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Masakazu Akiyama

Centrosome position determines cleavage pattern

Prof. Akiyama and his team are trying to understand how a single fertilized egg can develop into an adult organism, through an ever changing pattern of shape changes and growth. Which principles are hiding behind seemingly endless, consecutive changes of 3D shapes? Which mechanisms are involved? In search for answers, they have focused on the question of how spatial coordination is achieved during the very first cell divisions, after fertilization of the egg. In particular, they are trying to understand why cell divisions occur the way they occur: which mechanism determines whether and when a meridional cleavage (perpendicular to the animal-vegetal pole) or a latitudinal cleavage (parallel to the animal-vegetal pole) is going to occur?

Fertilized egg of a sea urchin IS THIS CORRECT?

Fig 1. Fertilized egg of a sea urchin

Meanwhile, several studies have shown that the direction of cleavage patterns is linked to the position that both centrosomes occupy, immediately before cell division. These organelles lie at the heart of the complex cytoskeletal machinery that divides the nucleus (karyokinesis), after which a contractile ring cuts the cell into two daughter cells (cytokinesis) along a plane perpendicular to the orientation of the spindle apparatus. Or in other words: one specific position of the centrosomes will lead to a meridional cleavage (“vertical”), whereas another position will result in a latitudinal cleavage (“horizontal”). At least one fundamental question remains unanswered: at present, it is completely unknown which mechanism controls the direction of movement and the ultimate position that both centrosomes will occupy, prior to cell cleavage.

3D models: early embryogenesis in silico?

First embryonic cell divisions in the sea urchin

Fig 2. First embryonic cell divisions in the sea urchin

Using the sea urchin as a model organism, Prof. Akiyama and his co-workers have focused on the very early cleavage patterns. The fertilized egg goes through alternating meridional and latitudinal cleavages: 1st meridional, 2nd meridional, 3rd latitudinal, 4th meridional, 5th latitudinal… This highly orchestrated sequence of consecutive cell cleavages eventually gives rise to a multicellular sphere: the blastula. Prof. Akiyama's 3D simulation model is based on a small defined set of premises, the most important being:

* The positions and movements of both centrosomes are depicted as two vectors (r1, r2) in a Cartesian coordinate system, representing one cell.
* Through diffusion, two different chemical substances form a concentration gradient from the poles towards the equator of the cell: substance A diffuses from the animal pole, while substance B diffuses from the vegetal pole. This double gradient assumption was based on the pioneering work of the Swedish embryologist Sven Hörstadius (1898-1996), who experimentally demonstrated the existence of such gradients in sea urchin embryos.
* In response to this double gradient, both centrosomes show chemo-repulsion, away from the animal pole and chemo-attraction, towards the vegetal pole.
* Both centrosomes (connected through microtubuli) create a repulsive force against each other and towards the cell membrane. As a result, a second repulsive force is generated from the membrane.

Some essential features of the 3D model, simulating early cell divisions during sea urchin developmentt

Fig 3. Some essential features of the 3D model, simulating early cell divisions during sea urchin developmentt

In other words, the 3D model postulates that an elaborate interplay between mechanical and chemical forces directs the movement of both centrosomes towards a given position, resulting in a specific cleavage pattern: meridional or latitudinal. Depending on the cleavage plane, the daughter cells will adopt a characteristic size and shape (e.g. spherical or rugby ball shaped), which will influence the quantitative values of the parameters - in the new Cartesian coordinate system of each daughter cell - and consequently the next cleavage type.

Translating these a priori assumptions into the language of Mathematics - through formulating a defined set of equations - Prof. Akiyama and his team could indeed simulate the developmental program of the early cleavage pattern, characteristic of a sea urchin. But that was not the end of the story: resetting the quantitative values for specific parameters resulted in different spatio-temporal sequences of meridional and latitudinal cleavages in silico. Amazingly, such alternative morphogenetic strategies are employed by nature itself: the 3D model could infallibly recapitulate the early embryonic cleavage patterns of other echinoderms, such as sea stars and sea cucumbers…

A 3D model for hindgut rotation in Drosophila

A 3D model simulating hindgut rotation during Drosophila embryogenesis

Fig 4. A 3D model simulating hindgut rotation during Drosophila embryogenesis

As part of a collaborative effort with Prof. Kenji Matsuno (Osaka University) , Prof. Akiyama developed a 3D model that simulated hindgut rotation during Drosophila embryogenesis. The embryonic hindgut is a single layered epithelial tube that rotates 90 degrees anti-clockwise, forming a rightward curving structure: a process that is guided by the epithelial cells and is not accompanied by cell rearrangements, cell proliferation or apoptosis. Based on a defined set of parameters (e.g. size, shape and number of cells) this 3D model recapitulates all cell and tissue deformations, relevant to hindgut rotation. Moreover, the algorithm predicted that epithelial hindgut cells should have a different shape at the apical versus the basal side: a hitherto unobserved feature that could be corroborated in vivo by Prof. Matsuno and his team: reality confirmed the model!

