| Academic Year |
2025Year |
School/Graduate School |
Graduate School of Integrated Sciences for Life (Master's Course) Division of Integrated Sciences for Life Program of Mathematical and Life Sciences |
| Lecture Code |
WG114003 |
Subject Classification |
Specialized Education |
| Subject Name |
数理生物学 |
Subject Name
（Katakana） |
スウリセイブツガク |
Subject Name in
English |
Mathematical Biology |
| Instructor |
FUJIMOTO KOICHI |
Instructor
(Katakana) |
フジモト コウイチ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, Second Semester, 3Term |
| Days, Periods, and Classrooms |
(3T) Weds1,Weds4：Online, (3T) Weds2-3 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Online (on-demand) |
| |
| Credits |
2.0 |
Class Hours/Week |
4 |
Language of Instruction |
J
:
Japanese |
| Course Level |
5
:
Graduate Basic
|
| Course Area（Area） |
26
:
Biological and Life Sciences |
| Course Area（Discipline） |
04
:
Life Sciences |
| Eligible Students |
|
| Keywords |
Cellular-level phenomena, basic mathematical modeling, differential equations, probability distributions, diffusion |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Class Objectives
/Class Outline |
In living systems, many molecules and cells cooperate with each other and perform complex temporal and spatial regulation. In this course, students will acquire a basic ability to understand living systems physically and mathematically through the study of examples of experiments that appropriately capture the spatio-temporal characteristics of living organisms and the related mathematics.
Objective: To be able to explain natural phenomena by formulating models based on ordinary differential equations, probability distributions, and diffusion equations. To be able to obtain the time evolution of linear ordinary differential equations. To be able to derive ordinary differential equations for gene expression levels according to chemical reaction kinetics. To be able to analyze the steady-state stability of ordinary differential equations. Can explain the characteristics of multiple probability distributions and the mechanism of generation of such distributions. Be able to list the characteristics of diffusion. Can explain the connection between diffusion and random walk. Analyze the steady-state stability of the reaction-diffusion equation. |
| Class Schedule |
The course will be divided into three thematic lectures on physical and mathematical views of life phenomena. Each will introduce a key cellular or individual-level life phenomenon (time variation, stochasticity, spatial patterns). In parallel, students will learn the framework for mathematical understanding of these phenomena in space-time (differential equations, probability distributions, diffusion equations, etc.) and will be introduced to elementary theories of nonlinear nonequilibrium systems and networks.
1st-7th: Time variation: Guidance, Representation of cell growth and differentiation by differential equations, Representation of gene expression by differential equations, Role of positive feedback (switch, history phenomenon), Role of negative feedback (stabilization, temporal oscillation).
8-11th: Stochasticity: Stochastic behavior of cells, from binomial distribution to normal distribution, why stochasticity cannot be ignored in biochemical reactions in cells, from binomial distribution to Poisson distribution, superposition of distributions, network structure of genes and human society as seen from probability distributions
12-15th: Spatial patterns: from Brownian motion to the diffusion equation, derivation of morphogen concentration gradient from the diffusion equation, various spatial patterns of reaction and diffusion, theory of Turing's pattern (diffusion-induced instability).
There will be some variation as we progress.
|
Text/Reference
Books,etc. |
Textbooks, reference books, etc. To be announced. |
PC or AV used in
Class,etc. |
|
| (More Details) |
Handouts, slides, videos
|
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
Students should review the mathematics (vector analysis, linear algebra, calculus, differential equations, probability [binomial distribution, expected value]) that they have learned up to the second year. |
| Requirements |
|
| Grading Method |
reports |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |