Understanding effects on excitability of simulated <Emphasis Type="Italic">I</Emphasis><Subscript>h</Subscript> modulation in simple neuronal models

The hyperpolarization-activated, inward, mixed cation current, I _h, appears in a wide variety of cells in the nervous system, contributes to diverse neuronal properties, and is up-regulated by a number of important neurotransmitters. Up-regulation of I _h is usually associated with an excitability-enhancing depolarization of resting membrane potential and an excitability-depressing shunting effect caused by a decrease in input resistance. In order to gain a better understanding of the interaction of these effects and their influence on excitability with I _h modulation, we systematically analyze changes in neuronal properties associated with excitability during I _h modulation in simplified, yet, biophysical neuron models based on a hippocampal pyramidal neuron. We simulate I _h modulation by varying both its maximal conductance and its half-activation voltage, mimicking the effects of cAMP-linked neurotransmitters, through ranges of physiologically realistic parameter regimes. Of particular interest is the contribution of the different effects of I _h up-regulation when membrane potentials are held at common levels and neuronal excitability is probed. Our modeling results suggest that, although holding potentials at common levels may compensate for changes in resting membrane potentials, this protocol may exaggerate the excitability-depressing influences of changes in input resistances with I _h up-regulation.     

Ion Channel Gradients in the Apical Tuft Region of CA1 Pyramidal Neurons

Dendritic ion channels play a critical role in shaping synaptic input and are fundamentally important for synaptic integration and plasticity. In the hippocampal region CA1, somato-dendritic gradients of AMPA receptors and the hyperpolarization-activated cation conductance (I_h) counteract the effects of dendritic filtering on the amplitude, time-course, and temporal integration of distal Schaffer collateral (SC) synaptic inputs within stratum radiatum (SR). While ion channel gradients in CA1 distal apical trunk dendrites within SR have been well characterized, little is known about the patterns of ion channel expression in the distal apical tuft dendrites within stratum lacunosum moleculare (SLM) that receive distinct input from the entorhinal cortex via perforant path (PP) axons. Here, we measured local ion channels densities within these distal apical tuft dendrites to determine if the somato-dendritic gradients of I_h and AMPA receptors extend into distal tuft dendrites. We also determined the densities of voltage-gated sodium channels and NMDA receptors. We found that the densities of AMPA receptors, I_h, and voltage-gated sodium channels are similar in tuft dendrites in SLM when compared with distal apical dendrites in SR, while the ratio of NMDA receptors to AMPA receptors increases in tuft dendrites relative to distal apical dendrites within SR. These data indicate that the somato-dendritic gradients of I_h and AMPA receptors in apical dendrites do not extend into the distal tuft, and the relative densities of voltage-gated sodium channels and NMDA receptors are poised to support nonlinear integration of correlated SC and PP input.     

Roles of I<Subscript>A</Subscript> and morphology in action potential propagation in CA1 pyramidal cell dendrites

Dendrites of CA1 pyramidal cells of the hippocampus, along with those of a wide range of other cell types, support active backpropagation of axonal action potentials. Consistent with previous work, recent experiments demonstrating that properties of synaptic plasticity are different for distal synapses, suggest an important functional role of bAPs, which are known to be prone to failure in distal locations. Using conductance-based models of CA1 pyramidal cells, we show that underlying “traveling wave attractors” control action potential propagation in the apical dendrites. By computing these attractors, we dissect and quantify the effects of I_A channels and dendritic morphology on bAP amplitudes. We find that non-uniform activation properties of I_A can lead to backpropagation failure similar to that observed experimentally in these cells. Amplitude of forward propagation of dendritic spikes also depends strongly on the activation dynamics of I_A. I_A channel properties also influence transients at dendritic branch points and whether or not propagation failure results. The branching pattern in the distal apical dendrites, combined with I_A channel properties in this region, ensure propagation failure in the apical tuft for a large range of I_A conductance densities. At the same time, these same properties ensure failure of forward propagating dendritic spikes initiated in the distal tuft in the absence of some form of cooperativity of synaptic activation. Electronic supplemary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Action Editor: Alain Destexhe     

