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List of systems biology modeling software

Topic: Biology

 From HandWiki - Reading time: 14 min

Systems biology relies heavily on building mathematical models to help understand and make predictions of biological processes. Specialized software to assist in building models has been developed since the arrival of the first digital computers.[1][2][3][4] The following list gives the currently supported software applications available to researchers. The vast majority of modern systems biology modeling software support SBML, which is the de facto standard for exchanging models of biological cellular processes. Some tools also support CellML, a standard used for representing physiological processes. The advantage of using standard formats is that even though a particular software application may eventually become unsupported and even unusable, the models developed by that application can be easily transferred to more modern equivalents. This allows scientific research to be reproducible long after the original publication of the work.

To obtain more information about a particular tool, click on the name of the tool. This will direct you either to a peer-reviewed publication or, in some rare cases, to a dedicated Wikipedia page.

Actively supported open-source software applications

General information

When an entry in the SBML column states "Yes, but only for reactions.", it means that the tool only supports the reaction component of SBML. For example, rules, events, etc. are not supported.

Name Description/Notability OS License Site SBML Support
iBioSim iBioSim[5][6] is a computer-aided design (CAD) tool for the modeling, analysis, and design of genetic circuits. multiplatform (Java/C++) Apache License [1] Yes
CompuCell3D GUI/Scripting tool[7] for building and simulating multicellular models. multiplatform (C++/Python) MIT [2] Yes, but only for reactions.
COPASI GUI tool[8][9] for analyzing and simulating SBML models. multiplatform (C++) Artistic License [3] Yes
Cytosim Spatial simulator for flexible cytoskeletal filaments and motor proteins[10] Mac, Linux, Cygwin (C++) GPL3 [4] Not applicable
libroadrunner High-performance software library for simulation and analysis of SBML models[11][12] multiplatform (C/C++) Apache License [5] Yes
massPy Simulation tool [13][14] that can work with COBRApy[15] multiplatform (Python) MIT [6] Yes
MCell GUI tool for particle-based spatial stochastic simulation with individual molecules[16][17][18] multiplatform MIT and GPLv2 [7] Not applicable
OpenCOR A cross-platform modelling environment, which is aimed at organizing, editing, simulating, and analysing CellML files on Windows, Linux and macOS. multiplatform (C++/Python) GPLv3 [8] Uses CellML
PhysiBoSS A specialized form of the PhysiCell agent-based modeling platform that directly integrates Boolean signaling networks into cell Agents[19] multiplatform (C++) BSD-3 [9] Yes, but only for reactions
PhysiCell A agent-based[20] modeling framework for multicellular systems biology. multiplatform (C++) BSD-3 [10] Yes, but only for reactions
PySCeS Python tool for modeling and analyzing SBML models[21][22][23] multiplatform (Python) BSD-3 [11] Yes
pySB Python-based[24] platform with specialization in rule-based models. multiplatform (Python) BSD-3 [12] Partial
ReaDDy Particle-based spatial simulator with intermolecular potentials[25] Linux and Mac Custom [13] Not applicable
SBSCL Java library[26][27] with efficient and exhaustive support for SBML multiplatform (Java) LGPL [14] Yes
SBW (software) A distributed workbench[28][29] that includes many modeling tools multiplatform (C/C++) BSD-3 [15] Yes
Smoldyn Particle-based simulator for spatial stochastic simulations with individual molecules[30][31][32][33] multiplatform (C/C++/Python) LGPL [16] Not applicable
Spatiocyte Spatial modeling software that uses a fine lattice with up to one molecule per site[34][35] multiplatform Unknown [17] Not applicable
SpringSaLaD Particle-based spatial simulator in which molecules are spheres that are linked by springs[36] multiplatform Unknown [18] Not applicable
STEPS Stochastic reaction-diffusion and membrane potential solver on distributed meshes[37][38][39][40] multiplatform (C++/Python) GPLv2 [19] Partial [20]
Tellurium (software) Simulation environment,[41][42] that packages multiple libraries into one platform. multiplatform (Python) Apache License [21] Yes
URDME Stochastic reaction-diffusion simulation on unstructured meshes[43] MatLab on Mac, Linux GPL3 [22] Not applicable
VCell Comprehensive modeling platform[44][45] for non-spatial, spatial, deterministic and stochastic simulations, including both reaction networks and reaction rules. multiplatform (Java) MIT [23] Yes

Specialist Tools

The following table lists specialist tools that cannot be grouped with the modeling tools.

