Nanonetwork is defined as a mathematical model of nanosize objects with biological, physical and chemical attributes, which are interconnected within certain dynamical process. To demonstrate the potentials of this modeling approach for quantitative study of complexity at nanoscale, in this survey, we consider three kinds of nanonetworks: Genes of a yeast are connected by weighted links corresponding to their coexpression along the cell cycle; Gold nanoparticles, arranged on a substrate, are linked via quantum tunneling junctions which enable single-electron conduction; A network of similar profiles of force–distance curves consists of sequences of states of a molecular complex from HIV–1 virus observed in repeated single-molecule force spectroscopy experiments. The graph-theory analysis of these systems reveals their organizational principles, quantifies the relation between the function of nanostructured materials and their architecture, and helps understand the character of fluctuations at nanoscale.
@article{bwmeta1.element.doi-10_2478_nsmmt-2013-0003,
author = {Jelena \v Zivkovic and Bosiljka Tadic},
title = {Nanonetworks: The graph theory framework for modeling nanoscale systems},
journal = {Nanoscale Systems: Mathematical Modeling, Theory and Applications},
volume = {2},
year = {2013},
pages = {30-48},
zbl = {1272.05211},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_nsmmt-2013-0003}
}
Jelena Živkovic; Bosiljka Tadic. Nanonetworks: The graph theory framework for modeling nanoscale systems. Nanoscale Systems: Mathematical Modeling, Theory and Applications, Tome 2 (2013) pp. 30-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_nsmmt-2013-0003/
A. K. Boal, F. Ilhan, J. E. DeRouchey, T. Thurn-Albrecht, T. P. Russell, and V. M. Rotello. Self-assembly of nanoparticles into structured spherical and network aggregates. Nature, 404, 746–748 (2000).
C. A. Mirkin. Programming the assembly of two- and three-dimensional architectures with DNA and nanoscale inorganic building blocks. Inorg. Chem., 39, 2258–2272 (2000).
P. Moriarty. Nanostructured materials. Reports on Progress in Physics, 64, 297–381 (2001).
P. Scharff and E. Buzaneva, editors. Frontiers of Multifunctional Integrated Nanosystems. Springer, Berlin (2004).
Y. Yin and A. P. Alivisatos. Colloidal nanocrystal synthesis and the organic-inorganic interface. Nature, 437, 664–670 (2004).
M.P. Pileni. Slef-assembly of inorganic nanocrystals: Fabrication and collective intrinsic properties. Acc. Chem. Res., 40, 685–693 (2007). [Crossref]
M. O. Blunt, C. P. Martin, M. Ahola-Tuomi, E. Pauliac-Vaujour, P. Sharp, P. Nativo, M. Brust, and P. Moriarty. Coerced mechanical coarsening of nanoparticle assemblies. Nature Nanotechnology, 2, 167–170 (2007). [PubMed][Crossref]
B. Tadic. From microscopic rules to emergent cooperativity in large-scale patterns, in "Systems self-assembly: Multidisciplinary snapshots", N. Krasnogor, S. Gustafson, D.A. Pelta and J.L. Verdegay, editors. Volume 5, Studies in multidisciplinarity, Elsevier, Amsterdam, pp. 259-278 (2008).
E. Barkai, F.L.H. Brown, M. Orrit, and H. Yang, editors. Theory and Evaluation of Single-Molecule Signals. World Scientific, Singapore (2008).
I. Kotsireas, R.V.N. Melnik, and B. West, editors. Advances in Mathematical and Computational Methods: Addressing Modern Challenges of Science, Technology and Society. American Institute of Physics Vol. 1368 (2011).
P. R. Villas Boas, F. A. Rodrigues, G. Travieso, and L. da Fontoura Costa. Chain motifs: The tails and handles of complex networks. Physical Review E, 77, 026106 (2008).
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D-U. Hwang. Complex networks: Structure and dynamics. Physics Reports, 424, 175–308 (2006).
B. Bollobás. Modern Graph Theory. Springer, New York (1998). | Zbl 0902.05016
R.K. Ahuja, T.L. Magnanti, and J.B. Orlin. Network Flows: Theory, Algorithms and Applications. Prentice-Hall International, Ltd., London, UK (1993). | Zbl 1201.90001
B.H. Junker and F. Schreiber, editors. Analysis of biological networks. A Wiley Interscience Publication, Hoboken, New Jersey (2008).
V. Janjic and N. Pržulj. The core diseasome. Molecular BioSystems, 8, 2614–2625 (2012). [Crossref][PubMed]
R.N. Mantegna and E.H. Stanley. An introduction to econophysics: correlations and complexity in finance. Cambridge University Press, Cambridge, UK (2000). | Zbl 1138.91300
P.J. Carrington, J. Scott, and S. Wasserman, editors. Models and methods in social network analysis. Cambridge University Press, Cambridge, UK (2005).
