PosterPDF Available

Modelling and Analysis of Chevron Formation in the Fish Myotome

Authors:
Fabian Rost at Center for Regenerative Therapies, Dresden
Fabian Rost
Lutz Brusch
Lutz Brusch
Lutz Brusch
  • This person is not on ResearchGate, or hasn't claimed this research yet.
Andrew Charles Oates at Max Planck Institute of Molecular Cell Biology and Genetics
Andrew Charles Oates
Download file PDF
Read file
Download citation

Abstract

About 10 hours after fertilization of the zebrafish egg the first somites begin to appear (at 28.5°C). The boundary surfaces between the newly formed somites are planar. During the following 3 hours one observes that the boundaries change their shape into so-called chevrons. Simultaneously, the muscle cells form the myotome and finally connect pairs of somite boundaries [1]. So far, the only suggested mechanism for chevron formation in zebrafish relates swimming movements to somite boundary changes [2]. We review this hypothesis and search for an alternative mechanism which also accounts for chevron formation in non-moving mutants. We analysed movies of developing zebrafish embryos [3] to quantify the boundary shape changes. We suggest that they are due to the forces generated by the developing muscle cells. In a first mathematical model we minimize the energy of a chain of coupled springs. Model analysis yields the exponential increase in boundary bending as a function of somite index which has been observed for the anterior somites. We furthermore outline the application of coupled amplitude equations as a mathematical model for chevron formation in trunk somites. The aim of our ongoing work is to predict how observed shapes emerge and change under modified conditions. [1] Kimmel, C. B., Ballard, W. W., Kimmel, S. R., Ullmann, B., & Schilling, T. F. (1995). Stages of embryonic development of the zebrafish. Dev. Dyn., 203, 253-310. [2] Van Raamsdonk, W., Mos, W., Tekronnie, G., Pool, C., & Mijzen, P. (1979). Differentiation of the musculature of the teleost brachydanio-rerio. 2. effects of immobilization on the shape and structure of somites. Acta Morphologica Neerlando-Scandinavica, 17, 259-274. [3] Schröter, C., Herrgen, L., Cardona, A., Brouhard, G. J., Feldman, B., & Oates, A. C. (2008). Dynamics of zebrafish somitogenesis. Dev. Dyn., 237, 545-553.
Content uploaded by Fabian Rost
Author content
All content in this area was uploaded by Fabian Rost on Apr 17, 2015
Content may be subject to copyright.
Modelling and Analysis of
Chevron Formation in the Fish Myotome
Fabian Rost1
fabian.rost@zih.tu-dresden.de
Lutz Brusch1
lutz.brusch@tu-dresden.de
Andrew C. Oates2
oates@mpi-cbg.de
1Dresden University of Technology, Centre of Information Services and High Performance Computing, 01062 Dresden, Germany
2Max Planck Institue of Molecular Cell Biology, Pfotenhauerstr. 108, 01307 Dresden, Germany
Introduction
Myotomes of adult teleost have a folded shape often referred to as
chevron shape. The chevron shape has been proposed to be optimal
for the alternating body bending during swimming. Much less is
known about which processes underly the ontogenetic development
of the myotome shape.
As far as we know, the only study that deals with this topic was
done by Van Raamsdonk et al. (1974, 1977, 1979). They conclude
”that the lateral body movements have both a shape determining
and a shape-stabilizing role during the early stages of somite mor-
phogenesis.”
We aim to shed new light on the mechanisms that shape the my-
otome chevrons by developing and analysing a mathematical model
of the interactions between muscle fibres and somite boundaries.
3D shape of a myotome of a 3 weeks old zebrafish larva, from Van
Raamsdonk (1979).
Confocal micrographs of β-catenin stained 17 hpf zebrafish
embryo. Side view, anterior to the left, somites 15-19. Red:
Somite boundaries, blue: elongating cells, cyan: cells spanning the
somite. Modified from Henry (2004).
