The effect of neuronal growth on synaptic integration

The way in which the dimensions of neurons change during postembryonic development has important effects on their electrotonic structures. Theoretically, only one mode of growth can conserve the electrotonic structures of growing neurons without employing changes in membrane electrical properties. If the dendritic diameters of a neuron increase as the square of the increase in dendritic lengths, then the neuron's electrotonic structure is conserved. We call this special mode of allometric growth isoelectrotonic growth. In this study we compared the developmental changes in morphology of two identified invertebrate neurons with theoretical growth curves. We found that a cricket neuron, MGI, grows isoelectrotonically and thereby preserves its electrotonic properties. In contrast, the crayfish neuron, LG, grows in a nearly isometric manner resulting in an increase in its electrotonic length.     

Scaling properties of pyramidal neurons in mice neocortex

Dendritic morphology is the structural correlate for receiving and processing inputs to a neuron. An interesting question then is what the design principles and the functional consequences of enlarged or shrinked dendritic trees might be. As yet, only a few studies have examined the effects of neuron size changes. Two theoretical scaling modes have been analyzed, conservative (isoelectrotonic) scaling (preserves the passive and active response properties) and isometric scaling (steps up low pass-filtering of inputs). It has been suggested that both scaling modes were verified in neuroanatomical studies. To overcome obvious limitations of these studies like small size of analyzed samples and restricted validity of utilized scaling measures, we considered the scaling problem of neurons on the basis of large sample data and by employing a more general method of scaling analysis. This method consists in computing the morphoelectrotonic transform (MET) of neurons. The MET maps the neuron from anatomical space into electrotonic space using the logarithm of voltage attenuation as the distance metric. The theory underlying this approach is described and then applied to two samples of morphologically reconstructed pyramidal neurons (cells from neocortex of wildtype and synRas transgenic mice) using the NEURON simulator. In a previous study, we could verify a striking increase of dendritic tree size in synRas pyramidal neurons. Surprisingly, in this study the statistical analysis of the sample MET dendrograms revealed that the electrotonic architecture of these neurons scaled roughly in a MET-conserving mode. In conclusion, our results suggest only a minor impact of the Ras protein on dendritic electroanatomy, with non-significant changes of most regions of the corresponding METs.     

Dendritic analysis of lobster stretch receptor neurons: Electrotonic properties with single and distributed inputs

Using steady-state cable analysis as derived by Rall, electrotonic properties of the dendritic trees of the tonic stretch receptor neuron of the spiny lobster, Panulirus interruptus,have been examined. By directly measuring the somatic input resistance and by visualizing the dendritic trees of this neuron by backfilling the axon with cobalt, the electrotonic properties of the dendritic trees have been derived. The calculated membrane resistivity is 800-3600 -cm ². Voltage and current transfer functions were calculated for (a) single dendritic tips the size observed in the cobalt preparations and (b) for processes 2 µm or smaller, as observed in electron microscopy. Current transfer to the soma was high in both cases (greater than 80%). Voltage transfer was 22% for large and 4% for small dendrites. When a more natural simultaneous conductance change at the tips of all major dendrites was modeled, voltage transfer was 84% and current transfer 56%. But the dynamic range of the cell (rheobase to saturation) is well-predicted by varying the simultaneous inputs, not by scaling up a single input, thus illustrating that convenient indices of electrotonic properties may not prove useful in appreciating the integrative properties of a neuron.     

Distinct mammalian precursors are committed to generate neurons with defined dendritic projection patterns

The mechanisms that regulate how dendrites target different neurons to establish connections with specific cell types remain largely unknown. In particular, the formation of cell-type–specific connectivity during postnatal neurogenesis could be either determined by the local environment of the mature neuronal circuit or by cell-autonomous properties of the immature neurons, already determined by their precursors. Using retroviral fate mapping, we studied the lamina-specific dendritic targeting of one neuronal type as defined by its morphology and intrinsic somatic electrical properties in neonatal and adult neurogenesis. Fate mapping revealed the existence of two separate populations of neuronal precursors that gave rise to the same neuronal type with two distinct patterns of dendritic targeting—innervating either a deep or superficial lamina, where they connect to different types of principal neurons. Furthermore, heterochronic and heterotopic transplantation demonstrated that these precursors were largely restricted to generate neurons with a predetermined pattern of dendritic targeting that was independent of the host environment. Our results demonstrate that, at least in the neonatal and adult mammalian brain, the pattern of dendritic targeting of a given neuron is a cell-autonomous property of their precursors.     

