The maintenance of ion channel homeostasis, or channelostasis, is a complex puzzle in neurons with extensive dendritic arborization, encompassing a combinatorial diversity of proteins that encode these channels and their auxiliary subunits, their localization profiles, and associated signaling machinery. Despite this, neurons exhibit amazingly stereotypic, topographically continuous maps of several functional properties along their active dendritic arbor. Here, we asked whether the membrane composition of neurons, at the level of individual ion channels, is constrained by this structural requirement of sustaining several functional maps along the same topograph. We performed global sensitivity analysis on morphologically realistic conductance-based models of hippocampal pyramidal neurons that coexpressed six well-characterized functional maps along their trunk. We generated randomized models by varying 32 underlying parameters and constrained these models with quantitative experimental measurements from the soma and dendrites of hippocampal pyramidal neurons. Analyzing valid models that satisfied experimental constraints on all six functional maps, we found topographically analogous functional maps to emerge from disparate model parameters with weak pairwise correlations between parameters. Finally, we derived a methodology to assess the contribution of individual channel conductances to the various functional measurements, using virtual knockout simulations on the valid model population. We found that the virtual knockout of individual channels resulted in variable, measurementand location-specific impacts across the population. Our results suggest collective channelostasis as a mechanism behind the robust emergence of analogous functional maps and have significant ramifications for the localization and targeting of ion channels and enzymes that regulate neural coding and homeostasis. C hannel homeostasis, or channelostasis, refers to the regulation of the density, kinetics, voltage dependence, binding interactions, and the subcellular localization of individual ion channel types within a given cell [compared to proteostasis (1)]. Hippocampal CA1 pyramidal neurons are endowed with complex dendritic morphology and express numerous voltage-gated ion channels (VGICs), which govern critical neuronal functions across their somatodendritic arbor (2-6). Channelostasis in such neurons is an exceptionally complex puzzle, given the enormous morphological and molecular complexities accompanied by a myriad of subcellular channel localization profiles, resulting in an immense combinatorial diversity in channel expression profiles (4, 7-11). A further conundrum that compounds this complex puzzle is that neurons, despite these underlying complexities, exhibit amazingly regular gradients in several functional properties that manifest as maps along a continuous neuronal topograph (3). The coexistence of all these topographically continuous maps along the same neuronal topograph is mediated by intricately regulated subcellular l...

Key points• Voltage-gated ion channels (VGICs) play a critical role in determining how neurons respond to oscillatory inputs at various frequencies. How do inactivating VGICs regulate neuronal response properties to oscillatory inputs? • T-type Ca 2+ channels mediate resonance in response to oscillatory inputs, without being accompanied by a lead in the intrinsic phase response, and A-type K + channels act analogous to a leak channel with reference to many measurements characterizing intrinsic response dynamics (IRD).• Coexpression of these channels with a hyperpolarization-activated h channel augmented the range of parameters over which they sustained resonance and phase lead.• Global sensitivity analysis demonstrates that functionally similar models could be achieved even when underlying parameters displayed tremendous variability and exhibited weak pair-wise correlations.• A simplistic one-parameter-a-time analysis that does not account for the complex and non-linear interactions between channels would fail to provide a full understanding of subthreshold IRD.Abstract Voltage-gated ion channels play a critical role in regulating neuronal intrinsic response dynamics (IRD). Here, we computationally analysed the roles of the two inactivating subthreshold conductances (A and T), individually and in various combinations with the non-inactivating h conductance, in regulating several physiological IRD measurements in the theta frequency range. We found that the independent presence of a T conductance, unlike that of an h conductance, was unable to sustain an inductive phase lead in the theta frequency range, despite its ability to mediate theta frequency resonance. The A conductance, on the other hand, when expressed independently, acted in a manner similar to a leak conductance with reference to most IRD measurements. Next, analysing the impact of pair-wise coexpression of these channels, we found that the coexpression of the h and T conductances augmented the range of parameters over which they sustained resonance and inductive phase lead. Additionally, coexpression of the A conductance with the h or the T conductance elicited changes in IRD measurements that were similar to those obtained with the expression of a leak conductance with a resonating conductance. Finally, to understand the global sensitivity of IRD measurements to all parameters associated with models expressing all three channels, we generated 100,000 neuronal models, each built with a unique set of parametric values. We categorized valid models among these by matching their IRD measurements with experimental counterparts, and found that functionally similar models could be achieved even when underlying parameters displayed tremendous variability and exhibited weak pair-wise correlations. Our results suggest that the three prominent subthreshold conductances contribute differently to intrinsic excitability and to phase coding. We postulate that the differential expression and activity-dependent plasticity of these conductances contribute to robustne...