Development of chevrons in the zebrafish myotome. From left to right: 10 somite stage: somite boundaries straight, anterior boundaries begin to
fold. 26 somite stage: most anterior boundaries fairly straight, trunk somites have constant angle, newly formed posterior somites begin folding.
Larva shortly before hatching. Camera Lucida sketches, scale bar = 250µm, taken from zebrafish stageing series from Kimmel (1995).
Model Framework
a1a2a3
x3
x2
x2
Kx
KxKa
Kx
Ka
KxKxKx
L L L
We minimize the energy of a chain of coupled springs:
E=1
2
n
X
i=1
Kxx2
i+Kaa2
i
L=xi+ai−ai−1, i = 1 . . . n
Model analysis yields the exponential increase in
boundary bending as a function of somite index:
ai=C1λi
1+C2λi
2
0
2
4
6
8
10
5 10 15 20 25 30
ai
Somite Number
Ka/Kx:
0.01
0.1
1
10
Data Analysis
We measured angle βin light field time-lapse movies of
dechorionated zebrafish embryos using ImageJ. We calculated
α= 90 −β
2. The movies were provided by Christian Schroeter.
0
10
20
30
40
120 160 200
α [´]
Time [min]
Somite 20
Somite 21
Somite 22
-10
0
10
20
30
40
50
0 10 20 30
α [´]
Somite Number i
Zebrafish
Xenopus
Top: Lateral view of a stage 29/30 xenopus embryo expressing
Dvl1 in the somites. From Gray et al. (2009). Bottom: Lateral
view of a 27-somites stage zebrafish embryo. From Schroeter et
al. (2008).
Model Variant: Variable Spring Constants
•Constant chevron angles for all somites can be obtained for
a=K1
x−K2
x
K1
a+K1
x
=K2
x−K3
x
Ka
=· · · =Ki
x−Ki+1
x
Ki
a
=· · · =Kn
x
Kn
a
.
.
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25 30
Kx/Ka
Somite Number
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25 30
ai
Somite Number
Solution of the equation above with Ki
a=const,a= 0.1.
•Linear increasing angle ai=m·ican be reproduced with
m=K2
x−K1
x
K2
x−K1
x−K1
a
=K3
x−K2
x
K3
x−K2
x−2K2
a
=· · · =Ki+1
x−Ki
x
Ki+1
x−Ki
x−iKi
a
=· · · =Kn
x
Kn
x+nKn
a
.
0
10
20
30
40
50
5 10 15 20 25 30
Kx/Ka
Somite Number
0
0.02
0.04
0.06
0.08
0.1
0 5 10 15 20 25 30
ai
Somite Number
m=1/300
Model Variant: Anharmonic Energy
Introducing anharmonic springs leads to different somite angles. For in-
stance E=1
2Pn
i=1 Kxx2
i+Kae2aican lead to
5
10
15
20
25
30
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
.
We aim to find a potential that leads to a linear increase in ai.
Conclusions
Although our model is not yet able to completely predict the correct
chevron angles in zebrafish we believe our outlined extensions will be able
to do so. The current hypothesis that elongating muscle pioneers which
exert forces on the somite boundaries and therefore are responsible for
the chevron formation is compatible with our model. Data from mutants
with defect chevron or mechanically perturbed embryos would help to
validate our model furthermore.
References
Gray, R.S. et al. Diversification of the expression patterns and developmental functions of the dishevelled gene family during chordate evolution. Dev.
Dyn. 238, 2044-2057 (2009).
Kimmel, C. et al. Stages of embryonic development of the zebrafish. Dev. Dyn. 203, 253-310 (1995).
Raamsdonk, W. et al. Differentiation of the musculature of the teleost Brachydanio rerio. Anat. and Embr. 145, 321-342 (1974).
Raamsdonk, W. et al. Differentiation of the Musculature of the Teleost Brachydanio-Rerio. 2. Effects of Immobilization on the Shape and Structure of
Somites. Acta Mor. Neerl.-Scand. 17, 259-274 (1979).
