The discovery of voltage-gated ion channels (VGICs) in the dendrites of various neurons constitutes an important breakthrough in neuroscience research. These VGICs express with a wide range of subcellular localization profiles across the somatodendritic arbor, and undergo localized or global plasticity under several physiological and pathophysiological conditions. Recent findings suggest that changes in VGICs and the consequent changes in intrinsic properties, apart from and in conjunction with traditionally considered synaptic changes, could play important roles in encoding information in a single neuron. Against this, research in our laboratory is focused on understanding the physiological roles of the various VGICs that are expressed in neuronal dendrites. The overall goal is to understand the roles of the presence and plasticity of VGICs in terms of spatiotemporal interactions with each other, and how they enable neural coding and signal propagation in single neurons. We employ a combination of experimental (in vitro and in vivo electrophysiology and imaging from the rat hippocampus) and computational techniques to address questions that arise towards achieving this goal.

Emergence of functional maps within a single neuron

Several VGICs express subcellular gradients in their expression profiles and mediate gradients in physiological measurements that have been referred to as “functional maps” within a neuron (Narayanan and Johnston, J. Neurophysiology, 2012). Assessment of spatial interactions among ion channels is critical from the standpoint of how such functional maps emerge from gradients in VGIC conductances, especially given the complex dendritic morphology associated with neurons.

To assess spatial interactions among ion channels, we developed a generalized quantitative framework (that we referred to as “influence field”) to analyze the extent of influence of a spatially localized VGIC conductance on different physiological properties along the stretch of a neuron (Rathour and Narayanan, J. Neurophysiology, 2012). Employing this framework, we reconstructed functional maps of specific physiological measurements from VGIC conductance gradients. Analyses of these reconstructions revealed that the cumulative contribution of VGIC conductances in adjacent compartments plays a critical role in the emergence of functional maps within a single neuron. Additionally, we also demonstrated that these functional maps cease to exist if the dendritic arbor were significantly atrophied (Dhupia et al., Frontiers in Cellular Neuroscience, 2015). These results have important implications for neuronal physiology under pathological conditions where significant dendritic atrophy has been reported.

A direct analogy for how influence fields could be employed in models of single neuron function (e.g., neural coding, learning) could be drawn from models of cortical circuitry employed in the sensory map literature. In sensory map models, a Mexican-hat function (panel A above) is used as an abstraction for intracortical connectivity between neurons in the model network. Such interactions have been demonstrated to be extremely critical in the self-organized formation of sensory maps, and are responsible for the conversion of local computations by simplified neuronal units to global order. Influence fields could be envisioned as a mechanism for intercompartmental interactions within a neuron (Panel B above), as opposed to Mexican-hat interactions across neurons. Here, given the existence of local plasticity in VGICs, it becomes important to assess the roles that such local computations play and analyze if these could translate into global order within the neuron — such as gradients in specific ion channel densities across the neuronal arbor.

Related references

Neha Dhupia, Rahul Kumar Rathour and Rishikesh Narayanan, Dendritic atrophy constricts functional maps in resonance and impedance properties of hippocampal model neurons, Frontiers in Cellular Neuroscience, 8, 456: 1-17, January 2015. [PDF file] [Article at publisher's site]

Rahul Kumar Rathour and Rishikesh Narayanan, Influence fields: A quantitative framework for the representation and analysis of active dendrites, Journal of Neurophysiology, 107(9), 2313–2334, May 2012. [PDF File] [Link to paper at publisher's site]

Rishikesh Narayanan and Daniel Johnston, Functional maps within a single neuron, Journal of Neurophysiology, 108(9), 2343–2351, November 2012. [PDF file] [Link to paper at publisher's site]

Variability, interactions and intrinsic response dynamics

Hippocampal neurons reside within an oscillating neuronal network. These oscillations span multiple frequency ranges, sometimes with each frequency range reflective of a specific behavioral state of the animal. Intrinsic response dynamics (IRD) constitute the manner in which a single neuron intrinsically responds to such oscillatory inputs emerging from differential spatiotemporal patterns of activation. Whereas the spatial aspect is governed by the dendritic locations of the input stimuli, the temporal aspect is dictated by the arrival times of synaptic inputs. In addition to providing a detailed picture of neuronal information processing, IRD also offers an alternate, and much less-explored, cellular correlate for learning and memory. The passive properties of the dendritic tree in conjunction with the densities and characteristics of different VGICs located at various dendritic locations mediate the IRD of a neuron. Given the ability of VGICs to amplify or suppress specific input frequencies, it has been emerging from recent results that these channels can sculpt IRD in a manner suitable for the neuron and its network, through variable expression and/or activity-dependent plasticity.

