Asymptotics of pooling design performance

We analyse the expected performance of various group testing, or pooling, designs. The context is that of identifying characterized clones in a large collection of clones. Here we choose as performance criterion the expected number of unresolved ‘negative’ clones, and we aim to minimize this quantity. Technically, long inclusion–exclusion summations are encountered which, aside from being computationally demanding, give little inkling of the qualitative effect of parametric control on the pooling strategy. We show that readily-interpreted re-summation can be performed, leading to asymptotic forms and systematic corrections. We apply our results to randomized designs, illustrating how they might be implemented for approximating combinatorial formulae.

Preliminary implementation of new data mining techniques for the analysis of simulation data from Genetic Analysis Workshop 12: problem 2

We introduce a new data mining method applicable to complex disease genetics. Our approach is suited to a broad spectrum of diseases, identifying the noteworthy sharing of combinations of alleles in unrelated affected individuals. Furthermore, this approach may be extended to comprise the common types of genotype data, including single-nucleotide polymorphisms, candidate-gene sequences, etc. Using a method derived from data-mining computer algorithms, we analyze a data set of unrelated affected individuals chosen from the simulated pedigrees of problem 2 of the Genetics Analysis Workshop 12. We observe that most marker subsets containing a flanking marker for each of six or seven of the disease-gene loci yield significant numbers of individuals manifesting substantially similar genotypes. However, initial attempts (blind to the generating model) to identify the predisposing loci have not been successful. Refining our methods so that such loci may routinely be found and validated is underway.

Discovery of association rules in medical data

Data mining is a technique for discovering useful information from large databases. This technique is currently being profitably used by a number of industries. A common approach for information discovery is to identify association rules which reveal relationships among different items. In this paper, we use this approach to analyse a large database containing medical-record data. Our aim is to obtain association rules indicating relationships between procedures performed on a patient and the reported diagnoses. Random sampling was used to obtain these association rules. After reviewing the basic concepts associated with data mining, we discuss our approach for identifying association rules and report on the rules generated.

The stationary statistical properties of human coding sequences

We introduce a generally applicable method for the discovery and quantitation of all of the characteristic statistical properties of a class of biological sequences, given examples from the class. This method employs a reversible binary encoding of sequences into the binary digits -1 and +1. Then, provided that the sample is sufficient, the sample cumulants on the subsets of digit positions will manifest all of the statistical properties of the class. As an illustration, we present the main results of a complete characterization of the stationary statistical properties of human coding sequences, in terms of their sample cumulants. Many of the telling sample cumulants are described.

The design of pooling experiments for screening a clone map

We consider nonadaptive pooling designs for unique-sequence screening of a 1530-clone map of Aspergillus nidulans. The map has the properties that the clones are, with possibly a few exceptions, ordered and no more than 2 of them cover any point on the genome. We propose two subdesigns of the Steiner system S(3, 5, 65), one with 65 pools and approximately 118 clones per pool, the other with 54 pools and about 142 clones per pool. Each design allows 1 or 2 positive clones to be detected, even in the presence of substantial experimental error rates. More efficient designs are possible if the overlap information in the map is exploited, if there is no constraint on the number of clones in a pool, and if no error tolerance is required. An information theory lower bound requires at least 12 pools to satisfy these minimal criteria, and an "interleaved binary" design can be constructed on 20 pools, with about 380 clones per pool. However, the designs with more pools have important properties of robustness to various possible errors and general applicability to a wider class of pooling experiments.

Interpretation of pooling experiments using the Markov chain Monte Carlo method

This paper describes an effective method for extracting as much information as possible from pooling experiments for library screening. Pools are collections of clones, and screening a pool with a probe determines whether any of these clones are positive for the probe. The results of the pool screenings are interpreted, or decoded, to infer which clones are candidates to be positive. These candidate positives are subjected to confirmatory testing. Decoding the pool screening results is complicated by the presence of errors, which typically lead to ambiguities in the inference of positive clones. However, in many applications there are reasonable models for the prior distributions for positives and for errors, and Bayes inference is the preferred method for ranking candidate positives. Because of the combinatoric complexity of the Bayes formulation, we implemented a decoding algorithm using a Markov chain Monte Carlo method. The algorithm was used in screening a library with 1298 clones using 47 pools. We corroborated the posterior probabilities for positives with results from confirmatory screening. We also simulated the screening of a 10-fold coverage library of 33,000 clones using 253 pools. The use of our algorithm, effective under conditions where combinatorial decoding techniques are imprudent, allows the use of fewer pools and also introduces needed robustness.

