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Neuronal signal integration and information processing in cortical networks critically depend on the organization of synaptic connectivity. During development, neurons can form synaptic connections when their axonal and dendritic arborizations come within close proximity of each other. Although many signaling cues are thought to be involved in guiding neuronal extensions, the extent to which accidental appositions between axons and dendrites can already account for synaptic connectivity remains unclear. To investigate this, we generated a local network of cortical L2/3 neurons that grew out independently of each other and that were not guided by any extracellular cues. Synapses were formed when axonal and dendritic branches came by chance within a threshold distance of each other. Despite the absence of guidance cues, we found that the emerging synaptic connectivity showed a good agreement with available experimental data on spatial locations of synapses on dendrites and axons, number of synapses by which neurons are connected, connection probability between neurons, distance between connected neurons, and pattern of synaptic connectivity. The connectivity pattern had a small-world topology but was not scale free. Together, our results suggest that baseline synaptic connectivity in local cortical circuits may largely result from accidentally overlapping axonal and dendritic branches of independently outgrowing neurons.

We present a simulation framework, called NETMORPH, for the developmental generation of 3D large-scale neuronal networks with realistic neuron morphologies. In NETMORPH, neuronal morphogenesis is simulated from the perspective of the individual growth cone. For each growth cone in a growing axonal or dendritic tree, its actions of elongation, branching and turning are described in a stochastic, phenomenological manner. In this way, neurons with realistic axonal and dendritic morphologies, including neurite curvature, can be generated. Synapses are formed as neurons grow out and axonal and dendritic branches come in close proximity of each other. NETMORPH is a flexible tool that can be applied to a wide variety of research questions regarding morphology and connectivity. Research applications include studying the complex relationship between neuronal morphology and global patterns of synaptic connectivity. Possible future developments of NETMORPH are discussed.

To study plasticity, we cultured cortical networks on multielectrode arrays, enabling simultaneous recording from multiple neurons. We used conditional firing probabilities to describe functional network connections by their strength and latency. These are abstract representations of neuronal pathways and may arise from direct pathways between two neurons or from a common input. Functional connections based on direct pathways should reflect synaptic properties. Therefore, we searched for long-term potentiation (this mechanism occurs in vivo when presynaptic action potentials precede postsynaptic ones with interspike intervals up to approximately 20 ms) in vitro. To investigate if the strength of functional connections showed a similar latency-related development, we selected periods of monotonously increasing or decreasing strength. We observed increased incidence of short latencies (5-30 ms) during strengthening, whereas these rarely occurred during weakening. Furthermore, we saw an increased incidence of 40-65 ms latencies during weakening. Conversely, functional connections tended to strengthen in periods with short latency, whereas strengthening was significantly less than average during long latency. Our data suggest that functional connections contain information about synaptic connections, that conditional firing probability analysis is sensitive enough to detect it and that a substantial fraction of all functional connections is based on direct pathways.

Within the context of an updated thorough review of the literature concerning activity-dependent cerebro-cortical development, a survey is made of recent experiments which utilize spontaneous spike-trains as the dependent variable in rodent neocortex cultures when synaptic transmission is interfered with during early ontogeny. Emphasis is placed on the complexity of homeostatic adaptations to reduced as well as intensified firing. Two kinds of adaptation are distinguished: (i) rapid recovery (within several hours) towards baseline levels despite sustained blockade of excitatory synaptic transmission, and (ii) the generation of essentially normal firing patterns in cultures assayed in control medium following development in the presence of excitatory receptor blockers. The former category of homeostatic responses is strongly dependent on the type of preparation, with isolated organotypic explants showing greatly limited plasticity in comparison with co-cultures of matching contralateral pieces of cortical tissue. In such co-cultures, compensatory excitatory drive manifests itself even when all three known types of ionotropic glutamate receptors are chronically blocked, and is then mediated by (muscarinic) cholinergic mechanisms which normally do not contribute measurably to spontaneous activity. The rapid return of high levels of spontaneous firing during sustained selective glutamatergic receptor blockade appears to protect neuronal cultures treated in this way from becoming hyperexcitable. In particular, quasi-epileptiform paroxysmal bursting upon return to control medium, such as appears in preparations where bioelectric activity has been totally suppressed during network formation, fails to appear in chronically receptor blocked cultures. On the contrary, desensitization of blocked glutamate receptors, as a physiological compensation for the up-regulation of non-blocked receptors, could be demonstrated for both the AMPA and the NMDA glutamate receptor sub-types. This wide range of homeostatic responses underscores the importance of spontaneous neuronal discharges for setting and maintaining an optimal balance between excitatory and inhibitory mechanisms in developing neocortical networks.