Glutamate-Bound NMDARs Arising from In Vivo-like Network Activity Extend Spatio-temporal Integration in a L5 Cortical Pyramidal Cell Model

In vivo, cortical pyramidal cells are bombarded by asynchronous synaptic input arising from ongoing network activity. However, little is known about how such ‘background’ synaptic input interacts with nonlinear dendritic mechanisms. We have modified an existing model of a layer 5 (L5) pyramidal cell to explore how dendritic integration in the apical dendritic tuft could be altered by the levels of network activity observed in vivo. Here we show that asynchronous background excitatory input increases neuronal gain and extends both temporal and spatial integration of stimulus-evoked synaptic input onto the dendritic tuft. Addition of fast and slow inhibitory synaptic conductances, with properties similar to those from dendritic targeting interneurons, that provided a ‘balanced’ background configuration, partially counteracted these effects, suggesting that inhibition can tune spatio-temporal integration in the tuft. Excitatory background input lowered the threshold for NMDA receptor-mediated dendritic spikes, extended their duration and increased the probability of additional regenerative events occurring in neighbouring branches. These effects were also observed in a passive model where all the non-synaptic voltage-gated conductances were removed. Our results show that glutamate-bound NMDA receptors arising from ongoing network activity can provide a powerful spatially distributed nonlinear dendritic conductance. This may enable L5 pyramidal cells to change their integrative properties as a function of local network activity, potentially allowing both clustered and spatially distributed synaptic inputs to be integrated over extended timescales.     

Mechanism and Function of Mixed-Mode Oscillations in Vibrissa Motoneurons

Vibrissa motoneurons in the facial nucleus innervate the intrinsic and extrinsic muscles that move the whiskers. Their intrinsic properties affect the way they process fast synaptic input from the vIRT and Bötzinger nuclei together with serotonergic neuromodulation. In response to constant current (I _app) injection, vibrissa motoneurons may respond with mixed mode oscillations (MMOs), in which sub-threshold oscillations (STOs) are intermittently mixed with spikes. This study investigates the mechanisms involved in generating MMOs in vibrissa motoneurons and their function in motor control. It presents a conductance-based model that includes the M-type K⁺ conductance, g _M, the persistent Na⁺ conductance, g _NaP, and the cationic h conductance, g _h. For g _h = 0 and moderate values of g _M and g _NaP, the model neuron generates STOs, but not MMOs, in response to I _app injection. STOs transform abruptly to tonic spiking as the current increases. In addition to STOs, MMOs are generated for g _h>0 for larger values of I _app; the I _app range in which MMOs appear increases linearly with g _h. In the MMOs regime, the firing rate increases with I _app like a Devil''s staircase. Stochastic noise disrupts the temporal structure of the MMOs, but for a moderate noise level, the coefficient of variation (CV) is much less than one and varies non-monotonically with I _app. Furthermore, the estimated time period between voltage peaks, based on Bernoulli process statistics, is much higher in the MMOs regime than in the tonic regime. These two phenomena do not appear when moderate noise generates MMOs without an intrinsic MMO mechanism. Therefore, and since STOs do not appear in spinal motoneurons, the analysis can be used to differentiate different MMOs mechanisms. MMO firing activity in vibrissa motoneurons suggests a scenario in which moderate periodic inputs from the vIRT and Bötzinger nuclei control whisking frequency, whereas serotonergic neuromodulation controls whisking amplitude.     

Branching dendrites with resonant membrane: a “sum-over-trips” approach

Dendrites form the major components of neurons. They are complex branching structures that receive and process thousands of synaptic inputs from other neurons. It is well known that dendritic morphology plays an important role in the function of dendrites. Another important contribution to the response characteristics of a single neuron comes from the intrinsic resonant properties of dendritic membrane. In this paper we combine the effects of dendritic branching and resonant membrane dynamics by generalising the “sum-over-trips” approach (Abbott et al. in Biol Cybernetics 66, 49–60 1991). To illustrate how this formalism can shed light on the role of architecture and resonances in determining neuronal output we consider dual recording and reconstruction data from a rat CA1 hippocampal pyramidal cell. Specifically we explore the way in which an I _h current contributes to a voltage overshoot at the soma.     

