1. 森下喜弘 氏：「発生生物学への数理的アプローチ」

我々ヒトを含む動物の発生過程では、各器官は上皮や間充織といった組織が細胞の成長や増殖を 通じて膨らんだり、プログラム細胞死（アポトーシス）によって細部が削り取られたりすることで その複雑な形態を実現する。また同時に、組織の各部分が異なる分化運命（例えば骨や筋肉）を たどることで空間非一様な解剖学的構造が形成される。目標の外形や骨格パタンを実現するための 最初のステップは、各細胞が自身の位置を正確に認識し、適切に応答（分裂、細胞死、分化など） をすることである。位置に関する情報はモルフォゲンと呼ばれる拡散性分子の濃度勾配によって 与えられるが、その濃度分布は生体内のゆらぎのために個体ごとにばらつきが生じる。 本発表の前半では、ゆらいだ環境の中で細胞により正確な位置情報を伝えるためのメカニズムを、 数理モデルや具体的なデータを用いて説明する。また後半では、細胞分裂などを通じて組織が 成長していく様子を記述するための数理モデルを、現在研究中であるニワトリ四肢発生における 組織変形プロセスに関するデータを交えて紹介する。

2. Jens Starke 氏：「Mathematical modelling and analysis of complex nonlinear processes in the olfactory system」

Various types of nonlinear behaviour can be observed in the olfactory system which serves as important model case for other brain regions. Mathematical modelling and analyis of several stages of the odor signal processing from receptor neurons over axons to the glomeruli level and a neural network of mitral and granular cells will be presented.
(1) Nonlinear dynamics in receptor neurons where biochemical mechanisms are responsible for adaptation and oscillations. The existence of an oscillatory regime based on a Hopf bifurcation is proven using stoichiometric network analysis where the knowledge of exact reaction rates is not required.
(2) Axon sorting by self-organization where about one million axons sort in the embyonal phase according to their type, i.e. those of the same type converge to the same positions. A proof of this sorting property will be presented for a simple model with attracting and repulsive interactions.
(3) Spatio-temporal pattern formation in the olfactory bulb. Odors evoke a variety of stimulus specific spatio-temporal patterns on the levels of glomeruli and downstream neural network of mitral and granular cells in the olfactory bulb. Equation-free techniques are used for systematic investigations of macroscopic network activities (bifurcation analysis) and their dependence on the network topology.

3. 柴田達夫 氏：「Spontaneous symmetry breaking in chemotactic signaling systems」

Mathematical modeling is one of the way to integrate the informations of complex biological processes into higher-level phenomena. For developing a mathematical model, quantitative imaging analysis of living cells is increasingly important. Here, I will show examples of mathematical modeling based on statistical analysis of single cell imaging data. Chemotactic cells exhibit spontaneous cell migration even without external chemoattractant gradient, which is generated by intracellular processes of self-polarization and local locomotive activities. We found that at the non-stimulated resting-state self-organized spatiotemoral pattern formation takes place in the phosphatidylinositol (PtdIns) lipids signaling system, which generates an intracellular cue responsible for cellular migration in Dictyostelium cells. From the time-lapse data of fluorescent images of each single cell, we reconstructed a phase portrait of the characteristic oscillatory dynamics in the PtdIns lipids system. Based on the reconstructed dynamics, we developed a reaction-diffusion model that successfully reproduced several spatiotemporal patterns observed experimentally. The constructed mathematical model can explain the mechanism of stable response to shallow chemoattractant gradient.

4. Eamonn Gaffney 氏：「Aspects of ciliary and flagellar dynamics」

Biological evolution has developed remarkable and robust mechanisms for controlling fluids at microscopic scales via cilia and flagella, which are slender cellular appendages whose mechanicxs underlies numerous diverse phenomenam ranging from cellular swimming to the physiological pumping of fluids in the developing embryo, the lung and the cerebrospinal system. We highlight opportunities for fluid and continuum dynamics to provide novel insights concerning the mechanics of spermatozoa cells during their remarkable journey to the egg, with a detailed examples focussing on the interpretation of recent high resolution imaging and further explore how related mathematical models reveal the dynamics of cilia in left-right symmetry breaking within early development and review how recent experiments test this theory.

5. 石原秀至 氏：「Mechanical control of cell configuration in a growing epithelial tissue」

In the course of animal development, tissues undergo series of deformation driven by the mechanical forces generated by the activity of constituent cells. To elucidate physical process as well as molecular processes that determine the eventual forms of their bodies, we have developed a theoretical framework that estimates a pressure of each cell and a tension of each cell-cell contact surface; we derived balance equations of forces that contain the pressures and the tensions as unknown variables, and solve them based on inverse problem technique. The present method is applicable to variety of systems, and allows us to investigate how molecular activity regulates cellular and tissue dynamics in terms of mechanical process. We applied this method to the Drosophila wing, and the estimated values of tension were consistent with responsesto cutting edges. All of the estimated tension and the stress direction, distribution of myosin subunits, responses to laser cutting and shapes of cells consistently indicated that external force stretches the wing along the proximal-distal axis, respectively. Using numerical simulations and force relaxing experiments, the anisotropic force is suggested to accelerate hexagonal cell packing, which is a novel mechanism of cell rearrangement.