Name Description/Notability OS License Site
PySCeSToolbox PySCeSToolbox[46] is a set of metabolic model analysis tools. Among other features, it can be used to generate the control analysis equations that relate the elasticities to the control coefficients. The package is cross-platform and requires PySCeS and Maxima to operate. multiplatform (C++/Python) BSD-3 [24]

Feature Tables

Supported modeling paradigms

Name ODE Constraint based Stochastic Logical Agent based Spatial (particle) Spatial (continuous)
iBioSim Yes No Yes No Limited No No
CompuCell3D Yes No No No Yes No Yes
COPASI Yes No Yes No No No No
Cytosim No No Yes No ? Yes ?
libroadrunner Yes No Yes No No No No
massPy Uses libroadrunner Uses COBRApy No No No No
MCell No No Yes No No Yes No
OpenCOR Yes No No No No No No
PhysiBoSS
PhysiCell Uses libroadrunner No No No Yes ? Yes
PySCeS Yes No ? No No No No
pySB Yes No No No No No No
ReaDDy
SBSCL Yes ? ? No No No No
SBW Yes No Yes No No No No
Smoldyn No No Yes No No Yes No
Spatiocyte
SpringSaLaD
STEPS
Tellurium (software) Uses libroadrunner
URDME
VCell Yes No ? No No No Single Cell

Differential equation specific features

Name Non-stiff solver Stiff solver Steady-state solver Steady-state sensitivities Time-dependent sensitivities Bifurcation Analysis
iBioSim Yes Yes No No ? No
CompuCell3D Uses libroadrunner NA
COPASI Yes Yes Yes Yes ? Limited
libroadrunner Yes Yes Yes Yes Yes via AUTO2000 plugin
masspy Uses libroadrunner
OpenCOR Yes Yes ? ? ? No
PhysiBoSS
PhysiCell Uses libroadrunner
PySCeS Yes Yes Yes Yes ? Limited+
pySB Yes No No No No No
SBSCL
SBW Uses C# edition of roadrunner Yes
Tellurium (software) Uses libroadrunner
VCell Yes Yes No No No No

File format support and interface type

Name Import Export Primary Interface Network visualization (editing)
iBioSim SBML SBML GUI Yes (Yes)
CompuCell3D Native XML specification format and SBML Native XML GUI/Python scripting No
COPASI Native XML specification format and SBML Native XML and SBML GUI Yes (No)
libroadrunner SBML SBML Python scripting No
masspy SBML SBML Python scripting No

Advanced features (where applicable)

Name Stoichiometry matrix Reduced stoich matrix Conserved moiety analysis Jacobian MCA
COPASI Yes Yes Yes Yes Yes
libroadrunner Yes Yes Yes Yes Yes
masspy via libroadrunner
PySCeS Yes Yes Yes Yes Yes
VCell ? ? ? ? Limited

Other features

Name Parameter Estimation DAE support Units support
iBioSim No ? ?
ComputeCell3D NA NA ?
COPASI Yes Limited Yes
libroadrunner via Python packages Limited Yes
masspy via Python packages Limited Yes

Particle-based simulators

Particle based simulators treat each molecule of interest as an individual particle in continuous space, simulating molecular diffusion, molecule-membrane interactions and chemical reactions.[47]

Comparison of particle-based simulators

The following list compares the features for several particle-based simulators. This table is edited from a version that was originally published in the Encyclopedia of Computational Neuroscience.[48] System boundaries codes: R = reflecting, A = absorbing, T = transmitting, P = periodic, and I = interacting. * Algorithm is exact but software produced incorrect results at the time of original table compilation. † These benchmark run times are not comparable with others due to differing levels of detail.