To properly observe induced connectivity changes after training sessions, one needs a network model that describes individual relationships in sufficient detail to enable observation of induced changes and yet reveals some kind of stability in these relationships. We analyzed spontaneous firing activity in dissociated rat cortical networks cultured on multi-electrode arrays by means of the conditional firing probability. For all pairs (i, j) of the 60 electrodes, we calculated conditional firing probability (CFP(i,j)[tau]) as the probability of an action potential at electrode j at t = tau, given that one was detected at electrode i at t = 0. If a CFP(i,j)[tau] distribution clearly deviated from a flat one, electrodes i and j were considered to be related. For all related electrode pairs, a function was fitted to the CFP-curve to obtain parameters for 'strength' and 'delay' (i.e. maximum and latency of the maximum of the curve) of each relationship. In young cultures the set of identified relationships changed rather quickly. At 16 days in vitro (DIV) 50% of the set changed within 2 days. Beyond 25 DIV this set stabilized: during a week more than 50% of the set remained intact. Most individual relationships developed rather gradually. Moreover, beyond 25 DIV relational strength appeared quite stable, with coefficients of variation (100 x SD/mean) around 25% in periods of approximately 10 h. CFP analysis provides a robust method to describe the underlying probabilistic structure of highly varying spontaneous activity in cultured cortical networks. It may offer a suitable basis for plasticity studies, in the case of changes in the probabilistic structure. CFP analysis monitors all pairs of electrodes instead of just a selected one. Still, it is likely to describe the network in sufficient detail to detect subtle changes in individual relationships.

Networks of cortical neurons were grown over multi electrode arrays to enable simultaneous measurement of signals from multiple neurons. We described functional connectivity in these networks by relationships between individual electrodes, based on conditional firing probabilities. In this study we investigated periods in which the strength of a relationship monotonously increased (strengthening) or decreased (weakening) during periods of 24 or 10 hours. We observed a slightly increased incidence of latencies up to 25 ms during strengthening, while these latencies rarely occurred during weakening. Next, it appeared that relationships tended to strengthen more than average in periods with latencies in the range 5-30 ms, whereas strengthening was significantly less than average in latencies 40-65 ms.

In order to further examine the role of spontaneous action potential (SAP) discharges in neocortical development, amino-acid-mediated synaptic transmission was selectively blocked in an improved organotypic neocortex culture preparation. Contralateral occipital cortex slices from neonatal rats were co-cultured for several weeks in a ventricle-to-ventricle orientation known to greatly enhance cyto-morphological and electrophysiological maturation. Such preparations are highly resistant to attempts to suppress neuronal firing by blocking ionotropic glutamate receptors: not only can kainate receptors partly substitute for NMDA- and AMPA-mediated neurotransmission when these receptors are pharmacologically blocked, but (muscarinic) cholinergic receptors also begin to drive SAP activity when the kainate receptors, too, are chronically blocked. Only tetrodotoxin proved able to eliminate SAPs altogether in these co-cultures, while GABAergic receptor blockade (using bicucculine) led to persistent epileptiform discharges. Treatment effects were assayed upon transfer to control medium by means of a quantitative analysis of spontaneously occurring polyneuronal spike trains. Total suppression of action potentials for several weeks (by tetrodotoxin treatment) led, as in earlier experiments, to strongly intensified burst firing upon transfer to control medium. Chronic glutamate receptor blocked cultures, on the other hand, showed only minor deviations from control firing levels and patterns when assayed in normal medium. Protection against the development of hyperactivity despite partial blockade of synaptic transmission was roughly proportional to the degree to which spontaneous firing during the treatment period approximated normal SAP levels. This homeostatic response to chronically reduced excitatory drive thus differs from earlier results using isolated organotypic cortex cultures, in which the restoration of SAP activity failed to prevent the development of network hyperactivity. Chronic bicucculine treatment, in contrast, had little or no homeostatic effect on SAP firing patterns; on the contrary, opposite to earlier findings using isolated occipital cortex explants, paroxysmal discharges persisted even after transfer to control medium.

