Structure-Dependent Electrical and Concentration Processes in the Dendrites of Pyramidal Neurons of Superficial Neocortical Layers: Model Study

On mathematical models of pyramidal neurons localized in the neocortical layers 2/3, whose reconstructed dendritic arborization possessed passive linear or active nonlinear membrane properties, we studied the effect of morphology of the dendrites on their passive electrical transfer characteristics and also on the formation of patterns of spike discharges at the output of the cell under conditions of tonic activation via uniformly distributed excitatory synapses along the dendrites. For this purpose, we calculated morphometric characteristics of the size, complexity, metric asymmetry, and function of effectiveness of somatopetal transmission of the current (with estimation of the sensitivity of this efficacy to changes in the uniform membrane conductance) for the reconstructed dendritic arborization in general and also for its apical and basal subtrees. Spatial maps of the membrane potential and intracellular calcium concentration, which corresponded to certain temporal patterns of spike discharges generated by the neuron upon different intensities of synaptic activation, were superimposed on the 3D image and dendrograms of the neuron. These maps were considered “spatial autographs” of the above patterns. The main discharge pattern included periodic two-spike bursts (dublets) generated with relatively stable intraburst interspike intervals and interburst intervals decreasing with a rise in the intensity of activation. Under conditions of intense activation, the interburst intervals became close to the intraburst intervals, so the cell began to generate continuous trains of action potentials. Such a repertoire (consisting of two patterns of the activity, periodical dublets and continuous discharges) is considerably scantier than that described earlier in pyramidal neurons of the neocortical layer 5. Under analogous conditions of activation, we observed in the latter cells a variety of patterns of output discharges of different complexities, including stochastic ones. A relatively short length of the apical dendrite subtree of layer 2/3 neurons and, correspondingly, a smaller metric asymmetry (differences between the lengths of the apical and basal dendritic branches and paths), as compared with those in layer 5 pyramidal neurons, are morphological factors responsible for the predominance of periodic spike dublets. As a result, there were two combinations of different electrical states of the sites of dendritic arborization (“spatial autographs”). In the case of dublets, these were high depolarization of the apical dendrites vs. low depolarization of the basal dendrites and a reverse combination; only the latter (reverse) combination corresponded to the case of continuous discharges. The relative simplicity and uniformity of spike patterns in the cells, apparently, promotes the predominance of network interaction in the processes of formation of the activity of pyramidal neurons of layers 2/3 and, thereby, a higher efficiency of the processes of intracortical association.     

Local Diameter Fully Constrains Dendritic Size in Basal but not Apical Trees of CA1 Pyramidal Neurons

Computational modeling of dendritic morphology is a powerful tool for quantitatively describing complex geometrical relationships, uncovering principles of dendritic development, and synthesizing virtual neurons to systematically investigate cellular biophysics and network dynamics. A feature common to many morphological models is a dependence of the branching probability on local diameter. Previous models of this type have been able to recreate a wide variety of dendritic morphologies. However, these diameter-dependent models have so far failed to properly constrain branching when applied to hippocampal CA1 pyramidal cells, leading to explosive growth. Here we present a simple modification of this basic approach, in which all parameter sampling, not just bifurcation probability, depends on branch diameter. This added constraint prevents explosive growth in both apical and basal trees of simulated CA1 neurons, yielding arborizations with average numbers and patterns of bifurcations extremely close to those observed in real cells. However, simulated apical trees are much more varied in size than the corresponding real dendrites. We show that, in this model, the excessive variability of simulated trees is a direct consequence of the natural variability of diameter changes at and between bifurcations observed in apical, but not basal, dendrites. Conversely, some aspects of branch distribution were better matched by virtual apical trees than by virtual basal trees. Dendritic morphometrics related to spatial position, such as path distance from the soma or branch order, may be necessary to fully constrain CA1 apical tree size and basal branching pattern.     

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.     

