Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-25T17:42:12.664Z Has data issue: false hasContentIssue false
  • English
  • Français

Multi-level modelling via stochastic multi-level multiset rewriting†

Published online by Cambridge University Press:  28 February 2013

NICOLAS OURY  and
GORDON PLOTKIN
NICOLAS OURY
Affiliation:
University of Edinburgh, Edinburgh, United Kingdom Email: Gordon.Plotkin@ed.ac.uk, Nicolas.Oury@ed.ac.uk
GORDON PLOTKIN
Affiliation:
University of Edinburgh, Edinburgh, United Kingdom Email: Gordon.Plotkin@ed.ac.uk, Nicolas.Oury@ed.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a simple stochastic rule-based approach to multi-level modelling for computational systems biology. Populations are modelled using multi-level multisets; these contain both species and agents, with the latter possibly containing further such multisets. Rules are pairs of such multisets, but they may now also include variables (as well as species and agents), together with an associated stochastic rate.

We give two illustrative examples. The first is an extracellular model of virus infection, coupled with an intracellular model of viral reproduction; this model can demonstrate successive waves of infection. The second is a model of cell division in which a repressor protein is diluted in successive generations, so eventually repression no longer occurs. The multi-level multiset approach can also be seen in terms of stochastic term rewriting for the theory of a commutative monoid equipped with extra constants (for the species) and unary operations (for the agents). We further discuss the relationship of this approach with two others: Krivine et al.'s stochastic bigraphs, restricted to Milner's place graphs, and Coppo et al.'s Stochastic Calculus of Wrapped Compartments. These various relationships provide evidence for the fundamental nature of the approach.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Special Issue 2: Developments In Computational Models 2010 , April 2013 , pp. 471 - 503
Copyright
Copyright © Cambridge University Press 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

This work was supported by BBSRC/EPSRC Grant BB/D019621/1, and by a Royal Society–Wolfson Award.