J. Giles. Computational social science: Making the links. Nature, 488, 448–450 (2012).
M. Mitrovic, G. Paltoglou, and B. Tadic. Quantitative analysis of bloggers’ collective behavior powered by emotions. Journal of Statistical Mechanics: Theory and Experiment, P02005 (2011). DOI:10.1088/1742-5468/2011/02/P02005 [Crossref]
J. Živkovic, M. Mitrovic, L. Janssen, H. A. Heus, B. Tadic, and S. Speller. Network theory approach for data evaluation in the dynamic force spectroscopy of biomolecular interactions. Europhysics Letters, 89, 68004 (2010).
D.J. Lockhart and E.A. Winzler. Genomics, gene expression and DNA arrays. Nature, 405, 827–836 (2000).
M. Lynch. The evolution of genetic networks by non-adaptive processes. Nature Reviews Genetics, 8, 803–813 (2007). [PubMed][Crossref]
S.J. Dixon, M. Costanzo, A. Baryshnikova, B. Andrews, and Ch. Boone. Systematic mapping of genetic interaction networks. Annual Review of Genetics, 43, 601–625 (2009). [PubMed][Crossref]
D. Stokic, R. Hanel, and S. Thurner. A fast and efficient gene-network reconstruction method from multiple overexpression experiments. arXiv:0806.3048 (2008).
A. Madi, Y. Friedman, D. Roth, T. Regev, S. Bransburg-Zabary, and E.B. Jacob. Genome holography: Deciphering function-form motifs from gene expression data. PLoS ONE, 3, e2708 (2008).
J. Živkovic, B. Tadic, N. Wick, and S. Thurner. Statistical indicators of collective behavior and functional clusters in gene networks of yeast. European Physical Journal B, 50, 255–258 (2006). [Crossref]
J. Živkovic, M. Mitrovic, and B. Tadic. Correlation patterns in gene expressions along the cell cycle of yeast. In S. Fortunato, G. Mangioni, R. Menezes, and V. Nicosia, editors. Complex Networks, volume 207 of Studies in Computational Intelligence, Springer, Berlin / Heidelberg, pp. 23–34 (2009). DOI:10.1007/978-3-642-01206-8−3. [Crossref]
M. Šuvakov and B. Tadic. Modeling collective charge transport in nanoparticle assemblies. Journal of Physics: Condensed Matter, 22, 163201, (2010). DOI:10.1088/0953-8984/22/16/163201. [Crossref]
N. Goubet, H. Portales, C. Yan, I. Arfaoui, P-A. Albouy, A. Mermet, and M-P. Pileni. Simultaneous growth of gold colloidal crystals. JACS, 134, 3714–3719 (2012).
K. Lee, V.P. Drachev, and J. Irudayaraj. DNA–gold nanoparticle reversible networks grown on cell surface marker sites: Application in diagnostics. ACS NANO, 5, 2109–2117 (2011). [PubMed][Crossref]
L. Hu, H. Wu, S.S. Hong, L. Cui, J.R. McDonough, S. Bohy, and Y. Cui. Si nanoparticle-decorated Si nanowire networks for Li-ion batery anodes. Chem. Comm., 47, 367-369 (2011).
G. Trefalt, B. Tadic, and M. Kosec. Formation of colloidal assemblies in suspensions for Pb(Mg1/3Nb2/3)O3 synthesis: Monte carlo simulation study. Soft Matter, 7, 5566–5577 (2011).
C. P. Martin, M. O. Blunt, and P. Moriarty. Nanoparticle networks on silicon: Self-organized or disorganized? Nano Letters, 4, 2389–2392 (2004). [Crossref]
M. O. Blunt, M. Šuvakov, F. Pulizzi, C. P. Martin, E. Pauliac-Vaujour, A. Stannard, A.W. Rushforth, B. Tadic, and P. Moriarty. Charge transport in cellular nanoparticle networks: meandering through nanoscale mazes. Nano Letters, 7, 855–860 (2007). [Crossref][PubMed]
M. Blunt, A. Stannard, E. Pauliac-Vaujour, C. Martin, I. Vancea, M. Šuvakov, U. Thiele, B. Tadic, and P. Moriarty. Pattrens and pathways in nanoparticle self-organization, in book "Nanoscience and Nanotechnology, Part I: Physcs and Chemistry of Nanomaterials" , A.V. Narlikar and Y.Y.Fu, editors. Oxford University Press, Oxford, UK pp. 214–248 (2008).
T. Narumi, M. Suzuki, Y. Hidaka, and S. Kai. Size dependence of current-voltage properties in Coulomb blockade networks. Journal of the Physical Soc. Japan, 80, 114704 (2011).