Electrical Bistability of the Motoneuronal Dendritic Membrane Determined by Non-inactivating Inward Currents: a Model Study

We investigated features of the spatial pattern of electrical bistable states of dendrites using a computer model of an abducens motoneuron with the dendritic branching reconstructed in detail. The dendritic membrane has an N-shaped current-voltage relation (I-V curve) determined mainly by the presence of L-type calcium channels. Such channels, according to indirect experimental data, are present in the dendrites of these cells together with glutamatergic NMDA-type channels also capable of determining electrical bistability of the membrane and the corresponding specific patterns of electrical activity generated by such neurons. For our model, we obtained steady-state local I-V curves and transferred spatial distribution maps of the membrane potential difference (surface density of transmembrane currents), as well as increments of the axial dendritic current, to three-dimensional images of the reconstructed branching dendrites. The latter increments determine the contribution of a dendritic site in general axial current delivering the charge to the trigger zone of a neuron. The simulation results showed that incorporation of non-inactivating calcium channels into dendritic membrane leads to the origination of a pattern of spatial distribution of bistable electrical states in the dendrites, which were not described earlier. Such features are most important under conditions of a stable state of high depolarization of the relevant parts of the dendrites. In this case, the respective feature was the existence of a zone of maximum density of the inward transmembrane current, which covers areas of first-order branching of all dendrites. Since the greatest relative contribution to the total current belongs to the inward calcium current, the above zone of first branchings can be considered a “hot spot” zone characterized by increased entry of Ca²⁺. This may have important functional consequences for local intracellular calcium signaling.     

Initiation of Sodium Spikelets in Basal Dendrites of Neocortical Pyramidal Neurons

Cortical information processing relies critically on the processing of electrical signals in pyramidal neurons. Electrical transients mainly arise when excitatory synaptic inputs impinge upon distal dendritic regions. To study the dendritic aspect of synaptic integration one must record electrical signals in distal dendrites. Since thin dendritic branches, such as oblique and basal dendrites, do not support routine glass electrode measurements, we turned our effort towards voltage-sensitive dye recordings. Using the optical imaging approach we found and reported previously that basal dendrites of neocortical pyramidal neurons show an elaborate repertoire of electrical signals, including backpropagating action potentials and glutamate-evoked plateau potentials. Here we report a novel form of electrical signal, qualitatively and quantitatively different from backpropagating action potentials and dendritic plateau potentials. Strong glutamatergic stimulation of an individual basal dendrite is capable of triggering a fast spike, which precedes the dendritic plateau potential. The amplitude of the fast initial spikelet was actually smaller that the amplitude of the backpropagating action potential in the same dendritic segment. Therefore, the fast initial spike was dubbed “spikelet”. Both the basal spikelet and plateau potential propagate decrementally towards the cell body, where they are reflected in the somatic whole-cell recordings. The low incidence of basal spikelets in the somatic intracellular recordings and the impact of basal spikelets on soma-axon action potential initiation are discussed.     

Phosphorylation of CRMP2 is involved in proper bifurcation of the apical dendrite of hippocampal CA1 pyramidal neurons

The neural circuit in the hippocampus is important for higher brain functions. Dendrites of CA1 pyramidal neurons mainly receive input from the axons of CA3 pyramidal neurons in this neural circuit. A CA1 pyramidal neuron has a single apical dendrite and multiple basal dendrites. In wild‐type mice, most of CA1 pyramidal neurons extend a single trunk, or alternatively, the apical dendrite bifurcates into two daughter trunks at the stratum radiatum layer. We previously reported the proximal bifurcation phenotype in Sema3A?/?, p35?/?, and CRMP4?/? mice. Cdk5/p35 phosphorylates CRMP2 at Ser522, and inhibition of this phosphorylation suppressed Sema3A‐induced growth cone collapse. In this study, we analyzed the bifurcation points of the apical dendrites of hippocampal CA1 pyramidal neurons in CRMP2KI/KI mice in which the Cdk5/p35‐phosphorylation site Ser522 was mutated into an Ala residue. The proximal bifurcation phenotype was not observed in CRMP2KI/KI mice; however, severe proximal bifurcation of apical dendrites was found in CRMP2KI/KI;CRMP4?/? mice. Cultured hippocampal neurons from CRMP2KI/KI and CRMP2KI/KI;CRMP4?/? embryos showed an increased number of dendritic branching points compared to those from wild‐type embryos. Sema3A increased the number of branching points and the total length of dendrites in wild‐type hippocampal neurons, but these effects of Sema3A for dendrites were notobserved in CRMP2KI/KI and CRMP2KI/KI;CRMP4?/?hippocampal neurons. Binding of CRMP2 to tubulin increased in both CRMP2KI/KI and CRMP2KI/KI:CRMP4?/? brain lysates. These results suggest that CRMP2 and CRMP4 synergistically regulate dendritic development, and CRMP2 phosphorylation is critical for proper bifurcation of apical dendrite of CA1 pyramidal neurons. © 2012 Wiley Periodicals, Inc. Develop Neurobiol, 2013     

