Aurel A. Lazar, Tingkai Liu, Yiyin Zhou Google Meet: meet.google.com/xfg-fkpg-crh
A recent empirical model of the olfactory sensory neurons (OSNs) described on the molecular level the mechanics of the Odorant Transduction Process (OTP, Fig. 1(A) top) [1]. A system of nonlinear differ- ential equations modeling the OTP in cascade with a biological spike generator successfully captured the experimentally observed responses of OSNs.
Here we functionally identify the OTP model on the algorithmic level with two state-of-the-art system identification methods (i) Channel Identification Machines (CIMs) [2] (Fig. 1(A) middle) and (ii) Divisive Normalization Processors (DNPs) [3, 4] (Fig. 1(A) bottom). We examined 5 model structures with different degrees of freedom under these two model architectures (Fig. 1(B1)).
Overall, the full temporal DNP successfully captured the OTP dynamics with the highest average and peak signal-to-noise ratios (ASNR & PSNR) of 36.6 dB and 41.5 dB respectively when predicting the response to a novel stimulus (Fig. 1(B2)). This is a 6 dB higher than the identified CIM model of comparable model complexity (rank 2), and 4 dB higher than the full-rank CIM. While the linear filter alone identified by the CIM has a PSNR of 29.2 dB that is comparable to the prediction given by the DNP with only FF-D processor, a closer examination revealed that it did not predict very well the transient responses at the onset of the stimulus that is critical in the context of olfactory encoding. The highly nonlinear transient response is nonetheless well captured by the full temporal DNP (Fig. 1(B2) inset).
Furthermore, we observed that the FF-N and FF-D processors identified in the full temporal DNP consistently resemble each other in their functional forms, with FF-N generally having higher 3 dB Bandwidth than FF-D (data not shown). This prompted us to closely examine the mechanism that gives rise to the OTP’s 2D encoding property where the output of OTP model captures both the odorant concentration and concentration gradient. We instantiated a DNP with FF-N and FF-D processors modeled as linear lowpass filters with different bandwidths. Surprisingly, the simple model is able to capture the essential 2D encoding across all stimuli described in [1] (data not shown), suggesting a general approach that enables simultaneous encoding of input signal’s amplitude and gradient with divisive normalization.
Concluding, by evaluating two functional identification methods, we established a functional description of the empirical OTP model using divisive normalization processors. In addition, the identified DNP pro- vided insights on the form of divisive normalization that leads to the simultaneous encoding of both the concentration and concentration gradient. Divisive processing has previously been used as a key component in describing the functional dynamics of blowfly photoreceptors [5], suggesting that DNPs may be universally employed for the identification of nonlinear processing in the early sensory systems.
Acknowledgments
The research reported here was supported by AFOSR under grant #FA9550-16-1-0410 and by DARPA under contract #HR0011-19-9-0035.