Dynamic modification of dendritic cable properties and synaptic transmission by voltage-gated potassium channels

Computer simulations of a dendrite possessing voltage-sensitive potassium conductances were used to determine the effects of these conductances on synaptic transmission and on the propagation of synaptic signals within the dendritic tree. Potassium conductances had two principal effects on voltage transients generated by current injections or synaptic conductances. Locally (near the source of the transient), voltage-gated potassium channels produced a potassium shunt current that reduced the amplitude of voltage transients generated by depolarizing currents. This shunt current increased as the amplitude of the depolarizing transient increased and so acted to prevent large synaptic transients from reaching levels that would saturate due to a reduction in driving force. In the presence of rapidly activating potassium currents, excitatory synapses produced larger synaptic currents that were more linearly related to synaptic conductance, but these produced smaller voltage transients. The maximum amplitudes of the voltage transients were limited by the voltage sensitivity of the K⁺ conductance and the rate at which it could activate. Sufficiently rapid synaptic currents could outrun the K⁺ conductance and thus achieve high local peak amplitudes. These effects of K⁺ conductances were unrelated to whether they were located on dendrites or not, being related only to their proximity to the source of synaptic current. The second class of effects of K⁺ conductances depended on their alteration of the electrotonic structure of the postsynaptic cell and so were observed only when they were located on postsynaptic dendrites. Voltage-gated K⁺ conductances produced voltage-dependent electrotonic expansion of depolarized dendrites, which had the effect of isolating synaptic inputs on depolarized dendrites from events on the rest of the neuron. Thus, synapses on the same dendrite interacted destructively to a degree much greater than that expected from the classical driving force nonlinearity. Synapses located proximally to a depolarized dendritic region were less effected than those located distally, and the range of the nonlinear interaction between synapses was dependent on the kinetics of activation and deactivation of the conductance. When present in conjunction with rapidly activating dendritic sodium conductance, the potassium conductance sharpened the requirement for spatial and temporal coincidence to produce synaptic boosting by inward currents, and suppressed out-of-synchrony synaptic inputs.     

Processing of retinal signals in normal and HCN deficient mice

This study investigates the role of two different HCN channel isoforms in the light response of the outer retina. Taking advantage of HCN-deficient mice models and of in vitro (patch-clamp) and in vivo (ERG) recordings of retinal activity we show that HCN1 and HCN2 channels are expressed at distinct retinal sites and serve different functions. Specifically, HCN1 operate mainly at the level of the photoreceptor inner segment from where, together with other voltage sensitive channels, they control the time course of the response to bright light. Conversely, HCN2 channels are mainly expressed on the dendrites of bipolar cells and affect the response to dim lights. Single cell recordings in HCN1^−/− mice or during a pharmacological blockade of I_h show that, contrary to previous reports, I_kx alone is able to generate the fast initial transient in the rod bright flash response. Here we demonstrate that the relative contribution of I_h and I_kx to the rods'' temporal tuning depends on the membrane potential. This is the first instance in which the light response of normal and HCN1- or HCN2-deficient mice is analyzed in single cells in retinal slice preparations and in integrated full field ERG responses from intact animals. This comparison reveals a high degree of correlation between single cell current clamp data and ERG measurements. A novel picture emerges showing that the temporal profile of the visual response to dim and bright luminance changes is separately determined by the coordinated gating of distinct voltage dependent conductances in photoreceptors and bipolar cells.     

Hyperpolarization-Activated Current (Ih) Is Reduced in Hippocampal Neurons from Gabra5?/? Mice

