Idan Segev

Dendritic asymmetry cannot account for directional responses of neurons in visual cortex

A simple model was proposed to account for the direction selectivity of neurons in the primary visual cortex, area V1. In this model, the temporal asymmetries in the summation of inhibition and excitation that produce directionality were generated by structural asymmetries in the tangential organization of the basal dendritic tree of cortical neurons. We reconstructed dendritic trees of neurons with known direction preferences and found no correlation between the small biases of a neurons dendritic morphology and its direction preference. Detailed simulations indicated that even when the electrotonic asymmetries in the dendrites were extreme, as in cortical Meynert cells, the biophysical properties of single neurons could contribute only partially to the directionality of cortical neurons.

Ion channel stochasticity may be critical in determining the reliability and precision of spike timing

The firing reliability and precision of an isopotential membrane patch consisting of a realistically large number of ion channels is investigated using a stochastic Hodgkin-Huxley (HH) model. In sharp contrast to the deterministic HH model, the biophysically inspired stochastic model reproduces qualitatively the different reliability and precision characteristics of spike firing in response to DC and fluctuating current input in neocortical neurons, as reported by Mainen & Sejnowski (1995). For DC inputs, spike timing is highly unreliable; the reliability and precision are significantly increased for fluctuating current input. This behavior is critically determined by the relatively small number of excitable channels that are opened near threshold for spike firing rather than by the total number of channels that exist in the membrane patch. Channel fluctuations, together with the inherent bistability in the HH equations, give rise to three additional experimentally observed phenomena: subthreshold oscillations in the membrane voltage for DC input, spontaneous spikes for subthreshold inputs, and missing spikes for suprathreshold inputs. We suggest that the noise inherent in the operation of ion channels enables neurons to act as smart encoders. Slowly varying, uncorrelated inputs are coded with low reliability and accuracy and, hence, the information about such inputs is encoded almost exclusively by the spike rate. On the other hand, correlated presynaptic activity produces sharp fluctuations in the input to the postsynaptic cell, which are then encoded with high reliability and accuracy. In this case, information about the input exists in the exact timing of the spikes. We conclude that channel stochasticity should be considered in realistic models of neurons.

The role of single neurons in information processing

Neurons carry out the many operations that extract meaningful information from sensory receptor arrays at the organisms periphery and translate these into action, imagery and memory. Within todays dominant computational paradigm, these operations, involving synapses, membrane ionic channels and changes in membrane potential, are thought of as steps in an algorithm or as computations. The role of neurons in these computations has evolved conceptually from that of a simple integrator of synaptic inputs until a threshold is reached and an output pulse is initiated, to a much more sophisticated processor with mixed analog-digital logic and highly adaptive synaptic elements.

Reconstruction and Simulation of Neocortical Microcircuitry

UNLABELLED We present a first-draft digital reconstruction of the microcircuitry of somatosensory cortex of juvenile rat. The reconstruction uses cellular and synaptic organizing principles to algorithmically reconstruct detailed anatomy and physiology from sparse experimental data. An objective anatomical method defines a neocortical volume of 0.29 ± 0.01 mm(3) containing ~31,000 neurons, and patch-clamp studies identify 55 layer-specific morphological and 207 morpho-electrical neuron subtypes. When digitally reconstructed neurons are positioned in the volume and synapse formation is restricted to biological bouton densities and numbers of synapses per connection, their overlapping arbors form ~8 million connections with ~37 million synapses. Simulations reproduce an array of in vitro and in vivo experiments without parameter tuning. Additionally, we find a spectrum of network states with a sharp transition from synchronous to asynchronous activity, modulated by physiological mechanisms. The spectrum of network states, dynamically reconfigured around this transition, supports diverse information processing strategies. PAPERCLIP VIDEO ABSTRACT.

Subthreshold oscillations and resonant frequency in guinea‐pig cortical neurons: physiology and modelling.

