling extrinsic cell death, PLoS Biology, vol.6, issue.12, pp.2831-2852, 2008.

F. Bertaux, S. Stoma, D. Drasdo, and G. Batt, Modeling Dynamics of Cell-to-Cell Variability in TRAIL-Induced Apoptosis Explains Fractional Killing and Predicts Reversible Resistance, PLoS Comput Biol, vol.10, issue.10, p.14, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00942885

X. Boyen and D. Koller, Tractable inference for complex stochastic processes, Proc.of Uncertainty in Artificial Intelligence, pp.33-42, 1998.

K. S. Brown, C. C. Hill, G. A. Calero, K. H. Lee, J. P. Sethna et al., The statistical mechanics of complex signaling networks: nerve growth factor signaling, Physical Biology, vol.1, pp.184-195, 2004.

C. K. Chow and C. N. Liu, Approximating discrete probability distributions with dependence tree, IEEE Trans. on Information Theory, vol.14, issue.3, pp.462-467, 1968.

I. Csiszar, I-divergence geometry of probability distributions and minimization problems, The Annals of Probability, vol.3, pp.146-158, 1975.

F. Malvestuto, Approximating Discrete Probability Distributions with Decomposable Models, In Trans. on Systems, Man and Cybernetics, vol.21, issue.5, pp.1287-1294, 1991.

X. Gao, C. Arpin, J. Marvel, S. Prokopiou, O. Gandrillon et al., IL-2 sensitivity and exogenous IL-2 concentration gradient tune the productive contact duration of CD8+ T cell-APC: a multiscale modeling study, BMC Systems Biology, vol.10, p.77, 2016.
URL : https://hal.archives-ouvertes.fr/inserm-01354185

J. Feret, V. Danos, J. Krivine, R. Harmer, and W. Fontana, Internal coarse-graining of molecular systems, PNAS, vol.106, issue.16, pp.6453-6461, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00528330

D. Gilbert, M. Heiner, K. Takahashi, and A. Uhrmacher, Multiscale Spatial Computational Systems Biology, In Dagstuhl Reports, Seminar, vol.14481, issue.4, p.11, 2015.

B. Liu, J. Zhang, P. Y. Tan, D. Hsu, A. M. Blom et al., A computational and experimental study of the regulatory mechanisms of the complement system, PLoS Comput Biol, vol.7, issue.1, p.1001059, 2011.

B. Liu, D. Hsu, and P. Thiagarajan, Probabilistic approximations of odes based bio-pathway dynamics, Theoretical Computer Science, vol.412, issue.21, pp.2188-2206, 2011.

B. Munsky and M. Khammash, The finite state projection algorithm for the solution of the chemical master equation, J. Chem. Phys, vol.124, issue.4, pp.44-104, 2006.

K. Murphy and Y. Weiss, The factored frontier algorithm for approximate inference in DBNs, Proc. of Uncertainty in Artificial Intelligence, pp.378-385, 2001.

S. K. Palaniappan, M. Pichené, G. Batt, E. Fabre, and B. Genest, A look-ahead simulation algorithm for dbn models of biochemical pathways, HSB, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01406115

S. K. Palaniappan, F. Bertaux, M. Pichené, E. Fabre, G. Batt et al., Stochastic Abstraction of Biological Pathway Dynamics: A case study of the Apoptosis Pathway, BIOINFOR-MATICS, btx095, 2017.

S. K. Palaniappan, S. Akshay, B. Liu, B. Genest, and P. Thiagarajan, A Hybrid Factored Frontier Algorithm for Dynamic Bayesian Networks with a Biopathways Application, In TCBB, vol.9, issue.5, pp.1352-1365, 2012.

B. Waclaw, I. Bozic, M. Pittman, M. Hruban, B. Vogelstein et al., A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity, Nature, vol.525, pp.261-264, 2015.

, We now refine Algo. 2, that performs approximated inference, in order to lower the exponential factor of |V | from |î ??| + 2 to max(|î|, |?|) + 2. The improvement can thus be significant. Theorem 2. Given B 0 = P 0 , one can compute B 1, B T in time O(T · |I| · (|I| + |V |) · ? · |V | +1 )