Yasuhiro Inoue

Physical force guides morphogenesis

Fig 1. 3D vertex simulation of cell behavior on top of an elastic matrix: cell proliferation occurs in the central area of the tissue sheet, resulting in tube formation and elongation in an upward direction.

As early as the beginning of the twentieth century, the Scottish mathematical biologist D'Arcy Wentworth Thompson (1860-1948) postulated in his magnum opus “On growth and Form” that animals and plants are created by the progressive division and subdivision of space, orchestrated by nothing more than physical forces. Whether true or false remains to be proven, but only few will deny that the instrumental role of mechanical forces during morphogenesis has been severely underestimated for many years – not in the least because the unraveling of the cellular and molecular machinery involved in the control of developmental processes has been so successful. In the mean time however, it has dawned upon many that an all encompassing understanding of embryonic development - call it a “holistic” view, if you want - will not be realized without a thorough analysis of mechanical forces and the role they play.

Prof. Inoue and his team are trying to fill in this gap, thereby focusing on physical parameters that control the dynamic behavior of epithelial sheets. As a matter of fact, morphogenesis is frequently driven by characteristic tissue deformations, such as invagination, evagination, lumen formation, folding, branching and elongation. The mechanical forces that provoke such deformations can be generated by a variety of cellular activities: torsion, adhesion, mitosis, contraction, etc. One of the main unsolved problems, preventing a thorough understanding of how biological form arises from mechanical activities, is: “How do cells and tissues sense and adapt to the mechanical environment?” In trying to answer that question, Prof. Inoue and his co-workers have translated the parameters that control epithelial deformations into a defined set of mathematical equations. In doing so, they could develop computer algorithms that recapitulate essential features of mechanosensing and mechanical adaptation during morphogenesis.

The Fine Cell model recapitulates dynamic tissue deformations

Fig 2. Fine cell simulation: the centripetal motion of cells in a sheet would normally result in so called “traffic jam”, but as a result of rotational motion such chaotic behavior is avoided and cells are moving towards another direction.

The role of computational models as powerful tools to study cell and tissue mechanics during development is not disputed. Indeed, simulation models can be used for abstract representations of morphogenetic phenomena that allow testing hypotheses and generating new predictions that can be validated experimentally. The computer algorithm developed by Prof. Inoue can be described as a 3D vertex model, whereby individual cells are represented as polyhedrons, expressed by vertices that comprise a single network: the tissue field. Tissue deformations are represented as mathematical equations that describe the movement of vertices as a response to physical force, e.g. resulting from growth or torsion within a cell.

Fig 3. The Fine cell model recapitulates cell division - technically challenging to simulate - using a computational geometry algorithm.

An important advantage of 3D vertex models is that cells are thus represented as individual objects and can be distinguished from one another. However, in conventional 3D vertex models this individuality has its limits: cells are still considered to adhere tightly to each other and consequently cannot move separately within the field. To free the model from these constraints, Prof. Inoue has developed the Fine Cell model, whereby individuality of single cells is taken to the next level. In his model each cell is enclosed by an elastic membrane and cellular interactions - e.g. how tight cells are connected to each other - are introduced as a set of mathematical equations. Such an algorithm allows freedom of movement for each individual cell and can simulate any cell rearrangement or tissue deformation in a 3D space.

Simulating signal-dependent epithelial sculpting

The size of a developing tissue determines the magnitude of the physical force generated within that tissue. As such, signal dependent epithelial growth can result in various morphogenetic movements, eventually resulting in a variety of shapes.

Fig 4. The size of a developing tissue determines the magnitude of the physical force generated within that tissue. As such, signal dependent epithelial growth can result in various morphogenetic movements, eventually resulting in a variety of shapes.

Multicellular structures emerge from a complex interplay between biochemical factors and physical forces during embryogenesis. Notably, biochemical patterning is dynamically coupled with signal-dependent cell activities, such as adhesion, torsion, migration, proliferation and apoptosis: a process that is only beginning to be understood. In search for general principles that guide this mechanochemical coupling, Prof. Inoue and his co-workers are trying to reveal how the distribution of a morphogen - a gradient of a diffusible signaling molecule, essentially laying down instructions in a 2D field - is translated into coordinated tissue deformations in a 3D field. To that end, they have developed a novel 3D vertex model that recapitulates essential features of mechanical tissue deformations in response to molecular signaling. By specifying a given density of a signaling molecule for each individual cell - while expressing intercellular transport through a defined set of mathematical equations - they could simulate signal-dependent epithelial growth and observe various types of tissue behavior, relevant to morphogenesis: arrest, expansion, invagination and evagination.

Apical constriction, cell elongation and cell migration collectively drive neural tube formation.

Cellular and tissue deformations during neural tube formation are recapitulated using the 3D vertex model.

Fig 5. Cellular and tissue deformations during neural tube formation are recapitulated using the 3D vertex model.

Recently, in a collaborative effort with Prof. Naoto Ueno (National Institute for Basic Biology, Okazaki), Prof. Inoue and his team have demonstrated that three physical events at the cellular level are sufficient to mechanically drive neural tube formation - the anlage of the central nervous system that gives rise to the brain and spinal cord - in Xenopus: apical constriction, cell elongation and cell migration.

* During neural tube closure, cells in the superficial layer of the neuroectoderm undergo apical constriction: actomyosin contractility causes shrinkage of the apical surface area of each cell and leads to a change in cell morphology from a columnar to a wedge-like shape.
* Cells undergoing apical constriction also undergo elongation, whereby cell length (height) increases in the apical-basal direction.
* Prof. Ueno and his team have recently demonstrated that migration of non-neuroectodermal cells in the deep layer (which itself does not give rise to the neural tube) does play a role during neural tube closure.