Golgi-type I and Golgi-type II Neurons in the Ventral Anterior Thalamic Nucleus of the Adult Human: Morphological Features and Quantitative Analysis

The morphological and quantitative features of neurons in the adult human ventral anterior thalamic nucleus were studied in Golgi preparations. Two neuronal types were found and their quantitative features were studied. Golgi-type I neurons were medium to large cells with dense dendritic trees and dendritic protrusions and short hair-like appendages. They have somatic mean diameter of 30.8 μm (±9.4, n = 85). They have an average 100.3 dendritic branches, 48.97 dendritic branching points, and 58.85 dendritic tips. The mean diameters of their primary, secondary, and tertiary dendrites were 3.1 μm (±1, n = 80), 1.85 μm (±0.8, n = 145), and 1.5 μm (±0.4, n = 160), respectively. Golgi-type II neurons were small to medium cells with few sparsely branching dendrites and dendritic stalked appendages with or without terminal swellings. They have somatic mean diameters of 22.2 μm (±5.8, n = 120). They have an average 33.76 dendritic branches, 16.49 dendritic branching points, and 21.97 dendritic tips. The mean diameters of their primary, secondary, and tertiary dendrites were 1.6 μm (±0.86, n = 70), 1.15 μm (±0.55, n = 118), and 1 μm (±0.70, n = 95), respectively. These quantitative data may form the basis for further quantitative studies involving aging or some degenerative diseases that may affect cell bodies and/or dendritic trees of the Golgi-type I and/or Golgi-type II thalamic neurons.     

Responses of cortical neurons to local application of excitatory amino acids to their dendrites and soma

The efficacy of excitation induced by iontophoretic application of excitatory amino acids to the soma or different parts of the dendritic tree has been compared in experiments performed on parietal cortex slices. Spike activity was recorded extracellularly from single nerve cells of layer V. In total, the responses of 125 neurons were analyzed. Upon application of glutamate and aspartate to the neuronal soma and the majority of dendrites, latencies of excitatory responses did not exceed 500 msec. In 18% of cases, neuronal responses to transmitter application to basal and apical dendrites had longer (2–3 sec) latencies. The maximum intensity of responses was observed when excitatory amino acids had been applied to the soma or proximal parts of dendrites. If applied at a distance of over 100 µm to basal and 300 µm to apical dendrites, glutamate and aspartate elicited cellular responses whose intensity was 2–3 times lower than that of the responses induced by application to the soma. The maximum distances at which somatic spike responses could be recorded were 350 µm and 800 µm for basal and apical dendrites, respectively. Different latencies of the responses to somatic and dendritic applications of excitatory amino acids in some neurons, as well as high efficacy of responses to stimulation of remote parts of dendritic tree, may indicate nonidentity of electrical properties of dendritic and somatic membranes.Neirofiziologiya/Neurophysiology, Vol. 25, No. 6, pp. 437–446, November–December, 1993.     

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     

Patterns of Impulsation Generated by Abducens Motoneurons with Active Reconstructed Dendrites: a Simulation Study

