MITEs inserted into protein-coding genes were recruited as introns in <i>N</i>. <i>bombycis</i>.

<p>(A) A dot-plot sequencing comparison of MITE-inserted gene <i>NBO_283gi001</i> with its expressed sequences tag. (B) A dot-plot sequencing comparison of MITE-inserted gene <i>NBO_6gi004</i> with its expressed sequences tag. The structural comparison of targeted gene and its homologous genes from <i>N</i>. <i>antheraeae</i>, <i>N</i>. <i>ceranae</i> and <i>Encephalitozoon cuniculi</i> are presented as dot plots, respectively.</p

Time series with/without noise in the case of strong coupling.

<p>The evolution of four randomly chosen oscillators without noise <i>D</i> = 0 (A), and with noise <i>D</i> = 0.4 (B). (C) The evolution of the mean field in the case of <i>D</i> = 0 and <i>D</i> = 0.4 respectively. <i>g</i> represents the coupling strength.</p

Phylogenetic analysis of the mitochondrial genomes in bees (Hymenoptera: Apoidea: Anthophila)

<div><p>In this study, the first complete mitogenome of Andrenidae, namely <i>Andrena camellia</i>, is newly sequenced. It includes 13 protein-coding (PCG) genes, 22 transfer RNA (rRNA) genes, two ribosomal RNA (tRNA) genes, and a control region. Among PCGs, high conservation is observed in cytochrome oxidase genes with <i>cox1</i> exhibits the highest conservation. Conversely, NADH dehydrogenase and ATPase subunit genes are more variable with <i>atp8</i> presents the maximal variation. Comparison of the gene order indicates complex rearrangement in bees. Most of the rearranged events are located in the tRNA clusters of <i>trnI</i>-<i>trnQ</i>-<i>trnM</i>, <i>trnW</i>-<i>trnC</i>-<i>trnY</i>, and <i>trnA-trnR-trnN-trnS1-trnE-trnF</i>. Furthermore, we present the most comprehensive mitochondrial phylogeny of bee families. The monophyly of each family and the long-tongued bees is highly supported. However, short-tongued bees are inferred as paraphyletic relative to the sister relationship between Melittidae and other bee families. Furthermore, to improve the resolution of phylogeny, various datasets and analytical approaches are performed. It is indicated that datasets including third codons of PCGs facilitate to produce identical topology and higher nodal support. The tRNA genes that have typical cloverleaf secondary structures also exhibit similar positive effects. However, rRNAs present poor sequence alignment and distinct substitution saturation, which result in negative effects on both tree topology and nodal support. In addition, Gblocks treatment can increase the congruence of topologies, but has opposite effects on nodal support between the two inference methods of maximum likelihood and Bayesian inference.</p></div

Previous phylogenetic analyses of bees.

(A) bees were divided into long-tongued bees and short-tongued bees; (B) Melittidae was inferred as the basal lineage of bees or sister to other bee families; (C) and (D) Andrenidae was suggested as sister to all other bees except Melittidae or sister to Melittidae, respectively.</p

Saturation substitution tests for PCGs, rRNAs, and tRNAs of mitogenomes of bees.

<p>Saturation substitution tests for PCGs, rRNAs, and tRNAs of mitogenomes of bees.</p

Schematic diagram of the Goodwin model.