Feature MCell Smoldyn eGFRD SpringSaLaD ReaDDy
Time steps ~1 us ns to ms event-based ~10 ns ~0.1 ns to us
Molecules points points, spheres spheres multi-spheres multi-spheres
Dimensions 2,3 1,2,3 3 3 3
System boundaries R,A,P,T R,A,P,T P R P,I
Surfaces triangle mesh many primitives - 1 flat surface plane, sphere
Surface molecules 1/tile, 2 states unlimited, 4 states - unlimited, 3 states -
Excluded volume - excellent exact good excellent
Multimers states only rule-based model - explicit explicit
Allostery - yes - yes -
Reaction accuracy very good excellent exact* excellent excellent
Dissociation products stochastic fixed separation adjacent adjacent adjacent
Molecule-surface interactions good excellent - to sites only potentials
Long-range interactions - yes - - yes
Benchmark run time 67 s 22 s 13 days† 9.1 months† 13 minutes
Distribution executable executable self-compile Java file self-compile
User interface GUI, text text text GUI Python script
Graphical output excellent good partial support partial support good
Library interface Python C/C++, Python - - Python
References

[49][50][51]

[52][53] [54][55][56] [57] [58]

Model calibration software

Model calibration is a key activity when developing systems biology models. This table highlights some of the current model calibration tools available to systems biology modelers. The first table list tools that are SBML compatible.

Tool PEtab Compatible P1 P2
pyPESTO[59] Yes NA NA
COPASI Yes NA NA

PEtab[60] is a community standard for specifying model calibration runs.

Legacy open-source software applications

The following list some very early software for modeling biochemical systems that were developed pre-1980s There are listed for historical interest.

Name Description/Notability Language Terminus ante quem[61]
BIOSIM[62] The first ever recorded digital simulator of biochemical networks (by David Garfinkel) FORTRAN IV 1968
KDF 9[63] First simulator to support MCA. Developed by the late Jim Burns in Edinburgh Early form of FORTRAN 1968
METASIM[64] Early simulator by Park and Wright PL/1 1973

The following list shows some of the software modeling applications that were developed in the 1980s and 1990s. There are listed for historical interest.

Name Description/Notability Language SBML Support Terminus ante quem[65]
COR[66] First public CellML-based environment. Object Pascal Uses CellML 2010
DBsolve[67] Early GUI based simulation platform. C/C++ No 1999
E-Cell[68] One of the earliest attempts at a whole-cell modeling platform. C/C++ No 1999
Gepasi[69] First GUI application that supported metabolic control analysis and parameter estimation. C/C++ Yes 1993
Jarnac[70] First GUI based application to support scripting in systems biology modeling. Object Pascal Yes 2000
JSim[71] First Java-based systems biology modeling platform Java Yes 2003
MetaMod[72] One of the first PC-based systems biology simulators BBC Micro No 1986
MetaModel[73] Early PC-based systems biology simulator Turbo Pascal 5.0 No 1991
MIST[74] GUI based simulator Borland Pascal 7.0 No 1995
SCAMP[75] First application to support metabolic control analysis and simulation on a PC Pascal, later in C No 1985 (Thesis)

