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

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4 Fluorescence Tracking Experimentsbottom side of the glass plate. Thereby the light rays hit the plate under an angle α i , which isgreater than the critical angle α c , hence leading to a total internal reflection of the radiance and itsrecirculation into the objective.On the upper side of the glass plate an evanescent electromagnetic wave of the same frequency,as the excitation light arises and propagates through the media above the plate, where for examplefluorophores or with fluorophores labeled particles are moving.The intensity of the evanescent wave decays with the penetration depth, and the penetration depthdepends on the angle α i under which excitation light hits the glass plate. Thus one is able to adjustthe penetration depth of the evanescent field and hence adjust the size of the area which is resolvedthrough the subsequent fluorescence light emission of the fluorophores in this area. This allowsthe detection of only those particles which are in the direct vicinity of the boundary surface.The TIRFM method combined with wide-field detection through sensitive CCD-cameras deliversa good method in order to resolve single molecules at room temperature, especially in the directproximity of the membrane. This will be presented in the next section by means of the singlemolecule tracking experiments on the G-Protein transducin.4.5 Tracking Of the Transducin Proteins via Wide-FieldFluorescence Spectroscopy combined with Total InternalReflection Fluorescence Microscopy (TIRFM)In this chapter we described the experimental techniques that allow tracking of single molecules,and how to obtain trajectory data via these experiments. The experimental setup for the specialpurpose to track single transducin molecules (performed by Alexiev 2 et. al.) is based on the widefieldfluorescence spectroscopy (WFFS) method, shown in Figure 4.3 on page 65, combined withthe total internal reflection fluorescence microscopy (TIRFM) method, schematically shown inFigure 4.6. The probe is illuminated via an objective in the wide-field at an angle, which is abovethe critical angle, leading to a total internal reflection of the light and emergence of an evanescentfield at the upper boundary surface.The probe preparation is shown in Figure 4.7 on the next page.Bovine retinal rod disc membranes were cracked open and then placed on the bottom of a glasscontainer filled with a solvent. The solvent contains diffusing single transducin molecules whichare labeled with fluorophores. They are absorbing light of the same frequency as the evanescentwave. Afterwards emitted fluorescence light is collected by the objective. For the detection ofthis fluorescence light a sensitive CCD-camera is used. The time-resolved recording of the fluorescencesignals of single transducin molecules lead to a two-dimensional trajectory in time. TheTIRFM setup causes only the transducins in the direct proximity of the disc membranes to beresolved.Additionally the membrane integral proteins rhodopsin can be activated through an additional laserwith a different frequency. The state where the rhodopsins are not activated, will be denoted by the2 For contact informations look at http://users.physik.fu-berlin.de/~alexiev/70
4.6 The expected range for the Transducin Diffusion Coefficientsterm ”Dark State”, while the activated state of the rhodopsin will be denoted by the term ”BrightState”.Transducinlipid-anchorRhodopsinEvanescentfieldlipid-bilayermembraneRhodopsinanchorGlassplate i rFluorescenceObjectivewith CCDcameraFigure 4.7: Experimental preparation of disc membranes, in order to get the movement of singletransducin proteins within a solvent. Description in text.4.6 The expected range for the Transducin DiffusionCoefficientsAlready very early works on the rhodopsin-transducin system, such as the one from the year1989 by Saxton and Owicki, have investigated the rhodopsin-transducin system (see [31]). Laterworks also investigated the case thoroughly (see in the appendix, section A.2 on page 101 for apresentation of selected works on the rhodopsin-transducin system).Saxton and Owicki investigate the question how the concentration of the considered proteins affect71
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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
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3.2 Markov Chains, Markov Processes
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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 and 76: 4.2 Fluorescence SpectroscopyAfter
Page 77 and 78: 4.3 Single Molecule Tracking via Wi
Page 79 and 80: 4.4 Total Internal Reflection Fluor
Page 81: 4.4 Total Internal Reflection Fluor
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
Page 127 and 128: A.9 Deriving the Fokker-Planck Equa
Page 129 and 130: A.9 Deriving the Fokker-Planck Equa
Page 131 and 132: DanksagungenIch möchte folgenden M
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AffirmationHereby I, Arash Azhand,
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