Undecidable Properties of Limit Set Dynamics of Cellular Automata

Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial properties of limit sets are undecidable. In this paper we consider properties of limit set dynamics, i.e. properties of the dynamics of Cellular Automata restricted to their limit sets. There can be no equivalent of Kari's Theorem for limit set dynamics. Anyway we show that there is a large class of undecidable properties of limit set dynamics, namely all properties of limit set dynamics which imply stability or the existence of a unique subshift attractor. As a consequence we have that it is undecidable whether the cellular automaton map restricted to the limit set is the identity, closing, injective, expansive, positively expansive, transitive

Decidable properties for regular cellular automata

We investigate decidable properties for regular cellular automata. In particular, we show that regularity itself is an undecidable property and that nilpotency, equicontinuity and positively expansiveness became decidable if we restrict to regular cellular automata4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI

NET-GE: a novel NETwork-based Gene Enrichment for detecting biological processes associated to Mendelian diseases

Enrichment analysis is a widely applied procedure for shedding light on the molecular mechanisms and functions at the basis of phenotypes, for enlarging the dataset of possibly related genes/proteins and for helping interpretation and prioritization of newly determined variations. Several standard and Network-based enrichment methods are available. Both approaches rely on the annotations that characterize the genes/proteins included in the input set; network based ones also include in different ways physical and functional relationships among different genes or proteins that can be extracted from the available biological networks of interactions

Decidable properties for regular cellular automata

We investigate decidable properties for regular cellular automata. In particular, we show that regularity itself is an undecidable property and that nilpotency, equicontinuity and positively expansiveness became decidable if we restrict to regular cellular automata4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI

Estimage: a webserver hub for the computation of methylation age

Methylage is an epigenetic marker of biological age that exploits the correlation between the methylation state of specific CG dinucleotides (CpGs) and chronological age (in years), gestational age (in weeks), cellular age (in cell cycles or as telomere length, in kilobases). Using DNA methylation data, methylage is measurable via the so called epigenetic clocks. Importantly, alterations of the correlation between methylage and age (age acceleration or deceleration) have been stably associated with pathological states and occur long before clinical signs of diseases become overt, making epigenetic clocks a potentially disruptive tool in preventive, diagnostic and also in forensic applications. Nevertheless, methylage dependency from CpGs selection, mathematical modelling, tissue specificity and age range, still makes the potential of this biomarker limited. In order to enhance model comparisons, interchange, availability, robustness and standardization, we organized a selected set of clocks within a hub webservice, EstimAge (Estimate of methylation Age, http://estimage.iac.rm.cnr.it), which intuitively and informatively enables quick identification, computation and comparison of available clocks, with the support of standard statistics