Sagittal slices of neonatal rat neocortex, extending from the prefrontal to the occipital area, were cultured separately or in pairs, oriented in such a way that axons projecting from the ventricular surface of each explant could innervate the other one. Functional connections were made between as well as within the explants, and spontaneous field potentials and associated action potentials occurred in variable bursts, and with varying degrees of synchrony. Spike-train analysis revealed that the activity patterns seen in these 'mega' co-cultures closely mimic 'tracé alternant' patterns, consisting of trains of burst discharges recurring several times per minute, which are characteristic for the immature intact cerebral cortex during slow-wave sleep. The prefrontal region was consistently less active than the occipital area but the two were qualitatively similar with respect to their patterns of neuronal firing. Isolated mega-cultures, on the other hand, despite their large size, exhibited only intermittent brief bursts that closely resembled those observed both in occipital cortex tissue fragments and in dissociated cell cultures. The mega-co-culture preparation thus appears to give the best currently available approximation to intrinsic cerebral discharge patterns in vivo.

Extracellular action potentials were recorded from developing dissociated rat neocortical networks continuously for up to 49 days in vitro using planar multielectrode arrays. Spontaneous neuronal activity emerged toward the end of the first week in vitro and from then on exhibited periods of elevated firing rates, lasting for a few days up to weeks, which were largely uncorrelated among different recording sites. On a time scale of seconds to minutes, network activity typically displayed an ongoing repetition of distinctive firing patterns, including short episodes of synchronous firing at many sites (network bursts). Network bursts were highly variable in their individual spatio-temporal firing patterns but showed a remarkably stable underlying probabilistic structure (obtained by summing consecutive bursts) on a time scale of hours. On still longer time scales, network bursts evolved gradually, with a significant broadening (to about 2 s) in the third week in vitro, followed by a drastic shortening after about one month in vitro. Bursts at this age were characterized by highly synchronized onsets reaching peak firing levels within less than ca. 60 ms. This pattern persisted for the rest of the culture period. Throughout the recording period, active sites showed highly persistent temporal relationships within network bursts. These longitudinal recordings of network firing have, thus, brought to light a reproducible pattern of complex changes in spontaneous firing dynamics of bursts during the development of isolated cortical neurons into synaptically interconnected networks.

Spontaneous action potentials were recorded longitudinally for 4-7 weeks from dissociated rat occipital cortex cells cultured on planar multi-electrode plates, during their development from isolated neurons into synaptically connected neuronal networks. Activity typically consisted of generalized bursts lasting up to several seconds, separated by variable epochs of sporadic firing at some of the active sites. These network bursts displayed discharge patterns with age-dependent firing rate profiles, and durations significantly increasing in the 3rd week in vitro and decreasing after about 1 month in vitro, when they evolved into short events with prompt onsets. These findings indicate that after about a month in vitro these cultured neuronal networks have developed a degree of excitability that allows almost instantaneous triggering of generalized discharges. Individual neurons tend to fire in specific and persistent temporal relationships to one another within these network bursts, suggesting that network connectivity maintains a core topology during its development.

Morphological data on two classes of neurons from mammalian midbrain have quantitatively been analyzed for dendritic shape parameters. Their frequency distributions were used to optimize the parameters of a dendritic growth model which describes dendritic morphology by a stochastic growth process of segment branching. The model assumes randomness with respect to both the selection of the branching segment out of the tree segments and the occurrence of the branching event in time. Model-generated trees have shape properties closely matching the observed ones. The dendritic trees of each of the two classes of neurons are represented by a specific set of growth model parameters, thus achieving morphological data compression.

Knowledge about the relationship between morphology and the function of neurons is an important instrument in understanding the role that neurons play in information processing in the brain. In paricular, the diameter and length of segments in dendritic arborization are considered to be crucial morphological features. Consequently, accurate detection of morphological features such as centre line position and diameter is a prerequisite to establish this relationship. Accurate detection of neuron morphology from confocal microscope images is hampered by the low signal to noise ratio of the images and the properties of the microscope point spread function (PSF). The size and the anisotropy of the PSF causes feature detection to be biased and orientation dependent. We deal with these problems by utilizing Gaussian image derivatives for feature detection. Gaussian kernels provide for image derivative estimates with low noise sensitivity. Features of interest such as centre line positions and diameter in a tubular neuronal segment of a dendritic tree can be detected by calculating and subsequently utilizing Gaussian image derivatives. For diameter measurement the microscope PSF is incorporated into the derivative calculation. Results on real and simulated confocal images reveal that centre line position and diameter can be estimated accurately and are bias free even under realistic imaging conditions.

