383 lines
18 KiB
TeX
Executable File
383 lines
18 KiB
TeX
Executable File
\documentclass[12pt,a4paper,pdftex]{article}
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\usepackage[left=25mm, right=25mm, top=20mm, bottom=25mm]{geometry}
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\usepackage{graphicx}
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\usepackage{amsmath}
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\usepackage{natbib}
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\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=false,citecolor=blue]{hyperref}
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\usepackage[utf8x]{inputenc}
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\usepackage[english]{babel}
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%\usepackage{float}
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\usepackage{floatrow}
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\usepackage{listings} % für den code am Ende
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\newcommand{\todo}[1]{{(\color{red} TODO: #1) }}
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\newcommand{\AptLepto}{{\textit{Apteronotus leptorhynchus}}}
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\newcommand{\lepto}{{\textit{A. leptorhynchus}}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Ab hier beginnt der eigentliche Text:
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Titelseite
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{titlepage}
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\begin{center}
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{\Huge TITEL \par}
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\vspace{0.75cm}
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{\Large Masterthesis \par}
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\vspace{0.25cm}
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{der Mathematisch-Naturwissenschaftlichen Fakultät \par} {der Eberhard Karls Universität Tübingen \par}
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\vspace{0.75cm}
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{Erstkorrektor: \\
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Zweitkorrektor: Prof.~Dr.~Jan Benda \par}
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\vspace{0.25cm}
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{Lehrbereich für Neuroethologie}
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\vfill
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\large vorgelegt von \par
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\large Alexander Mathias Ott \par
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Abgabedatum: 30.11.2017
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\end{center}
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\end{titlepage}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Erklärung
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\section*{Eigenständigkeitserklärung}
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\vspace{0.5cm}
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Hiermit erkläre ich, dass ich die vorgelegte Arbeit selbstständig verfasst habe und keine anderen als die angegebenen Quellen und Hilfsmittel benutzt habe.
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\vspace{2mm}
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\noindent
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Außerdem erkläre ich, dass die eingereichte Arbeit weder vollständig noch in wesentlichen Teilen Gegenstand eines anderen Prüfungsverfahrens gewesen ist.
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\vfill
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\begin{tabular}{ll}
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$\overline{\text{Unterschrift}\hspace{6cm}}$ & $\overline{\text{Ort, Datum}\hspace{4cm}}$ \\
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\end{tabular}
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\newpage\newpage
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Inhalsverzeichnis
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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{
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\hypersetup{linkcolor=black}
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\tableofcontents
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Zusammenfassung
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Abstract}
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%Einleitung + Ergebnisse der Diskussion in kurz
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Einleitung
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Introduction}
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\begin{enumerate}
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\item electric fish
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\begin{enumerate}
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\item general: habitat,
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\item as model animal for ethology
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\item electric organ + eod
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\item sensory neurons p- and t(?)-type
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\end{enumerate}
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\item sensory perception
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\begin{enumerate}
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\item receptor -> heterogenic population
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\item further analysis limited by what receptors code for - P-Units encoding
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\item p-type neurons code AMs
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\end{enumerate}
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\item goal be able to simulate heterogenic population to analyze full coding properties -> many cells at the same time needed -> only possible in vitro/ with model simulations
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\item Possible to draw representative values for model parameters to generate a population ?
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\end{enumerate}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Methoden
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Materials and Methods}
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\subsection{Notes:}
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\begin{enumerate}
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\item Data generation
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\begin{enumerate}
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\item How data was measured / which data used
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\item How data was chosen -> at least 30s baseline, 7 contrasts with 7 trials
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\item experimental protocols were allowed by XYZ (before 2012: All experimental protocols were approved and complied with national and regional laws (file no. 55.2-1-54-2531-135-09). between 2013-2016 ZP 1/13 Regierungspräsidium Tübingen and after 2016 ZP 1/16 Regierungspräsidium Tübingen)
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\item description of data -> Baseline properties, FI-Curve with images made from cells
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\item make a point of using also bursty cells as part of what is new in this work!
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\end{enumerate}
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\item behavior parameters:
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\begin{enumerate}
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\item which behaviors were looked at / calculated and why (bf, vs, sc, cv, fi-curve...)