Features of Active Electrical States of Asymmetrical Dendrites of Brainstem Motoneurons during Generation of Stochastic Implulse Patterns: a Simulation Study

On models of motoneurons of the n. abducens nucleus with reconstructed dendritic arborizations having an active membrane, we investigated features of the relationships between passive transfer properties and dynamics of excitation states of asymmetrical dendrites during generation of complex periodical and stochastic impulse patterns (output neuronal codes). Various patterns were obtained by varying the intensity of tonic synaptic excitation homogeneously distributed over the dendrites. The electrical states of sites belonging to branches of the same dendrite or different dendrites were compared. For this comparison, branches were selected, which, according to the earlier performed cluster analysis, were assigned to the groups (electrotonic clusters) with a high and a low effectiveness of passive transfer of the somatopetal current. The selection took into account features of the dendritic structure of neurons of the exemined type. These were: (i) the presence of groups of the asymmetrical branches differing from each other according to their belonging to different clusters (high or low transfer effectiveness) in different dendrites, and (ii) the presence of branches belonging to different dendrites characterized by significantly different orientations in three-dimensional space of the brainstem within each electrical cluster. Comparative analysis showed that, in a given dendrite during generation of a complex periodical pattern, the asymmetrical branches belonging to high- or low-efficiency clusters were characterized by being in different states (high or low depolarization) in different phases of generation of repeated sequences of action potentials (APs). This relationship was consistent with those previously detected in neurons of other types and in other specimens of neurons of the above-mentioned type. During generation of such periodical spike patterns, the branches of different dendrites belonging to the same electrotonic cluster were in similar states. Similar relationships between the states of the branches of the same dendrite belonging to different clusters were also observed during generation of complex stochastic (non-periodical) impulse patterns. In the latter case, however, the essential feature was that the branches of different dendrites belonging to the same electrotonic cluster were often in opposite states. Thus, the number of combinations of discrete electrical states of asymmetrical parts of the dendritic arborization was much greater. Probably, it is precisely this circumstance that determined the quasi-stochastic nature of the output impulse pattern.     

Single-neuron theory of consciousness

By most accounts, the mind arises from the integrated activity of large populations of neurons distributed across multiple brain regions. A contrasting model is presented in the present paper that places the mind/brain interface not at the whole brain level but at the level of single neurons. Specifically, it is proposed that each neuron in the nervous system is independently conscious, with conscious content corresponding to the spatial pattern of a portion of that neuron's dendritic electrical activity. For most neurons, such as those in the hypothalamus or posterior sensory cortices, the conscious activity would be assumed to be simple and unable to directly affect the organism's macroscopic conscious behavior. For a subpopulation of layer 5 pyramidal neurons in the lateral prefrontal cortices, however, an arrangement is proposed to be present such that, at any given moment: (i) the spatial pattern of electrical activity in a portion of the dendritic tree of each neuron in the subpopulation individually manifests a complexity and diversity sufficient to account for the complexity and diversity of conscious experience; (ii) the dendritic trees of the neurons in the subpopulation all contain similar spatial electrical patterns; (iii) the spatial electrical pattern in the dendritic tree of each neuron interacts non-linearly with the remaining ambient dendritic electrical activity to determine the neuron's overall axonal response; (iv) the dendritic spatial pattern is reexpressed at the population level by the spatial pattern exhibited by a synchronously firing subgroup of the conscious neurons, thereby providing a mechanism by which conscious activity at the neuronal level can influence overall behavior. The resulting scheme is one in which conscious behavior appears to be the product of a single macroscopic mind, but is actually the integrated output of a chorus of minds, each associated with a different neuron.     