1. Intracellular recordings were made from neurons in slices from guinea‐pig frontal cortex. In 50% of the cells, sustained subthreshold voltage oscillations were evoked by long (> 6 s) depolarizing pulses. The peak‐to‐peak amplitude of these oscillations was less than 5 mV and the frequency was voltage dependent, increasing with depolarization from 4 (near rest) to 20 Hz (at 30 mV depolarization). 2. The impedance‐frequency relationship of both oscillating and non‐oscillating cells was studied by intracellular injection of sinusoidal current with linearly changing frequency. In most cells, a peak in the impedance magnitude (resonant behaviour) was observed at depolarized levels. The frequency of the peak impedance (peak frequency) increased with depolarization from 3 (near rest) to 15 Hz (at 30 mV depolarization). 3. Application of TTX (10(‐6) M) significantly decreased the impedance magnitude near the peak frequency. The subthreshold oscillations, however, as well as the action potentials, were fully blocked by TTX. On the other hand, TEA (15 mM) and Cs+ (5 mM) abolished both the subthreshold oscillations and the resonant behaviour. Replacing Ca2+ with Co2+ (5 mM) or Ni2+ (1 mM) did not abolish the subthreshold oscillations. The peak in the frequency‐response curve was only slightly reduced. 4. An isopotential membrane model, consisting of a leak current, a fast persistent sodium current, a slow non‐inactivating potassium current (with the kinetics of the M‐current) and membrane capacitance, is sufficient to produce both voltage oscillations and resonant behaviour. The kinetics of the K+ current by itself is sufficient to produce resonance behaviour. The Na+ current amplifies the peak impedance magnitude and is essential for the generation of subthreshold oscillation. The model correctly predicted the behaviour of the frequency response before and after TTX and TEA application, as well as the relation between the expected passive impedance and the experimental impedance. 5. We speculate that the tendency of the neurons to generate voltage signals at a certain frequency (as a result of the subthreshold oscillations) and to preferentially respond to inputs arriving at the same frequency (the resonance behaviour) promotes population activity at that preferred frequency.

A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data

We present a novel framework for automatically constraining parameters of compartmental models of neurons, given a large set of experimentally measured responses of these neurons. In experiments, intrinsic noise gives rise to a large variability (e.g., in firing pattern) in the voltage responses to repetitions of the exact same input. Thus, the common approach of fitting models by attempting to perfectly replicate, point by point, a single chosen trace out of the spectrum of variable responses does not seem to do justice to the data. In addition, finding a single error function that faithfully characterizes the distance between two spiking traces is not a trivial pursuit. To address these issues, one can adopt a multiple objective optimization approach that allows the use of several error functions jointly. When more than one error function is available, the comparison between experimental voltage traces and model response can be performed on the basis of individual features of interest (e.g., spike rate, spike width). Each feature can be compared between model and experimental mean, in units of its experimental variability, thereby incorporating into the fitting this variability. We demonstrate the success of this approach, when used in conjunction with genetic algorithm optimization, in generating an excellent fit between model behavior and the firing pattern of two distinct electrical classes of cortical interneurons, accommodating and fast-spiking. We argue that the multiple, diverse models generated by this method could serve as the building blocks for the realistic simulation of large neuronal networks.

Excitable dendrites and spines: earlier theoretical insights elucidate recent direct observations

Important advances in experimental methods have made it possible to measure the electrical events in dendrites directly and to record optically from dendritic spines. These new techniques allow us to focus on the input region of the neuron and highlight the excitable properties of the dendritic membrane. Interestingly, some of the recent experimental findings were anticipated by earlier theoretical research, for example, the observation that some spines possess excitable channels that might generate local all-or-none events. Computer models were used previously to explore the conditions for initiating an action potential at the dendritic tree, in particular, at the spine head, and for active propagation between excitable spines and excitable dendritic arbors. The consequences for synaptic amplification, for the extent of active spread in the tree and for non-linear discriminations between different patterns of synaptic inputs were also considered. Here we review the biophysical insights gained from the theory and demonstrate how these elucidate the recent experimental results.

Physiology, morphology and detailed passive models of guinea‐pig cerebellar Purkinje cells.

1. Purkinje cells (PCs) from guinea‐pig cerebellar slices were physiologically characterized using intracellular techniques. Extracellular caesium ions were used to linearize the membrane properties of PCs near the resting potential. Under these conditions the average input resistance, RN, was 29 M omega, the average system time constant, tau 0, was 82 ms and the average cable length, LN, was 0.59. 2. Three PCs were fully reconstructed following physiological measurements and staining with horseradish peroxidase. Assuming that each spine has an area of 1 micron 2 and that the spine density over the spiny dendrites is ten spines per micrometre length, the total membrane area of each PC is approximately 150,000 microns 2, of which approximately 100,000 microns 2 is in the spines. 3. Detailed passive cable and compartmental models were built for each of the three reconstructed PCs. Computational methods were devised to incorporate globally the huge number of spines into these models. In all three cells the models predict that the specific membrane resistivity, Rm, of the soma is much lower than the dendritic Rm (approximately 500 and approximately 100,000 omega cm2 respectively). The specific membrane capacitance, Cm, is estimated to be 1.5‐2 muF cm‐2 and the specific cytoplasm resistivity, Ri, is 250 omega cm. 4. The average cable length of the dendrites according to the model is 0.13 lambda, suggesting that under caesium conditions PCs are electrically very compact. Brief somatic spikes, however, are expected to attenuate 30‐fold when spreading passively into the dendritic terminals. A simulated 200 Hz train of fast, 90 mV somatic spikes produced a smooth 12 mV steady depolarization at the dendritic terminals. 5. A transient synaptic conductance increase, with a 1 nS peak at 0.5 ms and a driving force of 60 mV, is expected to produce approximately 20 mV peak depolarization at the spine head membrane. This EPSP then attenuates between 200‐ and 900‐fold into the soma. Approximately 800 randomly distributed and synchronously activated spiny inputs are required to fire the soma. 6. The passive model of the PC predicts a poor resolution of the spatio‐temporal pattern of the parallel fibre input. An equally sized, randomly distributed group of approximately 1% of the parallel fibres, activated within a time window of a few milliseconds, would result in approximately the same composite EPSP at the soma.