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\item how exactly were they calculated in the cell and model
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\item stimulus protocols
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\end{enumerate}
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\item Construction of model
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\begin{enumerate}
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\item Explain general LIF
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\item parameters explanation, dif. equations
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\item Explain addition of adaption current
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\item note addition of noise + factor for the independence from step size
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\item addition of refractory period
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\item check between alpha in fire-rate model adaption and a-delta in LIFAC
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\end{enumerate}
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\item Fitting of model to data
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\begin{enumerate}
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\item which variables where determined beforehand (None, just for start parameters)
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\item which variables where fit
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\item What method was used (Nelder-Mead) and why/(how it works?)
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\item fit routine ? (currently just all at the same time)
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\end{enumerate}
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\end{enumerate}
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\subsection{Leaky Integrate and Fire Model}
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% add info about simulation by euler integration and which time steps!
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% show voltage dynamics with resistance :
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also show function with membrane resistance before explaining that is is unknown an left out: $ \tau_m \frac{dV}{dt} = -V + I$
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% explain subthreshold behaviour first then add V_{th} and adaption etc
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% explain modeling of the adaption current see Benda2010
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% table with explanation of variables ?
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\todo{restructure sounds horrible}
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The P-units were modeled with an noisy leaky integrate-and-fire neuron with an adaption current (LIFAC). The basic voltage dynamics in this model follows equation \ref{basic_voltage_dynamics}. The voltage is integrated over time while also exponentially decaying back to zero. When a voltage threshold is reached the voltage is set back to zero and a spike is recorded. The currents in this model carry the unit mV as the the cell bodies of p-units are inaccessible during the recordings and as such the resistance of the cell membrane is unknown \todo{ref mem res p-units}.
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The current can be split into three parts: the adaption current, the input current and the bias current (Eq. \ref{currents_lifac}). The input current is the stimulus from outside the cell, the bias current models the general activity of the cell and the adaption current models a combination of the M-type, mAHP-type and sodium adaption currents \todo{ref Benda 2005}.
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The adaption current is modeled as an exponential decay with the time constant $\tau_A$ and a strength called $\Delta_A$ (Eq. \ref{Adaption_dynamics}). $\Delta_A$ is multiplied with the sum of events in the spike train ($\delta (t)$) of the model cell itself. For the simulation using the Euler integration this results in an increase of $I_A$ by $\Delta_A$ in every time step where a spike is recorded. \todo{image of model simulation with voltage adaption and spikes?}
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Finally a noise current and an absolute refractory period where added to the model. The noise $\xi$ is drawn in from a Gaussian noise with values between 0 and 1 and divided by $\sqrt{\Delta t}$ to get a noise which autocorrelation function is independent of the integration step size $\Delta t$. After an excitation of the model the voltage is kept at zero for the duration of the refractory period.
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\begin{equation}
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\tau_m \frac{dV}{dt} = -V + I
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\label{basic_voltage_dynamics}
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\end{equation}
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\begin{equation}
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I = \alpha I_{Input} - I_A + I_{Bias}
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\label{currents_lifac}
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\end{equation}
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\begin{equation}
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\tau_A \frac{dI_A}{dt} = -I_A + \Delta_A \sum \delta (t)
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\label{Adaption_dynamics}
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\end{equation}
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\begin{equation}
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\tau_m \frac{dV}{dt} = -V+I_{Bias} +\alpha I_{Input} - I_{A} + \sqrt{2D}\frac{\xi}{\sqrt{\Delta t}}
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\label{full_voltage_dynamics}
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\end{equation}
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\subsection{Data Generation}
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The data for this master's thesis was collected as part of other previous studies \todo{ref other studies}. The collection method provided here is only an overview for the exact details see \todo{link papers}.
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The in vivo intracellular recordings of P-unit electroreceptors of \AptLepto were done in the lateral line nerve . The fish were an anesthetized with MS-222 (100-130 mg/l; PharmaQ; Fordingbridge, UK) and the part of the skin covering the lateral line just behind the skull was removed
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general anesthetic MS-222 (100-130 mg/l; PharmaQ; Fordingbridge, UK)
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local anesthetics Lidocaine (2\%; bela-pharm; Vechta, Germany)
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immobilization with (Tubocurarine; Sigma-Aldrich; Steinheim, Germany, 25–50 $\mu l$ of 5\. mg/ml solution)
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\subsection{Stimulus Protocols}
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% image of Baseline stimulus as baseline doesn't mean no stimulus here
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% image of Fi curve stimulus sinusoidal step
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% image of SAM stimulus
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\subsection{Fitting of the Model}
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\subsection{Henriette's structure:}
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\begin{enumerate}
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\item data generation - recordings
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\item model simulations - construction of model
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\item Simulation protocols
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\item Data analysis - calculation of behavior parameters
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\begin{enumerate}
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\item calculation of baseline parameters
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\item calculation of fi curve parameters
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\item stimuli step SAM(?) noise(?)
