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@ARTICLE{Krishnan:864627,
      author       = {Krishnan, Jeyashree and Torabi, Reza and Di Napoli, Edoardo
                      and Schuppert, Andreas},
      title        = {{A} {M}odified {I}sing {M}odel of {B}arabási-{A}lbert
                      {N}etwork with {G}ene-type {S}pins},
      journal      = {Journal of mathematical biology},
      volume       = {81},
      issn         = {0303-6812},
      address      = {New York},
      publisher    = {Springer},
      reportid     = {FZJ-2019-04332},
      pages        = {769–798},
      year         = {2020},
      abstract     = {The central question of systems biology is to understand
                      how individual components of a biological system such as
                      genes or proteins cooperate in emerging phenotypes resulting
                      in the evolution of diseases. As living cells are open
                      systems in quasi-steady state type equilibrium in continuous
                      exchange with their environment, computational techniques
                      that have been successfully applied in statistical
                      thermodynamics to describe phase transitions may provide new
                      insights to emerging behavior of biological systems. Here we
                      will systematically evaluate the translation of
                      computational techniques from solid-state physics to network
                      models that closely resemble biological networks and develop
                      specific translational rules to tackle problems unique to
                      living systems. Hence we will focus on logic models
                      exhibiting only two states in each network node. Motivated
                      by the apparent asymmetry between biological states where an
                      entity exhibits boolean states i.e. is active or inactive,
                      we present an adaptation of symmetric Ising model towards an
                      asymmetric one fitting to living systems here referred to as
                      the modified Ising model with gene-type spins. We analyze
                      phase transitions by Monte Carlo simulations and propose
                      mean-field solution of modified Ising model of a network
                      type that closely resembles real-world network, the
                      $Barab\'{a}si-Albert$ model of scale-free networks. We show
                      that asymmetric Ising models show similarities to symmetric
                      Ising models with external field and undergoes a
                      discontinuous phase transition of the first-order and
                      exhibits hysteresis. The simulation setup presented here can
                      be directly used for any biological network connectivity
                      dataset and is also applicable for other networks that
                      exhibit similar states of activity. This is a general
                      statistical method to deal with non-linear large scale
                      models arising in the context of biological systems and is
                      scalable to any network size.},
      cin          = {JSC},
      ddc          = {570},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / Simulation and Data Laboratory Quantum
                      Materials (SDLQM) (SDLQM)},
      pid          = {G:(DE-HGF)POF3-511 / G:(DE-Juel1)SDLQM},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {1908.06872},
      howpublished = {arXiv:1908.06872},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1908.06872;\%\%$},
      pubmed       = {pmid:32897406},
      UT           = {WOS:000567448200001},
      doi          = {10.1007/s00285-020-01518-6},
      url          = {https://juser.fz-juelich.de/record/864627},
}