|
A Boolean network consists of a discrete set of Boolean variables each of which has a boolean function (possibly different for each variable) assigned to it which takes inputs from a subset of those variables and output that determines the state of the variable it is assigned to. This set of functions in effect determines a topology (connectivity) on the set of variables, which then become nodes in a network. Usually, the dynamics of the system is taken as a discrete time series where the state of the entire network at time ''t''+1 is determined by evaluating each variable's function on the state of the network at time ''t''. This may be done synchronously or asynchronously. Although Boolean networks are a crude simplification of genetic reality where genes are not simple binary switches, there are several cases where they correctly capture the correct pattern of expressed and suppressed genes. The seemingly mathematical easy (synchronous) model was only fully understood in the mid 2000s. == Classical model == A Boolean network is a particular kind of sequential dynamical system, where time and states are discrete, i.e. both the set of variables and the set of states in the time series each have a bijection onto an integer series. Boolean networks are related to cellular automata. Usually, cellular automata are defined with an homogeneous topology, i.e. a single line of nodes, a square or hexagonal grid of nodes or an even higher-dimensional structure, but each variable (node in the grid) may take on more than two values (and hence not be boolean). A random Boolean network (RBN) is one that is randomly selected from the set of all possible boolean networks of a particular size, ''N''. One then can study statistically, how the expected properties of such networks depend on various statistical properties of the ensemble of all possible networks. For example, one may study how the RBN behavior changes as the average connectivity is changed. The first Boolean networks were proposed by Stuart A. Kauffman in 1969, as random models of genetic regulatory networks. Random Boolean networks (RBNs) are known as ''NK'' networks or Kauffman networks (Dubrova 2005). An RBN is a system of ''N'' binary-state nodes (representing genes) with ''K'' inputs to each node representing regulatory mechanisms. The two states (on/off) represent respectively, the status of a gene being active or inactive. The variable ''K'' is typically held constant, but it can also be varied across all genes. In the simplest case each gene is assigned, at random, ''K'' regulatory inputs from among the ''N'' genes, and one of the possible Boolean functions of ''K'' inputs. This gives a single random sample from the ensemble of possible networks of size ''N'' and either connectivity =''k'' or with connectivities with some deviation around ''k''. The state of a network at any point in time is given by the current states of all ''N'' genes. Thus the size of the state space of any such network is 2''N''. Simulation of RBNs is done in discrete time steps. The state of a node at time ''t''+1 is computed by applying the boolean function associated with the node to the state of its input nodes at time ''t''. The sequence of states of the whole network starting from some initial state is called the trajectory of that state. The behavior of specific RBNs and generalized classes of them has been the subject of much of Kauffman's (and others) research. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Boolean network」の詳細全文を読む スポンサード リンク
|