HCN channels enhance spike phase coherence and regulate the phase of spikes and LFPs in the theta-frequency range

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1 HCN cannels enance spike pase coerence and regulate te pase of spikes and LFPs in te teta-frequency range Manisa Sina and Risikes Narayanan 1 Cellular Neuropysiology Laboratory, Molecular Biopysics Unit, Indian Institute of Science, Bangalore , India Edited by Terrence J. Sejnowski, Salk Institute for Biological Studies, La Jolla, CA, and approved Marc 24, 2015 (received for review October 2, 2014) Wat are te implications for te existence of subtresold ion cannels, teir localization profiles, and plasticity on local field potentials (LFPs)? Here, we assessed te role of yperpolarizationactivated cyclic-nucleotide gated (HCN) cannels in altering ippocampal teta-frequency LFPs and te associated spike pase. We presented spatiotemporally randomized, balanced teta-modulated excitatory and inibitory inputs to somatically aligned, morpologically realistic pyramidal neuron models spread across a cylindrical neuropil. We computed LFPs from seven electrode sites and found tat te insertion of an experimentally constrained HCN-conductance gradient into tese neurons introduced a location-dependent lead in te LFP pase witout significantly altering its amplitude. Furter, neurons fired action potentials at a specific teta pase of te LFP, and te insertion of HCN cannels introduced large lags in tis spike pase and a striking enancement in neuronal spike-pase coerence. Importantly, graded canges in eiter HCN conductance or its alf-maximal activation voltage resulted in graded canges in LFP and spike pases. Our conclusions on te impact of HCN cannels on LFPs and spike pase were invariant to canges in neuropil size, to morpological eterogeneity, to excitatory or inibitory synaptic scaling, and to sifts in te onset pase of inibitory inputs. Finally, we selectively abolised te inductive lead in te impedance pase introduced by HCN cannels witout altering neuronal excitability and found tat tis inductive pase lead contributed significantly to canges in LFP and spike pase. Our results uncover specific roles for HCN cannels and teir plasticity in pase-coding scemas and in te formation and dynamic reconfiguration of neuronal cell assemblies. active dendrites local field potential neuronal inductor pase coding cannel localization Local field potentials (LFPs) ave been largely believed to be a reflection of te synaptic drive tat impinges on a neuron. In recent experimental and modeling studies, tere as been a lot of debate on te source and spatial extent of LFPs (1 9). However, most of tese studies ave used neurons wit passive dendrites in teir models and/or ave largely focused on te contribution of spike-generating conductances to LFPs (7, 8, 10, 11). Despite te widely acknowledged regulatory roles of subtresold-activated ion cannels and teir somatodendritic gradients in te pysiology and patopysiology of synapses and neurons (12 17), te implications for teir existence on LFPs and neuronal spike pase ave surprisingly remained unexplored. Tis lacuna in LFP analysis is especially striking because local and widespread plasticity of tese cannels as been observed across several pysiological and patological conditions, translating to putative roles for tese cannels in neural coding, omeostasis, disease etiology and remedies, learning, and memory (16, 18 23). In tis study, we focus on te role of yperpolarization-activated cyclic nucleotide-gated (HCN) cannels tat mediate te current (I ) in regulating LFPs and teta-frequency spike pase. From a single-neuron perspective, HCN cannels in CA1 pyramidal neurons play a critical role in regulating neuronal integration and excitability (14, 24 27) and importantly introduce an inductive pase lead in te voltage response to teta-frequency oscillatory inputs (28), tereby enabling intraneuronal syncrony of incoming teta-frequency inputs (29). Given tese and teir predominant dendritic expression (25), we ypotesized HCN cannels as regulators of LFPs troug teir ability to alter te amplitude and pase of te intracellular voltage response, tereby altering several somatodendritic transmembrane currents tat contribute to LFPs. Te CA1 region of te ippocampus offers an ideal setup to test tis ypotesis, given te regular, open-field organization (4, 6, 7) of te pyramidal neurons endowed wit well-establised somatodendritic gradients in ion cannel densities (16). As tis organization enables us to assess te role of location-dependent cannel expression profiles on LFPs across different strata, we tested our ypotesis, using a computational sceme involving morpologically realistic, pysiologically constrained conductance-based model neurons. Our results positively test our ypotesis and provide specific evidence for novel roles for HCN cannels and teir inductive component in regulating LFP and spike pases, apart from enancing spike-pase coerence. Tese results identify definite roles for HCN cannels in pase-coding scemas and in te formation and dynamic reconfiguration of neuronal cell assemblies and argue for te incorporation of subtresold-activated ion cannels, teir gradients, and teir plasticity into te computation of LFPs. Results We performed our experiments on a neuropil containing 440 morpologically realistic, conductance-based CA1 pyramidal neuronal models, wose somata were distributed witin a cylindrical volume of 200 μm diameter and 40 μm eigt (Fig. 1A). We stimulated te neuronal compartments wit teta-modulated Significance Te impact of te pacemaking yperpolarization-activated cyclic-nucleotide gated (HCN) cannels on local field potentials (LFP) as not been analyzed. Here, employing a neuropil of several morpologically precise ippocampal neuronal models tat received systematically randomized rytmic synaptic inputs, we demonstrate tat HCN cannels alter te pase, but not te amplitude, of LFPs. Furter, it is known tat te spike timings of individual neurons follow te beat of te LFPs and fire at precise pases of te LFP beat. We demonstrate tat te presence of HCN cannels alters tis pase and enances te precision to wic te spikes follow te LFP beat. Tese results unveil several important roles for HCN cannels, extending teir regulatory potential beyond single-neuron pysiology. Autor contributions: M.S. and R.N. designed researc; M.S. performed researc; M.S. analyzed data; and M.S. and R.N. wrote te paper. Te autors declare no conflict of interest. Tis article is a PNAS Direct Submission. 