References

Agha, G. A., Meseguer, J. and Sen, K. (2006) PMaude: Rewrite-based specification language for probabilistic object systems. Electronic Notes in Theoretical Computer Science 153 (2)213–239.CrossRefGoogle Scholar
Amir-Kroll, H., Sadot, A., Cohen, I. R. and Harel, D. (2008) GemCell: A generic platform for modeling multi-cellular biological systems. In: Priami, C. (ed.) Converging Sciences: Informatics and Biology. Theoretical Computer Science 391 (3)276–290.CrossRefGoogle Scholar
Baader, F. and Nipkow, T. (1999) Term Rewriting and All That, Cambridge University Press.Google Scholar
Barbuti, R., Caravagna, G., Maggiolo-Schettini, A., Milazzo, P. and Pardini, G. (2008a) The calculus of looping sequences. In: Bernardo, M., Degano, P. and Zavattaro, G. (eds.) Formal Methods for Computational Systems Biology. Springer-Verlag Lecture Notes in Computer Science 5016 387–423.CrossRefGoogle Scholar
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tiberi, P. and Troina, A. (2008b) Stochastic CLS for the modeling and simulation of biological systems. Transactions on Computational Systems Biology IX 5121 86–113.Google Scholar
Bauer, A. L., Beauchemin, C. A. A. and Perelson, A. S. (2009) Agent-based modeling of host pathogen systems: The successes and challenges. Information Sciences 179 (10)1379–1389.CrossRefGoogle ScholarPubMed
Bezem, M., Klop, J. W. and de Vrijer, R. (eds.)‡ (2003) Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science 55, Cambridge University Press.Google Scholar
Bournez, O. and Hoyrup, M. (2003) Rewriting logic and probabilities. In: Nieuwenhuis, R. (ed.) Proceedings 14th International Conference on Rewriting Techniques and Applications. Springer-Verlag Lecture Notes in Computer Science 2706 61–75.CrossRefGoogle Scholar
Bournez, O. and Kirchner, C. (2002) Probabilistic rewrite strategies. Applications to ELAN. In: Tison, S. (ed.) Proceedings 13th International Conference on Rewriting Techniques and Applications. Springer-Verlag Lecture Notes in Computer Science 2378 252–266.CrossRefGoogle Scholar
Cardelli, L. (2005) Brane calculi. In: Danos, V. and Schächter, V. (eds.) International Conference on Computational Methods in Systems Biology. Revised Selected Papers. Springer-Verlag Lecture Notes in Computer Science 3082 257–27.CrossRefGoogle Scholar
Cardelli, L. (2008) Bitonal membrane systems: interactions of biological membranes. Theoretical Computer Science 404 (1–2)5–18.CrossRefGoogle Scholar
Chickarmane, V., Roeder, A. H. K., Tarr, P. T., Cunha, A., Tobin, C. and Meyerowitz, E. M. (2010) Computational morphodynamics: a modeling framework to understand plant growth. Annual Review of Plant Biology 6 65–87.CrossRefGoogle Scholar
Cickovski, T., Aras, K., Swat, M., Merks, R. M. H., Glimm, T., George, H., Hentschel, E., Alber, M. S., Glazier, J. A., Newman, S. A. and Izaguirre, J. A. (2007) From genes to organisms via the cell: a problem-solving environment for multicellular development. Computing in Science and Engineering 9 (4)50–60.CrossRefGoogle ScholarPubMed
Coppo, M., Damiani, F., Drocco, M., Grassi, E. and Troina, A. (2010a) Stochastic calculus of wrapped compartments. In: Di Pierro, A. and Norman, G. (eds.) Proceedings 8th Workshop on Quantitative Aspects of Programming Languages. Electronic Proceedings in Theoretical Computer Science 28 82–98.CrossRefGoogle Scholar
Coppo, M., Damiani, F., Drocco, M., Grassi, E., Sciacca, E., Spinella, S. and Troina, A. (2010b) Hybrid calculus of wrapped compartments. In: Ciobanu, G. and Koutny, M. (eds.) Proceedings 4th International Meeting on Membrane Computing and Biologically Inspired Process Calculi. Electronic Proceedings in Theoretical Computer Science 40 102–120.CrossRefGoogle Scholar
Danos, V. and Laneve, C. (2003) Core formal molecular biology. In: Degano, P. (ed.) Proceedings 12th European Symposium on Programming. Springer-Verlag Lecture Notes in Computer Science 2618 302–318.CrossRefGoogle Scholar
Frisco, P. (2009) Computing with Cells: Advances in Membrane Computing, Oxford University Press.CrossRefGoogle Scholar
Gillespie, D. (1977) Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81 2340–2361.CrossRefGoogle Scholar
Grieneisen, V. A. and Scheres, B. (2009) Back to the future: evolution of computational models in plant morphogenesis. In: Lohmann, J. and Nemhauser, J. (eds.) Cell signalling and gene regulation. Current Opinion in Plant Biology 12 (5)606–614.CrossRefGoogle Scholar
Harel, D. and Kugler, H. (2010) Some Thoughts on the Semantics of Biocharts. In: Manna, Z. and Peled, D. (eds.) Time for Verification: Essays in Memory of Amir Pnueli. Springer-Verlag Lecture Notes in Computer Science 6200 185–194.CrossRefGoogle Scholar
Haseltine, E. L., Rawlings, J. B. and Yin, J. (2005) Dynamics of viral infections: incorporating both the intracellular and extracellular levels. In: Maranas, C. and Hatzimanikatis, V. (eds.) Computational Challenges in Biology. Computers and Chemical Engineering 29 (3)675–686.CrossRefGoogle Scholar
Krivine, J., Milner, R. and Troina, A. (2008) Stochastic bigraphs. Electronic Notes in Theoretical Computer Science 218 73–96.CrossRefGoogle Scholar
Kugler, H., Larjo, A. and Harel, D. (2010) Biocharts: a visual formalism for complex biological systems. Journal of the Royal Society Interface 7 (48)1015–1024.CrossRefGoogle ScholarPubMed
Manes, E. G. (1998) Implementing collection classes with monads. Mathematical Structures in Computer Science 8 (3)231–276.CrossRefGoogle Scholar
Meier-Schellersheim, M., Fraser, I. D. and Klauschen, F. (2009) Multi-scale modeling in cell biology. Wiley Interdisciplinary Reviews: Systems Biology and Medicine 1 (1)4–14.Google Scholar
Meier-Schellersheim, M., Xu, X., Angermann, B., Kunkel, E. J., Jin, T. and Germain, R. N. (2006) Key role of local regulation in chemosensing revealed by a new molecular interaction-based modeling method. PLOS Computational Biology 2 (7)e82.CrossRefGoogle ScholarPubMed
Milner, R. (2009) The Space and Motion of Communicating Agents, Cambridge University Press.CrossRefGoogle Scholar
Mjolsness, E. and Yosiphon, G. (2006) Stochastic process semantics for dynamical grammars. Annals of Mathematics and Artificial Intelligence 47 329–5.CrossRefGoogle Scholar
Noble, D. (2002) Modeling the heart—from genes to cells to the whole heart. Science 295 1678–1682.CrossRefGoogle Scholar
P&acaron;un, G. (2001) P systems with active membranes: attacking NP-complete problems. Journal of Automata, Languages and Combinatorics 6 (1)75–90.Google Scholar
P&acaron;un, G. (2008) Membrane computing and brane calculi. Old, new, and future bridges. Theoretical Computer Science 404 (1–2)19–25.Google Scholar
Pedersen, M. and Plotkin, G. D. (2010) A language for biochemical systems: design and formal specification. In: Priami, C., Breitling, R., Gilbert, D., Heiner, M. and Uhrmacher, A. M. (eds.) Transactions on Computational Systems Biology XII. Special Issue on Modeling Methodologies. Springer-Verlag Lecture Notes in Computer Science 5945 77–145.CrossRefGoogle Scholar
Priami, C., Regev, A., Shapiro, E. Y. and Silverman, W. (2001) Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Information Processing Letters 80 (1)25–31.CrossRefGoogle Scholar
Regev, A., Panina, E. M., Silverman, W., Cardelli, L. and Shapiro, E. Y. (2004) BioAmbients: an abstraction for biological compartments. Theoretical Computer Science 325 (1)141–167.CrossRefGoogle Scholar
Rosenfeld, N., Young, J. W., Alon, U., Swain, P. S. and Elowitz, M. B. (2005) Gene regulation at the single-cell level. Science 307 (5717) 1962–1965.CrossRefGoogle ScholarPubMed
Spicher, A., Michel, O., Cieslak, M., Giavitto, J-L. and Prusinkiewicz, P. (2008) Stochastic P systems and the simulation of biochemical processes with dynamic compartments. BioSystems 91 458–472.CrossRefGoogle ScholarPubMed
Srivastava, R., You, L., Summers, J. and Yin, J. (2002) Stochastic vs. deterministic modeling of intracellular viral kinetics. Journal of Theoretical Biology 218 (3)309–321.CrossRefGoogle ScholarPubMed