Single-base sequencing and similarity comparisons

A "single-base sequence" is a DNA sequence in which the identities and locations of bases of only one type have been determined. We present experimental procedures for single-base sequencing and describe the effective use of existing software (FASTA) in similarity comparisons of single-base sequences. We determined the theoretical and experimental minimum sequence lengths required for identification of a sequence within a large dataset and optimized the FASTA parameters for use in single-base similarity comparisons. Single-base sequences have been used to identify cDNAs occurring in a database. Single-base sequencing could be used to reduce the redundancy of "shot-gun sequencing."

Efficient pooling designs for library screening

We describe efficient methods for screening clone libraries, based on pooling schemes that we call "random k-sets designs." In these designs, the pools in which any clone occurs are equally likely to be any possible selection of k from the v pools. The values of k and v can be chosen to optimize desirable properties. Random k-sets designs have substantial advantages over alternative pooling schemes: they are efficient, flexible, and easy to specify, require fewer pools, and have error-correcting and error-detecting capabilities. In addition, screening can often be achieved in only one pass, thus facilitating automation. For design comparison, we assume a binomial distribution for the number of "positive" clones, with parameters n, the number of clones, and c, the coverage. We propose the expected number of resolved positive clones--clones that are definitely positive based upon the pool assays--as a criterion for the efficiency of a pooling design. We determine the value of k that is optimal, with respect to this criterion, as a function of v, n, and c. We also describe superior k-sets designs called k-sets packing designs. As an illustration, we discuss a robotically implemented design for a 2.5-fold-coverage, human chromosome 16 YAC library of n = 1298 clones. We also estimate the probability that each clone is positive, given the pool-assay data and a model for experimental errors.

Base compositional structure of genomes

We model the base compositional structure of the human and Escherichia coli genomes. Three particular properties are first quantified: (1) There is a significant tendency for any region of either genome to have a strand-symmetric base composition. (2) The variation in base composition from region to region, within each genome, is very much larger than expected from common homogeneous stochastic models. (3) A given local base composition tends to persist over a scale of at least kilobases (E. coli) or tens of kilobases (human). Multidomain stochastic models from the literature are reviewed and sharpened. In particular, quantitative measurements of the third property lead us to suggest a significant shift in the style of domain models, in which the variation of A+T content with position is modeled by a random walk with frequent small steps rather than with large quantum jumps. As an application, we suggest a way to reduce the amount of computation in the assembly of large sequences from sequences of randomly chosen fragments.

Statistical analysis of DNA fingerprint data for ordered clone physical mapping of human chromosomes

A statistical framework is proposed for analysing DNA fingerprint data from experiments aimed at constructing ordered clone physical maps of chromosomes. The fingerprint data consists of the lengths and hybridization states of restriction digest fragments and the paper develops a solution to the fundamental problem of deciding whether or not two randomly selected clones overlap. Overlap probabilities are calculated using Bayes' rule together with appropriate statistical descriptions of the chromosome and experimental procedure. The analysis is flexible, allowing a variety of assumptions to account for experimental errors and difficulties, such as unobserved fragments. The approach described here provides a basis for predicting the rate of progress of an experimental protocol and hence for comparing alternate protocols. It is readily generalized to related problems with a wide range of possible data. Results are presented for the clone mapping protocol currently being employed at Los Alamos National Laboratory on human chromosome 16 (Stallings et al., 1990, Proc. natl. Acad. Sci. U.S.A., 87, 6218-6222).

