Single-Molecule Temporal Resolution in Dilute Solution and Live Cell without external forces. Super-resolution microscopy is about spatial resolution and developments of super-resolution techniques have pushed the limits of spatial resolution in a diffraction limited optical system (beyond Abbe's limit). The temporal resolution of single-molecule detection (which I refer to) depends on the stochastic diffusive process (Brownian motion) of the single molecule/particle within the observation volume. Whatever is used to detect or image molecules in liquids or live cells without immobilization on a solid phase or membrane as well as without significant hydrodynamic flow (e.g., detection/imaging by super-resolution microscopy, fluorescence correlation spectroscopy, FRET, laser scanning microscopy, single-particle tracking, etc.), the concentration dependence of the meaningful time, that is the thermodynamic single-molecule time resolution, has not to be violated. For example, if there is one molecule/particle per observation volume, then the single-molecule time resolution is 2,7183 times the diffusion time of that particular molecule/particle. If the detection or observation time is greater than the single-molecule time resolution, then averaging over many molecules/particles is performed and this should be avoided in single-molecule studies: https://lnkd.in/dKC5xns Zeno Földes-Papp.

1. 1
15 October 2005
Vermelding onderdeel organisatie
Theoretical Testing of Single-Molecule
FCS and Two-Color FCCS without
Immobilization or Hydrodynamic Focusing
Application: solution, live cell
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
November 27, 2007
2/23
Overview Presentation
1. Problem Description
• Motivation
• Objectives
• Method
2. Modeling
3. Results and Discussions
Introduction – Problem – Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN

2. 2
3/23
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
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN
4/23
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
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN

3. 3
5/23
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?
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN
6/23
Objectives
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
Procedure
1. To develop an accurate hidden Markov model for this challenging
application
2. Unravel the position of a single molecule with time
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN

4. 4
7/23
Configuration Set-Up
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN
8/23
Numerical Modeling
object
Solution generation:
• Reentries depend on motional rates
•
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN

5. 5
9/23
Time Step Restrictions
Hence: Ansatz:
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN
10/23
Validation Using Special Solutions
Summarizing:
•
•
Extend this method to meaningful reentries !!!
If the molecule number < 1 then the corresponding time rate of motional
single-molecule reentries is given by the diffusion time of the molecule.
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN

6. 6
11/23
Verification Using Special Solutions
Numerical model:
•
•
Close-up at the Leading Edge:
Non-meaningful reentries:
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
Meaningful reentries:
fine
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
Remember - Solution generation:
Reentries depend on motional rates
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN
12/23
Verification Using Special Solutions
Numerical model:
•
• HENCE, the meaningful time in the
confocal observation volume is
Close-up at the Leading Edge:
Meaningful reentries:
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
Meaningful reentries
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
Remember - Solution generation:
Reentries depend on motional rates
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:
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN

7. 7
13/23
Verification Using Special Solutions
Numerical model:
•
Close-up at the Leading Edge:
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
Meaningful reentries:
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
Remember - Solution generation:
Reentries depend on motional rates
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN
14/23
Verification Using Special Solutions
Numerical model:
•
Close-up at the Leading Edge:
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
Meaningful reentries:
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
Remember - Solution generation:
Reentries depend on motional rates
fine
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN

8. 8
15/23
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
Verification Using an Another Approach
Chance that the Reentering Molecule is not the Original
Molecule
As Function of the Time from Last Entry
I take the two-dimensional Poisson probability distribution of finding fluorescent
molecules in the detection volume of the bulk phase
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN
16/23
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
Chance that the Reentering Molecule is not the Original
Molecule
As Function of the Time from Last Entry
Verification Using an Another Approach
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN

9. 9
17/23
Definition of Motion Parameters
3D parameters:
for the axially-
symmetric,
cylindrical
volume element
in terms of
cylindrical polars
(q, φφφφ, z) with
radial diffusion
in space (three-
dimensional)
•Density Function
of Diffusive
Spreading:
n (q, φφφφ, z, t) =
n (q, t)
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN
18/23
Kinematic Models
3D parameters:
for the axially-
symmetric,
cylindrical
volume element
in terms of
cylindrical polars
(q, φφφφ, z) with
radial diffusion
in space (three-
dimensional)
•Density Function of
Diffusive Spreading:
n (q, φφφφ, z, t) =
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
n (q, t) = f (q, t)
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN

10. 10
19/23
Kinematic Models
3D parameters:
for the axially-
symmetric,
cylindrical
volume element
in terms of
cylindrical polars
(q, φφφφ, z) with
radial diffusion
in space (three-
dimensional)
•Density Function of
Diffusive Spreading:
n (q, φφφφ, z, t) =
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
n (q, t) = f (q, t)
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN
20/23
Summary of Main Results
Remember - Solution generation: Reentries depend on motional rates
and and
Take a closer look at the experiments done so far
Exact
Analytic
solution
first
found
Meaningful timeMeaningful
reentries
Non-meaningful
reentries
Model
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN

11. 11
21/23
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), 261-273.
Földes-Papp (2007). ‘True’ single-molecule molecule observations by fluorescence
correlation spectroscopy and two-color fluorescence cross-correlation spectroscopy. Exp.
Mol. Pathol. 82 (2), 147-155.
Földes-Papp (2006). What it means to measure a single molecule in a solution by
fluorescence fluctuation spectroscopy. Exp. Mol. Pathol. 80 (3), 209-218.
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), 291-300 .
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN
22/23
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 2008.
Introduction – Problem – Numerical Modeling – Validation – Kinematic Modeling – Results – Conclusions
PD Dr.med.habil. Dr.rer.nat. Zeno Földes-Papp
10th International Workshop on FCS and Related Methods, Sapporo, Nov. 26-28, 2007, JAPAN