Raamsdonk, W. et al. On the relation between movements and the shape of the somites in early embryos of the teleost Brachydanio rerio. Contrib. Zool
46, 261-274 (1977).
Schroeter, C. et al. Dynamics of zebrafish somitogenesis. Dev. Dyn. 237, 545-553 (2008).
... Zebrafish muscle segments take on a similar folded shape as the muscle segments in the regenerating axolotl tail. Previously, I proposed a mechanism involving cells that exert mechanical forces to organize the observed segment shapes (Rost 2010). Here, I quantify the segment shapes to test whether the proposed cellular behavior could drive the shaping of muscle tissue. ...
... Contrary to previous suggestions, I show that a particular cell type, the muscle pioneer, is not required for initial shape formation. Finally, I test the tension-and-resistance mechanism that I proposed in my diploma thesis (Rost 2010). This mechanism involves interactions between intra-segmental tension, possibly due to a particular cell differentiation pattern, and segment boundaries. ...
... In particular, I show that muscle pioneers are not required for chevron formation. I test the tension-and-resistance mechanism that I proposed previously (Rost 2010). This mechanism involves interactions between intra-segmental tension and segment boundaries. ...
Data-driven Modeling of Cell Behavior, Morphogenesis and Growth in Regeneration and Development
Thesis
Full-text available
  • Aug 2017
The cell is the central functional unit of life. Cell behaviors, such as cell division, movements, differentiation, cell death as well as cell shape and size changes, determine how tissues change shape and grow during regeneration and development. However, a generally applicable framework to measure and describe the behavior of the multitude of cells in a developing tissue is still lacking. Furthermore, the specific contribution of individual cell behaviors, and how exactly these cell behaviors collectively lead to the morphogenesis and growth of tissues are not clear for many developmental and regenerative processes. A promising strategy to fill these gaps is the continuing effort of making developmental biology a quantitative science. Recent advances in methods, especially in imaging, enable measurements of cell behaviors and tissue shapes in unprecedented detail and accuracy. Consequently, formalizing hypotheses in terms of mathematical models to obtain testable quantitative predictions is emerging as a powerful tool. Tests of the hypotheses involve the comparison of model predictions to experimentally observed data. The available data is often noisy and based on only few samples. Hence, this comparison of data and model predictions often requires very careful use of statistical inference methods. If one chooses this quantitative approach, the challenges are the choice of observables, i.e. what to measure, and the design of appropriate data-driven models to answer relevant questions. In this thesis, I applied this data-driven modeling approach to vertebrate morphogenesis, growth and regeneration. In particular, I study spinal cord and muscle regeneration in axolotl, muscle development in zebrafish, and neuron development and maintenance in the adult human brain. To do so, I analyzed images to quantify cell behaviors and tissue shapes. Especially for cell behaviors in post-embryonic tissues, measurements of some cell behavior parameters, such as the proliferation rate, could not be made directly. Hence, I developed mathematical models that are specifically designed to infer these parameters from indirect experimental data. To understand how cell behaviors shape tissues, I developed mechanistic models that causally connect the cell and tissue scales. Specifically, I first investigated the behaviors of neural stem cells that underlie the regenerative outgrowth of the spinal cord after tail amputation in the axolotl. To do so, I quantified all relevant cell behaviors. A detailed analysis of the proliferation pattern in space and time revealed that the cell cycle is accelerated between 3–4 days after amputation in a high-proliferation zone, initially spanning from 800 µm anterior to the amputation plane. The activation of quiescent stem cells and cell movements into the high-proliferation zone also contribute to spinal cord growth but I did not find contributions by cellular rearrangements or cell shape changes. I developed a mathematical model of spinal cord outgrowth involving all contributing cell behaviors which revealed that the acceleration of the cell cycle is the major driver of spinal cord outgrowth. To compare the behavior of neural stem cells with cell behaviors