Natural Computing

, Volume 17, Issue 2, pp 345–373 | Cite as

Process calculi for biological processes

  • Andrea Bernini
  • Linda Brodo
  • Pierpaolo Degano
  • Moreno Falaschi
  • Diana Hermith


Systems biology is a research area devoted to developing computational frameworks for modeling biological systems in a holistic fashion. Within this approach, the typical advantages of using computer systems and formal methodologies are applicable. Experiments can indeed be carried on in silico that turn out to be much quicker and less expensive than wet-lab experiments. This paper surveys a specific computational approach to systems biology, based on the so-called process calculi, a formalism for describing concurrent systems. After a gentle, intuitive introduction to both fields, we present the most successful process calculi designed and used for this purpose. We start from a basic process calculus that is then extended with increasingly expressive features to better reflect the biological aspects of interest. We then compare the expressive power of the resulting calculi, mentioning if they are supported by software tools. From this comparison we derive some suggestions on the most suitable frameworks for dealing with specific cases of interest, with the help of three relevant case studies.


Algorithmic Systems Biology In-silico simulation Functional and dynamic modeling Quantitative biology 



We are deeply indebted with Grzegorz Rozenberg for many precious suggestions and advices on the structure of this work, and for having urged us to write this survey. We thank Corrado Priami and Chiara Bodei for many careful comments and remarks, as well as the anonymous reviewers for their detailed and very useful criticisms and recommendations that greatly helped us to improve our paper.


  1. Abate A, Bai Y, Sznajder N, Talcott CL, Tiwari A (2007) Quantitative and probabilistic modeling in pathway logic. In: ‘BIBE’, pp 922–929Google Scholar
  2. Akman O, Ciocchetta F, Degasperi A, Guerriero M (2009) Modelling biological clocks with Bio-PEPA: stochasticity and robustness for the neurospora crassa circadian network. In: Degano P, Gorrieri R (eds) Computational methods in systems biology, CMSB 2009. Springer, pp 52–67Google Scholar
  3. Akman O, Guerriero M, Loewe L, Troein C (2010) Complementary approaches to understanding the plant circadian clock. In: Proc. Third Workshop From Biology To Concurrency and back, FBTC 2010. EPTCS, pp 1–19Google Scholar
  4. Alon U (2006) An introduction to systems biology: design principles of biological circuits. Chapman and Hall, LondonzbMATHGoogle Scholar
  5. Arkin A, Ross J, McAdams H (1998) Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics 149(4):1633–1648Google Scholar
  6. Balázsi G, van Oudenaarden A, Collins JJ (2011) Cellular decision making and biological noise: from microbes to mammals. Cell 144(6):910–925CrossRefGoogle Scholar
  7. Barabási A-L, Oltvai ZN (2004) Network biology: understanding the cell’s functional organization. Nat Rev Genet 5:101–113CrossRefGoogle Scholar
  8. Barbuti R, Maggiolo-Schettini A, Milazzo P, Pardini G, Tesei L (2011) Spatial P systems. Nat Comput 10(1):3–16MathSciNetzbMATHCrossRefGoogle Scholar
  9. Bartholomay AF (1960) Molecular set theory: a mathematical representation for chemical reaction mechanisms. Bull Math Biophys 22(3):285–307MathSciNetCrossRefGoogle Scholar
  10. Bartocci E, Liò P (2016) Computational modeling, formal analysis, and tools for systems biology. PLoS Comput Biol 12(1):e1004591CrossRefGoogle Scholar
  11. Bartocci E, Corradini F, di Berardini M, Merelli E, Tesei L (2010) Shape calculus. A spatial mobile calculus for 3D shapes. Sci Ann Comput Sci 20:1–31MathSciNetGoogle Scholar