1 To wom correspondence sould be addressed. risi@mbu.iisc.ernet.in. Tis article contains supporting information online at /pnas /-/DCSupplemental. NEUROSCIENCE PNAS PLUS PNAS Publised online April 13, 2015 E2207 E2216

2 Fig. 1. Model components and computation of local-field potentials and spike teta pase. (A, Left) A single electrode wit seven recording sites, located at te center of te cylindrical neuropil, spanned all strata of te CA1 (SO, stratum oriens; SP, stratum pyramidale; SR, stratum radiatum; and SLM, stratum lacunosum moleculare). (A, Rigt) Te line source approximation metod. Sown is a single line segment of lengt l, separated by a radial (perpendicular) distance r from a recording site. Te nearest distance between te compartment and te perpendicular is denoted by and s = l +. (B) Distribution of unitary somatic EPSP amplitudes (v uepsp ) as a function of radial distance from te soma, depicting distance invariance of v uepsp.(c and D) Input resistance (C) and local and transfer resonance frequency (D) in te presence of a sigmoidal gradient of HCN conductance (C, Inset), all plotted along te somatoapical trunk. (E) Transfer impedance pase profile for four different locations along te somatoapical trunk. Arrow indicates te syncronization frequency at 8 Hz. (F, Left) Normalized LFP traces (1 s) computed using LSA for SO, SP, SR, and SLM. (F, Rigt) LFP pase (mean ± SEM, 10 cycles) at eac recording site, wit reference to te SP LFP. (G, Bottom) SP LFP wit spikes (ticks) and intracellular voltage for a single neuron. (G, Top) Distribution of spike pases of te neuron, at various cycles, wit reference to te SP LFP. (H, Bottom) Raster plot for 25 neurons and corresponding spike time istogram and SP LFP. (H, Top) Histogram of te spike pases wit reference to te SP LFP for te population of 25 neurons. (8 Hz) excitatory and inibitory inputs, wit an experimentally constrained synaptic distribution (Fig. 1B). Te passive properties and te gradient in HCN-cannel density (Fig. 1C) were set to matc te functional maps of input resistance (R in ) (Fig. 1C), local (f R ), and transfer (f TR ) resonance frequencies (Fig. 1D), apart from setting te syncronization frequency (Fig. 1E) at 8 Hz (16, 25, 26, 28, 29). As a first step, we removed all voltage-gated ion cannels (VGIC) from te entire neuronal population and computed LFPs, using te line-source approximation metod (4, 6 8, 30, 31). As a direct consequence of teta-modulated synaptic inputs (8 Hz) tat drove te neuronal compartments, te LFPs across strata depicted teta-band modulation (Fig. 1F). Wit an openfield dipole oriented wit te sink in te stratum radiatum (SR) and a source around te perisomatic region (4, 6, 7), te tetafrequency LFP recorded across different sites exibited a progressive pase sift across recording sites adding to 180 (Fig. 1F). Next, we introduced Na + and delayed-rectifier K + cannels into te somatodendritic arbor of tese neurons and recorded somatic intracellular voltages to calculate neuronal spike pases wit reference to te stratum pyramidale (SP) LFP (Fig. 1G). We found tat neuronal spikes were triggered at specific teta pases close to te troug of te SP LFP (Fig. 1 G and H). Tese conclusions on pase sifts in cross-strata teta-frequency LFPs and spikes aligned to specific pases of te SP LFP are consistent wit experimental measurements from rodent ippocampus (32 35). HCN Cannels Introduced a Pase Lead in LFPs Across Strata. To assess te role of HCN cannels and teir graded plasticity (16, 22 24, 26, 28) on LFPs, we next measured LFPs in models wit tree different base values (g Base = 55 μs/cm 2,85μS/cm 2,and 160 μs/cm 2 ) for te somatodendritic gradient (Fig. 1C) of HCN cannels, set across te arbor of all constituent neurons (Fig. S1 A C). Because of te domination of te underlying rytmic E Sina and Narayanan

3 ig-conductance state (36), te LFP amplitudes across recording sites were not significantly different wit te insertion of HCN cannels. However, te incorporation of HCN cannels introduced a significant location-dependent pase lead in te LFPs across all recording sites, wen compared wit corresponding LFPs computed in te absence of HCN cannels (Fig. 2A). Assessing te mecanistic basis for tis, we noted tat te incorporation of HCN cannels introduced an inductive lead in te intracellular local response voltage (28, 29) wit reference to te response voltage in te passive neuron. Consequently, te transmembrane leak current in tese compartments (wic, by definition, followed te local voltage) exibited a pase lead wit reference to te leak current recorded in te absence of HCN cannels. As LFPs are correlated wit te net transmembrane current, LFPs computed in te presence of HCN cannels sowed a pase lead across all strata in comparison to te LFPs computed in teir absence (Fig. 2A). Te pase of te local leak current and its somatodendritic distribution, in conjunction wit te density of HCN cannels (iger in distal apical dendrites) and te differential activation of HCN cannels as a consequence of te relative pase difference and localization profiles of synaptic types (inibition induces perisomatic yperpolarization, wereas excitation induces SR depolarization, wit a 60 pase sift) ten explains te location dependence of LFP pase lead introduced by HCN cannels. Consistent wit tis inference, we found tat te LFP pase lead was graded and increased progressively wit increase in HCN conductance (Fig. 2B), suggesting a graded influence of global HCN-cannel plasticity on LFP pase. NEUROSCIENCE PNAS PLUS Fig. 2. Incorporating HCN cannels resulted in a location-dependent lead in te LFP pase, a lag in te spike pase, and a reduction in spike-pase jitter. (A, Left) Normalized LFP traces (1 s) for different strata in te presence (g Base = 85 μs/cm 2 ) and in te absence (g Base = 0 μs/cm 2 ) of HCN cannels. (A, Center) LFP pase (mean ± SEM over 10 cycles) wit reference to te stratum pyramidale (SP) LFP for corresponding traces in A, Left. (A, Rigt) Strata-wise cycle-matced difference (mean ± SEM) between te LFP pase obtained wit g Base = 85 μs/cm 2 and 0 μs/cm 2.(B, Top) Normalized LFP traces (1 s) for different g Base values depicted wit reference to te excitatory input θ. (B, Bottom) LFP pase (SP recording site) wit reference to te excitatory input θ, plotted for different g Base values. (C) Population spike time istograms (1 s) wit corresponding SP LFP, plotted for different g Base values. (D) Spike-pase difference (cycle matced for 8cycles;mean± SEM) between te spike pase for te said g Base value and for te case were g Base = 0 μs/cm 2 (n = 24 neurons for g Base = 85 μs/cm 2 and 160 μs/cm 2 ). (E) LFP pase wit reference to te excitatory input θ (mean ± SEM, 10 cycles) for baseline V 1=2 (ΔV 1=2 = 0 mv) and yperpolarized (ΔV 1=2 = 5 mv) and depolarized V 1=2 (ΔV 1=2 =+5 mv) of HCN-cannel activation. (F) Population spike time istograms (1 s) wit corresponding SP LFP wit ΔV 1=2 = 5 mvand ΔV 1=2 =+5mV.(G) Spike-pase difference (cycle matced for 8 cycles; mean ± SEM) between te spike pase for te case were ΔV 1=2 = 5/+5 mv and tose wit ΔV 1=2 = 0mV(n = 24 neurons). (A, B, and E) *P < 0.05, **P < (Wilcoxon signed-rank test). (D and G) **P < (Student s t test on te null ypotesis of no spike-pase difference). Sina and Narayanan PNAS Publised online April 13, 2015 E2209

4 HCN Cannels Induced a Lag in te Spike Pase and Enanced Neuronal Spike Pase Coerence. How does te presence of and plasticity in (26, 27) HCN-cannel conductance alter te teta pase of neuronal spikes? We plotted te population spiketiming istogram and te corresponding SP LFP for eac HCNcannel density under consideration (Fig. 2C). Wit increase in g Base, we observed tat te jitter associated wit spike pases decreased, tereby enancing teir coerence wit reference to te SP LFP (Fig. 2C). To quantify tis, we calculated spike-pase coerence, C Φ (37), and observed tat C Φ increased wit increasing g Base. Tis is consistent wit earlier observations tat HCN cannels reduce temporal summation (14, 24 26), in effect reducing te temporal window for spike-generating coincidence detection (38, 39), a property tat critically depends on teir ability to introduce an inductive component (38). Specifically, te presence of HCN cannels constricts te ability of a neuron to spike across a large span of te teta oscillation, tereby leading to enanced spike-pase coerence (Fig. 2C). Finally, we found tat te teta pase of te spikes sowed a progressive and significant lag wit increase in HCN-cannel density (Fig. 2D), implying a graded influence of global HCN plasticity on spike pase. Apart from canges in conductance, plasticity and cyclic nucleotide-dependent modulation of HCN cannels ave been demonstrated (40 43) to also manifest as sifts in teir alfmaximal activation voltage (V 1/2 ). To assess te impact of suc sifts on LFP and spike pase, we repeated our simulations and analyses wit different values of HCN-cannel V 1/2 (Fig. 2 E G). We found tat depolarization of V 1/2 resulted in an increased lead in LFP pase (Fig. 2E and Fig. S1 D and E), an increased spike-pase coerence (Fig. 2F), and an increased lag in spike pase (Fig. 2G). We noted tat our observations wit depolarization of V 1/2 were similar to tose wit increase in g Base (Fig. 2 A D). Tis sould be expected given tat I increases eiter wit increase in g Base or wit depolarization of V 1/2, given similarities in te impact of eiter cange on several intrinsic properties (26, 28). Regulation of LFP and Spike Pases by HCN Cannels Was Invariant to Canges in Neuropil Size and to Morpological Heterogeneity. Our analyses tus far were performed wit a small 200-μm diameter cylindrical neuropil in an effort to reduce computational burden. How dependent were our conclusions on te size of te neuropil? To address tis, we repeated our simulations wit two additional neuropils wit 400 μm diameter (total number of neurons: 1,797) and 1,000 μm diameter (total number of neurons: 11,297; Fig. 3A), wile retaining te same density of neurons across neuropils and wit identical electrode location at te center of te neuropil. As expected (7), te LFP amplitude increased wit increase in neuropil size (Fig. 3B, Left and Fig. S2). However, te contribution per neuron from te distal annuli decreased by orders of magnitude (Fig. 3B, Rigt), suggesting minimal contribution of neurons from tese annuli to te LFP. Importantly, te introduction of an HCN-cannel gradient (Fig. 1 C E) into te constituent neurons resulted in a lead in te LFP pase witout significant canges in LFP amplitude (Fig. 3 B D and Fig. S2), an increase in spike-pase coerence (Fig. 3E), and a lag in te associated spike pase (Fig. 3F) across all tested neuropils. Next, altoug our analyses tus far were performed wit independently rotated versions of a morpological reconstruction wit randomly located probabilistic synaptic input (7), tey were derived from a single morpological reconstruction (n123; Fig. 1A). To address te impact of morpological eterogeneity, we employed an additional morpological reconstruction (ri04; Fig. S3A), tuned its intrinsic and synaptic properties along its somatodendritic arbor to matc wit experimental observations (Fig. S3 B E), and uniformly distributed te two morpologies wit random rotations across te neuropil (Fig. 3G). Comparing LFPs and spikes obtained in te absence and te presence of HCN cannels, we found te impact of HCN cannels in introducing a lead in LFP pase (Fig. 3H and Fig. S3 F and G), an increase in spike-pase coerence (Fig. 3I and Fig. S3H), and a lag in spike pase (Fig. 3J) to be invariant to morpological eterogeneity. Togeter, tese results suggested tat te impact of HCN cannels on LFP pase, spike pase, and spike coerence was invariant to canges in neuropil size and to morpological eterogeneity. Regulation of LFP and Spike Pases by HCN Cannels Was Invariant to Canges in Synaptic Parameters. Were our conclusions on te role of HCN cannels in altering LFP and spike pases (Figs. 2 and 3) specific to our coice of parameters associated wit te excitatory and inibitory drive? To address tese, we performed detailed sensitivity analyses on parameters (Fig. 4 and Figs. S4 S7) associated wit excitatory and inibitory synapses. We found tat te introduction of HCN cannels resulted in a lead in te LFP pase, an enancement in spike-pase coerence, and a lag in te spike pase, irrespective of up- or down-regulation of excitatory (Fig. 4 A C) or inibitory (Fig. 4 D F) synapses. Next, we reanalyzed te data presented in Fig. 4 A F to ask weter synaptic scaling of excitatory or inibitory inputs altered LFPs and spikes. Wereas increasing AMPAR conductances induced a lag in te SP LFP and a lead in te spike pase (Fig. S4), increase in GABA A R conductances resulted in a lead in te SP LFP and a lag in te spike pase (Fig. S5). We noted tat te spike-pase coerence was not significantly altered by synaptic scaling (Fig. 4 B and E and Figs. S4 and S5). How dependent were our conclusions on te specific coice of te pase difference, ϕ gin, between te excitatory and inibitory teta-frequency synaptic inputs, tus far fixed at 60? We canged ϕ gin to various values and compared LFPs and spike pases across different values of ϕ gin in neurons, in te presence or te absence of HCN cannels. We found tat te introduction of HCN cannels resulted in a lead in te LFP pase, an enancement in spike-pase coerence, and a lag in te spike pase, irrespective of te specific value of ϕ gin (Fig. 4 G I). Next, we reanalyzed te data presented in Fig. 4 G I to ask weter canges in ϕ gin altered LFPs and spikes. We observed a striking sift in te SP LFP pase on canging ϕ gin, wit te LFP pase leading by 120 wen ϕ gin sifted from 60 to 60, a magnitude of sift tat strictly followed magnitude of cange in ϕ gin (Fig. 4G and Fig. S6). Altoug we did not observe any significant difference in te population spike-pase coerence on canging ϕ gin (Fig. 4H and Fig. S6), spike pase displayed a dependence tat would be expected from te sift in SP LFP. Specifically, sifting ϕ gin from 60 to 60 resulted in 120 lag in te spike pase (Fig. S6). Finally, we performed a sensitivity analysis on te reversal potential of te GABA A receptor and found tat except for te expected cange in LFP amplitude due to canges in driving force, our conclusions on te impact of HCN cannels were invariant to canges in te reversal potential of te GABA A receptor (Fig. S7). Togeter tese results suggest tat our conclusions on HCNcannel regulation of LFPs and spikes were invariant to canges in synaptic parameters. Furter, tese results also reveal an important role for synaptic scaling and for temporal structure of excitatory inibitory inputs in regulating LFP and spike pases, but not in spike-pase coerence. A Single Neuron Can Sift Its Spike Pase Troug HCN Plasticity. Te kind of global canges in HCN cannel density spanning a large set of neurons tat we assessed tus far ave been sown to occur only under patopysiological conditions (18 20, 22, 23). Under pysiological conditions, neurons are known to sift teir spike pase over a course of time, eiter as part of a beavioral task or in te process of te neuron being reassigned to anoter cell assembly (33 35). As HCN plasticity as been demonstrated E Sina and Narayanan

5 NEUROSCIENCE PNAS PLUS Fig. 3. HCN-cannel induced canges in LFP and spike pases were invariant to canges in neuropil size and to morpological eterogeneity. (A) Tree neuropils of different sizes, used for analyses presented in B F, depicted wit te distribution of neurons. (B, Left) SP LFP amplitude computed in te presence (g Base = 85 μs/cm 2 ) and in te absence (g Base = 0 μs/cm 2 ) of HCN cannels, for tree different neuropil sizes. (B, Rigt) Per neuron contribution to te LFP amplitude computed wit g Base = 0 μs/cm 2 and 85 μs/cm 2 for te tree annuli (A). (C, Left) Normalized LFP traces (1 s) for different strata wit g Base = 0 μs/cm 2 and 85 μs/cm 2 for te largest (1,000 μm diameter) neuropil. (C, Rigt, Bottom axis) LFP pase wit reference to te excitatory input θ (mean ± SEM, 10 cycles) for corresponding traces in C, Left. (C, Rigt, Top axis) Strata-matced pase difference between LFPs obtained wit g Base = 85 μs/cm 2 and 0 μs/cm 2.