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  1. Abstract Background

    Cells progressing from an early state to a developed state give rise to lineages in cell differentiation. Knowledge of these lineages is central to developmental biology. Each biological lineage corresponds to a trajectory in a dynamical system. Emerging single-cell technologies such as single-cell RNA sequencing can capture molecular abundance in diverse cell types in a developing tissue. Many computational methods have been developed to infer trajectories from single-cell data. However, to our knowledge, none of the existing methods address the problem of determining the existence of a trajectory in observed data before attempting trajectory inference.


    We introduce a method to identify the existence of a trajectory using three graph-based statistics. A permutation test is utilized to calculate the empirical distribution of the test statistic under the null hypothesis that a trajectory does not exist. Finally, ap-value is calculated to quantify the statistical significance for the presence of trajectory in the data.


    Our work contributes new statistics to assess the level of uncertainty in trajectory inference to increase the understanding of biological system dynamics.

  2. Countering prior beliefs that epistasis is rare, genomics advancements suggest the other way. Current practice often filters out genomic loci with low variant counts before detecting epistasis. We argue that this practice is far from optimal because it can throw away strong epistatic patterns. Instead, we present the compensated Sharma–Song test to infer genetic epistasis in genome-wide association studies by differential departure from independence. The test does not require a minimum number of replicates for each variant. We also introduce algorithms to simulate epistatic patterns that differentially depart from independence. Using two simulators, the test performed comparably to the original Sharma–Song test when variant frequencies at a locus are marginally uniform; encouragingly, it has a marked advantage over alternatives when variant frequencies are marginally nonuniform. The test further revealed uniquely clean epistatic variants associated with chicken abdominal fat content that are not prioritized by other methods. Genes involved in most numbers of inferred epistasis between single nucleotide polymorphisms (SNPs) belong to pathways known for obesity regulation; many top SNPs are located on chromosome 20 and in intergenic regions. Measuring differential departure from independence, the compensated Sharma–Song test offers a practical choice for studying epistasis robust to nonuniform genetic variant frequencies.
    Free, publicly-accessible full text available May 23, 2023
  3. Iakoucheva, Lilia M. (Ed.)
    The complexity of biological processes such as cell differentiation is reflected in dynamic transitions between cellular states. Trajectory inference arranges the states into a progression using methodologies propelled by single-cell biology. However, current methods, all returning a best trajectory, do not adequately assess statistical significance of noisy patterns, leading to uncertainty in inferred trajectories. We introduce a tree dimension test for trajectory presence in multivariate data by a dimension measure of Euclidean minimum spanning tree, a test statistic, and a null distribution. Computable in linear time to tree size, the tree dimension measure summarizes the extent of branching more effectively than globally insensitive number of leaves or tree diameter indifferent to secondary branches. The test statistic quantifies trajectory presence and its null distribution is estimated under the null hypothesis of no trajectory in data. On simulated and real single-cell datasets, the test outperformed the intuitive number of leaves and tree diameter statistics. Next, we developed a measure for the tissue specificity of the dynamics of a subset, based on the minimum subtree cover of the subset in a minimum spanning tree. We found that tissue specificity of pathway gene expression dynamics is conserved in human and mouse development: several signalmore »transduction pathways including calcium and Wnt signaling are most tissue specific, while genetic information processing pathways such as ribosome and mismatch repair are least so. Neither the tree dimension test nor the subset specificity measure has any user parameter to tune. Our work opens a window to prioritize cellular dynamics and pathways in development and other multivariate dynamical systems.« less
  4. Abstract Motivation

    Computer inference of biological mechanisms is increasingly approachable due to dynamically rich data sources such as single-cell genomics. Inferred molecular interactions can prioritize hypotheses for wet-lab experiments to expedite biological discovery. However, complex data often come with unwanted biological or technical variations, exposing biases over marginal distribution and sample size in current methods to favor spurious causal relationships.