The impact of parallel fiber background activity on the cable properties of cerebellar Purkinje cells

Neurons in the mammalian CNS receive 104-105 synaptic inputs onto their dendritic tree. Each of these inputs may fire spontaneously at a rate of a few spikes per second. Consequently, the cell is bombarded by several hundred synapses in each and every millisecond. An extreme example is the cerebellar Purkinje cell (PC) receiving approximately 100,000 excitatory synapses from the parallel fibers (p.f.s) onto dendritic spines covering the thin dendritic branchlets. What is the effect of the p.f.s activity on the integrative capabilities of the PC? This question is explored theoretically using analytical cable models as well as compartmental models of a morphologically and physiologically characterized PC from the guinea pig cerebellum. The input of individual p.f.s was modeled as a transient conductance change, peaking at 0.4 nS with a rise time of 0.3 msec and a reversal potential of +60 mV relative to rest. We found that already at a firing frequency of a few spikes per second the membrane conductance is several times larger than the membrane conductance in the absence of synaptic activity. As a result, the cable properties of the PC significantly change; the most sensitive parameters are the system time constant (0) and the steady-state attenuation factor from dendritic terminal to soma. The implication is that the cable properties of central neurons in freely behaving animals are different from those measured in slice preparation or in anesthetized animals, where most of the synaptic inputs are inactive. We conclude that, because of the large conductance increase produced by the background activity of the p.f.s, the activity of the PC will be altered from this background level either when the p.f.s change their firing frequency for a period of several tens of milliseconds or when a large population of the p.f.s fires during a narrow time window.

Effect of geometrical irregularities on propagation delay in axonal trees

Multiple successive geometrical inhomogeneities, such as extensive arborization and terminal varicosities, are usual characteristics of axons. Near such regions the velocity of the action potential (AP) changes. This study uses AXONTREE, a modeling tool developed in the companion paper for two purposes: (a) to gain insights into the consequence of these irregularities for the propagation delay along axons, and (b) to simulate the propagation of APs along a reconstructed axon from a cortical cell, taking into account information concerning the distribution of boutons (release sites) along such axons to estimate the distribution of arrival times of APs to the axons release sites. We used Hodgkin and Huxley (1952) like membrane properties at 20 degrees C. Focusing on the propagation delay which results from geometrical changes along the axon (and not from the actual diameters or length of the axon), the main results are: (a) the propagation delay at a region of a single geometrical change (a step change in axon diameter or a branch point) is in the order of a few tenths of a millisecond. This delay critically depends on the kinetics and the density of the excitable channels; (b) as a general rule, the lag imposed on the AP propagation at a region with a geometrical ratio GR greater than 1 is larger than the lead obtained at a region with a reciprocal of that GR value; (c) when the electronic distance between two successive geometrical changes (Xdis) is small, the delay is not the sum of the individual delays at each geometrical change, when isolated. When both geometrical changes are with GR greater than 1 or both with GR less than 1, this delay is supralinear (larger than the sum of individual delays). The two other combinations yield a sublinear delay; and (d) in a varicose axon, where the diameter changes frequently from thin to thick and back to thin, the propagation velocity may be slower than the velocity along a uniform axon with the thin diameter. Finally, we computed propagation delays along a morphologically characterized axon from layer V of the somatosensory cortex of the cat. This axon projects mainly to area 4 but also sends collaterals to areas 3b and 3a. The model predicts that, for this axon, areas 3a, 3b, and the proximal part of area 4 are activated approximately 2 ms before the activation of the distal part of area 4.