Electrotonic measurements by electric field-induced polarization in neurons: theory and experimental estimation

We present a theory for estimation of the dendritic electrotonic length constant and the membrane time constant from the transmembrane potential (TMP) induced by an applied electric field. The theory is adapted to morphologically defined neurons with homogeneous passive electric properties. Frequency characteristics and transients at the onset and offset of the DC field are considered. Two relations are useful for estimating the electrotonic parameters: 1) steady-state polarization versus the dendritic electrotonic length constant; 2) membrane time constant versus length constant. These relations are monotonic and may provide a unique estimate of the electrotonic parameters for 3D-reconstructed neurons. Equivalent tip-to-tip electrotonic length of the dendritic tree was estimated by measuring the equalization time of the field-induced TMP. For 11 turtle spinal motoneurons, the electrotonic length from tip to tip of the dendrites was in the range of 1-2.5 lambda, whereas classical estimation using injection of current pulses gave an average dendrite length of 0.9-1.1 lambda. For seven ventral horn interneurons, the estimates were 0.7-2.6 lambda and 0.6-0.9 lambda, respectively. The measurements of the field-induced polarization promise to be a useful addition to the conventional methods using microelectrode stimulation.     

Effect of environmental enrichment on morphology of deep layer III and layer V pyramidal cells of occipital cortex in oldest-old rat - A quantitative golgi cox study

Dendrites and dendritic spine density regress extensively during aging in rats housed under standard conditions (SC), which can be ameliorated by housing in the enriched environment (EE). This event is particularly pronounced on neurons where high rates of plasticity are conceivable, such as on projection neurons of archicortical regions of dentate gyrus'. However, effects of EE on neocortical projection neurons are still poorly understood. Therefore, we investigated the effect of EE housing on a deep layer III (L3) and layer V pyramidal cell (L5) morphology in the associative occipital neocortex of male Sprague-Dawley rats at 24 months of age. Rats were randomly distributed in two groups and reared under either SC (n=5) or EE conditions (n=6) for 26 days. In depth quantitative analysis of dendritic tree morphology and spine density on occipital projection neurons, from Golgi-Cox stained sections, showed similar trend in both EE occipital layers L3 and L5. Significant increase was found in total number of dendritic segments (L3 - 37.5 %, L5 - 33 %) and in dendritic diameter of intermediate segments (for more than 20 %), while increase in total spine number was around the level of significance (p>0.55; L3 - 30 %, L5 - 64 %). These findings suggest an outgrowth of new dendritic segments, When compared to archicortical region of dentate gyrus, effects of aging in the associative occipital cortex were less pronounced. Taken together, these findings suggest that structures being more affected by the aging process are more susceptible to the environmental enrichment in old age.     

Preserving Neural Function under Extreme Scaling

Important brain functions need to be conserved throughout organisms of extremely varying sizes. Here we study the scaling properties of an essential component of computation in the brain: the single neuron. We compare morphology and signal propagation of a uniquely identifiable interneuron, the HS cell, in the blowfly (Calliphora) with its exact counterpart in the fruit fly (Drosophila) which is about four times smaller in each dimension. Anatomical features of the HS cell scale isometrically and minimise wiring costs but, by themselves, do not scale to preserve the electrotonic behaviour. However, the membrane properties are set to conserve dendritic as well as axonal delays and attenuation as well as dendritic integration of visual information. In conclusion, the electrotonic structure of a neuron, the HS cell in this case, is surprisingly stable over a wide range of morphological scales.     

Cortical integration in the visual system of the macaque monkey: large-scale morphological differences in the pyramidal neurons in the occipital, parietal and temporal lobes.

Layer III pyramidal neurons were injected with Lucifer yellow in tangential cortical slices taken from the inferior temporal cortex (area TE) and the superior temporal polysensory (STP) area of the macaque monkey. Basal dendritic field areas of layer III pyramidal neurons in area STP are significantly larger, and their dendritic arborizations more complex, than those of cells in area TE. Moreover, the dendritic fields of layer III pyramidal neurons in both STP and TE are many times larger and more complex than those in areas forming 'lower' stages in cortical visual processing, such as the first (V1), second (V2), fourth (V4) and middle temporal (MT) visual areas. By combining data on spine density with those of Sholl analyses, we were able to estimate the average number of spines in the basal dendritic field of layer III pyramidal neurons in each area. These calculations revealed a 13-fold difference in the number of spines in the basal dendritic field between areas STP and V1 in animals of similar age. The large differences in complexity of the same kind of neuron in different visual areas go against arguments for isopotentiality of different cortical regions and provide a basis that allows pyramidal neurons in temporal areas TE and STP to integrate more inputs than neurons in more caudal visual areas.     

