A recipe for randomness

Despite many diverse theories that address closely related themes—e.g., probability theory, algorithmic complexity, cryptoanalysis, and pseudorandom number generation—a near-void remains in constructive methods certified to yield the desired “random” output. Herein, we provide explicit techniques to produce broad sets of both highly irregular finite and normal infinite sequences, based on constructions and properties derived from approximate entropy (ApEn), a computable formulation of sequential irregularity. Furthermore, for infinite sequences, we considerably refine normality, by providing methods for constructing diverse classes of normal numbers, classified by the extent to which initial segments deviate from maximal irregularity.

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.

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.

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.

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.