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

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2 Visual TransductionVision is a complex process which not only enables us humans to percept the environment by absorbingand converting the visual electromagnetic spectrum in between 400nm and 700nm whichis reflected on or emitted from our surrounding, to electric potentials. Therefore we can react onand master any kind of challenge nature gives us.Visual processing which is the conversion of lightto an electrical signal in retinal photo-receptors, consists of numerous sub processes [7].Figure 2.2: The layers of the retina. On the bottomlayer the two receptor cells, Cones andRods, are situated. Here the light, afterpassing through the upper layers, is convertedto an electrical signal, that transmittedvia the Horizontal, Amacrine andBipolar cells, is reaching the Ganglioncells. The whole bunch of signals, gatheredby these Ganglion cells will betransmitted via nerve fibers to the visualcortex of the brain.This first stage of the visual processing willbe described here. Light first propagatesthrough the lens and will be focused on theretina (see Figure 2.1). The retina finally isthe place where visual transduction, namelythe conversion of light to an electrical signaltakes place.The retina consists of manylayers and on the inner layers the photoreceptorcells are situated (see Figure 2.2).Two types of photoreceptor cells are foundthere, namely about 120 million rods andabout 6 − 7 million cones.The cones are necessary for color (photopic)vision and there are at least threetypes of cones excited by three distinctwavelength areas (red, green and blue). Buthere we will not discuss the cones and focuson the rods. In evolutionary terms [7]rods have arisen more recently than conesand numerically rods are the dominant classof photoreceptor cells in the human eye.Furthermore they function at exceedinglylow intensities, corresponding to starlightor moonlight.This means that rods are saturated at normallight conditions. It has been shownthat rods are able to ”detect individual photonsof light [Hecht et al., 1942], and thesubsequent circuitry of the scotopic visualsystem is designed to be able to detect justa few photon hits scattered over large areas[Barlow et al., 1971]. This enablesthe visual system to operate in a ’photoncounting’mode [Rose, 1948]. The enormousnumber of rods is employed primarilyto catch just about every photon that reaches the retina” [7]. As we can see in Figure 2.3, Rods (butalso Cones) consist of three primary functional parts: outer segment, inner segment and synapticending.6
(a)(b)(c)Figure 2.3: (a) The anatomy of the rod photoreceptor cell (from [7]). It is consisting of an innersegment, outer segment, a nucleus and a synaptic terminal that at the end transmits theelectrical signal to the higher-ranking nerve cells. On the outer segment are situatedstacks of several hundreds to thousands of vesicular discs. (b) The scheme of the visualtransduction process in these retinal rod discs (presented also in Figure 2.4). (c) On themembranes of these discs the 7TM receptor molecule rhodopsin is situated (see alsoFigure 2.5).For the purpose of this thesis the focus will be only on the outer segment. Several hundreds tothousands of membrane pairs are stacked along this outer segment. This structures which arecompletely separated from the plasma membrane, are forming intracellular organelles and arecalled discs. Many of the proteins and other components of the visual transduction cascade residein (or at the surface of) this discs. The most abundant protein in the disc membrane is thelight-capturing protein, called rhodopsin. The disc membranes in fact are densely packed withrhodopsin molecules, about 30.000 molecules per µm 2 .Rhodopsin is part of the 7TM serpentine receptor family. Without going too much into detail,one can say that ”all these receptors share a common architectural theme. Their polypeptide chainmakes seven passes through the membrane (see figure 2.5)” [36, p. 169]. That is the reason, whythey are called seven trans-membrane or serpentine receptors.”The 7TM receptors share not only a common architectural theme but also a common intermembranousmethod of signal amplification”[36, p. 169]. This mechanism grounds on the lateralmobility of the so called G-Proteins. G-Proteins are members of a large class of guanine nucleotidebinding proteins and they function more or less as biochemical switches, which can turnon and turn off the activity of other molecules. In the case of the visual transduction process inrod discs the G-Protein is called transducin. For more information about the serpentine-receptorfamily and G-Proteins in general, see [36, chapter 8]. In the following we solely concentrate on7
Page 1: Diploma ThesisDepartment for Theore
Page 5 and 6: AbstractAnomalous diffusion is a ub
Page 7 and 8: Zusammenfassung 1Anomale Diffusion
Page 9 and 10: Contents1 Motivation 12 Visual Tran
Page 11 and 12: List of Figures2.1 Anatomy of the e
Page 13 and 14: 1 Motivation„NEC FASCES, NEC OPES
Page 15 and 16: Theoretically we profit from enormo
Page 17: 2 Visual Transduction”The eye owe
Page 21 and 22: effect of generating the photorecep
Page 23 and 24: 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
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3.13 Global Optimization Methods3.1
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3.13 Global Optimization MethodsEve
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4 Fluorescence Tracking Experiments
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4.2 Fluorescence SpectroscopyAfter
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4.3 Single Molecule Tracking via Wi
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4.4 Total Internal Reflection Fluor
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4.4 Total Internal Reflection Fluor
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4.6 The expected range for the Tran
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5 Modeling of the Experiment”The
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5.1 Experimental Data(a)(b)(c)(d)Fi
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5.2 Model Ansatz and Estimation of
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5.2 Model Ansatz and Estimation of
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5.3 Testing the Modelalgorithm was
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5.5 Estimation of the Noise Intensi
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5.6 Estimation on the Basis of Diff
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6 Conclusion and OutlookThe main as
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7 Bibliography[1] R. C. Aster, B. B
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[36] C. U. M. Smith: Elements of Mo
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Index11-cis retinal isomer, 87TM se
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A AppendixA.1 From Copernicus to Ne
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A.2 Important Papers on the Rhodops
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A.3 Probability TheoryDefinition A.
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A.4 Definitions for OptimizationDef
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A.4 Definitions for OptimizationDef
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A.7 The Fluctuation-Dissipation-The
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A.7 The Fluctuation-Dissipation-The
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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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Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

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