Distinguishing head morphologies of four different flatworm species.

<p><b>A.</b> Application of our method to parametrize head morphology of four different flatworm species. For each species, time-lapse sequences of different worms were recorded as two independent runs of duration frames. The head is defined as most anterior of the worm body. Radial distances are computed with respect to the midpoint of the head (red dot at of the worm length from the tip of the head). <b>B.</b> By applying PCA to this multi-species data set, we obtain two shape modes, which together account for of the shape variability. Deformations of the mean shape with respect to the the two modes are shown (black: mean shape, red: superposition of mean shape and first mode with and second mode with , respectively). We represent head morphology of the four species in a combined shape space of these two modes. Average head shapes for each species are indicated by crosses, with ellipses of variance including (dark color) and (light color) of motility-associated shape variability, respectively.</p

Principal shape modes of sperm flagellar beating.

<p><b>A.</b> High-precision tracking of planar flagellar centerline shapes (, red) are characterized by their tangent angle as a function of arc-length along the flagellum. <b>B.</b> The time-evolution of this flagellar tangent angle is shown as a kymograph. The periodicity of the flagellar beat is reflected by the regular stripe patterns in this kymograph; the slope of these stripes is related to the propagation of bending waves along the flagellum from base to tip. By averaging over the time-dimension, we define a mean flagellar shape characterized by a tangent angle profile . For illustration, this mean flagellar shape is shown in black superimposed to tracked flagellar shapes (grey). <b>C.</b> We define a feature-feature covariance matrix from the centered tangent angle data matrix as explained in the text. The negative correlation at arc-length distance reflects the half-wavelength of the flagellar bending waves. <b>D.</b> The normalized eigenvalue spectrum of the covariance matrix sharply drops after the second eigenvalue, implying that the eigenvectors corresponding to the first two eigenvalues together account for 97% of the observed variance in the tangent angle data. <b>E.</b> Using principal component analysis, we define two principal shape modes (blue, red), which correspond precisely to the two maximal eigenvalues of the covariance matrix in panel C. The lower plot shows the reconstruction of a tracked flagellar shape (black) by a superposition of the mean flagellar shape and these two principal shape modes (magenta). In addition to tangent angle profiles, respective flagellar shapes are shown on the right. <b>F.</b> Each tracked flagellar shape can now be assigned a pair of shape scores and , indicating the relative weight of the two principal shape modes in reconstruction this shape. This defines a two-dimensional abstract shape space. A sequence of shapes corresponds to a point cloud in this shape space. We find that these point form a closed loop, reflecting the periodicity of the flagellar beat. We can define a shape limit cycle by fitting a curve to the point cloud. By projecting the shape points on this shape limit cycle, we can assign a unique flagellar phase modulo to each shape. This procedure amounts to a binning of flagellar shapes according to shape similarity. <b>G.</b> By requiring that the phase variable should change continuously, we obtain a representation of the beating flagellum as a phase oscillator. The flagellar phase increases at a rate equal to the frequency of the flagellar beat and rectifies the progression through subsequent beat cycles by increasing by . <b>H.</b> Amplitude fluctuations of flagellar beating as a function of flagellar phase. An instantaneous amplitude of the flagellar beat is defined as the radial distance of a point in the -shape space, normalized by the radial distance of the corresponding point on the limit cycle of same phase. A phase-dependent standard deviation was fitted to the data (black solid line). Also shown are fits for additional cells (gray; the position of was defined using a common set of shape modes). <b>J.</b> Swimming path of the head center during one beat cycle computed for the flagellar wave given by the shape limit cycle (panel F) using resistive force theory <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113083#pone.0113083-Gray1" target="_blank">[18]</a> as described previously <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113083#pone.0113083-Friedrich1" target="_blank">[19]</a>. The path is characterized by a wiggling motion of the head superimposed to net propulsion. For a ‘standing wave’ beat pattern characterized by the oscillation of only one shape mode, net propulsion vanishes.</p

Illustration of principal component analysis.

