Statistical Mechanics

A cell is made of lots of atoms moving around, so before learning about biology, we ought to learn about the physics of many-body systems.

The language of statistical mechanics describes the collective behavior of many interacting atoms. It helps us answer questions such as:

• Of all the copies of protein ABC in a cell, what fraction are in an active conformation vs an inactive conformation?
• What does it mean for a protein to "bind tightly" to something?
• How long does it take for a metabolite to diffuse from one end of a cell to another?
• Why (and how!?) do our cells maintain differing concentrations of ions and metabolites on different sides of a membrane?
• How do our cells drive chemical reactions that cost energy to perform?

As we'll see, the main idea behind stat mech is that when there's so many atoms jiggling around and trading energy with each other, the overall behavior can be summarized by "thermodynamic variables" such as the temperature or the chemical potential. The motion of individual atoms is irrelevant to the bigger picture; biological function is governed by just a few thermodynamic variables that tell us what's favorable or not favorable.

Statistical mechanics is a powerful framework to understand the driving forces behind cellular behavior. In the subsections below, we'll learn how to think about protein-protein binding, the energetics (and "entropics") of concentration gradients, diffusion, and more.

Outline of Statistical Mechanics

• Fundamental assumptions about equilibrium and entropy
• Describing subsystems using the Boltzmann factor and free energy
• The equipartition theorem explains temperature
• Chemical potential
• Diffusion and fluctuations