Mathematical Modeling in Systems Biology

Mathematical Modeling in Systems Biology#

Course information#

👩‍🏫 Instructor: An-Chi Wei @ MD 521

🦜 Teaching assistant: Wen-Wei Tseng @ MD 705

📝 Announcements & homeworks: NTU Cool

📗 Textbook: Mathematical Modeling in Systems Biology(2013), by Brian P. Ingalls (pdf, MATLAB code)

📚 Additional materials

  • An Introduction to Stochastic Processes with Applications to Biology (Google the pdf file)

Course content#

Chapter 1-4 describes mathematical modelling in molecular systems biology.

  • Basic notions of mathematical modelling.

  • Dynamic mathematical models of chemical reaction networks. (ODE models)

  • Biochemical kinetics of enzyme-catalysed reactions and cooperative binding.

  • Model reductions.

  • Analyzing differential equation models: phase plane, stability, bifurcations, sensitivity analysis.

Chapter 5 and beyond are applications in specific biological domain(s).

  • Stoichiometric modelling for large-scale metabolic networks. e.g. COBRA

  • Signal transduction pathways.

  • Gene regulatory networks.

  • Electrophysiology and action potentials in exitable cells.

Other topics:

  • Agent-based modeling (ABM)

  • (Metabolic) flux balance analysis

Runtime information#

import Pkg
Pkg.status()

Status `~/work/mmsb-bebi-5009/mmsb-bebi-5009/Project.toml`
  [336ed68f] CSV v0.10.15
  [479239e8] Catalyst v14.4.1
  [a93c6f00] DataFrames v1.7.0
  [459566f4] DiffEqCallbacks v4.2.2
  [0c46a032] DifferentialEquations v7.15.0
  [0b91fe84] DisplayAs v0.1.6
  [31c24e10] Distributions v0.25.115
  [f6369f11] ForwardDiff v0.10.38
  [a98d9a8b] Interpolations v0.15.1
  [ccbc3e58] JumpProcesses v9.14.0
  [961ee093] ModelingToolkit v9.59.0
  [1dea7af3] OrdinaryDiffEq v6.90.1
  [91a5bcdd] Plots v1.40.9
  [ce78b400] SimpleUnPack v1.1.0
  [10745b16] Statistics v1.11.1
  [2913bbd2] StatsBase v0.34.4
  [9672c7b4] SteadyStateDiffEq v2.4.1
  [9a3f8284] Random v1.11.0

import InteractiveUtils
InteractiveUtils.versioninfo()

Julia Version 1.11.2
Commit 5e9a32e7af2 (2024-12-01 20:02 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 2 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_CI = true
  LD_LIBRARY_PATH = /opt/hostedtoolcache/Python/3.12.8/x64/lib
  JULIA_PROJECT = /home/runner/work/mmsb-bebi-5009/mmsb-bebi-5009/Project.toml
  JULIA_DEPOT_PATH = /home/runner/.julia:/opt/hostedtoolcache/julia/1.11.2/x64/local/share/julia:/opt/hostedtoolcache/julia/1.11.2/x64/share/julia
  JULIA_CONDAPKG_BACKEND = Null
  JULIA_NUM_THREADS = 2
  JULIA_LOAD_PATH = @:@v#.#:@stdlib

This notebook was generated using Literate.jl.