The electro-dynamics of the dendritic space in Purkinje cells of the cerebellum

The functional geometry of the reconstructed dendritic arborization of Purkinje neurons is the object of this work. The combined effects of the local geometry of the dendritic branches and of the membrane mechanisms are computed in passive configuration to obtain the electrotonic structure of the arborization. Steady-currents applied to the soma and expressed as a function of the path distance from the soma form different clusters of profiles in which dendritic branches are similar in voltages and current transfer effectiveness. The locations of the different clusters are mapped on the dendrograms and 3D representations of the arborization. It reveals the presence of different spatial dendritic sectors clearly separated in 3D space that shape the arborization in ordered electrical domains, each with similar passive charge transfer efficiencies. Further simulations are performed in active configuration with a realistic cocktail of conductances to find out whether similar spatial domains found in the passive model also characterize the active dendritic arborization. During tonic activation of excitatory synaptic inputs homogeneously distributed over the whole arborization, the Purkinje cell generates regular oscillatory potentials. The temporal patterns of the electrical oscillations induce similar spatial sectors in the arborization as those observed in the passive electrotonic structure. By taking a video of the dendritic maps of the membrane potentials during a single oscillation, we demonstrate that the functional dendritic field of a Purkinje neuron displays dynamic changes which occur in the spatial distribution of membrane potentials in the course of the oscillation. We conclude that the branching pattern of the arborization explains such continuous reconfiguration and discuss its functional implications.     

Reliable, responsive pacemaking and pattern generation with minimal cell numbers: the crustacean cardiac ganglion

Investigations of the electrophysiology of crustacean cardiac ganglia over the last half-century are reviewed for their contributions to elucidating the cellular mechanisms and interactions by which a small (as few as nine cells) neuronal network accomplishes extremely reliable, rhythmical, patterned activation of muscular activity-in this case, beating of the neurogenic heart. This ganglion is thus a model for pacemaking and central pattern generation. Favorable anatomy has permitted voltage- and space-clamp analyses of voltage-dependent ionic currents that endow each neuron with the intrinsic ability to respond with rhythmical, patterned impulse activity to nonpatterned stimulation. The crustacean soma and initial axon segment do not support impulse generation but integrate input from stretch-sensitive dendrites and electrotonic and chemically mediated synapses on axonal processes in neuropils. The soma and initial axon produce a depolarization-activated, calcium-mediated, sustained potential, the "driver potential," so-called because it drives a train of impulses at the "trigger zone" of the axon. Extreme reliability results from redundancy and the electrotonic coupling and synaptic interaction among all the neurons. Complex modulation by central nervous system inputs and by neurohormones to adjust heart pumping to physiological demands has long been demonstrated, but much remains to be learned about the cellular and molecular mechanisms of action. The continuing relevance of the crustacean cardiac ganglion as a relatively simple model for pacemaking and central pattern generation is confirmed by the rapidly widening documentation of intrinsic potentials such as plateau potentials in neurons of all major animal groups. The suite of ionic currents (a slowly inactivating calcium current and various potassium currents, with variations) observed for the crustacean cardiac ganglion have been implicated in or proven to underlie a majority of the intrinsic potentials of neurons involved in pattern generation.     

The Role of Ongoing Dendritic Oscillations in Single-Neuron Dynamics

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.     

Synaptic organization of retinotectal connections of the frog application of pulse triggered averaging

Pulse-triggered averaging technique was applied to retinotectal connections of the frog. An extracellular single unit was first isolated from the terminals of retinal fibers, and then intracellular responses were recorded from a tectal neuron in the vicinity of the extracellular recording electrode. Intracellular potentials in response to a moving stimulus were averaged by triggering with the isolated presynaptic impulses. The results show that "on-off" retinal fibers monosynaptically excite E-E type (EPSP at "on" and "off" of light) and EI-EI type (EPSP-IPSP at "on" and "off" of light). One of the E-E type neurons was identified as a large ganglionic neuron in layer 8.     

