A Formalization of Linkage Analysis

Anna Ingólfsdóttir
Anders Lyhne Christensen
Jens Alsted Hansen
Jacob Johnsen
John Knudsen
Jacob Illum Rasmussen

February 2002


In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been established. Initially, the biological model is presented. On the basis of this biological model we establish a formalization that enables reasoning about algorithms used in linkage analysis. The formalization applies both for single and multi point linkage analysis. We illustrate the usage of the formalization in correctness proofs of central algorithms and optimisations for linkage analysis. A further use of the formalization is to reason about alternative methods for linkage analysis. We discuss the use of MTBDDs and PDGs in linkage analysis, since they have proven efficient for other computationally hard problems involving large state spaces. We conclude that none of the techniques discussed are directly applicable to linkage analysis, however further research is needed in order to investigated whether a modified version of one or more of these are applicable

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