Changes in the expression of γ-aminobutyric acid type A (GABA_A) receptors can either drive or mediate homeostatic alterations in neuronal excitability. A homeostatic relationship between α5 subunit-containing GABA_A (α5GABA_A) receptors that generate a tonic inhibitory conductance, and HCN channels that generate a hyperpolarization-activated cation current (I_h) was recently described for cortical neurons, where a reduction in I_h was accompanied by a reciprocal increase in the expression of α5GABA_A receptors resulting in the preservation of dendritosomatic synaptic function. Here, we report that in mice that lack the α5 subunit gene (Gabra5−/−), cultured embryonic hippocampal pyramidal neurons and ex vivo CA1 hippocampal neurons unexpectedly exhibited a decrease in I_h current density (by 40% and 28%, respectively), compared with neurons from wild-type (WT) mice. The resting membrane potential and membrane hyperpolarization induced by blockade of I_h with ZD-7288 were similar in cultured WT and Gabra5−/− neurons. In contrast, membrane hyperpolarization measured after a train of action potentials was lower in Gabra5−/− neurons than in WT neurons. Also, membrane impedance measured in response to low frequency stimulation was greater in cultured Gabra5−/− neurons. Finally, the expression of HCN1 protein that generates I_h was reduced by 41% in the hippocampus of Gabra5−/− mice. These data indicate that loss of a tonic GABAergic inhibitory conductance was followed by a compensatory reduction in I_h. The results further suggest that the maintenance of resting membrane potential is preferentially maintained in mature and immature hippocampal neurons through the homeostatic co-regulation of structurally and biophysically distinct cation and anion channels.     

Filamin A Promotes Dynamin-dependent Internalization of Hyperpolarization-activated Cyclic Nucleotide-gated Type 1 (HCN1) Channels and Restricts Ih in Hippocampal Neurons

The actin-binding protein filamin A (FLNa) regulates neuronal migration during development, yet its roles in the mature brain remain largely obscure. Here, we probed the effects of FLNa on the regulation of ion channels that influence neuronal properties. We focused on the HCN1 channels that conduct I_h, a hyperpolarization-activated current crucial for shaping intrinsic neuronal properties. Whereas regulation of HCN1 channels by FLNa has been observed in melanoma cell lines, its physiological relevance to neuronal function and the underlying cellular pathways that govern this regulation remain unknown. Using a combination of mutational, pharmacological, and imaging approaches, we find here that FLNa facilitates a selective and reversible dynamin-dependent internalization of HCN1 channels in HEK293 cells. This internalization is accompanied by a redistribution of HCN1 channels on the cell surface, by accumulation of the channels in endosomal compartments, and by reduced I_h density. In hippocampal neurons, expression of a truncated dominant-negative FLNa enhances the expression of native HCN1. Furthermore, acute abrogation of HCN1-FLNa interaction in neurons, with the use of decoy peptides that mimic the FLNa-binding domain of HCN1, abolishes the punctate distribution of HCN1 channels in neuronal cell bodies, augments endogenous I_h, and enhances the rebound-response (“voltage-sag”) of the neuronal membrane to transient hyperpolarizing events. Together, these results support a major function of FLNa in modulating ion channel abundance and membrane trafficking in neurons, thereby shaping their biophysical properties and function.     

Functional contributions of HCN channels in the primary auditory neurons of the mouse inner ear

The hyperpolarization-activated current, I_h, is carried by members of the Hcn channel family and contributes to resting potential and firing properties in excitable cells of various systems, including the auditory system. I_h has been identified in spiral ganglion neurons (SGNs); however, its molecular correlates and their functional contributions have not been well characterized. To investigate the molecular composition of the channels that carry I_h in SGNs, we examined Hcn mRNA harvested from spiral ganglia of neonatal and adult mice using quantitative RT-PCR. The data indicate expression of Hcn1, Hcn2, and Hcn4 subunits in SGNs, with Hcn1 being the most highly expressed at both stages. To investigate the functional contributions of HCN subunits, we used the whole-cell, tight-seal technique to record from wild-type SGNs and those deficient in Hcn1, Hcn2, or both. We found that HCN1 is the most prominent subunit contributing to I_h in SGNs. Deletion of Hcn1 resulted in reduced conductance (G_h), slower activation kinetics (τ_fast), and hyperpolarized half-activation (V_1/2) potentials. We demonstrate that I_h contributes to SGN function with depolarized resting potentials, depolarized sag and rebound potentials, accelerated rebound spikes after hyperpolarization, and minimized jitter in spike latency for small depolarizing stimuli. Auditory brainstem responses of Hcn1-deficient mice showed longer latencies, suggesting that HCN1-mediated I_h is critical for synchronized spike timing in SGNs. Together, our data indicate that I_h contributes to SGN membrane properties and plays a role in temporal aspects of signal transmission between the cochlea and the brain, which are critical for normal auditory function.     

