Methods of Membrane Domain Investigation in Noisy Environments Audi Byrne October 17 th CDB WIP

Anne Kenworthy Lab Cell membrane structure Membrane microdomains Membrane Trafficking Signal Transduction FCS, FRAP, FRET Ras Palmitoylation

We investigate ways in which FRET could be used to determine existence and properties of domains in cell membranes. Project Overview: How are molecules organized in the cell membrane?

WIP Outline I.Biological Motivation: how are molecules organized within the cell membrane? II.FRET: light microscopy with nanoscale resolution Computer model: Point Distribution → FRET signature III. FRET Signature of Disk-shaped Domain Model Future Directions: Model for Domain Formation based on lipid-lipid interactions

A. Biological question: how are lipids organized within the cell membrane? B.FRET: experimental tool 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 Talk Outline I. How do molecules organize within biomembranes?

Are lipids and proteins arranged randomly throughout the biomembrane, or is there micro- organization?

The Lipid Raft Hypothesis  The cell membrane phase separates into liquid- ordered 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.

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 enable replication Cancer: Ras proteins, implicated in 30% of cancers, are thought to signal by compartmentalizing within different domains

“focused light is the only way to examine living cells non-invasively” Westphal and Hell, 2005 Studying molecule organization by “looking” at the membrane.. Light Microscopy

Domains cannot be seen by normal fluorescence because they’re too small and too abundant.

Diffraction-Limited Resolution in Light Microscopes Ernst Abbe, 1873 Diffraction limit ~200nm s = λ /(2n sin α) where n sin α = numerical aperture of the objective λ = light wavelength The wavelength of visable light ~.5 microns.

Optical Microscopy Beyond the Diffraction Limit STED Stimulated Emission Depletion nm resolution FRET Fluorescence Resonance Energy Transfer 1-10 nm resolution

Latest technology… Current best resolution is ~40 nm with STED technique. Stefan W Hell and colleagues, Max Plank Institute Stimulated Emission Depletion (STED) microscopy

II. FRET Fluorescence Resonance Energy Transfer

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 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.

Two fluorophores: One “donor” fluorophore One “acceptor” fluorophore 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.) Resonance Energy Transfer

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. K t =K D (R 0 /r 6 ) K t  1/r 6 FRET Rate

Due to the sensitive dependence of FRET on inter- molecular separation, FRET has been used as an amazingly accurate “spectroscopic ruler” [Stryer, 1967].

No FRET Signal CFP is excited by light and emits light CFP is more than 10 nm distant from YFP YFP is not excited and does not emit light FRET Signal CFP is excited by light but does emit little light CFP is in close proximity (1-10 nm) to YFP YFP is not excited by light but does emit light

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.

Model for FRET Berney and Danuser [Biophys J, 2004]

Model for FRET 1.Begin with a space-point distribution of molecules. 1.From ECM data, 2.“drawn” from simple rules 3. generated by simulations 2. Molecules are randomly labeled with “donors” and “acceptors” that can undergo “FRET”. 3. Fluorophores are assigned “states” Initially, all fluorophores are assigned state ‘0’ “off”. 0Un-excited0 → 1Excitation 1Excited1 → 0 Decay or Transfer

1. Donor Excitation Transfer occurs between every unexcited acceptor and every excited donor at rate k T, which depends upon their molecular separation r : 2. Transfer k t = k D * (R 0 /r) 6 Donors excite with constant rate k E, which models constant illumination. 3. Donor and Acceptor Decay Excited fluorophores decay with constant rate k D, which models exponential decay: Y = Y 0 e -t/K D The lifetime of the fluorophore Is 1/K D = .

These processes occur simultaneously, and thus compete over time. Small timesteps (<<  ) must be chosen to model the rates accurately. Donor Excitation Donor and Acceptor Decay Transfer

FRET for a Clustered Distribution FRET Efficiency = (# Actual Transfers) / (# Possible Transfers) = (Acceptor Fluorescence) / (Acceptor + Donor Fluorescence) Over 10 Nanoseconds 1 TS =.1 ns  D = 5 ns  A = 10 ns kE =.25/ns

FRET for a Clustered Distribution FRET Efficiency = (# Actual Transfers) / (# Possible Transfers) = (Acceptor Fluorescence) / (Acceptor + Donor Fluorescence) Over 10 Nanoseconds 1 TS =.1 ns  D = 5 ns  A = 10 ns kE =.25/ns

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!

III. FRET for Disk-shaped Domains

Modeling Approach 1.Specify a class of molecule distributions: random or regular? domains? molecule exclusion radius D exc number of molecules (etc) 2. Randomly label molecules with acceptors and donors. 3. Simulate FRET for the population of fluorophores. 4. What is the ‘FRET signature’ of this class of distributions?

Modeling Approach 1.Specify a class of molecule distributions: random or regular? domains? molecule exclusion radius D exc number of molecules (etc) 2. Randomly label molecules with acceptors and donors. 3. Simulate FRET for the population of fluorophores. 4. What is the ‘FRET signature’ of this class of distributions?

