Overview Presentation. Theoretical Testing of Single-Molecule FCS and Two-Color FCCS without Immobilization or Hydrodynamic Focusing

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1 Theoretical Testing of Single-Molecule FCS and Two-Color FCCS without Immobilization or Hydrodynamic Focusing Application: solution, live cell 15 November October , 2007 Vermelding onderdeel organisatie Overview Presentation 1. Problem Description Motivation Objectives Method 2. Modeling 3. Results and Discussions Introduction Problem Modeling Results Conclusions 2/23 1

2 Background - Motivation (1/2) Reentries of a single molecule are a major problem: FCS theory could not predict motion of a single molecule Experiments showed highly sensitive detection: Goodwin and Keller (2003) approached fm-range with two-color FCCS Multi-parameter fluorescence detection offers an experimental basis for the collection of both TCSPC data and FCS/FCCS data Likelihood estimators 3/23 Background - Motivation (2/2) Fluctuations are stochastic The detected fluorescence signals become digital Fluorescence bursts are only detected when single molecules pass through the confocal observation volume 4/23 2

3 Problem Statement Reentries of a single molecule give raise to fluctuation phenomena The molecule diffusing through the focal periphery causes some fluorescence, which is only weakly correlated with that from the sharp focal plane ( spot ) Main Question What happens if the molecule starts near a boundary, i.e. it sits at the border of the confocal observation volume, crosses in and out, and therefore has many reentries but none of them are meaningful? 5/23 Objectives 1. To develop an accurate hidden Markov model for this challenging application 2. Unravel the position of a single molecule with time Procedure 1. Modeling using general tools to solve Markov chains 2. Validation of the model using special solutions 3. Investigate influence of kinematics to point single-molecule motion 6/23 3

4 Configuration Set-Up 7/23 Numerical Modeling object Solution generation: Reentries depend on motional rates 8/23 4

5 Time Step Restrictions Hence: Ansatz: 9/23 Validation Using Special Solutions Summarizing: If the molecule number < 1 then the corresponding time rate of motional single-molecule reentries is given by the diffusion time of the molecule. Extend this method to meaningful reentries!!! 10/23 5

6 Verification Using Special Solutions Close-up at the Leading Edge: Remember - Solution generation: Reentries depend on motional rates Numerical model: Non-meaningful reentries: Meaningful reentries: fine 11/23 Verification Using Special Solutions Close-up at the Leading Edge: Remember - Solution generation: Reentries depend on motional rates Numerical model: Meaningful reentries HENCE, the meaningful time in the confocal observation volume is If the observed N value becomes N < 1 then N stands for the Poisson probability of finding a single molecule in the confocal probe region (arrival of a single molecule). Under this condition, N < 1, <C> = C is the average frequency that the confocal probe region contains a single molecule: Meaningful reentries: 12/23 6

7 Verification Using Special Solutions Close-up at the Leading Edge: Remember - Solution generation: Reentries depend on motional rates Numerical model: Meaningful reentries: 13/23 Verification Using Special Solutions Close-up at the Leading Edge: Numerical model: Remember - Solution generation: Reentries depend on motional rates Meaningful reentries: fine 14/23 7

8 Verification Using an Another Approach I take the two-dimensional Poisson probability distribution of finding fluorescent molecules in the detection volume of the bulk phase Chance that the Reentering Molecule is not the Original Molecule As Function of the Time from Last Entry 15/23 Verification Using an Another Approach Chance that the Reentering Molecule is not the Original Molecule As Function of the Time from Last Entry 16/23 8

9 3D parameters: for the axiallysymmetric, cylindrical volume element in terms of cylindrical polars (q, φ, z) with radial diffusion in space (threedimensional) Density Function of Diffusive Spreading: n (q, φ, z, t) = n (q, t) Definition of Motion Parameters 17/23 3D parameters: for the axiallysymmetric, cylindrical volume element in terms of cylindrical polars (q, φ, z) with radial diffusion in space (threedimensional) Density Function of Diffusive Spreading: n (q, φ, z, t) = n (q, t) = f (q, t) Kinematic Models 18/23 9

10 3D parameters: for the axiallysymmetric, cylindrical volume element in terms of cylindrical polars (q, φ, z) with radial diffusion in space (threedimensional) Density Function of Diffusive Spreading: n (q, φ, z, t) = n (q, t) = f (q, t) Kinematic Models 19/23 Summary of Main Results Model Non-meaningful reentries Meaningful reentries Meaningful time Exact Analytic solution first found Remember - Solution generation: Reentries depend on motional rates and and Take a closer look at the experiments done so far 20/23 10

11 Summary of Main Results Remember - Solution generation: Földes-Papp (2007). Fluorescence fluctuation spectroscopic approaches to the study of a single molecule diffusing in solution and a live cell without systemic drift or convection: a theoretical study. Curr. Pharm. Biotechnol. 8 (5), Földes-Papp (2007). True single-molecule molecule observations by fluorescence correlation spectroscopy and two-color fluorescence cross-correlation spectroscopy. Exp. Mol. Pathol. 82 (2), Földes-Papp (2006). What it means to measure a single molecule in a solution by fluorescence fluctuation spectroscopy. Exp. Mol. Pathol. 80 (3), Földes-Papp, Baumann, Kinjo, Tamura (2005). Single-phase single-molecule fluorescence correlation spectroscopy (SPSM-FCS). Distinguished article entry. In: J Fuchs, M Podda (Eds), Encyclopedia of Medical Genomics & Proteomics, Marcel Dekker, New York. Földes-Papp (2002). A new dimension for the development of fluorescence-based assays in solution: from physical principles of FCS detection to biological applications (assays of single molecules in solution). Exp. Biol. Med. 227 (5), /23 Conclusions Földes-Papp (2008). Viral Chip Technology for Genomic Medicine. In: H.F. Willard, G.S. Ginsburg (Eds.), Handbook of Genomic Medicine, Part I The Basics, Technolgies. Academic Press, New York. Upcoming in October /23 11