  12. Bhattacharjee M, Raju R, Radhakrishnan A et al (2012) A bioinformatics resource for TWEAK-Fn14 signaling pathway. J Signal TransductGoogle Scholar
  13. Bodei C (2009) A control flow analysis for beta-binders with and without static compartments. Theor Comput Sci 410(33–34):3110–3127MathSciNetzbMATHCrossRefGoogle Scholar
  14. Bodei C, Brodo L, Bruni R, Chiarugi D (2014) A flat process calculus for nested membrane interactions. Sci Ann Comput Sci 24(1):91–136MathSciNetGoogle Scholar
  15. Bodei C, Gori R, Levi F (2015a) Causal static analysis for brane calculi. Theor Comput Sci 587:73–103MathSciNetzbMATHCrossRefGoogle Scholar
  16. Bodei C, Brodo L, Gori R, Hermith D, Levi F (2015b) A global occurrence counting analysis for brane calculi. In: Proc. of LOPSTR 2015, vol 9527 of Lecture Notes in Computer Science. Springer, pp 179–200Google Scholar
  17. Bodei C, Brodo L, Gori R, Levi F, Bernini A, Hermith D (2017) A static analysis for Brane Calculi providing global occurrence counting information. Theor Comput Sci 696:11–51MathSciNetzbMATHCrossRefGoogle Scholar
  18. Borman S (2004) Much ado about enzyme mechanisms. Chem Eng News 82(8):35CrossRefGoogle Scholar
  19. Bortolussi L, Policriti A (2008a) Modeling biological systems in stochastic concurrent constraint programming. Constraints 13(1–2):66–90MathSciNetzbMATHCrossRefGoogle Scholar
  20. Bortolussi L, Policriti A (2008b) Hybrid systems and biology. In: Bernardo M, Degano P, Zavattaro G (eds) Formal methods for computational systems biology, SFM 2008, vol 5016 of Lecture Notes in Computer Science. Springer, pp 424–448Google Scholar
  21. Bracciali A, Degano P (2012) Process calculi, systems biology and artificial chemistry. In: Rozenberg G, Bäck T, Kok JN (eds) Handbook of natural computing, vol 4. Springer, Berlin, pp 1863–1896Google Scholar
  22. Bracciali A, Brunelli M, Cataldo E, Degano P (2008) Synapses as stochastic concurrent systems. Theor Comput Sci 408(1):66–82MathSciNetzbMATHCrossRefGoogle Scholar
  23. Brijder R, Ehrenfeucht A, Main MG, Rozenberg G (2011) A tour of reaction systems. Int J Found Comput Sci 22(7):1499–1517MathSciNetzbMATHCrossRefGoogle Scholar
  24. Brodo L (2011) On the expressiveness of the pi-calculus and the mobile ambients. In: Algebraic Methodology and Software Technology. AMAST 2010’, vol 6486 of Lecture Notes in Computer Science. Springer, pp 44–59Google Scholar
  25. Brodo L, Degano P, Priami C (2007) A stochastic semantics for bioambients. In: Malyshkin V (ed) Parallel computing technologies, vol 4671 of Lecture Notes in Computer Science. Springer, pp 22–34Google Scholar
  26. Buti F, Cacciagrano D, Corradini F, Merelli E, Tesei L (2010) Bioshape: a spatial shape-based scale-independent simulation environment for biological systems. Procedia Comput Sci 1(1):827–835. Proc. of 7th Int. Workshop on Multiphysics Multiscale Systems, ICCS 2010Google Scholar
  27. Buti F, Corradini F, Merelli E, Tesei L (2012) A geometrical refinement of shape calculus enabling direct simulation. In: Proc. of the 2nd international conference on simulation and modeling methodologies, technologies and applications—volume 1: SIMULTECH’, pp 218–227Google Scholar
  28. Cacciagrano D, Corradini F, Merelli E, Tesei L (2017) Uniformity in multiscale models: from complex automata to bioshape. J Cell Autom 12(5):333–359MathSciNetGoogle Scholar
  29. Caires L, Cardelli L (2003) A spatial logic for concurrency (part I). Inf Comput 186(2):194–235zbMATHCrossRefGoogle Scholar
  30. Calder M, Hillston J (2009) Process algebra modelling styles for biomolecular processes. In: Priami C, Back R-J, Petre I (eds) Transactions on computational systems biology XI’, vol 5750 of Lecture Notes in Computer Science. Springer, pp 1–25Google Scholar
  31. Cao Y, Liang J (2008) Optimal enumeration of state space of finitely buffered stochastic molecular networks and exact computation of steady state landscape probability. BMC Syst Biol 2(1):30CrossRefMathSciNetGoogle Scholar
