239 lines
37 KiB
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239 lines
37 KiB
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\emailauthor{jan.greqe@uni-tuebingen.de}{Jan Grewe\corref {cor1}}
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\emailauthor{jan.greqe@uni-tuebingen.de}{Jan Grewe\corref {cor1}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Nonlinearity in an electrophysiologically recorded P-unit of \textit {Apteronotus leptorhynchus}{} in a three-fish setting. Receiver with EOD frequency $\ensuremath {f_{EOD}}{} =664$\,Hz encounters fish with EOD frequencies $f_{1}=631$\,Hz and $f_{2}=797$\,Hz. Both encountered fish lead to a beat contrast of 10\,\%. Top: Interference of the receiver EOD with the EODs of other fish. Second row: Spike trains of the P-unit. Third row: Firing rate, retrieved as the convolution of the spike trains with a Gaussian kernel ($\sigma = 1$\,ms). Bottom row: Power spectrum of the firing rate. \figitem {A} Baseline condition: Only the receiver is present. The mean baseline firing rate \ensuremath {f_{Base}}{} dominates the power spectrum of the firing rate. \figitem {B} The receiver and the fish with EOD frequency $f_{1}=631$\,Hz are present. \figitem {C} The receiver and the fish with EOD frequency $f_{2}=797$\,Hz are present. \figitem {D} All three fish with the EOD frequencies \ensuremath {f_{EOD}}{}, $f_{1}$ and $f_{2}$ are present. Nonlinear peaks occur at the sum and difference of the two beat frequencies in the power spectrum of the firing rate. \relax }}{3}{figure.caption.2}\protected@file@percent }
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\newlabel{motivation}{{1}{3}{Nonlinearity in an electrophysiologically recorded P-unit of \lepto {} in a three-fish setting. Receiver with EOD frequency $\feod {} =664$\,Hz encounters fish with EOD frequencies $f_{1}=631$\,Hz and $f_{2}=797$\,Hz. Both encountered fish lead to a beat contrast of 10\,\%. Top: Interference of the receiver EOD with the EODs of other fish. Second row: Spike trains of the P-unit. Third row: Firing rate, retrieved as the convolution of the spike trains with a Gaussian kernel ($\sigma = 1$\,ms). Bottom row: Power spectrum of the firing rate. \figitem {A} Baseline condition: Only the receiver is present. The mean baseline firing rate \fbase {} dominates the power spectrum of the firing rate. \figitem {B} The receiver and the fish with EOD frequency $f_{1}=631$\,Hz are present. \figitem {C} The receiver and the fish with EOD frequency $f_{2}=797$\,Hz are present. \figitem {D} All three fish with the EOD frequencies \feod {}, $f_{1}$ and $f_{2}$ are present. Nonlinear peaks occur at the sum and difference of the two beat frequencies in the power spectrum of the firing rate. \relax }{figure.caption.2}{}}
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\newlabel{cells_suscept}{{2}{5}{Response of experimentally measured P-units to RAM stimuli. Light purple -- low RAM contrast. Dark purple -- high RAM contrast. \figitem {A} Regular firing low-CV P-unit. \figitem [i]{A} Left: Interspike intervals (ISI) distribution during baseline. Right: Baseline power spectrum of the firing rate. \figitem [ii]{A} Top: EOD carrier (gray) with RAM (red). Middle: Spike trains in response to a low RAM contrast. Bottom: Spike trains in response to a high RAM contrast. \figitem [iii]{A} First-order susceptibility (see \eqnref {linearencoding_methods}). \figitem [iv]{A} Absolute value of the second-order susceptibility, \eqnref {susceptibility}, for the low RAM contrast. Pink lines -- edges of the structure when \fone , \ftwo {} or \fsum {} are equal to \fbase {}. Orange line -- part of the structure when \fsum {} is equal to half \feod . \figitem [v]{A} Absolute value of the second-order susceptibility for the higher RAM contrast. \figitem [vi]{A} Projected diagonals, calculated as the mean of the anti-diagonals of the matrices in \panel [iv,v]{A}. Gray dots: \fbase {}. Gray area: $\fbase {} \pm 5$\,Hz. Dashed lines: Medians of the projected diagonals. \figitem {B} Noisy high-CV P-Unit. Panels as in \panel {A}. \relax }{figure.caption.5}{}}