<p>(A) the number of neuronal oscillators <i>N</i> is 1, i.e. the neuronal oscillator is isolated. The clock gene mRNA <i>X</i>, clock protein <i>Y</i> and transcriptional inhibitor <i>Z</i> constitute a negative feedback loop. The transmitter <i>V</i> is produced by <i>X</i> and then <i>X</i> absorbs the mean field <i>F</i> which is, in this case, equal to <i>V</i>, with the coupling strength (absorbing ability) <i>g</i>. <i>ζ</i> stands for the external noise. (B) the number of neuronal oscillators in a network, where the number <i>N</i> is 2. The mean field <i>F</i> is the mean value of the transmitter from these two neurons. We used the first-order Milshtein method[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0145360#pone.0145360.ref027" target="_blank">27</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0145360#pone.0145360.ref028" target="_blank">28</a>] for numerical simulations of the Goodwin model as presented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0145360#pone.0145360.e001" target="_blank">Eq 1</a> with the time increment of 0.001 h. The equations of the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0145360#pone.0145360.e001" target="_blank">Eq 1</a> are represented as: </p><p><math><msub><mi>X</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi>Δ</mi><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>X</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><msub><mi>α</mi><mn>1</mn></msub><mrow><msubsup><mi>k</mi><mn>1</mn><mi>n</mi></msubsup></mrow><mrow><msubsup><mi>k</mi><mn>1</mn><mi>n</mi></msubsup><mo>+</mo><msubsup><mi>Z</mi><mi>i</mi><mi>n</mi></msubsup><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>−</mo><msub><mi>α</mi><mn>2</mn></msub><mrow><msub><mi>X</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mi>k</mi><mn>2</mn></msub><mo>+</mo><msub><mi>X</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo>+</mo><msub><mi>α</mi><mi>c</mi></msub><mrow><mi>g</mi><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mi>k</mi><mi>c</mi></msub><mo>+</mo><mi>g</mi><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">)</mo><mi>Δ</mi><mi>t</mi><mo>+</mo><mrow><mi>D</mi><mn>2</mn><msub><mi>X</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mn>2</mn><mi>Δ</mi><mi>t</mi><mo>+</mo><msub><mi>X</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msqrt><mrow><mi>D</mi><mn>2</mn><msub><mi>ζ</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mi>Δ</mi><mi>t</mi></mrow></msqrt><msub><mi>Y</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi>Δ</mi><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>Y</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><msub><mi>k</mi><mn>3</mn></msub><msub><mi>X</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><msub><mi>α</mi><mn>4</mn></msub><mrow><msub><mi>Y</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mi>k</mi><mn>4</mn></msub><mo>+</mo><msub><mi>Y</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">)</mo><mi>Δ</mi><mi>t</mi><msub><mi>Z</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi>Δ</mi><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>Z</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><msub><mi>k</mi><mn>5</mn></msub><msub><mi>Y</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><msub><mi>α</mi><mn>6</mn></msub><mrow><msub><mi>Z</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mi>k</mi><mn>6</mn></msub><mo>+</mo><msub><mi>Z</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">)</mo><mi>Δ</mi><mi>t</mi><msub><mi>V</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi>Δ</mi><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>V</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><msub><mi>k</mi><mn>7</mn></msub><msub><mi>X</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><msub><mi>α</mi><mn>8</mn></msub><mrow><msub><mi>V</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mi>k</mi><mn>8</mn></msub><mo>+</mo><msub><mi>V</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mo stretchy="false">)</mo><mi>Δ</mi><mi>t</mi><mi>F</mi><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mi>Δ</mi><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mi>N</mi><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi><mrow><msub><mi>V</mi><mi>j</mi></msub></mrow><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math>(2) </p> where Δ<i>t</i> is the time increment. The last two terms of the right side of the first equation in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0145360#pone.0145360.e004" target="_blank">Eq 2</a> represent the noise terms. The initial 5,000,000 time steps were neglected in order to avoid the influence of transients. The number of oscillators <i>N</i> was 500. The initial conditions for each variable were selected randomly from a uniform distribution in the range (0–1) for <i>X</i>, <i>Y</i>, <i>Z</i>, and <i>V</i> in the Goodwin model.<p></p

Noise Induces Oscillation and Synchronization of the Circadian Neurons

<div><p>The principle clock of mammals, named suprachiasmatic nucleus (SCN), coordinates the circadian rhythms of behavioral and physiological activity to the external 24 h light-dark cycle. In the absence of the daily cycle, the SCN acts as an endogenous clock that regulates the ~24h rhythm of activity. Experimental and theoretical studies usually take the light-dark cycle as a main external influence, and often ignore light pollution as an external influence. However, in modern society, the light pollution such as induced by electrical lighting influences the circadian clock. In the present study, we examined the effect of external noise (light pollution) on the collective behavior of coupled circadian oscillators under constant darkness using a Goodwin model. We found that the external noise plays distinct roles in the network behavior of neurons for weak or strong coupling between the neurons. In the case of strong coupling, the noise reduces the synchronization and the period of the SCN network. Interestingly, in the case of weak coupling, the noise induces a circadian rhythm in the SCN network which is absent in noise-free condition. In addition, the noise increases the synchronization and decreases the period of the SCN network. Our findings may shed new light on the impact of the external noise on the collective behavior of SCN neurons.</p></div

Gene arrangement of the mitogenomes of bees.

<p>PCGs, rRNAs, tRNAs, and the control region are marked with yellow, pink, green, and grey, respectively. Gene with underscore indicates that it is encoded in the N strand.</p

MITE-derived small RNAs in <i>Nosema bombycis</i>.

<p>(A) Length distribution of small RNAs generated by MITE sequences. (B) Density (sense, black; antisense, red) of small RNA tags assigned to MITE sequences. Frequency is shown along the Y-axis. Relative nucleotide position within the consensus sequence is indicated along the X-axis.</p

The effect of noise on the collective behavior of the SCN neuronal oscillators in the case of strong coupling.

<p>(A) The relationship between the synchronization degree <i>R</i> and the noise intensity <i>D</i>. (B) The relationship between the period <i>T</i> of the SCN population and the noise intensity <i>D</i>. <i>g</i> represents the coupling strength.</p