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.     

Role of a Tetraethylammonium-Sensitive Component of Potassium Currents in High-Frequency Tonic Impulsation Generated by Rat Retinal Ganglion Cells

Using the voltage/current clamp technique in the whole-cell configuration, we studied the role of the highly tetraethylammonium (TEA) -sensitive component of integral potassium current in the generation of high-frequency tonic impulsation by rat retinal ganglion cells (RGCs). Application of 0.5 mM TEA led to a decrease in the frequency of evoked tonic impulsation by RGCs by 63% (from 55 ± 10 sec^–1 in the control to 26 ± 5 sec^–1 in the presence of the blocker; n = 11). In this case, the duration of single action potentials at the level of 50% their amplitude increased by 64% (from 1.1 ± 0.1 to 1.8 ± 0.1 msec; n = 11), the rate of repolarization decreased by 54% (from −101 ± 9 to −46 ± 5 mV/msec; n = 11), and the amplitude of afterhyperpolarization dropped by 62% (from −16 ± 2 to −6 ± 2 mV; n = 11). Upon the action of 0.5 mM TEA, the amplitude of the integral potassium current in RGCs decreased; the current component sensitive to the above blocker was equal to 0.41 ± 0.05 nA (n = 6), while the respective value in the control was 1.62 ± 0.14 nA (n = 12). Thus, a moderate (on average, by 25%) decrease in the amplitude of the above potassium current significantly influenced the characteristics of impulse activity generated by RGCs. The TEA-sensitive component of the current was similar to the Kv3.1/Kv3.2 potassium current described earlier. The obtained data are indicative of the key role of the highly TEA-sensitive component of the potassium current (passed probably via Kv3.1/Kv3 channels) in high-frequency tonic activity generated by RGCs.     

Resonantlike Synchronization and Bursting in a Model of Pulse-Coupled Neurons with Active Dendrites

We analyze the dynamical effects of active, linearized dendritic membranes on the synchronization properties of neuronal interactions. We show that a pair of pulse-coupled integrate-and-fire neurons interacting via active dendritic cables can exhibit resonantlike synchronization when the frequency of the oscillators is approximately matched to the resonant frequency of the membrane impedance. For weak coupling the neurons are phase-locked with constant interspike intervals whereas for strong coupling periodic bursting patterns are observed. This bursting behavior is reflected by the occurrence of a Hopf bifurcation in the firingrates of a corresponding rate-coded model.     

Remote Modulation of Current Transfer from Dendritic Glutamatergic Synapses by GABA-ergic Synapses of the Somatic Zone of Motoneurons: a Simulation Study

Until now, information concerning spatial interaction of postsynaptic excitation and inhibition in neuronal dendrites remains rather limited. In model experiments, we studied spatial effects of tonic co-activation of GABA-ergic synapses situated on the soma and axon hillock of a motoneuron and dendritic glutamatergic synapses with receptors sensitive or insensitive to N-methyl-D-aspartate. We analyzed distribution maps of the transmembrane potentials and excitatory currents transferred toward the soma over the reconstructed dendritic arborization of a rat abducens motoneuron (three-dimensional reconstruction). In the motoneuron, isolated tonic excitation of glutamatergic synapses induced two stable states of low (downstate) or high (upstate) spatially heterogeneous dendritic depolarization, which decayed with unequal rates along different dendritic paths. In this case, the local steady-state current-voltage relation of the dendritic membrane became N-shaped due to a limb of the negative slope within a certain voltage range. The upstate corresponding to plateau potentials associated with stereotyped motor activity patterns was analyzed in detail. In this state, most proximal dendritic sites were the main sources of the excitatory current reaching the soma, while the contribution from distal sites was negligible. Co-activation of GABA-synapses located at the soma and axon hillock reduced this depolarization and shifted the main excitatory current source from a perisomatic location to the middle, structurally more complex, region of the dendritic arborization. The more remote dendritic region having a greater membrane area and receiving a greater number of synaptic contacts became directly involved in the supply of the trigger zone by the excitatory current. We suggest that a special, not described earlier, operational mechanism of postsynaptic inhibition is manifested in the above spatial effects of activation of strategically located inhibitory synapses, and that the list of known crucial inhibitory mechanisms (namely hyperpolarization and shunting of the postsynaptic membrane) must be expanded.     

