Team:USP-Brazil/OnlineLectures

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Human Practices

Online Courses in Synthetic Biology

In addition to the course in mathematical modelling, our team also prepared an online course on mathematical modelling in synthetic biology, as well as an online course on molecular biology and synthetic biology. The courses are in portuguese, with their english translation in preparation. The videos are being hosted at our team's youtube channel.

Mathematical Modeling in Synthetic Biology

This course aims at those with basic undergraduate molecular biology knowledge, i.e., knowing roughly what do enzymes, promoters and DNA do, and with high school level mathematics - essentially knowing what are functions, and some elementary examples, namely power functions, trigonometric functions and logarithms. The goal of part A is to teach the basics of differential and integral calculus, focusing on explaining differential equations. Part B turns to Mathematical Modeling, explaining how to use differential equations to model the behavior of a biological system - focusing then on the most common examples in synthetic biology. Part C is made of special extra topics, for those who are familiar with parts A and B and want to deal with more complicated problems.

Part A - Mathematical Concepts

  • Lesson 1 - Derivatives, rules of derivation
  • Lesson 2 - Integrals
  • Lesson 3 - Applications of calculus
  • Lesson 4 - Differentials equations
  • Lesson 5 - Solução numérica de equações diferenciais: Método de Euler e implementacao em python

Parte B - Modelagem

  • Lesson 1 - O que eh modelagem: apresentação sobre modelagem do Marcelo [camtasia]
  • Lesson 2 - Modelagem de uma população. Crescimento exponencial e Logístico (Lecture1, ate slide ~80)
  • Lesson 3 - Espécies (químicas) interagentes: Lotka-Volterra (Lecture2) e lei de ação das massas (e isso ja cobre praticamente toda reacao quimica) - exemplo: promotor, ativação, inibição
  • Lesson 4 - Modelos comuns em synbio: Cinetica enzimatica: Michaelis-Menten, Hill coefficient
  • Lesson 5 - Exemplo completo de modelagem: Cre, ou Detecthol

Parte C - Topicos extras

  • Lesson 1 - Linear stability analysis (eq.Logistica, allee growth)
  • Lesson 2 - Phase plane analysis (Lotka-Volterra)
  • Lesson 3 - Dinâmica espacial: difusão, advecção, saturacao (Lecture5 e mais alguma coisa)
  • Lesson 4 - Simulações estocásticas: algoritmo de Gillespie (só dar uma ideia mesmo)
  • Lesson 5 - Equacoes a diferencas (tempo discreto) e mapas

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