(D) LFP pase wit reference to te excitatory input θ for tree different neuropil sizes computed in te absence (PAS) and te presence (H) of HCN cannels. Note te increased variability in te LFP pases (computed across cycles) wit increase in neuropil size, a consequence of increased jitter in LFP traces wit increase in neuropil size (Fig. S2). (E) Population spike-time istograms (1 s) wit corresponding SP LFP for different neuropil sizes for g Base = 0 μs/cm 2 and 85 μs/cm 2. (F) For tree neuropil sizes, cycle-matced difference between spike pases obtained wit g Base = 85 μs/cm 2 and wit g Base = 0 μs/cm 2, for 24 different neurons (mean ± SEM). (G) Distribution of 440 neurons wit n123 (red, N n = 214) and ri04 (black, N n = 226) morpological reconstruction, used for te analyses in H J. (H) SP LFP pase wit reference to input θ (mean ± SEM, 10 cycles), computed in te absence (PAS) and te presence (H) of HCN cannels. (I) Population spiketime istograms (1 s) wit corresponding SP LFP. (J) Cycle-matced difference between spike pases obtained in te presence and in te absence of HCN cannels, for 22 different neurons (mean ± SEM). (C, D, and H)*P < 0.05, **P < (Wilcoxon signed rank test). (F and J)**P < (Student s t test on te null ypotesis of no spike-pase difference). to accompany bidirectional synaptic plasticity (16, 22, 24, 26 28) and plasticity in one or few neurons is pysiologically more plausible, we asked weter plasticity in HCN cannel density of a single neuron was sufficient to alter its spike pase. We altered te g Base of a single neuron wose soma was located among tose closest to te electrode to tree different values (as in Fig. 2 B D), wile g Base of all oter neurons was set at 85 μs/cm 2 (Fig. 5A). Despite suc proximal positioning, we observed no significant difference in te LFP amplitude (Fig. 5B) or pase (Fig. 5C) wit plasticity in HCN cannels of te neuron. Tis was to be expected because te LFP was calculated using compartments from 440 neurons, and a cange in HCNcannel density in one neuron sould not alter te LFP significantly. Next, we computed te spike pase of te cosen neuron wit reference to te corresponding LFPs and compared tem across different values of its g Base (Fig. 5D). We found no significant difference in te spike pase of te neuron wen g Base was decreased, but observed a significant lag in te spike pase wit iger g Base. We repeated te procedure across all input structures tat elicited spikes (24 of 25), by replacing te neuron at te specified location (Fig. 5A) by eac of te remaining 23 spiking neurons, and found our conclusions to be robust across different input structures (Fig. 5D). Tese results suggested tat HCN-cannel plasticity could act as a putative mecanism for a neuron to sift its spike pase wit reference to an externally driven teta oscillation (4, 33, 35, 44). Sina and Narayanan PNAS Publised online April 13, 2015 E2211

6 Fig. 4. HCN-cannel induced canges in LFP and spike pases were invariant to canges in synaptic properties. (A, Bottom axis) LFP pase wit reference to te excitatory input θ (mean ± SEM, 10 cycles), computed in te presence (g Base = 85 μs/cm 2 ) and in te absence (g Base = 0 μs/cm 2 ) of HCN cannels for different unitary EPSP (v uepsp ) values. Default value of v uepsp = 4.8 μv. (A, Top axis) Strata-matced pase difference between LFPs obtained wit g Base = 85 μs/cm 2 and 0 μs/cm 2.(B) Spike-pase coerence plotted for different v uepsp values, for g Base = 0, 85 μs/cm 2.(C) Cycle-matced difference between spike pases obtained wit g Base = 85 μs/cm 2 and wit g Base = 0 μs/cm 2 for different neurons (mean ± SEM), plotted for eac v uepsp.(d F) Same as A C, but for different values of inibitory synaptic conductance (g in ). Default value of g in = 100 ps. (G I) Same as A C, but for different values of pase difference (ϕ gin ) between te excitatory and inibitory teta-frequency synaptic inputs. Default value of ϕ gin = 60. Spike pases: n = 22 neurons for v uepsp = 4.3 μv, n = 23 neurons for g in = 200 ps, n = 24 neurons for v uepsp = 4.8 μv, for g in = 100 ps and for ϕ gin = 0 and 60. (A, D, and G) *P < 0.05, **P < (Wilcoxon signed-rank test). (C, F, and I) **P < (Student s t test on te null ypotesis of no spike-pase difference). A Faster HCN Cannel Nullified Inductive Impedance Witout Altering Intrinsic Excitability. Te presence of HCN cannels introduces two distinct sets of canges in a neuronal compartment. First, tey reduce intrinsic excitability (24 26, 45), and second, tey introduce an inductive component to te impedance profile. Wereas te former reflects as a reduction in R in and in te impedance amplitude across several frequencies, te latter manifests as resonance in impedance amplitude and a lead in impedance pase (28, 46, 47). Te manifestation of te inductive component of HCN cannels requires teir (de)activation time constant be slower tan tat of te membrane time constant(28, 46, 47). Concordantly, an ideal metod to test te relative contribution of intrinsic excitability vs. inductive component of te HCN cannel to any measurement is to render te cannel activation faster tan te membrane time constant wit an unaltered voltage-dependent gating profile. To address te question of wat specific property of te HCN cannel explains its impact on LFP and spike pases, we reduced te (de)activation time constant of HCN cannels (in wat follows, we call tem HCNFast cannels) to around 7 ms [from 33 ms, at 65 mv (25)], tereby nullifying teta-frequency resonance and te inductive pase lead (Fig. S8 A and B). As our analysis was confined to teta-modulated synaptic inputs (8 Hz), we matced neuronal excitability at 8 Hz at 250 μm from te soma to find appropriate values of g Base (for te HCNFast cannels) corresponding to eac g Base F analyzed earlier (Fig. S8 C E). By doing tis, we ensured tat all distance- and voltage-dependent properties of HCNFast cannels (including teir reversal potential) and teir impact on excitability were matced to te HCN counterparts, wit te only exception tat te presence of tese cannels would not introduce an inductive component onto te neuronal compartments. Fast HCN Cannels Revealed a Differential Role for Inductive and Excitability Canges Introduced by HCN Cannels. To discern te roles of te inductive vs. te excitability component in altering E Sina and Narayanan