Structure Dependence of the Calcium Dynamics in Purkinje Neuron Dendrites during Generation of Bursting Discharges: a Simulation Study

In the model of a cerebellar Purkinje neuron with reconstructed active dendrites, we investigated the impact of the ratio between volumes of the endoplasmic reticulum (organellar calcium store) and cytosol on the Ca²⁺ dynamics in asymmetrical parts of the dendritic arborization during generation of different structure-dependent patterns of bursting activity. Tonic synaptic excitation homogeneously distributed over the dendrites (a spatially homogeneous stationary input signal) caused spatially heterogeneous variations of the dendritic membrane potential (MP) accompanied by periodical or nonperiodical bursts of action potentials at the cell output. The MP waveforms recorded from the segments of asymmetrical dendrites were then applied to the membrane of selected dendrite segments as command voltages in a dynamic clamp mode. In these segments, the relative size of the stores was varied. This provided equal to each other local calcium currents and influxes into the cytosol of the segment differently filled with the organellar store. Regardless of the impulse pattern, microgeometry of the segment and the store modulated calcium transients exactly in the same way as in previous studies of electrical and concentration responses to local phasic synaptic excitation of the modeled neuron. Peak values of depolarization-induced elevations of the cytosolic Ca²⁺ concentration increased with the portion of the intracellular volume occupied by the store. The most important factor defining this dependence was the ratio of the membrane area vs the organelle-free cytosol volume of the dendritic segment. Concentrations of Са²⁺ deposited in equal-sized segments of asymmetrical parts of the dendritic arborization where asynchronous unequal variations of the MP were observed during generation of nonperiodical bursting at the output demonstrated considerable specificity. A greater amount of calcium was deposited in the segments staying, on average, in a high-depolarization state for a longer time (this intensified activation of calcium channels and amplified the corresponding Ca²⁺ influx into the cytosol). Hence, local dynamics of the Ca²⁺ concentration depend directly on local microgeometry and indirectly on global macrogeometry of the dendrite arborization, as the latter determines spatial asymmetry-related unequal transients in different parts of the dendritic arborization having active membrane properties.     

Dynamic Range of Vertebrate Retina Ganglion Cells: Importance of Active Dendrites and Coupling by Electrical Synapses

The vertebrate retina has a very high dynamic range. This is due to the concerted action of its diverse cell types. Ganglion cells, which are the output cells of the retina, have to preserve this high dynamic range to convey it to higher brain areas. Experimental evidence shows that the firing response of ganglion cells is strongly correlated with their total dendritic area and only weakly correlated with their dendritic branching complexity. On the other hand, theoretical studies with simple neuron models claim that active and large dendritic trees enhance the dynamic range of single neurons. Theoretical models also claim that electrical coupling between ganglion cells via gap junctions enhances their collective dynamic range. In this work we use morphologically reconstructed multi-compartmental ganglion cell models to perform two studies. In the first study we investigate the relationship between single ganglion cell dynamic range and number of dendritic branches/total dendritic area for both active and passive dendrites. Our results support the claim that large and active dendrites enhance the dynamic range of a single ganglion cell and show that total dendritic area has stronger correlation with dynamic range than with number of dendritic branches. In the second study we investigate the dynamic range of a square array of ganglion cells with passive or active dendritic trees coupled with each other via dendrodendritic gap junctions. Our results suggest that electrical coupling between active dendritic trees enhances the dynamic range of the ganglion cell array in comparison with both the uncoupled case and the coupled case with cells with passive dendrites. The results from our detailed computational modeling studies suggest that the key properties of the ganglion cells that endow them with a large dynamic range are large and active dendritic trees and electrical coupling via gap junctions.     

