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Wentian Li

Publications and source records attributed to Wentian Li.

At least 37 records · Page 2Linked to original sources
arXiv2013

Diminishing Return for Increased Mappability with Longer Sequencing Reads: Implications of the k-mer Distributions in the Human Genome

The amount of non-unique sequence (non-singletons) in a genome directly affects the difficulty of read alignment to a reference assembly for high throughput-sequencing data. Although a greater length increases the chance for reads being uniquely mapped to the reference genome, a quantitative analysis of the influence of read lengths on mappability has been lacking. To address this question, we evaluate the k-mer distribution of the human reference genome. The k-mer frequency is determined for k ranging from 20 to 1000 basepairs. We use the proportion of non-singleton k-mers to evaluate the mappability of reads for a corresponding read length. We observe that the proportion of non-singletons decreases slowly with increasing k, and can be fitted by piecewise power-law functions with different exponents at different k ranges. A faster decay at smaller values for k indicates more limited gains for read lengths > 200 basepairs. The frequency distributions of k-mers exhibit long tails in a power-law-like trend, and rank frequency plots exhibit a concave Zipf's curve. The location of the most frequent 1000-mers comprises 172 kilobase-ranged regions, including four large stretches on chromosomes 1 and X, containing genes with biomedical implications. Even the read length 1000 would be insufficient to reliably sequence these specific regions.

q-bio.GN↗
arXiv2012

Characterizing Ranked Chinese Syllable-to-Character Mapping Spectrum: A Bridge Between the Spoken and Written Chinese Language

One important aspect of the relationship between spoken and written Chinese is the ranked syllable-to-character mapping spectrum, which is the ranked list of syllables by the number of characters that map to the syllable. Previously, this spectrum is analyzed for more than 400 syllables without distinguishing the four intonations. In the current study, the spectrum with 1280 toned syllables is analyzed by logarithmic function, Beta rank function, and piecewise logarithmic function. Out of the three fitting functions, the two-piece logarithmic function fits the data the best, both by the smallest sum of squared errors (SSE) and by the lowest Akaike information criterion (AIC) value. The Beta rank function is the close second. By sampling from a Poisson distribution whose parameter value is chosen from the observed data, we empirically estimate the $p$-value for testing the two-piece-logarithmic-function being better than the Beta rank function hypothesis, to be 0.16. For practical purposes, the piecewise logarithmic function and the Beta rank function can be considered a tie.

cs.CL↗
arXiv2012

Analyses of Baby Name Popularity Distribution in U.S. for the Last 131 Years

We examine the complete dataset of baby name popularity collected by U.S. Social Security Administration for the last 131 years (1880-2010). The ranked baby name popularity can be fitted empirically by a piecewise function consisting of Beta function for the high-ranking names and power-law function for low-ranking names, but not power-law (Zipf's law) or Beta function by itself.

nlin.AO↗
arXiv2011

Effective Sample Size: Quick Estimation of the Effect of Related Samples in Genetic Case-Control Association Analyses

Affected relatives are essential for pedigree linkage analysis, however, they cause a violation of the independent sample assumption in case-control association studies. To avoid the correlation between samples, a common practice is to take only one affected sample per pedigree in association analysis. Although several methods exist in handling correlated samples, they are still not widely used in part because these are not easily implemented, or because they are not widely known. We advocate the effective sample size method as a simple and accessible approach for case-control association analysis with correlated samples. This method modifies the chi-square test statistic, p-value, and 95% confidence interval of the odds-ratio by replacing the apparent number of allele or genotype counts with the effective ones in the standard formula, without the need for specialized computer programs. We present a simple formula for calculating effective sample size for many types of relative pairs and relative sets. For allele frequency estimation, the effective sample size method captures the variance inflation exactly. For genotype frequency, simulations showed that effective sample size provides a satisfactory approximation. A gene which is previously identified as a type 1 diabetes susceptibility locus, the interferon-induced helicase gene (IFIH1), is shown to be significantly associated with rheumatoid arthritis when the effective sample size method is applied. This significant association is not established if only one affected sib per pedigree were used in the association analysis. Relationship between the effective sample size method and other methods -- the generalized estimation equation, variance of eigenvalues for correlation matrices, and genomic controls -- are discussed.

q-bio.QM↗
arXiv2011

Fitting Ranked English and Spanish Letter Frequency Distribution in U.S. and Mexican Presidential Speeches

