Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

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4 Fluorescence Tracking ExperimentsSince at room temperature (or much more at the physiological temperature of 37 ◦ C) the energywhich is needed for excitation of the molecular system is much higher than the thermal energy k B Tof the environment, spontaneous transition into the excited state is highly improbable. Thereforefluorescence spectroscopy is an experimental method giving the experimentalists a tool at handwhich has very high signal to noise ratios.In the biophysical and biochemical sciences the method of fluorescence spectroscopy is of highimportance. Here one is interested in any methods, in order to understand the processes that takeplace in biological systems, not least the processes that are going on in the cells, and within thesecells the molecular constituents which are responsible for the smoothly flow of these processes.Molecules of interest are for example proteins, molecular machines, diverse in their form andfunctionality, and thus making life in its thousandfold realizations possible. While proteins arebuilt up by amino acids, these amino acids exhibit fluorescence spectra much too low in theirintensities, and laying in the UV-area of the electromagnetic wave spectrum. An excitation withphotons of UV would irreversibly destroy the cell.This trouble leads to the employment of the so called fluorescence dyes, mostly small moleculeswith reactive chemical groups, enabling the scientists, easily ”to bond these dyes to the protein ofinterest, just according to a kind of recipe” [35].Not only the fact that these dyes can be easily sticked to the proteins makes them so important, butalso their brilliant fluorescence properties. The problem however is the difficulty arising in orderto transfer the dye-marked proteins back to the cell or into the organism to be investigated. Thisis a problem which led to the advent of another kind of marker molecule, the so called ”GreenFluorescent Protein” (GFP).This molecule can compete to any Laser dye with regard to the absorption cross section, the quantumyield and the photo-stability. But it has the great advantage of being genetically coded. Thusthe GFP can be assembled due to gene technical strategies in almost every arbitrary cell systemand subsequently can be specifically adhered to almost any protein. The enormous potential ofthe GFP led to the discovery of and the research on other proteins with related structure, so that tothis date there exist marker proteins of different kind which can be switched on and off by light oreven transform their color after radiation with short light pulses [35].Essentially one is distinguishing between two fluorescence spectroscopy methods:1. Wide-Field Fluorescence Spectroscopy:Planar illumination of a wide area, for example a whole cell or a cell colony. This spectroscopymethod allows the investigation of different areas of a cell simultaneously, whiledetection of the fluorescence signals is taking place by highly sensitive CCD- or video cameras.2. Confocal Fluorescence Spectroscopy:Point illumination is used to analyze a small measuring dot. Highly sensitive point detectorslike ”Avalanche Photo diodes” are imaging the signal of the measuring dot.Since it is today technically not possible to rise the spatial and the temporal resolution of the fluorescencespectroscopy simultaneously, today’s science in the field of fluorescence spectroscopy isdivided in two main streams [35]. One is the so called confocal fluorescence spectroscopy deliver-64
4.3 Single Molecule Tracking via Wide-Field Fluorescence Spectroscopying a temporal resolution in the investigation of biomolecular dynamics in the area of nanoseconds.We will not examine the Confocal Fluorescence Spectroscopy, since it is outside of the focus ofthis thesis. For more information about this method one is referred to [8]. Here we focus onthe second main stream of fluorescence spectroscopy, namely the so called single molecule imagingor rather -tracking. This is a spectroscopy method, enabling the scientists to investigate thetime-resolved position and movement of diverse bio molecules and other biological active particleswithin a cell. With this technique biological processes taking place over timescales betweenmilliseconds and some seconds up to hours can be investigated, with possible spatial resolutionsin the nanometer range ([58], [59]). Usually the single molecule tracking is done in the frameworkof the wide-field fluorescence spectroscopy which we will introduce in the next section.4.3 Single Molecule Tracking via Wide-Field FluorescenceSpectroscopyObjectlevelwith sampleLaserCondenserMicroscopeobjectiveDichroicmirrorLensFilterCCDCamera(a) Experimental Setup.