  32. Cao Y, Li H, Petzold L (2004) Efficient formulation of the stochastic simulation algorithm for chemically reacting system. J Chem Phys 121:4059–4067CrossRefGoogle Scholar
  33. Cao Y, Lu H, Liang J (2010) Probability landscape of heritable and robust epigenetic state of lysogeny in phage lambda. Proc Natl Acad Sci 107(43):18445–18450CrossRefGoogle Scholar
  34. Cardelli L (2005) Brane calculi. In: Danos V, Schachter V (eds) Computational methods in systems biology, vol 3082 of Lecture Notes in Computer Science, Springer, pp 257–278Google Scholar
  35. Cardelli L (2008) On process rate semantics. Theor Comput Sci 391(3):190–215MathSciNetzbMATHCrossRefGoogle Scholar
  36. Cardelli L (2009) A process model of actin polymerisation. Electron Notes Theor Comput Sci 229(1):127–144MathSciNetzbMATHCrossRefGoogle Scholar
  37. Cardelli L (2011) Strand algebras for DNA computing. Nat Comput 10(1):407–428MathSciNetzbMATHCrossRefGoogle Scholar
  38. Cardelli L, Csikász-Nagy A (2012) The cell cycle switch computes approximate majority. Sci Rep 2:656CrossRefGoogle Scholar
  39. Cardelli L, Gardner P (2012) Processes in space. Theor Comput Sci 431:40–55MathSciNetzbMATHCrossRefGoogle Scholar
  40. Cardelli L, Gordon A (2000) Mobile ambients. Theor Comput Sci 240(1):177–213MathSciNetzbMATHCrossRefGoogle Scholar
  41. Cardelli L, Phillips A (2006) Spim: stochastic pi machine.
  42. Cardelli L, Caron E, Gardner P, Kahramanoğulları O, Phillips A (2009) A process model of Rho GTP-binding proteins. Theor Comput Sci 410(33):3166–3185MathSciNetzbMATHCrossRefGoogle Scholar
  43. Cavalier-Smith T (2002) The neomuran origin of archaebacteria, the negibacterial root of the universal tree and bacterial megaclassification. Int J Syst Evol Microbiol 52(1):7–76CrossRefGoogle Scholar
  44. Chiarugi D, Degano P, Marangoni R (2007a) A computational approach to the functional screening of genomes. PLoS Comput Biol 9:1801–1806MathSciNetGoogle Scholar
  45. Chiarugi D, Degano P, Marangoni R (2007b) A computational approach to the functional screening of genomes. PLoS Comput Biol 3(9):e174MathSciNetCrossRefGoogle Scholar
  46. Chiarugi D, Curti M, Degano P, Marangoni R (2005) Vice: a virtual cell. In: Proceedings of the 20 international conference on computational methods in systems biology, CMSB’04, pp 207–220Google Scholar
  47. Chiarugi D, Falaschi M, Hermith D, Olarte C, torella L (2015) Modelling non-Markovian dynamics in biochemical reactions. BMC Syst Biol 9(S–3):S8CrossRefGoogle Scholar
  48. Ciocchetta F, Guerriero ML (2009) Modelling biological compartments in bio-PEPA. Electron Notes Theor Comput Sci 227:77–95zbMATHCrossRefGoogle Scholar
  49. Ciocchetta F, Hillston J (2008) Process algebras in systems biology. In: Bernardo M, Degano P, Zavattaro G (eds) Formal methods for computational systems biology, SFM 2008, vol 5016 of Lecture Notes in Computer Science. Springer, pp 265–312Google Scholar
  50. Ciocchetta F, Hillston J (2009) Bio-PEPA: a framework for the modelling and analysis of biochemical networks. Theor Comput Sci 410(33):3065–3084zbMATHCrossRefGoogle Scholar
  51. Ciocchetta F, Degasperi A, Heath J, Hillston J (2010a) Modelling and analysis of the NF-kappaB pathway in Bio-PEPA. Trans Comput Syst Biol 12:229–262CrossRefGoogle Scholar
  52. Ciocchetta F, Guerriero M, Hillston J (2010b) Investigating modularity in the analysis of process algebra models of biochemical systems. In: Proc. third workshop from biology to concurrency and back, FBTC 2010, pp 55–69Google Scholar
  53. Clavel M, Durán F, Escobar S, Eker S, Lincoln P, Martí-Oliet N, Meseguer J, Talcott C (2015) Maude manual (version 2.7), Technical report, University of Illinois at Urbana-Champaign.