<p><b>A.</b> As a minimal example, we consider a hypothetical data set of length and height measurements for a collection of individuals, <i>i.e.</i> there are just geometric features measured here. <b>B.</b> In this example, length and height are assumed to be strongly correlated, thus mimicking the partial redundancy of geometrical features commonly observed in real data. Principal component analysis now defines a change of coordinate system from the original (length,height)-axes (shown in a black) to a new set of axes (blue) that represent the principal axes of the feature-feature covariance matrix of the data. Briefly, the first new axis points in the direction of maximal data variability, while the second new axis points in the direction of minimal data variability. The change of coordinate system is indicated by a rotation around the center of the point cloud representing the data. By projecting the data on those axes that correspond to maximal feature-feature covariance, in this example the first axis, one can reduce the dimensionality of the data space, while retaining most of the variability of the data. In the context of morphology analysis, we will refer to these new axes as ‘shape modes’ , which represent specific combinations of features. The new coordinates are referred to as ‘shape scores’ .</p

Principal component analysis is used across different disciplines, giving rise to a diverse terminology, which is summarized here.

<p>Principal component analysis is used across different disciplines, giving rise to a diverse terminology, which is summarized here.</p

The mathematics behind principal component analysis (PCA).

<p><b>A.</b> For illustration, we start with a measurement matrix featuring the beat of a sperm flagellum with measurement (rows) and tangent angles at equidistant positions along the flagellar centerline (columns). Subtracting the mean defines the centered data matrix . The mathematical technique of singular value decomposition factors the data matrix into a product of a unitary matrix , a “diagonal” matrix that has non-zero entries only along its diagonal, and a unitary matrix . Singular value decomposition may be regarded as a generalization of the usual eigensystem decomposition of symmetric square matrices to non-square matrices. A unitary matrix U generalizes the concept of a rotation matrix to <i>n</i>-dimensional space.;it is defined by being equal to the identity matrix. <i>Second row:</i> A restriction to the top- singular values defines sub-matrices of , , of dimensions , , , respectively, whose product represents a useful approximation of the full factorization that reduces feature dimensions to only shape modes. <b>B.</b> The feature-feature covariance matrix is defined in terms of the centered data matrix . It can be written as a product of a diagonal matrix , whose diagonal features the eigenvalues of and a unitary -matrix V whose columns correspond to the respective (left) eigenvectors of . This matrix V is exactly the same as previously encountered in the singular value decomposition of . <b>C.</b> Similarly, the measurement-measurement covariance matrix , known as the Gram matrix, can be decomposed using a diagonal matrix and a unitary matrix . Importantly, the rows of V comprise just the shape modes of the data matrix as defined by linear PCA, while the columns of the matrix yield the corresponding shape scores.</p

Three shape modes characterize projected flatworm body shape dynamics.

<p><b>A.</b> Our custom-made MATLAB software tracks worms in movies and extracts worm boundary outline (red) and centerline (blue). <b>B.</b> The radial distance between the boundary points and midpoint of the centerline (, red dot) is calculated as a parameterization of worm shape. We normalize the radial distance profile of each worm by the mean radius . <b>C.</b> The second symmetry axis (dotted line) of the covariance matrix corresponds to statistically symmetric behavior of the worm with respect to its midline. <b>D.</b> The three shape modes with the largest eigenvalues account for 94% of the shape variations. The first shape mode characterizes bending of the worm and alone accounts for 61% of the observed shape variance. On the top, we show its normalized radial profile on the left as well as the boundary outline corresponding to the superposition of the mean worm shape and this first shape mode (solid red: , dashed red: , black: mean shape with ). The second shape mode describe lateral thinning (), while the third shape mode corresponds unlike deformations of head and tail (), giving the worm a wedge-shaped appearance. <b>E.</b> The first shape mode with score describing worm bending strongly correlates with the instantaneous turning rate of worm midpoint trajectories. <b>F.</b> We manually selected 30 movies where worms clearly show inch-worming and 50 movies with no inch-worming behavior. The variance of score and increases for the inch-worming worms. <b>G.</b> The autocorrelation of mode and the crosscorrelation between mode and mode reveals an inch-worming frequency of approximately , hinting at generic behavioral patterns.</p

Correction: LudusScope: Accessible Interactive Smartphone Microscopy for Life-Science Education

<p>Correction: LudusScope: Accessible Interactive Smartphone Microscopy for Life-Science Education</p

BUILD: All components of the LudusScope are designed to allow straightforward do-it-yourself (DIY) reproduction and emphasize learning in construction, optics, electronics, microfluidics, and microbiology.

