Transcript MMA2010 - University of South Alabama

Discrete Stochastic Models for FRET and
Domain Formation in Biological Membranes
Audi Byrne
March 1st
Biomath Seminar
Biomathematics Study Group
Anne Kenworthy Lab
Vanderbilt University Medical Center
protein trafficking
signal transduction
FCS, FRAP, FRET
lipid rafts, Ras
How are bio-molecules
(lipids and proteins)
organized in the cell membrane?
We investigate ways in which FRET
could be used to determine the microorganization of lipids and proteins.
Presentation Outline
I. Membrane Biology: how are molecules
organized within the cell membrane?
II. FRET
A. Light microscopy with nanoscale
resolution
B. Segregation FRET: to measure domain
separation
III. Computational Model For Segregation FRET
A. Comparison with Ripley’s K measure
B. Comparison with Hausdorff Measure
Talk Outline
A. Biological question: how are lipids organized
within the cell membrane?
I.B.How
do
lipids
organize
within
FRET: experimental tool
biomembranes?
C. Models:
a. FRET (Berney and Danuser, Biophys J, year)
b. Domain formation (loosely based Potts model)
D. Goal: Investigating the potential of FRET to
identify domains and domain characteristics.
a. Challenge: a highly underdetermined inverse
problem
b. Results: delimiting the “power” of FRET
Biological Membranes
Structurally composed of phospholipids…
Phospholipids have a hydrophobic part and a hydrophilic
part so they naturally form bi-layers:
http://academic.brooklyn.cuny.edu/biology
Biological Membranes
Structurally composed of phospholipids…
Phospholipids have a hydrophobic part and a hydrophilic
part so they naturally form bi-layers:
http://academic.brooklyn.cuny.edu/biology
Within the sea of phospholipids, there is a
diverse variety of proteins and other kinds
of lipids.
Are lipids and proteins arranged
randomly throughout the
biomembrane, or is there microorganization?
Hypotheses for lipid organization:
• Random / homogeneous distributions
• Highly ordered or regular
• Complexes/Domains
• Exotic organizations
Applications/Relevance
Immune system: Lipid domains are putatively required
for antigen recognition (and antibody production).
Vascular system: lipid domains are putatively required
for platelet aggregation.
HIV: lipid domains are putatively required to produce
virulogical synapses between T-lymphocytes that ennable
replication
Cancer: Ras proteins, implicated in 30% of cancers, are
thought to signal by compartmentalizing within different
domains
The positions of “n” molecules is described by 2n
numbers in continuous space, and no fewer number of
parameters can describe the distribution of points
Prior, Muncke,
Parton and
Hancock
However,
The organization of lipids are determined by
physical and biological parameters that may
greatly constrain the set of possible
distributions (modulo noise)
Example: if the distribution of lipids is genuinely
random, the entire distribution can be described
by 2 parameters!
Domain Formation In
Model Membranes
Gel Domains: Phospholipids
with long, ordered chains
Fluid Domains:
Phospholipids with short,
disordered chains
Cholesterol : Gel domains
form a liquid ordered phase
Heetderks and Weiss
Lipid-Lipid Interactions
The Lipid Raft Hypothesis
 The cell membrane phase separates into liquidordered domains and liquid-disordered domains.
 Liquid-Ordered Domains
- “lipid rafts”
- enriched in glycosphingolipids and cholesterol
- act to compartmentalize membrane proteins:
involved in signal transduction, protein sorting and
membrane transport.
Open Questions
 Whether domains form.
How large are these domains?
How dense are these domains?
More obliquely:
What is the domain separation?
We can measure domain separation for a point pattern using
Ripley’s K measure, the Hausdorff measure, or using segregation
FRET.
B. Direct Observation Yields
40-200 nm resolution
Studying molecule organization
by “looking” at the membrane..
Light Microscopy
“focused light is the only way to examine
living cells non-invasively”
Westphal and Hell, 2005
Diffraction-Limited Resolution in Light Microscopes
Ernst Abbe, 1873
s = λ /(2n sin α)
where
n sin α = numerical aperture of the objective
λ = light wavelength
The wavelength of visable light ~ .5 microns.
Diffraction limit ~200nm
Latest technology…
Current best
resolution is
~40 nm with
STED
technique.
Stimulated Emission Depletion (STED) microscopy
B. Indirect FRET Yields
1-10 nm resolution
What is FRET?
Fluorescence Resonance
Energy Transfer
Energy Transfer
Two fluorophores:
One “donor” fluorophore
One “acceptor” fluorophore
Resonance Energy Transfer
A fluorophore with an excited electron (the donor) may
transfer its electronic energy to another fluorophore (the
acceptor) by resonance if the the emission energy of the first
molecule matches the excitation energy of the second.
