Mathematics of Life
Course Description
KITP 2016 Summer School
Guiding questions:

Which molecules play a role in generating mechanics in living systems?

How do molecules come together to generate mechanics in cells and tissues?

Why do we need phenomenological theories for mechanics in biological systems?

What do phenomenological theories of mechanics look like?

How do we need connect molecular and phenomenological theories?

How do we measure mechanics, invivo?
30000ft view: Connecting our microscopic understanding of molecules to macroscopic phenomena.
Without an understanding of the molecular basis of mechanics, we would never move close to an understand of how geometry/shape/form is regulated/controlled. Without a phenomenological understanding of mechanics, we would be lost in the endless zoo of molecular biology. Connecting the two is, as we see it, an outstanding problem in biology and physics.
Goal of lectures and preparation for summer school: Emphasis will be on building physical intuition. At its best, physical intution and mathematical sophistication go hand in hand. While assuming mathematical sophistication is problematic, teaching it in a few hours is hopeless and misguided. We will try not to rely on advanced mathematical ideas or terminology, that said, comfort with Multivariable Calculus and Thermodynamics would be advantageous. Please prepare for the summer school by coming up to speed on these two topics. We recommend reading Part I and II of Phil Nelson's Biological Physics. These lecture notes (Chapter 13 in particular) on math methods in physics are a reasonable place to begin. These lecture notes are also a good resource. Furthermore, for those that haven't had experience with matlabstyle coding (a good web tutorial can be found here) and image analysis (a good tutorial can be found here) it would be advisable to work on these as preparation. We will make extensive use of matlab and the pixel classification algorithm based in Ilastik.
Content:
1. Molecules
1.1 Biopolymers: Polymerization, Polarity, Thermodynamics and Statistical Mechanics of polymers. Emphasis on length scales, time scales, energy scales, the importance of dynamics, mathematical models, single molecule studies. Chapter 9.1 in Nelson.
1.2 Molecular Motors: Chemical to mechanical energy, Interaction with biopolymers, Polarization, Thermodynamics and Statistical Mechanics. Emphasis on length scales, time scales, and energy scales, the importance of dynamics, mathematical models. Chapter 10.4.3 in Nelson.
1.3 Adhesion: Structure and biophysics of cadherins. Single molecule experiments. Leckband.
2. Mechanics
2.1 Continuum models: Underlying physical assumptions and its validity. Definitions of stress, strain, and strain rate tensors.
2.3 Fluid Mechanics: Basics physics, dimensional analysis, and scaling. Life at Low Reynolds number. Examples of simple flows.
2.4 Solid Mechanics: Basic physics, dimensional analysis, and scaling. Constitutive models.
2.5 Plates, Shells, and Membranes: Dimensionality and basic physics.
3. Measurements of Forces
3.1 FRET
3.2 Droplets
3.3 Model based
3.4 Traction Force Microscopy
3.5 Lazer ablation and tweezing
4. Analysis of Imaging Data
4.1 Image Analysis in Matlab
4.2 Pixel Classification in Ilastik
4.3 Statistical Quantitation and a primer on statistics
4.4 Confronting theory to data