in the regenerating muscle tissue that surrounds the spinal cord, I also quantified proliferation of mesenchymal progenitor cells and found similar proliferation parameters. I showed that the zone of mesenchymal progenitors that gives rise to the regenerating muscle segments is at least 350 µm long, which is consistent with the length of the high-proliferation zone in the spinal cord. Second, I investigated shape changes in developing zebrafish muscle segments by quantifying time-lapse movies of developing zebrafish embryos. These data challenged or ruled out a number of previously proposed mechanisms. Motivated by reported cellular behaviors happening simultaneously in the anterior segments, I had previously proposed the existence of a simple tension-and-resistance mechanism that shapes the muscle segments. Here, I could verify the predictions of this mechanism for the final segment shape pattern. My results support the notion that a simple physical mechanism suffices to self-organize the observed spatiotemporal pattern in the muscle segments. Third, I corroborated and refined previous estimates of neuronal cell turnover rates in the adult human hippocampus. Previous work approached this question by combining quantitative data and mathematical modeling of the incorporation of the carbon isotope C-14. I reanalyzed published data using the published deterministic neuron turnover model but I extended the model by a better justified measurement error model. Most importantly, I found that human adult neurogenesis might occur at an even higher rate than currently believed. The tools I used throughout were (1) the careful quantification of the involved processes, mainly by image analysis, and (2) the derivation and application of mathematical models designed to integrate the data through (3) statistical inference. Mathematical models were used for different purposes such as estimating unknown parameters from indirect experiments, summarizing datasets with a few meaningful parameters, formalizing mechanistic hypotheses, as well as for model-guided experimental planning. I venture an outlook on how additional open questions regarding cell turnover measurements could be answered using my approach. Finally, I conclude that the mechanistic understanding of development and regeneration can be advanced by comparing quantitative data to the predictions of specifically designed mathematical models by means of statistical inference methods.
View
On the Relation between Movements and the Shape of Somites in Early Embryos of the Teleost Brachydanio Rerio
Article
Full-text available
  • Jan 1977
As a working hypothesis it is supposed that in the teleost Brachydanio rerio , the muscle contractions, the growth, and probably some other factors, cause the first changes in the shape of the somites. Furthermore, the movements of the embryo could yield the forces by which the somites are brought to their theoretically optimal shape. In order to test this hypothesis, we investigated the somite shape and structure of spontaneously immobile embryos. Although the results are difficult to interpret, they certainly do not contradict the hypothesis. For further analysis we applied two kinds of lesions in order to immobilize early embryos: removal of the brain, and damage to the midbody somites. The results of these experiments indicate that both the development of the shape of the somite and the arrangement of the muscle fibres are dependent on movements of the embryo.
View
Diversification of the expression patterns and developmental functions of the Dishevelled gene family during chordate evolution
Article
Full-text available
  • Aug 2009
Dishevelled (Dvl) proteins are key transducers of Wnt signaling encoded by members of a multi-gene family in vertebrates. We report here the divergent, tissue-specific expression patterns for all three Dvl genes in Xenopus embryos, which contrast dramatically with their expression patterns in mice. Moreover, we find that the expression patterns of Dvl genes in the chick diverge significantly from those of Xenopus. In addition, in hemichordates, an outgroup to chordates, we find that the one Dvl gene is dynamically expressed in a tissue-specific manner. Using knockdowns, we find that Dvl1 and Dvl2 are required for early neural crest specification and for somite segmentation in Xenopus. Most strikingly, we report a novel role for Dvl3 in the maintenance of gene expression in muscle and in the development of the Xenopus sclerotome. These data demonstrate that the expression patterns and developmental functions of specific Dvl genes have diverged significantly during chordate evolution.
