Statistical Analysis of Zebrafish Locomotor Response

Zebrafish larvae display rich locomotor behaviour upon external stimulation. The movement can be simultaneously tracked from many larvae arranged in multi-well plates. The resulting time-series locomotor data have been used to reveal new insights into neurobiology and pharmacology. However, the data are of large scale, and the corresponding locomotor behavior is affected by multiple factors. These issues pose a statistical challenge for comparing larval activities. To address this gap, this study has analyzed a visually-driven locomotor behaviour named the visual motor response (VMR) by the Hotelling's T-squared test. This test is congruent with comparing locomotor profiles from a time period. Different wild-type (WT) strains were compared using the test, which shows that they responded differently to light change at different developmental stages. The performance of this test was evaluated by a power analysis, which shows that the test was sensitive for detecting differences between experimental groups with sample numbers that were commonly used in various studies. In addition, this study investigated the effects of various factors that might affect the VMR by multivariate analysis of variance (MANOVA). The results indicate that the larval activity was generally affected by stage, light stimulus, their interaction, and location in the plate. Nonetheless, different factors affected larval activity differently over time, as indicated by a dynamical analysis of the activity at each second. Intriguingly, this analysis also shows that biological and technical repeats had negligible effect on larval activity. This finding is consistent with that from the Hotelling's T-squared test, and suggests that experimental repeats can be combined to enhance statistical power. Together, these investigations have established a statistical framework for analyzing VMR data, a framework that should be generally applicable to other locomotor data with similar structure

VMR experimental scheme.

<p>The experimental scheme for the VMR assay was adopted from Emran and colleague (2008). In the scheme, the larvae arrayed in the 96-well plate were first dark adapted for 3.5 hrs (long black bar on the left). Then, they were subjected to three consecutive trials of light onset (Light-On; grey bars) and light offset (Light-Off; short black bars). Each Light-On or Light-Off session lasted for 30 mins. In this study, we extracted the data from 30 s before light change (red bars; not to scale) to 30 s after light change (blue bars; not to scale) for statistical analyses. In some cases, the analyses separately handled the extracted data around the Light-On stimulus (yellow boxes) and Light-Off stimulus (green boxes). Furthermore, in our MANOVA models, the effect of three consecutive trials was explicitly evaluated (purple boxes in different colour values), regardless of the nature of light change.</p

Power analysis.

<p>(Top left) Four hypothetical activity profiles. <i>μ</i>₁ (red circles) and <i>μ</i>₂ (red pluses) are two vectors with very small difference and without any overlap. <i>μ</i>₃ (blue triangles) and <i>μ</i>₄ (blue crosses) are two vectors with very small difference and overlap. (Top right) These vectors were used for power analysis of three comparisons: (1) <i>μ</i>₁ vs. <i>μ</i>₂ (red curve); (2) <i>μ</i>₃ vs. <i>μ</i>₄ (blue dash curve); and (3) <i>μ</i>₁ vs. <i>μ</i>₃ (pink dotted curve). In the plot, the y-axis shows the statistical power, while the x-axis shows the sample size in each group. (Middle left) The power analysis results of two comparisons: (1) <i>μ</i>_<i>AB</i> vs. <i>μ</i>_<i>TLAB</i> before light change (-29–0 s) of the Light-On stimulus at 6 dpf (black curve); (2) <i>μ</i>_<i>AB</i> vs. <i>μ</i>_<i>TLAB</i> after light change (1–30 s) of the Light-On stimulus (red dash curve). (Middle right) The power analysis results of two comparisons: (1) <i>μ</i>_<i>AB</i> vs. <i>μ</i>_<i>TLAB</i> before light change of the Light-Off stimulus (black curve); (2) <i>μ</i>_<i>AB</i> vs. <i>μ</i>_<i>TLAB</i> after light change of the Light-Off stimulus (red dash curve). In these four comparisons, the y-axis shows the statistical power, while the x-axis shows the sample size in each group. This sample size can be further reduced in real experiments because they often have multiple biological and technical repeats, which can be combined as indicated by our analyses. For example, one sixth of the samples can be used to attain the same theoretical power if an experiment is conducted with 2 biological repeats and 3 technical repeats, a typical VMR design that was used in this study. These sample numbers are shown in the parenthesis in the x-axis. (Bottom) The relationship between the length of time period and sample size under different effect size. In this simulation, the significance level and statistical power is fixed at 0.05 and 0.8 respectively, and the effect size is calculated as <i>Δ</i> = (<i>μ</i>⁽¹⁾ − <i>μ</i>⁽²⁾)′<i>Σ</i>⁻¹(<i>μ</i>⁽¹⁾ − <i>μ</i>⁽²⁾). Four sample effect sizes (0.5, 0.6, 0.7 and 0.8) were used in the simulation for time period ranges from 2 to 100. The results indicate that as the length of time period becomes shorter, fewer samples are needed to attain statistical significance. The sample size can be further proportionally reduced by proper experimental replications.</p

Dynamical effect of different variables on VMR during light change.

<p>The dynamic effect size of each factor for Light-On stimulus (top) and Light-Off stimulus (bottom). These figures show the change in effect size of various factors under different light stimuli from 30 s before light change to 30 s after light change. The light and dark periods are indicated by white and black bars at the top of the figures. The sample size in each model is 11634, the same number for the MANOVA models for Light-On and Light-Off VMR (Tables <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139521#pone.0139521.t008" target="_blank">8</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139521#pone.0139521.t009" target="_blank">9</a>).</p

A MANOVA model of the VMR.

<p>*Pillai is the Pillai-Bartlett Trace is the sum of the variance that can be explained by the factors (see Section 2.2.2.3). The sample size in this model is 23268.</p><p>A MANOVA model of the VMR.</p

The Hotelling’s T-squared test of VMR between different strains at 6 dpf.

<p>The Hotelling’s T-squared test of VMR between different strains at 6 dpf.</p

The Hotelling’s T-squared test of Light-On VMR between different technical repeats of the same strain at 6 dpf.

<p>The Hotelling’s T-squared test of Light-On VMR between different technical repeats of the same strain at 6 dpf.</p

The Hotelling’s T-squared test of Light-On VMR between different stages of the same strain.

<p>The Hotelling’s T-squared test of Light-On VMR between different stages of the same strain.</p

The Hotelling’s T-squared test of Light-Off VMR between different stages of the same strain.

<p>The Hotelling’s T-squared test of Light-Off VMR between different stages of the same strain.</p

The VMR of 6-dpf WT strains across three sequential technical repeats.

<p>The VMR of three WT strains: AB (left), TL (middle) and TLAB (right) was measured as described in the methods. The activity was defined as the fraction of frames in each second that a larva in the video was detected moving (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139521#sec002" target="_blank">methods</a> for the detailed definition). There were three sequential technical repeats in the VMR run. For each strain, the activities in each technical repeat were averaged and shown in different colours (repeat 1 = red; repeat 2 = green; repeat 3 = blue). The Light-On and Light-Off results are separately plotted on the top and bottom rows respectively. These plots show the mean activity from 30 s before the light change to 30 s after the light change. The corresponding error in 1 S.D. is shown by the colour ribbon surrounding the mean activity trace. The light and dark periods are indicated by white and black bars at the top of the figures. The sample size was 191 for AB, 176 for TL, and 185 for TLAB respectively. These values are the total observation from the two biological repeats.</p