Abstract
Many biological molecules exist in multiple variants, such as proteins with different posttranslational modifications, DNAs with different sequences, and phospholipids with different chain lengths. Representing these variants as distinct species, as most biochemical simulators do, leads to the problem that the number of species, and chemical reactions that interconvert them, typically increase combinatorially with the number of ways that the molecules can vary. This can be alleviated by “rule-based modeling methods,” in which software generates the chemical reaction network from relatively simple “rules.” This chapter presents a new approach to rule-based modeling. It is based on wildcards that match to species names, much as wildcards can match to file names in computer operating systems. It is much simpler to use than the formal rule-based modeling approaches developed previously but can lead to unintended consequences if not used carefully. This chapter demonstrates rule-based modeling with wildcards through examples for signaling systems, protein complexation, polymerization, nucleic acid sequence copying and mutation, the “SMILES” chemical notation, and others. The method is implemented in Smoldyn, a spatial and stochastic biochemical simulator, for both generate-first and on-the-fly expansion, meaning whether the reaction network is generated before or during the simulation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boyle R (1661) The Sceptical Chymist. F. Cadwell, London
Waage P, Guldberg CM (1864) Studier over affiniteten. Forhandlinger: Videnskabs-Selskabet i Christiania, p 35–40
Michaelis L, Menten ML (1913) Die kinetik der invertinwirkung. Biochem Z 49:333–369
Gibbs JW (1875–1878) On the equilibrium of heterogeneous substances. In: Transactions of the Connecticut Academy, vol 3. The Academy, New Haven, pp 108–248, 343–524
Jaynes ET (1992) The Gibbs paradox. In: Smith CR, Erickson GJ, Neudorfer PO (eds) Maximum Entropy and Bayesian Methods. Kluwer Academic Publishers, Dordrecht, pp 1–22
Alves R, Antunes F, Salvador A (2006) Tools for kinetic modeling of biochemical networks. Nat Biotechnol 24:667–672
Andrews SS, Dinh T, Arkin AP (2009) Stochastic models of biological processes. In: Meyers RA (ed) Encyclopedia of complexity and system science, vol 9. Springer, New York, pp 8730–8749
Bray D, Lay S (1997) Computer-based analysis of the binding steps in protein complex formation. Proc Natl Acad Sci U S A 94:13493–13498
Goldman J, Andrews SS, Bray D (2004) Size and composition of membrane protein clusters predicted by Monte Carlo analysis. Eur Biophys J 33:506–512
Sneddon MW, Faeder JR, Emonet T (2011) Efficient modeling, simulation and coarse-graining of biological complexity with NFsim. Nat Methods 8:177–183
Gruenert G, Ibrahim B, Lenser T, Lohel M, Hinze T, Dittrich P (2010) Rule-based spatial modeling with diffusing, geometrically constrained molecules. BMC Bioinformatics 11:307
Schöneberg J, Noé F (2013) ReaDDy – a software for particle-based reaction-diffusion dynamics in crowded cellular environments. PLoS One 8:e74261
Morton-Firth CJ, Bray D (1998) Predicting temporal fluctuations in an intracellular signalling pathway. J Theor Biol 192:117–128
Bittig AT, Haack F, Maus C, Uhrmacher AM (2011) Adapting rule-based model descriptions for simulating in continuous and hybrid space. In: Proceedings of the 9th International Conference on Computational Methods in Systems Biology, ACM, pp 161–70
Stefan MI, Bartol TM, Sejnowski TJ, Kennedy MB (2014) Multi-state modeling of biomolecules. PLoS Comp Biol 10:e1003844
Andrews SS, Addy NJ, Brent R, Arkin AP (2010) Detailed simulation of cell biology with Smoldyn 2.1. PLoS Comp Biol 6:e1000705
Tolle DP, Le Novère N (2010) Meredys, a multi-compartment reaction-diffusion simulator using multistate realistic molecular complexes. BMC Systems Biol 4:24
Hlavacek WS, Faeder JR, Blinov ML, Posner RG, Hucka M, Fontana W (2006) Rules for modeling signal-transduction systems. Sci STKE 2006:re6
Blinov ML, Faeder JR, Goldstein B, Hlavacek WS (2004) BioNetGen: software for rule based modeling of signal transduction based on the interactions of molecular domains. Bioinformatics 20:3289–3291