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\item goodness of fit
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\item sensitivity analysis (influence of par on model)
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\end{enumerate}
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\end{enumerate}
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\section{Results}
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\begin{enumerate}
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\item how well does the fitting work?
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\item distribution of behavior parameters (cells and models)
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\item distributions of parameters
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\item correlations: between parameters between parameters and behavior
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\item correlation between final error and behavior parameters of the cell -> hard to fit cell types
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\item (response to SAM stimuli)
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\end{enumerate}
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\section{Discussion}
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\section{Possible Sources}
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\subsection{Henriette Walz - Thesis}
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\subsubsection{Nervous system - Signal encoding}
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\begin{enumerate}
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\item single neurons are the building blocks of the nervous system (Cajal 1899)
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\item encoding of information in spike frequency - rate code(first description(?) Adrian 1928) also find examples! (light flash intensity Barlow et al. 1971, )
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\item encoding info in inter spike intervals (Singer and Gary 1995)
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\item encoding time window (Theunissen and Miller 1995) "This time window is the time scale in which the encoding is assumed to take placewithin the nervous system
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\item encoding is noisy (Mainen and Sejnowski 1995, Tolhurst et al 1983, Tomko and Crapper 1974 -> review Faisal et al 2008) in part because of stimulus properties but also cell properties (Ion channel stochasticity (van Rossum et al.,2003))
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\item noise can be beneficial to encoding -> "stochastic resonance" (weak stimuli on thresholding devices like neurons, noise allows coding of sub threshold stimuli) (Benzi et al., 1981)
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\item single neurons are anatomically and computationally independent units, the
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representation and processing of information in vertebrate nervous systems is distributed
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over groups or networks of cells (for a review, see Pouget et al., 2000)
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\item It has
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been shown that the synchrony among cells carries information on a very fine temporal
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scale in different modalities, from olfaction (Laurent, 1996) to vision (Dan et al., 1998)
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\item In the electrosensory system it was shown before that communication signals change the synchrony of the receptor population (Benda et al., 2005, 2006)
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and that this is read out by cells in the successive stages of the electrosensory pathway
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(Marsat and Maler, 2010, 2012; Marsat et al., 2009).
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\item An advantage of rate coding in populations is that it is fast. The rate in
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single neurons has to be averaged over a time window, that is at least as long as the
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minimum interspike interval. In contrast, the population rate can follow the stimulus
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instantaneous, as it does not have to be averaged over time but can be averaged over
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cells (Knight, 1972a).
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\item In a population of neurons subject to neuronal noise, stochastic resonance occurs
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even if the stimulus is strong enough to trigger action potentials itself (supra-threshold
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stochastic resonance described by Stocks, 2000; see Fig. 1.1 B
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\item Cells of the same type and from the same population often vary in their stimulus sen-
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sitivity (Ringach et al., 2002) as well as in their baseline activity properties (Gussin et al., 2007; Hospedales et al., 2008)
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\item Heterogeneity has been shown to improve information coding in both situations, in the presence of noise correlations, for example in
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the visual system cells (Chelaru and Dragoi, 2008) or when correlations mainly originate
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from shared input as in the olfactory system (Padmanabhan and Urban, 2010)
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\item A prerequisite to a neural code thus is that it can be read out by other neurons (Perkel
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and Bullock, 1968).
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\item Development and evolution shape the functioning of many physiological systems and there is evidence that they also shape the encoding mechanisms of nervous systems. For example, the development of frequency
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selectivity in the auditory cortex has been shown to be delayed in animals stimulated
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with white noise only (Chang and Merzenich, 2003). Also, several encoding mechanisms can be related to the selective pressure that the energetic consumption of the nervous system has exerted on its evolution (Laughlin, 2001; Niven and Laughlin, 2008).
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These finding conformed earlier theoretical predictions that had proposed that coding
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should be optimized to encode natural stimuli in an energy-efficient way (Barlow, 1972). -> importance of using natural stimuli as the coding and nervous system could be optimized for unknown stimuli features not contained in the artificial stimuli like white noise.
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\end{enumerate}
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\subsubsection{electrosensory system - electric fish}
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\begin{enumerate}
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\item For decades, studies examining the neurophysiological systems of weakly electric
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fish have provided insights into how natural behaviors are generated using relatively
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simple sensorimotor circuits (for recent reviews see: Chacron et al., 2011; Fortune, 2006;
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Marsat and Maler, 2012). Further, electrocommunication signals are relatively easy to
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describe, classify and simulate, facilitating quantification and experimental manipulation. Weakly electric fish are therefore an ideal system for examining how communication signals influence sensory scenes, drive sensory system responses, and consequently
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exert effects on conspecific behavior.