Hypotheses for lipid organization: Random / homogeneous distributions Exotic organizations Complexes/Oligomers

1.Specify a class of molecule distributions. Disk-shaped Domain Model (i)Domains of radius ‘r’ (ii) Each domain has n molecules (iii) Fluorophores between domains do not interact

Examples of Distributions in Class

Modeling Approach 1.Specify a distribution of molecules: random or regular? domains? molecule exclusion radius D exc number of molecules (etc) 2. Randomly label molecules with acceptors and donors. 3. Simulate FRET for the population of fluorophores. 4. What is the ‘FRET signature’ of this class of distributions?

Labeling Molecules f A fraction of molecules labeled with acceptors f D fraction of molecules labeled with donors R DA ratio of donor-labeled and acceptor labeled molecules Intra-domain FRET

Modeling Approach 1.Specify a distribution of molecules: random or regular? domains? molecule exclusion radius D exc number of molecules (etc) 2. Randomly label molecules with acceptors and donors. 3. Simulate FRET for the population of fluorophores. 4. What is the ‘FRET signature’ of this class of distributions?

Model Results: Dependence on fraction of molecules labeled with acceptors

Model Results: Dependence on ratio of molecules labeled with acceptors and donors

Modeling Approach 1.Specify a class of molecule distributions: random or regular? domains? molecule exclusion radius D exc number of molecules (etc) 2. Randomly label molecules with acceptors and donors. 3. Simulate FRET for the population of fluorophores. 4. What is the ‘FRET signature’ of this class of distributions?

Acceptor Density Within Domains Consolidating Model Results: All results described by a single dependence on the intra-domain acceptor density

Acceptor Density Within Domains Consolidating Model Results: All results described by a single dependence on the intra-domain acceptor density Functional dependence  Measured FRET efficiency reliably indicates acceptor density within domains

The two distributions have the same acceptor density since the one with more molecules is also larger. Implication: Two distributions may not be distinguishable even if they are different sizes!

Solution: consider interaction of fluorophores within domains with labeled molecules outside domains. Implication: Two distributions may not be distinguishable even if they are different sizes!

Intra-domain FRET Inter-domain FRET

Inter-Domain FRET Results: FRET depends on domain radius independent of molecule density in domains

Application: Combining Approaches to Determine Domain Parameters

Intra-domain FRET indicates the intra-domain density . Inter-domain FRET indicates the domain radius r. Combining known r with known , the number of molecules per domain can be computed:  = n /  r 2 so n =  *  r 2.

Future Directions Investigate FRET for classes of distributions that are generated by a simulation based on lipid-lipid interactions.

Model for domain formation based on lipid-lipid interactions -Will generate classes of distributions that are irregular (not disk-shaped) -May be more realistic and biologically relevant since based on molecular interactions -Can systematically vary and test the effect of different concentrations of proteins or lipids

Heetderks and Weiss Lipid-Lipid Interactions Gel Domains: Phospholipids with long, ordered chains Fluid Domains: Phospholipids with short, disordered chains Cholesterol : Gel domains form a liquid ordered phase Domain Formation In Model Membranes

Model for Domain Formation

Model Components Different Lipid Species Different lipid species are assigned different labels ‘  ’. Plasma Membrane NxN Square Lattice Every node is occupied by a single lipid. ( lipids)

Plasma Membrane

Lipid 2 Lipid 1 Lipid 3

Model Components II Every pair of lipid types is assigned an “interface energy”. Lipid Interaction Lattice Energy The total energy of the system is defined as the sum of the interface energies of all adjacent nodes on the lattice. 0 <   1  2 < 1 Example Like lipids:  = 0 Unlike lipids:  = 1

Lipid Diffusion 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 only if the local temperature is high enough. (random variable)

Simulation Results Random Initial Conditions

Simulation Results

Generating three types of distributions: Vary the density of ‘black’ lipids labeled with acceptors.... what is the FRET efficiency verses acceptor density?

Summary So Far.. FRET is an important tool to study molecule organization since it does not alter the membrane and has nanometer resolution. Intra-domain FRET can be used to measure the density of molecules within domains but cannot uniquely determine the domain radius. Intra-domain FRET can be combined with a segregation FRET approach to determine the domain radius and the number of molecules per domain.

Conclusions Models for FRET can be used to evaluate the potential of different FRET approaches to determine membrane properties of interest. Models for domain formation can be used to restrict the classes of membrane distributions to those that are most biologically relevant.

Thank you!

Example Unlike Lipids δ =1 Lipid-Lipid Interface Energies Like Lipids δ=0 Local Interface Energy = 6

Example Unlike Lipids δ =1 Lipid-Lipid Interface Energies Like Lipids δ=0 Local Interface Energy = 6 Neighbor Switch

Example Unlike Lipids δ =1 Lipid-Lipid Interface Energies Like Lipids δ=0 Local Interface Energy = 6 Neighbor Switch Local Interface Energy = 3