Novel HCN2 Mutation Contributes to Febrile Seizures by Shifting the Channel's Kinetics in a Temperature-Dependent Manner

Hyperpolarization-activated cyclic nucleotide-gated (HCN) channel-mediated currents, known as I _h, are involved in the control of rhythmic activity in neuronal circuits and in determining neuronal properties including the resting membrane potential. Recent studies have shown that HCN channels play a role in seizure susceptibility and in absence and limbic epilepsy including temporal lobe epilepsy following long febrile seizures (FS). This study focused on the potential contributions of abnormalities in the HCN2 isoform and their role in FS. A novel heterozygous missense mutation in HCN2 exon 1 leading to p.S126L was identified in two unrelated patients with FS. The mutation was inherited from the mother who had suffered from FS in a pedigree. To determine the effect of this substitution we conducted whole-cell patch clamp electrophysiology. We found that mutant channels had elevated sensitivity to temperature. More specifically, they displayed faster kinetics at higher temperature. Kinetic shift by change of temperature sensitivity rather than the shift of voltage dependence led to increased availability of I _h in conditions promoting FS. Responses to cyclic AMP did not differ between wildtype and mutant channels. Thus, mutant HCN2 channels cause significant cAMP-independent enhanced availability of I _h during high temperatures, which may contribute to hyperthermia-induced neuronal hyperexcitability in some individuals with FS.     

Quantitative description of sodium and potassium currents and computed action potentials in Myxicola giant axons

All analysis of the sodium and potassium conductances of Myxicola giant axons was made in terms of the Hodgkin-Huxley m, n, and h variables. The potassium conductance is proportional to n². In the presence of conditioning hyperpolarization, the delayed current translates to the right along the time axis. When this effect was about saturated, the potassium conductance was proportional to n³. The sodium conductance was described by assuming it proportional to m³h. There is a range of potentials for which τ_h and h_∞ values fitted to the decay of the sodium conductance may be compared to those determined from the effects of conditioning pulses. τ_h values determined by the two methods do not agree. A comparison of h_∞ values determined by the two methods indicated that the inactivation of the sodium current is not governed by the Hodgkin-Huxley h variable. Computer simulations show that action potentials, threshold, and subthreshold behavior could be accounted for without reference to data on the effects of initial conditions. However, recovery phenomena (refractoriness, repetitive discharges) could be accounted for only by reference to such data. It was concluded that the sodium conductance is not governed by the product of two independent first order variables.     

Vestibular integrator neurons have quadratic functions due to voltage dependent conductances

The nonlinear properties of the dendrites of the prepositus hypoglossi nucleus (PHN) neurons are essential for the operation of the vestibular neural integrator that converts a head velocity signal to one that controls eye position. A novel system of frequency probing, namely quadratic sinusoidal analysis (QSA), was used to decode the intrinsic nonlinear behavior of these neurons under voltage clamp conditions. Voltage clamp currents were measured at harmonic and interactive frequencies using specific nonoverlapping stimulation frequencies. Eigenanalysis of the QSA matrix reduces it to a remarkably compact processing unit, composed of just one or two dominant components (eigenvalues). The QSA matrix of rat PHN neurons provides signatures of the voltage dependent conductances for their particular dendritic and somatic distributions. An important part of the nonlinear response is due to the persistent sodium conductance (g_NaP), which is likely to be essential for sustained effects needed for a neural integrator. It was found that responses in the range of 10 mV peak to peak could be well described by quadratic nonlinearities suggesting that effects of higher degree nonlinearities would add only marginal improvement. Therefore, the quadratic response is likely to sufficiently capture most of the nonlinear behavior of neuronal systems except for extremely large synaptic inputs. Thus, neurons have two distinct linear and quadratic functions, which shows that piecewise linear?+?quadratic analysis is much more complete than just piecewise linear analysis; in addition quadratic analysis can be done at a single holding potential. Furthermore, the nonlinear neuronal responses contain more frequencies over a wider frequency band than the input signal. As a consequence, they convert limited amplitude and bandwidth input signals to wider bandwidth and more complex output responses. Finally, simulations at subthreshold membrane potentials with realistic PHN neuron models suggest that the quadratic functions are fundamentally dominated by active dendritic structures and persistent sodium conductances.     