7 Fig. 5. Plasticity in HCN cannels of an individual neuron sifted its spike pase. (A) Top view of te neuropil (Fig. 1A) depicting te location of te neuron undergoing plasticity (red), wic is among te neurons closest to te electrode (yellow). (B) SP LFP (1 s), sown wit reference to excitatory input θ, computed wit g Base for te cosen neuron set to one of tree values: 55 μs/cm 2,85μS/cm 2,or160μS/cm 2. g Base value for te oter (439) neurons was set at te baseline value of 85 μs/cm 2.(C) SPLFPpase across cycles computed (wit reference to excitatory input θ; mean ± SEM, 10 cycles) for corresponding traces sown in B. P > 0.1, Kruskal Wallis test. (D, Top) Ticks representing spike timings of te single neuron undergoing plasticity wit reference to SP LFP. Color codes of ticks correspond to te different values of g Base (B). Histogram of spike timings of te oter 23 neurons not undergoing plasticity is also sown (black). (D, Bottom Left) Cycle-matced difference between te spike pase of te cosen neuron computed wit g Base = 55 μs/cm 2 or 160 μs/cm 2 and te spike pase of te same neuron obtained wit g Base = 85 μs/cm 2. Te different data points (n = 24; also mean ± SEM) correspond to tis spike-pase difference computed by placing different neurons at te specified location. **P < (Student s t test on te null ypotesis of no spike-pase difference). (D, Bottom Rigt) Histogram of te spike-pase differences obtained across tese 24 trials. LFPs, we replaced HCN cannels wit teir fast counterparts, computed SP LFP for different gf Base values, and compared tem wit te LFPs computed wit te corresponding (Fig. S8) g Base values (Fig. 6A). Consequent to excitability not being altered by cannel replacements (Fig. S8), we found tat tere was no significant difference in te LFP amplitudes (Fig. 6A). However, across strata, we found te lead observed in LFP pase in te presence of HCN cannels was significantly reversed in te presence of HCNFast cannels (Fig. 6 B D), suggesting tat te inductive properties of HCN cannels played a critical role in regulating te LFP pase lead. Furter, we also noted te amount of HCNFast-induced reversal decreased wit increase in conductance density (Fig. 6 B D), implying a role of canges in intrinsic excitability dominating in te presence of iger HCN conductances. Wen compared across HCNFast conductance values, LFP pase lead increased wit an increase in HCNFast conductance (Fig. S8F), albeit wit lower values for te pase lead in comparison to tose obtained wit HCN cannels (compare Fig. 2B). Next, we compared te population of spikes and teir teta pases in te presence of HCN or HCNFast cannels, across different conductance values (Fig. 6 E G). We observed tat te presence of HCNFast cannels reduced te spike-pase coerence compared to te presence of HCN cannels (Fig. 6 E and F), but wit coerence values iger tan tose obtained wit te passive case (Fig. 6F). Furter, te amount of HCNFastinduced reduction in spike-pase coerence was iger for lower conductance values tan for iger conductance values (Fig. 6F). Finally, te lag in teta pase of spikes introduced by HCN cannels was reduced in te presence of HCNFast cannels at lower HCN/HCNFast conductances, wereas wen te conductance value increased, tis lag remained intact (Fig. 6G). To furter assess te role of te (de)activation time constant of HCN cannels in regulating LFPs and spike pase, we increased te (de)activation time constant to 100 ms (HCNSlow) (Fig. S9A) and matced neuronal excitability at 8 Hz (Fig. S9B). Tis resulted in an increase in te impedance amplitude but at a lower resonance frequency (Fig. S9C) (28). As a direct consequence of te nonmonotonic canges in inductive pase lead wit increase in te time constant (28), te LFP pase lead introduced by HCN cannels across different strata was partially reversed by teir slower counterparts but not as muc as by teir faster counterparts (Fig. S9 D and E). Te spike pase obtained wit HCNSlow cannels, owever, exibited a lag tat was larger tan tat in te presence of HCN cannels, owing to te reduced impedance at te soma in te presence of te altered HCNSlow cannels (Fig. S9F). Finally, te spike-pase coerence acieved wit HCNSlow cannels was lower tan tat in te presence of HCN cannels (Fig. S9 G I). How would neuronal spike pases and teir dependencies on HCN/HCNFast cannels cange if we used LFP from a stratum oter tan te SP for computing spike pases? We noted a significant sift in te spike pase, apart from canges in te actual value of HCN-cannel induced pase lag in te spike pase, wen we used LFPs from oter strata as te reference (Fig. S10). Altoug tese results empasize te importance of electrode location wit reference to te source-sink dipole for spike-pase computation, our overall conclusions on HCN cannels and teir inductive components remained intact. Next, to confirm te validity of our results for a frequency oter tan 8 Hz, we repeated our experiments (Figs. 2 and 6) wit 5-Hz modulated synaptic inputs (Fig. S11) and found tese results to be consistent wit previous results. In summary, tese results suggested tat te inductive lead induced by te presence of HCN cannels and its regulation of transmembrane currents across te dendritic arbor critically contributed to te LFP pase lead, spike-pase lag, and enancement of spike-pase coerence, especially at lower values of HCN conductance. Discussion Te prime conclusion of our study is tat HCN cannels can significantly alter LFP pase and te associated teta-pase of neuronal firing, apart from enancing spike-pase coerence. Importantly, we found tat te ability of HCN cannels to introduce an inductive pase lead in intracellular voltage responses to teta-modulated synaptic currents played a significant role in altering LFP and spike pases. Tese, in conjunction wit our results on te implications for altering te kinetic and voltagedependent properties, togeter empasize a critical role for te NEUROSCIENCE PNAS PLUS Sina and Narayanan PNAS Publised online April 13, 2015 E2213