D. Joung, L. Zhai, and S.I. Khondaker. Coulomb blockade and hopping conduction in graphene quantum dots array. Physical Review B, 83, 115323 (2011).
A.R. Botello-Méndez, E. Cruz-Silva, J.M. Romo-Herrera, F. López-Urıas, M. Terrones, B. G. Sumpter et al. Quantum transport in graphene nanonetworks. Nano Letters, 11, 3058–3064 (2011). [Crossref]
J. Park, S. Wang, M. Li, C. Ahn, J. K. Hyun, D. S. Kim, et al. Three-dimensional nanonetworks for giant stretchability in dielectrics and conductors. Nature Communications, 3, 916 (2012). DOI:10.1038/ncomms1929 [Crossref][PubMed]
W. C. T. Lee, C. E. Kendrick, R. P. Millane, Z. Liu, S. P. Ringer, K. Washburn et al. Porous ZnO nanonetworks grown by molecular beam epitaxy, Journal of Physics D-Applied Physics, 45, 135301 (2012).
M. Gregori, I. Llatser, A. Cabellos-Aparicio, and E. Alarcon. Physical channel characterization for medium-range nanonetworks using flagellated bacteria Computer Networks, 55, 779–791 (2011). | Zbl 1211.92003
J.M. Bower and H. Bolouri, editors. Computational Modeling of Genetic and Biochemical Networks. A Bradford Book, The Massachusetts Institute of Technology Press, Cambridge, Massachusetts (2001).
I. F. Akyldiz, F. Brunetti, and C. Blázquez. Nanonetworks: A new communication paradigm Computer Networks 52, 2260–2279 (2008).
B. Atakan, S. Galmés, and O. B. Akan. Nanoscale Communication with Molecular Arrays in Nanonetworks, IEEE Transactions on Nanobioscience, 11, 149–160 (2012). [Crossref]
T. Nakano, Biologically Inspired Network Systems: A Review and Future Prospects, Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on, 41, 630–643 (2011).
S. N. Dorogovtsev and J. F. F. Mendes. Evolution of Networks. Oxford University Press, Oxford, UK (2003). | Zbl 1109.68537
S. N. Dorogovtsev. Lectures on Complex Networks. Oxford University Press, Inc., New York, USA (2010). | Zbl 1200.94003
M. Mitrovic and B. Tadic. Spectral and dynamical properties in classes of sparse networks with mesoscopic inhomogeneities. Physical Review E, 80, 026123 (2009). | Zbl 1188.68215
E. Estrada. Application of a novel graph-theoretic folding degree index to the study of steroid–DB3 antibody binding affinity. Computational Biology and Chemistry, 27, 305–313 (2003). [Crossref]
Zh. Du. An edge grafting theorem on the Estrada index of graphs and its applications. Discrete Appl. Math., 161, 134–139 (2013). | Zbl 1254.05100
Y. Shang. Perturbation results for the Estrada index in weighted networks. Journal of Physics A: Mathematical and Theoretical, 44, 075003 (2011). | Zbl 1228.05264
S. Fortunato. Community detection in graphs. Physics Reports, 486, 75–174 (2010).
V.D. Blondel, J.-L. Guillaume, R. Lambiotte, and E. Lefebvre. Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008, P10008 (2008).
http://vlado.fmf.uni-lj.si/pub/networks/pajek/ [PubMed]
http://www.cytoscape.org/
https://gephi.org/
N.J. Krogan, G. Cagney, H. Yu, G. Zhong, X. Guo, A. Ignatchenko, J. Li, Sh. Pu, N. Datta, et al. Global landscape of protein complexes in the yeast Saccharomyces cerevisiae. Nature, 440, 637–643 (2006).
V. Memiševic and N. Pržulj. C-GRAAL: Common-neighbors-based global graph alignment of biological networks. Integrative Biology, 4, 734–743 (2012). DOI:10.1039/c2ib00140c. [PubMed][Crossref]
Th.J. Perkins, J. Jaeger, J. Reinitz, and L. Glass. Reverse engineering the gap gene network of drosophila melanogaster. PLoS Comput. Biol., 2, e51 (2006). [Crossref]
T.I. Lee, N.J. Rinaldi, F. Robert, D.T. Odom, Z. Bar-Joseph, G.K. Gerber, et al. Transcriptional regulatory networks in saccharomyces cerevisiae. Science, 298, 799-804 (2002).
S. Balaji, M. M. Babu, L. M. Iyer, N.M. Luscombe, and L. Aravind. Comprehensive analysis of combinatorial regulation using the transcriptional regulatory network of yeast. J. Mol. Biol., 360, 213–227 (2006).
J. Wang, Ch. Lia, E. Wang, and X. Wang. Uncovering the rules for protein-protein interactions from yeast genomic data. PNAS, 106, 3752–3757 (2009).
