Stochastic Models of Microdomain
Formation in Biological Membranes
Anne Kenworthy Lab: Maria Byrne, Kimberly Drake, Shawn Goodwin, Minchul Kang, Carl Rogers
Lattice Energy
Lipid Species
Each lipid species is
The coupling energy (e.g., partition
Lipids diffuse by stochastic random walk in
assigned an indice 
coefficient) between any two lipid
a way which decreases system energy by the
and each node of a
species i and j is  i i. The total
Metropolis algorithm: Neighboring lipids switch
square lattice is
energy of the system is defined as
locations if switching decreases the energy of
occupied by exactly
the sum of the coupling energies of
the system. Otherwise, the switch is permitted
one lipid species.
all adjacent nodes on the lattice.
depending on the temperature of the system.
Sorting After 100 Timesteps
Examples of A 3-Lipid Mixture:
Rule: “like” lipids have lower coupling
energies than unlike.
clusters
Putative Lipid Rafts Isolated by
Detergent Extraction
Cholesterol and glycosphingolipids, along with
putative raft proteins, are resistant to cold Triton X100 extraction. However, the “raft proteins” can be
extracted from cholesterol-depleted membranes.
A Discrete Stochastic
Model For FRET
FRET: Fluorescence Resonance Energy Transfer
A fluorophore with an excited electron may transfer its electronic
energy to another fluorophore (by resonance) if:
1. the second fluorophore is near and
2. the emission energy of the first molecule
matches the excitation energy of the second.
This occurs by dipole-dipole interaction.
Research Problem
The micro-organization of lipids and proteins within
the cell membrane is an open question. It is
hypothesized that many proteins organize within
glycosphingolipid and cholesterol-enriched “lipidraft” domains. We investigate:
(1) Clustering mechanisms which would result in
distinct protein organizations within lipid rafts and
Example B
Low
Heetderks and Weiss
sort from a random distribution into
Example C
Low
Drawn by P. Kinnunen, CEO of Kibron, Inc
Low
These rules cause lipid species to
Lipid-Lipid Interactions
In simple lipid mixtures, phospholipids
with long, ordered chains sort into gel
domains and those with short, disordered
chains sort into fluid domains. The
addition of cholesterol to gel domains
forms a liquid ordered phase, the
proposed state of lipid rafts.
Example A
(2) Ways in which FRET could be used to distinguish
among these possibilities in native cell
membranes.
Conclusions
• For cluster mechanisms which are known to result
in a random distribution of a lipid (or protein) within
another lipid domain, FRET reports unambiguously
on the concentration of the lipid (or protein) within
the domain.
Ro =distance when transfer
rate equals decay rate
Dipole-dipole interaction is highly dependent upon
distance. In 1948, T.M. Förster calculated that the
rate of resonance energy transfer between two
fluorophores would depend on the inverse of the
sixth power of their separation.
Due to the sensitive dependence of FRET on inter-molecular
separation, FRET has been used as an amazingly accurate
“spectroscopic ruler” [Stryer, 1967].
Lipid3 Partitions Slightly Within
Lipid2: L2-L2 coupling energy is
less than L2-L3 coupling energy
Lipid3 Doesn’t Partition Within
Lipid2
Results
General Results For FRET When Lipid3 is
Randomly Distributed Within Lipid2
For a wide range of
experimental
conditions in which
lipid 3 is labeled
(varying acceptor to
donor ratio, percent
labeling) and any
cluster mechanism
resulting in a random
distribution of lipid3
within regions of
lipid2, FRET efficiency
shows very regular
behavior.
• For more complex cluster mechanisms (e.g., ones
which do not result in random distributions within
subdomains) FRET can distinguish between
models. Modeling can be used to determine the
most sensitive experimental approach.
FRET Rate and Förster Distance
Lipid 3 Partitions Within Lipid 2
High
Lattice
Energy
Over Time
Lipid 1 and Lipid 2 occur in 1:1 ratio.
Lipid 1: lighter color
Lipid 1 and Lipid 2 do not mix.
Lipid 2: darker color
Lipid 3 increases in concentration
Lipid 3: white pixels
from low to high.
High
The Fluid-Mosaic Model With Microdomains
High
Random Initial Conditions
The fluid-mosaic model of Singer and Nicholson, in which the
plasma membrane is a phospholipid bilayer embedded with
proteins, includes lipid membrane domains within the “mosaic”.
Protein clustering occurs as proteins form complexes or
preferentially partition into different membrane domains: the
protein caveolin clusters in flask-shaped structures called
caveolae and GPI-anchored proteins cluster in the apical ends
of epithelial cells.
Lipid Diffusion
Intermediate
Evidence for Lipid Rafts In
Cell Membranes
Models for Lipid Raft Formation
Intermediate
It is hypothesized that separation of discrete liquid-ordered and liquid-disordered phase domains
occurs in membranes containing sufficient amounts of sphingolipid and sterol. The proposed
liquid-ordered lipid “rafts” would be involved in signal transduction, protein sorting and
membrane transport.
Intermediate
The Lipid Raft Hypothesis
Distinguishing 3 Different Models
for Raft Formation With FRET
All figures show FRET efficiency verses concentration of Lipid 3 for
Example A (blue), Example B (violet) and Example C (pink).
[Low=1%, Medium=10%, High=30%]
FRET Efficiency = (# Actual Transfers) / (# Possible Transfers)
= (Acceptor Fluorescence) / (Acceptor + Donor Fluorescence)
Modeling: Fluorophore Excitation States
Donors excite with
0 Un-excited
0 → 1Excitation
constant rate kE., which
1
Excited
1 → 0 Decay or Transfer
models constant
illumination.
Transfer occurs between every unexcited acceptor and
every excited donor at rate kT, which depends upon their
molecular separation r :
kt = kD * (R0/r)6
Excited fluorophores
decay with constant rate
KD, which models
exponential decay.
-kDt
Y = Y0 e
The lifetime of the
fluorophore
Is 1/KD=.
Labeling Lipid 3 with 50%
acceptors and 50% donors:
The three models cannot be
distinguished.
Labeling Lipid 3 with donors
(100%) and Lipid 2 with
acceptors (25%)::
The most extreme model C can
be distinguished.
Labeling Lipid 3 with donors
(100%) and Lipid 1 with
acceptors (25%)::
All models can be distinguished.