Disseminating Jewish Literatures. Knowledge, Research, Curricula

The multilingualism and polyphony of Jewish literary writing across the globe demands a collaborative, comparative, and interdisciplinary investigation into questions regarding methods of researching and teaching literatures. This volume compiles case studies that represent a broad range of approaches to the Jewish literary corpus across many languages, including Arabic, English, French, German, Hebrew, Hungarian, Russian, Spanish, and Turkish

Isometric Scaling in Developing Long Bones Is Achieved by an Optimal Epiphyseal Growth Balance.

One of the major challenges that developing organs face is scaling, that is, the adjustment of physical proportions during the massive increase in size. Although organ scaling is fundamental for development and function, little is known about the mechanisms that regulate it. Bone superstructures are projections that typically serve for tendon and ligament insertion or articulation and, therefore, their position along the bone is crucial for musculoskeletal functionality. As bones are rigid structures that elongate only from their ends, it is unclear how superstructure positions are regulated during growth to end up in the right locations. Here, we document the process of longitudinal scaling in developing mouse long bones and uncover the mechanism that regulates it. To that end, we performed a computational analysis of hundreds of three-dimensional micro-CT images, using a newly developed method for recovering the morphogenetic sequence of developing bones. Strikingly, analysis revealed that the relative position of all superstructures along the bone is highly preserved during more than a 5-fold increase in length, indicating isometric scaling. It has been suggested that during development, bone superstructures are continuously reconstructed and relocated along the shaft, a process known as drift. Surprisingly, our results showed that most superstructures did not drift at all. Instead, we identified a novel mechanism for bone scaling, whereby each bone exhibits a specific and unique balance between proximal and distal growth rates, which accurately maintains the relative position of its superstructures. Moreover, we show mathematically that this mechanism minimizes the cumulative drift of all superstructures, thereby optimizing the scaling process. Our study reveals a general mechanism for the scaling of developing bones. More broadly, these findings suggest an evolutionary mechanism that facilitates variability in bone morphology by controlling the activity of individual epiphyseal plates

Element drift plays a restricted role in long bone isometric scaling.

<p>Graphs showing the physical position of each element throughout development. On the right of each graph is a 3D representation of an adult bone with colored marks of element locations. As indicated by thick gray background, elements remain stationary for periods ranging from several days to most of the developmental process. Data for this figure are provided in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002212#pbio.1002212.s002" target="_blank">S2 Data</a>.</p

Symmetry-breaking elements define longitudinal proportions in long bones.

<p>Three-dimensional reconstruction from micro-CT scans of the six limb long bones at P40. The longitudinal position of each element is indicated either by a single colored mark on the tip of the superstructure or by two colored marks at its proximal (P) and distal (D) margins, depending on the size and the morphology of the superstructure. Margins that overlap with the end of the bone or with a growth plate were not marked.</p

A flowchart of the algorithm for rigid registration of multiple bone images.

