Description
Most teenagers are told off by their parents because their bedroom is a complete mess. Yet, the 2nd law of thermodynamics tells us that disorder in an isolated system will always increase and so teenagers bedrooms are only natural. Given that nature should be nothing but a big mess how could living organisms, which are very ordered systems, ever be created?If we could zoom in inside our body at the molecular scale, we would see atoms that constantly colliding with each other around 1015 times per seconds. Temperature is actually a measurement of the average kinetic energy that each atoms has and it must be large enough, but not too large either.
In our bodies, most atoms or molecule are linked together by chemical bounds or hydrogen bonds and the constant molecular agitation sometime leads to the spontaneous, but random, detachment of some atoms or molecules. These fluctuations is what makes us work as living organisms. As you read these lines, your understanding is nothing but the result of a huge number of these completely random molecular linkings and unlinkings in your neurones.
Cells don't have brain, yet, they must respond to change to their environment. Most of it is done by the cell manufacturing specific proteins that must then be transported to a suitable part of the cell. There is no blood stream or neurones in a cell. Instead there is a blind delivery service, blind in the sense that there is no organised way to deliver parcels from A to B. Instead each parcel is tagged with a key that matches that of its recipient. The parcel is then transported randomly inside the cell until it reaches it destination which it recognises by marching its key. Like most cell process, this is totally random, but it works and this is what makes us live. What we have just described is just one example of a random process but there are many more.
The aim of the project will be to model some biophysical systems in a cell. We will start by studying the structure of a cell and then we will move on to studying various macromolecular components such as proteins, DNA, motors or what is called the cytoskeleton. We will also model how these cell components interact with each other to keep cell alive.
From the description above, the project might seem to involve a fair amount of physics and biology, but we will actually focus on the mathematical side of the modelling. Some basic cell biology will need to be learned, but the few physical principles that we will use will be motivated during the weekly meetings and you won't be expected to derive them. Mathematically the project involves mostly differential and algebraic equations but also some relatively simple simulations.
Prerequisites
- Analysis in many variable II (MATH2031)
Resources
- The Biology Primer
- Cell Biology Primer
- Structure and Function of the Cell
- Cell Biology T.D. Pollard and W.C. Earnshaw.
- Physical Biology of the Cell R. Philips, J. Kondev and J. Theriot.
- Biological Physics Philip Nelson.
- Biological Thermodynamics D.T Haynie.
- Chemical Biophysics D.A. Beard and H.Qian.