Extracting Wave Structure from Biological Data with Application to Responses in Turtle Visual Cortex

Waves have long been thought to be a fundamental mechanism for communicating information within a medium and are widely observed in biological systems. However, a quantitative analysis of biological waves is confounded by the variability and complexity of the response. This paper proposes a robust technique for extracting wave structure from experimental data by calculating "wave subspaces" from the KL decomposition of the data set. If a wave subspace contains a substantial portion of the data set energy during a particular time interval, one can deduce the structure of the wave and potentially isolate its information content. This paper uses the wave subspace technique to extract and compare wave structure in data from three different preparations of the turtle visual cortex. The paper demonstrates that wave subspace caricatures from the three cortical preparations have qualitative similarities. In the numerical model, where information about the underlying dynamics is available, wave subspace landmarks are related to activation and changes in behavior of other dynamic variables besides membrane potential.     

MAPRes: an efficient method to analyze protein sequence around post-translational modification sites

Functional switches are often regulated by dynamic protein modifications. Assessing protein functions, in vivo, and their functional switches remains still a great challenge in this age of development. An alternative methodology based on in silico procedures may facilitate assessing the multifunctionality of proteins and, in addition, allow predicting functions of those proteins that exhibit their functionality through transitory modifications. Extensive research is ongoing to predict the sequence of protein modification sites and analyze their dynamic nature. This study reports the analysis performed on phosphorylation, Phospho.ELM (version 3.0) and glycosylation, OGlycBase (version 6.0) data for mining association patterns utilizing a newly developed algorithm, MAPRes. This method, MAPRes (Mining Association Patterns among preferred amino acid residues in the vicinity of amino acids targeted for post-translational modifications), is based on mining association among significantly preferred amino acids of neighboring sequence environment and modification sites themselves. Association patterns arrived at by association pattern/rule mining were in significant conformity with the results of different approaches. However, attempts to analyze substrate sequence environment of phosphorylation sites catalyzed for Tyr kinases and the sequence data for O-GlcNAc modification were not successful, due to the limited data available. Using the MAPRes algorithm for developing an association among PTM site with its vicinal amino acids is a valid method with many potential uses: this is indeed the first method ever to apply the association pattern mining technique to protein post-translational modification data.     

Beyond LDL oxidation: ROS in vascular signal transduction

The notion that oxidative stress contributes to the pathogenesis of vascular disease was originally driven by observations that low-density lipoprotein (LDL) modification is a prominent feature of atherosclerosis. More recently, it has become clear that the relation between oxidative stress and vascular disease goes beyond LDL oxidation and involves cellular production of reactive oxygen species (ROS). Considerable data now indicate that ROS represent an important means of cellular signaling, although the precise mechanisms whereby ROS accomplish this function remain unclear. Emerging data point to protein thiol groups as important targets for post-translational protein modification by ROS. In this review, the data linking ROS to cell signaling is discussed and the notion that ROS mediate a vascular "injury" response is proposed.     

基于ChIP-seq的差异组蛋白修饰区域的筛选

组蛋白修饰是在基因组水平上起到重要调控作用的表观遗传修饰,随着ChIP-Seq的广泛使用,高通量数据的积累,为从全基因组研究组蛋白修饰模式奠定了基础。但目前缺乏在多样本间筛选疾病相关的调控区域的方法,因而本文开发了一种多细胞系的差异筛选算法来识别差异组蛋白修饰区域。本文通过窗口移动法来估计组蛋白修饰水平,并根据信息熵理论定量各个细胞系之间的差异。基于随机背景来确定差异显著性阈值。利用此算法来筛选人类全基因组9个细胞系间H3K4me3差异的区域,结果显示这些区域显著富集在基因启动子上和其他重要的染色质状态上,且与先前人们发现的活性启动子染色质状态显著重叠。通过文献挖掘进一步证实了与白血病相关的基因组标记。这些结果表明基于熵的策略可有效地挖掘多细胞系间以及与疾病相关的差异组蛋白修饰。     