Degeneracy, defined as the ability of structurally disparate elements to perform analogous function, has largely been assessed from the perspective of maintaining robustness of physiology or plasticity. How does the framework of degeneracy assimilate into an encoding system where the ability to change is an essential ingredient for storing new incoming information? Could degeneracy maintain the balance between the apparently contradictory goals of the need to change for encoding and the need to resist change towards maintaining homeostasis? In this review, we explore these fundamental questions with the mammalian hippocampus as an example encoding system. We systematically catalog lines of evidence, spanning multiple scales of analysis that point to the expression of degeneracy in hippocampal physiology and plasticity. We assess the potential of degeneracy as a framework to achieve the conjoint goals of encoding and homeostasis without cross‐interferences. We postulate that biological complexity, involving interactions among the numerous parameters spanning different scales of analysis, could establish disparate routes towards accomplishing these conjoint goals. These disparate routes then provide several degrees of freedom to the encoding‐homeostasis system in accomplishing its tasks in an input‐ and state‐dependent manner. Finally, the expression of degeneracy spanning multiple scales offers an ideal reconciliation to several outstanding controversies, through the recognition that the seemingly contradictory disparate observations are merely alternate routes that the system might recruit towards accomplishment of its goals.

Strings on a violin are tuned to generate distinct sound frequencies in a manner that is firmly dependent on finger location along the fingerboard. Sound frequencies emerging from different violins could be very different based on their architecture, the nature of strings and their tuning. Analogously, active neuronal dendrites, dendrites endowed with active channel conductances, are tuned to distinct input frequencies in a manner that is dependent on the dendritic location of the synaptic inputs. Further, disparate channel expression profiles and differences in morphological characteristics could result in dendrites on different neurons of the same subtype tuned to distinct frequency ranges. Alternately, similar location-dependence along dendritic structures could be achieved through disparate combinations of channel profiles and morphological characteristics, leading to degeneracy in active dendritic spectral tuning. Akin to strings on a violin being tuned to different frequencies than those on a viola or a cello, different neuronal subtypes exhibit distinct channel profiles and disparate morphological characteristics endowing each neuronal subtype with unique location-dependent frequency selectivity. Finally, similar to the tunability of musical instruments to elicit distinct location-dependent sounds, neuronal frequency selectivity and its location-dependence are tunable through activity-dependent plasticity of ion channels and morphology. In this morceau, we explore the origins of neuronal frequency selectivity, and survey the literature on the mechanisms behind the emergence of location-dependence in distinct forms of frequency tuning. As a coda to this composition, we present some future directions for this exciting convergence of biophysical mechanisms that endow a neuron with frequency multiplexing capabilities.

Hippocampal pyramidal neurons express an intraneuronal map of spectral tuning mediated by hyperpolarization-activated cyclic-nucleotide-gated nonspecific-cation channels. Modeling studies have predicted a critical regulatory role for A-type potassium (KA) channels towards augmenting functional robustness of this map. To test this, we performed patch-clamp recordings from soma and dendrites of rat hippocampal pyramidal neurons, and measured spectral tuning before and after blocking KA channels using two structurally distinct pharmacological agents. Consistent with computational predictions, we found that blocking KA channels resulted in a significant reduction in resonance frequency and significant increases in input resistance, impedance amplitude and action-potential firing frequency across the somato-apical trunk. Furthermore, across all measured locations, blocking KA channels enhanced temporal summation of postsynaptic potentials and critically altered the impedance phase profile, resulting in a significant reduction in total inductive phase. Finally, pair-wise correlations between intraneuronal percentage changes (after blocking KA channels) in different measurements were mostly weak, suggesting differential regulation of different physiological properties by KA channels. Our results unveil a pivotal role for fast transient channels in regulating theta-frequency spectral tuning and intrinsic phase response, and suggest that degeneracy with reference to several coexisting functional maps is mediated by cross-channel interactions across the active dendritic arbor.