We have systematically analyzed the roles of the two inactivating subthreshold VGICs (A-type K⁺ and T-type Ca²⁺), individually and in various combinations with the noninactivating h conductance, in regulating several physiological IRD measurements. We found that the coexpression of the h and T-type Ca²⁺ conductances augmented the range of parameters over which they sustained resonance and inductive phase lead. Additionally, coexpression of the A-type K⁺ conductance with the h or the T-type Ca²⁺ conductance elicited changes in IRD measurements that were similar to those obtained with the expression of a leak conductance with a resonating conductance. Further, we employed the global sensitivity of IRD measurements to all parameters associated with models expressing all three VGICs, and found that functionally similar models could be achieved even when underlying parameters displayed tremendous variability and exhibited weak pair-wise correlations. Shown in the above figure are six color-coded model neurons displaying very similar IRD measurements (panels A–D above) despite tremendous variability in underlying parameters (panel E above). Based on these results, we postulate that the differential expression and activity-dependent plasticity of these VGICs contribute to robustness of subthreshold IRD, whereby response homeostasis is achieved by recruiting several non-unique combinations of these channel parameters (Rathour and Narayanan, J. Physiology, 2012).

How do neurons with complex morphologies maintain these functional maps despite constant turnover of and plasticity in the several ion channels that mediate them? We addressed this question within a global sensitivity analysis framework spanning channels and measurements from the cell body and dendrites of hippocampal neurons. Our results demonstrated that individual channel properties or their densities need not be maintained at constant levels in achieving overall homeostasis of several coexistent functional maps. We suggested collective channelostasis, where several channels regulate their properties and expression profiles in an uncorrelated manner, as an alternative for accomplishing homeostasis of functional maps (Rathour and Narayanan, PNAS (USA), 2014).

Although these studies explored the role of interactions among ion channels in regulating IRD under in vitro conditions, the impact of sustained high-conductance states (observed under in vivo conditions) on these interactions has not been assessed. To fill this lacuna, we assessed the impact of interactions between HCN and A-type K⁺ channels on several measures of intrinsic excitability. We found that high-conductance states and A-type K⁺ channels are potential regulators of the conductance-current balance triggered by the presence of HCN channels (Mishra and Narayanan, J. Neurophysiology, 2015). These results together suggested that intrinsic response dynamics of neurons under physiological and pathophysiological neuronal states are critically reliant on interactions among several subthreshold channels and on high-conductance states.

Related references

Poonam Mishra and Rishikesh Narayanan, High-conductance states and A-type K⁺ channels are potential regulators of the conductance-current balance triggered by HCN channels, Journal of Neurophysiology, 113(1): 23-43, January 2015. [PDF File] [Article at publisher's site]

Rahul Kumar Rathour and Rishikesh Narayanan, Homeostasis of functional maps in active dendrites emerges in the absence of individual channelostasis, Proceedings of the National Academy of Sciences (USA), 111(17), E1787-E1796, April 2014. [PDF File] [Link to paper at publisher's site]

Rahul Kumar Rathour and Rishikesh Narayanan, Inactivating ion channels augment robustness of subthreshold intrinsic response dynamics to parametric variability in hippocampal model neurons, The Journal of Physiology (London), 590 (22), 5629–5652, November 2012. [PDF File] [Supplementary PDF File] [Link to paper at publisher's site]

Rahul Kumar Rathour, Ruchi Malik and Rishikesh Narayanan, Transient potassium channels augment degeneracy in hippocampal active dendritic spectral tuning, Scientific Reports, 6, 24678: 1-14, April 2016. [PDF File] [Supplementary PDF File] [Article at publisher's site]

Active dendrites, spectral selectivity & coincidence detection

How does the presence of plastic active dendrites in a pyramidal neuron alter its spike initiation dynamics? To answer this question, we measured the spike-triggered average (STA) from experimentally constrained, conductance-based hippocampal neuronal models of various morphological complexities. We transformed the STA computed from these models to the spectral and the spectrotemporal domains and found that the spike initiation dynamics exhibited temporally localized selectivity to a characteristic frequency. In the presence of the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, the STA characteristic frequency strongly correlated with the subthreshold resonance frequency in the theta frequency range. Increases in HCN channel density or in input variance increased the STA characteristic frequency and its selectivity strength. In the absence of HCN channels, the STA exhibited weak delta frequency selectivity and the characteristic frequency was related to the repolarization dynamics of the action potentials and the recovery kinetics of sodium channels from inactivation.

Comparison of STA obtained with inputs at various dendritic locations revealed that nonspiking and spiking dendrites increased and reduced the spectrotemporal integration window of the STA with increasing distance from the soma as direct consequences of passive filtering and dendritic spike initiation, respectively. Finally, the presence of HCN channels set the STA characteristic frequency in the theta range across the somatodendritic arbor and specific STA measurements were strongly related to equivalent transfer-impedance-related measurements. Our results identify explicit roles for plastic active dendrites in neural coding and strongly recommend a dynamically reconfigurable multi-STA model (below) to characterize location-dependent input feature selectivity in pyramidal neurons (Das and Narayanan, J. Neuroscience, 2015).

