Physical Fluorescence Excitation Dr Maria Kiskowski Byrne, Department of Mathematics, Vanderbilt University. Dr Anne Kenworthy, Depts. of Molecular Physiology & Biophysics and Cell & Developmental Biology, Vanderbilt University School of Medicine. Components of a Discrete Stochastic Model For FRET FRET: Fluorescence Resonance Energy Transfer ComputationalTheoretical Fluorescence and phosphorescence both occur when an electron becomes excited by absorption of photons. Optical spectroscopic phenomena: Absorption Fluorescence Phosphorescence Emission Chemiluminescence Fluorescence VS Phosphorescence During phosphorescence, an electron is excited to a higher energy level, but the electron spin is switched, so that the electron cannot relax without again switching. The lifetime of this excited state is very long (several seconds). Pauli Exclusion principle: No two electrons in the same orbital may have the same spin. Fluorescence Emission & Stokes Shift When an excited electron relaxes from the higher energy level, a photon is emitted. Usually, the emitted photon has a little less energy than the one absorbed and thus has a longer wavelength. EXCITATION EMISSION Resonance Energy Transfer FRET Rate and Förster Distance 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. Donors excite with constant rate k E., which models constant illumination. These processes occur simultaneously, and thus compete over time. Small time steps (<<  ) must be chosen to model the rates accurately. Role of Diffusion This model for membrane FRET is similar to that of Berney and Danuser [Biophys J, 2004]. While they used a “time-stepper approach”, this model proceeds with discrete time steps. FRET on a Cell Membrane Their distribution satisfies a hard-body exclusion radius. N D donors and N A acceptors are assigned to the planar region. Fluorophores: Assigned Excitation States Donor Excitation Transfer occurs between every unexcited acceptor and every excited donor at rate k T, which depends upon their molecular separation r : Donor and Acceptor Decay Excited fluorophores decay with constant rate K D, which models exponential decay: Y = Y 0 e -k D t Transfer k t = k D * (R 0 /r) 6 The lifetime of the fluorophore Is 1/K D = . Ro  =distance when transfer rate equals decay rate k t =k D (R 0 /r 6 ) Forward Problem Inverse Problem Clustering in Membranes Preliminary Results In our model, fluorophore positions are static and do not diffuse. This is justified because while a typical protein diffuses at a rate of.5-2 um 2 per second, fluorescence occurs over scales of 1-10 nanoseconds. The effect of diffusion is greatest at closest separations and largest Förster lengths. For ranges in the table below, the effect of diffusion is negligible. For larger Förster lengths, FRET may be “diffusion-enhanced”. The computation model solves the forward problem: given a known distribution of fluorophores, our model simulates FRET so that FRET efficiency, lifetimes, etc., may be calculated. A more challenging problem is the inverse problem: given observed FRET measurements, what is the fluorophore distribution? Note that FRET maps an N-dimensional distribution of fluorophores to a finite set of experimental measures, so the inverse problem is impossibly under-determined unless the distributions are highly constrained. Protein clustering occurs as proteins form complexes or preferentially partition into different membrane domains. For example, the protein caveolin clusters in flask-shaped structures called caveolae and GPI-anchored protein clusters in the apical ends of epithelial cells. While these are well-known examples, scientists would like to know much more about the distribution of proteins within membranes. We model FRET on a cell membrane and assume a membrane protein is labeled with fluorophores. The cell membrane is modeled as a planar region. Förster LengthDiffusion RateMin SeparationLifetimeMax Effect of Diffusion on FRET Rate <10nm< 2 um 2 > 5nm<10nsVaries from to 6.4 transfers per ns The Plasma Membrane The fluid-mosaic model of Singer and Nicholson was modified in the 1990’s to include membrane domains of different lipid species. This was largely motivated by the observation that lipids sort into domains in model membranes. Drawn by P. Kinnunen, CEO of Kibron, Inc J. Heetderks and P.S. Weiss A fluorophore with an excited electron may transfer its electronic energy to another fluorophore non-radiatively (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. Due to the sensitive dependence of FRET on inter-molecular separation, FRET has been used as an amazingly accurate “spectroscopic ruler” [Stryer, 1967]. Future Directions: Investigate ways of dividing distributions into classes in terms of random, clustered and local density so that the inverse problem becomes more tractable. Solid lines: Our model results for varying donor to acceptor ratios in a random population. Dotted lines: results of Berney et al, Looking at effect of cluster size and monomer fraction. 0Un-excited0 → 1Excitation 1Excited1 → 0 Decay or Transfer During fluorescence, an electron is excited to a higher energy level, but 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).