DNA Mapping Algorithms: Strategies for Single Restriction Enzyme and Multiple Restriction Enzyme Mapping

An approach to high-resolution restriction-fragment DNA mapping, known as Multiple-Restriction-Enzyme mapping (MRE mapping), is present. This approach significantly reduces the uncertainty of clone placement by using clone ends to synchronize the position in of clones within different maps, each map being constructed from fragment-length data produced by digestion of each clone with a specific restriction enzyme. Maps containing both fragments-length data and clone-end data are maintained for each restriction enzyme, and synchronization between two such maps is achieved by requiring them to have compatible clone-end map projections. Basic definitions of different kinds of maps, such as restriction sites maps, restriction fragment maps and clone end maps, are presented. Several specifications notations, such as sequence-set notation and sequence-set-tree notation, for describing the structure of these maps, are defined. Basic concepts, such as the match/merge approach to map incorporation, extension vs. assimilation and ambiguity, are exposed. Supporting techniques, such as window sizing, window placement, and ambiguity resolution, are also discussed. A mathematical analysis of how MRE mapping effects false positives and false negatives is presented. For concreteness, MRE mapping is presented using a specific methodological framework. However, many of the concepts and techniques have a wider range of use than just high-resolution restriction-fragment mapping

Interval Maintenance of Dynamically Changing Flow Graphs

Many compilers incorporate an optimization phase during the development of the final object code. Most optimization phases utilize a flow graph and partition it into disjoint single entry regions to perform various global flow analyses. The interval is a commonly used single entry region and interval analyses have been developed for performing standard analyses such as live variable analysis, etc. This paper presents a technique for maintaining the interval structure as the underlying flow graph is dynamically modified. The techniques presented preserve the interval order required by many interval analyses and do not require that the underlying flow graph be reducible

Number of Binary Trees

A data encoding scheme involving binary tree encodements is presented and analyzed. A closed-form formula for the number of n-bit legal memory configurations is developed. It is shown that the storage capacity loss due the use of this scheme is not significant for large n

DNA Mapping Algorithms: Synchronized Double Digest Mapping

A technique called Synchronized Double Digest Mapping (SDDM) is presented; it combines classical Double Digest Mapping (DDM) and Multiple-Restriction-Enzyme Mapping (MREM). Classical DDM is a technique for determining the order of restriction fragments in a clone given three digestions of the clone: a digestion by enzyme1, a digestion by enzyme2, and a digestion by enzyme1 and enzyme2 combined. All algorithms for applying this technique are exponential (in the number of fragments present in the clone) in nature. MREM is an extension of classical high-resolution restriction-fragment mapping of a YAC or a genome, in which the overlaps among a set of clones are used to infer a partial order of the restriction fragments. The extension produces maps for several different restriction enzymes concurrently, using clone-end information as a synchronizing mechanism to guarantee consistent and precise clone placement in all maps. These two techniques can be combined if MREM is performed on clones digested in three ways: a digestion by enzyme1, a digestion by enzyme2, and a digestion by enzyme1 and enzyme2 combined. The three resulting maps contain groups of fragments (each group significantly smaller than a clone) to which classical DDM can be applied. Clone-end information is again used to synchronize the selection and extraction, from each map, of appropriate regions (corresponding to the same portion of the underlying genome) to which classical DDM can be applied. Fragment orderings determined for small regions are used as seeds for determining fragment orderings in other adjacent or overlapping regions. A technique for hypothesizing small missing unregistered fragments (i.e., undetected by the electrophoresis technology) is also presented. Such hypothesized fragments are retained only if their consistency with the remainder of the data can be verified. In essence, MREM supplies a divide-and-conquer mechanism for DDM. The computational complexity of SDDM across the entire YAC or genome is shown to be, in practice, polynomial in time instead of exponential in time

DNA Mapping Algorithms: Fragment Matching Mistake Detection and Correction

When using random clone overlap based methods to make DNA maps, fragment matching mistakes, the incorrect matching of similar length restriction fragments, are a common problem that produces incorrect maps. Previous work presented the Restricted Splitting Algorithm (or RSA), which is useful for repairing a map containing a fragment mistake when the location of the mistake is known. This work presents an algorithm, called FIX, which attempts to identify the location of the fragment matching mistake and then uses the RSA to repair the map containing the mistake. In essense, the two techniques combined constitute a hypothesis formulation/hypothesis verification paradigm for correcting restriction maps that contain fragment matching mistakes

DNA Mapping Algorithms: Abstract Data Types - Concepts and Implementation

The conceptual aspects of and the implementation details of a set of self-identifying abstract data types (ADT) are described. Each of the ADTs constitutes a specific class of object, upon which a set of well-defined access functions is available. The intent of these ADTs is to supply a paradigm in which a class of object is available for manipulation, but in which the underlying implementation is hidden from the application programmer. Specific ADTs are the described in some detail. The tagged architecture used to achieve the self-identifying property of the ADTs is presented, and a set of required system-backbone access function is defined. Their combination is shown to produce a robust system in which complex aggregate ADT classes can be flexibly created and managed with little effort on the part of the application programmer. Memory management and statistics reporting techniques are presented