A statistical framework for testing modularity in multidimensional data

Modular variation of multivariate traits results from modular distribution of effects of genetic and epigenetic interactions among those traits. However, statistical methods rarely detect truly modular patterns, possibly because the processes that generate intramodular associations may overlap spatially. Methodologically, this overlap may cause multiple patterns of modularity to be equally consistent with observed covariances. To deal with this indeterminacy, the present study outlines a framework for testing a priori hypotheses of modularity in which putative modules are mathematically represented as multidimensional subspaces embedded in the data. Model expectations are computed by subdividing the data into arrays of variables, and intermodular interactions are represented by overlapping arrays. Covariance structures are thus modeled as the outcome of complex and nonorthogonal intermodular interactions. This approach is demonstrated by analyzing mandibular modularity in nine rodent species. A total of 620 models are fit to each species, and the most strongly supported are heuristically modified to improve their fit. Five modules common to all species are identified, which approximately map to the developmental modules of the mandible. Within species, these modules are embedded within larger "super-modules," suggesting that these conserved modules act as building blocks from which covariation patterns are built.     

A late developmental change in lysosomal enzyme sulfation specific to newly synthesized proteins in Dictyostelium discoideum

During development in Dictyostelium discoideum, several lysosomal glycosidases undergo changes in post-translational modification that are thought to involve differences in the extent of sulfation or phosphorylation, and appear to be required for the maintenance of cellular enzyme activity late in development. We have used monoclonal antibodies specific to the lysosomal enzyme alpha-mannosidase-1 to study the major late (12 hr) developmental change in the modification system. Pulse-chase experiments performed both early and late in development reveal that the substrate for the late form of modification is restricted to newly synthesized alpha-mannosidase-1 precursor protein. We have identified one modification difference between the two developmentally distinct isozymes of alpha-mannosidase-1: 35SO4 pulse-chase data show that the newly synthesized "late" enzyme precursor is significantly undersulfated in comparison with the enzyme synthesized early in development. This apparent lack of sulfation is associated with the lack of acquisition of endoglycosidase H resistance. By contrast, an aggregation-deficient mutant, which is defective with regard to the accumulation of alpha-mannosidase-1 activity late in development, synthesizes the "early" sulfated form of the enzyme throughout development. We conclude that the late developmental change in post-translational modification specifically involves one of the biochemical steps in which the N-linked oligosaccharide side chains of the newly synthesized alpha-mannosidase-1 precursor are modified by sulfation.     

Application of projection pursuit based robust principal component analysis to ECG enhancement

The paper presents an application of principal component analysis (PCA) to ECG processing. For this purpose the ECG beats are time-aligned and stored in the columns of an auxiliary matrix. The matrix, considered as a set of multidimensional variables, undergoes PCA. Reconstruction of the respective columns on the basis of a low dimensional principal subspace leads to the enhancement of the stored ECG beats. A few modifications of this classical approach to ECG signal filtering by means of a multivariate analysis are introduced. The first one is based on replacing the classical PCA by its robust extension. The second consists in replacing the analysis of the whole synchronized beats by the analysis of shorter signal segments. This creates the background for the third modification, which introduces the concept of variable dimensions of the subspaces corresponding to different parts of ECG beats. The experiments performed show that introduction of the respective modifications significantly improves the classical approach to ECG processing by application of principal component analysis.     

SysPTM: A Systematic Resource for Proteomic Research on Post-translational Modifications