  54. Cohen J (2008) The crucial role of CS in systems and synthetic biology. Commun ACM 51(5):15–18CrossRefGoogle Scholar
  55. Corradini F, Merelli E, Tesei L, Cacciagrano D, Di Bernardi M, Bartocci E, Buti F (2011) The bioshape simulator. Accessed: 2017-04-30
  56. Credia A, Garavellia M, Laneve C, Pradalierc S, Silvi S, Zavattaro G (2008) nano$\kappa $: a calculus for the modeling and simulation of nano devices. Theor Comput Sci 408:17–30MathSciNetCrossRefGoogle Scholar
  57. Dalchau N, Phillips A, G LD, Howarth M, Cardelli L, Emmott S, Elliott T, Werner J (2011) A peptide filtering relation quantifies MHC class I peptide optimization. PLoS Comput Biol 7(10):e1002144CrossRefGoogle Scholar
  58. Danos V, Laneve C (2004) Formal molecular biology. Theor Comput Sci 325(1):69–110MathSciNetzbMATHCrossRefGoogle Scholar
  59. Degano P, De Nicola R, Montanari U (1988) A distributed operational semantics for CCS based on condition/event systems. Acta Inf 26(1/2):59–91MathSciNetzbMATHCrossRefGoogle Scholar
  60. Demattè L, Priami C, Romanel A (2008a) The Beta Workbench: a computational tool to study the dynamics of biological systems. Brief Bioinform 9(5):437–449CrossRefGoogle Scholar
  61. Demattè L, Priami C, Romanel A (2008b) The BlenX Language: a tutorial. In: Bernardo M, Degano P, Zavattaro G (eds) Formal methods for computational systems biology, vol 5016 of Lecture Notes in Computer Science. Springer, pp 313–365Google Scholar
  62. Demattè L, Larcher R, Palmisano A, Priami C, Romanel A (2010) Programming biology in blenx. Syst Biol Signal Netw 1:777–820CrossRefGoogle Scholar
  63. Di Ventura B, Lemerle C, Michalodimitrakis K, Serrano L (2006) From in vivo to in silico biology and back. Nature 443(7111):527–533CrossRefGoogle Scholar
  64. Dooms G, Deville Y, Dupont P (2004) Constrained path finding in biochemical networks. In: 5emes Journees Ouvertes Biologie Informatique Mathematiques, p 40Google Scholar
  65. Doudna JA, Cech TR (2002) Review article the chemical repertoire of natural ribozymes. Nature 418:222–228CrossRefGoogle Scholar
  66. Duguid A, Gilmore S, Guerriero M, Hillston J, Loewe L (2009) Design and development of software tools for Bio-PEPA. In: Winter Simulation Conference, WSC ’09, pp 956–967Google Scholar
  67. Ehrenfeucht A, Rozenberg G (2007) Reaction systems. Fundam Inform 75(1–4):263–280MathSciNetzbMATHGoogle Scholar
  68. Ehrenfeucht A, Rozenberg G (2010a) Reaction systems: a formal framework for processes based on biochemical interactions. ECEASST 26Google Scholar
  69. Ehrenfeucht A, Rozenberg G (2010b) Reaction systems: a model of computation inspired by biochemistry. In: Springer (ed) Developments in language theory, DLT 2010, vol 6224 of Lecture Notes in Computer Science, pp 1–3Google Scholar
  70. Errampalli D, Priami C, Quaglia P (2005) A formal language for computational systems biology. OMICS 8(4):370–380CrossRefGoogle Scholar
  71. Fages F, Soliman S (2006) Type inference in systems biology. In: Proceedings of the 2006 international conference on computational methods in systems biology, CMSB’06. Springer, pp 48–62Google Scholar
  72. Fages F, Soliman S (2008) Formal cell biology in biocham. In: Formal methods for computational systems biology, SFM 2008, vol 5016 of Lecture Notes in Computer Science. Springer, pp 54–80Google Scholar
  73. Fellermann H, Cardelli L (2014) Programming chemistry in DNA-addressable bioreactors. J R Soc Interface 11(99):407–428CrossRefGoogle Scholar
  74. Fisher J, Henzinger T (2007) Executable cell biology. Nat Biotechnol 25(11):1239–1249CrossRefGoogle Scholar
  75. Fontana W, Buss LW (1994) The arrival of the fittest: toward a theory of biological organization. Bull Math Biol 56:1–64zbMATHGoogle Scholar
  76. Galpin V (2014) Hybrid semantics for Bio-PEPA. Inf Comput 236(C):122–145MathSciNetzbMATHCrossRefGoogle Scholar
  77. Gibson MA, Bruck J (2000) Efficient exact stochastic simulation of chemical systems with many species and many channels. J Phys Chem 104(9):1876–1889CrossRefGoogle Scholar
  78. Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22(4):403–434MathSciNetCrossRefGoogle Scholar
  79. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361CrossRefGoogle Scholar
