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\newcommand{\AptLepto}{{\textit{Apteronotus leptorhynchus}}}
\newcommand{\lepto}{{\textit{A. leptorhynchus}}}

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\section{To-note}

other models/papers to P-units:

Bastian 1981a Electrolocation I. How the electroreceptors of Apteronotus albifrons code for moving objects and other electrical stimuli


%Benda and Herz 2003 
\citep{benda2003universal}



\section{Introduction}

\begin{enumerate}
	\item electric fish
	\begin{enumerate}
		\item general: habitat, 
		\item as model animal for ethology
		\item electric organ + eod
		\item sensory neurons p- and t(?)-type
	\end{enumerate}
	\item sensory perception
	\begin{enumerate}
		\item receptor $\rightarrow$ heterogenic population
		\item further analysis limited by what receptors code for - P-Units encoding 
		\item p-type neurons code AMs
	\end{enumerate}
	
	\item goal be able to simulate heterogenic population to analyze full coding properties $\rightarrow$  many cells at the same time needed $\rightarrow$  only possible in vitro/ with model simulations
	
	\item Possible to draw representative values for model parameters to generate a population ?
	

\end{enumerate}

\subsection{Apteronotus leptorynchus}

\begin{itemize}

\item to mention: size range, tank conditions, 

\item continuous sinusoidal electric organ discharge EOD with near constant amplitude and frequency (Moortgat et al. 1998)

\item EOD carrier signal for AMs caused by nearby objects like prey or other electric fish

\item prey stimuli are dominated by low frequencies
\end{itemize}

\subsection{general P-unit notes}
\begin{itemize}

\item consist of 25-40 receptor cells and a nerve fiber that makes synaptic contact to at least 16 active neurotransmitter release sites per receptor cell. (M.V.L. Bennett, C. Sandri, K. Akert, Fine Structure of the tuberous electroreceptor of the high-frequency electric "sh Sternachus albifrons (gymnotiformes), J. Neurocytol. 18 (1989) 265.)

\item most abundant tuberous receptor 

\item spikes in probabilistic manner to upward phase of EOD

\item important characterization P-value probability of spiking per EOD cycle estimated as p-unit frequency divided by EOD frequency typical values 0.1-0.6 (Bastian 1981a, Xu et al 1997)

\item rapidly adapting (\cite{benda2005spike} \cite{xu1996logarithmic}) often studied with SAMs or RAMs 

\item can predict up to 80\% of the AM using reverse correlation and coherence but no obvious decoding mechanism  

\item linear coders of intensity, additive noise models are suitable Gussin et al. 2007

\item ISI correlations important to detect both slow and fast varying stimuli \citep{chacron2001negative}
	The negative correlation reduce low frequency noise and information is preserved at higher/central neurons  \citep{chacron2005electroreceptor}

\end{itemize}

\subsection{neural and population coding}


\subsection{nerve recordings}

\begin{itemize}

\item sample descriptions in: Hernriettes phd, Gussin et al. 2007, Benda et al. 2005
\end{itemize}

\section{Mat\&amp;Met}

\begin{enumerate}
	\item Data generation
	\begin{enumerate}
		\item How data was measured / which data used
		\item How data was chosen -&gt; at least 30s baseline, 7 contrasts with 7 trials
		\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)
		\item description of data -&gt; Baseline properties, FI-Curve with images made from cells
		\item make a point of using also bursty cells as part of what is new in this work!
	\end{enumerate}
		
	\item behavior parameters:
	\begin{enumerate}
		\item which behaviors were looked at / calculated and why (bf, vs, sc, cv, fi-curve...)
		\item how exactly were they calculated in the cell and model
		\item stimulus protocols
	\end{enumerate}			
	
	\item Construction of model
	\begin{enumerate}
		\item Explain general LIF
		\item parameters explanation, dif. equations
		\item Explain addition of adaption current
		\item note addition of noise + factor for the independence from step size
		\item addition of refractory period 
		\item check between alpha in fire-rate model adaption and a-delta in LIFAC
	\end{enumerate}
	