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\newlabel{ampullary}{{3}{6}{Response of an experimentally measured ampullary cell. Light green -- low noise stimulus contrast. Dark green -- high noise stimulus contrast. \figitem [i]{A} Left: ISI distribution during baseline. Right: Baseline power spectrum of the firing rate. \figitem [ii]{A} Top: EOD carrier (gray) plus a band-pass limited white noise (red, see methods section \ref {rammethods}). Middle: Spike trains in response to a low noise stimulus contrast. Bottom: Spike trains in response to a high noise stimulus contrast. \figitem [iii]{A} First-order susceptibility (see \eqnref {linearencoding_methods}). \figitem [iv]{A} Absolute value of the second-order susceptibility (\eqnref {susceptibility}) for the low noise stimulus contrast. Pink lines -- edges of the structure when \fone , \ftwo {} or \fsum {} are equal to \fbase {}. Orange line -- part of the structure when \fsum {} is equal to half \feod . \figitem [v]{A} Second-order susceptibility matrix for the higher noise stimulus contrast. Colored lines as in \panel [iv]{A}. \figitem [vi]{A} Projected diagonals, calculated as the mean of the anti-diagonals of the matrices in \panel [iv,v]{A}. Gray dot: \fbase {}. Gray area: $\fbase {} \pm 5$\,Hz. Dashed lines: Medians of the projected diagonals. \relax }{figure.caption.7}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces The influence of the RAM stimulus realization number $\ensuremath {N}$, the RAM contrast $c$, and the split of the total intrinsic noise in a signal and noise component on the nonlinearity structures of the second-order susceptibility of an electrophysiologically recorded low-CV P-unit and its LIF model (see table\nobreakspace {}\ref {modelparams} for model parameters of 2012-07-03-ak). Pink lines in the matrices mark the edges of the structure when $f_{1}${}, $f_{2}${} or \ensuremath {f_{1} + f_{2}}{} are equal to \ensuremath {f_{Base}}{}. The orange line in the matrices marks a part of the line at $\ensuremath {f_{1} + f_{2}}{}=f_{EOD}/2$. \figitem [i]{A},\,\panel [i]{\textbf {B}},\,\panel [i]{\textbf {C}} Red -- RAM stimulus. The total intrinsic noise can be split into a noise component (gray) and a signal component (purple), maintaining the same CV and \ensuremath {f_{Base}}{} as before the split (see methods section \ref {intrinsicsplit_methods}). The calculation is performed on the sum of the signal component (purple) and the RAM (red) in Eq.\nobreakspace {}(\ref {susceptibility}). \figitem [ii]{A} Absolute value of the second-order susceptibility of an electrophysiologically recorded P-unit, with $\ensuremath {N}{}=11$ RAM stimulus realizations. \figitem [iii]{A},\,\panel [iii]{\textbf {B}},\,\panel [iii]{\textbf {C}} Absolute value of the model second-order susceptibility with $\ensuremath {N}{}=11$ RAM stimulus realizations. \figitem [iv]{A},\,\panel [iv]{\textbf {B}},\,\panel [iv]{\textbf {C}} Absolute value of the model second-order susceptibility with 1 million RAM stimulus realizations. \figitem {A} RAM contrast of 1\,$\%$. The band at $\ensuremath {f_{1} + f_{2}}=\ensuremath {f_{Base}}{}${} is visible in the matrices. \figitem {B} No RAM stimulus, but a total noise split into a signal component (purple) and a noise component (gray). The band at $\ensuremath {f_{1} + f_{2}}=\ensuremath {f_{Base}}{}${} is visible in \panel [iii]{B} and \panel [iv]{B}. Besides that horizontal and vertical nonlinearities appear at $f_{1}=\ensuremath {f_{Base}}{}${} and $f_{2}=\ensuremath {f_{Base}}{}${} in \panel [iv]{B}. \figitem {C} A RAM stimulus (red) and a total noise split into a signal component (purple) and a noise component (gray). Only the band at $\ensuremath {f_{1} + f_{2}}=\ensuremath {f_{Base}}{}${} is visible in the matrices. \relax }}{7}{figure.caption.10}\protected@file@percent }