References

  1. ↑ Chance, Britton; Garfinkel, David; Higgins, Joseph; Hess, Benno; Chance, E.M. (August 1960). "Metabolic Control Mechanisms". Journal of Biological Chemistry 235 (8): 2426–2439. doi:10.1016/S0021-9258(18)64638-1. 
  2. ↑ Chance, Britton; Higgins, Joseph; Garfinkel, David (1962). Analogue and digital computer representations of biochemical processes. Federation of American Societies for Experimental Biology..: Federation Proceedings, Vol 12. No. 1-2. pp. 75. 
  3. ↑ Burns, Jim (1 March 1973). Metabolic Control Analysis. Thesis (Thesis). doi:10.5281/zenodo.7240738.
  4. ↑ Garfinkel, David (August 1968). "A machine-independent language for the simulation of complex chemical and biochemical systems". Computers and Biomedical Research 2 (1): 31–44. doi:10.1016/0010-4809(68)90006-2. PMID 5743538. 
  5. ↑ Watanabe, Leandro; Nguyen, Tramy; Zhang, Michael; Zundel, Zach; Zhang, Zhen; Madsen, Curtis; Roehner, Nicholas; Myers, Chris (19 July 2019). "iBioSim3: A Tool for Model-Based Genetic Circuit Design". ACS Synthetic Biology 8 (7): 1560–1563. doi:10.1021/acssynbio.8b00078. PMID 29944839. 
  6. ↑ Martínez-García, Esteban; Goñi-Moreno, Angel; Bartley, Bryan; McLaughlin, James; Sánchez-Sampedro, Lucas; Pascual del Pozo, Héctor; Prieto Hernández, Clara; Marletta, Ada Serena et al. (8 January 2020). "SEVA 3.0: an update of the Standard European Vector Architecture for enabling portability of genetic constructs among diverse bacterial hosts". Nucleic Acids Research 48 (D1): D1164–D1170. doi:10.1093/nar/gkz1024. PMID 31740968. 
  7. ↑ Swat, Maciej H.; Thomas, Gilberto L.; Belmonte, Julio M.; Shirinifard, Abbas; Hmeljak, Dimitrij; Glazier, James A. (2012). "Multi-Scale Modeling of Tissues Using CompuCell3D". Computational Methods in Cell Biology. 110. pp. 325–366. doi:10.1016/B978-0-12-388403-9.00013-8. ISBN 9780123884039. 
  8. ↑ Bergmann, Frank T.; Hoops, Stefan; Klahn, Brian; Kummer, Ursula; Mendes, Pedro; Pahle, Jürgen; Sahle, Sven (November 2017). "COPASI and its applications in biotechnology". Journal of Biotechnology 261: 215–220. doi:10.1016/j.jbiotec.2017.06.1200. PMID 28655634. 
  9. ↑ Yeoh, Jing Wui; Ng, Kai Boon Ivan; Teh, Ai Ying; Zhang, JingYun; Chee, Wai Kit David; Poh, Chueh Loo (19 July 2019). "An Automated Biomodel Selection System (BMSS) for Gene Circuit Designs". ACS Synthetic Biology 8 (7): 1484–1497. doi:10.1021/acssynbio.8b00523. PMID 31035759. 
  10. ↑ Nedelec, Francois; Foethke, Dietrich (2007). "Collective Langevin dynamics of flexible cytoskeletal fibers". New Journal of Physics 9 (11): 427. doi:10.1088/1367-2630/9/11/427. Bibcode: 2007NJPh....9..427N. 
  11. ↑ Somogyi, Endre T.; Bouteiller, Jean-Marie; Glazier, James A.; König, Matthias; Medley, J. Kyle; Swat, Maciej H.; Sauro, Herbert M. (15 October 2015). "libRoadRunner: a high performance SBML simulation and analysis library: Table 1.". Bioinformatics 31 (20): 3315–3321. doi:10.1093/bioinformatics/btv363. PMID 26085503. 
  12. ↑ Ghaffarizadeh, Ahmadreza; Heiland, Randy; Friedman, Samuel H.; Mumenthaler, Shannon M.; Macklin, Paul (23 February 2018). "PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems". PLOS Computational Biology 14 (2): e1005991. doi:10.1371/journal.pcbi.1005991. PMID 29474446. Bibcode: 2018PLSCB..14E5991G. 
