il teorema ergodico e le Monte Carlo Markov Chains

Le catene di Markov devono il loro nome al matematico russo Andrej Andreevič Markov, il quale introdusse questa classe di processi stocastici a tempo discreto nei primi anni del 1900. Lo scopo originario dello studioso era mostrare che alcuni risultati di convergenza validi per successioni di variabili aleatorie indipendenti identicamente distribuite, quali la legge dei grandi numeri, potevano essere estesi a processi che ammettono una piccola dipendenza dal passato. Negli anni successivi queste catene si sono dimostrate utilissime in più settori e vantano svariate applicazioni in fisica, biologia, ingegneria elettronica e altri campi. La proprietà caratterizzante le catene di Markov è una sorta di perdita di memoria: lo stato attuale della catena è la massima informazione che possiamo avere per determinare lo stato successivo, mentre gli stati precedenti non influiscono. Il primo capitolo si sofferma sulle catene di Markov discrete. L'interesse principale è per le catene omogenee e irriducibili, che saranno classificate come ricorrenti positive, ricorrenti nulle o transitorie. Si definisce inoltre la distribuzione stazionaria e se ne dimostrano esistenza e unicità per catene ricorrenti positive. Il capitolo si conclude col teorema ergodico, il quale ci fornisce un importante risultato di convergenza per le catene omogenee, irriducibili, ricorrenti positive. Il secondo capitolo inizia trattando brevemente il metodo Monte Carlo classico, fornendone un esempio con il metodo di acceptance-rejection. Dopo aver introdotto i concetti di periodicità e reversibilità di una catena di Markov, si presenta il metodo Monte Carlo Markov Chains per catene a valori in uno spazio finito e se ne fornisce un esempio: l'algoritmo di Metropolis-Hastings. L'elaborato si conclude con degli esempi di applicazione dell'algoritmo

Empirical Optimization of Interactions between Proteins and Chemical Denaturants in Molecular Simulations

Chemical denaturants are the most commonly used perturbation applied to study protein stability and folding kinetics as well as the properties of unfolded polypeptides. We build on recent work balancing the interactions of proteins and water, and accurate models for the solution properties of urea and guanidinium chloride, to develop a combined force field that is able to capture the strength of interactions between proteins and denaturants. We use solubility data for a model tetraglycine peptide in each denaturant to tune the protein-denaturant interaction by a novel simulation methodology. We validate the results against data for more complex sequences: single-molecule Förster resonance energy transfer data for a 34-residue fragment of the globular protein CspTm and photoinduced electron transfer quenching data for the disordered peptides C(AGQ)nW in denaturant solution as well as the chemical denaturation of the mini-protein Trp cage. The combined force field model should aid our understanding of denaturation mechanisms and the interpretation of experiment

Polyelectrolyte interactions enable rapid association and dissociation in high-affinity disordered protein complexes

Highly charged intrinsically disordered proteins can form complexes with very high affinity in which both binding partners fully retain their disorder and dynamics, exemplified by the positively charged linker histone H1.0 and its chaperone, the negatively charged prothymosin α. Their interaction exhibits another surprising feature: The association/dissociation kinetics switch from slow two-state-like exchange at low protein concentrations to fast exchange at higher, physiologically relevant concentrations. Here we show that this change in mechanism can be explained by the formation of transient ternary complexes favored at high protein concentrations that accelerate the exchange between bound and unbound populations by orders of magnitude. Molecular simulations show how the extreme disorder in such polyelectrolyte complexes facilitates (i) diffusion-limited binding, (ii) transient ternary complex formation, and (iii) fast exchange of monomers by competitive substitution, which together enable rapid kinetics. Biological polyelectrolytes thus have the potential to keep regulatory networks highly responsive even for interactions with extremely high affinities

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Spatial Organization and Molecular Correlation of Tumor-Infiltrating Lymphocytes Using Deep Learning on Pathology Images

Beyond sample curation and basic pathologic characterization, the digitized H&E-stained images of TCGA samples remain underutilized. To highlight this resource, we present mappings of tumorinfiltrating lymphocytes (TILs) based on H&E images from 13 TCGA tumor types. These TIL maps are derived through computational staining using a convolutional neural network trained to classify patches of images. Affinity propagation revealed local spatial structure in TIL patterns and correlation with overall survival. TIL map structural patterns were grouped using standard histopathological parameters. These patterns are enriched in particular T cell subpopulations derived from molecular measures. TIL densities and spatial structure were differentially enriched among tumor types, immune subtypes, and tumor molecular subtypes, implying that spatial infiltrate state could reflect particular tumor cell aberration states. Obtaining spatial lymphocytic patterns linked to the rich genomic characterization of TCGA samples demonstrates one use for the TCGA image archives with insights into the tumor-immune microenvironment