(b) Result of a measurement.Figure 4.3: Wide-Field Fluorescence Spectroscopy (from [22]). With a wide-field fluorescencemicroscope for the tracking of single molecules, the light of the laser will be focusedon the rear focal plane, so that the object is illuminated in the wide-field (a). Theobjective gathers the reflected fluorescence light and is imaging it on a highly sensitiveCCD-camera. The fluorescence of the single molecules is occurring as bright dotson the CCD-camera (b1). From the detailed structure of the fluorescence image oneobtains the intensity profile which can be fit by a two-dimensional Gaussian function(b2).65
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Diploma ThesisDepartment for Theore
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AbstractAnomalous diffusion is a ub
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Zusammenfassung 1Anomale Diffusion
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Contents1 Motivation 12 Visual Tran
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List of Figures2.1 Anatomy of the e
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1 Motivation„NEC FASCES, NEC OPES
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Theoretically we profit from enormo
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2 Visual Transduction”The eye owe
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(a)(b)(c)Figure 2.3: (a) The anatom
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effect of generating the photorecep
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3 Theory”The theory is the net, t
Page 25 and 26: 3.2 Markov Chains, Markov Processes
Page 31 and 32: 3.3 Hidden Markov ModelsP[X(t + τ)
Page 33 and 34: 3.4 Maximum Likelihood Principlewit
Page 35 and 36: 3.5 Optimization3.5 OptimizationAcc
Page 37 and 38: 3.7 Baum-Welch-AlgorithmAlgorithm 3
Page 39 and 40: 3.8 Two Approaches on Stochastic Sy
Page 41 and 42: 3.9 DiffusionConsider a basin fille
Page 43 and 44: 3.9 Diffusion169].Rearranging (3.34
Page 45 and 46: 3.9 Diffusionwith τ = t −t ′ .
Page 47 and 48: 3.9 DiffusionD = 2k2 B T 2σ . (3.4
Page 49 and 50: 3.10 Hidden Markov Models with Stoc
Page 55 and 56: 3.11 Hidden Markov Model - Vector A
Page 57 and 58: 3.11 Hidden Markov Model - Vector A
Page 59 and 60: 3.12 Artificial Test Examples for H
Page 69 and 70: 3.13 Global Optimization Methods3.1
Page 71 and 72: 3.13 Global Optimization MethodsEve
Page 73 and 74: 4 Fluorescence Tracking Experiments
Page 75: 4.2 Fluorescence SpectroscopyAfter
Page 79 and 80: 4.4 Total Internal Reflection Fluor
Page 81 and 82: 4.4 Total Internal Reflection Fluor
Page 83 and 84: 4.6 The expected range for the Tran
Page 85 and 86: 5 Modeling of the Experiment”The
Page 87 and 88: 5.1 Experimental Data(a)(b)(c)(d)Fi
Page 89 and 90: 5.2 Model Ansatz and Estimation of
Page 91 and 92: 5.2 Model Ansatz and Estimation of
Page 93 and 94: 5.3 Testing the Modelalgorithm was
Page 95 and 96: 5.5 Estimation of the Noise Intensi
Page 97 and 98: 5.6 Estimation on the Basis of Diff
Page 103 and 104: 6 Conclusion and OutlookThe main as
Page 105 and 106: 7 Bibliography[1] R. C. Aster, B. B
Page 107 and 108: [36] C. U. M. Smith: Elements of Mo
Page 109 and 110: Index11-cis retinal isomer, 87TM se
Page 111 and 112: A AppendixA.1 From Copernicus to Ne
Page 113 and 114: A.2 Important Papers on the Rhodops
Page 115 and 116: A.3 Probability TheoryDefinition A.
Page 117 and 118: A.4 Definitions for OptimizationDef
Page 119 and 120: A.4 Definitions for OptimizationDef
Page 121 and 122: A.7 The Fluctuation-Dissipation-The
Page 123 and 124: A.7 The Fluctuation-Dissipation-The
Page 125 and 126: A.8 Kramers-Moyal Forward Expansion
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A.9 Deriving the Fokker-Planck Equa
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A.9 Deriving the Fokker-Planck Equa
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DanksagungenIch möchte folgenden M
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AffirmationHereby I, Arash Azhand,
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