The goal of this course is to expose students to various aspects of modern physics of liquid crystals. Membranes are bilayer liquid-crystal films, which are macroscopic in the lateral direction. The course contains foundations of theory of elasticity of liquid crystals initially developed for 3D systems, and then adapted for description of bilayer membranes. Thermodynamics and kinetics of phase transitions in multicomponent systems are recounted concerning biological membranes, which contain proteins and several lipid components. Gibbs’ phase diagrams are introduced, and various 2D lattice models are considered. Local phase transitions, occurring in the vicinity of protein complexes due to so-called wetting phenomenon under conditions of absence of global phase transition in the surrounding membrane, are described in the framework of wetting theory adapted for biological membranes. Various mechanisms of protein-lipid interactions as well as conditions for macroscopic wetting films formation are considered. Dependence of cellular processes rates on energetic of formed membrane structures is illustrated for exo- and endocytosis.
Instruction will consist of 34 hours of lecture and 17 hours of discussion. Assigned problem set will be provided.
Hours of lecture
Hours of discussion
Hours of class preparation
Please note that students are expected to study outside of class for three hours for every hour in class.
The plan is to work through the following topics:
Properties of 3D liquid crystals
Elements of the classical theory of elasticity
Classification: nematics, cholesterics, and smectics
Phase diagrams “lipid-water”
Structure of bilayer lipid membranes
Features of membrane elasticity theory
Fundamental deformations in membranes
Equation of local volumetric incompressibility
Painted membranes as the systems with variable number of particles
Energy of contact of two planar bilayers of different thickness
Phenomenological Flory model
Interaction of membrane inclusions, mediated by membrane deformations
A pore in lipid bilayer
Life cycle of an enveloped virus
Fission of model membranes
The basic models of the dynamin function
Phase transitions in multicomponent membranes
Hierarchy of lipid-protein structures in biological membranes
Some kinds of lipidic fluorophores
The analysis of diffusion for determination of raft size in cells
Method of membrane nanotube pulling
Phase diagrams of two- three-, and multicomponent membranes
A problem of stability of small domains
Kinetic stabilization of small domains ensemble
Methods of measurement of line tension of rafts boundary
The mechanical model based on hydrophobic mismatch.
Hybrid mechanical-chemical model
Stability of small rafts in cellular membranes
Bilayer structure of rafts
Electrical properties of membranes
Electrolyte solution and Debye screening
A double electrical layer
Methods of measurement of membrane potential components.
Weekly, 1 problem set in total, due at the beginning of the lecture. You may also submit via e-mail before the due date/time. It is of outmost importance that you invest your own effort into solving problems. Should you consult any sources, please provide references. Homework assignments should be typed. Legible handwritten assignments are acceptable.