This occurs by dipole-dipole interaction. (The fluorophores
must be close but not too close.)
Fluorescence occurs when an electron becomes
excited by absorption of photons.
The electron is excited to a higher energy level
and the electron spin is preserved, so that the
electron may relax at any time. The lifetime of this
excited state is very short (less than 10-5 s).
Pauli Exclusion principle:
No two electrons in the same
orbital may have the same spin.
Fluorescence occurs when an electron becomes
excited by absorption of photons.
http://www.olympusfluoview.com
http://www.pfid.org/html/un_fret
FRET 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.
Since then, this has been borne out by rigorous experimental tests.
Kt 1/r6
Kt =KD(R0
6
/r )
Due to the sensitive dependence of FRET on intermolecular separation, FRET has been used as an
amazingly accurate “spectroscopic ruler” [Stryer,
1967].
Example: Two amino acids in a protein P are tagged
with GFP. However, they can’t be resolved with a
microscope (separation less than 200nm).
Example: Two amino acids in a protein P are tagged
with GFP. However, they can’t be resolved with a
microscope (separation less than 200nm).
One amino acid is labeled with a donor (absorbs
blue light, emits green) and one is labeled with an
acceptor (absorbs green light, emits yellow).
Under blue light illumination, the protein reflects
75% green light and 25% yellow light.
The transfer rate is .25! The distance that gives
that transfer rate can be calculated.
k =k
t
6
*
(R
/r)
D
0
Model for FRET
Berney and Danuser
[Biophys J, 2004]
Modeling FRET (Forward Problem)
1. Begin with a space-point distribution of lipids.
1. From ECM data,
2. “drawn” from simple rules
3. generated by simulations
2. Lipids are randomly labeled with “donors” and
“acceptors” that can undergo “FRET”.
3. Lipids are assigned “states”
0
Un-excited
0 → 1Excitation
1
Excited
1 → 0 Decay or Transfer
Initially, all fluorophores are assigned state ‘0’ “off”.
1. Donor Excitation
Donors excite with constant rate kE, which models constant
illumination.
2. Transfer
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
3. Donor and Acceptor Decay
Excited fluorophores decay with constant rate kD, which models
exponential decay:
The lifetime
of the
-t/KD
fluorophore
Y = Y0 e
Is 1/KD=.
Donor Excitation
Transfer
Donor and Acceptor Decay
These processes occur simultaneously, and thus
compete over time. Small timesteps (<< ) must
be chosen to model the rates accurately.
FRET for a Clustered Distribution
Over 10 Nanoseconds
1 TS = .1 ns
D = 5 ns
A = 10 ns
kE = .25/ns
FRET Efficiency = (# Actual Transfers) / (# Possible Transfers)
= (Acceptor Fluorescence) / (Acceptor + Donor Fluorescence)
FRET for a Clustered Distribution
Over 10 Nanoseconds
1 TS = .1 ns
D = 5 ns
A = 10 ns
kE = .25/ns
FRET Efficiency = (# Actual Transfers) / (# Possible Transfers)
= (Acceptor Fluorescence) / (Acceptor + Donor Fluorescence)
Zooming in on a Single Cluster
Zooming in on a Single Cluster
Goal: Investigating the potential of FRET to
identify domains and domain
characteristics.
Challenge: a highly underdetermined
inverse problem
Results: delimiting the “power” of FRET
The challenge…
Lipid distributions are under-determined by FRET:
And potentially complex!
.
Approach:
Instances of the forward problem
Disk-shaped Domain Model
(i) domains of radius ‘r’
(ii) Each domain has N molecules
(iii) Molecules are stochastically labeled with donors
and acceptors in different ways
(iv)fluorophores between domains do not interact
Results found in the literature:
Combined in single functional relationship:
Acceptor Density Within Domains
An important consequence:
Average distance between
probes within a domain are
the same!
One set of domains is smaller
=> less “edge” interaction with
probes between domains.
Two distributions with the same acceptor density
cannot be distinguished!
However, this is for idealized domains!
Acceptor Density Within Domains
Future Directions
Investigate how to quantitatively distinguish (a) from (b) below:
Future Directions
Investigate how to quantitatively distinguish (a) from (b) below:
Future Directions
Investigate how to quantitatively distinguish (a) from (b) below:
Investigate other models for domain formation:
Oligomerization (e.g., mass action)
Cell-controlled organization
Protein “corals”
Thank you!