With the rapid expansion of protein post-translational modification (PTM) research based on large-scale proteomic work, there is an increasing demand for a suitable repository to analyze PTM data. Here we present a curated, web-accessible PTM data base, SysPTM. SysPTM provides a systematic and sophisticated platform for proteomic PTM research equipped not only with a knowledge base of manually curated multi-type modification data but also with four fully developed, in-depth data mining tools. Currently, SysPTM contains data detailing 117,349 experimentally determined PTM sites on 33,421 proteins involving nearly 50 PTM types, curated from public resources including five data bases and four web servers and more than one hundred peer-reviewed mass spectrometry papers. Protein annotations including Pfam domains, KEGG pathways, GO functional classification, and ortholog groups are integrated into the data base. Four online tools have been developed and incorporated, including PTMBlast, to compare a user''s PTM dataset with PTM data in SysPTM; PTMPathway, to map PTM proteins to KEGG pathways; PTMPhylog, to discover potentially conserved PTM sites; and PTMCluster, to find clusters of multi-site modifications. The workflow of SysPTM was demonstrated by analyzing an in-house phosphorylation dataset identified by MS/MS. It is shown that in SysPTM, the role of single-type and multi-type modifications can be systematically investigated in a full biological context. SysPTM could be an important contribution to modificomics research. SysPTM is freely available online at www.sysbio.ac.cn/SysPTM.Post-translational modifications (PTMs)¹ are various processing events that change the maturity, activity, and/or turnover of proteins. More than 200 different types of PTMs have been found, with new ones still being reported (1). PTMs not only change the physicochemical properties of proteins (2) but also dynamically regulate various biological events such as protein degradation, subcellular localization, conformational change, protein-protein interaction, and signal transduction (3–5). Previous studies have revealed the central roles of PTMs in human health and disease. For example, phosphorylation of pRB1 has been associated with tumorigenesis through controlling cell division (6); S-nitrosylation of parkin regulates its E3 ligase activity, resulting in protein accumulation in sporadic Parkinson disease (7); and defects in protein glycosylation have been related to several forms of congenital muscular dystrophy (8). Given this important role in health and disease, PTMs have been regarded as potential disease biomarkers or therapeutic targets. For example, Erlotinib (Tarceva), an inhibitor of epidermal growth factor receptor tyrosine kinase, has been approved by the Food and Drug Administration to treat non-small cell lung cancer (9); and histone deacetylase inhibitors have been demonstrated to have a potential therapeutic role in Huntington disease (10). The broad range of important roles played by PTMs in physiological and pathological processes has made PTM research an active field in recent years. Yet we remain limited in our knowledge of the full scope of PTM distribution on proteins and the precise location of PTM sites.There are two major kinds of experimental methods to identify PTMs: 1) traditional biological experiments such as radiolabeling PTM proteins (11), Western analysis with antibodies against specific modifications (12), and site-directed mutagenesis of potential modification sites (13); and 2) large-scale proteomic experiments, especially multiple-dimensional liquid chromatography tandem mass spectrometry. Traditional experiments are laborious and time-consuming, resulting in slow data accumulation. By contrast, more recent MS/MS experiments have led to the discovery of thousands of new phosphorylation (14), glycosylation (15), acetylation (16), sumoylation (17), S-nitrosylation (18), and other modification sites. For example, based on MS/MS data, more than 6,000 phosphopeptides have been reported in HeLa cells (14), and 159 candidate sumoylated proteins have been found in yeast (17). Although advanced technologies have allowed PTM data to accumulate rapidly, it is impossible to identify all PTM sites for a set of proteins in one experiment, due to biased modification enrichment related to experimental protocol, limited sensitivity of mass spectrometer instrumentation, and failures in spectrum matching. Data bases are needed to amass PTM data from various experiments for comprehensive understanding of PTMs.Most data bases for storing PTM information have fallen into two general classes. One class focuses on a single modification type, such as Phospho.ELM (19) for phosphorylation or O-GLYCBASE (20) for glycosylation. Although these data bases have been widely used, they are limited in utility due to recording only a single modification type. The other class of PTM data base is the primary protein data base; these data bases collect PTM information with multiple modification types but are more broadly focused on providing diverse information about proteins, rather than PTM information specifically. Swiss-Prot (21) and HPRD (22) are examples of such data bases. As compared with either of the above two types of data base, integrated PTM data bases are more desirable. One example is dbPTM (23), which integrated experimentally determined PTM information from four external data bases. PhosphoSite started the harvesting of phosphorylation sites from published literature with a focus on in vivo mammalian phosphorylation data (24), but recently it has expanded to integrate nine other modification types. Even integrated data bases, however, have not taken into full consideration the aforementioned quickly accumulating PTM data from MS/MS experiments. These data, many of which are reported in the published literature but not collected in any data base, continue to increase rapidly due to new experiments. Such a wealth of information should be incorporated more comprehensively into the current PTM knowledge domain.At the same time, the high-throughput nature and complexity of MS/MS data pose computational challenges for proteome-scale PTM analyses in a biological context. A pure data repository is insufficient for such tasks. Powerful computational tools must accompany data repositories to allow knowledge extraction.To address these needs, we developed a systematic resource for PTM research, SysPTM, consisting of a PTM data base and four analysis tools. The SysPTM data base incorporates the existing features of numerous previous data bases, with an emphasis on collecting modification datasets from MS/MS experiments reported in the literature. The current release of SysPTM (v1.1) contains data detailing 117,349 PTM sites on 33,421 proteins involving nearly 50 modification types. The four analysis tools are PTMBlast, PTMPathway, PTMPhylog, and PTMCluster, which, respectively, can compare user PTM datasets with PTM data stored in SysPTM, map PTM proteins to KEGG pathways, discover potentially conserved PTM sites, and find significant clusters of multi-site modifications.In this work, an in-house MS/MS phosphorylation dataset from mouse embryonic stem cells was analyzed to demonstrate the SysPTM workflow. SysPTM can be accessed online.     

