Boolean networks  (Page 3/3)

Fortunately, the results were very promising. By using binary gene expression data, generated via cDNA microarrays, and the Hamming distance as a similarity metric, a clear separation between different sub-types of gliomas as well as between different sarcomas was showed. This seems to suggest that a good deal of meaningful biological information, to the extent that it is contained in the measured continuous-domain gene expression data, is retained when it is binarized.

Biological example

Below an example id presented, borrowed from (Shmulevich et al., 2002), showing the logical representation of cell cycle regulation. This process of cellular growth and division is highly regulated. A disbalance in this process results in unregulated cell growth in diseases such as cancer. In order for cells to move from the G1 phase to the S phase, when the genetic material, DNA, is replicated for the daughter cells, a series of molecules such as cyclin E and cyclin dependent kinase 2 (cdk2) work together to phosphorylate the retinoblastoma (Rb) protein and inactivate it, thus releasing cells into the S phase. Cdk2/cyclin E is regulated by two switches: the positive switch complex called cdk activating kinase (CAK) and the negative switch p21/WAF1. The CAK complex can be composed of two gene products: cyclin H and cdk7. When cyclin H and cdk7 are present, the complex can activate cdk2/cyclin E. A negative regulator of cdk2/cyclin E is p21/WAF1, which in turn can be activated by p53. When p21/WAF1 binds to cdk2/cyclin E, the kinase complex is turned off (Gartel and Tyner, 1999). Further, p53 can inhibit cyclin H, a positive regulator of cyclin E/cdk2 (Schneider et al., 1998). This negative regulation is an important defensive system in the cells.For example, when cells are exposed to mutagen, DNA damage occurs. It is to the benefit of cells to repair the damage before DNA replication so that the damaged genetic materials do not pass onto the next generation. Extensive amount of work has demonstrated that DNA damage triggers switches that turn on p53, which then turns on p21/WAF1. p21/WAF1 then inhibits cdk2/cyclin E, thus Rb becomes activated and DNA synthesis stops. As an extra measure, p53 also inhibits cyclin H, thus turning off the switch that turns on cdk2/cyclin E. Such delicate genetic switch networks in the cells are the basis for cellular homeostasis—the ability of an organism to maintain equilibrium.

For purposes of illustration, let consider a simplified diagram, shown in Figure3 , illustrating the effects of cdk7/cyclin H, cdk2/cyclin E, and p21/WAF1 on Rb. Thus, p53 and other known regulatory factors are not considered. While this diagram represents the above relationships from a pathway perspective, one may also represent the activity of Rb in terms of the other variables in a logic-based fashion. Figure4 contains a logic circuit diagram of the activity of Rb (‘on’or‘off’) as a Boolean function of four input variables: cdk7, cyclin H, cyclin E, and p21/WAF1. Note that cdk2 is shown to be completely determined by the values of cdk7 and cyclin H using the AND operation and thus, cdk2 is not an independent input variable. Also, in Figure3 , p21/WAF1 is shown to have an inhibitive effect on the cdk2/cyclin E complex, which in turn regulates Rb, while in Figure4 , we see that from a logic-based perspective, the value of p21/WAF1 works together with cdk2 and cyclin E to determine the value of Rb.