Lok L, Brent R (2005) Automatic generation of cellular reaction networks with Molecularizer 1.0. Nat Biotech 23:131–136
Danos V, Feret J, Fontana W, Harmer R, Hayman J, Krivine J, Thompson-Walsh C, Winskel G (2012) Graphs, rewriting, and pathway reconstruction for rule-based models. In: LIPIcs-Leibniz International Proceedings in Informatics, Schloss Dagstuhl-Leibniz-Zentrum fuor Informatik, vol 18. Dagstuhl Publishing, Germany
Andrews SS (2017) Smoldyn: particle-based simulation with rule-based modeling, improved molecular interaction and a library interface. Bioinformatics 33:710–717
Andrews SS, Bray D (2004) Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys Biol 1:137–151
Andrews SS (2009) Accurate particle-based simulation of adsorption, desorption, and partial transmission. Phys Biol 6:46015
Andrews SS (2018) Particle-based stochastic simulators. In: Jaeger D, Jung R (eds) Encyclopedia of computational neuroscience. Springer, New York
Faeder JR, Blinov ML, Hlavacek WS (2009) Rule-based modeling of biochemical systems with BioNetGen. Methods Mol Biol 500:113–167
Danos V, Laneve C (2004) Formal molecular biology. Theor Comput Sci 325:69–110
Andrews SS (2012) Spatial and stochastic cellular modeling with the Smoldyn simulator. Methods Mol Biol 804:519–542
Bardwell L (2005) A walk-through of the yeast mating pheromone response pathway. Peptides 26:339–350
Blinov ML, Faeder JR, Yang J, Goldstein B, Hlavacek WS (2005) ‘On-the-fly’ or ‘generate-first’ modeling? Nat Biotechnol 23:1344–1345
Suderman R, Deeds EJ (2013) Machines vs. ensembles: effective MAPK signaling through heterogeneous sets of protein complexes. PLoS Comp Biol 9:e1003278
Dix JA, Verkman AS (2008) Crowding effects on diffusion in solutions and cells. Annu Rev Biophys 37:247–263
Robinson M, Andrews SS, Erban R (2015) Multiscale reaction-diffusion simulations with Smoldyn. Bioinformatics 31:2406–2408
Alberts B, Johnson A, Lewis J, Raff M, Robers K, Walter P (2008) Molecular biology of the cell. Garland Science, New York
Sutherland EW, Oye I, Butcher RW (1964) The action of epinephrine and the role of the adenyl cyclase system in hormone action. Recent Prog Horm Res 21:623–646
Claeys Bouuaert C, Lipkow K, Andrews SS, Liu D, Chalmers R (2013) The autoregulation of a eukaryotic DNA transposon. elife 2:e00668
Marianayagam NJ, Sunde M, Matthews JM (2004) The power of two: protein dimerization in biology. Trends Biochem Sci 29:618–625
Hubbard SR, Till JH (2000) Protein tyrosine kinase structure and function. Annu Rev Biochem 69:373–398
Lutkenhaus J (2007) Assembly and dynamics of the bacterial MinCDE system and spatial regulation of the Z ring. Annu Rev Biochem 76:539–562
Loose M, Kruse K, Schwille P (2011) Protein self-organization: lessons from the Min system. Annu Rev Biophys 40:315–336
Howard M, Kruse K (2005) Cellular organization by self-organization: mechanisms and models for Min protein dynamics. J Cell Biol 168:533–536
Kruse K, Howard M, Margolin W (2007) An experimentalist’s guide to computational modelling of the Min system. Mol Microbiol 63:1279–1284
Cytrynbaum E, Marshall BDL (2007) A multi-stranded polymer model explains MinDE dynamics in E. coli cell division. Biophys J 93:1134–1150
Zhang Y, Rowland S, King G, Braswell E, Rothfield L (1998) The relationship between hetero-oligomer formation and function of the topological specificity domain of the Escherichia coli MinE protein. Mol Microbiol 30:265–273
Hu Z, Lutkenhaus J (2003) A conserved sequence at the C-terminus of MinD is required for binding to the membrane and targeting MinC to the septum. Mol Microbiol 47:345–355
Hu Z, Saez C, Lutkenhaus J (2003) Recruitment of MinC, an inhibitor of Z-ring formation, to the membrane in Escherichia coli: role of MinD and MinE. J Bact 185:196–203
Andrews SS, Moghaddam A, Groves JT (2006) Quantification of reaction rates in the E. coli Min system. American Chemical Society National Meeting, San Francisco, CA
Milo R, Jorgensen P, Moran U, Weber G, Springer M (2010) BioNumbers – the database of key numbers in molecular and cell biology. Nucleic Acids Res 38:D750–DD53