The limited range in its abscissa of ranked letter frequency distributions causes multiple functions to fit the observed distribution reasonably well. In order to critically compare various functions, we apply the statistical model selections on ten functions, using the texts of U.S. and Mexican presidential speeches in the last 1-2 centuries. Dispite minor switching of ranking order of certain letters during the temporal evolution for both datasets, the letter usage is generally stable. The best fitting function, judged by either least-square-error or by AIC/BIC model selection, is the Cocho/Beta function. We also use a novel method to discover clusters of letters by their observed-over-expected frequency ratios.

cs.CL↗
arXiv2009

Partial correlation analysis indicates causal relationships between GC-content, exon density and recombination rate in the human genome

{\bf Background}: Several features are known to correlate with the GC-content in the human genome, including recombination rate, gene density and distance to telomere. However, by testing for pairwise correlation only, it is impossible to distinguish direct associations from indirect ones and to distinguish between causes and effects. {\bf Results}: We use partial correlations to construct partially directed graphs for the following four variables: GC-content, recombination rate, exon density and distance-to-telomere. Recombination rate and exon density are unconditionally uncorrelated, but become inversely correlated by conditioning on GC-content. This pattern indicates a model where recombination rate and exon density are two independent causes of GC-content variation. {\bf Conclusions}: Causal inference and graphical models are useful methods to understand genome evolution and the mechanisms of isochore evolution in the human genome.

q-bio.GN↗
arXiv2009

Copy-number-variation and copy-number-alteration region detection by cumulative plots

Background: Regions with copy number variations (in germline cells) or copy number alteration (in somatic cells) are of great interest for human disease gene mapping and cancer studies. They represent a new type of mutation and are larger-scaled than the single nucleotide polymorphisms. Using genotyping microarray for copy number variation detection has become standard, and there is a need for improving analysis methods. Results: We apply the cumulative plot to the detection of regions with copy number variation/alteration, on samples taken from a chronic lymphocytic leukemia patient. Two sets of whole-genome genotyping of 317k single nucleotide polymorphisms, one from the normal cell and another from the cancer cell, are analyzed. We demonstrate the utility of cumulative plot in detecting a 9Mb (9 x 10^6 bases) hemizygous deletion and 1Mb homozygous deletion on chromosome 13. We also show the possibility to detect smaller copy number variation/alteration regions below the 100kb range. Conclusions: As a graphic tool, the cumulative plot is an intuitive and a scale-free (window-less) way for detecting copy number variation/alteration regions, especially when such regions are small.

q-bio.GN↗
arXiv2009

Exploring Case-Control Genetic Association Tests Using Phase Diagrams

Background: By a new concept called "phase diagram", we compare two commonly used genotype-based tests for case-control genetic analysis, one is a Cochran-Armitage trend test (CAT test at $x=0.5$, or CAT0.5) and another (called MAX2) is the maximization of two chi-square test results: one from the two-by-two genotype count table that combines the baseline homozygotes and heterozygotes, and another from the table that combines heterozygotes with risk homozygotes. CAT0.5 is more suitable for multiplicative disease models and MAX2 is better for dominant/recessive models. Methods: We define the CAT0.5-MAX2 phase diagram on the disease model space such that regions where MAX2 is more powerful than CAT0.5 are separated from regions where the CAT0.5 is more powerful, and the task is to choose the appropriate parameterization to make the separation possible. Results: We find that using the difference of allele frequencies ($δ_p$) and the difference of Hardy-Weinberg disequilibrium coefficients ($δ_ε$) can separate the two phases well, and the phase boundaries are determined by the angle $tan^{-1}(δ_p/δ_ε)$, which is an improvement over the disease model selection using $δ_ε$ only. Conclusions: We argue that phase diagrams similar to the one for CAT0.5-MAX2 have graphical appeals in understanding power performance of various tests, clarifying simulation schemes, summarizing case-control datasets, and guessing the possible mode of inheritance.