View
Stages of Embryonic-Development of the Zebrafish
Article
We describe a series of stages for development of the embryo of the zebrafish, Danio (Brachydanio) rerio. We define seven broad periods of embryogenesis—the zygote, cleavage, blastula, gastrula, segmentation, pharyngula, and hatching periods. These divisions highlight the changing spectrum of major developmental processes that occur during the first 3 days after fertilization, and we review some of what is known about morphogenesis and other significant events that occur during each of the periods. Stages subdivide the periods. Stages are named, not numbered as in most other series, providing for flexibility and continued evolution of the staging series as we learn more about development in this species. The stages, and their names, are based on morphological features, generally readily identified by examination of the live embryo with the dissecting stereomicroscope. The descriptions also fully utilize the optical transparancy of the live embryo, which provides for visibility of even very deep structures when the embryo is examined with the compound microscope and Nomarski interference contrast illumination. Photomicrographs and composite camera lucida line drawings characterize the stages pictorially. Other figures chart the development of distinctive characters used as staging aid signposts. ©1995 Wiley-Liss, Inc.
View
Differentiation of the musculature of the teleost Brachydanio rerio. II. Effects of immobilization on the shape and structure of somites
Article
  • Jan 1980
The development of the shape and structure of somites in the teleost Brachydanio rerio was studied in embryos under normal conditions and in immobilized embryos. Three different immobilization methods were applied: enclosure in agar, a glass rod in the neural tube and anaesthesia in MS-222. When the performance of the lateral body movements is prevented, the shape development of the somites in embryos and young larvae becomes reversed. When the agar-immobilization is terminated, the larvae resume their normal movements. In about 10 days, the shape of the somites is again as in control larvae. We conclude, that the lateral body movements have both a shape-determining and a shape-stabilizing role during the early stages of somite morphogenesis. It is suggested that in normal embryos differences in shortening between lateral and medial muscle fibres, cause differences in longitudinal growth of the muscle fibres and that the oblique muscle fibre arrangement is a consequence of these differences in growth. In immobilized embryos and larvae, the longitudinal growth of the muscle fibres is decreased. Also the difference in the longitudinal growth rate between lateral and medial muscle fibres diminishes in all somites. We conclude that for the normal morphogenesis of the somites the performance of the specific function, that is to bring about lateral body movements, is required. We suggest, that the impact of the lateral body movements on the development of the structure of the somites is mediated through adaptive growth of the muscle fibres. The suggestion may also apply to the development of the pinnate structure of muscles of higher vertebrates.
View
Differentiation of the musculature of the teleost Brachydanio rerio. I. Myotome shape and movements in the embryo
Article
  • Feb 1974
The histological differentiations of myotomes and myosepts in the teleost Brachydanio rerio were studied in relation to function and shape development of the myotomes. The presence of contractile elements, intercellular space, growth by cell proliferation and the collagenous structure of the myosepts were considered as important characteristics. To a certain extent, the first deformations of the somites could be explained with these characteristics. It is suggested that firm attachment of the myosept collagen to the notochord sheath and the asymmetrical growth of the myotomes, might be of importance for the development of the oblique orientation of the muscle fibres. The sequence of the differentiation processes is not the same for all muscle cells. Cells next to the notochord synthetize myofilaments before they become polynuclear, while cells elsewhere in the myotome become polynuclear by fusion before they start to synthetize myofilaments. Some aspects of the histological differentiation of the myotomes in B. rerio were compared with myotome development in the chick, Gallus domesticus.
View
Dynamics of zebrafish somitogenesis
Article
  • Mar 2008
Vertebrate somitogenesis is a rhythmically repeated morphogenetic process. The dependence of somitogenesis dynamics on axial position and temperature has not been investigated systematically in any species. Here we use multiple embryo time-lapse imaging to precisely estimate somitogenesis period and somite length under various conditions in the zebrafish embryo. Somites form at a constant period along the trunk, but the period gradually increases in the tail. Somite length varies along the axis in a stereotypical manner, with tail somites decreasing in size. Therefore, our measurements prompt important modifications to the steady-state Clock and Wavefront model: somitogenesis period, somite length, and wavefront velocity all change with axial position. Finally, we show that somitogenesis period changes more than threefold across the standard developmental temperature range, whereas the axial somite length distribution is temperature invariant. This finding indicates that the temperature-induced change in somitogenesis period exactly compensates for altered axial growth.
View