In search for mechanistic explanations, Prof. Akiyama decided to reverse cause and outcome and approached the problem from the opposite angle: twist the tube and see what happens to the cells. Consequently, a virtual physical force was generated as to provoke an in silico twisting of the hindgut tube. And most intriguingly, cell shape changes were indeed observed - more specifically, a torsion spreading through each columnar cell from the apical to the basal side - associated with the twisting of the hindgut. As such, the 3D model suggests a direct link between individual cell shape changes and rotation of the hindgut. Based on these observations, a hypothesis was formulated, stating that coordinated cell shape changes - twisting of each cell, whereby the relative position of the basal and apical surface changes towards each other - cause rotation of the hindgut. The in vivo data thus far obtained by Prof. Matsuno and his team, deliver evidence for hitherto unobserved collective cell behavior: epithelial cells twist clockwise before rotation of the hindgut and re-twist anticlockwise after rotation, essentially confirming the predictions of the 3D model. Given this scenario, it is tempting to speculate that torque - generated by collective winding and rewinding of cells - provides the mechanical force that drives tissue deformations, associated with hindgut rotation.

A look into the Future
Science Fiction
Science or Fiction?
Prof. Akiyama, in which directions are your research projects developing?
Prof. Akiyama:
Up till now, our model for early embryogenesis in the sea urchin is essentially based on calculations in a 2-dimensional field, although the algorithm actually simulates a 3-dimensional event: the early cleavage patterns of a zygote in the sea urchin - and by extension, other echinoderms. At present, we are refining our computer model by including 3-dimensional calculations. The aim is to develop mathematical models that accurately describe complex morphogenetic events. To that end we collaborate with other groups in the 3D Patterning Consortium to tackle specific questions in the field of morphogenesis by means of mathematical modeling, as an alternative and complementary research strategy.
Why do you expect a theoretical model to shed light on what happens in the embryo?
Prof. Akiyama:
During the past decades, a lot of knowledge has been gathered on morphogenetic events in model organisms: genetic data, genomic data, molecular data, anatomical data and so on. And as a result of intensive academic research, quite often hand in hand with technological advancements, ever more data are becoming available. Including these biological data in a working hypothesis - in search for an all encompassing explanation of a given morphogenetic event, such as early embryonic cleavage or hindgut rotation - leads to an enormous complexity. As a matter of fact, a complexity which cannot longer be intuitively grasped. Mathematics enables us to describe a morphogenetic event at its most fundamental level and constructing simple 3D models - based on a defined set of parameters - that recapitulate the in vivo event, can be a very powerful tool to extract basic principles from nature.
Like your model for hindgut rotation in the fruit fly?
Prof. Akiyama:
Exactly, our 3D model to simulate embryonic hindgut rotation in Drosophila has offered some surprising insights and answers to relevant questions and has opened new experimental perspectives. At the moment, I am trying to understand how chirality of hindgut epithelial cells is coordinated. I am constructing a mathematical model, based on the assumption that the chirality of one single cell can determine the chirality of other cells. You could compare this to, let's say, 8 guests at a round dinner table. Let's assume that in front of each guest is a plate, a knife, a fork and a napkin: the parameters. If one guest uses the napkin at his right side, then all other guests will also take a napkin at their right side. In Mathematics or Theoretical Biology this would be defined as a cellular automaton, where each cell in a field has a finite number of states, such as on and off or left and right. In my simulation program, a single cell can force its chirality status upon the other cells: one cell is twisted and consequently the entire tissue is twisted.
REFERENCES
  1. Akiyama M et al. A mathematical model of cleavage.v J Theor Biol. 2010 May 7;264(1):84-94. doi: 10.1016/j.jtbi.2009.12.016. Epub 2010 Jan 4.
Who is Who?

Prof. Akiyama

Prof. Masakazu Akiyama

Prof. Masakazu Akiyama was born in Okayama and studied Mathematics at Hiroshima University. An encounter there with Prof. Ryo Kobayashi - who uses mathematical approaches to understand biological phenomena - won him over to the field of Applied Mathematics. As a consequence, Prof. Akiyama did his PhD work at the Department of Mathematics and Life Sciences (under supervision of Prof. Kobayashi) on constructing mathematical models of early embryonic cell cleavage. Following a post-doctoral training at Hokkaido University, supervised by Ig Nobel laureate Prof. Toshiyuki Nakagaki, Prof. Akiyama moved to Kyushu University, where he developed computer algorithms to simulate locomotion in horses and dogs. At present, Prof. Akiyama is Associate Professor at the Research Institute for Electronic Science (led by Prof. Masaharu Nagayama) of Hokkaido University, where he is involved in mathematical modeling of 3D morphogenesis.

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