q-bio.PE↗
arXiv2009

Two-Parameter Characterization of Chromosome-Scale Recombination Rate

The genome-wide recombination rate ($RR$) of a species is often described by one parameter, the ratio between total genetic map length ($G$) and physical map length ($P$), measured in centiMorgans per Megabase (cM/Mb). The value of this parameter varies greatly between species, but the cause for these differences is not entirely clear. A constraining factor of overall $RR$ in a species, which may cause increased $RR$ for smaller chromosomes, is the requirement of at least one chiasma per chromosome (or chromosome-arm) per meiosis. In the present study, we quantify the relative excess of recombination events on smaller chromosomes by a linear regression model, which relates the genetic length of chromosomes to their physical length. We find for several species that the two-parameter regression, $G= G_0 + k \cdot P$ provides a better characterization of the relationship between genetic and physical map length than the one-parameter regression that runs through the origin. A non-zero intercept ($G_0$) indicates a relative excess of recombination on smaller chromosomes in a genome. Given $G_0$, the parameter $k$ predicts the increase of genetic map length over the increase of physical map length. The observed values of $G_0$ have a similar magnitude for diverse species, whereas $k$ varies by two orders of magnitude. The implications of this strategy for the genetic maps of human, mouse, rat, chicken, honeybee, worm and yeast are discussed.

q-bio.GN↗
arXiv2009

Fractal Characterizations of MAX Statistical Distribution in Genetic Association Studies

Two non-integer parameters are defined for MAX statistics, which are maxima of $d$ simpler test statistics. The first parameter, $d_{MAX}$, is the fractional number of tests, representing the equivalent numbers of independent tests in MAX. If the $d$ tests are dependent, $d_{MAX} < d$. The second parameter is the fractional degrees of freedom $k$ of the chi-square distribution $χ^2_k$ that fits the MAX null distribution. These two parameters, $d_{MAX}$ and $k$, can be independently defined, and $k$ can be non-integer even if $d_{MAX}$ is an integer. We illustrate these two parameters using the example of MAX2 and MAX3 statistics in genetic case-control studies. We speculate that $k$ is related to the amount of ambiguity of the model inferred by the test. In the case-control genetic association, tests with low $k$ (e.g. $k=1$) are able to provide definitive information about the disease model, as versus tests with high $k$ (e.g. $k=2$) that are completely uncertain about the disease model. Similar to Heisenberg's uncertain principle, the ability to infer disease model and the ability to detect significant association may not be simultaneously optimized, and $k$ seems to measure the level of their balance.

q-bio.QM↗
arXiv2008

Genotype-based Case-Control Analysis, Violation of Hardy-Weinberg Equilibrium, and Phase Diagrams

We study in detail a particular statistical method in genetic case-control analysis, labeled "genotype-based association", in which the two test results from assuming dominant and recessive model are combined in one optimal output. This method differs both from the allele-based association which artificially doubles the sample size, and the direct chi-square test on 3-by-2 contingency table which may overestimate the degree of freedom. We conclude that the comparative advantage (or disadvantage) of the genotype-based test over the allele-based test mainly depends on two parameters, the allele frequency difference delta and the Hardy-Weinberg disequilibrium coefficient difference delta_epsilon. Six different situations, called "phases", characterized by the two X^2 test statistics in allele-based and genotype-based test, are well separated in the phase diagram parameterized by delta and delta_epsilon. For two major groups of phases, a single parameter theta = tan^-1 (delta/delta_epsilon) is able to achieves an almost perfect phase separation. We also applied the analytic result to several types of disease models. It is shown that for dominant and additive models, genotype-based tests are favored over allele-based tests.

q-bio.QM↗
arXiv2006

Large-scale Oscillation of Structure-Related DNA Sequence Features in Human Chromosome 21

Human chromosome 21 is the only chromosome in human genome that exhibits oscillation of (G+C)-content of cycle length of hundreds kilobases (500 kb near the right telomere). We aim at establishing the existence of similar periodicity in structure-related sequence features in order to relate this (G+C)% oscillation to other biological phenomena. The following quantities are shown to oscillate with the same 500kb periodicity in human chromosome 21: binding energy calculated by two sets of dinucleotide-based thermodynamic parameters, AA/TT and AAA/TTT bi-/tri-nucleotide density, 5'-TA-3' dinucleotide density, and signal for 10/11-base periodicity of AA/TT or AAA/TTT. These intrinsic quantities are related to structural features of the double helix of DNA molecules, such as base-pair binding, untwisting/unwinding, stiffness, and a putative tendency for nucleosome formation.

q-bio.GN↗
arXiv2006

Overlapping Probabilities of Top Ranking Gene Lists, Hypergeometric Distribution, and Stringency of Gene Selection Criterion

When the same set of genes appear in two top ranking gene lists in two different studies, it is often of interest to estimate the probability for this being a chance event. This overlapping probability is well known to follow the hypergeometric distribution. Usually, the lengths of top-ranking gene lists are assumed to be fixed, by using a pre-set criterion on, e.g., $p$-value for the t-test. We investigate how overlapping probability changes with the gene selection criterion, or simply, with the length of the top-ranking gene lists. It is concluded that overlapping probability is indeed a function of the gene list length, and its statistical significance should be quoted in the context of gene selection criterion.

q-bio.QM↗
arXiv2006

Does Logarithm Transformation of Microarray Data Affect Ranking Order of Differentially Expressed Genes?