Mathematical models of abducens motoneurons with reconstructed dendritic arborizations were investigated. The two types of models differed from each other in electrical properties of the dendrites, either passive (model group 1) or active and non-linear (model group 2). The relations between morphology of the dendrites, their electrical transfer characteristics, and formation of impulse patterns at the cell output were studied under conditions of tonic activation of glutamatergic (NMDA-type) excitatory synapses homogeneously distributed over the dendrites. For reconstructed dendritic arborizations, their morphometric characteristics (size, complexity, and metrical asymmetry) and electrical ones (somatopetal current transfer effectiveness function and sensitivity of the latter to variations of the homogeneous membrane conductivity) were computed. Changes in the membrane potential were also studied in different parts of the dendritic arborization during generation of various patterns of discharges of action potentials (APs) at the neuronal output under different intensities of synaptic activation; this allowed us to reveal “spatial signatures” of the above-mentioned temporal patterns. The output patterns and their “spatial signatures” changed in a certain manner with increase in the intensity of synaptic activation. A simple periodical discharge of low-frequency APs with constant interspike intervals was replaced by a complex periodical or nonperiodical (stochastic) bursting pattern, which then was replaced again by a simple rhythmic but high-frequency discharge. Simple periodical patterns were associated with generation of synchronous oscillatory dendritic depolarizations phase-shifted in metrically asymmetrical parts of the arborization. In the case of generation of complex periodical or stochastic patterns, depolarization processes in asymmetrical dendritic parts were asynchronous and differed from each other in their amplitude and duration. Such a structure-dependent repertoire of output discharge patterns was quite compatible with that observed earlier in examined simulated neocortical pyramidal and cerebellar Purkinje neurons. This fact is indicative of a possible similarity of the rules governing the formation of specific output patterns in neurons with active membrane properties of the dendrites based on intrinsic mophological/functional features of the dendritic arborization of a given neuron.     

Dynamics of process formation during differentiation of tectal neurons in embryonic zebrafish

Neurons acquire their distinct shapes after passing through many transitional stages in early development. To reveal the dynamics and spatiotemporal sequence of process formation in situ, the growth of neurons in the optic tectum of live zebrafish embryos (54 to >100 h old) was monitored using time-lapse videorecordings. Neurons were labeled by injecting the fluorescent vital dye DiO into the cell-rich layer of the developing tectum in 50- to 70-h-old embryos. In phase 1, tectal neurons possess an apical “primary process” which reaches to the ventral aspect of the tectal neuropil. The primary process produces at its tip short transitory branches, some with growth cones, over a period of roughly 6 h. One of the growth cones then elongates rapidly and grows toward the caudal tectum via a route characteristic of efferent axons. After retraction of excess branches and growth cones, branching activity resumes at the tip of the primary process to form the dendritic tree (phase 2). The dendritic tree develops in the tectal neuropil through emission and retraction of many branches during a period of >20 h (our longest continuous time-lapse movie). The tectal territory “explored” in this way is larger than the area finally covered by the tree resulting from growth and loss of branches. The dynamics observed here directly are probably characteristic for dendrite formation in vertebrates. Moreover, consistent with the sequence of neuronal differentiation observed in vitro, the growth of the axon precedes that of the dendrites, although both emerge from a common primary process in this type of tectal neuron. © 1997 John Wiley & Sons, Inc. J Neurobiol 32: 627–639, 1997     

CRMP4 suppresses apical dendrite bifurcation of CA1 pyramidal neurons in the mouse hippocampus

Collapsin response mediator proteins (CRMPs) are a family of cytosolic phosphoproteins that consist of 5 members (CRMP 1–5). CRMP2 and CRMP4 regulate neurite outgrowth by binding to tubulin heterodimers, resulting in the assembly of microtubules. CRMP2 also mediates the growth cone collapse response to the repulsive guidance molecule semaphorin‐3A (Sema3A). However, the role of CRMP4 in Sema3A signaling and its function in the developing mouse brain remain unclear. We generated CRMP4?/? mice in order to study the in vivo function of CRMP4 and identified a phenotype of proximal bifurcation of apical dendrites in the CA1 pyramidal neurons of CRMP4?/? mice. We also observed increased dendritic branching in cultured CRMP4?/? hippocampal neurons as well as in cultured cortical neurons treated with CRMP4 shRNA. Sema3A induces extension and branching of the dendrites of hippocampal neurons; however, these inductions were compromised in the CRMP4?/? hippocampal neurons. These results suggest that CRMP4 suppresses apical dendrite bifurcation of CA1 pyramidal neurons in the mouse hippocampus and that this is partly dependent on Sema3A signaling. © 2012 Wiley Periodicals, Inc. Develop Neurobiol, 2012     

Cell type-specific dendritic polarity in the absence of spatially organized external cues

Pyramidal neurons of the hippocampus and cortex have polarized dendritic arbors, but little is known about the cellular mechanisms distinguishing apical and basal dendrites. We used morphometric analysis and time lapse imaging of cultured hippocampal neurons to show that glutamatergic neurons develop progressive dendritic asymmetry in the absence of polarized extrinsic cues. Thus, pyramidal neurons have a cellular program for polarized dendrite growth independent of tissue microenvironment.     