Neuronal firing patterns are influenced by both membrane properties and dendritic morphology. Distinguishing two sources of morphological variability-metrics and topology-we investigate the extent to which model neurons that have the same metrical and membrane properties can still produce different firing patterns as a result of differences in dendritic topology. Within a set of dendritic trees that have the same number of terminal segments and the same total dendritic length, we show that firing frequency strongly correlates with topology as expressed by the mean dendritic path length. The effect of dendritic topology on firing frequency is bigger for trees with equal segment diameters than for trees whose segment diameters obey Rall's 3/2 power law. If active dendritic channels are present, dendritic topology influences not only firing frequency but also type of firing (regular, bursting).

This paper addresses in an integrated and systematic fashion the relatively overlooked but increasingly important issue of measuring and characterizing the geometrical properties of nerve cells and structures, an area often called neuromorphology. After discussing the main motivation for such an endeavour, a comprehensive mathematical framework for characterizing neural shapes, capable of expressing variations over time, is presented and used to underline the main issues in neuromorphology. Three particularly powerful and versatile families of neuromorphological approaches, including differential measures, symmetry axes/skeletons, and complexity, are presented and their respective potentials for applications in neuroscience are identified. Examples of applications of such measures are provided based on experimental investigations related to automated dendrogram extraction, mental retardation characterization, and axon growth analysis.

Neurons connect to each other through a myriad of dendritic and axonal arborisations. Dendritic structures provide the substrate for integration of postsynaptic potentials and control of action potential generation. Axonal structures provide the substrate for action potential dissemination and signalling to target neurons. The morphological complexity of dendritic arborisations is assumed to play a critical role in the transformation of spatio-temporal patterns of postsynaptic potentials into time-structured series of action potentials. Although these transformations lie at the basis of information processing in the brain, it is still far from understood how their details are influenced by dendritic shape. To facilitate research in this area, it is necessary that data on both the morphology and electrical properties of neurons, as well as computational tools for analysis, become available in an integrated way. This requires a combined effort from the fields of informatics and neurosciences (together called neuroinformatics) in order to create data acquisition, databasing and computational tools. Focusing on neuronal morphology, this chapter will give a brief review of the current neuroinformatics developments in both reconstruction techniques, morphological quantification, modeling of morphological complexity, modeling of function and the need for databasing neuronal morphologies. Additionally, one of the dendritic modeling approaches is described in more detail in the Appendix.

The effects of depolarizing stimuli on neurite outgrowth have been shown to depend on an influx of extracellular calcium. However, the role of calcium under non-stimulated growth conditions is less well established. Here we investigated the contribution of calcium signaling to early neuronal morphogenesis of rat cerebral cortex neurons at three levels by blocking L-type voltage sensitive calcium channels, by depleting intracellular calcium or by blocking myosin light chain kinase. Detailed quantitative morphological analysis of neurons treated for 1 day revealed that depletion of intracellular calcium strongly decreased the density of filopodia, arrested axonal outgrowth and strongly decreased dendritic branching. Preventing calcium influx through L-type voltage sensitive calcium channels and blocking of myosin light chain kinase activity selectively decreased dendritic branching. Our observations support an essential role for basal intracellular calcium levels in axonal elongation. Furthermore, under non-stimulated conditions calcium entry through L-type voltage sensitive calcium channels and myosin light chain kinase play an important role in dendritic branching.

