Dynamic Gain Analysis of Neuronal Response in Experimental and Computational Models under Electrical and Optogenetic Stimulation
by Neil Lewis Wesch
Date of Examination:2025-07-10
Date of issue:2025-12-17
Advisor:Dr. Andreas Neef
Referee:Dr. Andreas Neef
Referee:Prof. Dr. Fred Wolf
Persistent Address:
http://dx.doi.org/10.53846/goediss-11708
Files in this item
Name:NeilWesch_PhDthesis.pdf
Size:66.9Mb
Format:PDF
The following license files are associated with this item:
Abstract
English
Local cortical circuits in the mammalian neocortex encode and process information through the coordinated spiking activity of large neuronal populations. Despite the high variability and low firing rate of individual spike trains, cortical networks use population-level encoding strategies to reliably represent sensory, motor, and cognitive signals. A fundamental information channel in these circuits is the \emph{population-averaged firing rate} - the instantaneous probability of spiking averaged across a local network. Most cortical circuits operate in a fluctuation-driven regime, where a neuron's average membrane potential remains below firing threshold and spiking is triggered by transient fluctuations in synaptic input. While individual neurons fire sparsely and irregularly, their collective activity generates a stable and consistent signal. In this thesis, we investigate the phenomenon of \emph{ultrafast population response} - the ability of the population firing rate to react to changes in the shared input mean or variance on a millisecond timescale. In the frequency domain, this capability is known as \emph{high-bandwidth encoding}, where the population firing rate can reliably follow low-amplitude, time-varying inputs with frequency components up to several hundred Hertz. To assess the fidelity of the population response to time-varying inputs, we use the \emph{dynamic gain function} $G(\omega)$, a spectral measure derived from linear response theory that quantifies how input fluctuations are translated into firing rate fluctuations. In this framework, neurons act as linear filters, and the dynamic gain function represents the filter kernel. This kernel characterizes which frequency components of the input are selectively amplified or suppressed. Unlike the kernel of a strictly linear system, the shape of the dynamic gain is strongly influenced by the statistical properties of the input - most notably, its correlation time. As a result, the neuronal population behaves as an adaptive filter, dynamically emphasizing different frequency components based on the overall structure of the input. To dissect the mechanisms underlying this adaptive filtering, we decompose $G(\omega)$ into two components: a subthreshold filter $Z(\omega)$, known as the \emph{effective impedance}, which maps input current fluctuations to membrane potential fluctuations; and a suprathreshold filter $B(\omega)$, called the \emph{spike boost}, which maps voltage fluctuations to firing rate modulations. Using fluctuation-dissipation theory, both $Z(\omega)$ and $B(\omega)$ can be expressed as a ratio of cross- and auto-covariances. For the leaky integrate-and-fire model we derive closed-form expressions for these quantities: \begin{equation*} G(\omega) \propto (1+\tau_m^2\omega^2)^{-1/4} \hspace{15mm} Z(\omega) \propto (1+\tau_m^2\omega^2)^{-1/2} \hspace{15mm} B(\omega) \propto (1+\tau_m^2\omega^2)^{1/4} \end{equation*} To investigate how passive neuronal morphology and active biophysical mechanisms shape $G(\omega)$, we performed dynamic gain analysis on two sets of experimental recordings from murine CA1 hippocampal neurons. First, we examined the effects of axon initial segment (AIS) destabilization in cells with otherwise normal morphology. The median cutoff frequency $f_0$ - a measure of encoding bandwidth - was reduced from 170.28 Hz in wild-type cells to 135.90 Hz in qv3J-mutants. This reduction was accompanied by a drop in action potential (AP) onset rapidity, from 12.49 to 6.74 $\mathrm{ms^{-1}}$, suggesting that \emph{suprathreshold contributions to the dynamic gain are largely determined by the precision of AP initiation in the AIS}. Second, we investigated how dendritic arbour growth during development in culture affects $G(\omega)$. The mean cutoff frequency increased from 39.93 Hz at 8-10 DIV to 164.47 Hz at 21-37 DIV. This was accompanied by a rise in the impedance corner frequency from 4.58 to 7.81 Hz, indicating that the \emph{subthreshold contributions to dynamic gain are primarily shaped by electrotonic filtering and capacitive load of the dendritic compartment}. Together, these findings elucidate how distinct morphological and biophysical features shape the encoding bandwidth of cortical neuronal populations. In both experimental paradigms, in-vivo-like operating conditions were emulated by mechanically injecting fluctuating inputs, modelled as Ornstein-Uhlenbeck (OU) processes. A parallel aim of this thesis is the development of optical methods to non-invasively replicate in vivo synaptic bombardment in neurons expressing channelrhodopsins. \emph{We demonstrate that stochastic noise illumination of Channelrhodopsin-2 and Chronos reliably generates conductances that follow Ornstein-Uhlenbeck statistics.} Using eight-state Markov models that have been shown to quantitatively reproduce the light-dependent conductance dynamics of these opsins, we derived a linear approximation of their response to time-varying illumination patterns. Inverting the corresponding linear transfer function allowed us to \emph{compute the specific illumination waveform required to generate a desired target conductance waveform}. The resulting channelrhodopsin conductances closely match the target OU processes, achieving a mean Pearson correlation coefficient of 97.7\% $\pm$ 1.1\% across illumination intensities between 0.01 and 10 $\mathrm{mW/mm^2}$ and correlation times ranging from 5 to 50 ms. This novel approach enables the flexible synthesis of OU-like conductances, \emph{providing a non-invasive method for optogenetic dynamic gain measurements in channelrhodopsin-expressing neurons under in-vivo-like conditions.} Together, these theoretical and methodological advances provide new insights into the biophysical basis of high-bandwidth encoding and establish an optogenetic framework for studying neuronal dynamics in fluctuating regimes. This work connects cellular biophysics with systems-level computation, advancing our understanding of how neural populations encode information on fast timescales.
Keywords: dynamic gain function; high-bandwidth encoding; ultrafast population response
