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.

Fas-induced apoptosis of T cells occurs independently of ceramide generation

The Fas receptor is one of a number of important physiological inducers of programmed cell death (apoptosis). Current models for regulation of this process involve rapid conversion of sphingomyelin to ceramide by cellular sphingomyelinases. Induced changes in cellular levels of such sphingosine-based ceramides are normally extrapolated from measurements of sphingomyelinase activity or following their conversion to ceramide phosphate by treatment of cellular lipid extracts with bacterial diacylglycerol kinase (DAGK). To allow direct study of cellular sphingosine- and sphinganine-based ceramide levels, we developed a mass spectrometric technique capable of determining inducible changes in both overall ceramide levels and species distribution in cellular lipid preparations. Contrary to current models, we detected no changes in cellular ceramide levels up to 2 hr poststimulation of Jurkat T cells with an anti-Fas IgM, although this treatment did induce apoptosis. We also determined in the same system that, when utilizing the DAGK assay, increased phosphorylation of substrates that comigrated with ceramide standards was apparent but that this effect was due to an enhancement of DAGK activity rather than increases in levels of cellular ceramides as substrates per se. Thus, the first direct measurement of ceramides present in cells undergoing apoptosis indicates that, insofar as it can be measured, the induction of apoptosis does not involve the generation of sphingosine-based ceramides, contrary to many published accounts.

Quantitative insight into proliferation and differentiation of oligodendrocyte type 2 astrocyte progenitor cells in vitro

As part of our attempts at understanding fundamental principles that underlie the generation of nondividing terminally differentiated progeny from dividing precursor cells, we have developed approaches to a quantitative analysis of proliferation and differentiation of oligodendrocyte type 2 astrocyte (O-2A) progenitor cells at the clonal level. Owing to extensive previous studies of clonal differentiation in this lineage, O-2A progenitor cells represent an excellent system for such an analysis. Previous studies have resulted in two competing hypotheses; one of them suggests that progenitor cell differentiation is symmetric, the other hypothesis introduces an asymmetric process of differentiation. We propose a general model that incorporates both such extreme hypotheses as special cases. Our analysis of experimental data has shown, however, that neither of these extreme cases completely explains the observed kinetics of O-2A progenitor cell proliferation and oligodendrocyte generation in vitro. Instead, our results indicate that O-2A progenitor cells become competent for differentiation after they complete a certain number of critical mitotic cycles that represent a period of symmetric development. This number varies from clone to clone and may be thought of as a random variable; its probability distribution was estimated from experimental data. Those O-2A cells that have undergone the critical divisions then may differentiate into an oligodendrocyte in each of the subsequent mitotic cycles with a certain probability, thereby exhibiting the asymmetric type of differentiation.

A first-generation X-inactivation profile of the human X chromosome

In females, most genes on the X chromosome are generally assumed to be transcriptionally silenced on the inactive X as a result of X inactivation. However, particularly in humans, an increasing number of genes are known to “escape” X inactivation and are expressed from both the active (Xa) and inactive (Xi) X chromosomes; such genes reflect different molecular and epigenetic responses to X inactivation and are candidates for phenotypes associated with X aneuploidy. To identify genes that escape X inactivation and to generate a first-generation X-inactivation profile of the X, we have evaluated the expression of 224 X-linked genes and expressed sequence tags by reverse-transcription–PCR analysis of a panel of multiple independent mouse/human somatic cell hybrids containing a normal human Xi but no Xa. The resulting survey yields an initial X-inactivation profile that is estimated to represent ≈10% of all X-linked transcripts. Of the 224 transcripts tested here, 34 (three of which are pseudoautosomal) were expressed in as many as nine Xi hybrids and thus appear to escape inactivation. The genes that escape inactivation are distributed nonrandomly along the X; 31 of 34 such transcripts map to Xp, implying that the two arms of the X are epigenetically and/or evolutionarily distinct and suggesting that genetic imbalance of Xp may be more severe clinically than imbalance of Xq. A complete X-inactivation profile will provide information relevant to clinical genetics and genetic counseling and should yield insight into the genomic and epigenetic organization of the X chromosome.

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.

Predicting crossover generation in DNA shuffling

We introduce a quantitative framework for assessing the generation of crossovers in DNA shuffling experiments. The approach uses free energy calculations and complete sequence information to model the annealing process. Statistics obtained for the annealing events then are combined with a reassembly algorithm to infer crossover allocation in the reassembled sequences. The fraction of reassembled sequences containing zero, one, two, or more crossovers and the probability that a given nucleotide position in a reassembled sequence is the site of a crossover event are estimated. Comparisons of the predictions against experimental data for five example systems demonstrate good agreement despite the fact that no adjustable parameters are used. An in silico case study of a set of 12 subtilases examines the effect of fragmentation length, annealing temperature, sequence identity and number of shuffled sequences on the number, type, and distribution of crossovers. A computational verification of crossover aggregation in regions of near-perfect sequence identity and the presence of synergistic reassembly in family DNA shuffling is obtained.

Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.

Generation of a high-titer retroviral vector capable of expressing high levels of the human beta-globin gene.

Retrovirus-mediated gene transfer into hematopoietic cells may provide a means of treating both inherited and acquired diseases involving hematopoietic cells. Implementation of this approach for disorders resulting from mutations affecting the beta-globin gene (e.g., beta-thalassemia and sickle cell anemia), however, has been hampered by the inability to generate recombinant viruses able to efficiently and faithfully transmit the necessary sequences for appropriate gene expression. We have addressed this problem by carefully examining the interactions between retroviral and beta-globin gene sequences which affect vector transmission, stability, and expression. First, we examined the transmission properties of a large number of different recombinant proviral genomes which vary both in the precise nature of vector, beta-globin structural gene, and locus control region (LCR) core sequences incorporated and in the placement and orientation of those sequences. Through this analysis, we identified one specific vector, termed M beta 6L, which carries both the human beta-globin gene and core elements HS2, HS3, and HS4 from the LCR and faithfully transmits recombinant proviral sequences to cells with titers greater than 10(6) per ml. Populations of murine erythroleukemia (MEL) cells transduced by this virus expressed levels of human beta-globin transcript which, on a per gene copy basis, were 78% of the levels detected in an MEL-derived cell line, Hu11, which carries human chromosome 11, the site of the beta-globin locus. Analysis of individual transduced MEL cell clones, however, indicated that, while expression was detected in every clone tested (n = 17), the levels of human beta-globin treatment varied between 4% and 146% of the levels in Hu11. This clonal variation in expression levels suggests that small beta-globin LCR sequences may not provide for as strict chromosomal position-independent expression of beta-globin as previously suspected, at least in the context of retrovirus-mediated gene transfer.