  80. Gillespie DT (2000) The chemical Langevin equation. J Chem Phys 113(1):297–306CrossRefGoogle Scholar
  81. Gillespie D (2007) Stochastic simulation of chemical kinetics. Annu Rev Phys Chem 58:35–55CrossRefGoogle Scholar
  82. Gilmore S (2008) Bio-PEPA workbench.
  83. Gómez-Uribe C, Verghese G (2007) Mass fluctuation kinetics: capturing stochastic effects in systems of chemical reactions through coupled mean-variance computations. J Chem Phys 126(2):024109CrossRefGoogle Scholar
  84. Gong H, Zuliani P, Komuravelli A, Faeder JR, Clarke EM (2010) Computational modeling and verification of signaling pathways in cancer. In: HK, NM, PN (eds) Proc. of algebraic and numeric biology (ANB’10), vol 6479 of Lecture Notes in Computer Science. Springer, pp 117–135Google Scholar
  85. Gori R, Levi F (2006) An analysis for proving temporal properties of biological systems. In: Kobayashi N (ed) Programming languages and systems, vol 4279 of Lecture Notes in Computer Science. Springer, pp 234–252Google Scholar
  86. Gorrieri R (2017) Process algebras for Petri nets—the alphabetization of distributed systems. Monographs in Theoretical Computer Science, An EATCS Series. SpringerGoogle Scholar
  87. Gorrieri R, Versari C (2015) CCS: a calculus of communicating systems. In: Introduction to concurrency theory: transition systems and CCS. Springer International Publishing, chapter 3:81–161Google Scholar
  88. Guerriero M (2009) Qualitative and quantitative analysis of a Bio-PEPA model of the gp130/jak/stat signalling pathway. In: Priami C, Back R-J, Petre I (eds) Transactions on computational systems biology XI, vol 5750 of Lecture Notes in Computer Science. Springer, pp 90–115Google Scholar
  89. Guerriero ML, Priami C, Romanel A (2007) Modeling static biological compartments with beta-binders. In: Anai H, Horimoto K, Kutsia T (eds) Algebraic biology, vol 4545 of LNCS. Springer, pp 247–261Google Scholar
  90. Guerriero ML, Prandi D, Priami C, Quaglia P (2009) Process calculi abstractions for biology. In: Condon A, Harel D, Kok JN, Salomaa A, Winfree E (eds) Algorithmic Bioprocesses. Natural computing. Springer, Berlin, pp 463–486CrossRefGoogle Scholar
  91. Guerriero M, Pokhilko A, Fernández A, Halliday K, Millar A, Hillston J (2012) Stochastic properties of the plant circadian clock. J R Soc Interface 9(69):744–756CrossRefGoogle Scholar
  92. Henzinger TA, Mateescu M, Wolf V (2009) Sliding window abstraction for infinite Markov chains. Lect Notes Comput Sci 5643:337–352zbMATHCrossRefGoogle Scholar
  93. Hillston J (1993) PEPA—performance enhanced process algebra. Ph.D. thesis, University of Edinburgh, Computer Science DepartmentGoogle Scholar
  94. Hinton A, Kwiatkowska M, Norman G, Parker D (2006) Prism: a tool for automatic verification of probabilistic systems. In: Hermanns H, Palsberg J (eds) TACAS’06, vol 3920 of Lecture Notes in Computer Science. Springer, pp 441–444Google Scholar
  95. Hood L, Galas D (2003) The digital code of DNA. Nature 421(6921):444–448CrossRefGoogle Scholar
  96. Kampen NV (2007) Stochastic processes in physics and chemistry. North-Holland Personal Library, AmsterdamzbMATHGoogle Scholar
  97. Karamanogullari O, Lecca P, Morpurgo D, Fantaccini G, Priami C (2012) Algorithmic modeling quantifies the complementary contribution of metabolic inhibitions to gemcitabine efficacy. PLoS ONE 7(12):e50176CrossRefGoogle Scholar
  98. Kitano H (2001) Foundations of systems biology. The Massachusetts Institute of Technology Press, CambridgeGoogle Scholar
  99. Koch I (2015) Petri nets in systems biology. Softw Syst Model 14(2):703–710CrossRefMathSciNetGoogle Scholar
