title: Intervention in a family of Boolean networks.
abstract: BACKGROUND
  Intervention in a gene regulatory network is used to avoid undesirable states, such as those associated with a disease. Several types of intervention have been studied in the framework of a probabilistic Boolean network (PBN), which is a collection of Boolean networks in which the gene state vector transitions according to the rules of one of the constituent networks and where network choice is governed by a selection distribution. The theory of automatic control has been applied to find optimal strategies for manipulating external control variables that affect the transition probabilities to desirably affect dynamic evolution over a finite time horizon. In this paper we treat a case in which we lack the governing probability structure for Boolean network selection, so we simply have a family of Boolean networks, but where these networks possess a common attractor structure. This corresponds to the situation in which network construction is treated as an ill-posed inverse problem in which there are many Boolean networks created from the data under the constraint that they all possess attractor structures matching the data states, which are assumed to arise from sampling the steady state of the real biological network.
  
  
  RESULTS
  Given a family of Boolean networks possessing a common attractor structure composed of singleton attractors, a control algorithm is derived by minimizing a composite finite-horizon cost function that is a weighted average over all the individual networks, the idea being that we desire a control policy that on average suits the networks because these are viewed as equivalent relative to the data. The weighting for each network at any time point is taken to be proportional to the instantaneous estimated probability of that network being the underlying network governing the state transition. The results are applied to a family of Boolean networks derived from gene-expression data collected in a study of metastatic melanoma, the intent being to devise a control strategy that reduces the WNT5A gene's action in affecting biological regulation.
  
  
  BACKGROUND
  The software is available on request.
  
  
  BACKGROUND
  The supplementary Information is available at http://ee.tamu.edu/~edward/tree
authors.affiliation: Department of Electrical Engineering, Texas A and M University College Station, TX 77843, USA.
authors.forename: Ashish
authors.initials: A
authors.lastname: Choudhary
authors.forename: Aniruddha
authors.initials: A
authors.lastname: Datta
authors.forename: Michael L
authors.initials: ML
authors.lastname: Bittner
authors.forename: Edward R
authors.initials: ER
authors.lastname: Dougherty
mesh_terms: D000465:Algorithms; D045744:Cell Line, Tumor; D005246:Feedback; D020869:Gene Expression Profiling / Q000379:methods*; D015972:Gene Expression Regulation, Neoplastic / Q000235:genetics*; D006801:Humans; D008545:Melanoma / Q000235:genetics* / Q000378:metabolism / Q000556:secondary; D008957:Models, Genetic; D015233:Models, Statistical; D015202:Protein Engineering / Q000379:methods; D011518:Proto-Oncogene Proteins / Q000235:genetics* / Q000378:metabolism; D011994:Recombinant Proteins / Q000378:metabolism; D015398:Signal Transduction / Q000235:genetics*; D051153:Wnt Proteins / Q000235:genetics* / Q000378:metabolism; D000071818:Wnt-5a Protein
chemical_list: D011518:Proto-Oncogene Proteins; D011994:Recombinant Proteins; C085389:WNT5A protein, human; D051153:Wnt Proteins; D000071818:Wnt-5a Protein