The cost of linearization

Linear additivity of synaptic input is a pervasive assumption in computational neuroscience, and previously Bernander et al. (Journal of Neurophysiology 72:2743–2753, 1994) point out that the sublinear additivity of a passive neuronal model can be linearized with voltage-dependent currents. Here we re-examine this perspective in light of more recent findings and issues. Based on in vivo intracellular recordings, three voltage-dependent conductances seem to be of interest for pyramidal cells of the forebrain: two of them are amplifying, I _NaP and I _h ; and one of them is attenuating, I _A . Based on particular I-V characteristics reported in the literature, each of these three voltage-dependent currents linearizes a particular range of synaptic excitation. Computational simulations use a steady-state, one-compartment model. They establish maximal linear ranges, where supralinear effects—due to adding too much of any one conductance—limit these ranges. Specific, carefully selected pairwise combinations of these currents can linearize larger ranges than either current alone. In terms of parameters, the steady-state I-V characteristics of each current are critical. On the other hand, the relationships between the results here and resting conductance to ground, synaptic conductance, and number of active synapses are simple and easily scaled; thus in regard to these three latter dependences, the results here are easily generalized. Finally, to improve our understanding of evolved function, the relative metabolic costs of linearization are quantified. In one case, there is a clear preference arising from this cost consideration (a particular I _h , I _NaP pairing is less costly compared to a particular I _A , I _NaP pairing that produces an equivalent, linearized range). However in other cases, a preference will depend on the required range; but in any event, the largest linearized range observed here (28 mV), from a combination of I _h and I _A , is significantly more costly than the 20 mV range that the I _h , I _NaP pair produces.     

Neuromodulation to the Rescue: Compensation of Temperature-Induced Breakdown of Rhythmic Motor Patterns via Extrinsic Neuromodulatory Input

Stable rhythmic neural activity depends on the well-coordinated interplay of synaptic and cell-intrinsic conductances. Since all biophysical processes are temperature dependent, this interplay is challenged during temperature fluctuations. How the nervous system remains functional during temperature perturbations remains mostly unknown. We present a hitherto unknown mechanism of how temperature-induced changes in neural networks are compensated by changing their neuromodulatory state: activation of neuromodulatory pathways establishes a dynamic coregulation of synaptic and intrinsic conductances with opposing effects on neuronal activity when temperature changes, hence rescuing neuronal activity. Using the well-studied gastric mill pattern generator of the crab, we show that modest temperature increase can abolish rhythmic activity in isolated neural circuits due to increased leak currents in rhythm-generating neurons. Dynamic clamp-mediated addition of leak currents was sufficient to stop neuronal oscillations at low temperatures, and subtraction of additional leak currents at elevated temperatures was sufficient to rescue the rhythm. Despite the apparent sensitivity of the isolated nervous system to temperature fluctuations, the rhythm could be stabilized by activating extrinsic neuromodulatory inputs from descending projection neurons, a strategy that we indeed found to be implemented in intact animals. In the isolated nervous system, temperature compensation was achieved by stronger extrinsic neuromodulatory input from projection neurons or by augmenting projection neuron influence via bath application of the peptide cotransmitter Cancer borealis tachykinin-related peptide Ia (CabTRP Ia). CabTRP Ia activates the modulator-induced current I_MI (a nonlinear voltage-gated inward current) that effectively acted as a negative leak current and counterbalanced the temperature-induced leak to rescue neuronal oscillations. Computational modelling revealed the ability of I_MI to reduce detrimental leak-current influences on neuronal networks over a broad conductance range and indicated that leak and I_MI are closely coregulated in the biological system to enable stable motor patterns. In conclusion, these results show that temperature compensation does not need to be implemented within the network itself but can be conditionally provided by extrinsic neuromodulatory input that counterbalances temperature-induced modifications of circuit-intrinsic properties.     