Dendritic/axonal growth has been examined in long-term organotypic neocortical explants taken from neonatal rat pups and grown either as isolated slices or as co-cultures. The quantitative light microscopic measurement of dendritic and axonal branching patterns within both types of explants was carried out on Golgi-stained materials. Spontaneous bioelectric activity (SBA) was blocked within both types of explants using a combination of APV and DNQX, NMDA and non-NMDA receptor antagonists, respectively. No extracellularly measurable SBA was observed to occur in the silenced explants in the presence of both antagonists but reappeared following wash-out with control medium. In both control and silenced explants, the overall cellular organization of the slice was maintained throughout the culturing period, with distinguishable pyramidal and non-pyramidal neurons located within the same layers and with the same orientations as observed in situ. The major findings of the present study show the following. (i) Pyramidal neurones chronically exposed to APV/DNQX exhibited no basal dendritic growth in co-cultured explants, while growth of apical dendritic lengths was similar to control values in the absence of SBA. (ii) Pyramidal neurones, nonetheless, exhibited significant terminal segment growth under SBA blockade which was correlated with a concomitant decrease in number of basal dendrites. (iii) Axonal growth in co-cultures was not sustained in silenced pyramidal neurones. (iv) Non-pyramidal neurones showed significant total dendritic and axonal growth in co-cultures following APV/DNQX treatment. (v) Non-pyramidal cells in co-cultures experienced an increase in terminal segment length at 2 weeks which declined in the third week. This increase-decrease was correlated with a decrease-increase in the total number of dendritic segments during the second and third weeks, respectively. (vi) In isolated explants the only departure from control growth curves was a significant increase in terminal segment length which was offset by a similar decrease in number of dendritic segments under APV/DNQX growth conditions. Thus the chronic loss of glutamate-mediated SBA differentially effected pyramidal and non-pyramidal neurones in isolated and co-cultured explants, with pyramidal neurones experiencing the more pronounced effects. We conclude that SBA effects the dynamics of neuritic elongation and branching and that these changes are most dramatically seen in co-cultures which cross-innervate one another, presumably via pyramidal axons. We hypothesize that the activity-dependent changes associated with reduction in pyramidal dendritic and axonal growth may be associated with neurotrophin receptor production/maturation.

A study was made of the possible basis for naturally occurring variations in the number of segments in individual dendritic trees. Distributions of the number of terminal segments have been studied in dendrites from rat, cat, and frog motoneurons, basal dendrites from rat visual cortex pyramidal and non-pyramidal neurons, in rat cerebellar Purkinje cell dendritic trees, and in human hippocampal dentate granule cells. By means of a mathematical model for dendritic branching, it was shown that the variation in the number of dendritic segments can be accounted for by assuming that new branches during neurite outgrowth are formed randomly at terminal segments. The observed terminal segment number distributions could be closely approximated by additionally assuming that branching probabilities decline with increasing number of terminal segments in growing dendrites. The pyramidal neuron group differed significantly from the other neuron groups in such a way as to suggest that this decline is stronger than in the dendrites of other types of neurons. By using literature data on the mean number of terminal segments in rat cerebellar Purkinje cells, measured at different times during early development, an estimate could be obtained of the time-course of the branching probabilities. The branching probability of a terminal segment was found to be in the order of 0.002 per hour in the first 4 weeks postnatal with a 5-fold transient increase in the second week.

Dendritic growth has been studied in long-term organotypic neonatal rat occipital neocortex grown either apart as isolated explants or in tandem as cocultures. Quantitative light microscopic measurement of dendritic and axonal branching patterns within the cortical slice was accomplished using rapid Golgi stained materials. In both isolates and cocultures the overall cellular organization of the slice was maintained over 4 weeks in vitro with morphologically distinguishable pyramidal and nonpyramidal neurons located within the same layers and with the same orientations as observed in situ. Long-term increases in the total length of basal dendrites, apical dendrite and axons were observed only in cocultures and were similar to growth patterns reported for in situ materials. Dendritic growth was mainly due to elongation of terminal dendritic segments. Surprisingly, isolated explants showed no long-term increases in total (basal) dendrites, apical dendrites or axons with time in vitro. A transient decrease in the number of basal dendritic segments and increase in terminal segment lengths at the end of the first week in vitro, however, was observed in nonpyramidal neurons. It is hypothesized that (i) afferent inputs and/or efferent targets develop only in cocultures and provide a crucial conditions for the continued growth of dendritic/axonal arborization for neocortical neurons in vitro, (ii) intrinsic interconnectivity within isolated explants is not sufficient to maintain long-term growth of neuritic arbors, and (iii) remodelling of dendritic arbors within isolated explants occurs at the same time as these explants are showing noticeable increases in the level of spontaneous bioelectric activity, which suggests that dendritic growth and network formation may be function dependent.

