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Lecture

Dynamic Systems in Biology

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 introduces the formalism and bases of dynamic systems, focusing on population dynamics. It covers analytical and numerical methods, trajectories, stability of fixed points, and qualitative analysis using geometric methods.

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

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Related concepts (28)

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Population dynamics of fisheries

A fishery is an area with an associated fish or aquatic population which is harvested for its commercial or recreational value. Fisheries can be wild or farmed. Population dynamics describes the ways in which a given population grows and shrinks over time, as controlled by birth, death, and migration. It is the basis for understanding changing fishery patterns and issues such as habitat destruction, predation and optimal harvesting rates. The population dynamics of fisheries is used by fisheries scientists to determine sustainable yields.

Population dynamics

Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years, although over the last century the scope of mathematical biology has greatly expanded. The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the Malthusian growth model.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Population model

A population model is a type of mathematical model that is applied to the study of population dynamics. Models allow a better understanding of how complex interactions and processes work. Modeling of dynamic interactions in nature can provide a manageable way of understanding how numbers change over time or in relation to each other. Many patterns can be noticed by using population modeling as a tool. Ecological population modeling is concerned with the changes in parameters such as population size and age distribution within a population.

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