Published in Volume XX, 2010, pages 1-31

**Authors:** E. Bartocci, F. Corradini, M.R Di Berardini, E. Merelli, and L. Tesei

### Abstract

We present a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel to naturally model binding sites on the surface of shapes. The calculus embeds collision detection and response, binding of compatible 3D processes and split of composed 3D processes.

Full Text (PDF)### References

[1] Meredys (www.ebi.ac.uk/compneur-srv/meredys.html).

[2] RCSB – Protein Data Bank (http://www.rcsb.org).

[3] S. S. Andrews and D. Bray. Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys. Biol., 1(3 4):137-151, 2004.

[4] R. Barbuti, A. Maggiolo-Schettini, P. Milazzo, and G. Pardini. Spatial Calculus of Looping Sequences. Electronic Notes in Theoretical Computer Science, 229(1):21-39, 2009.

[5] E. Bartocci, F. Corradini, M. R. Di Berardini, E. Merelli, and L. Tesei. Shape Calculus. A spatial calculus for 3D colliding shapes. Technical Report 6, Department of Mathematics and Computer Science, University of Camerino, Jan 2010. Available at http://s1report.cs.unicam.it/6/.

[6] E. Bartocci, M. R. Di Berardini, F. Corradini, M. Emanuela, and L. Tesei. A Shape Calculus for Biological Processes. In Proceedings of 11th Italian Conference on Theroretical Computer Science (ICTCS’09), pages 30-33, 2009.

[7] L. Bortolussi and A. Policriti. Stochastic concurrent constraint programming and dierential equations. Electronic Notes in Theoretical Computer Science, 190(3):27-42, 2007.

[8] L. Boulianne, S. Assaad, M. Dumontier, and W. Gross. GridCell: a stochastic particle-based biological system simulator. BMC Systems Biology, 2:66, 2008.

[9] F. Buti, D. Cacciagrano, F. Corradini, E. Merelli, M. Pani, and L. Tesei. Bone remodelling in BioShape. In Proceedings of Interactions between Computer Science and Biology, 1st International Workshop (CS2BIO’10), 2010. Available at http://cosy.cs.unicam.it/bioshape/cs2bio2010.pdf.

[10] F. Buti, D. Cacciagrano, F. Corradini, E. Merelli, and L. Tesei. BioShape: a spatial shape-based scale-independent simulation environment for biological systems. In Proceedings of Simulation of Multiphysics Multiscale Systems, 7th International Workshop (ICCS 2010), 2010. Available at http://cosy.cs.unicam.it/bioshape/iccs2010.pdf.

[11] D. Cacciagrano, F. Corradini, and M. Merelli. Bone remodelling: a Complex Automata-based model running in BioShape. In Proceedings of Cellular Automata for Research and Industry, 9th International Conference (ACRI’10), 2010. Available at http://cosy.cs.unicam.it/bioshape/acri2010.pdf.

[12] N. Cannata, F. Corradini, E. Merelli, and L. Tesei. A spatial model and simulator for metabolic pathways. In Proceedings of Bioinformatics Methods for Biomedical Complex System Applications (NETTAB’08), pages 40-42, 2008.

[13] N. Cannata, F. Corradini, E. Merelli, and L. Tesei. A spatial simulator for metabolic pathways. In Proceedings of MultiAgent Systems&Bioinformatics (MAS&BIO’08), pages 31-46, 2008.

[14] L. Cardelli. Brane calculi. In Computational Methods in Systems Biology, International Conference (CMSB’04), volume 3082 of Lecture Notes in Computer Science, pages 257-278, 2005.

[15] F. Ciocchetta and J. Hillston. Bio-PEPA: An extension of the process algebra PEPA for biochemical networks. Electronic Notes in Theoretical Computer Science, 194(3):103-117, 2008.

[16] F. Corradini and E. Merelli. Hermes: agent-base middleware for mobile computing. In Formal Methods for Mobile Computing, 5th International School on Formal Methods for the Design of Computer, Communication, and Software Systems (SFM-Moby’05), volume 3465 of Lecture Notes in Computer Science, pages 234-270, 2005.

[17] C. Ericson. Real-time collision detection. Elsevier North-Holland, Inc., 2005.

[18] A. Finkelstein, J. Hetherington, L. Li, O. Margoninski, P. Sarey, R. Seymour, and A. Warner. Computational challenges of systems biology. IEEE Computer, 37(5):26-33, 2004.

[19] D. T. Gillespie. Simulation methods in systems biology. In Formal Methods for Computational Systems Biology (SFM’08), pages 125-167.

[20] C. Hecker. Physics, part 3: Collision response. Game Developer Magazine, pages 11-18, 1997.

[21] P. Hunter, W. Li, A. McCulloch, and D. Noble. Multiscale modeling: Physiome project standards, tools, and databases. Computer, 39(11):48-54, 2006.

[22] M. John, R. Ewald, and A. Uhrmacher. A spatial extension to the π calculus. Electronic Notes in Theoretical Computer Science, 194(3):133 -148, 2008.

[23] M. C. Lin and S. Gottschalk. Collision detection between geometric models: A survey. In Proceedings of IMA Conference on Mathematics of Surfaces, pages 37-56, 1998.

[24] R. Milner. Communication and concurrency. Prentice-Hall, Inc. Upper Saddle River, NJ, USA, 1989.

[25] S. J. Plimpton and A. Slepoy. Microbial cell modeling via reacting diffusive particles. Journal of Physics: Conference Series, 16(1):305-309, 2005.

[26] C. Priami and P. Quaglia. Beta binders for biological interactions. In Computational Methods in Systems Biology (CMSB’04), pages 20-33, 2004.

[27] A. Regev, E. Panina, W. Silverman, L. Cardelli, and E. Shapiro. Bioambients: an abstraction for biological compartments. Theoretical Computer Science, 325(1):141-167, 2004.

[28] J. R. Stiles and T. M. Bartol. Monte Carlo methods for simulating realistic synaptic microphysiology using MCell. In E. D. Schutter, editor, Computational Neuroscience: Realistic Modeling for Experimentalists, pages 87-127. CRC Press, 2001.

[29] K. Takahashi, S. Arjunan, and M. Tomita. Space in systems biology of signaling pathwaystowards intracellular molecular crowding in silico. FEBS letters, 579(8):1783-1788, 2005.

[30] BioShape. (http://cosy.cs.unicam.it/bioshape/).

[31] W. Yi. Real-time behaviour of asynchronous agents. In Proceedings of CONCUR ’90, volume 458 of Lecture Notes in Computer Science, pages 502520, 1990.

### Bibtex

@article{sacscuza:bartocci2010scasmcf3s, title={Shape Calculus. A Spatial Mobile Calculus for 3D Shapes}, author={E. Bartocci and F. Corradini and M.R Di Berardini and E. Merelli and L. Tesei}, journal={Scientific Annals of Computer Science}, volume={20}, organization={``A.I. Cuza'' University, Iasi, Romania}, year={2010}, pages={1--31}, publisher={``A.I. Cuza'' University Press} }