  100. Koch I, Reisig W, Schreiber F (eds) (2011) Modeling in systems biology–the Petri net approach. Springer, BerlinzbMATHGoogle Scholar
  101. Kuttler C (2006) Simulating bacterial transcription and translation in a stochastic pi-calculus. Trans Comput Syst Biol V I(4220):113–149MathSciNetGoogle Scholar
  102. Kuznetsov A (2009) Genetic networks described in stochastic pi machine (spim) programming language: compositional design. J Comput Sci Syst Biol 2(5):272–282CrossRefGoogle Scholar
  103. Lakin MR, Youssef S, Cardelli L, Phillips A (2012) Abstractions for DNA circuit design. J R Soc Interface 9(68):470–486CrossRefGoogle Scholar
  104. Landin PJ (1966) The next 700 programming languages. Commun ACM 9(3):157–166zbMATHCrossRefGoogle Scholar
  105. Lecca P (2011) Blenx models of alpha-synuclein and parkin kinetics in neuropathology of Parkinson’s disease. J Biol Syst 19(2):149–181MathSciNetzbMATHCrossRefGoogle Scholar
  106. Lecca P, Priami C (2007) Cell cycle control in eukaryotes: a biospi model. Electron Notes Theor Comput Sci 180(3):51–63CrossRefGoogle Scholar
  107. Lecca P, Priami C, Laudanna C, Constantin G (2004) A biospi model of lymphocyte-endothelial interactions in inflamed brain venules. In: Online proceedings of Pacific Symposium on Biocomputing PSB 2004. World Scientific Publishing, pp 521–532Google Scholar
  108. Lecca P, Kahramanoullari O, Morpurgo D, Priami C, Soo RA (2011) Modelling and estimating dynamics of tumor shrinkage with BlenX and KInfer. In: Proc. of the 2011 UKSim 13th Int. conference on modelling and simulation, UKSIM ’11. IEEE, pp 75–80Google Scholar
  109. Liu F, Heiner M (2013) Modeling membrane systems using colored stochastic Petri nets. Nat Comput 12(4):617–629MathSciNetzbMATHCrossRefGoogle Scholar
  110. Lodish H, Berk A, Matsudaira P, Kaiser CA, Krieger M, Scott MP, Zipursky L, Darnell J (2004) Molecular cell biology. W.H. Freeman, New YorkGoogle Scholar
  111. Matsuno H, Doi A, Nagasaki M, Miyano S (2000) Hybrid Petri net representation of gene regulatory network. In: Proceedings of the Pacific Symposium on Biocomputing, vol 5, pp 341–352Google Scholar
  112. Mayr E (1998) Comparative biochemistry of archaea and bacteria. Proc Natl Acad Sci USA 95(17):9720–9723CrossRefGoogle Scholar
  113. McQuarrie DA (1967) Stochastic approach to chemical kinetics. J Appl Probab 4(3):413–478MathSciNetzbMATHCrossRefGoogle Scholar
  114. Miculan M, Bacci G (2006) Modal logics for brane calculus. In: Priami C (ed) Computational methods in systems biology, vol 4210. Lecture Notes in Computer Science. Springer, Berlin, pp 1–16Google Scholar
  115. Miller L, Spoolman S (2012) Environmental science. Cengage Learning, New YorkGoogle Scholar
  116. Milner R (1982) A calculus of communicating systems. Springer, New YorkzbMATHGoogle Scholar
  117. Muganthan V, Phillips A, Vigliotti M (2005) Bioambient machine (bam). Accessed: 2017-05-31
  118. Munsky B, Khammash M (2006) The finite state projection algorithm for the solution of the chemical master equation. J Chem Phys 124(4):044104zbMATHCrossRefGoogle Scholar
  119. Nassiri I, Lombardo R, Lauria M, Morine M, Moyseos P, Varma V, Nolen G, Knox B, Sloper D, Kaput J, Priami C (2016) Systems view of adipogenesis via novel omics-driven and tissue-specific activity scoring of network functional modules. Sci Rep 6:28851CrossRefGoogle Scholar
  120. Nurse P (2008) Life, logic and information. Nature 454(7203):424–426CrossRefGoogle Scholar
  121. Olarte C, Chiarugi D, Falaschi M, Hermith D (2016) A proof theoretic view of spatial and temporal dependencies in biochemical systems. Theor Comput Sci 641:25–42MathSciNetzbMATHCrossRefGoogle Scholar