	\item Fitting of model to data
	\begin{enumerate}
		\item which variables where determined beforehand (None, just for start parameters)
		\item which variables where fit 
		\item What method was used (Nelder-Mead) and why/(how it works?)
		\item fit routine ? (currently just all at the same time)
	\end{enumerate}
\end{enumerate}

\subsection{Equations characterization}

Baseline

p-Value:

\begin{equation}
p = \frac{neuron frequency}{EOD frequency}
\end{equation}

coefficient of variation:

\begin{equation}
CV = \frac{STD(ISI)}{\langle ISI \rangle}
\end{equation}

serial correlation: \todo{check!}

\begin{equation}
sc_i = \frac{\langle ISI_{k+j} ISI_k \rangle - \langle ISI_k \rangle^2}{VAR(ISI)}
\end{equation}

burstiness: \todo{what definition?}


vector strength:


FI-Curve:



\subsection{model construction}
\begin{itemize}

\item PIF - LIF - LIFAC - LIFAC + refractory period

\item explain why adaption current and not a dynamic threshold: chosen AC other possibilities(dyn. thresh. voltage hyperpol.) why AC is better.


\item what things could be the physiological base for the different parts of the model 
\end{itemize}


\section{Results}


\begin{itemize}

\item Results fitting

	\begin{itemize}	
	
	\item Errors of model behavior to cell behavior

	\item Comparison model-vs-cell behavior distribution
	
	\item correlations between parameters and behavior
	
	\item correlation between final error and behavior parameters of the cell $\rightarrow$ hard to fit cell "types"

	 \item 	
	
	\item comparison SAM stimuli response
	
	\end{itemize}
	
\item "working with the models"

	\begin{itemize}
	
	\item model parameter distribution
	
	\item model parameter correlations
	
	\item \todo{drawing random models ????}

	\end{itemize}

\end{itemize}



\section{Discussion}

\begin{itemize}
\item todo
\end{itemize}


















\newpage

\section{Paper}

\subsection{Limits of linear rate coding of dynamic stimuli by electroreceptor afferents}
 Daniel Gussin, Jan Benda, Leonard Maler, 2007, J neurophysiol
\citep{gussin2007limits}


P-units may code for the intensity and slope of the stimulus and if the higher neuronal structures can separate these two parts they can detect the very weak signals they use in their behavior. 
 
\subsubsection{Introduction}
\begin{itemize}

\item {definition of neural code needs map between external signal and resulting spike trains AND demonstration that downstream neural circuits can interpret this mapping and therefore direct behavioral output.

original code often assumed to be linear rate coding needs only temporal summation over some time window to decode}

linear code breaks down for dynamic signals and neurons with time-dependent conductances (adapting currents)!

then more sophisticated methods like spike-triggered stimulus averages (STA) are used to estimate the linear encoding of signals but no obvious decoding mechanisms are implied.  

\end{itemize}


\subsection{Simple models of bursting and non-bursting P-type electroreceptors}
Maurice J. Chacron, Andre H Longtin , Leonard Maler, 2001

\citep{chacron2001simple}

\begin{itemize}

\item simple math. model of P-units for just the \textbf{baseline behavior}.

\item uses dynamic threshold, abs refractory period, for bursty cells added a delayed depolarization current

\item wasn't "fitted" to data just compared, chosen and fixed(?) parameters 

\end{itemize}


\subsection{Negative Interspike Interval Correlations Increase the neuronal capacity for encoding time-dependent stimuli}
Maurice J. Chacron, Andre H Longtin , Leonard Maler, 2001

\citep{chacron2001negative}

\begin{itemize}
\item Based on baseline behavior and AM stimuli

\item Two different encoding might be used for low-frequency and high-frequency signals.

\item low-frequency: rate-code (mean firing frequency) in a counting time that reduces variability of the spike train (minimum in spike train variability caused by negative ISI correlations )

\item high-frequency: spike timing 

\end{itemize}


\subsection{Electroreceptor neuron dynamics shape information transfer}

Maurice J. Chacron, Leonard Maler, Joseph Bastian, 2005

\citep{chacron2005electroreceptor}

\begin{itemize}

\item increased low frequency information is contained in the spike trains because of the negative serial correlation. This increased information is still available in central neurons.

