Randomness and degrees of irregularity.

The fundamental question "Are sequential data random?" arises in myriad contexts, often with severe data length constraints. Furthermore, there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness--e.g., to evaluate the efficacy of therapy in medicine. We address both these issues from a computable framework via a quantification of regularity. ApEn (approximate entropy), defining maximal randomness for sequences of arbitrary length, indicating the applicability to sequences as short as N = 5 points. An infinite sequence formulation of randomness is introduced that retains the operational (and computable) features of the finite case. In the infinite sequence setting, we indicate how the "foundational" definition of independence in probability theory, and the definition of normality in number theory, reduce to limit theorems without rates of convergence, from which we utilize ApEn to address rates of convergence (of a deficit from maximal randomness), refining the aforementioned concepts in a computationally essential manner. Representative applications among many are indicated to assess (i) random number generation output; (ii) well-shuffled arrangements; and (iii) (the quality of) bootstrap replicates.

Rapid generation of nested chromosomal deletions on mouse chromosome 2

Nested chromosomal deletions are powerful genetic tools. They are particularly suited for identifying essential genes in development either directly or by screening induced mutations against a deletion. To apply this approach to the functional analysis of mouse chromosome 2, a strategy for the rapid generation of nested deletions with Cre recombinase was developed and tested. A loxP site was targeted to the Notch1 gene on chromosome 2. A targeted line was cotransfected with a second loxP site and a plasmid for transient expression of Cre. Independent random integrations of the second loxP site onto the targeted chromosome in direct repeat orientation created multiple nested deletions. By virtue of targeting in an F1 hybrid embryonic stem cell line, F1(129S1×Cast/Ei), the deletions could be verified and rapidly mapped. Ten deletions fell into seven size classes, with the largest extending six or seven centiMorgans. The cytology of the deletion chromosomes were determined by fluorescent in situ hybridization. Eight deletions were cytologically normal, but the two largest deletions had additional rearrangements. Three deletions, including the largest unrearranged deletion, have been transmitted through the germ line. Several endpoints also have been cloned by plasmid rescue. These experiments illustrate the means to rapidly create and map deletions anywhere in the mouse genome. They also demonstrate an improved method for generating nested deletions in embryonic stem cells.

Rapid generation of incremental truncation libraries for protein engineering using α-phosphothioate nucleotides

Incremental truncation for the creation of hybrid enzymes (ITCHY) is a novel tool for the generation of combinatorial libraries of hybrid proteins independent of DNA sequence homology. We herein report a fundamentally different methodology for creating incremental truncation libraries using nucleotide triphosphate analogs. Central to the method is the polymerase catalyzed, low frequency, random incorporation of α-phosphothioate dNTPs into the region of DNA targeted for truncation. The resulting phosphothioate internucleotide linkages are resistant to 3′→5′ exonuclease hydrolysis, rendering the target DNA resistant to degradation in a subsequent exonuclease III treatment. From an experimental perspective the protocol reported here to create incremental truncation libraries is simpler and less time consuming than previous approaches by combining the two gene fragments in a single vector and eliminating additional purification steps. As proof of principle, an incremental truncation library of fusions between the N-terminal fragment of Escherichia coli glycinamide ribonucleotide formyltransferase (PurN) and the C-terminal fragment of human glycinamide ribonucleotide formyltransferase (hGART) was prepared and successfully tested for functional hybrids in an auxotrophic E.coli host strain. Multiple active hybrid enzymes were identified, including ones fused in regions of low sequence homology.