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\item The weakly electric fish use active electroreception to navigate and communicate under
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low light conditions (Zupanc et al., 2001).
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\item In active electroreception, animals produce
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an electric field using and electric organ (and this electric field is therefore called the
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electric organ discharge, EOD) and infer, from changes of the EOD, information about
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the location and identification of objects and conspecifics in their vicinity (e.g. Kelly
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et al., 2008; MacIver et al., 2001). However, perturbations result not only from objects
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and other fish, but also from self-motion and other factors. All of these together make
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up the electrosensory scene. The perturbed version of the fish's own field on its skin
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is called the electric image (Caputi and Budelli, 2006), which is sensed via specialized
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receptors distributed over the body surface (Carr et al., 1982).
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\item In A. leptorhynchus, the
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dipole-like electric field (electric organ discharge, EOD) oscillates in a quasi-sinusoidal
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fashion at frequencies from 700 to 1100 Hz (Zakon et al., 2002) with males emitting at
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higher frequencies than females (Meyer et al., 1987).
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\item The EOD of each individual fish
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has a specific frequency (the EOD frequency, EODf) that remains stable in time (exhibit-
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ing a coefficient of variation of the interspikes intervals as low as $2 ∗ 10^{−4} $; Moortgat et al., 1998).
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\item During social encounters, wave-type fish often modulate the frequency as
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well as the amplitude of their field to communicate (Hagedorn and Heiligenberg, 1985).
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\item Communication signals in A. leptorhynchus have been classified into two classes: (i) chirps are transient and stereotyped EODf excursions over
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tens of milliseconds (Zupanc et al., 2006), while (ii) rises are longer duration and more
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variable modulations of EODf, typically lasting for hundreds of milliseconds to sec-
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onds (Hagedorn and Heiligenberg, 1985; Tallarovic and Zakon, 2002). (OLD INFO ? RISES NOW OVER MINUTES/HOURS)
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\end{enumerate}
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\subsubsection{P-Units encoding}
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\begin{enumerate}
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\item In baseline conditions (stimulus only own EOD), they fire irregularly at a certain baseline rate. Action potentials occur approximately at a certain phase of the EOD cycle, they are phase-locked to the EOD, but only with a certain probability to each cycle. The baseline rate differs from cell to cell (compare the two example cells in Fig. 2.2 A and B, Gussin et al., 2007)
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\item Since tuberous receptors are distributed over the whole body and the EOD spans the
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whole surrounding, all P-units of a given animal are stimulated with a similar stimulus
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(see Kelly et al. (2008) for an exact model of the EOD). Their noise sources are, however,
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uncorrelated (Chacron et al., 2005b).
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\item In response to a step increase in EOD amplitude, P-units exhibit pronounced spike frequency
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adaptation (Benda et al., 2005; Chacron et al., 2001b; Nelson et al., 1997; Xu et al., 1996).
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\end{enumerate}
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\subsubsection{Chapter 4 - other models}
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\begin{enumerate}
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\item Kashimori et al.
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(1996) built a conductance-based model of the whole electroreceptor unit and were able to qualitatively reproduce the behaviour of different types of tuberous units.
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\item Nelson
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et al. (1997) constrained a stochastically spiking model by linear filters of the previously determined P-unit frequency tuning.
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\item Kreiman et al. (2000) used the same frequency
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filters to stimulate a noisy perfect integrate-and-fire neuron with which they investi-
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gated the variability of cell responses to random amplitude modulations (RAMs).
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\item To reproduce the probabilistic phase-locked firing and the correlations of the ISIs, Chacron
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et al. (2000) used a noisy leaky integrate-and-fire model with refractoriness as well as a
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dynamical threshold.
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\item Benda et al. (2005) used a firing rate model with a negative adap-
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tation current to reproduce the high-pass behaviour of P-units.
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\end{enumerate}
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\subsection{Zakon: Negative Interspike Interval Correlations Increase the Neuronal
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Capacity for Encoding Time-Dependent Stimuli}
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\begin{enumerate}
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\item P-type electroreceptors on their skin detect amplitude modulations (AMs) of this field caused by nearby objects or conspecifics (for review, see Bastian, 1981; Zakon, 1986).
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\end{enumerate}
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\end{document} |