Theses Doctoral

Spatio-Temporal Divisive Normalization: Invariance and Change Detection in Biological Systems

Liu, Tingkai

A central dilemma faced by biological systems that process fluctuating signals is the need for balancing sensitivity and robustness to input variations. Termed “Change Detection” and “Invariance”, the balancing act between the two features of input processing is observed in the olfactory system (odorant onset detection vs. odorant identification) and in gene regulatory networks (fold-change detection). Focusing on the Drosophila olfactory pathway, we hypothesized that a simple, yet universal model could describe not only this ubiquitous phenomenon, but also provide a characterization of the functional logic organizing olfactory processing.

In this thesis, we introduced a class of operators, called Spatio-Temporal Divisive Normalization Processors (DNP), which we characterized at both the implementational level (differential DNP described by dynamical systems) and the algorithmic level (convolutional DNP described by nonlinear systems theory). We showed that the DNP is an invertible operator that naturally balances change detection and input invariance, and applied the DNP to circuit-level models of the Antennal Lobe and the Mushroom Body to describe the functional logic of mono-molecular and mixture odorant processing in the Drosophila early olfactory pathway.

First, we studied the Drosophila Antennal Lobe, which receives as input the output responses of the Olfactory Sensory Neurons (OSNs) in the Drosophila Antenna, where the odorant object identity is multiplicatively coupled with the odorant concentration waveform. We hypothesized that the Antennal Lobe decouples semantic information in the odorant object identity from the syntactic information in the odorant concentration waveform. We found that single-channel physiological recording of Projection Neurons can be linearly decomposed into a concentration-invariant piecewise-constant component, and two transient components boosting the positive/negative concentration contrast that indicates odorant onset/offset.

We hypothesized that the piecewise-constant component, in the multi-channel context, is the recovered odorant identity vector. We developed models of the Local Neuron (LN) pathways in the Antennal Lobe termed the differential Divisive Normalization Processors (DNPs) which robustly extract odorant identity (semantic information) and ON/OFF odorant event-timing (syntactic information). For real-time processing with spiking PNs, we showed that the phase-space of the PN Biophysical Spike Generator models offers an intuit perspective for the representations of recovered odorant semantics and computed odorant syntactics. Finally, we provided theoretical and computational evidence for the robustness of the functional logic of the AL as an ON-OFF odorant object identity recovery processor across odorant identities, concentration amplitudes, and waveform profiles.

Next, we studied the interface between Drosophila Antennal Lobe and the Mushroom Body. In particular, we developed a model for the expansion/normalization circuit comprised of the Projection Neurons (PNs), the Kenyon Cells (KCs), and the Anterior Paired Lateral Neuron (APL). By modeling the APL to KC inhibition using differential DNP, we show that the PN-KC-APL circuit can achieve a high-dimensional sparse spatio-temporal representation of odorant inputs across odorant identities, concentrations, and mixture compositions. By formulating the problem of identifying odorant components in a mixture as a blind source separation problem, we showed that the KC spatio-temporal representations of odorant mixture inputs lead to better odorant demixing performance than that of the PNs.

Furthermore, by comparing PN-KC-APL circuits with different configurations (e.g., the number of KCs, strengths of APL to KC inhibition, and the number of PNs connected to the same KC), we demonstrated computationally that both the expansion and normalization components of the PN-KC-APL circuits are necessary to achieve the improved odorant demixing performance. Additionally, we provided a theoretical characterization of the expansion/normalization circuit that explains the differences between mixture representations at the level of the PNs vs KCs. We, therefore, concluded that the Mushroom Body encoding of the odorant mixture is uniquely suited for balancing the sensitivity and specificity of odorant mixture representations.

Closely related to the differential DNP is its algorithmic analog termed the convolutional DNP, which has been previously shown to outperform other state-of-the-art algorithmic level models (e.g. Channel Identification Machines, Linear-Nonlear Cascade) in capturing the input/output relationships of differential DNP models. We showed that convolutional DNPs underlie many models of neural circuits arising in auditory and visual systems. However, due to the highly nonlinear nature of convolutional DNP in applications such as contrast gain control, there has been a lack of quantitative characterization of the information content of the signals at the output of these circuits. We studied the information content of convolutional DNP output by formulating the problem as input signal recovery given output samples. We show both theoretically and computationally that the convolutional DNP is an invertible transform given sufficient (potentially asynchronous) output samples.

Finally, we put forward the FlyBrainLab, an interactive computing platform that integrates 3D exploration/visualization of diverse datasets with interactive exploration of the functional logic of modeled executable brain circuits. FlyBrainLab’s User Interface, Utilities Libraries, Circuit Libraries as well as models of molecular transduction were instrumental in accelerating the computational explorations of the olfactory circuit models presented herein. Additionally, FlyBrainLab was designed with comparative studies in mind, which we demonstrated by juxtaposing, amongst others, models of odorant representation in the larval and adult Drosophila olfactory pathways.


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More About This Work

Academic Units
Electrical Engineering
Thesis Advisors
Lazar, Aurel A.
Ph.D., Columbia University
Published Here
January 11, 2023