Methods of Membrane Domain Investigation in Noisy EnvironmentsAnne Kenworthy Lab: Brooks Alford, Maria Byrne, Kimberly Drake, Minchul Kang, Carl Rogers

While protein clustering in the plasma cell membrane has been well-established, determining the size, longevity and importance of lipid domains within the bi-layer has proved elusive1. A promising experimental technique for studying lipid organization is FRET. FRET provides nanoscale resolution and reports on lipid positions without altering the membrane. [DETAILS ]The model of Berney and Danuser2 solves the forward problem: given a distribution of fluorophores, all relevant aspects of membrane FRET can be simulated with an individual-based model. However, of most interest experimentally is the inverse problem: given a specific FRET signature, what is the underlying distribution of fluorophores? We have answered this question in the context of lipids randomly distributed in idealized disk-shaped domains3 but further research is required to address these questions in the context of irregular, biologically relevant domains. For this, we have developed a stochastic model of domain formation based on simplified individual lipid-lipid interactions. [DETAILS ] We investigate the potential of FRET is identify domain properties in this context. [DETAILS ]

Lipid Partitioning Model

Motivation

The Fluid-Mosaic Model With MicrodomainsThe 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. Drawn by P. Kinnunen, CEO of Kibron

Image: Heetderks and Weiss

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.

It is hypothesized that this may also occur in vivo so that the cell membrane phase separates into liquid-ordered domains (lipid rafts) and liquid-disordered domains that compartmentalize membrane proteins.

The Lipid Raft Hypothesis

Caveolae: flask-shaped structures enriched with caveolin.

GPI-anchored proteins cluster in the apical ends of epithelial cells.

Lipid rafts??? .. small, enriched in sphingolipid and cholesterol, involved in signal transduction, protein sorting and membrane transport..

The coupling energy (e.g., partition

coefficient) between any two lipid

species i and j is i i. The total

energy of the system is defined as

the sum of the coupling energies of

all adjacent nodes on the lattice. Lipi

d S

peci

es

Each lipid species is

assigned an index

and each node of a

square lattice is

occupied by exactly

one lipid species.

Lipids diffuse by stochastic random walk

in a way which decreases system energy by

the Metropolis algorithm: Neighboring lipids

switch locations if switching decreases the

energy of the system. Otherwise, the switch

is permitted depending on the temperature

of the system. Latt

ice

Ene

rgy

Lipi

d D

iffus

ion

These rules cause lipid species

to sort from a random

distribution into clusters.

Rule: “like” lipids have lower coupling energies than unlike.

Random Initial Conditions Sorting After 100 Timesteps Lattice Energy Over Time

Fluorescence Resonance Energy TransferA 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.

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 separation4.

Due to the sensitive dependence of FRET on inter-molecular separation, FRET has been used as an amazingly accurate “spectroscopic ruler”5.

Modeling FRET

FRET Efficiency = (# Actual Transfers) / (# Possible Transfers)= (Acceptor Fluorescence) / (Acceptor + Donor Fluorescence)

Donors excite with constant rate kE, which models constant illumination.

Transfer occurs between every unexcited acceptor and every excited donor at rate kT, which depends upon their molecular separation r :

Excited fluorophores decay with constant rate KD, which models exponential decay.

Y = Y0 e -kDt

kt = kD * (R0/r)6

The lifetime of the fluorophore

Is 1/KD=.

0 Un-excited 0 → 1 Excitation

1 Excited 1 → 0 Decay or Transfer

Lipid distributions are generated for varying raft fractions (blue) and varying domain size. To simulate FRET, fluorophores are randomly assigned to lipids.

Noisy Membranes

Comparison: Ripley’s KResults: Intra & Inter-Domain FRET

Summary

Intra-domain FRET: acceptors and donors are located within domains

For all distributions, FRET robustly depends upon the local acceptor density

δ=(N-1) fA/N

N = total # of lipids in a domain

fA = fraction of lipids labeled with acceptors

The ratio of the global density to the local density provides the domain fraction.

Inter-domain FRET: donors are located within domains and acceptors are located outside domains

FRET functionally depends upon the domain width.

Blue: distributions before the percolation transition

Red: during the percolation transition

Black: distributions after the percolation transition

Ripley’s K6 is the second moment property of a spatial point pattern (i.e., the expected # of points within a distance r of another point) normalized by the # of points per area .

For a random distribution, K(r) is r2. K can be normalized so that its expected value is r (linear): L(r)= [K(r)/]7.

K(r) and L(r) for points randomly distributed (dotted lines) and distributed

within domains of radius R, separation S.

Noisy domains have variable separation distances [A] and variable shape [B]. Domain interaction at multiple spatial scales and elongation of domains complicate the interpretation of Ripley’s K for

noisy membranes [C].

1. Edidin, M. 2003. The state of lipid rafts: from model membranes to cells. Annu. Rev. Biophys. Biomol. Struct. 32:257–283.

2. Berney C, Danuser G. 2003. FRET or no FRET: A quantitative comparison. Biophysical Journal 84(6):3992-4010.

3. Kiskowski, M., Kenworthy, A. 2007. In silico characterization of resonance energy transfer for disk-shaped membrane domains, Biophysical Journal, in press.

4. Forster, T. (1948). Intramolecular energy migration and fluorescence. Ann Phys. (Leipzig) 2: 55-75.

5. Stryer L, Haugland RP. Energy transfer: a spectroscopic ruler. Proc Natl Acad Sci U S A. 1967 Aug;58(2):719–726.

6. Ripley, B. D. 1978. Spectral analyses and the analysis of pattern in plant communities. Journal of Ecology 66: 965–981.

7. Besag, J.E. 1977, Comments on Ripley's paper: J. R. Stat. Soc. B. 39 193–195.

ReferencesA simple model based on lipid-lipid interactions generates stochastic distributions that vary systematically in domain fraction and domain size.

FRET simulations indicate that intra-domain FRET is a robust measure of the intra-domain probe density (that can be used to estimate the domain fraction) and inter-domain FRET provides a measure of the domain width before and after the percolation transition.

Domain interaction and variable domain shape make interpretation of the Ripley K statistic more complex. In particular the statistic measures the length of the domain along its widest dimension so that it would be most useful before the percolation transition.

A B

C

Raft Fraction

D

omai

n S

ize

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ime