8 Fig. 6. Te inductive component of HCN cannels played a critical role in regulating LFP and spike pase as well as spike-pase jitter. (A) SP LFP traces (1 s) for different g Base values (H) and corresponding g Base F values (HF), sown wit reference to te excitatory input θ (A, Bottom). (B) LFP pase (wit reference to excitatory input θ; mean± SEM, 10 cycles) across cycles plotted for tree different values of g Base and corresponding values of g Base F.PAS,gBase = g Base F = 0 μs/cm 2 ; H, HCN cannels inserted wit te depicted value of g Base ; HF, faster HCN cannels inserted wit te depicted value of g Base F.(C) Normalized LFP traces (1 s) for different strata for g Base = 160 μs/cm 2 and g Base F = 65 μs/cm 2, wit reference to excitatory input θ. (D) For eac recording site (C), quantification of te LFP pase wit reference to te excitatory input θ (mean ± SEM, 10 cycles) for g Base = g Base F = 0 μs/cm 2 (PAS), g Base = 160 μs/cm 2 (H), and its faster counterpart g Base F = 65 μs/cm 2 (HF). (E) Population spike-time istograms (1 s) wit corresponding SP LFP for g Base = g Base F = 0 μs/cm 2 (PAS), g Base = 55 μs/cm 2 (H), and its faster counterpart g Base F = 12 μs/cm 2 (HF). (F) Spike-pase coerence, C Φ, plotted as functions of g Base and g Base F.(G) Cycle-matced difference (8 cycles; mean ± SEM) between te spike pase for te said g Base and 160 μs/cm 2 and g Base F spike-pase difference). (H) or te corresponding g Base F (HF) value and te case were g Base = 65 μs/cm 2 ). (B) *P < 0.05, **P < (Wilcoxon signed-rank test). (G) **P < (Student s t test on te null ypotesis of no = 0 μs/cm 2 (n = 24 neurons for g Base = 85 μs/cm 2 unique voltage dependence and kinetic properties of HCN cannels in regulating LFP and spike pases. Apart from demonstrating tat our conclusions on HCN cannels were robust to canges in several model parameters, we also report tat synaptic scaling and excitatory inibitory pase difference could alter LFPs and spike pase, but not spike-pase coerence. Pase Coding and Somatodendritic Ion Cannels. LFPs ave been referred to as te internal clocks for several neuronal circuits, and groups of cells ave been sown to syncronize teir spike timings to specific pases of te LFP, tus forming cell assemblies. Te temporal/pase coding scema revolves around te fact tat LFPs and specific timings of te spike wit reference to tese LFPs can convey information about te inputs tat drove te spike, wit beavioral relevance suc as te animal s spatial location (4, 33, 35, 44). In tis context, our results establis tat te existence of and various forms of plasticity in HCN cannels and AMPA and GABA A receptors could regulate te emergence and te evolution of te pase code in response to beavioral states, troug state dependence and neuromodulation of teir properties. Te differences in spike pase introduced by plasticity/modulation in eiter HCN cannels or te synaptic conductances are significant and large, spanning up to around 100 (Figs. 2 D and G; 3F and J; 4C, F, and I;5D; and 6G). From te pase-coding perspective, especially wit reference to teta gamma coupling and gamma cell assemblies, te pysiological and beavioral implications for suc large differences in spike pases are enormous (4, 32, 33, 35, 44, 48 50). Togeter, our results argue for te incorporation of subtresold-activated ion cannels, teir subcellular gradients, and teir plasticity into te pysiological and patological studies on LFPs, pase coding, and neuronal cell assemblies. Our predictions on spike-pase coerence and about sifts in spike pases wit reference to E Sina and Narayanan

9 LFPs could be experimentally tested by introducing specific parmacological agents (tat intracellularly alter cannel properties) troug an in vivo wole-cell patc pipette, in a configuration tat involves awake-beaving extracellular and wole-cell recordings (51). Tese very conclusions also imply tat a group of cells can undergo specific forms of plasticity to syncronize teir spike pases, tus configuring a new cell assembly. Apart from global canges, our results delineate specific roles for pysiologically plausible localized canges in cannel densities in altering te pase code and in allowing a neuron to switc cell assemblies by altering its spike pase, witout significantly altering te external oscillator or its readout, te LFP (Fig. 5). Additionally, given suc a multitude of mecanisms tat can reconfigure pase codes and cell assemblies, tese results also empasize tat te interpretation of experiments wit parmacological agents to block cannels or wit transgenic animals lacking genes encoding cannel subunits sould be done wit utmost care. Suc interpretation sould account for our observation tat upon blockade of cannel currents, not only do spike timings cange, but also te local reference LFP pase could cange, tus resulting in a different reference point for te local temporal code. Finally, it is important tat te interpretation of results wit knockouts incorporates te differential impact of all compensatory mecanisms (52, 53) on LFPs and spike generation before attributing a specific role for a cannel/subunit. Limitations of te Analyses and Future Directions. First, similar to several previous studies (7, 8), our model assumes a omogenous and resistive extracellular field in arriving at te local field potentials. Altoug biopysical and experimental studies point to nonresistive components and nonomogeneities in te extracellular fields, te impacts of tese nonomogeneities and nonresistive components are largely confined to iger frequencies (54 56). From tese analyses, it stands to reason tat te resistive and omogeneity assumptions are not debilitating for te conclusions drawn in our study were te