R.J. Cho, M.J. Campbell, E.A. Winzeler, L. Steinmetz, A. Conway, L. Wodicka, et al. A genome-wide transcriptional analysis of the mitotic cell cycle. Molecular Cell, 2, 65–73 (1998). [PubMed][Crossref]
B. Lewin. Genes VIII. Pearson Prentis Hall, London, UK (2004).
Ch.T. Liu, S. Yuan, and K.-C. Li. Patterns of co-expression for protein complexes by size in Saccharomyces cerevisiae. Nucleic Acids Research, 37, 526–532 (2009).
M. Abel, K. Ahnert, J. Kurths, and S. Mandelj. Additive nonparametric reconstruction of dynamical systems from time series. Physical Review E, 71, 015203 (2005).
I. Baruchi and E. Ben-Jacob. Functional holography of recorded neuronal networks activity. Neuroinformatics, 2, 333–351 (2004). [PubMed][Crossref]
B. Tadic and M. Mitrovic. Jamming and correlation patterns in traffic of information on sparse modular networks. The European Physical Journal B - Condensed Matter and Complex Systems, 71, 631–640 (2009). DOI:10.1140/epjb/e2009-00190-7. [Crossref] | Zbl 1188.68215
MIPS Saccharomyces cerevisiae genome database. http://mips.helmholtz-muenchen.de/proj/yeast/ info/guide/cygd_index.html
S.Y. Park, A.K.R. Lytton-Jean, B. Lee, S. Weigand, G.C. Schatz, and C.A. Mirkin. DNA-programable nanoparticle crystallyzation. Nature, 451, 553–556 (2008).
D. Nykypanchuk, M.M. Maye, D. van der Lelie, and O. Gang. DNA-guided crystallization of colloidal nanoparticles. Nature, 451, 549–552 (2008).
B. Tadic, K. Malarz, and K. Kulakowski. Magnetization reversal in spin patterns with complex geometry. Physical Review Letters, 94, 137204 (2005).
B. Tadic, G.J. Rodgers, and S. Thurner. Transport on complex networks: Flow, jamming and optimization. International Journal of Bifurcation and Chaos, 17, 2363–2385 (2007). [Crossref] | Zbl 1163.90375
A. Zabet-Khosousi and A.A. Dhirani. Charge transport in nanoparticle assemblies. Chem. Rev., 108, 4072–124 (2008).
K.P. Loh, Q. Bao, G. Eda, and M. Chhowalla. Graphene oxide as chemically tunnable platform for optical applications. Nature Chemistry, 2, 1015–1024 (2010). [Crossref]
M. Šuvakov and B. Tadic. Collective charge fluctuations in single-electron processes on nanonetworks. Journal of Statistical Mechanics: Theory and Experiment, P02015-1-P02015-15 (2009). DOI:10.1088/1742- 5468/2009/02/P02015 [Crossref]
E. Zaccarelli. Colloidal gells: equilibrium and nonequilibrium routes. Journal of Physics: Condensed Matter, 32, 323101 (2007). [Crossref]
M. Šuvakov and B. Tadic. Topology of cell-aggregated planar graphs. In V. Alexandrov, G. van Albada, P. Sloot, and J. Dongarra, editors, Computational Science ICCS 2006, volume 3993 of Lecture Notes in Computer Science, Springer Berlin / Heidelberg, pp. 1098–1105 (2006). | Zbl 1157.05332
M. Šuvakov and B. Tadic. Simulation of the electron tunneling paths in networks of nano-particle films. In Y. Shi, G. van Albada, J. Dongarra, and P. Sloot, editors, Computational Science ICCS 2007, volume 4488 of Lecture Notes in Computer Science, Springer Berlin / Heidelberg, pp. 641–648 (2007).
A. A. Middleton and N. S. Wingreen. Collective transport in arrays of small metallic dots. Physical Review Letters, 71, 3198–3201 (1993).
C. I. Duruöz, R. M. Clarke, C. M. Marcus, and J. S. Harris, Jr. Conduction threshold, switching, and hysteresis in quantum dot arrays. Physical Review Letters, 74, 3237–3240 (1995). [PubMed][Crossref]
J. Živkovic, AFM Study on RNA and Protein Complexes, PhD Thesis, Radboud University, Nijmegen, The Netherlands (2012).
J. Živkovic, L. Janssen, F. Alvarado, S. Speller, and H.A. Heus. Force spectroscopy of Rev-peptide-RRE interaction from HIV–1. Soft Matter, 8, 2103–2109 (2012). [Crossref]
O.K. Dudko, G. Hummer, and A. Szabo. Theory, analysis, and interpretation of single-molecule force spectroscopy experiments. PNAS, 105, 15755–15760 (2008).