Editorial: Computational Methods for Analysis of DNA Methylation Data

DNA methylation is among the most studied epigenetic modifications in eukaryotes. The interest in DNA methylation stems from its role in development, as well as its well- established association with phenotypic changes. Particularly, there is strong evidence that methylation pattern alterations in mammals are linked to developmental disorders and cancer (Kulis and Esteller, 2010). Owing to its potential as a prognostic marker for preventive medicine, in recent years, the analysis of DNA methylation data has garnered interest in many different contexts of computational biology (Bock, 2012). As it typically happens with omic data, processing, analyzing and interpreting large-scale DNA methylation datasets requires computational methods and software tools that address multiple challenges. In the present Research Topic, we collected papers that tackle different aspects of computational approaches for the analysis of DNA methylation data. These manuscripts address novel computational solutions for copy number variation detection, cell-type deconvolution and methylation pattern imputation, while others discuss interpretations of well-established computational techniques. Over the last 10 years, DNA methylation profiles have been successfully exploited to develop biomarkers of age, also referred to as epigenetic clocks (Bell et al., 2019). Epigenetic clocks accurately estimate both chronological and biological age from methylation levels. DNA methylation age and, most importantly, its deviation from chronological age have been shown to be associated with a variety of health issues. More recently, a second generation of epigenetic clocks has emerged. The new generation of clocks incorporates not only methylation profiles but also environmental variants, such as smoking and alcohol consumption, and they outperform the first generation in mortality prediction and prognosis of certain diseases. In our collection, the review by Chen et al. compares the first and second generation of epigenetic clocks that predict cancer risk and discusses pathways known to exhibit altered methylation in aging tissues and cancer. Differentially methylated regions (DMRs), that is genomic regions that show significant differences in methylation levels across distinct biological and/or medical conditions (e.g., normal vs. disease), have been reported to be implicated in a variety of disorders (Rakyan et al., 2011). As a result, identifying DMRs is one of the most critical and fundamental challenges in deciphering disease mechanisms at the molecular level. Although DNA methylation patterns remain stable during normal somatic cell growth, alterations in genomic methylation may be caused by genetic alterations, or vice versa. However, standard DMR analysis often ignores whether methylation alterations should be viewed as a cause or an effect. Rhamani et al. discuss the effect of model directionality, i.e. whether the condition of interest (phenotype) may be affected by methylation or whether it may affect methylation, in differential methylation analyses at the cell-type level. They show that correctly accounting for model directionality has a significant impact on the ability to identify cell type specific differential methylation. Different cell types exhibit DMRs at many genomic regions and such rich information can be exploited to infer underlying cell type proportions using deconvolution techniques. DNA methylation-based cell mixture deconvolution approaches can be classified into two main categories: reference-based and reference-free. While the latter are more broadly applicable, as they do not rely on the availability of methylation profiles from each of the purified cell types that compose a tissue of interest, they are also less precise. Reference-based approaches use DMRs specific to cell types (reference library) to determine the underlying cellular composition within a DNA methylation sample. The quality of the reference library has a big impact on the accuracy of reference-based approaches. Bell-Glenn et al. present RESET, a framework for reference library selection for deconvolution algorithms exploiting a modified version of the Dispersion Separability Criteria score, for the inference of the best DMRs composing the library, contributing to de facto standards (Koestler et al., 2016). In short, RESET does not require researchers to identify a priori the size of the reference library (number of DMRs), nor to rely on costly associated purified cells’ mDNA profiles. Within a cellular population, the methylation patterns of different cell types and at specific genomic locations are indicative of cellular heterogeneity. Alterations of such heterogeneity are predictive of development as well as prognostic markers of diseases. Computational methods that exploit heterogeneity in methylation patterns are typically constrained by partially observed patterns due to the nature of shotgun sequencing, which frequently generates limited coverage for downstream analysis. One possible solution to overcome such limitations is offered by Chang et al. presenting BSImp, a probabilistic based imputation method that uses local information to impute partially observed methylation patterns. They show that using this approach they are able to recover heterogeneity estimates at 15% more regions with moderate sequencing depths. This should therefore improve our ability to study how methylation heterogeneity is associated with disease. Finally, recent studies have shown how the associations between Copy Number Variations (CNVs) and methylation alterations offer a richer and hence more informative picture of the samples under study, in particular for tumor data characterized by large scale genomic rearrangements (Sun et al., 2018). Consequently, recent technological and methodological developments have enabled the possibility to measure CNVs from DNA methylation data. The main advantage of DNA methylation based CNV approaches is that they offer the possibility to integrate both genomic (copy number) and epigenomic (methylation) information. Mariani et al. propose MethylMasteR, an R software package that integrates DNA methylation-based CNV calling routines, facilitating standardization, comparison and customization of CNV analyses. This package, built into the Docker architecture to seamlessly mange dependencies, includes four of the most commonly used routines for this integrated analysis, ChAMP (Morris et al., 2014), SeSAMe (Zhou et al., 2018), Epicopy (Cho et al., 2019), plus a custom version of cnAnalysis450k (Knoll et al., 2017), overall enabling analysis of comparative results. All the topics in this issue, although limited to specific aspects of DNA methylation analysis, highlight the importance of research in this field, the associated computational challenges and illustrate the significant impact that this type of data will likely have on preventive medicine

Methylation data imputation performances under different representations and missingness patterns

Background: High-throughput technologies enable the cost-effective collection and analysis of DNA methylation data throughout the human genome. This naturally entails missing values management that can complicate the analysis of the data. Several general and specific imputation methods are suitable for DNA methylation data. However, there are no detailed studies of their performances under different missing data mechanisms –(completely) at random or not- and different representations of DNA methylation levels (β and M-value). Results: We make an extensive analysis of the imputation performances of seven imputation methods on simulated missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR) methylation data. We further consider imputation performances on the popular β- and M-value representations of methylation levels. Overall, β-values enable better imputation performances than M- values. Imputation accuracy is lower for mid-range β-values, while it is generally more accurate for values at the extremes of the β-value range. The MAR values distribution is on the average more dense in the mid-range in comparison to the expected β-value distribution. As a consequence, MAR values are on average harder to impute. Conclusions: The results of the analysis provide guidelines for the most suitable imputation approaches for DNA methylation data under different representations of DNA methylation levels and different missing data mechanisms

Strictly Temporally Periodic Points in Cellular Automata

We study the set of strictly periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but they not spatially periodic. This set turns out to be dense for almost equicontinuous surjective cellular automata while it is empty for the positively expansive ones. In the class of additive cellular automata, the set of strictly periodic points can be either dense or empty. The latter happens if and only if the cellular automaton is topologically transitive

Blurring contact maps of thousands of proteins: what we can learn by reconstructing 3D structure

<p>Abstract</p> <p>Background</p> <p>The present knowledge of protein structures at atomic level derives from some 60,000 molecules. Yet the exponential ever growing set of hypothetical protein sequences comprises some 10 million chains and this makes the problem of protein structure prediction one of the challenging goals of bioinformatics. In this context, the protein representation with contact maps is an intermediate step of fold recognition and constitutes the input of contact map predictors. However contact map representations require fast and reliable methods to reconstruct the specific folding of the protein backbone.</p> <p>Methods</p> <p>In this paper, by adopting a GRID technology, our algorithm for 3D reconstruction FT-COMAR is benchmarked on a huge set of non redundant proteins (1716) taking random noise into consideration and this makes our computation the largest ever performed for the task at hand.</p> <p>Results</p> <p>We can observe the effects of introducing random noise on 3D reconstruction and derive some considerations useful for future implementations. The dimension of the protein set allows also statistical considerations after grouping per SCOP structural classes.</p> <p>Conclusions</p> <p>All together our data indicate that the quality of 3D reconstruction is unaffected by deleting up to an average 75% of the real contacts while only few percentage of randomly generated contacts in place of non-contacts are sufficient to hamper 3D reconstruction.</p