Lattice Models, Runs-related Statistics, and Their Applications to Computational Biology

Lattice models are widely used in physics, chemistry, and biophysics. The traditional method for studying lattice models is the transfer matrix method. Two alternative methods were developed recently, which have several advantages over the transfer matrix method. The recurrence theory utilizes the symmetry in the binding configurations to reduce the size of the matrix (or the order of the recurrence). A somewhat counter-intuitive conclusion proved by the method is that linear models are in general simpler than circular ones, although the open ends break symmetry in the linear models. The second method uses generating functions of individual "runs" to get the partition functions of the whole system. This method proves to be more efficient for handling a large range of models in biophysics and chemistry. Furthermore, recent developments show that it has direct application in the study of runs-related statistics. This method provides the general tools to handle many runs-related distributions, including the distributions of longest runs. Explicit formulas lead naturally to easy calculations of the distributions. Runs-related statistics contain useful information about the content and structure of the biological sequences, but they have not been widely used by the computational biology community. It is hoped that the new calculation methods, when combined with other measurements such as oligomer frequency, will improve the current computational methods for biological sequence analysis.

Top of Page