Neidhardt FC, Umbarger HE (1996) In: Neidhardt FC (ed) Chemical composition of Escherichia coli in Escherichia coli and Salmonella. ASM Press, Washington, DC
Shih Y-L, Fu X, King GF, Le T, Rothfield L (2002) Division site placement in E. coli: mutations that prevent formation of the MinE ring lead to loss of the normal midcell arrest of growth of polar MinD membrane domains. EMBO J 21:3347–3357
Yaginuma H, Kawai S, Tabata KV, Tomiyama K, Kakizuka A, Komatsuzaki T, Noji H, Imamura H (2014) Diversity in ATP concentrations in a single bacterial cell population revealed by quantitative single-cell imaging. Sci Rep 4:6522
Tran QH, Unden G (1998) Changes in the proton potential and the cellular energetics of Escherichia coli during growth by aerobic and anaerobic respiration or by fermentation. Eur J Biochem 251:538–543
de Boer PAJ, Crossley RE, Rothfield LI (1989) A division inhibitor and a topological specificity factor coded for by the minicell locus determine proper placement of the division septum in E. coli. Cell 56:641–649
Huang KC, Meir Y, Wingreen NS (2003) Dynamic structures in Escherichia coli: spontaneous formation of MinE rings and MinD polar zones. Proc Natl Acad Sci U S A 100:12724–12728
de Boer PAJ, Crossley RE, Hand AR, Rothfield LI (1991) The MinD protein is a membrane ATPase required for the correct placement of the Escherichia coli division site. EMBO J 10:4371–4380
Lackner LL, Raskin DM, de Boer PAJ (2003) ATP-dependent interactions between Escherichia coli Min proteins and the phospholipid membrane in vitro. J Bacteriol 185:735–749
Hu Z, Lutkenhaus J (2001) Topological regulation of cell division in E. coli. Spatiotemporal oscillation of MinD requires stimulation of its ATPase by MinE and phospholipid. Mol Cell 7:1337–1343
Alberts B, Bray D, Lewis J, Raff M, Roberts K, Watson JD (1994) Molecular biology of the cell. Garland Publishing, New York
Ross CA, Poirier MA (2005) What is the role of protein aggregation in neurodegeneration? Nat Rev Mol Cell Biol 6:891–898
Andrews SS (2014) Physical models and computational methods for modeling cytoskeletal and DNA filaments. Phys Biol 11:011001
Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, Ithaca, NY
Doi M, Edwards SF (1986) The theory of polymer dynamics. Oxford University Press, Oxford
Berg OG (1978) A model for the statistical fluctuations of protein numbers in a microbial population. J Theor Biol 71:587–603
Weininger D (1988) SMILES, a chemical language and information system. 1. Introduction to methodology and encoding rules. J Chem Inf Comput Sci 28:31–36
Emiola A, Andrews SS, Heller C, George J (2016) Crosstalk between the lipopolysaccharide and phospholipid pathways during outer membrane biogenesis in Escherichia coli. Proc Natl Acad Sci U S A 113:3108–3113
Acknowledgments
I thank Ronnie Chalmers, Akintunde Emiola, Jim Faeder, and Karen Lipkow for useful discussions. Much of this work was carried out during a visit to the Isaac Newton Institute for Mathematical Sciences, for which I thank Radek Erban, David Holcman, Sam Isaacson, and Konstantinos Zygalakis, who were the program organizers, and the institute staff. I also thank Roger Brent, Erick Matsen, and Harlan Robbins for providing space for me at the FHCRC, where the work was completed. This work was supported by a Simons Foundation grant awarded to SSA and by EPSRC grant EP/K032208/1 awarded to the Isaac Newton Institute.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
1 Electronic Supplementary Material
Supplementary File 1
(DOCX 752 kb)
Rights and permissions
Copyright information
© 2019 Springer Science+Business Media, LLC, part of Springer Nature
About this protocol
Cite this protocol
Andrews, S.S. (2019). Rule-Based Modeling Using Wildcards in the Smoldyn Simulator. In: Hlavacek, W. (eds) Modeling Biomolecular Site Dynamics. Methods in Molecular Biology, vol 1945. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-9102-0_8
Download citation
DOI: https://doi.org/10.1007/978-1-4939-9102-0_8
Published:
Publisher Name: Humana Press, New York, NY
Print ISBN: 978-1-4939-9100-6
Online ISBN: 978-1-4939-9102-0
eBook Packages: Springer Protocols