\item conventional tuning curves don't capture the contained low-freq information and predict bad tuning for low frequencies, information tuning curves show the good coding of low frequencies.

\item ISI correlations have a noise shaping effect that increases the low-freq coding potential


\end{itemize}


\subsection{Characterization and modeling of P-type electrosensory afferent responses to amplitude modulations in wave-type electric fish}
M.E. Nelson, Z. Xu, J.R. Payne, 1997

\citep{nelson1997characterization} \todo{go over once more how does their model work}

\begin{itemize}

\item quantitative model of baseline and response to AM stimuli

\item not a LIF model 
\end{itemize}


\subsection{Non renewal statistics of electrosensory afferent spike trains: Implications for detection of weak sensory signals}

Rama Ratman and Mark E. Nelson, 2000

\citep{ratnam2000nonrenewal}


\begin{itemize}

\item 

\end{itemize}


\subsection{Delayed excitatory and inhibitory feedback shape neural information transmission}
Maurice J. Chacron, Andre H Longtin , Leonard Maler, 2005

\citep{chacron2005delayed}

\begin{itemize}

\item 
\end{itemize}


\subsection{Encoding of Communication Signals in Heterogeneous Populations of Electroreceptors}
Henriette Walz PhD 2013
\citep{walz2013phd}


\begin{enumerate}

\item data generation - recordings
\item model simulations - construction of model
\item Simulation protocols
\item Data analysis - calculation of behavior parameters		
	\begin{enumerate}
	\item calculation of baseline parameters
	\item calculation of fi curve parameters
	\item stimuli step SAM(?) noise(?)
	\item goodness of fit
	\item sensitivity analysis (influence of par on model)
	
	\end{enumerate}

\end{enumerate}

\section{Possible Sources}

\subsection{Henriette Walz - Thesis}
\subsubsection{Nervous system - Signal encoding}
\begin{enumerate}
\item single neurons are the building blocks of the nervous system (Cajal 1899)
\item encoding of information in spike frequency - rate code(first description(?) Adrian 1928) also find examples! (light flash intensity Barlow et al. 1971, )
\item encoding info in inter spike intervals (Singer and Gary 1995)
\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
\item encoding is noisy (Mainen and Sejnowski 1995, Tolhurst et al 1983, Tomko and Crapper 1974 -&gt; review Faisal et al 2008) in part because of stimulus properties but also cell properties (Ion channel stochasticity (van Rossum et al.,2003))
\item noise can be beneficial to encoding -&gt; "stochastic resonance" (weak stimuli on thresholding devices like neurons, noise allows coding of sub threshold stimuli) (Benzi et al., 1981)
\item single neurons are anatomically and computationally independent units, the
representation and processing of information in vertebrate nervous systems is distributed
over groups or networks of cells (for a review, see Pouget et al., 2000)
\item It has
been shown that the synchrony among cells carries information on a very fine temporal
scale in different modalities, from olfaction (Laurent, 1996) to vision (Dan et al., 1998)
\item In the electrosensory system it was shown before that communication signals change the synchrony of the receptor population (Benda et al., 2005, 2006)
and that this is read out by cells in the successive stages of the electrosensory pathway
(Marsat and Maler, 2010, 2012; Marsat et al., 2009).
\item An advantage of rate coding in populations is that it is fast. The rate in
single neurons has to be averaged over a time window, that is at least as long as the
minimum interspike interval. In contrast, the population rate can follow the stimulus
instantaneous, as it does not have to be averaged over time but can be averaged over
cells (Knight, 1972a).
\item In a population of neurons subject to neuronal noise, stochastic resonance occurs
even if the stimulus is strong enough to trigger action potentials itself (supra-threshold
stochastic resonance described by Stocks, 2000; see Fig. 1.1 B
\item Cells of the same type and from the same population often vary in their stimulus sen-
sitivity (Ringach et al., 2002) as well as in their baseline activity properties (Gussin et al., 2007; Hospedales et al., 2008)
\item Heterogeneity has been shown to improve information coding in both situations, in the presence of noise correlations, for example in
the visual system cells (Chelaru and Dragoi, 2008) or when correlations mainly originate
from shared input as in the olfactory system (Padmanabhan and Urban, 2010)
\item A prerequisite to a neural code thus is that it can be read out by other neurons (Perkel
and Bullock, 1968).
\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
selectivity in the auditory cortex has been shown to be delayed in animals stimulated
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).
These finding conformed earlier theoretical predictions that had proposed that coding
should be optimized to encode natural stimuli in an energy-efficient way (Barlow, 1972). -&gt; 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.
\end{enumerate}
\subsubsection{electrosensory system - electric fish}