  122. Paoletti N, Liò P, Merelli E, Viceconti M (2012) Multilevel computational modeling and quantitative analysis of bone remodeling. IEEE ACM Trans Comput Biol Bioinform 9(5):1366–1378CrossRefGoogle Scholar
  123. Paulevè L, Youssef S, Lakin M, Phillips A (2010) A generic abstract machine for stochastic process calculi. In: Proc. of the 8th int. conference on computational methods in systems biology, CMSB ’10, pp 43–54Google Scholar
  124. Paulsson J, Berg OG, Ehrenberg M (2000) Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation. Proc Natl Acad Sci 97(13):7148–7153CrossRefGoogle Scholar
  125. Păun G (2001) From cells to computers: computing with membranes (p systems). Biosystems 59(3):139–158CrossRefGoogle Scholar
  126. Petri CA (1962) Kommunikation mit automaten. Ph.D. thesis, Technical report, University of BonnGoogle Scholar
  127. Phillips A (2009a) A visual process calculus for biology. In: Iyengar MS (ed) Symbolic systems biology: theory and methods. Jones and Bartlett Publ., chapter 5Google Scholar
  128. Phillips A (2009b) An abstract machine for the stochastic bioambient calculus. Electron Notes Theor Comput Sci 227:143–159zbMATHCrossRefGoogle Scholar
  129. Phillips A, Cardelli L, Castagna G (2006), A graphical representation for biological processes in the stochastic pi-calculus. In: Priami C, Ingólfsdóttir A, Mishra B, Nielson HR (eds) Transactions on computational systems biology, vol VII. Springer, pp 123–152Google Scholar
  130. Plotkin GD (2004) The origins of structural operational semantics. J Log Algebraic Semant 60–61:3–15MathSciNetzbMATHCrossRefGoogle Scholar
  131. Pokhilko A, Hodge SK, Stratford K, Knox K, Edwards KD, Thomson AW, Mizuno T, Millar AJ (2010) Data assimilation constrains new connections and components in a complex, eukaryotic circadian clock model. Mol Syst Biol 6(1):416Google Scholar
  132. Priami C (2009a) Algorithmic systems biology. Commun ACM 52(5):80–88CrossRefGoogle Scholar
  133. Priami C (2009b) Algorithmic systems biology: computer science propels systems biology. In: Rozenberg G, Back T, Kok J (eds) Handbook of natural computing. Springer, Berlin, pp 1835–1862Google Scholar
  134. Priami C, Morine M (2015) Analysis of biological systems. Imperial College Press, LondonCrossRefGoogle Scholar
  135. Priami C, Quaglia P (2004) Modeling the dynamics of biosystems. Brief Bioinform 5(3):259–269CrossRefGoogle Scholar
  136. Priami C, Quaglia P (2005) Beta binders for biological interactions. In: Danos V, Schachter V (eds) Computational methods in systems biology, vol 3082. LNCS. Springer, Berlin, pp 20–33Google Scholar
  137. Priami C, Regev A, Shapiro E, Silvermann W (2009a) Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Theor Comput Sci 325:141–167Google Scholar
  138. Priami C, Ballarini P, Quaglia P (2009b) Blenx4bio—blenx for biologists. In: Degano P, Gorrieri R (eds) Computational methods in systems biology: 7th Int. Conference, CMSB 2009. Springer, pp 26–51Google Scholar
  139. Programming DNA Circuits (2009) Accessed: 2017-03-30
  140. Raj A, Rifkin SA, Andersen E, van Oudenaarden A (2010) Variability in gene expression underlies incomplete penetrance. Nature 463:913–918CrossRefGoogle Scholar
  141. Rao CV, Arkin AP (2003) Stochastic chemical kinetics and the quasi- steady-state assumption: application to the gillespie algorithm. J Chem Phys 118(11):4999–5010CrossRefGoogle Scholar
  142. Regev A, Shapiro E (2002) Cellular abstractions: cells as computation. Nature 419(6905):343CrossRefGoogle Scholar
  143. Regev A, Shapiro E (2004) The $\pi $-calculus as an abstraction for biomolecular systems. In: Ciobanu G, Rozenberg G (eds) Modelling in molecular biology. Springer, Berlin, pp 219–266CrossRefGoogle Scholar