    Considering function direction and strength as evidence for causality, we present an adapted functional chi-squared test (AdpFunChisq) that rewards functional patterns over non-functional or independent patterns. On synthetic and three biology datasets, we demonstrate the advantages of AdpFunChisq over 10 methods on overcoming biases that give rise to wide fluctuations in the performance of alternative approaches. On single-cell multiomics data of multiple phenotype acute leukemia, we found that the T-cell surface glycoprotein CD3 delta chain may causally mediate specific genes in the viral carcinogenesis pathway. Using the causality-by-functionality principle, AdpFunChisq offers a viable option for robust causal inference in dynamical systems.

    Availability and implementation

    The AdpFunChisq test is implemented in the R package ‘FunChisq’ (2.5.2 or above) at All other source code along with pre-processed data is available at Code Ocean

    Supplementary information

    Supplementary materials are available at Bioinformatics online.

  5. Round genomes are found in bacteria, plant chloroplasts, and mitochondria. Genetic or epigenetic marks can present biologically interesting clusters along a circular genome. The circular data clustering problem groups N points on a circle into K clusters to minimize the within-cluster sum of squared distances. Repeatedly applying the K-means algorithm takes quadratic time, impractical for large circular datasets. To overcome this issue, we developed a fast, reproducible, and optimal circular clustering (FOCC) algorithm of worst-case O(KN log^2 N) time. The core is a fast optimal framed clustering algorithm, which we designed by integrating two divide-and-conquer and one bracket dynamic programming strategies. The algorithm is optimal based on a property of monotonic increasing cluster borders over frames on linearized data. On clustering 50,000 circular data points, FOCC outruns brute-force or heuristic circular clustering by three orders of magnitude. We produced clusters of CpG sites and genes along three round genomes, exhibiting higher quality than heuristic clustering. More broadly, the presented subquadratic-time algorithms offer the fastest known solution to not only framed and circular clustering, but also angular, periodical, and looped clustering. We implemented these algorithms in the R package OptCirClust (
  6. Kelso, Janet (Ed.)
    Abstract Motivation Genetic or epigenetic events can rewire molecular networks to induce extraordinary phenotypical divergences. Among the many network rewiring approaches, no model-free statistical methods can differentiate gene-gene pattern changes not attributed to marginal changes. This may obscure fundamental rewiring from superficial changes. Results Here we introduce a model-free Sharma-Song test to determine if patterns differ in the second order, meaning that the deviation of the joint distribution from the product of marginal distributions is unequal across conditions. We prove an asymptotic chi-squared null distribution for the test statistic. Simulation studies demonstrate its advantage over alternative methods in detecting second-order differential patterns. Applying the test on three independent mammalian developmental transcriptome datasets, we report a lower frequency of co-expression network rewiring between human and mouse for the same tissue group than the frequency of rewiring between tissue groups within the same species. We also find secondorder differential patterns between microRNA promoters and genes contrasting cerebellum and liver development in mice. These patterns are enriched in the spliceosome pathway regulating tissue specificity. Complementary to previous mammalian comparative studies mostly driven by first-order effects, our findings contribute an understanding of system-wide second-order gene network rewiring within and across mammalian systems. Second-order differentialmore »patterns constitute evidence for fundamentally rewired biological circuitry due to evolution, environment, or disease. Availability The generic Sharma-Song test is available from the R package ‘DiffXTables’ at Other code and data are described in Methods. Supplementary information Supplementary data are available at Bioinformatics online.« less