\begin{enumerate}
\item For decades, studies examining the neurophysiological systems of weakly electric
fish have provided insights into how natural behaviors are generated using relatively
simple sensorimotor circuits (for recent reviews see: Chacron et al., 2011; Fortune, 2006;
Marsat and Maler, 2012). Further, electrocommunication signals are relatively easy to
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
exert effects on conspecific behavior.
\item The weakly electric fish use active electroreception to navigate and communicate under
low light conditions (Zupanc et al., 2001).
\item In active electroreception, animals produce
an electric field using and electric organ (and this electric field is therefore called the
electric organ discharge, EOD) and infer, from changes of the EOD, information about
the location and identification of objects and conspecifics in their vicinity (e.g. Kelly
et al., 2008; MacIver et al., 2001). However, perturbations result not only from objects
and other fish, but also from self-motion and other factors. All of these together make
up the electrosensory scene. The perturbed version of the fish's own field on its skin
is called the electric image (Caputi and Budelli, 2006), which is sensed via specialized
receptors distributed over the body surface (Carr et al., 1982).
\item In A. leptorhynchus, the
dipole-like electric field (electric organ discharge, EOD) oscillates in a quasi-sinusoidal
fashion at frequencies from 700 to 1100 Hz (Zakon et al., 2002) with males emitting at
higher frequencies than females (Meyer et al., 1987).
\item The EOD of each individual fish
has a specific frequency (the EOD frequency, EODf) that remains stable in time (exhibit-
ing a coefficient of variation of the interspikes intervals as low as $2 ∗ 10^{−4} $; Moortgat et al., 1998).
\item During social encounters, wave-type fish often modulate the frequency as
well as the amplitude of their field to communicate (Hagedorn and Heiligenberg, 1985).
\item Communication signals in A. leptorhynchus have been classified into two classes: (i) chirps are transient and stereotyped EODf excursions over
tens of milliseconds (Zupanc et al., 2006), while (ii) rises are longer duration and more
variable modulations of EODf, typically lasting for hundreds of milliseconds to sec-
onds (Hagedorn and Heiligenberg, 1985; Tallarovic and Zakon, 2002). (OLD INFO ? RISES NOW OVER MINUTES/HOURS)
\end{enumerate}

\subsubsection{P-Units encoding}

\begin{enumerate}
\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)
\item Since tuberous receptors are distributed over the whole body and the EOD spans the
whole surrounding, all P-units of a given animal are stimulated with a similar stimulus
(see Kelly et al. (2008) for an exact model of the EOD). Their noise sources are, however,
uncorrelated (Chacron et al., 2005b).
\item In response to a step increase in EOD amplitude, P-units exhibit pronounced spike frequency
adaptation (Benda et al., 2005; Chacron et al., 2001b; Nelson et al., 1997; Xu et al., 1996).
\end{enumerate}

\subsubsection{Chapter 4 - other models}
\begin{enumerate}
\item Kashimori et al.
(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.
\item Nelson
et al. (1997) constrained a stochastically spiking model by linear filters of the previously determined P-unit frequency tuning.
\item Kreiman et al. (2000) used the same frequency
filters to stimulate a noisy perfect integrate-and-fire neuron with which they investi-
gated the variability of cell responses to random amplitude modulations (RAMs).
\item To reproduce the probabilistic phase-locked firing and the correlations of the ISIs, Chacron
et al. (2000) used a noisy leaky integrate-and-fire model with refractoriness as well as a
dynamical threshold.
\item Benda et al. (2005) used a firing rate model with a negative adap-
tation current to reproduce the high-pass behaviour of P-units.
\end{enumerate}


\bibliography{../../citations} 
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