Comparison of circadian and ultradian rhythms.

<p>: circadian rhythm, : area of circadian component (a.u: arbitrary unit), : area of ultradian component (a.u), : ratio of ultradian to circadian component. Values are shown as mean ± SEM.</p>*<p>indicates the significant difference from WT mice (Dunnett’s multiple comparison, <i>p</i><0.05). Note that <i>Bmal1</i>^−/− mice were excluded from the group comparison of due to the extinction of the circadian rhythm (refer to Results).</p

Spectrum density of locomotor activity.

<p>Group-averaged spectrum estimated from the CWT modulus for (<b>a</b>) WT, (<b>b</b>) <i>mPer2^Brdm1</i>, (<b>c</b>) <i>Clock/Clock</i>, and (<b>d</b>) <i>Bmal1⁻</i>^/− mice on a semi-logarithmic scale (thick solid red curves). The spectrum of each mouse (broken curve) is superimposed. The vertical blue line corresponds to 1.2×10⁻⁵ Hz (approximately 24 h).</p

Cumulative distributions of resting and active period durations in clock gene-deficient mice.

<p>(<b>a</b>)–(<b>c</b>) Comparison of group-averaged cumulative distributions of rescaled resting period durations between the WT mice and (<b>a</b>) <i>mPer2^Brdm1</i>, (<b>b</b>) <i>Clock/Clock</i>, and (<b>c</b>) <i>Bmal1⁻</i>^/− mice, where a non-zero mean is used as the threshold value. Error bars indicate standard error of the mean. Straight lines are eye guides with the group mean parameter values (WT, ; <i>mPer2^Brdm1</i>, ; <i>Clock/Clock</i>: ; <i>Bmal1</i>^−/−, ). (<b>d</b>)–(<b>f</b>) Group-averaged cumulative distributions of active period durations. The broken (WT mice) and solid (deficient mice) curves are stretched exponential functions with the group mean parameter values shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058884#pone-0058884-t002" target="_blank">Table 2</a>. Note that the resting distributions are shifted along the vertical axis to take the same value at , and the distributions are plotted with wider bins () for the purpose of illustration. The results for the WT and <i>mPer2^Brdm1</i> mice are reproduced from our previous study <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058884#pone.0058884-Nakamura1" target="_blank">[10]</a>.</p

Fluctuation of locomotor activity.

<p>Illustrative examples of locomotor activity data (local variance with window size 60 s) of a (<b>a</b>) WT, (<b>b</b>) <i>mPer2^Brdm1</i>, (<b>c</b>) <i>Clock/Clock</i>, and (<b>d</b>) <i>Bmal1⁻</i>^/− mouse over 3 consecutive days (left panels). The middle panels are magnifications of the left panels with 4-h periods during subjective daytime. The overall average of non-zero activity levels is used as a threshold (horizontal dotted line), and the period during which the levels are continuously below or above the threshold is coded as a resting (open bar in bottom panels) or active (closed bar) period, respectively. Because body weight varies across individuals, activity levels in the vertical axis (nVar) are normalized by the mean variance of each record. The right panels are the moduli of CWT of locomotor activity shown in the left panels. Values of moduli are color coded according to their magnitude (blue indicates a low and red a large value), and the ordinates are represented on a logarithmic scale.</p

Sequence of resting period durations and the model.

<p>(<b>a</b>) Probability density function for choosing a demand/stimulus with priority <i>x</i>. The sequence of onset of activity bursts (resting durations) derived from locomotor activity of a (<b>b1</b>) WT (), (<b>b2</b>) <i>mPer2^Brdm1</i> (), (<b>b3</b>) <i>Clock/Clock</i> (), and (<b>b4</b>) <i>Bmal1⁻</i>^/− mouse () for 100 s. Note that these mouse data were calculated from locomotor activity shown in Fig. 1. (<b>b5</b>) The sequence of waiting times simulated from the priority stochastic queuing model with (i.e., ) and (<b>b6</b>) (i.e., ). The simulated sequences of waiting time were generated on the base of the stochastic priority queuing model <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0058884#pone.0058884-Barabsi1" target="_blank">[2]</a> with a priority list comprising <i>L</i> = 10 demands, where a priority parameter <i>x_i</i> (<i>i = </i>1, …,<i>L</i>) chosen from a uniform distribution is assigned to each demand. At each time step, one demand is selected from the list (in the brain) according to for execution (or act), and then removed from the list. At that moment, a new demand is added to the list with a priority randomly selected from . The probability that a demand with priority <i>x</i> is executed at time <i>t</i> is given by , and the average waiting time of a demand with priority <i>x</i> is obtained by averaging over <i>t</i> weighted with , giving rise to . Analytically, with conservation law of probability (), the waiting time distribution of the demands is given by . Note that each vertical line separates the successive waiting time of demands chosen according to their priority.</p

Dependency of distribution parameters on threshold values.

<p>The values of <i>γ</i> with different threshold values of 0.6, 0.7, …, 1.7, and 1.8 times the overall average for the non-zero mean for (<b>a</b>) <i>mPer2^Brdm1</i>, (<b>b</b>) <i>Clock/Clock</i>, and (<b>c</b>) <i>Bmal1⁻</i>^/− mice. (<b>d</b>)–(<b>f</b>) The same as (<b>a</b>)–(<b>c</b>) but for <i>β</i>. Bars indicate standard error of the mean.</p

Association of 2 SNPs with current and lifetime maximum BMI in control and case subjects.

<p>Association of 2 SNPs with current and lifetime maximum BMI in control and case subjects.</p

Association of the various aspects of BMI history with type 2 diabetes.

<p>Association of the various aspects of BMI history with type 2 diabetes.</p

Association results between 2 SNPs and type 2 diabetes.

<p>Association results between 2 SNPs and type 2 diabetes.</p

Genotype, allele frequencies, and HWE of 2SNPs within <i>FTO</i> gene in the present population.

<p>Genotype, allele frequencies, and HWE of 2SNPs within <i>FTO</i> gene in the present population.</p