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\newlabel{model_and_data}{{4}{7}{The influence of the RAM stimulus realization number $\n $, the RAM contrast $c$, and the split of the total intrinsic noise in a signal and noise component on the nonlinearity structures of the second-order susceptibility of an electrophysiologically recorded low-CV P-unit and its LIF model (see table~\ref {modelparams} for model parameters of 2012-07-03-ak). Pink lines in the matrices mark the edges of the structure when \fone {}, \ftwo {} or \fsum {} are equal to \fbase {}. The orange line in the matrices marks a part of the line at \fsumehalf . \figitem [i]{A},\,\panel [i]{\textbf {B}},\,\panel [i]{\textbf {C}} Red -- RAM stimulus. The total intrinsic noise can be split into a noise component (gray) and a signal component (purple), maintaining the same CV and \fbase {} as before the split (see methods section \ref {intrinsicsplit_methods}). The calculation is performed on the sum of the signal component (purple) and the RAM (red) in \eqnref {susceptibility}. \figitem [ii]{A} Absolute value of the second-order susceptibility of an electrophysiologically recorded P-unit, with $\n {}=11$ RAM stimulus realizations. \figitem [iii]{A},\,\panel [iii]{\textbf {B}},\,\panel [iii]{\textbf {C}} Absolute value of the model second-order susceptibility with $\n {}=11$ RAM stimulus realizations. \figitem [iv]{A},\,\panel [iv]{\textbf {B}},\,\panel [iv]{\textbf {C}} Absolute value of the model second-order susceptibility with 1 million RAM stimulus realizations. \figitem {A} RAM contrast of 1\,$\%$. The band at \fsumb {} is visible in the matrices. \figitem {B} No RAM stimulus, but a total noise split into a signal component (purple) and a noise component (gray). The band at \fsumb {} is visible in \panel [iii]{B} and \panel [iv]{B}. Besides that horizontal and vertical nonlinearities appear at \foneb {} and \ftwob {} in \panel [iv]{B}. \figitem {C} A RAM stimulus (red) and a total noise split into a signal component (purple) and a noise component (gray). Only the band at \fsumb {} is visible in the matrices. \relax }{figure.caption.10}{}}
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\newlabel{model_full}{{5}{8}{Second-order susceptibility of an electrophysiologically recorded P-unit and of the corresponding model (see table~\ref {modelparams} for model parameters of 2012-07-03-ak). White lines -- coordinate axis. The nonlinearity at \fsum {} in the firing rate is quantified in the upper right and lower left quadrants (\eqnref {susceptibility}). The nonlinearity at \fdiff {} in the firing rate is quantified in the upper left and lower right quadrants. Mean baseline firing rate $\fbase {}=120$\,Hz. \figitem {A} Absolute value of the second-order susceptibility of an electrophysiologically recorded P-unit. RAM stimulus realizations $N=11$. Diagonal bands appear when the sum of the frequencies \fsum {} or the difference \fdiff {} is equal to \fbase {}. \figitem {B} Absolute value of the model second-order susceptibility, with $N=1$\,million stimulus realizations and the intrinsic noise split (see methods section \ref {intrinsicsplit_methods}). The diagonals, that were present in \panel {A}, are complemented by vertical and horizontal lines when \fone {} or \ftwo {} are equal to \fbase {}.\relax }{figure.caption.11}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Nonlinearity for a population of ampullary cells (\panel {A, C}) and P-units (\panel {B, D}). NLI\ensuremath {(\ensuremath {f_{Base}}{})}{} is calculated as the maximal value in the range $\ensuremath {f_{Base}}{} \pm 5$\,Hz of the projected diagonal divided by its median (see Eq.\nobreakspace {}(\ref {nli_equation})). There are maximally two noise contrasts per cell in a population. \figitem {A, B} There is a negative correlation between the CV during baseline and NLI\ensuremath {(\ensuremath {f_{Base}}{})}. \figitem {C, D} Response modulation, Eq.\nobreakspace {}(\ref {response_modulation}), is an indicator of the subjective stimulus strength for a cell. There is a negative correlation between response modulation and NLI\ensuremath {(\ensuremath {f_{Base}}{})}. \relax }}{9}{figure.caption.13}\protected@file@percent }