A common practice in microarray analysis is to transform the microarray raw data (light intensity) by a logarithmic transformation, and the justification for this transformation is to make the distribution more symmetric and Gaussian-like. Since this transformation is not universally practiced in all microarray analysis, we examined whether the discrepancy of this treatment of raw data affect the "high level" analysis result. In particular, whether the differentially expressed genes as obtained by $t$-test, regularized t-test, or logistic regression have altered rank orders due to presence or absence of the transformation. We show that as much as 20%--40% of significant genes are "discordant" (significant only in one form of the data and not in both), depending on the test being used and the threshold value for claiming significance. The t-test is more likely to be affected by logarithmic transformation than logistic regression, and regularized $t$-test more affected than t-test. On the other hand, the very top ranking genes (e.g. up to top 20--50 genes, depending on the test) are not affected by the logarithmic transformation.

q-bio.QM↗
arXiv2004

An Unusual 500,000 Bases Long Oscillation of Guanine and Cytosine Content in Human Chromosome 21

An oscillation with a period of around 500 kb in guanine and cytosine content (GC%) is observed in the DNA sequence of human chromosome 21. This oscillation is localized in the rightmost one-eighth region of the chromosome, from 43.5 Mb to 46.5 Mb. Five cycles of oscillation are observed in this region with six GC-rich peaks and five GC-poor valleys. The GC-poor valleys comprise regions with low density of CpG islands and, alternating between the two DNA strands, low gene density regions. Consequently, the long-range oscillation of GC% result in spacing patterns of both CpG island density, and to a lesser extent, gene densities.

q-bio.GN↗
arXiv2004

Universal 1/f noise, cross-overs of scaling exponents, and chromosome specific patterns of GC content in DNA sequences of the human genome

Spatial fluctuations of guanine and cytosine base content (GC%) are studied by spectral analysis for the complete set of human genomic DNA sequences. We find that (i) the 1/f^alpha decay is universally observed in the power spectra of all twenty-four chromosomes, and that (ii) the exponent alpha \approx 1 extends to about 10^7 bases, one order of magnitude longer than what has previously been observed. We further find that (iii) almost all human chromosomes exhibit a cross-over from alpha_1 \approx 1 (1/f^alpha_1) at lower frequency to alpha_2 < 1 (1/f^alpha_2) at higher frequency, typically occurring at around 30,000--100,000 bases, while (iv) the cross-over in this frequency range is virtually absent in human chromosome 22. In addition to the universal 1/f^alpha noise in power spectra, we find (v) several lines of evidence for chromosome-specific correlation structures, including a 500,000 bases long oscillation in human chromosome 21. The universal 1/f^alpha spectrum in human genome is further substantiated by a resistance to variance reduction in guanine and cytosine content when the window size is increased.

q-bio.GN↗
arXiv2004

Spectral Analysis of Guanine and Cytosine Fluctuations of Mouse Genomic DNA

We study global fluctuations of the guanine and cytosine base content (GC%) in mouse genomic DNA using spectral analyses. Power spectra S(f) of GC% fluctuations in all nineteen autosomal and two sex chromosomes are observed to have the universal functional form S(f) \sim 1/f^alpha (alpha \approx 1) over several orders of magnitude in the frequency range 10^-7< f < 10^-5 cycle/base, corresponding to long-ranging GC% correlations at distances between 100 kb and 10 Mb. S(f) for higher frequencies (f > 10^-5 cycle/base) shows a flattened power-law function with alpha < 1 across all twenty-one chromosomes. The substitution of about 38% interspersed repeats does not affect the functional form of S(f), indicating that these are not predominantly responsible for the long-ranged multi-scale GC% fluctuations in mammalian genomes. Several biological implications of the large-scale GC% fluctuation are discussed, including neutral evolutionary history by DNA duplication, chromosomal bands, spatial distribution of transcription units (genes), replication timing, and recombination hot spots.

q-bio.GN↗