Evolution and distribution of (GT)n repetitive sequences in mammalian genomes

The dinucleotide repetitive sequence, (GT)n, is highly interspersed in eukaryotic genomes and may have functional roles in genetic recombination or the modulation of transcriptional activity. We have examined the distribution and conservation of position of GT repetitive sequences in several mammalian genomes. The distribution of GT repetitive sequences in the human genome was determined by the analysis of over 3700 cosmid clones containing human insert DNA. On average, a GT repetitive sequence occurs every 30 kb in DNA from euchromatic regions. GT repetitive sequences are significantly underrepresented in centric heterochromatin. The density of GT repetitive sequences in the human genome could also be estimated by analyzing GenBank genomic sequences that include introns and flanking sequences. The frequency of GT repetitive sequences found in GenBank human DNA sequences was in close agreement with that obtained by experimental methods. GenBank genomic sequences also revealed that (GT)n repetitive sequences (n greater than 6) occur every 18 and 21 kb, on average, in mouse and rat genomes. Comparative analysis of 31 homologous sequences containing (GT)n repetitive sequences from several mammals representing four orders revealed that the positions of these repeats have been conserved between closely related species, such as humans and other primates. To a lesser extent, positions of GT repetitive sequences have been conserved between species in distantly related groups such as primates and rodents. The distribution and conservation of GT repetitive sequences is discussed with respect to possible functional roles of the repetitive sequence.

Mapping using unique sequences

Theoretical predictions are given for the progress expected, when mapping DNA by identifying clones containing specific unique sequences. Progress is measured in three ways; however, all results depend on (dimensionless counterparts of) the number of clones and the number of unique sequences used. Furthermore, the effects of clone length dispersion are included in the theoretical predictions. Both the clones in the library and the unique sequences are assumed to be generated randomly, with uniform probability of originating at any base in the region to be mapped. The first measure of progress is the expected length fraction of the region to be mapped covered by at least one clone, when clones containing at least one unique sequence are included in the map. The second measure of progress is the expected length fraction of the region to be mapped in "covered intervals", an interval being the region between adjacent unique sequences. Alternative definitions for clones covering an interval are analyzed. The third measure of progress is the expected number of clone islands generated; an island covers successive intervals. Finally, using these measures of progress, we compare the efficiency of this new mapping strategy with conventional clone mapping strategies.

Physical mapping of human chromosomes by repetitive sequence fingerprinting

We have developed an approach for identifying overlapping cosmid clones by exploiting the high density of repetitive sequences in complex genomes. Individual clones are fingerprinted, using a combination of restriction enzyme digestions followed by hybridization with selected classes of repetitive sequences. This "repeat fingerprinting" technique allows small regions of clone overlap (10-20%) to be unambiguously assigned. We demonstrate the utility of this approach, using the fingerprinting of 3145 cosmid clones (1.25 x coverage), containing one or more (GT)n repeats, from human chromosome 16. A statistical analysis was used to link these clones into 460 contiguous sequences (contigs), averaging 106 kilobases (kb) in length and representing approximately 54% (48.7 Mb) of the euchromatic arms of this chromosome. These values are consistent with theoretical calculations and indicate that 150- to 200-kb contigs can be generated with 1.5 x coverage. This strategy requires the fingerprinting of approximately one-fourth as many cosmids as random strategies requiring 50% minimum overlap for overlap detection. By "nucleating" at specific regions in the human genome, and exploiting the high density of interspersed sequences, this approach allows (i) the rapid generation of large (greater than 100-kb) contigs in the early stages of contig mapping and (ii) the production of a contig map with useful landmarks for rapid integration of the genetic and physical maps.

Competition between solution and cell surface receptors for ligand. Dissociation of hapten bound to surface antibody in the presence of solution antibody