<p>(<b>A</b>) Computer-aided design and assembly of the 3D-printed components of the LudusScope. Alternatively, a variation of the sample holder and phone holder (pink) enable mounting to a conventional microscope (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162602#pone.0162602.s005" target="_blank">S1 Fig</a>). (<b>B</b>) The optical components consist of a smartphone camera, an eyepiece, and a closed-circuit television (CCTV) board lens. Utilizing a conventional eyepiece allows two-way compatibility of the smartphone and software with regular microscopes. The DIY scope is able to resolve Group 7, Element 6 targets, corresponding to a resolution of 4.4 μm. (<b>C</b>) Simple electronic circuit for analog light stimulus control of the four LEDs via joystick; a potentiometer controls the illumination LED of the microscope. (<b>D</b>) Sample holder with microfluidic slide and four directional LEDs pointing toward the center of the holder. (<b>E</b>) The microfluidic chamber is built via sticker microfluidics. A pair of syringe reservoirs connected to both ends of the chamber allows long-term <i>Euglena</i> culturing. (<b>F</b>) <i>Euglena</i> is used given its robust phototactic behavior and easy culturing conditions.</p

LudusScope: Accessible Interactive Smartphone Microscopy for Life-Science Education

<div><p>For centuries, observational microscopy has greatly facilitated biology education, but we still cannot easily and playfully interact with the microscopic world we see. We therefore developed the LudusScope, an accessible, interactive do-it-yourself smartphone microscopy platform that promotes exploratory stimulation and observation of microscopic organisms, in a design that combines the educational modalities of build, play, and inquire. The LudusScope’s touchscreen and joystick allow the selection and stimulation of phototactic microorganisms such as <i>Euglena gracilis</i> with light. Organismal behavior is tracked and displayed in real time, enabling open and structured game play as well as scientific inquiry via quantitative experimentation. Furthermore, we used the Scratch programming language to incorporate biophysical modeling. This platform is designed as an accessible, low-cost educational kit for easy construction and expansion. User testing with both teachers and students demonstrates the educational potential of the LudusScope, and we anticipate additional synergy with the maker movement. Transforming observational microscopy into an interactive experience will make microbiology more tangible to society, and effectively support the interdisciplinary learning required by the Next Generation Science Standards.</p></div

INQUIRE: The LudusScope enables scientific inquiry via quantitative hypothesis testing, measurement, and modeling.

<p>(<b>A</b>) Free-play exploration interface emphasizes learning with grid overlay. (<b>B</b>) Screenshot of app in which the user quantitatively tests hypotheses of whether <i>Euglena</i> cells swim faster under different conditions (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162602#pone.0162602.s018" target="_blank">S8 Video</a>). Elements of the screenshot have been rearranged for illustrative purposes. In this case, the experiments do not support this hypothesis, as the differences between the mean are well within the standard deviation and standard error of mean (not shown). (<b>C</b>) With the same app, speed can be tracked over multiple days. In this example, four isolated populations were tracked for three days. The error bars are standard deviation, and show the large variability in <i>Euglena</i> speeds. (<b>D</b>) Another application allows the user to select individual <i>Euglena</i> and display their swimming traces; the blue and green portions represent the time before and after a change in light stimuli (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162602#pone.0162602.s015" target="_blank">S5 Video</a>). (<b>E</b>) Models (simulations) of <i>Euglena</i> behavior in response to light are programmed in Scratch. The code portion displayed contains all relevant governing equations; the model parameters (orange) are speed, turning sensitivity to light, and noisiness of swimming path. (<b>F</b>) Euglena game emulations can be programmed and model parameters can be tuned to match the behavior of real <i>Euglena</i> (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162602#pone.0162602.s016" target="_blank">S6 Video</a>). (<b>G</b>) Co-culturing <i>Volvox</i> (green) and <i>Euglena</i> (blue) demonstrates opposite phototactic response to light (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162602#pone.0162602.s019" target="_blank">S9 Video</a>).</p