<p>The input of the algorithm is <i>N</i> 3D micro-CT images {<i>I</i>^<i>N</i>} and the index of the root image (<i>I</i>^<i>Root</i>; 1 ≤ <i>Root</i> ≤ <i>N</i>) to which all other images will be registered. <b>(A)</b> Preprocessing. For each input image <i>I</i>^<i>N</i>: 1. Zero-out all trabecular regions. 2. Zero-out all background regions. 3. Align bone to axes by applying PCA. 4. Extract cylindrical shape descriptor. <b>(B)</b> Pairwise Registration. For a pair of a source (<i>I</i>^<i>s</i>) and a target (<i>I</i>^<i>t</i>) image: 5. For each of the four basic alignments between the bones (with or without proximal-distal inversion × with or without right-left side inversion), calculate the affinity (<b><i>Ψ</i></b>) between the extracted shape descriptors of <i>I</i>^<i>s</i> and <i>I</i>^<i>t</i> as a function of the rotation angle (<b><i>Θ</i></b>) of <i>I</i>^<i>t</i> about <i>PC1</i>. 6. From each local optimum in the calculated affinity function, perform several volume-based registration steps using NCC as a similarity measure and downhill descent as the optimization method. 7. Identify the path that reached the highest NCC score and optimize it using additional volume-based registration steps until convergence is reached. 8. If NCC <0.7, perform manual validation of the registration. <b>(C)</b> Agglomeration of pairwise to multiple image registration and interpolation. 9. Sort and re-index all bones based on their lengths, from shortest (“1”) to longest (“<i>N</i>”). 10. Register all pairs of bones <i>I</i>^<i>s</i>, <i>I</i>^<i>t</i> (<i>s</i> < <i>t</i>) adhering to either one of the following criteria: <i>I</i>^<i>s</i> and <i>I</i>^<i>t</i> are lengthwise consecutive: <i>t</i> − <i>s</i> = 1 (subdiagonal entries in <i>D</i>; in blue), or <i>t</i> – <i>s</i> > 1 ∧ <i>Length</i>(<i>I</i>^<i>t</i>)/<i>Length</i>(<i>I</i>^<i>s</i>) ≤ 1.2 (non-subdiagonal entries in <i>D</i>; in green). Assign the resulting NCC score in the corresponding cell in <i>D</i>. 11. Calculate the MST of the graph inspired by <i>D</i>, with <i>I</i>^<i>Root</i> being the root of the tree. 12. Infer all final transformations (<i>A</i>^<i>N</i>) based on the MST. 13. Transform/interpolate each image <i>I</i>^<i>N</i> according to its inferred final transformation. The output is <i>N</i> 4 × 4 homogenous transformation matrices </p><p></p><p></p><p></p><p><mo>{</mo></p><p></p><p><mi>A</mi></p><p><mi>f</mi><mi>i</mi><mi>n</mi><mi>a</mi><mi>l</mi></p><mi>N</mi><p></p><p></p><mo>}</mo><p></p><p></p><p></p><p></p>, each aligns the corresponding input image <i>I</i>^<i>N</i> to the root image <i>I</i>^<i>Root</i>, and the <i>N</i> transformed images. For more details, see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002212#sec011" target="_blank">Materials and Methods</a>.<p></p

Growth balance is optimized for minimum element drifting activity.

<p>Graphs showing the range of relative positions of the FP in which the total drifting activity of symmetry-breaking elements is minimal and the actual relative position of the FP in each bone as a function of total bone length. On the right of each graph is a 3D representation of an adult bone with colored marks of element locations. Throughout the development of all bones, the FP either overlaps or is in high proximity to the range of values that leads to minimal element drifting activity. Data for this figure are provided in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002212#pbio.1002212.s004" target="_blank">S4 Data</a>.</p

The fixed plane model for isometric scaling of long bones.

<p>Illustration of fixed planes formed at the transverse plane where the ratio between the distances from the distal and the proximal ends of the bone is equal to the ratio between the distal and the proximal growth rates. <b>(A)</b> When growth is symmetric, the relative position of an element located at 50% length (rectangle) is maintained, whereas an element located at 75% length (triangle) drifts proximally to maintain its relative position. <b>(B)</b> When distal growth rate is three times higher than proximal growth rate, the location of the FP is at the 75% length. As a result, the relative position of the triangle element is maintained, whereas the rectangle element drifts distally to maintain its relative position.</p

Growth balance remains invariant when stationary elements are present.

<p>Graphs showing growth at the proximal and distal ends of each bone as a function of the total length of the bone. Black vertical tags mark the ends of fitted lines, indicating time points at which an element either becomes stationary or begins to drift (the stationary elements are indicated by gray thick background in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002212#pbio.1002212.g006" target="_blank">Fig 6</a>). Regression analysis shows that at all intervals during which a stationary element is detected, the proximal/distal growth rate balance remains invariable (0.87 ≤ <i>R</i>^<i>2</i> ≤ 0.99, <i>p</i>-value < 10e-05). Data for this figure are provided in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002212#pbio.1002212.s003" target="_blank">S3 Data</a>.</p