Biological arm motion through reinforcement learning

The present paper discusses an optimal learning control method using reinforcement learning for biological systems with a redundant actuator. It is difficult to apply reinforcement learning to biological control systems because of the redundancy in muscle activation space. We solve this problem with the following method. First, we divide the control input space into two subspaces according to a priority order of learning and restrict the search noise for reinforcement learning to the first priority subspace. Then the constraint is reduced as the learning progresses, with the search space extending to the second priority subspace. The higher priority subspace is designed so that the impedance of the arm can be high. A smooth reaching motion is obtained through reinforcement learning without any previous knowledge of the arms dynamics.     

FLIPDock: docking flexible ligands into flexible receptors

Conformational changes of biological macromolecules when binding with ligands have long been observed and remain a challenge for automated docking methods. Here we present a novel protein-ligand docking software called FLIPDock (Flexible LIgand-Protein Docking) allowing the automated docking of flexible ligand molecules into active sites of flexible receptor molecules. In FLIPDock, conformational spaces of molecules are encoded using a data structure that we have developed recently called the Flexibility Tree (FT). While the FT can represent fully flexible ligands, it was initially designed as a hierarchical and multiresolution data structure for the selective encoding of conformational subspaces of large biological macromolecules. These conformational subspaces can be built to span a range of conformations important for the biological activity of a protein. A variety of motions can be combined, ranging from domains moving as rigid bodies or backbone atoms undergoing normal mode-based deformations, to side chains assuming rotameric conformations. In addition, these conformational subspaces are parameterized by a small number of variables which can be searched during the docking process, thus effectively modeling the conformational changes in a flexible receptor. FLIPDock searches the variables using genetic algorithm-based search techniques and evaluates putative docking complexes with a scoring function based on the AutoDock3.05 force-field. In this paper, we describe the concepts behind FLIPDock and the overall architecture of the program. We demonstrate FLIPDock's ability to solve docking problems in which the assumption of a rigid receptor previously prevented the successful docking of known ligands. In particular, we repeat an earlier cross docking experiment and demonstrate an increased success rate of 93.5%, compared to original 72% success rate achieved by AutoDock over the 400 cross-docking calculations. We also demonstrate FLIPDock's ability to handle conformational changes involving backbone motion by docking balanol to an adenosine-binding pocket of protein kinase A.     

Effects of Italian smoking regulation on rates of hospital admission for acute coronary events: a country-wide study

Background

Several studies have reported a reduction in acute coronary events (ACEs) in the general population after the enforcement of smoking regulations, although there is uncertainty concerning the magnitude of the effect of such interventions. We conducted a country-wide evaluation of the health effects of the introduction of a smoking ban in public places, using data on hospital admissions for ACEs from the Italian population after the implementation of a national smoking regulation in January 2005.

Methods and Findings

Rates of admission for ACEs in the 20 Italian regions from January 2002 to November 2006 were analysed using mixed-effect regression models that allowed for long-term trends and seasonality. Standard methods for interrupted time-series were adopted to assess the immediate and gradual effects of the smoking ban. Effect modification by age was investigated, with the assumption that exposure to passive smoking in public places would be greater among young people. In total, 936,519 hospital admissions for ACEs occurred in the Italian population during the study period. A 4% reduction in hospital admissions for ACEs among persons aged less than 70 years was evident after the introduction of the ban (Rate Ratio [RR], 0.96; 95% Confidence Interval [CI], 0.95–0.98). No effect was found among persons aged at least 70 years (RR 1.00; 95% CI 0.99–1.02). Effect modification by age was further suggested by analyses using narrower age categories.

Conclusions

Smoke-free policies can constitute a simple and inexpensive intervention for the prevention of cardiovascular diseases and thus should be included in prevention programmes.     

