Nonlinear Model
nonlinear model
Shallow networks run deep: How peripheral preprocessing facilitates odor classification
Drosophila olfactory sensory hairs ("sensilla") typically house two olfactory receptor neurons (ORNs) which can laterally inhibit each other via electrical ("ephaptic") coupling. ORN pairing is highly stereotyped and genetically determined. Thus, olfactory signals arriving in the Antennal Lobe (AL) have been pre-processed by a fixed and shallow network at the periphery. To uncover the functional significance of this organization, we developed a nonlinear phenomenological model of asymmetrically coupled ORNs responding to odor mixture stimuli. We derived an analytical solution to the ORNs’ dynamics, which shows that the peripheral network can extract the valence of specific odor mixtures via transient amplification. Our model predicts that for efficient read-out of the amplified valence signal there must exist specific patterns of downstream connectivity that reflect the organization at the periphery. Analysis of AL→Lateral Horn (LH) fly connectomic data reveals evidence directly supporting this prediction. We further studied the effect of ephaptic coupling on olfactory processing in the AL→Mushroom Body (MB) pathway. We show that stereotyped ephaptic interactions between ORNs lead to a clustered odor representation of glomerular responses. Such clustering in the AL is an essential assumption of theoretical studies on odor recognition in the MB. Together our work shows that preprocessing of olfactory stimuli by a fixed and shallow network increases sensitivity to specific odor mixtures, and aids in the learning of novel olfactory stimuli. Work led by Palka Puri, in collaboration with Chih-Ying Su and Shiuan-Tze Wu.
A nonlinear shot noise model for calcium-based synaptic plasticity
Activity dependent synaptic plasticity is considered to be a primary mechanism underlying learning and memory. Yet it is unclear whether plasticity rules such as STDP measured in vitro apply in vivo. Network models with STDP predict that activity patterns (e.g., place-cell spatial selectivity) should change much faster than observed experimentally. We address this gap by investigating a nonlinear calcium-based plasticity rule fit to experiments done in physiological conditions. In this model, LTP and LTD result from intracellular calcium transients arising almost exclusively from synchronous coactivation of pre- and postsynaptic neurons. We analytically approximate the full distribution of nonlinear calcium transients as a function of pre- and postsynaptic firing rates, and temporal correlations. This analysis directly relates activity statistics that can be measured in vivo to the changes in synaptic efficacy they cause. Our results highlight that both high-firing rates and temporal correlations can lead to significant changes to synaptic efficacy. Using a mean-field theory, we show that the nonlinear plasticity rule, without any fine-tuning, gives a stable, unimodal synaptic weight distribution characterized by many strong synapses which remain stable over long periods of time, consistent with electrophysiological and behavioral studies. Moreover, our theory explains how memories encoded by strong synapses can be preferentially stabilized by the plasticity rule. We confirmed our analytical results in a spiking recurrent network. Interestingly, although most synapses are weak and undergo rapid turnover, the fraction of strong synapses are sufficient for supporting realistic spiking dynamics and serve to maintain the network’s cluster structure. Our results provide a mechanistic understanding of how stable memories may emerge on the behavioral level from an STDP rule measured in physiological conditions. Furthermore, the plasticity rule we investigate is mathematically equivalent to other learning rules which rely on the statistics of coincidences, so we expect that our formalism will be useful to study other learning processes beyond the calcium-based plasticity rule.
Optimal control of oscillations and synchrony in nonlinear models of neural population dynamics
Bernstein Conference 2024