  13. ↑ Haiman, Zachary B.; Zielinski, Daniel C.; Koike, Yuko; Yurkovich, James T.; Palsson, Bernhard O. (28 January 2021). "MASSpy: Building, simulating, and visualizing dynamic biological models in Python using mass action kinetics". PLOS Computational Biology 17 (1): e1008208. doi:10.1371/journal.pcbi.1008208. PMID 33507922. Bibcode: 2021PLSCB..17E8208H. 
  14. ↑ Foster, Charles J; Wang, Lin; Dinh, Hoang V; Suthers, Patrick F; Maranas, Costas D (February 2021). "Building kinetic models for metabolic engineering". Current Opinion in Biotechnology 67: 35–41. doi:10.1016/j.copbio.2020.11.010. PMID 33360621. 
  15. ↑ Ebrahim, Ali; Lerman, Joshua A; Palsson, Bernhard O; Hyduke, Daniel R (December 2013). "COBRApy: COnstraints-Based Reconstruction and Analysis for Python". BMC Systems Biology 7 (1): 74. doi:10.1186/1752-0509-7-74. PMID 23927696. 
  16. ↑ Stiles, Joel R.; Van Helden, Dirk; Bartol, Thomas M.; Salpeter, Edwin E.; Salpeter, Miriam M (1996). "Miniature endplate current rise times <100 us from improved dual recordings can be modeled with passive acetylcholine diffusion from a synaptic vesicle". Proc. Natl. Acad. Sci. USA 93 (12): 5747–5752. doi:10.1073/pnas.93.12.5747. PMID 8650164. 
  17. ↑ Stiles, Joel R.; Bartol, Thomas M. (2001). "Monte Carlo methods for simulating realistic synaptic microphysiology using MCell". Computational Neuroscience: Realistic Modeling for Experimentalists: 87–127. 
  18. ↑ Kerr, R; Bartol, TM; Kaminsky, B; Dittrich, M; Chang, JCJ; Baden, S; Sejnowski, TJ; Stiles, JR (2008). "Fast Monte Carlo simulation methods for biological reaction-diffusion systems in solution and on surfaces". SIAM J. Sci. Comput. 30 (6): 3126–3149. doi:10.1137/070692017. PMID 20151023. Bibcode: 2008SJSC...30.3126K. 
  19. ↑ Letort, Gaelle; Montagud, Arnau; Stoll, Gautier; Heiland, Randy; Barillot, Emmanuel; Macklin, Paul; Zinovyev, Andrei; Calzone, Laurence (1 April 2019). "PhysiBoSS: a multi-scale agent-based modelling framework integrating physical dimension and cell signalling". Bioinformatics 35 (7): 1188–1196. doi:10.1093/bioinformatics/bty766. PMID 30169736. 
  20. ↑ Ghaffarizadeh, Ahmadreza; Heiland, Randy; Friedman, Samuel H.; Mumenthaler, Shannon M.; Macklin, Paul (23 February 2018). "PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems". PLOS Computational Biology 14 (2): e1005991. doi:10.1371/journal.pcbi.1005991. PMID 29474446. Bibcode: 2018PLSCB..14E5991G. 
  21. ↑ Olivier, B. G.; Rohwer, J. M.; Hofmeyr, J.-H. S. (15 February 2005). "Modelling cellular systems with PySCeS". Bioinformatics 21 (4): 560–561. doi:10.1093/bioinformatics/bti046. PMID 15454409. 
  22. ↑ Mendoza-Cózatl, David G.; Moreno-Sánchez, Rafael (February 2006). "Control of glutathione and phytochelatin synthesis under cadmium stress. Pathway modeling for plants". Journal of Theoretical Biology 238 (4): 919–936. doi:10.1016/j.jtbi.2005.07.003. PMID 16125728. Bibcode: 2006JThBi.238..919M. 
  23. ↑ Ghaffarizadeh, Ahmadreza; Heiland, Randy; Friedman, Samuel H.; Mumenthaler, Shannon M.; Macklin, Paul (23 February 2018). "PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems". PLOS Computational Biology 14 (2): e1005991. doi:10.1371/journal.pcbi.1005991. PMID 29474446. Bibcode: 2018PLSCB..14E5991G. 