Bayesian robust inference for differential gene expression in microarrays with multiple samples

We consider the problem of identifying differentially expressed genes under different conditions using gene expression microarrays. Because of the many steps involved in the experimental process, from hybridization to image analysis, cDNA microarray data often contain outliers. For example, an outlying data value could occur because of scratches or dust on the surface, imperfections in the glass, or imperfections in the array production. We develop a robust Bayesian hierarchical model for testing for differential expression. Errors are modeled explicitly using a t-distribution, which accounts for outliers. The model includes an exchangeable prior for the variances, which allows different variances for the genes but still shrinks extreme empirical variances. Our model can be used for testing for differentially expressed genes among multiple samples, and it can distinguish between the different possible patterns of differential expression when there are three or more samples. Parameter estimation is carried out using a novel version of Markov chain Monte Carlo that is appropriate when the model puts mass on subspaces of the full parameter space. The method is illustrated using two publicly available gene expression data sets. We compare our method to six other baseline and commonly used techniques, namely the t-test, the Bonferroni-adjusted t-test, significance analysis of microarrays (SAM), Efron's empirical Bayes, and EBarrays in both its lognormal-normal and gamma-gamma forms. In an experiment with HIV data, our method performed better than these alternatives, on the basis of between-replicate agreement and disagreement.     

qDNAmod: a statistical model-based tool to reveal intercellular heterogeneity of DNA modification from SMRT sequencing data

In an isogenic cell population, phenotypic heterogeneity among individual cells is common and critical for survival of the population under different environment conditions. DNA modification is an important epigenetic factor that can regulate phenotypic heterogeneity. The single molecule real-time (SMRT) sequencing technology provides a unique platform for detecting a wide range of DNA modifications, including N6-methyladenine (6-mA), N4-methylcytosine (4-mC) and 5-methylcytosine (5-mC). Here we present qDNAmod, a novel bioinformatic tool for genome-wide quantitative profiling of intercellular heterogeneity of DNA modification from SMRT sequencing data. It is capable of estimating proportion of isogenic haploid cells, in which the same loci of the genome are differentially modified. We tested the reliability of qDNAmod with the SMRT sequencing data of Streptococcus pneumoniae strain ST556. qDNAmod detected extensive intercellular heterogeneity of DNA methylation (6-mA) in a clonal population of ST556. Subsequent biochemical analyses revealed that the recognition sequences of two type I restriction–modification (R-M) systems are responsible for the intercellular heterogeneity of DNA methylation initially identified by qDNAmod. qDNAmod thus represents a valuable tool for studying intercellular phenotypic heterogeneity from genome-wide DNA modification.     

Physiological state control of fermentation processes

In this article a novel approach to the control of fermentation processes is introduced. A "physiological state control approach" has been developed using the concept of representing fermentation processes through the current physiological state of the cell culture. No conventional mathematical model is required for the synthesis of such a control system.The main idea is based on the fact that during batch, feed-batch, or even continuous cultivation the physiological characteristics of the cell population, jointly expressed by the term "physiological state", are not constant but rather variable, which is reflected in expected or unexpected changes in the behavior of the control plant, and which requires flexible alteration of the current control strategy. The proposed approach involves decomposition of the physiological state space into several subspaces called "physiological situations." In every physiological situation the cell population expresses stable characteristics, and therefore an invariant control strategy can be effectively applied. The on-line functions of the physiological state control system consist of the calculation of physiological state variables, determination of the current physiological situation as an element of a previously defined set of known physiological situations, switching of the relevant control strategy, and calculation of the control action. Attention is focused on the synthesis of the novel and nonstandard part of the control system - the algorithm for online recognition of the current physiological state. To this end an effective approach, based on artificial intelligence methods, particularly fuzzy sets theory and pattern recognition theory, was developed. Its practical realization is demonstrated using data from a continuous fermentation process for single cell protein production.     

Modification by N-acetyltransferase 1 genotype on the association between dietary heterocyclic amines and colon cancer in a multiethnic study