Simulation Study of Non-Organellar Binding of Calcium by Fast and Slow Buffers in Dendrites Containing an Organellar Store

Dependences of intracellular calcium signals on the concentrations of endogenous buffers (slow, parvalbumin, and fast, calmodulin) and a calcium-sensitive fluorophore (Fura-4F) were investigated on mathematical models of compartments of the reconstructed dendrite of a cerebellum Purkinje neuron. A Ca²⁺-storing cistern of the endoplasmic reticulum (ER) was present in the dendrite. Calcium signals developed when the neuron generated responses to single synaptic excitation or intrinsic non-periodical impulse activity. The dynamics of the buffer binding capacity were also studied; this capacity was characterized by the ratio of concentrations of bound and free calcium or concentration increments of the latter. The plasma membrane of the dendrite possessed ion channels (including those of synaptic currents) and the calcium pump characteristic of the mentioned neuron. Model equations took into account Ca²⁺ exchange between the cytosol, buffers, ER, and extracellular medium, as well as diffusion processes. The ER membrane contained the calcium pump, leakage channels, and channels of calcium-induced release and inositol-3-phosphate-dependent releases of Ca²⁺. The ER cistern occupied 1 to 36% of the intracellular volume. Upon different occupancies of the dendrite by the organelle store, an increase in the concentration of the slow buffer insignificantly decreased the cytosolic Ca²⁺ transients with no effect on their shape. The fast buffer and the dye with similar kinetic properties caused slowing down of the rising phase of Ca²⁺ transients, decrease in the early component, and increase in the late component of the latter. In the case of nonperiodical and asynchronous intrinsic oscillations of the membrane potential typical of asymmetrical active dendrites, the slow buffer, like the ER store, bound more Ca²⁺ in compartments of compatible sizes and fillings by the organelles belonging to those metrically asymmetrical branches, which, on average, stayed longer in the state of high depolarization; this provided a greater Ca²⁺ entry from outside. Hence, the pattern of structural/functional organization of calcium signalization in the dendrites can be complemented in the part of both the direct influences of local microgeometry of the dendrite and the indirect ones related to global macrogeometry of the dendritic arborization.     

Experimental Study of a Starting Vortex Ring Generated by a Thin Circular Disk

The formation process of vortex ring generated by a thin circular disk was studied experimentally in this paper. A thin circular disk installed a linear motion stage was used to generate the vortex rings. Digital Particle Image Velocimetry (DPIV) was used to measure the velocity and vorticity fields. The finite-time Lyapunov exponent field corresponding to the vortex flow was computed to identify Lagrangian coherent structures of the starting vortex. The results reveal the existence of a flux window between repelling Lagrangian Coherent Structures (rLCS) and attracting Lagrangian Coherent Structures (aLCS), through which the shear flow is entrained into the vortex. The flux window is closed gradually during the starting process. Once the flux window shut down, the formation process of the vortex ring finishes, as the shear flow with vorticity cannot be entrained in the vortex ring.     

A Strategy to Calculate the Patterns of Nutrient Consumption by Microorganisms Applying a Two-Level Optimisation Principle to Reconstructed Metabolic Networks

Bacterial responses to environmental changes rely on a complex network of biochemical reactions. The properties of the metabolic network determining these responses can be divided into two groups: the stoichiometric properties, given by the stoichiometry matrix, and the kinetic/thermodynamic properties, given by the rate equations of the reaction steps. The stoichiometry matrix represents the maximal metabolic capabilities of the organism, and the regulatory mechanisms based on the rate laws could be considered as being responsible for the administration of these capabilities. Post-genomic reconstruction of metabolic networks provides us with the stoichiometry matrix of particular strains of microorganisms, but the kinetic aspects of in vivo rate laws are still largely unknown. Therefore, the validity of predictions of cellular responses requiring detailed knowledge of the rate equations is difficult to assert. In this paper, we show that by applying optimisation criteria to the core stoichiometric network of the metabolism of Escherichia coli, and including information about reversibility/irreversibility only of the reaction steps, it is possible to calculate bacterial responses to growth media with different amounts of glucose and galactose. The target was the minimisation of the number of active reactions (subject to attaining a growth rate higher than a lower limit) and subsequent maximisation of the growth rate (subject to the number of active reactions being equal to the minimum previously calculated). Using this two-level target, we were able to obtain by calculation four fundamental behaviours found experimentally: inhibition of respiration at high glucose concentrations in aerobic conditions, turning on of respiration when glucose decreases, induction of galactose utilisation when the system is depleted of glucose and simultaneous use of glucose and galactose as carbon sources when both sugars are present in low concentrations. Preliminary results of the coarse pattern of sugar utilisation were also obtained with a genome-scale E. coli reconstructed network, yielding similar qualitative results.     

