title: On finite-horizon control of genetic regulatory networks with multiple hard-constraints.
abstract: BACKGROUND
  Probabilistic Boolean Networks (PBNs) provide a convenient tool for studying genetic regulatory networks. There are three major approaches to develop intervention strategies: (1) resetting the state of the PBN to a desirable initial state and letting the network evolve from there, (2) changing the steady-state behavior of the genetic network by minimally altering the rule-based structure and (3) manipulating external control variables which alter the transition probabilities of the network and therefore desirably affects the dynamic evolution. Many literatures study various types of external control problems, with a common drawback of ignoring the number of times that external control(s) can be applied.
  
  
  RESULTS
  This paper studies the intervention problem by manipulating multiple external controls in a finite time interval in a PBN. The maximum numbers of times that each control method can be applied are given. We treat the problem as an optimization problem with multi-constraints. Here we introduce an algorithm, the "Reserving Place Algorithm'', to find all optimal intervention strategies. Given a fixed number of times that a certain control method is applied, the algorithm can provide all the sub-optimal control policies. Theoretical analysis for the upper bound of the computational cost is also given. We also develop a heuristic algorithm based on Genetic Algorithm, to find the possible optimal intervention strategy for networks of large size.
  
  
  CONCLUSIONS
  Studying the finite-horizon control problem with multiple hard-constraints is meaningful. The problem proposed is NP-hard. The Reserving Place Algorithm can provide more than one optimal intervention strategies if there are. Moreover, the algorithm can find all the sub-optimal control strategies corresponding to the number of times that certain control method is conducted. To speed up the computational time, a heuristic algorithm based on Genetic Algorithm is proposed for genetic networks of large size.
authors.affiliation: Advanced Modeling and Applied Computing, Department of Mathematics, The University of Hong Kong, Hong Kong. congyang0305@yahoo.com.cn
authors.forename: Cong
authors.initials: C
authors.lastname: Yang
authors.forename: Ching
authors.initials: C
authors.lastname: Wai-Ki
authors.forename: Tsing
authors.initials: T
authors.lastname: Nam-Kiu
authors.forename: Leung
authors.initials: L
authors.lastname: Ho-Yin
mesh_terms: D000465:Algorithms; D020342:Finite Element Analysis; D005786:Gene Expression Regulation; D053263:Gene Regulatory Networks; D008957:Models, Genetic; D015233:Models, Statistical