Degeneracy, defined as the ability of structurally disparate elements to perform analogous function, has largely been assessed from the perspective of maintaining robustness of physiology or plasticity. How does the framework of degeneracy assimilate into an encoding system where the ability to change is an essential ingredient for storing new incoming information? Could degeneracy maintain the balance between the apparently contradictory goals of the need to change for encoding and the need to resist change towards maintaining homeostasis? In this review, we explore these fundamental questions with the mammalian hippocampus as an example encoding system. We systematically catalog lines of evidence, spanning multiple scales of analysis, that demonstrate the expression of degeneracy in hippocampal physiology and plasticity. We assess the potential of degeneracy as a framework to achieve encoding and homeostasis without cross-interferences, and postulate that multiscale parametric and interactional complexity could establish disparate routes towards accomplishing these conjoint goals. These disparate routes then provide several degrees of freedom to the encodinghomeostasis system in accomplishing its tasks in an input-and state-dependent manner. Finally, the expression of degeneracy spanning multiple scales offers an ideal reconciliation to several outstanding controversies, through the recognition that the seemingly contradictory disparate observations are merely alternate routes that the system might recruit towards accomplishment of its goals. Juxtaposed against the ubiquitous prevalence of degeneracy and its strong links to evolution, it is perhaps apt to add a corollary to Theodosius Dobzhansky's famous quote and state "nothing in physiology makes sense except in the light of degeneracy".peer-reviewed)

Neuronal dendrites express numerous voltage-gated ion channels (VGICs), typically with spatial gradients in their densities and properties. Dendritic VGICs, their gradients, and their plasticity endow neurons with information processing capabilities that are higher than those of neurons with passive dendrites. Despite this, frameworks that incorporate dendritic VGICs and their plasticity into neurophysiological and learning theory models have been far and few. Here, we develop a generalized quantitative framework to analyze the extent of influence of a spatially localized VGIC conductance on different physiological properties along the entire stretch of a neuron. Employing this framework, we show that the extent of influence of a VGIC conductance is largely independent of the conductance magnitude but is heavily dependent on the specific physiological property and background conductances. Morphologically, our analyses demonstrate that the influences of different VGIC conductances located on an oblique dendrite are confined within that oblique dendrite, thus providing further credence to the postulate that dendritic branches act as independent computational units. Furthermore, distinguishing between active and passive propagation of signals within a neuron, we demonstrate that the influence of a VGIC conductance is spatially confined only when propagation is active. Finally, we reconstruct functional gradients from VGIC conductance gradients using influence fields and demonstrate that the cumulative contribution of VGIC conductances in adjacent compartments plays a critical role in determining physiological properties at a given location. We suggest that our framework provides a quantitative basis for unraveling the roles of dendritic VGICs and their plasticity in neural coding, learning, and homeostasis.

Fragile X syndrome is the most common form of inherited mental impairment and autism. The prefrontal cortex is responsible for higher order cognitive processing, and prefrontal dysfunction is believed to underlie many of the cognitive and behavioural phenotypes associated with fragile X syndrome. We recently demonstrated that somatic and dendritic excitability of layer (L) 5 pyramidal neurons in the prefrontal cortex of the fmr1 mouse is significantly altered due to changes in several voltage-gated ion channels. In addition to L5 pyramidal neurons, L2/3 pyramidal neurons play an important role in prefrontal circuitry, integrating inputs from both lower brain regions and the contralateral cortex. Using whole-cell current clamp recording, we found that L2/3 pyramidal neurons in prefrontal cortex of fmr1 mouse fired more action potentials for a given stimulus compared with wild-type neurons. In addition, action potentials in fmr1 neurons were significantly larger, faster and narrower. Voltage clamp of outside-out patches from L2/3 neurons revealed that the transient Na current was significantly larger in fmr1 neurons. Furthermore, the activation curve of somatic A-type K current was depolarized. Realistic conductance-based simulations revealed that these biophysical changes in Na and K channel function could reliably reproduce the observed increase in action potential firing and altered action potential waveform. These results, in conjunction with our prior findings on L5 neurons, suggest that principal neurons in the circuitry of the medial prefrontal cortex are altered in distinct ways in the fmr1 mouse and may contribute to dysfunctional prefrontal cortex processing in fragile X syndrome.