Empirical studies have demonstrated that electrical activity of the neuron can directly affect neurite outgrowth. High levels of activity cause neurites to retract, whereas low levels allow further outgrowth. Previously we studied networks in which all the cells reacted in the same way on electrical activity. Since experiments have shown that neurons may in fact react differentially, we study in this paper networks in which the range of activity where outgrowth takes place varies among cells. We show that this can lead to complex periodic behaviour in electrical activity and connectivity of individual cells. The precise behaviour depends on the spatial distribution of the cells and the distribution of the outgrowth properties over the cells. Any other cellular property that adapts slowly to electrical activity such that neuronal activity is attempted to be maintained at a given level, can lead to similar results.

Many structural and functional properties of neuronal networks find their origin in the dynamic behavior of growth cones during development. The variation in dendritic morphologies can be traced back to random branching of growth cones. Segment length characteristics arise under random branching and steady growth cone propagation. Delayed outgrowth, as a result of competition between growth cones after splitting, is hypothesized to explain different lengths of paired terminal segments in Purkinje cells. The implications of activity-dependent neurite outgrowth were studied using an outgrowth function based on the theory of Kater et al. (1988, 1990). This theory embodies a homeostatic principle, according to which a neuron adapts its neuritic field so as to maintain a certain level bioelectric activity. It is shown that such homeostasis has many implications for neuromorphogenesis and network formation, as it may underlie phenomena such as overshoot during development, size differences among cells, differentiation between excitatory and inhibitory cells and compensatory sprouting. Finally, function-dependent regulation of development involves physiological as well as morphological variables. For instance, activity dependent regulation of ionic conductances such as to stabilize functional activity can result in a differentiation of certain neurons into, respectively, bursting and regular firing sub-types (Abbot et al., 1993; LeMasson et al., 1993). Similarly, the GABAergic phenotype comes fully to expression in hindbrain (cerebellar) and forebrain (neocortical) networks only if the level of ongoing excitatory activity during development is sufficiently high, whereas chronically intensified activity leads to a compensatory hypertrophy of inhibitory mechanisms (for review, see Corner 1994). Many of these results could only have been obtained by the use of mathematical models which allow rigorous analysis of the consequences of basic assumptions in the dynamics of neurite outgrowth. All in all, the findings further emphasize the role of spontaneous bioelectric activity during early development in neuronal network formation, the importance of which was first established in cultures of developing neural tissue.

Empirical studies have demonstrated that electrical activity of the neuron can directly affect neurite outgrowth. In this paper, we study the possible implications of activity-dependent neurite outgrowth for neuronal morphology and network development, using a model in which initially disconnected cells organize themselves into a network under the influence of their intrinsic activity. A neuron is modelled as a neuritic field, the growth of which depends on its own level of activity, and neurons become connected when their fields overlap. In a purely excitatory network, we have previously demonstrated that activity-dependent outgrowth in combination with a neuronal response function with some form of firing threshold is sufficient to cause a transient overproduction (overshoot) in the number of connections or synapses. Here we show that overshoot still takes place in a network of excitatory and inhibitory cells, and can even be enhanced. With delayed development of inhibition the growth curve of the number of inhibitory connections no longer exhibits overshoot. An interesting emergent property of the model is that, solely as the result of simple outgrowth rules and cell interactions, the (dendritic) fields of the inhibitory cells tend to become smaller than those of the excitatory cells, even if both type of cells have the same outgrowth properties. Other consequences of the interactions among outgrowth, excitation and inhibition are that (i) the spatial distribution of inhibitory cells becomes important in determining the level of inhibition; (ii) pruning of connections can no longer take place if the network has grown without proper electrical activity for longer than a certain critical period; (iii) inhibitory cells, by inducing outgrowth, can help to connect different parts of a structure. Further, the model predicts that excitatory cell death will be accompanied by an increased neuritic field of surviving neurons ("compensatory sprouting"). The similarities of the model with findings in developing tissue cultures of dissociated cells are extensively discussed.