We present a joint theoretical and experimental study on the effects of competition for ligand between receptors in solution and receptors on cell surfaces. We focus on the following experiment. After ligand and cell surface receptors equilibrate, solution receptors are introduced, and the dissociation of surface bound ligand is monitored. We derive theoretical expressions for the dissociation rate and compare with experiment. In a standard dissociation experiment (no solution receptors present) dissociation may be slowed by rebinding, i.e., at high receptor densities a ligand that dissociates from one receptor may rebind to other receptors before separating from the cell. Our theory predicts that rebinding will be prevented when S much greater than N2Kon/(16 pi 2D a4), where S is the free receptor site concentration in solution, N the number of free surface receptor sites per cell, Kon the forward rate constant for ligand-receptor binding in solution, D the diffusion coefficient of the ligand, and a the cell radius. The predicted concentration of solution receptors needed to prevent rebinding is proportional to the square of the cell surface receptor density. The experimental system used in these studies consists of a monovalent ligand, 2,4-dinitrophenyl (DNP)-aminocaproyl-L-tyrosine (DCT), that reversibly binds to a monoclonal anti-DNP immunoglobulin E (IgE). This IgE is both a solution receptor and, when anchored to its high affinity Fc epsilon receptor on rat basophilic leukemia (RBL) cells, a surface receptor. For RBL cells with 6 x 10(5) binding sites per cell, our theory predicts that to prevent DCT rebinding to cell surface IgE during dissociation requires S much greater than 2,400 nM. We show that for S = 200-1,700 nM, the dissociation rate of DCT from surface IgE is substantially slower than from solution IgE where no rebinding occurs. Other predictions are also tested and shown to be consistent with experiment.

The distribution of interspersed repetitive DNA sequences in the human genome

The distribution of interspersed repetitive DNA sequences in the human genome has been investigated, using a combination of biochemical, cytological, computational, and recombinant DNA approaches. "Low-resolution" biochemical experiments indicate that the general distribution of repetitive sequences in human DNA can be adequately described by models that assume a random spacing, with an average distance of 3 kb. A detailed "high-resolution" map of the repetitive sequence organization along 400 kb of cloned human DNA, including 150 kb of DNA fragments isolated for this study, is consistent with this general distribution pattern. However, a higher frequency of spacing distances greater than 9.5 kb was observed in this genomic DNA sample. While the overall repetitive sequence distribution is best described by models that assume a random distribution, an analysis of the distribution of Alu repetitive sequences appearing in the GenBank sequence database indicates that there are local domains with varying Alu placement densities. In situ hybridization to human metaphase chromosomes indicates that local density domains for Alu placement can be observed cytologically. Centric heterochromatin regions, in particular, are at least 50-fold underrepresented in Alu sequences. The observed distribution for repetitive sequences in human DNA is the expected result for sequences that transpose throughout the genome, with local regions of "preference" or "exclusion" for integration.

The reaction-limited kinetics of membrane-to-surface adhesion and detachment

Biological adhesion is frequently mediated by specific membrane proteins (adhesion molecules). Starting with the notion of adhesion molecules, we present a simple model of the physics of membrane-to-surface attachment and detachment. This model consists of coupling the equations for deformation of an elastic membrane with equations for the chemical kinetics of the adhesion molecules. We propose a set of constitutive laws relating bond stress to bond strain and also relating the chemical rate constants of the adhesion molecules to bond strain. We derive an exact formula for the critical tension. We also describe a fast and accurate finite difference algorithm for generating numerical solutions of our model. Using this algorithm, we are able to compute the transient behaviour during the initial phases of adhesion and detachment as well as the steady-state geometry of adhesion and the velocity of the contact. An unexpected consequence of our model is the predicted occurrence of states in which adhesion cannot be reversed by application of tension. Such states occur only if the adhesion molecules have certain constitutive properties (catch-bonds). We discuss the rational for such catch-bonds and their possible biological significance. Finally, by analysis of numerical solutions, we derive an accurate and general expression for the steady-state velocity of attachment and detachment. As applications of the theory, we discuss data on the rolling velocity of granulocytes in post-capillary venules and data on lectin-mediated adhesion of red cells.

Life, evolution, and the pursuit of single photon sensitivity

Evolutionary forces have designed a large family of rod and cone photoreceptors, each member of which suits the lifestyle requirements and circadian patterns of a particular species. The three-segment architecture of signal transduction is conspicuous in the biochemistry of photoreceptors and supports their demonstrated properties of extreme sensitivity, low noise levels, extended dynamic range, and light adaptation. The designs elaborated by evolution reflect a gradual process of modification, with the sequential elaboration of layers of control and refinements in control. The end results of this long evolutionary labor are the functional efficiency and dynamic range that give the rod its utility. Our conceptual problems in deriving observed rod properties from the collective features of known rod gene products may well give way when we have learned more about the true composition and topology of the outer segment gene set and both bound and free nucleotide concentrations. The invertebrates have developed alternative solutions to the problems of photoreceptor sensitivity and wide dynamic range. The vertebrate rod represents a truly optimized way to capture and interpret low-intensity photon signals. One may anticipate, with some enthusiasm, those molecular and kinetic data that will permit an understanding of how cones differ from rods and how release from the requirement for single photon detection has shaped the design of this wavelength-specific companion photoreceptor. The utilization by evolution of the three-segment architecture of GTP-dependent signal transduction for other modalities of sensory perception, such as olfaction (Lancet et al., this volume) and gustation (Jones et al., this volume), is certainly a reasonable and successful choice.(ABSTRACT TRUNCATED AT 250 WORDS)

