OSAKA UNIVERSITY,
Center for Mathematical
Modeling and Data Science
Takashi Suzuki

This modeling approach aims to be not only qualitative but also quantitative.

Since the main factors are eliminated to achieve coarse graining, few basic parameters are used.

Therefore, in many cases, those parameters can be set by only adopting dimensional analysis, in addition to typical experimental values.

To verify correctness of the model, numerical simulations are adopted in the first place.

After the model is tentatively determined through the simulations, mathematical analysis is then used for remodeling to predict the life dynamics.

Also in this case, it is important to visualize a biological phenomenon through the numerical simulations.

With respect to the partial differential equations including spatial distributions in this case, the model and the numerical simulations are clearly separated from each other in consideration.

A main variable representing particles is discretely varied to give fluctuation, whereas adaptive simulations are conducted according to a trend of an environmental variable.

Such complex simulations are referred to as hybrid simulations.

A distinctive feature of the hybrid simulations is to construct particle motion and formation of its field with flexible rules by grasping the essence of the model, instead of literally and faithfully quantizing the model.

So far, I have been engaged in construction of the theory of the mathematical science and development of relevant technologies as described above, while targeting malignant progression of cancer cells, as “integral mathematical oncology”.

In this research region “mathematical signal”, this method will further be expanded to describe events penetrating a bio-hierarchy inside and outside the cell or over the cells.

This will establish a technique for unraveling the biological phenomenon.

This research project has been initiated from analysis of NFkB standard paths, and currently found out that a vibration phenomenon for signaling can be explained by using a simple dynamical system of the ordinary differential equation system, which is contracted to three components, through analysis of the classical model.

From now on, the research project will be conducted with the above mathematical analysis plan being freely used, while trying to introduce results of systems biologic methods and structural analysis.

Various approaches will be conducted such that this research region establishes a status in which the mathematical modeling assists promotion of highly-attractive wet research, and suggests new research directions.