Further, different classes of neurons are known to depict different forms of STA, with Class I excitability neurons showing integrator-like properties, and Class II/III neurons endowed with coincidence detector-like features. Our results demonstrate that different parts of a neuron can span the Integrator-Coincidence Detector continuum depending on the density of HCN channels. These results together suggest that neural coding and learning in neurons with plastic active dendrites should not be viewed from the limited perspective of synaptic properties and their plasticity, but should incorporate the profiles and plasticity of different voltage-gated ion channels and other intrinsic mechanisms as well. We also extended this analysis to interactions among several subthreshold VGICs, and found that spatiotemporal interactions among these channels critically regulate the STA and coincidence detection window (CDW) in hippocampal neurons. Specifically, we showed that the presence of resonating and spike-generating conductances serve as a mechanism underlying the emergence of stratified gamma-range coincidence detection in the dendrites of CA1 pyramidal neurons (slow-gamma CDW in proximal dendrites and a fast-gamma CDW in distal dendrites), enabling them to perform behaviour- and state-dependent gamma frequency multiplexing (Das and Narayanan, J. Physiology (London), 2015).

Related references

Anindita Das and Rishikesh Narayanan, Theta-frequency selectivity in the somatic spike triggered average of rat hippocampal pyramidal neurons is dependent on HCN channels, Journal of Neurophysiology, In Press, August 2017. [PDF File] [Article at publisher's site]

Anindita Das and Rishikesh Narayanan, Active dendrites mediate stratified gamma-range coincidence detection in hippocampal model neurons, The Journal of Physiology (London), 593(16): 3549–3576, August 2015. [PDF File] [Article at publisher's site]

Anindita Das and Rishikesh Narayanan, Active dendrites regulate spectral selectivity in location-dependent spike initiation dynamics of hippocampal model neurons, The Journal of Neuroscience, 34(4): 1195-1211, January 2014. [PDF file] [Link to paper at publisher's site]

Anindita Das, Rahul Kumar Rathour and Rishikesh Narayanan, Strings on a violin: Location dependence of frequency tuning in active dendrites, Frontiers in Cellular Neuroscience, 11, 72: 1-8, March 2017. [PDF file] [Article at publisher's site]

Dendritic ion channels and local field potentials

What are the implications for the existence of subthreshold VGICs, their localization profiles and plasticity on local field potentials (LFPs)? We assessed the role of HCN channels in altering hippocampal theta-frequency LFPs and associated spike phase. To do this, we presented spatiotemporally randomized, balanced theta-modulated excitatory and inhibitory inputs to somatically aligned, morphologically realistic pyramidal neuron models spread across a cylindrical neuropil. We computed LFPs from seven electrode sites and found that the insertion of an experimentally constrained HCN-conductance gradient into these neurons introduced a location-dependent lead in the LFP phase without significantly altering its amplitude. Further, neurons fired action potentials at specific theta-phase of the LFP, and the insertion of HCN channels introduced large lags in this spike phase and a striking enhancement in neuronal spike phase coherence. These results uncover specific roles for HCN channels and their plasticity in phase coding schemas and in the formation and dynamic reconfiguration of neuronal cell assemblies (Sinha and Narayanan, PNAS (USA), 2015).

Related references

Manisha Sinha and Rishikesh Narayanan, HCN channels enhance spike phase coherence and regulate the phase of spikes and LFPs in the theta-frequency range, Proceedings of the National Academy of Sciences (USA), 112(17): E2207-E2216, April 2015. [PDF File] [Article at publisher's site]

The Endoplasmic Reticulum in Neurons and Astrocytes

Neuronal physiology is defined not just by spatiotemporal interactions amongst plasma membrane VGICs. The endoplasmic reticulum (ER) spans the entire neuronal morphology and is endowed with numerous ion channels on its membrane. Along an active dendritic membrane, this arrangement constitutes the presence of two continuous membranes that can modulate and propagate information by recruiting channels on either of them. Therefore, we explored interactions between these two membranes and their implications for neuronal physiology and information encoding within neurons.

Roles of dendritic ion channels in modulating release of calcium from the ER stores: The ER membrane is endowed with inositol triphosphate receptors (InsP₃R) that are permeable to calcium and can sustain active propagation of calcium waves within neurons. Focusing specifically on the interactions between the A-type K⁺ channels and InsP₃Rs, we have demonstrated that A-type K⁺ channels could regulate Ca²⁺ release through InsP₃Rs, thereby altering propagation of Ca²⁺ waves and induction of synaptic plasticity. Our results suggest that such interactions between conductances on the dendritic membrane and Ca²⁺ channels on the ER membrane could critically regulate biophysical/biochemical signal integration and steer the spatiotemporal spread of signaling microdomains within neurons (Ashhad and Narayanan, J. Physiology, 2012).

