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Lecture

Bistability in Genetic Networks

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 concept of bistability in genetic networks, focusing on the mathematical analysis of fixed points and stability. The instructor explains the phase portraits and isoclines for different scenarios, illustrating the absence of spirals and the presence of stable points. The lecture also delves into the experimental implementation of bistability using synthetic plasmids in E. coli.

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

Ontological neighbourhood

Systems science and engineering

Systems theory: Chaos theory

Related concepts (32)

Fixed point (mathematics)

hatnote|1=Fixed points in mathematics are not to be confused with other uses of "fixed point", or stationary points where math|1=f(x) = 0. In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically for functions, a fixed point is an element that is mapped to itself by the function. Formally, c is a fixed point of a function f if c belongs to both the domain and the codomain of f, and f(c) = c.

Fixed-point iteration

In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.

Kakutani fixed-point theorem

In mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. It provides sufficient conditions for a set-valued function defined on a convex, compact subset of a Euclidean space to have a fixed point, i.e. a point which is mapped to a set containing it. The Kakutani fixed point theorem is a generalization of the Brouwer fixed point theorem. The Brouwer fixed point theorem is a fundamental result in topology which proves the existence of fixed points for continuous functions defined on compact, convex subsets of Euclidean spaces.

Fixed-point theorem

In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. The Banach fixed-point theorem (1922) gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point.

Stability theory

In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.

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