  144. Regev A, Silverman W, Shapiro EY (2001) Representation and simulation of biochemical processes using the pi-calculus process algebra. In: Pacific Symposium on Biocomputing, pp 459–470Google Scholar
  145. Regev A, Panina E, Silverman W, Cardelli L, Shapiro E (2005) Bioambients: an abstraction for biological compartments. Theor Comput Sci 325(1):141–167MathSciNetzbMATHCrossRefGoogle Scholar
  146. Samoilov M, Plyasunov S, Arkin AP (2005) Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations. Proc Natl Acad Sci 102(7):2310–2315CrossRefGoogle Scholar
  147. Sangers F, Nicklen S, Coulson AR (1977) DNA sequencing with chain-terminating inhibitors. Proc Nat Acad Sci 74:5463–5467CrossRefGoogle Scholar
  148. Sangiorgi D, Walker D (2001) PI-calculus: a theory of mobile processes. Cambridge University Press, CambridgezbMATHGoogle Scholar
  149. Schuster SC (2008) Next-generation sequencing transforms today’s biology. Nat Methods 5(1):16–18CrossRefGoogle Scholar
  150. Scotti M (2012) The role of stochastic simulations to extend food web analyses. In: Lecca P, Tulpan D, Rajaraman K (eds) Systemic approaches in bioinformatics and computational systems biology: recent advances. IGI Global, pp 163–196Google Scholar
  151. Scotti M, Gjata N, Livi C, Jordán F (2012) Dynamical effects of weak trophic interactions in a stochastic food web simulation. Community Ecol 13(2):230–237CrossRefGoogle Scholar
  152. Searls D (2002) The language of genes. Nature 420(6912):211–217CrossRefGoogle Scholar
  153. Steinfeld J-I, Francisco J-S, Hase W-L (1989) Chemical kinetics and dynamics. Prentice Hall, Upper Saddle RiverGoogle Scholar
  154. Stumpf M, Balding DJ, Girolami M (2011) Handbook of statistical systems biology. Wiley, New YorkzbMATHCrossRefGoogle Scholar
  155. Thanh VH, Zunino R, Priami C (2016) Accelerating rejection-based simulation of biochemical reactions with bounded acceptance probability. J Chem Phys 144(22):22410CrossRefGoogle Scholar
  156. Thanh VH, Zunino R, Priami C (2017) Efficient constant-time complexity algorithm for stochastic simulation of large reaction networks. IEEE/ACM Trans Comput Biol Bioinform 14(3):657–667CrossRefGoogle Scholar
  157. The Beta WorkBench (2008) Accessed: 2017-05-31
  158. The System Biology Markup Language (2001)
  159. Veliz-Cuba A, Salam JA, Reinhard L (2010) The origins of structural operational semantics. Bioinformatics 26:13CrossRefGoogle Scholar
  160. Voit E (2000) Computational analysis of biochemical systems—a practical guide for biochemists and molecular biologists. Cambridge University Press, CambridgeGoogle Scholar
  161. Wang DY, Cardelli L, Phillips A, Piterman N, Fisher J (2009) Computational modeling of the EGFR network elucidates control mechanisms regulating signal dynamics. BMC Syst Biol 3(1):118CrossRefGoogle Scholar
  162. Wolkenhauer O, Kitano H, Kwang-Hyun C (2003) Systems biology: looking at opportunities and challenges in applying systems theory to molecular and cell biology. IEEE Control Syst Mag 23(4):38–48CrossRefGoogle Scholar
  163. XML Tutorial (n.d.)

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Andrea Bernini
    • 1
  • Linda Brodo
    • 2
  • Pierpaolo Degano
    • 3
  • Moreno Falaschi
    • 4
  • Diana Hermith
    • 5
  1. 1.Dipartimento di Biotecnologie, Chimica e FarmaciaUniversità di SienaSienaItaly
  2. 2.Dipartimento di Scienze Economiche e AziendaliUniversità di SassariSassariItaly
  3. 3.Dipartimento di InformaticaUniversità di PisaPisaItaly
  4. 4.Dipartimento di Ingegneria dell’Informazione e Scienze MatematicheUniversità di SienaSienaItaly
  5. 5.Facultad de IngenieríaPontificia Universidad JaverianaCaliColombia

Personalised recommendations