  24. ↑ Stefan, Melanie I.; Bartol, Thomas M.; Sejnowski, Terrence J.; Kennedy, Mary B. (25 September 2014). "Multi-state Modeling of Biomolecules". PLOS Computational Biology 10 (9): e1003844. doi:10.1371/journal.pcbi.1003844. PMID 25254957. Bibcode: 2014PLSCB..10E3844S. 
  25. ↑ Schöneberg, J.; Ullrich, A.; Noé, F. (2014). "Simulation tools for particle-based reaction-diffusion dynamics in continuous space". BMC Biophys. 7: 11. doi:10.1186/s13628-014-0011-5. PMID 25737778. 
  26. ↑ Panchiwala, H; Shah, S; Planatscher, H; Zakharchuk, M; König, M; Dräger, A (23 September 2021). "The Systems Biology Simulation Core Library.". Bioinformatics 38 (3): 864–865. doi:10.1093/bioinformatics/btab669. PMID 34554191. 
  27. ↑ Tangherloni, Andrea; Nobile, Marco S.; Cazzaniga, Paolo; Capitoli, Giulia; Spolaor, Simone; Rundo, Leonardo; Mauri, Giancarlo; Besozzi, Daniela (9 September 2021). "FiCoS: A fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks". PLOS Computational Biology 17 (9): e1009410. doi:10.1371/journal.pcbi.1009410. PMID 34499658. Bibcode: 2021PLSCB..17E9410T. 
  28. ↑ Hucka, M.; Finney, A.; Sauro, H. M.; Bolouri, H.; Doyle, J.; Kitano, H. (December 2001). "The Erato Systems Biology Workbench: Enabling Interaction and Exchange Between Software Tools for Computational Biology". Biocomputing 2002: 450–461. doi:10.1142/9789812799623_0042. ISBN 978-981-02-4777-5. PMID 11928498. https://resolver.caltech.edu/CaltechAUTHORS:20130108-142104885. 
  29. ↑ Kawasaki, Regiane; Baraúna, Rafael A.; Silva, Artur; Carepo, Marta S. P.; Oliveira, Rui; Marques, Rodolfo; Ramos, Rommel T. J.; Schneider, Maria P. C. (2016). "Reconstruction of the Fatty Acid Biosynthetic Pathway of Exiguobacterium antarcticum B7 Based on Genomic and Bibliomic Data". BioMed Research International 2016: 1–9. doi:10.1155/2016/7863706. PMID 27595107. 
  30. ↑ Andrews, Steven S.; Bray, Dennis (2004). "Stochastic simulation of chemical reactions with spatial resolution and single molecule detail". Physical Biology 1 (3–4): 137–151. doi:10.1088/1478-3967/1/3/001. PMID 16204833. Bibcode: 2004PhBio...1..137A. 
  31. ↑ Andrews, Steven S.; Addy, Nathan J.; Brent, Roger; Arkin, Adam P. (2010). "Detailed simulations of cell biology with Smoldyn 2.1". PLOS Comput. Biol. 6 (3): e1000705. doi:10.1371/journal.pcbi.1000705. PMID 20300644. Bibcode: 2010PLSCB...6E0705A. 
  32. ↑ Andrews, Steven S. (2017). "Smoldyn: particle-based simulation with rule-based modeling, improved molecular interaction, and a library interface". Bioinformatics 33 (5): 710–717. doi:10.1093/bioinformatics/btw700. PMID 28365760. 
  33. ↑ Singh, Dilawar; Andrews, Steven S. (2022). "Python interfaces for the Smoldyn simulator". Bioinformatics 38 (1): 291–293. doi:10.1093/bioinformatics/btab530. PMID 34293100. 
  34. ↑ Arjunan, S.N.V.; Takahashi, K. (2017). Multi-algorithm particle simulations with Spatiocyte. Methods in Molecular Biology. 1611. pp. 219–236. 
  35. ↑ Arjunan, S.N.V.; Miyauchi, A.; Iwamoto, K.; Takahashi, K. (2020). "pSpatiocyte: a high-performance simulator for intracellular reaction-diffusion systems". BMC Bioinformatics 21 (1): 33. doi:10.1186/s12859-019-3338-8. PMID 31996129. 
  36. ↑ Michalski, P.J.; Loew, L.M. (2016). "SpringSaLaD: a spatial, particle-based biochemical simulation platform with excluded volume". Biophys. J. 110 (3): 523–529. doi:10.1016/j.bpj.2015.12.026. PMID 26840718. Bibcode: 2016BpJ...110..523M. 
