The Embedding Problem for Markov Models of Nucleotide Substitution

10.1371/journal.pone.0069187PLoS ONE87-POLN

A unique H2A histone variant occupies the transcriptional start site of active genes

Transcriptional activation is controlled by chromatin, which needs to be unfolded and remodeled to ensure access to the transcription start site (TSS). However, the mechanisms that yield such an 'open' chromatin structure, and how these processes are coordinately regulated during differentiation, are poorly understood. We identify the mouse (Mus musculus) H2A histone variant H2A.Lap1 as a previously undescribed component of the TSS of active genes expressed during specific stages of spermatogenesis. This unique chromatin landscape also includes a second histone variant, H2A.Z. In the later stages of round spermatid development, H2A.Lap1 dynamically loads onto the inactive X chromosome, enabling the transcriptional activation of previously repressed genes. Mechanistically, we show that H2A.Lap1 imparts unique unfolding properties to chromatin. We therefore propose that H2A.Lap1 coordinately regulates gene expression by directly opening the chromatin structure of the TSS at genes regulated during spermatogenesis

Testing scheme.

<p>Testing scheme.</p

Non-Embeddability-D2 (Opossum) Mitochondrial Protein coding genes (11 Alignments).

<p> Steps to identify Non-embeddability 1. , 2. Negative eigenvalues have odd algebraic multiplicity, 3. Complex eigenvalues occur in non-conjugate pairs, 4. The set of eigenvalues, , lie outside the region in the complex plane, 5. – negative off-diagonals – threshold −0.1, NE =  Non-Embeddable, No. rejections of from parametric bootstrap scheme with a p-value (percentage of total tests), 3 Alignments failed to find stable estimates.</p

Average difference between matrices produced by the continuous () and discrete () models (i.e. ) for alignments with non-embeddable () matrices which were found to be (a) Non-embeddable or (b) Embeddable using the parametric bootstrap.

<p>Where represents a larger transition probability in (e.g. ) and ▪ indicates a larger transition probability in (e.g. ).</p

Non-Embeddability- D4 Microbial Protein Coding Gene (1140 Triads).

<p> Steps to identify Non-embeddability 1. , 2. Negative eigenvalues have odd algebraic multiplicity, 3. Complex eigenvalues occur in non-conjugate pairs, 4. The set of eigenvalues, , lie outside the region in the complex plane, 5. – negative off-diagonals – threshold −0.1, NE =  Non-Embeddable, No. rejections of from parametric bootstrap scheme with a p-value , 584 Alignments failed to find stable estimates.</p

GC percentage for the Non-Embeddable () vs Embeddable (▪) Matrices for the Mouse, Human and Opossum Triad at the third codon position.

<p>GC percentage for the Non-Embeddable () vs Embeddable (▪) Matrices for the Mouse, Human and Opossum Triad at the third codon position.</p

Non-Embeddability – D3: Primate Introns Dinucleotide Model (62 alignments).

<p> Steps to identify Non-embeddability 1. , 2. Negative eigenvalues have odd algebraic multiplicity, 3. Complex eigenvalues occur in non-conjugate pairs, 4. The set of eigenvalues, , lie outside the region in the complex plane, 5. – negative off-diagonals – threshold −0.1, NE =  Non-Embeddable, No. rejections of from parametric bootstrap scheme with a p-value (percentage of total tests).</p

Non-Embeddability – D1 Human, Rat, Mouse Triad (8394 Alignments).

<p> Steps to identify Non-embeddability 1. , 2. Negative eigenvalues have odd algebraic multiplicity, 3. Complex eigenvalues occur in non-conjugate pairs, 4. The set of eigenvalues, , lie outside the region in the complex plane, 5. – negative off-diagonals – threshold −0.1, NE =  Non-Embeddable, No. rejections of from parametric bootstrap scheme with a p-value (percentage of total tests), 1 Alignment failed to find stable estimates.</p

Summary of Datasets.

<p> – C: Chimpanzee, H:Human, M:Mouse, Ma:Macaque, O:Opossum, R:Rat, bad:Bifidobacterium adolescentis, bas: Buchnera aphidicola Sg, bba:Bdellovibrio bacteriovorus, bbu:Borrelia burgdorferi B31, bpn: Candidatus Blochmannia pennsylvanicus, bvu: Bacteroides vulgatus, cjk:Corynebacterium jeikeium, dps:Desulfotalea psychrophila, eca:Pectobacterium atrosepticum, ent:Enterobacter sp. 638, kra:Kineococcus radiotolerans, lla:Lactococcus lactis subsp. lactis IL1403, lre:Lactobacillus reuteri DSM 20016, mgi:Mycobacterium gilvum, mle:Mycobacterium leprae TN, mta:Moorella thermoacetica, ppe:Pediococcus pentosaceus, pth:Pelotomaculum thermopropionicum, sma:Streptomyces avermitilis, wsu:Wolinella succinogenes, – average length from consensus tree , -All possible triads (1140).</p