title: Network class superposition analyses.
abstract: Networks are often used to understand a whole system by modeling the interactions among its pieces. Examples include biomolecules in a cell interacting to provide some primary function, or species in an environment forming a stable community. However, these interactions are often unknown; instead, the pieces' dynamic states are known, and network structure must be inferred. Because observed function may be explained by many different networks (e.g., ≈ 10(30) for the yeast cell cycle process), considering dynamics beyond this primary function means picking a single network or suitable sample: measuring over all networks exhibiting the primary function is computationally infeasible. We circumvent that obstacle by calculating the network class ensemble. We represent the ensemble by a stochastic matrix T, which is a transition-by-transition superposition of the system dynamics for each member of the class. We present concrete results for T derived from boolean time series dynamics on networks obeying the Strong Inhibition rule, by applying T to several traditional questions about network dynamics. We show that the distribution of the number of point attractors can be accurately estimated with T. We show how to generate Derrida plots based on T. We show that T-based Shannon entropy outperforms other methods at selecting experiments to further narrow the network structure. We also outline an experimental test of predictions based on T. We motivate all of these results in terms of a popular molecular biology boolean network model for the yeast cell cycle, but the methods and analyses we introduce are general. We conclude with open questions for T, for example, application to other models, computational considerations when scaling up to larger systems, and other potential analyses.
authors.affiliation: Emerging Pathogens Institute, University of Florida, Gainesville, Florida, United States of America. cap10@ufl.edu
authors.forename: Carl A B
authors.initials: CA
authors.lastname: Pearson
authors.forename: Chen
authors.initials: C
authors.lastname: Zeng
authors.forename: Rahul
authors.initials: R
authors.lastname: Simha
mesh_terms: D000465:Algorithms; D002453:Cell Cycle / Q000502:physiology; D003198:Computer Simulation; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D012372:ROC Curve; D015003:Yeasts / Q000235:genetics / Q000378:metabolism
references.citation: J Theor Biol. 1973 Apr;39(1):103-29
references.pmid: 4741704
references.citation: Nature. 2000 Jul 27;406(6794):378-82
references.pmid: 10935628
references.citation: Proc Biol Sci. 2008 Jan 7;275(1630):91-100
references.pmid: 17971325
references.citation: Genome Res. 2003 Nov;13(11):2498-504
references.pmid: 14597658
references.citation: Science. 1999 Oct 15;286(5439):509-12
references.pmid: 10521342
references.citation: PLoS One. 2012;7(7):e40330
references.pmid: 22815739
references.citation: Trends Ecol Evol. 2006 Jul;21(7):394-9
references.pmid: 16815438
references.citation: PLoS Comput Biol. 2009 Jul;5(7):e1000442
references.pmid: 19629157
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 May;75(5 Pt 1):051907
references.pmid: 17677098
references.citation: Science. 2002 Oct 25;298(5594):824-7
references.pmid: 12399590
references.citation: Annu Rev Biophys. 2008;37:289-316
references.pmid: 18573083
references.citation: Science. 2002 Mar 1;295(5560):1662-4
references.pmid: 11872829
references.citation: Proc Natl Acad Sci U S A. 2010 Jun 8;107(23):10478-83
references.pmid: 20498084
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Nov;72(5 Pt 2):055101
references.pmid: 16383673
references.citation: Nature. 1999 Jan 14;397(6715):168-71
references.pmid: 9923680
references.citation: J Theor Biol. 2003 Jul 7;223(1):1-18
references.pmid: 12782112
references.citation: Phys Rev Lett. 2003 Mar 7;90(9):098701
references.pmid: 12689263
references.citation: Proc Natl Acad Sci U S A. 1996 Jan 9;93(1):397-401
references.pmid: 8552647
references.citation: Trends Ecol Evol. 2005 Jun;20(6):345-53
references.pmid: 16701391
references.citation: Proc Natl Acad Sci U S A. 2004 Dec 7;101(49):17102-7
references.pmid: 15572453
references.citation: J Theor Biol. 2005 Aug 7;235(3):431-49
references.pmid: 15882705
references.citation: Annu Rev Cell Dev Biol. 2010;26:721-44
references.pmid: 20604711
references.citation: Phys Rev Lett. 2000 Dec 18;85(25):5468-71
references.pmid: 11136023
references.citation: Pac Symp Biocomput. 2000;:305-16
references.pmid: 10902179
references.citation: J R Soc Interface. 2008 Aug 6;5 Suppl 1:S85-94
references.pmid: 18508746
references.citation: Annu Rev Genomics Hum Genet. 2001;2:343-72
references.pmid: 11701654
references.citation: Radiology. 1973 Nov;109(2):297-303
references.pmid: 4742316
references.citation: Proc Natl Acad Sci U S A. 2003 Dec 9;100(25):14796-9
references.pmid: 14657375
references.citation: Proc Natl Acad Sci U S A. 2004 Apr 6;101(14):4781-6
references.pmid: 15037758
references.citation: J Theor Biol. 1969 Mar;22(3):437-67
references.pmid: 5803332