The 3D vertex model constructed by Prof. Inoue, accounts for the mechanical properties of tissue components and successfully recapitulates tissue deformations during neural tube formation. Using this model, apical constriction, cell elongation, and cell migration were independently perturbed in silico and their effects on tissue morphology were examined: neural plates of various shapes could thus be observed. Moreover, by experimentally inhibiting apical constriction and cell elongation at the appropriate developmental stage in Xenopus embryos, Prof. Ueno and his team could show that the resulting cell and tissue shapes resembled the corresponding simulation results, thereby validating the 3D vertex model in vivo.

Meanwhile, Prof. Inoue and his team have improved the 3D vertex model by taking into account another physical parameter: the elasticity of the extracellular matrix (ECM). As such, they could convincingly demonstrate that the mechanical properties of the extracellular environment have an impact on neural tube formation and can drastically alter the 3D shape of an epithelial tissue. Indeed, the in silico simulations of neural tube formation without cell elongation, showed a causal link between the 3D shape of the neural plate and ECM elasticity. On the other hand, no such relationship could be observed during simulations with cell elongation (whereby the 3D shape of the neural plate was quasi insensitive to ECM elasticity). These data therefore suggest that robustness - the neural tube adopts its correct 3D shape, despite developmental noise - is ensured by cell elongation during morphogenetic events.

A look into the Future
Science Fiction
Science or Fiction?
Prof. Inoue, in which directions are your research projects developing?
Prof. Inoue:
We are continuously striving at improving our 3D models, as to enable us to simulate epithelial deformations that resemble more and more in vivo situations. In this manner we hope to identify mechanical key components that control morphogenetic events.
What are your research aims?
Prof. Inoue:
I would like to understand feed-back mechanisms that are mediated by mechanical parameters. Morphogenesis must somehow rely on a feed-back system that couples mechanosensing and response. To dissect and understand such phenomena is a major challenge and may require - in addition to physical and biological research methods, be it theoretical or experimental - other approaches, for example concepts borrowed from information theory. In this context, it is probably also meaningful to make a distinction between short term causality - individual cells possess mechanosensitivity, enabling them to alter their behavior as an immediate response to a mechanical trigger - and long-term causality, by which various morphogenetic events are coordinated in space and time.
Which kind of cell behavior could be triggered by mechanical force?
Prof. Inoue:
For example, a cell can modify the plane in which mitosis occurs - let's say: meridional or latitudinal - in response to mechanical stress. It has been demonstrated that the direction of cell division is an important physical parameter that controls 3D folding. Now, a population of cells going through successive rounds of mitosis within a confined area can generate elastic energy, capable of inducing deformations. After a deformation has taken place, this elastic energy or equivalent stress is relaxed and a new equilibrium level is reached. In a next developmental stage, a cell may be responsive again to a new stress field.
What would be your ultimate scientific dream?
Prof. Inoue:
When we talk about my scientific dreams, “universality” is certainly a key word that comes to my mind.
Prof. Inoue:
Yes indeed. We can observe similar or very analogous physical phenomena in diverse systems, even across the boundaries that separate the living from the non-living world. For example, liquid crystals are usually aligned in a specific, non random manner. When a rearrangement of one or a few crystals is provoked - as a result of a mechanical trigger, for example - the other crystals in the field realign themselves in response. Intriguingly, similar dynamic rearrangements can be observed in a school of fish or a flock of birds and have been described for cells in an epithelial sheet in vivo. Likewise, we have observed such behavior of individual cells with our 3D vertex model. I am tempting to believe that these phenomena are somehow connected and that behind the complex 3D patterning events observed during embryonic development, some common general rules are hidden. It is my scientific dream to understand this universality and find unifying principles behind what we observe.
  1. Okuda S, Inoue Y, Watanabe T, Adachi T. Coupling intercellular molecular signalling with multicellular deformation for simulating three-dimensional tissue morphogenesis. Interface Focus, 5, 20140095, 2015.
  2. Inoue Y, Suzuki M, Watanabe T, Yasue N, Tateo I, Adachi T, Ueno N. Mechanical roles of apical constriction, cell elongation, and cell migration during neural tube formation in Xenopus. Biomech Model Mechanobiol. 2016. DOI: 10.1007/s10237-016-0794-1
Who is Who?

Prof. Inoue

Prof. Yasuhiro Inoue

Prof. Yasuhiro Inoue was born and raised in Okaya, in the central part of Japan. After finishing his junior and high school years in Nagano and his bachelor studies in Physics at Hokkaido University, he went to the University of Tokyo to do his doctoral work on the hydrodynamics of complex fluids - at the Department of Quantum Engineering and Systems Science - under supervision of Prof. Hirotada Ohashi. Staying at the same University, Prof. Inoue switched thereafter to the Department of Mechanical Engineering, to absolve a post-doctoral training in the field of molecular dynamics. After developing computer models to simulate cell and tissue migration (with special emphasis on fish keratocytes) at the Riken Research Institute, Prof. Inoue accepted a position as Assistant Professor at the Department of Mechanical Engineering at Kyoto University. At present, Prof. Inoue is Associate Professor at the Institute for Frontier Life and Medical Sciences at the same University, doing research on cell migration and tissue deformations from a theoretical perspective.