The GTP-binding protein of rod outer segments. I. Role of each subunit in the GTP hydrolytic cycle

The GTP-binding protein of Bufo marinus rod outer segments (ROS) is composed of 3 subunits: G alpha, 39,000; G beta, 36,000; and G gamma, approximately 6,500. A stepwise analysis of the GTP hydrolytic cycle (GTP binding, GTP hydrolysis, and GDP release) was facilitated by using purified subunits of the GTP-binding protein. When G alpha and G beta, gamma concentrations were held constant, the initial rate of guanosine-5'-O-(3-thiotriphosphate) (GTP gamma-s) binding to G alpha was dependent upon the amount of bleached rhodopsin present (as illuminated, urea-washed ROS disc membranes). When G alpha and the quantity of these membranes was held constant, the initial rate of GTP gamma-s binding to G alpha was markedly enhanced by increasing the amount of G beta, gamma. G beta preparations (free of G gamma) also stimulated the binding of GTP gamma-s to G alpha to the same extent as G beta, gamma preparations, suggesting that G gamma is not an essential component of the G beta, gamma-dependent stimulation of the rate of GTP gamma-s binding to G alpha. Nonlinear regression analysis revealed a single class of binding sites with an apparent stoichiometry of 1 mol of site/mol of G alpha under optimal binding conditions. Following GTP binding to G alpha, the GTP X G alpha complex dissociates from G beta, gamma which remains primarily bound to the ROS disc membranes. Moreover, while GTP remains in excess, the rates of GTP hydrolysis exhibited saturation in the presence of increasing amounts of G beta, gamma. Nonlinear regression analysis of these data argues against a direct role for G beta, gamma in the hydrolysis of GTP. Thus, both topologic and kinetic data support the concept that GTP hydrolysis is carried out by G alpha alone. After hydrolysis of GTP, the GDP X G alpha complex returned to the ROS disc membrane when G beta, gamma was present on the membrane surface, in the presence and absence of light. Without guanine nucleotides GDP release occurred in the presence of illuminated ROS disc membranes and G beta, gamma. Guanine nucleotides (GTP gamma-s approximately equal to GTP approximately equal to guanosine 5'-(beta, gamma-imido)triphosphate greater than GDP) could effectively displace GDP from G alpha under these conditions.(ABSTRACT TRUNCATED AT 400 WORDS)

Thermodynamics of cell adhesion. II. Freely mobile repellers

The equilibrium adhesion of a cell or vesicle to a substrate is analyzed in a theoretical model in which two types of mobile molecules in the cell membrane are of interest: receptors that can form bonds with fixed ligands in the substrate and repellers that repel the substrate. If the repulsion between the repeller molecule and substrate is greater than kT, there is substantial redistribution of the repellers from the contact area. Coexisting equilibrium states are observed having comparable free energies (a) with unstretched bonds and repeller redistribution and (b) with stretched bonds and partial redistribution.

On the adhesion of vesicles by cell adhesion molecules

This paper gives a detailed analysis of experiments on the kinetics of aggregation of lipid vesicles containing neural cell adhesion molecules (N-CAM). An explanation for the dependence of the "initial aggregation rate," kagg, on the square of the vesicle concentration is given, accounting both for Brownian motion of the vesicles and shear effects. A model in which trimers of N-CAM are one-half of the molecular unit bridging two vesicles explains the observed dependence of kagg on up to the sixth power of the lateral N-CAM concentration and corroborates electron micrographic evidence for N-CAM "triskelions."