Deterministic vs. Stochastic Models

The Two Equations Used to Model Gene Expression

Determinisic
A deterministic equation uses a rate equation to describe the transcription and translation of genes. Deterministic equations are characterized as behaving predictably; more specifically a single input will consitently produce the same output. Returning to one of the Collins graphs, the blue line represents the deterministic model and the red line represents the stochastic model (figre 1).

Figure 1

Figure 1 was obtained at http://www.ncbi.nlm.nih.gov/sites/entrez?db=pubmed&uid=15883588&cmd=showdetailview&indexed=google permission pending

Figure 1 displays a stochastic function superimposed on a corresponding deterministic function.

Stochastic
Stochastic models take into account the "randomness" of transcription and translation by utilizing variables for the formation and decay of single molecules and multi-component complexes.
Figure 2

Figure 2 was obtained at http://www.pnas.org/cgi/content/abstract/0608451104v1 permission pending

Figure 3

Figure 3 was obtained at http://www.pnas.org/cgi/content/abstract/99/20/12795 permission pending Here are two visual representation of stochastic models. In the first, nodes represent states of molecular complexes while arrows represent binding of transcriptional, translational and degredation proteins. The second also details transcription and translation but goes into detail about competition for the leader region of mRNA between degradosomes and protiens that induce translation (MRu represents the leader region of mRNA).

Next Section in Modeling Stochasticity | Back to Modeling Stochasticity