Synaptic integration in dendritic trees

Most neurons have elaborate dendritic trees that receive tens of thousands of synaptic inputs. Because postsynaptic responses to individual synaptic events are usually small and transient, the integration of many synaptic responses is needed to depolarize most neurons to action potential threshold. Over the past decade, advances in electrical and optical recording techniques have led to new insights into how synaptic responses propagate and interact within dendritic trees. In addition to their passive electrical and morphological properties, dendrites express active conductances that shape individual synaptic responses and influence synaptic integration locally within dendrites. Dendritic voltage-gated Na(+) and Ca(2+) channels support action potential backpropagation into the dendritic tree and local initiation of dendritic spikes, whereas K(+) conductances act to dampen dendritic excitability. While all dendrites investigated to date express active conductances, different neuronal types show specific patterns of dendritic channel expression leading to cell-specific differences in the way synaptic responses are integrated within dendritic trees. This review explores the way active and passive dendritic properties shape synaptic responses in the dendrites of central neurons, and emphasizes their role in synaptic integration.     

Modelling intrinsic electrophysiological properties of ON and OFF retinal ganglion cells

ON and OFF retinal ganglion cells (RGCs) display differences in their intrinsic electrophysiology: OFF cells maintain spontaneous activity in the absence of any input, exhibit subthreshold membrane potential oscillations, rebound excitation and burst firing; ON cells require excitatory input to drive their activity and display none of the aforementioned phenomena. The goal of this study was to identify and characterize ionic currents that explain these intrinsic electrophysiological differences between ON and OFF RGCs. A mathematical model of the electrophysiological properties of ON and OFF RGCs was constructed and validated using published patch-clamp data from isolated intact mouse retina. The model incorporates three ionic currents hypothesized to play a role in generating behaviors that are different between ON and OFF RGCs. These currents are persistent Na⁺, I _NaP, hyperpolarization-activated, I _h, and low voltage activated Ca^2 +, I _T, currents. Using computer simulations of Hodgkin-Huxley type neuron with a single compartment model we found two distinct sets of I _NaP, I _h, I _T conductances that correspond to ON and OFF RGCs populations. Simulations indicated that special properties of I _T explain the differences in intrinsic electrophysiology between ON and OFF RGCs examined here. The modelling shows that the maximum conductance of I _T is higher in OFF than in ON cells, in agreement with recent experimental data.     

Transfer properties of neuronal dendrites with tonically activated conductances

The somatopetal current transfer was studied in the mathematical models of a reconstructed brainstem motoneuron with tonically activated excitatory synaptic inputs uniformly distributed over dendritic arborization. The soma and axon provided a constant passive leak. The extrasynaptic dendritic membrane was either passive or active (of a Hodgkin-Huxley type). The longitudinal membrane current density (per unit path length) was used as an estimate of the current transfer effectiveness of different dendritic paths. Introduction of a steady uniform voltage-independent conductance per unit membrane area simulated such a synaptic activation. This actions always produced a spatially inhomogeneous membrane depolarization decaying from the distal dendritic tips toward the soma. The reason for such an inhomogeneity was the preponderance of somatopetal over somatofugal input conductance at every site in the dendrites with sealed distal ends and a leaky somatic end. In active dendrites, partial voltage-dependent extrasynaptic conductances followed this depolarization according to their activation-inactivation kinetics. The greater the local depolarization, the greater the contribution of the non-inactivating potassium conductance to the total membrane conductance. The contribution of the inactivated sodium conductance was one order of magnitude smaller. Correspondingly, the effective equilibrium potential of the total transmembrane current became spatially inhomogeneous and shifted to the potassium equilibrium potential. In the passive dendrites, the equilibrium potential remained spatially homogeneous. Inhomogeneities of the dendritic geometry (abrupt change in the diameter and, especially, asymmetrical branching) caused characteristic perturbations in the voltage gradient, so that the path profiles of the voltage, conductances, and currents diverged. This indicated a geometry-induced separation of the dendritic paths in their transfer effectiveness. Active dendrites of the same geometry were less effective than passive ones due to the effect of the potassium conductance associated with the hyperpolarizing equilibrium potential.