A model is developed to describe neuronal elongation as a result of the polymerization of microtubules and elastic stretching of the neurites by force produced by the growth cone. The model for a single segment with a single growth cone revealed a constant elongation rate, while the concentration of tubulin in the soma rises, and the concentration of tubulin becomes constant in the growth cone. Extending the model to a neurite with a single branch point and two growth cones revealed the same results. When the assembly or the disassembly rate of microtubules is unequal in both growth cones, transient retraction of one of the terminal segments occurs, which results in complete retraction of the segment when the difference in (dis)assembly rate between the two growth cones is large enough. When the model is applied to large trees, a maximal sustainable number of terminal segments as a function of the production rate of tubulin appears. Mechanisms to stop outgrowth are discussed in relation to the establishment of synaptical contacts between cells.

A basic but neglected property of neuronal trees is their finite length. This finite length restricts the length of a segment to a certain maximum. The implications of the finite length of the tree with respect to the segment length distributions of terminal and intermediate segments are shown by means of a stochastic model. In the model it is assumed that branching is governed by a Poisson process. The model shows that terminal segments are expected to be longer than intermediate segments. Terminal and intermediate segments are expected to decrease in length with increasing centrifugal order. The results are compared with data from in vivo pyramidal cells from rat brain and tissue cultured ganglion cells from chicken. A good agreement between data and model was found.

The geometrical properties of neurons are important for the way they function within neural circuits. The arborescent processes of neurons that are necessary for the transmission of the information are formed by branching and elongation of segments. In studies that model the outgrowth the tree structures have generally been considered as binary. However, multifurcations do occur. It will be shown that if the multifurcations can be considered as aggregates of bifurcations they may be included in the topological analysis of neuronal branching patterns.

The vertex ratio is the crucial quantity in vertex analysis, which is a method to characterize the mode of growth of neuronal tree structures (i.e. dendrites and axons). In this report we propose the use of the Monte Carlo test to calculate a level of significance for the vertex ratio. As a result the vertex ratio can be used to analyse neuronal trees with respect to a range of growth hypotheses, including terminal and segmental growth.

Statistical analysis of the frequencies of observed branching patterns of neuronal arborescences is an important means of studying neuronal growth and of characterizing axonal or dendritic populations. We recently derived simple formulae for the exact probabilities of occurrence of types of neuronal trees for both segmental and terminal growth. Additionally, the existence of a natural ordering of the neuronal tree types enables the application of the Kolmogorov goodness-of-fit test. In the present report it is illustrated how these facilities can be incorporated in the analysis of neuronal arborizations. Interesting features are that very large neuronal arborizations can be analyzed completely and that only small sample sizes are required for the estimation of the critical level corresponding to the growth hypothesis. Further, it is indicated how populations of neuronal tree structures may be compared with each other without reference to a particular growth theory.

The morphology of neurons is an important factor for the identification and the study of the changes that occur in the nervous system during development or as a result of disease or an experimental treatment. A number of methods to describe the topological aspects of neuronal morphology is discussed. Furthermore it is illustrated how different groups of neurons can be compared. Although both topological and metrical aspects are considered in the comparative sections emphasis is put on counting instead of measuring. Our intention is to present quick and easy methods that are applicable to camera lucida drawings.

The complexity of a neuronal cell shape is known to be related to its function. Specifically, among other indicators, a decreased complexity in the dendritic trees of cortical pyramidal neurons has been associated with mental retardation. In this paper we develop a procedure to address the characterization of morphological changes induced in cultured neurons by over-expressing a gene involved in mental retardation. Measures associated with the multiscale connectivity, an additive image functional, are found to give a reasonable separation criterion between two categories of cells. One category consists of a control group and two transfected groups of neurons, and the other, a class of cat ganglionary cells. The reported framework also identified a trend towards lower complexity in one of the transfected groups. Such results establish the suggested measures as an effective descriptors of cell shape. [ABSTRACT FROM AUTHOR]

The article presents an abstract of the study "Selected Growth of Neocortical Pyramidal Basal Dendrites Chronically Exposed to Brain-Derived Neurotrophic Factor." The interplay between brain derived neurotrophic factor and spontaneous bioelectric activity on dendritic elongation from neonatal rat neocortex was studied. Both adenoviral vector and exogenous additions of Brain-Derived Neurotrophic Factor peptide resulted in the potent promotion of only basal dendritic growth in pyramidal neurons.