Differentiation of Apical and Basal Dendrites in Pyramidal Cells and Granule Cells in Dissociated Hippocampal Cultures

Hippocampal pyramidal cells and dentate granule cells develop morphologically distinct dendritic arbors, yet also share some common features. Both cell types form a long apical dendrite which extends from the apex of the cell soma, while short basal dendrites are developed only in pyramidal cells. Using quantitative morphometric analyses of mouse hippocampal cultures, we evaluated the differences in dendritic arborization patterns between pyramidal and granule cells. Furthermore, we observed and described the final apical dendrite determination during dendritic polarization by time-lapse imaging. Pyramidal and granule cells in culture exhibited similar dendritic patterns with a single principal dendrite and several minor dendrites so that the cell types were not readily distinguished by appearance. While basal dendrites in granule cells are normally degraded by adulthood in vivo, cultured granule cells retained their minor dendrites. Asymmetric growth of a single principal dendrite harboring the Golgi was observed in both cell types soon after the onset of dendritic growth. Time-lapse imaging revealed that up until the second week in culture, final principal dendrite designation was not stabilized, but was frequently replaced by other minor dendrites. Before dendritic polarity was stabilized, the Golgi moved dynamically within the soma and was repeatedly repositioned at newly emerging principal dendrites. Our results suggest that polarized growth of the apical dendrite is regulated by cell intrinsic programs, while regression of basal dendrites requires cue(s) from the extracellular environment in the dentate gyrus. The apical dendrite designation is determined from among multiple growing dendrites of young developing neurons.     

Dendritic morphology is altered in hippocampal neurons following prenatal compromise

Chronic placental insufficiency (CPI), a known cause of intrauterine growth restriction, can lead to structural alterations in the developing brain that might underlie postnatal neurological deficits. We have previously demonstrated significant reductions in the volumes of hippocampal neuropil layers in fetal guinea pig brains following experimentally induced growth restriction. To determine the components of the neuropil affected in the brains of growth restricted (GR) fetuses, the dendritic morphology of CA1 pyramidal neurons and dentate granule cells was examined. CPI was induced by unilateral uterine artery ligation in pregnant guinea pigs at midgestation (term approximately 67 days). Hippocampi from control and GR fetuses were stained using the Rapid Golgi technique and the growth and branching of the dendritic arbors were quantified using the Sholl method. In addition, the density of dendritic spines was determined on the apical arbors of each population. In GR brains (n = 7) compared to controls (n = 7), there was a reduction in dendritic elongation (p < 0.005) and an alteration in the branch point distribution in CA1 basal arbors, and a reduction both in the outgrowth (p < 0.05) and branch point number (p < 0.05) of CA1 apical arbors. Dentate granule cells from GR brains also demonstrated reduced dendritic outgrowth (p < 0.05). There was an increase in dendritic spine density in both neuronal populations; this might be due either to altered synaptic pruning or as a compensatory mechanism for reduced dendritic length. These findings demonstrate that a chronic prenatal insult causes selective changes in the morphology of hippocampal cell dendrites and may lead to alterations in hippocampal function in the postnatal period.     

Immunocytochemical demonstration of tubulin microheterogeneity within rat cortical and hippocampal pyramidal neurons

Summary Rat cortical and hippocampal pyramidal cells were immunocytochemically investigated using the TU-01 monoclonal antibody recognizing α-tubulin. The isotypic specificity of this antibody is distinct from that of other available α-tubulin antibodies; therefore, an intracellular heterogeneity among neuronal microtubules could be revealed by observing intensely immunostained apical dendritic microtubules in the complete absence of staining of the microtubules in the basal dendrites and perikarya of the same pyramidal cells.     