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\newlabel{data_overview_mod}{{6}{9}{Nonlinearity for a population of ampullary cells (\panel {A, C}) and P-units (\panel {B, D}). \nli {} is calculated as the maximal value in the range $\fbase {} \pm 5$\,Hz of the projected diagonal divided by its median (see \eqnref {nli_equation}). There are maximally two noise contrasts per cell in a population. \figitem {A, B} There is a negative correlation between the CV during baseline and \nli . \figitem {C, D} Response modulation, \eqnref {response_modulation}, is an indicator of the subjective stimulus strength for a cell. There is a negative correlation between response modulation and \nli . \relax }{figure.caption.13}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {A.9}{\ignorespaces Response of experimentally measured P-units to RAM stimuli. Light purple -- low RAM contrast. Dark purple -- high RAM contrast. \figitem {A} Regular firing low-CV P-unit. \figitem [i]{A} Left: Interspike intervals (ISI) distribution during baseline. Right: Baseline power spectrum of the firing rate. \figitem [ii]{A} Top: EOD carrier (gray) with RAM (red). Middle: Spike trains in response to a low RAM contrast. Bottom: Spike trains in response to a high RAM contrast. \figitem [iii]{A} First-order susceptibility (see Eq.\nobreakspace {}(\ref {linearencoding_methods})). \figitem [iv]{A} Absolute value of the second-order susceptibility, Eq.\nobreakspace {}(\ref {susceptibility}), for the low RAM contrast. Pink lines -- edges of the structure when $f_{1}$, $f_{2}${} or \ensuremath {f_{1} + f_{2}}{} are equal to \ensuremath {f_{Base}}{}. Orange line -- part of the structure when \ensuremath {f_{1} + f_{2}}{} is equal to half \ensuremath {f_{EOD}}. \figitem [v]{A} Absolute value of the second-order susceptibility for the higher RAM contrast. \figitem [vi]{A} Projected diagonals, calculated as the mean of the anti-diagonals of the matrices in \panel [iv,v]{A}. Gray dots: \ensuremath {f_{Base}}{}. Gray area: $\ensuremath {f_{Base}}{} \pm 5$\,Hz. Dashed lines: Medians of the projected diagonals. \figitem {B} Noisy high-CV P-Unit. Panels as in \panel {A}. \relax }}{18}{figure.caption.46}\protected@file@percent }
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\newlabel{cells_suscept_high_CV}{{A.9}{18}{Response of experimentally measured P-units to RAM stimuli. Light purple -- low RAM contrast. Dark purple -- high RAM contrast. \figitem {A} Regular firing low-CV P-unit. \figitem [i]{A} Left: Interspike intervals (ISI) distribution during baseline. Right: Baseline power spectrum of the firing rate. \figitem [ii]{A} Top: EOD carrier (gray) with RAM (red). Middle: Spike trains in response to a low RAM contrast. Bottom: Spike trains in response to a high RAM contrast. \figitem [iii]{A} First-order susceptibility (see \eqnref {linearencoding_methods}). \figitem [iv]{A} Absolute value of the second-order susceptibility, \eqnref {susceptibility}, for the low RAM contrast. Pink lines -- edges of the structure when \fone , \ftwo {} or \fsum {} are equal to \fbase {}. Orange line -- part of the structure when \fsum {} is equal to half \feod . \figitem [v]{A} Absolute value of the second-order susceptibility for the higher RAM contrast. \figitem [vi]{A} Projected diagonals, calculated as the mean of the anti-diagonals of the matrices in \panel [iv,v]{A}. Gray dots: \fbase {}. Gray area: $\fbase {} \pm 5$\,Hz. Dashed lines: Medians of the projected diagonals. \figitem {B} Noisy high-CV P-Unit. Panels as in \panel {A}. \relax }{figure.caption.46}{}}
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