OBJECTIVE: Colorectal cancer incidence is greater among African Americans, compared to whites in the U.S., and may be due in part to differences in diet, genetic variation at metabolic loci, and/or the joint effect of diet and genetic susceptibility. We examined whether our previously reported associations between meat-derived heterocyclic amine (HCA) intake and colon cancer were modified by N-acetyltransferase 1 (NAT1) or 2 (NAT2) genotypes and whether there were differences by race. METHODS: In a population-based, case-control study of colon cancer, exposure to HCAs was assessed using a food-frequency questionnaire with a meat-cooking and doneness module, among African Americans (217 cases and 315 controls) and whites (290 cases and 534 controls). RESULTS: There was no association with NAT1*10 versus NAT1-non*10 genotypes for colon cancer. Among whites, there was a positive association for NAT2-"rapid/intermediate" genotype [odds ratio (OR)=1.4; 95% confidence interval (CI)=1.0, 1.8], compared to the NAT2-"slow" that was not observed among African Americans. Colon cancer associations with HCA intake were modified by NAT1, but not NAT2, regardless of race. However, the "at-risk" NAT1 genotype differed by race. For example, among African Americans, the positive association with 2-amino-1-methyl-6-phenyl-imidazo[4,5-b]pyridine (PhIP) was confined to those with NAT1*10 genotype (OR=1.8; 95% CI=1.0, 3.3; P for interaction=0.02, comparing highest to lowest intake), but among whites, an association with 2-amino-3,8-dimethylimidazo[4,5-f]quinoxaline (MeIQx) was confined to those with NAT1-non*10 genotype (OR=1.9; 95% CI=1.1, 3.1; P for interaction=0.03). CONCLUSIONS: Our data indicate modification by NAT1 for HCA and colon cancer associations, regardless of race. Although the at-risk NAT1 genotype differs by race, the magnitude of the individual HCA-related associations in both race groups are similar. Therefore, our data do not support the hypothesis that NAT1 by HCA interactions contribute to differences in colorectal cancer incidence between African Americans and whites.     

Nucleosome-interacting proteins regulated by DNA and histone methylation

Modifications on histones or on DNA recruit proteins that regulate chromatin function. Here, we use nucleosomes methylated on DNA and on histone H3 in an affinity assay, in conjunction with a SILAC-based proteomic analysis, to identify "crosstalk" between these two distinct classes of modification. Our analysis reveals proteins whose binding to nucleosomes is regulated by methylation of CpGs, H3K4, H3K9, and H3K27 or a combination thereof. We identify the origin recognition complex (ORC), including LRWD1 as a subunit, to be a methylation-sensitive nucleosome interactor that is recruited cooperatively by DNA and histone methylation. Other interactors, such as the lysine demethylase Fbxl11/KDM2A, recognize nucleosomes methylated on histones, but their recruitment is disrupted by DNA methylation. These data establish SILAC nucleosome affinity purifications (SNAP) as a tool for studying the dynamics between different chromatin modifications and provide a modification binding "profile" for proteins regulated by DNA and histone methylation.     

Epigene conversion: a proposal with implications for gene mapping in humans.

Epigenetic modification of DNA is now recognized as a potentially important factor in the inheritance and expression of some mutations; its ability to complicate human genetic analysis is concurrently becoming apparent. One unusual form of epigenetic modification, dominant position-effect variegation (PEV), has been used as a model for Huntington disease. In dominant PEV, a fully dominant mutant phenotype results from stable epigenetic inactivation of an allele adjacent to the structural alteration (cis-inactivation) combined with a complementary inactivation of the homologous normal allele (trans-inactivation). We now propose that trans-inactivation of the normal allele may occasionally persist through meiosis. Such "epigene conversion" occurring at the Huntington disease locus in a few percent of meioses would largely account for the published anomalies in that region's genetic map. This concept could also explain anomalous linkage map data for other disease-causing alleles in humans.     

基于DNA弯曲度的H2A.Z核小体定位与修饰研究

在真核生物染色质中,H2A.Z是高度保守的组蛋白变异体,与转录调控、基因组的稳定性密切相关。为了探讨组蛋白修饰、DNA弯曲度与H2A.Z核小体定位三者之间的关联,在得到实验所测的相关数据后,利用MINE算法并结合皮尔逊相关系数在酵母全基因组的转录起始位点周围探讨了三者间的线性与非线性关系。其中MIC算法可以定量的得出数据之间关联度大小的值,用于衡量数据之间是否存在着关联,而皮尔逊相关系数则用于检查是否为线性关联。结果除了发现大部分组蛋白修饰种类和核小体定位之间存在着线性关联外,还探测到有两种组蛋白修饰数据(H4ac修饰与GCN4修饰)和核小体定位数据之间存在着以往未发现的非线性关系(大致呈正余弦函数),并从数据的生物背景(组蛋白修饰与核小体位置)上探讨了出现非线性现象的原因。