Dependence of Transformation of Intrinsic Rhythmic Impulse Activity of Neurons on Spatio-Temporal Organization of Synaptic Actions on Dendrites: A Simulation Study

The aim of the study to elucidate the biophysical mechanisms able to determine specific transformations of the patterns of output signals of neurons (neuronal impulse codes) depending on the spatio-temporal organization of synaptic actions coming to the dendrites. We studied mathematical models of the neocortical layer 5 pyramidal neurons built according to the results of computer reconstruction of their dendritic arborizations and experimental data on the voltage-dependent conductivities of their dendritic membrane. This work is a continuation of our previous studies that showed the existence of certain relations between the complexity of neural impulse codes, on the one hand, and the complexity, size, metrical asymmetry of branching, and nonlinear membrane properties of the dendrites, on the other hand. This relation determines synchronous (with some phase shifts) or asynchronous transitions of asymmetrical dendritic subtrees between high and low depolarization states during the generation of output impulse patterns in response to distributed tonic activation of dendritic inputs. In this work we demonstrate the first time that the appearance and pattern of transformations of complex periodical impulse trains at the neuron’s output associated with receiving a short series of presynaptic action potentials are determined not only by the time of arrival of such a series, but also by their spatial addressing to asymmetric dendritic subtrees; the latter, in this case, may be in the same (synchronous transitions) or different (asynchronous transitions) electrical states. Biophysically, this phenomenon is based on a significant excess of the driving potential for a synaptic excitatory current in low-depolarization regions, as compared with that in high-depolarization dendritic regions receiving phasic synaptic stimuli. These findings open a novel aspect of the functioning of neurons and neuronal networks.     

Spatial Genetic Structure Patterns of Phenotype-Limited and Boundary-Limited Expanding Populations: A Simulation Study

Range expansions may create a unique spatial genetic pattern characterized by alternate genetically homogeneous domains and allele frequency clines. Previous attempts to model range expansions have mainly focused on the loss of genetic diversity during expansions. Using individual-based models, we examined spatial genetic patterns under two expansion scenarios, boundary-limited range expansions (BLRE) and phenotype-limited range expansions (PhLRE). Our simulation revealed that the genetic diversity within populations lost quickly during the range expansion, while the genetic difference accumulated between populations. Consequently, accompanying the expansions, the overall diversity featured a slow decrease. Specifically, during BLREs, high speed of boundary motion facilitated the maintenance of total genetic diversity and sharpened genetic clines. Very slight constraints on boundary motion of BLREs drastically narrowed the homogeneous domains and increased the allele frequency fluctuations from those levels exhibited by PhLREs. Even stronger constraints, however, surprisingly brought the width of homogeneous domains and the allele frequency fluctuations back to the normal levels of PhLREs. Furthermore, high migration rates maintained a higher total genetic diversity than low ones did during PhLREs. Whereas, the total genetic diversities during BLREs showed a contrary pattern: higher when migration was low than those when migration was high. Besides, the increase of migration rates helped maintain a greater number of homogeneous domains during PhLREs, but their effects on the number of homogeneous domains during BLREs were not monotonous. Previous studies have showed that the homogenous domains can merge to form a few broad domains as the expansion went on, leading to fewer homogeneous domains. Our simulations, meanwhile, revealed that the range expansions could also rebuild homogeneous domains from the clines during the range expansion. It is possible that that the number of homogeneous domains was determined by the interaction of merging and newly emerging homogeneous domains.     

Embryonic Origins of a Motor System:Motor Dendrites Form a Myotopic Mapin Drosophila

The organisational principles of locomotor networks are less well understood than those of many sensory systems, where in-growing axon terminals form a central map of peripheral characteristics. Using the neuromuscular system of the Drosophila embryo as a model and retrograde tracing and genetic methods, we have uncovered principles underlying the organisation of the motor system. We find that dendritic arbors of motor neurons, rather than their cell bodies, are partitioned into domains to form a myotopic map, which represents centrally the distribution of body wall muscles peripherally. While muscles are segmental, the myotopic map is parasegmental in organisation. It forms by an active process of dendritic growth independent of the presence of target muscles, proper differentiation of glial cells, or (in its initial partitioning) competitive interactions between adjacent dendritic domains. The arrangement of motor neuron dendrites into a myotopic map represents a first layer of organisation in the motor system. This is likely to be mirrored, at least in part, by endings of higher-order neurons from central pattern-generating circuits, which converge onto the motor neuron dendrites. These findings will greatly simplify the task of understanding how a locomotor system is assembled. Our results suggest that the cues that organise the myotopic map may be laid down early in development as the embryo subdivides into parasegmental units.     