Branching-pattern analysis of the dendritic arborization in the thalamic nuclei of the rat brain

We investigated the dendritic patterns of rapid Golgi-impregnated, highly similar multipolar neurons from two functionally different thalamic regions of the rat brain: two dorsal nuclei (the nucleus laterodorsalis thalami, pars dorsomedialis and the nucleus laterodorsalis thalami, pars ventrolateralis), and two ventral nuclei (the nucleus ventrolateralis thalami and the nucleus ventromedialis thalami). The analysis involved conventional morphometric parameters (height and size) and a new parameter derived from graph theory, the relative imbalance (RI), derived from the branching patterns of the dendrites, which permits quantitative characterization of the dendritic arborization of a neuron. On this basis, neurons can be grouped into three fundamentally different types: type A, or highly-polarized (imbalanced) neurons (RI values close to 1); type B, or medium-polarized neurons (RI values around 0.5); and type C, or balanced neurons with low polarization (RI values close to 0). The orientations of the dendritic arbor, and thus the receptive fields, of the dorsal and ventral thalamic neurons, were mutually perpendicular. The H and S values indicated that the neurons in the dorsal and ventral thalamic nuclei differed significantly. However, their RI values demonstrated that they were similar neurons of type B. Our data reveal that 1 ) the dendritic arbor cannot be reliably characterized purely on the basis of height and size, and 2) RI is a valuable morphometric parameter that identifies the true nature of the dendritic arborization.     

An Estimator for the Electrotonic Size of Neurons Independent of Charge Equalization Time Constants

Electrotonic properties are important aspects of neuronal function but have been difficult to estimate without accurate morphological reconstruction. The complexity of the branching dendritic cables often gives charging curves composed of a very large number of exponential functions, making it difficult to distinguish the time constants that are needed for electrotonic estimates. We describe an estimator P for the electrotonic size of neurons based on simple measures from voltage and current clamp recordings that does not rely on the higher rank exponential components of the response. Our estimator gives a bounded scale for the electrotonic size of the cell and can be used for categorization and comparison when morphology is not available.     

Morphology of calretinin and tyrosine hydroxylase-immunoreactive neurons in the pig retina

The morphology of calretinin- and tyrosine hydroxylase-immunoreactive (IR) neurons in adult pig retina was studied. These neurons were identified using antibody immunocytochemistry. Calretinin immunoreactivity was found in numerous cell bodies in the ganglion cell layer. Large ganglion cells, however, were not labeled. In the inner nuclear layer, the regular distribution of calretinin-IR neurons, the inner marginal location of their cell bodies in the inner nuclear layer, and the distinctive bilaminar morphologies of their dendritic arbors in the inner plexiform layer suggested that these calretinin-IR cells were AII amacrine cells. Calretinin immunoreactivity was observed in both A-and B-type horizontal cells. Neurons in the photoreceptor cell layer were not labeled by this antibody. The great majority of tyrosine hydroxylase-IR neurons were located at the innermost border of the inner nuclear layer (conventional amacrines). The processes were monostratified and ran laterally within layer 1 of the inner plexiform layer. Some of the tyrosine hydroxylase-IR neurons were located in the ganglion cell layer (displaced amacrines). The processes of displaced tyrosine hydroxylase-IR amacrine cells were also located within layer 1 of the inner plexiform layer. Some processes of a few neurons were located in the outer plexiform layer. A very low density of neurons had additional bands of tyrosine hydroxylase-IR processes in the middle and deep layers of the inner plexiform layer. The processes of tyrosine hydroxylase-IR neurons extended radially over a wide area and formed large, moderately branched dendritic fields. These processes occasionally had varicosities and formed "dendritic rings". These results indicate that calretinin- and tyrosine hydroxylase-IR neurons represent specific neuronal cell types in the pig retina.