  37. ↑ Hepburn, Iain; Chen, Weiliang; Wils, Stefan; De Schutter, Erik (May 2012). "STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies". BMC Systems Biology 7 (1): 36. doi:10.1186/1752-0509-6-36. PMID 22574658. 
  38. ↑ Chen, Weiliang; De Schutter, Erik (February 2017). "Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers". Frontiers in Neuroinformatics 11 (1): 13. doi:10.3389/fninf.2017.00013. PMID 28239346. 
  39. ↑ Hepburn, Iain; Chen, Weiliang; De Schutter, Erik (August 2016). "Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations". The Journal of Chemical Physics 145 (5): 054118. doi:10.1063/1.4960034. PMID 27497550. Bibcode: 2016JChPh.145e4118H. 
  40. ↑ Chen, Weiliang; Carel, Tristan; Awile, Omar; Cantarutti, Nicola; Castiglioni, Giacomo; Cattabiani, Alessandro; Del Marmol, Baudouin; Hepburn, Iain et al. (October 2022). "STEPS 4.0: Fast and memory-efficient molecular simulations of neurons at the nanoscale". Frontiers in Neuroinformatics 16: 883742. doi:10.3389/fninf.2022.883742. ISSN 1662-5196. PMID 36387588. 
  41. ↑ Choi, Kiri; Medley, J. Kyle; König, Matthias; Stocking, Kaylene; Smith, Lucian; Gu, Stanley; Sauro, Herbert M. (September 2018). "Tellurium: An extensible python-based modeling environment for systems and synthetic biology". Biosystems 171: 74–79. doi:10.1016/j.biosystems.2018.07.006. PMID 30053414. 
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  47. ↑ Schöneberg, J; Ullrich, A; Noé, F (2014). "Simulation tools for particle-based reaction-diffusion dynamics in continuous space". BMC Biophys 7 (1): 11. doi:10.1186/s13628-014-0011-5. PMID 25737778. 
  48. ↑ Andrews, Steven S. (2018). "Particle-Based Stochastic Simulators". Encyclopedia of Computational Neuroscience. 10. pp. 978–1. doi:10.1007/978-1-4614-7320-6_191-2. ISBN 978-1-4614-7320-6. 
  49. ↑ Stiles, JR; Bartol, TM (2001). Chapter 4, Monte Carlo methods for simulating realistic synaptic microphysiology using MCell. In: Computational neuroscience, realistic modeling for experimentalists, De Schutter, E (ed.). Boca Raton: CRC Press. pp. 87–127. 
  50. ↑ Stefan, MI; Bartol, TM; Sejnowski, TJ; Kennedy, MB (2014). "Multi-state modeling of biomolecules". PLOS Comput Biol 10 (9): e1003844. doi:10.1371/journal.pcbi.1003844. PMID 25254957. Bibcode: 2014PLSCB..10E3844S. 
  51. ↑ Stiles, JR; Van Helden, D; Bartol, TM; Salpeter, EE; Salpeter, MM (1996). "Miniature endplate current rise times less than 100 microseconds from improved dual recordings can be modeled with passive acetylcholine diffusion from a synaptic vesicle". Proceedings of the National Academy of Sciences, USA 93 (12): 5747–5752. doi:10.1073/pnas.93.12.5747. PMID 8650164. Bibcode: 1996PNAS...93.5747S. 
  52. ↑ Andrews, SS (2017). "Smoldyn: particle-based simulation with rule-based modeling, improved molecular interaction and a library interface". Bioinformatics 33 (5): 710–717. doi:10.1093/bioinformatics/btw700. PMID 28365760. 
  53. ↑ Andrews, SS; Addy, NJ; Brent, R; Arkin, AP (2010). "Detailed simulations of cell biology with Smoldyn 2.1". PLOS Comput Biol 6 (3): e1000705. doi:10.1371/journal.pcbi.1000705. PMID 20300644. Bibcode: 2010PLSCB...6E0705A. 
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