Lecture

Diffusion and Logistic Growth

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In course

BIO-341: Dynamical systems in biology

Life is non-linear. This course introduces dynamical systems as a technique for modelling simple biological processes. The emphasis is on the qualitative and numerical analysis of non-linear dynamical models. Examples are taken from biology and population ...

Description

This lecture covers the concepts of diffusion and logistic growth, focusing on the Kolmogorov-Fisher equation. It explains the dynamics of genetic circuits with negative feedback and the formation of morphogen gradients in embryos. The lecture also delves into the mathematical modeling of spatial patterns and wave propagation in biological systems.

Instructors (2)

Felix Naef

Felix Naef studied theoretical physics at the ETHZ and obtained his PhD from the EPFL in 2000. He then received postdoctoral training at the Center for Studies in Physics and Biology at the Rockefeller University (NYC) under the guidance of Prof. Magnasco. His research focuses on the modeling and interpretation of high-throughput functional data and the study of biomolecular oscillators. He joined ISREC as an associate scientist in early 2004 and is currently Associate Professor in the Institute of Bioengineering (IBI).

Julian Charles Shillcock

Julian received his PhD at Simon Fraser University in Canada for work on Monte Carlo simulations of liquid crystal phase transitions and the elastic properties of fluid and polymerized membranes. He was a Group Leader at the Max Planck Institute of Colloids and Interfaces, Germany for five years applying coarse-grained simulation techniques - principally Dissipative Particle Dynamics (DPD) and Brownian Dynamics - to equilibrium and dynamic properties of fluid lipid membranes. A major target of this research was to reveal the molecular rearrangements that occur during vesicle fusion. During this time, he developed a commercially-available, parallel DPD code that is being used by several universities. He was an Associate Professor at MEMPHYS in the Department of Physics and Chemistry, University of Southern Denmark. He has also worked in industry, designing and writing software for communication satellite simulations (British Aerospace, 1986-1990), and fluid simulation software (Accelrys, Inc., 1998-1999). He joined the Blue Brain Project in 2011, and uses mesoscale simulation techniques, together with theoretical analysis and collaborations with experimentalists, to study the dynamics of cellular processes. Current projects include simulating the formation of the post-synaptic density in dendritic spines and developing theoretical models of the supramolecular organisation of synapses. He also teaches Master's and PhD courses in computational cell biology and biophysics. He wrote and maintains an open source dissipative particle dynamics simulation code: https://github.com/Osprey-DPD/osprey-dpd Orcid: orcid.org/0000-0002-7885-735X

Official source

Related concepts (32)

Human embryonic development

Human embryonic development, or human embryogenesis, is the development and formation of the human embryo. It is characterised by the processes of cell division and cellular differentiation of the embryo that occurs during the early stages of development. In biological terms, the development of the human body entails growth from a one-celled zygote to an adult human being. Fertilization occurs when the sperm cell successfully enters and fuses with an egg cell (ovum).

Animal embryonic development

In developmental biology, animal embryonic development, also known as animal embryogenesis, is the developmental stage of an animal embryo. Embryonic development starts with the fertilization of an egg cell (ovum) by a sperm cell, (spermatozoon). Once fertilized, the ovum becomes a single diploid cell known as a zygote. The zygote undergoes mitotic divisions with no significant growth (a process known as cleavage) and cellular differentiation, leading to development of a multicellular embryo after passing through an organizational checkpoint during mid-embryogenesis.

Morphogen

A morphogen is a substance whose non-uniform distribution governs the pattern of tissue development in the process of morphogenesis or pattern formation, one of the core processes of developmental biology, establishing positions of the various specialized cell types within a tissue. More specifically, a morphogen is a signaling molecule that acts directly on cells to produce specific cellular responses depending on its local concentration.

Prenatal development

Prenatal development () includes the development of the embryo and of the fetus during a viviparous animal's gestation. Prenatal development starts with fertilization, in the germinal stage of embryonic development, and continues in fetal development until birth. In human pregnancy, prenatal development is also called antenatal development. The development of the human embryo follows fertilization, and continues as fetal development. By the end of the tenth week of gestational age the embryo has acquired its basic form and is referred to as a fetus.

French flag model

The French flag model is a conceptual definition of a morphogen, described by Lewis Wolpert in the 1960s. A morphogen is defined as a signaling molecule that acts directly on cells (not through serial induction) to produce specific cellular responses dependent on morphogen concentration. During early development, morphogen gradients generate different cell types in distinct spatial order. French flag patterning is often found in combination with others: vertebrate limb development is one of the many phenotypes exhibiting French flag patterning overlapped with a complementary pattern (in this case Turing pattern).

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