Roles of calcium released from the ER in modulating plasma membrane ion channels: We explored the counterpart to these interactions, whereby calcium release through InsP₃ receptors can alter the properties of channels that reside on the plasma membrane. In this case, we explored the interactions between InsP₃ receptors and HCN (h) channels that reside on the plasma membrane. We showed that the activation of InsP₃ receptors through intracellular InsP₃ injection is sufficient to elicit plasticity in neuronal intrinsic response dynamics through changes in the h current. We have also shown that this form of plasticity is dependent on calcium release through InsP₃ receptors and the PKA (protein kinase A) pathway (Ashhad et al., J. Neurophysiol., 2015).

Related references

Sufyan Ashhad, Daniel Johnston and Rishikesh Narayanan, Activation of InsP₃ receptors is sufficient for inducing graded intrinsic plasticity in rat hippocampal pyramidal neurons, Journal of Neurophysiology, 113(7): 2002-2013, April 2015. [PDF File] [Article at publisher's site]

Sufyan Ashhad and Rishikesh Narayanan, Quantitative interactions between the A-type K⁺ current and inositol trisphosphate receptors regulate intraneuronal Ca²⁺ waves and synaptic plasticity, The Journal of Physiology (London), 591 (7): 1645–1669, April 2013. [PDF file] [Link to paper at publisher's site]

Sufyan Ashhad and Rishikesh Narayanan, Active dendrites regulate the impact of gliotransmission on rat hippocampal pyramidal neurons, Proceedings of the National Academy of Sciences (USA), 113(23): E3280-E3289, June 2016. [PDF File] [Article at publisher's site]

Homeostasis through plasticity interactions

Neurons are dynamic entities with plasticity altering the density and properties of these VGICs/receptors across the somatodendritic arbor, with synergistic interactions among different forms of plasticity. How do neurons maintain activity homeostasis against such ubiquitous plasticity? How do they retain specific plasticity profiles despite tremendous variability in underlying channel properties?

To address the first question, we developed calcium-dependent plasticity rules for the HCN channels, and their interactions with calcium-dependent synaptic plasticity. In doing this, we demonstrated that the synergy between synaptic and HCN plasticity retains stability in the synaptic learning system, maintains firing rate homeostasis and enhances the robustness of information transfer across the neuron. Our study established a broad framework for the coexistence of synaptic and VGIC plasticity in neural systems that are required to stably encode memory in learning systems (Honnuraiah and Narayanan, PLoS ONE, 2013).

In answering the second question, we considered interactions among different channels and receptors through global sensitivity analysis. Analyzing valid models that were obtained from this analysis, we found that similar short- and long-term plasticity profiles could emerge with several nonunique parametric combinations and that parameters exhibited weak pairwise correlations. These results suggested that there are several nonunique routes to regulate synaptic plasticity profiles, and plasticity homeostasis could be achieved through any of these several routes (Anirudhan and Narayanan, J. Neuroscience, 2015; Mukunda and Narayanan, J. Physiology, 2017). In addition, we also showed that neurons can undergo variable plasticity in several ion channels towards reconciling the maintenance of calcium homeostasis with perpetual switches in behavioral-state-dependent afferent synaptic activity (Srikanth and Narayanan, eNeuro, 2015).

Related references

Arun Anirudhan and Rishikesh Narayanan, Analogous synaptic plasticity profiles emerge from disparate channel combinations, The Journal of Neuroscience, 35(11): 4691-4705, March 2015. [PDF File] [Article at publisher's site]

Chinmayee L Mukunda and Rishikesh Narayanan, Degeneracy in the regulation of short-term plasticity and synaptic filtering by presynaptic mechanisms, The Journal of Physiology (London), 595(8): 2611-2637, April 2017. [PDF

File] [Article at publisher's site]

Sunandha Srikanth and Rishikesh Narayanan, Variability in state-dependent plasticity of intrinsic properties during cell-autonomous self-regulation of calcium homeostasis in hippocampal model neurons, eNeuro, 2(4), e0053-15.2015: 1-24, August 2015. [PDF File] [Article at publisher's site]

Suraj Honnuraiah and Rishikesh Narayanan, A calcium-dependent plasticity rule for HCN channels maintains activity homeostasis and stable synaptic learning, PLoS One, 8(2), e55590: 1–17, February 2013. [PDF file][Supplementary PDF File] [Article at publisher's site]