Role of Calcium Electrogenesis in Apical Dendrites: Generation of Intrinsic Oscillations by an Axial Current

Dendrites are covered with conductances whose function is still mysterious. Using intracellular recording and calcium imaging, we describe an electrogenic band of calcium channels in distal apical dendrites of layer 5 pyramidal neurons (Yuste et al., 1994). We now explore the functional consequences of this distal electrogenic area with multicompartmental numerical simulations. A calcium imaging and electrophysiological database from a single neuron, recorded under blocked sodium and potassium conductances, is replicated by simulations having increased dendritic calcium current. In these models a significant axial current flows from the apical dendrite into the somatic region, activating low-threshold calcium channels and generating oscillations similar to those seen in the electrophysiological data. We propose that the distal electrogenic area in apical dendrites serves to inject current into the soma and produce intrinsic oscillatory dynamics.     

Coevolution: Patterns of legume predation by a lycaenid butterfly

Summary Perennial legumes in Gunnison County, Colorado suffer heavy differential flower predation by larvae of a lycaenid butterfly. The butterfly populations may be resource-limited, and seem in turn to be an important factor in the evolution and distribution of the various legume species.     

Morphological Diversity of the Rod Spherule: A Study of Serially Reconstructed Electron Micrographs

Purpose

Rod spherules are the site of the first synaptic contact in the retina’s rod pathway, linking rods to horizontal and bipolar cells. Rod spherules have been described and characterized through electron micrograph (EM) and other studies, but their morphological diversity related to retinal circuitry and their intracellular structures have not been quantified. Most rod spherules are connected to their soma by an axon, but spherules of rods on the surface of the Mus musculus outer plexiform layer often lack an axon and have a spherule structure that is morphologically distinct from rod spherules connected to their soma by an axon. Retraction of the rod axon and spherule is often observed in disease processes and aging, and the retracted rod spherule superficially resembles rod spherules lacking an axon. We hypothesized that retracted spherules take on an axonless spherule morphology, which may be easier to maintain in a diseased state. To test our hypothesis, we quantified the spatial organization and subcellular structures of rod spherules with and without axons. We then compared them to the retracted spherules in a disease model, mice that overexpress Dscam (Down syndrome cell adhesion molecule), to gain a better understanding of the rod synapse in health and disease.

Methods

We reconstructed serial EM images of wild type and Dscam^GoF (gain of function) rod spherules at a resolution of 7 nm in the X-Y axis and 60 nm in the Z axis. Rod spherules with and without axons, and retracted spherules in the Dscam^GoF retina, were reconstructed. The rod spherule intracellular organelles, the invaginating dendrites of rod bipolar cells and horizontal cell axon tips were also reconstructed for statistical analysis.

Results

Stereotypical rod (R1) spherules occupy the outer two-thirds of the outer plexiform layer (OPL), where they present as spherical terminals with large mitochondria. This spherule group is highly uniform and composed more than 90% of the rod spherule population. Rod spherules lacking an axon (R2) were also described and characterized. This rod spherule group consists of a specific spatial organization that is strictly located at the apical OPL-facing layer of the Outer Nuclear Layer (ONL). The R2 spherule displays a large bowl-shaped synaptic terminal that hugs the rod soma. Retracted spherules in the Dscam^GoF retina were also reconstructed to test if they are structurally similar to R2 spherules. The misplaced rod spherules in Dscam^GoF have a gross morphology that is similar to R2 spherules but have significant disruption in internal synapse organization.

Conclusion

We described a morphological diversity within Mus musculus rod spherules. This diversity is correlated with rod location in the ONL and contributes to the intracellular differences within spherules. Analysis of the Dscam^GoF retina indicated that their R2 spherules are not significantly different than wild type R2 spherules, but that their retracted rod spherules have abnormal synaptic organization.