Slit and Robo regulate dendrite branching and elongation of space-filling neurons in Drosophila

Space-filling neurons extensively sample their receptive fields with fine dendritic branches. In this study we show that a member of the conserved Robo receptor family, Robo, and its ligand Slit regulate the dendritic differentiation of space-filling neurons. Loss of Robo or Slit function leads to faster elongating and less branched dendrites of the complex and space-filling class IV multi-dendritic dendrite-arborization (md-da) neurons in the Drosophila embryonic peripheral nervous system, but not of the simpler class I neurons. The total dendrite length of Class IV neurons is not modified in robo or slit mutant embryos. Robo mediates this process cell-autonomously. Upon Robo over-expression in md-da neurons the dendritic tree is simplified and time-lapse analysis during larval stages indicates that this is due to reduction in the number of newly formed branches. We propose that Slit, through Robo, provides an extrinsic signal to coordinate the growth rate and the branching level of space-filling neurons, thus allowing them to appropriately cover their target field.     

Dendritic morphology of hippocampal and amygdalar neurons in adolescent mice is resilient to genetic differences in stress reactivity

Many studies have shown that chronic stress or corticosterone over-exposure in rodents leads to extensive dendritic remodeling, particularly of principal neurons in the CA3 hippocampal area and the basolateral amygdala. We here investigated to what extent genetic predisposition of mice to high versus low stress reactivity, achieved through selective breeding of CD-1 mice, is also associated with structural plasticity in Golgi-stained neurons. Earlier, it was shown that the highly stress reactive (HR) compared to the intermediate (IR) and low (LR) stress reactive mice line presents a phenotype, with respect to neuroendocrine parameters, sleep architecture, emotional behavior and cognition, that recapitulates some of the features observed in patients suffering from major depression. In late adolescent males of the HR, IR, and LR mouse lines, we observed no significant differences in total dendritic length, number of branch points and branch tips, summated tip order, number of primary dendrites or dendritic complexity of either CA3 pyramidal neurons (apical as well as basal dendrites) or principal neurons in the basolateral amygdala. Apical dendrites of CA1 pyramidal neurons were also unaffected by the differences in stress reactivity of the animals; marginally higher length and complexity of the basal dendrites were found in LR compared to IR but not HR mice. In the same CA1 pyramidal neurons, spine density of distal apical tertiary dendrites was significantly higher in LR compared to IR or HR animals. We tentatively conclude that the dendritic complexity of principal hippocampal and amygdala neurons is remarkably stable in the light of a genetic predisposition to high versus low stress reactivity, while spine density seems more plastic. The latter possibly contributes to the behavioral phenotype of LR versus HR animals.     

Burst control: Synaptic conditions for burst generation in cortical layer 5 pyramidal neurons

The output of neocortical layer 5 pyramidal cells (L5PCs) is expressed by a train of single spikes with intermittent bursts of multiple spikes at high frequencies. The bursts are the result of nonlinear dendritic properties, including Na⁺, Ca²⁺, and NMDA spikes, that interact with the ~10,000 synapses impinging on the neuron’s dendrites. Output spike bursts are thought to implement key dendritic computations, such as coincidence detection of bottom-up inputs (arriving mostly at the basal tree) and top-down inputs (arriving mostly at the apical tree). In this study we used a detailed nonlinear model of L5PC receiving excitatory and inhibitory synaptic inputs to explore the conditions for generating bursts and for modulating their properties. We established the excitatory input conditions on the basal versus the apical tree that favor burst and show that there are two distinct types of bursts. Bursts consisting of 3 or more spikes firing at < 200 Hz, which are generated by stronger excitatory input to the basal versus the apical tree, and bursts of ~2-spikes at ~250 Hz, generated by prominent apical tuft excitation. Localized and well-timed dendritic inhibition on the apical tree differentially modulates Na⁺, Ca²⁺, and NMDA spikes and, consequently, finely controls the burst output. Finally, we explored the implications of different burst classes and respective dendritic inhibition for regulating synaptic plasticity.     

Plant form based on the pipe model theory II. Quantitative analysis of ramification in morphology

Ramification in tree structure was investigated by the main axis cutting method, which differs from the ordinary stratified clipping method. An axis running from the arbitrary terminal leader of the shoot to the stem base was termed the “main axis”. Cutting the main axis into pieces of constant length gives the “segment layer”, which consists of segments of the main axis and all branches and leaves diverging from the respective segments. There was a linear relationship between the weight of a main axis segment (in the range where leaves exist) of constant length and that of all the parts above the segment. Since plant form is determined by branches diverging regularly from the mother branch or stem, this linear relationship is considered to support the concept of the pipe model theory. It is also suggested that the proportionality constant of the linear relationship may specify the branching structure or ramifications of plant form.