Abstract: In recent studies we have demonstrated that arsenic (As) metabolites change the composition of neuronal cytoskeletal proteins in vivo and in vitro. To further examine the mechanism of arsenic-induced neurotoxicity with various arsenate metabolites (iAsV, MMAV and DMAV) and arsenite metabolites (iAsIII, MMAIII and DMAIII), we investigated the role of the proteolytic enzyme calpain and its involvement in the cleavage of p35 protein to p25, and also mRNA expression levels of calpain, cyclin-dependent kinase 5 (cdk5) and glycogen synthase kinase 3 beta (gsk3ß). A HeLa cell line transfected with a p35 construct (HeLa-p35) was used as a model, since all other proteins such as calpain, CDK5 and GSK3β are already present in HeLa cells as they are in neuronal cells. HeLa-p35 cells were incubated with various As metabolites and concentrations of 0, 10 and 30μM for duration of 4h. Subsequently the cells were either lysed to study their relative quantification levels of these genes or to be examined on their p35-protein expression. P35-RNA expression levels were significantly (p <0.01) increased by arsenite metabolites, while p35 protein was cleaved to p25 (and p10) after incubation with these metabolites. The cleavage of p35 is caused by calcium (Ca2+) induced activation of calpain. Inhibition of calpain activity by calpeptin prevents cleavage of p35 to p25. These results suggest that cleavage of p35 to p25 by calpain, probably As-induced Ca2+-influx, may explain the mechanism by which arsenic induces its neurotoxic effects. [Copyright &y& Elsevier]

Abstract: Understanding how the information is coded in large neuronal networks is one of the major challenges for neuroscience. A possible approach to investigate the information processing capabilities of the neuronal ensembles is given by the use of dissociated neuronal cultures coupled to microelectrode arrays (MEAs). Here, we describe a new strategy, based on MEAs, for studying in vitro neuronal network dynamics in interconnected sub-populations of cortical neurons. The rationale is to sub-divide the neuronal network into communicating clusters while preserving a high degree of functional connectivity within each confined sub-population, i.e. to achieve a compromise between a completely random large neuronal population and a patterned network, such as currently used with conventional MEAs. To this end, we have realized and functionally characterized a Pt microelectrode array with an integrated EPON SU-8 clustering structure, allowing to confine five relatively large yet interconnected spontaneously developing neuronal networks (i.e. thousands of cells). The clustering structure consists of five chambers of 3mm in diameter interconnected via 800μm long and 300μm wide microchannels and is integrated on the MEA of 60 thin-film Pt electrodes of 30μm diameter. Tests of the Pt microelectrodes’ stability under stimulation showed a stable behavior up to 35,000 voltage stimuli and the biocompatibility was assessed with the cultures of dissociated rat''s cortical neurons achieving cultures’ viability up to 60 days in vitro. Compared to conventional MEAs, the monitoring of spontaneous and evoked activity and the computation of the Post-Stimulus Time Histogram (PSTH) within the clusters clearly demonstrates: (i) the capability to selectively activate (through poly-synaptic pathways) specific network regions and (ii) the confinement of the network dynamics mainly in the highly connected sub-networks. [Copyright &y& Elsevier]

Abstract: Cortical neurons extracted from the developing rat central nervous system and put in culture, show, after a few days, spontaneous activity with a typical electrophysiological pattern ranging from stochastic spiking to synchronized bursting. Using microelectrode arrays (MEA), on which dissociated cultures can be grown for long-term measurements, we recorded the electrophysiological activity of cortical networks during development, in order to monitor their responses at different stages of the maturation process. Employing algorithms for detection and analysis of bursts in single-channel spike trains and of synchronized network bursts in multi-channel spike trains, significant changes have been revealed in the firing dynamics at different stages of the developmental process. [Copyright &y& Elsevier]

In vitro cultured neurons form a bi-dimensional physical model of the brain. In spite of their simplified level of organization, they provide a useful framework to study information processing in the nervous system. NeuroBIT is an EU-funded project, aimed at developing algorithms and techniques that allow for establishing a bi-directional connection between cultured neurons and external devices (e.g., robots). The main purpose is to enable ‘embodied’ in vitro experiments, in which neural populations are provided with an actual physical body. Embodiment is likely to be crucial in studying the mechanisms of sensorimotor integration, control and adaptation in living systems. Here we present the general objectives of the project, and show the results of preliminary experiments and simulations. [Copyright &y& Elsevier]