  7. The complexity, dynamics, and scale of data acquired by modern biotechnology increasingly favor model-free computational methods that make minimal assumptions about underlying biological mechanisms. For example, single-cell transcriptome and proteome data have a throughput several orders more than bulk methods. Many model-free statistical methods for pattern discovery such as mutual information and chi-squared tests, however, require discrete data. Most discretization methods minimize squared errors for each variable independently, not necessarily retaining joint patterns. To address this issue, we present a joint grid discretization algorithm that preserves clusters in the original data. We evaluated this algorithm on simulated data to show its advantage over other methods in maintaining clusters as measured by the adjusted Rand index. We also show it promotes global functional patterns over independent patterns. On single-cell proteome and transcriptome of leukemia and healthy blood, joint grid discretization captured known protein-to-RNA regulatory relationships, while revealing previously unknown interactions. As such, the joint grid discretization is applicable as a data transformation step in associative, functional, and causal inference of molecular interactions fundamental to systems biology. The developed software is publicly available at
  8. Patterns of two molecules across biological systems are often labeled as conserved or differential. We argue that this classification is insufficient. Here, we introduce three types of relationships across systems. Upon stimuli, a type-0 pattern arises from conserved circuitry with active conserved trajectory; a type-1 pattern is conserved circuitry with active differential trajectory; a type-2 pattern is rewired circuitry with active trajectory. We present a 1st-order marginal change test, prove its optimality, and establish its asymptotic chi-squared distribution under the null hypothesis of identical marginals across conditions. The test outperformed other methods in detecting 1st-order difference in simulation studies. We also introduce a zeroth-order strength test to assess association of two variables across systems. We compared gene co-expression networks of planktonic microbial communities in cold California coastal water against the warm water of North Pacific Subtropical Gyre. The frequency of type-1 patterns is much higher than those of type-2 and type-0 patterns, revealing that the microbial communities are mostly conserved in molecular circuitry but responded differentially to ocean habitats. Type-1 and 2 patterns are enriched with genes known to respond to environmental changes or stress; type-0 patterns involve genes having essential function such as photosynthesis and general transcription. Our workmore »provides a deep understanding to effects of the environment on gene regulation in microbial communities. The method is generally applicable to other biological systems. All tests are provided in the R package 'DiffXTables' at Other source code and lists of significant gene patterns are available at« less
  9. Abstract Motivation Chromosomal patterning of gene expression in cancer can arise from aneuploidy, genome disorganization, or abnormal DNA methylation. To map such patterns, we introduce a weighted univariate clustering algorithm to guarantee linear runtime, optimality, and reproducibility. Results We present the chromosome clustering method, establish its optimality and runtime, and evaluate its performance. It uses dynamic programming enhanced with an algorithm to reduce search-space in-place to decrease runtime overhead. Using the method, we delineated outstanding genomic zones in 17 human cancer types. We identified strong continuity in dysregulation polarity—dominance by either up- or down-regulated genes in a zone—along chromosomes in all cancer types. Significantly polarized dysregulation zones specific to cancer types are found, offering potential diagnostic biomarkers. Unreported previously, a total of 109 loci with conserved dysregulation polarity across cancer types give insights into pan-cancer mechanisms. Efficient chromosomal clustering opens a window to characterize molecular patterns in cancer genome and beyond. Availability Weighted univariate clustering algorithms are implemented within the R package ‘Ckmeans.1d.dp’ (4.0.0 or above), freely available at Supplementary information Supplementary data are available at Bioinformatics online.
  10. Functional dependency can lead to discoveries of new mechanisms not possible via symmetric association. Most asymmetric methods for causal direction inference are not driven by the function-versus-independence question. A recent exact functional test (EFT) was designed to detect functionally dependent patterns model-free with an exact null distribution. However, the EFT lacked a theoretical justification, had not been compared with other asymmetric methods, and was practically slow. Here, we prove the functional optimality of the EFT statistic, demonstrate its advantage in functional inference accuracy over five other methods, and develop a branch-and-bound algorithm with dynamic and quadratic programming to run at orders of magnitude faster than its previous implementation. Our results make it practical to answer the exact functional dependency question arising from discovery-driven artificial intelligence applications. Software that implements EFT is freely available in the R package 'FunChisq' (≥2.5.0) at