range of frequencies is muc lower, in te teta range. Second, our study does not incorporate epaptic coupling across neurons in te overall analysis (4, 57). Altoug it is clear tat tese epaptic interactions, despite teir small-amplitude deflections, can entrain action potentials at lower frequencies (57), te impact of suc interactions on our conclusions is expected to be minimal. Te reasons beind tis are treefold: First, te presence of HCN cannels did not significantly alter te amplitude of te LFPs (Figs. 2 and 3). Because volume conduction critically relies on te amplitude of te field signal, te impact of epaptic interactions is not expected to cange significantly in te presence or absence of HCN cannels. Second, te open-field organization of ippocampal pyramidal neurons ensures tat te somato-dendritic gradient in HCN cannels is aligned wit te source-sink dipole along te neuronal axis. If epaptic coupling were present under a scenario were suc alignment was absent, adjacent compartments from different neurons wit uge differences in HCN-cannel density would interact epaptically, resulting in possible nullification of te impact of HCN cannels on te LFP. However, given te alignment, our conclusions are not expected to cange even in te presence of an additional distance-dependent epaptic coupling across neurons wit teir compartments endowed wit similar gradients in HCN-cannel density. Tird, wit reference to spike-pase coerence, altoug te presence of epaptic interactions migt furter enance te spike-pase coerence across neurons (57), our results are entirely related to te presence or absence of HCN cannels. Specifically, te enanced spike-pase coerence observed in te presence of HCN cannels is a direct consequence of te ability of tese cannels to reduce te temporal window for spikegenerating coincidence detection (38, 47) and is expected to be present even wit epaptic coupling in place. Finally, our study was limited to HCN cannels. However, our results call for te necessity to incorporate te wide array of somatodendritic subtresold-activated cannels (e.g., A-type K +, T-type Ca 2+ ), given teir ability to regulate several aspects of neuronal pysiology (15 17, 21, 58 62). Future studies sould terefore focus on ow te localization and targeting of tese cannel types are maintained across te somatodendritic arbor toward location-dependent regulation of LFPs, spike pases, and teir coerence. In tis context, it would be interesting to ask weter analogous LFPs and spike pases, and tereby analogous pase codes and cell assemblies, can be acieved wit different cannel/receptor combinations (58 60, 63). Models and Metods A detailed version of te simulated models and te metods employed is provided in SI Models and Metods. Briefly, we employed a forward modeling sceme wit morpologically realistic neuronal models toward understanding te impact of active dendritic conductances on LFPs and spike teta pase of ippocampal pyramidal neurons. LFPs were constructed troug line-source approximation (7, 8, 30, 31) of neuronal compartments from 440 (or 1,797 or 11,297; Fig. 3) morpologically realistic CA1 pyramidal neuron models. Two 3D reconstructions of a CA1 pyramidal neuron (n123, ri04) obtained from NeuroMorpo.Org (64 66) were employed (Fig. 1A and Fig. S3A) and were compartmentalized into 1,247 (n123)/1,351 (ri04) compartments. Somatodendritic passive, active, and synaptic parameters were set to matc experimental data from somatodendritic recordings (26, 28, 29, 67, 68), wit kinetics for te cannels adopted from cell-attaced recordings from soma and dendrites of ippocampal pyramidal neurons (25, 62, 69, 70). Specifically, te parameters were set to matc normalization of somatic excitatory postsynaptic potential (EPSP) amplitudes, functional maps in input resistance, local and transfer resonance frequencies, and te syncronization frequency (Fig. 1 B E for n123 and Fig. S3 B E for ri04). To account for te variability in teta-frequency LFP and in spike pase as te animal navigates in an arena (51), balanced rytmic ig-conductance state at teta frequency (default 8 Hz) was introduced troug systematic randomization of te spatiotemporal activation of excitatory and inibitory synapses distributed across te somatodendritic arbor. A pase difference (default 60 ) was introduced in te perisomatic inibitory inputs wit reference to te predominantly dendritic excitatory inputs (34, 71, 72). All simulations were performed in te NEURON simulation environment (73) wit an integration time constant of 25 μs. Computation of line-source approximated (LSA) currents was performed using MATLAB R2011a (Matworks), and analyses of LFP and spike pases were performed using MATLAB R2011a and Igor Pro (Wavemetrics). All statistical tests were performed using te R statistical package ( ACKNOWLEDGMENTS. Te autors tank Dr. Daniel Jonston and members of te cellular neuropysiology laboratory for elpful discussions. Tis work was supported by te International Human Frontier Science Program Organization (R.N.), te Department of Biotecnology troug te United States India brain researc collaborative program (R.N.), te Indian Institute of Science (R.N. and M.S.), and te Microsoft Researc India PD Fellowsip Award (to M.S.). NEUROSCIENCE PNAS PLUS 1. Katzner S, et al. (2009) Local origin of field potentials in visual cortex. Neuron 61(1): Xing D, Ye CI, Sapley RM (2009) Spatial spread of te local field potential and its laminar variation in visual cortex. J Neurosci 29(37): Kajikawa Y, Scroeder CE (2011) How local is te local field potential? Neuron 72(5): Buzsáki G, Anastassiou CA, Koc C (2012) Te origin of extracellular fields and currents EEG, ECoG, LFP and spikes. Nat Rev Neurosci 13(6): Lindén H, et al. (2011) Modeling te spatial reac of te LFP. 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