Efficient phase coding in hippocampal place cells

Abstract

Neural codes have been postulated to build efficient representations of the external world. The hippocampus, an encoding system, employs neuronal firing rates and spike phases to encode external space. Although the biophysical origin of such codes is at a single neuronal level, the role of neural components in efficient coding is not understood. The complexity of this problem lies in the dimensionality of the parametric space encompassing neural components, and is amplified by the enormous biological heterogeneity observed in each parameter. A central question that spans encoding systems therefore is how neurons arrive at efficient codes in the face of widespread biological heterogeneities. To answer this, we developed a conductance-based spiking model for phase precession, a phase code of external space exhibited by hippocampal place cells. Our model accounted for several experimental observations on place cell firing and electrophysiology: the emergence of phase precession from exact spike timings of conductance-based models with neuron-specific ion channels and receptors; biological heterogeneities in neural components and excitability; the emergence of subthreshold voltage ramp, increased firing rate, enhanced theta power within the place field; a signature reduction in extracellular theta frequency compared to its intracellular counterpart; and experience-dependent asymmetry in firing-rate profile. We formulated phase-coding efficiency, using Shannon's information theory, as an information maximization problem with spike phase as the response and external space within a single place field as the stimulus. We employed an unbiased stochastic search spanning an 11-dimensional neural space, involving thousands of iterations that accounted for the biophysical richness and neuron-to-neuron heterogeneities. We found a small subset of models that exhibited efficient spatial information transfer through the phase code, and investigated the distinguishing features of this subpopulation at the parametric and functional scales. At the parametric scale, which spans the molecular components that defined the neuron, several nonunique parametric combinations with weak pairwise correlations yielded models with similar high phase-coding efficiency. Importantly, placing additional constraints on these models in terms of matching other aspects of hippocampal neural responses did not hamper parametric degeneracy. We provide quantitative evidence demonstrating this parametric degeneracy to be a consequence of a many-to-one relationship between the different parameters and phase-coding efficiency. At the functional scale, involving the cellular-scale neural properties, our analyses revealed an important higher-order constraint that was exclusive to models exhibiting efficient phase coding. Specifically, we found a counterbalancing negative correlation between neuronal gain and the strength of external synaptic inputs as a critical functional constraint for the emergence of efficient phase coding. These observations implicate...

Ion‐channel degeneracy: Multiple ion channels heterogeneously regulate intrinsic physiology of rat hippocampal granule cells

“…Ion channel degeneracy plays a critical role in achieving robust function despite variability in ion channel conductances expressed in different neurons of the same subtype, because of the several degree of freedom available to the neuron through which signature functional outcomes could be achieved (Anirudhan & Narayanan, 2015 ; Basak & Narayanan, 2018 , 2020 ; Beining et al, 2017 ; Das & Narayanan, 2015 ; Das et al, 2017 ; Drion et al, 2015 ; Jain & Narayanan, 2020 ; Mishra & Narayanan, 2019 ; Mittal & Narayanan, 2018 ; Mukunda & Narayanan, 2017 ; O'Leary, 2018 ; Onasch & Gjorgjieva, 2020 ; Rathour et al, 2016 ; Rathour & Narayanan, 2012a , 2014 , 2019 ; Seenivasan & Narayanan, 2020 ). Such ion‐channel degeneracy also provides an explanation for the heterogeneities observed in the impact of specific channel blockade on different cells of the same subtype.…”

“…These population of neuronal models could then be employed to understand the specific impact of individual ion channels on the different measurements, and the specific mapping that are prevalent in each of these different subregions. The construction of such models could involve independent multi‐parametric multi‐objective stochastic search (MPMOSS) algorithms (Basak & Narayanan, 2018 ; Foster et al, 1993 ; Jain & Narayanan, 2020 ; Marder & Taylor, 2011 ; Mishra & Narayanan, 2019 ; Mittal & Narayanan, 2018 ; Rathour & Narayanan, 2012a , 2014 ; Seenivasan & Narayanan, 2020 ; Taylor et al, 2009 ) for each of the different subregions and sectors. Such analyses could involve the virtual knockout model strategy where all measurements are repeated across the population of models with each of the several ion channels individually eliminated (Anirudhan & Narayanan, 2015 ; Basak & Narayanan, 2018 , 2020 ; Jain & Narayanan, 2020 ; Mishra & Narayanan, 2021 ; Mukunda & Narayanan, 2017 ; Rathour & Narayanan, 2014 ; Sinha & Narayanan, 2015 ).…”

Ion-channel regulation of response decorrelation in a heterogeneous multi-scale model of the dentate gyrus

“…Analyzing the impact of individual ion channels on neuronal intrinsic properties in a single hand-tuned model introduces biases that are inherent to the specific model and would not account for the heterogeneities in ion channel expression or in intrinsic properties of the neurons. With the ubiquitous expression of ion-channel degeneracy, whereby synergistic interactions among disparate combinations of ion channels result in the emergence of similar single neuron physiological characteristics ( Mishra and Narayanan, 2019 ; Basak & Narayanan, 2018 , 2020 ; Das et al, 2017 ; Drion et al, 2015 ; Jain and Narayanan, 2020 ; Migliore et al, 2018 ; Mittal and Narayanan, 2018 ; Mukunda and Narayanan, 2017 ; Rathour et al, 2016 ; Rathour and Narayanan, 2012a , 2014 , 2019 ; Anirudhan and Narayanan, 2015 ; Seenivasan and Narayanan, 2020 ; Srikanth and Narayanan, 2015 ), such an approach would yield results that are not applicable to the entire population of neurons in the biological system ( Marder and Taylor, 2011 ). A well-established alternate to this approach, which accounts for degeneracy and heterogeneities across scales, is an unbiased stochastic search algorithm that spans the ion channel parametric space to arrive at neuronal models that satisfy cellular-scale physiological constraints ( Prinz et al, 2003 , 2004 ; Foster et al, 1993 ).…”

“…As disparate parametric combinations yielded similar physiological properties in heterogeneous populations of GC and BC models ( Mishra and Narayanan, 2019 ), it was important to independently assess the impact of ion channel elimination in each of the 126 GCs and 54 BCs. Within the degeneracy framework, virtual knockout models (VKMs) constitute a powerful technique to quantitatively assess the contribution of specific ion channels to chosen measurements in a heterogeneous population of models ( Basak & Narayanan, 2018 , 2020 ; Jain and Narayanan, 2020 ; Mittal and Narayanan, 2018 ; Mukunda and Narayanan, 2017 ; Anirudhan and Narayanan, 2015 ; Rathour and Narayanan, 2014 ; Seenivasan and Narayanan, 2020 ). Specifically, for the GC population, we virtually knocked-out one of the 9 active ion channels (by setting its conductance value to be zero) individually from each of the 126 valid models, and computed each of the 9 measurements after this knockout.…”

Active Dendrites and Local Field Potentials: Biophysical Mechanisms and Computational Explorations

“…A method that is commonly employed to generate biophysically and physiologically realistic neuron models that account for heterogeneities and degeneracy is the multi-parametric, multi-objective, stochastic search (MPMOSS) ( Foster et al, 1993 ; Taylor et al, 2009 ; Marder and Taylor, 2011 ; Rathour and Narayanan, 2012 , 2014 ; Basak and Narayanan, 2018 ; Mittal and Narayanan, 2018 ; Mishra and Narayanan, 2019 ; Jain and Narayanan, 2020 ; Seenivasan and Narayanan, 2020 ). The generic algorithm for a specific morphology for a given subtype of neuron in a given subregion involves the following steps ( Fig.…”