Transfer properties of neuronal dendrites with tonically activated conductances

The somatopetal current transfer was studied in the mathematical models of a reconstructed brainstem motoneuron with tonically activated excitatory synaptic inputs uniformly distributed over dendritic arborization. The soma and axon provided a constant passive leak. The extrasynaptic dendritic membrane was either passive or active (of a Hodgkin-Huxley type). The longitudinal membrane current density (per unit path length) was used as an estimate of the current transfer effectiveness of different dendritic paths. Introduction of a steady uniform voltage-independent conductance per unit membrane area simulated such a synaptic activation. This actions always produced a spatially inhomogeneous membrane depolarization decaying from the distal dendritic tips toward the soma. The reason for such an inhomogeneity was the preponderance of somatopetal over somatofugal input conductance at every site in the dendrites with sealed distal ends and a leaky somatic end. In active dendrites, partial voltage-dependent extrasynaptic conductances followed this depolarization according to their activation-inactivation kinetics. The greater the local depolarization, the greater the contribution of the non-inactivating potassium conductance to the total membrane conductance. The contribution of the inactivated sodium conductance was one order of magnitude smaller. Correspondingly, the effective equilibrium potential of the total transmembrane current became spatially inhomogeneous and shifted to the potassium equilibrium potential. In the passive dendrites, the equilibrium potential remained spatially homogeneous. Inhomogeneities of the dendritic geometry (abrupt change in the diameter and, especially, asymmetrical branching) caused characteristic perturbations in the voltage gradient, so that the path profiles of the voltage, conductances, and currents diverged. This indicated a geometry-induced separation of the dendritic paths in their transfer effectiveness. Active dendrites of the same geometry were less effective than passive ones due to the effect of the potassium conductance associated with the hyperpolarizing equilibrium potential.     

Geometry-induced features of current transfer in neuronal dendrites with tonically activated conductances

The impact of dendritic geometry on somatopetal transfer of the current generated by steady uniform activation of excitatory synaptic conductance distributed over passive, or active (Hodgkin-Huxley type), dendrites was studied in simulated neurons. Such tonic activation was delivered to the uniform dendrite and to the dendrites with symmetric or asymmetric branching with various ratios of branch diameters. Transfer effectiveness of the dendrites with distributed sources was estimated by the core current increment directly related to the total membrane current per unit path length. The effectiveness decreased with increasing path distance from the soma along uniform branches. The primary reason for this was the asymmetry of somatopetal vs somatofugal input core conductance met by synaptic current due to a greater leak conductance at the proximal end of the dendrite. Under these conditions, an increasing somatopetal core current and a corresponding drop of the depolarization membrane potential occurred. The voltage-dependent extrasynaptic conductances, if present, followed this depolarization. Consequently, the driving potential and membrane current densities decreased with increasing path distance from the soma. All path profiles were perturbed at bifurcations, being identical in symmetrical branches and diverging in asymmetrical ones. These perturbations were caused by voltage gradient breaks (abrupt change in the profile slope) occurring at the branching node due to coincident inhomogeneity of the dendritic core cross-section area and its conductance. The gradient was greater on the side of the smaller effective cross-section. Correspondingly, the path profiles of the somatopetal current transfer effectiveness were broken and/or diverged. The dendrites, their paths, and sites which were more effective in the current transfer from distributed sources were also more effective in the transfer from single-site inputs. The effectiveness of the active dendrite depended on the activation-inactivation kinetics of its voltage-gated conductances. In particular, dendrites with the same geometry were less effective with the Hodgkin-Huxley membrane than with the passive membrane, because of the effect of the noninactivating K⁺-conductance associated with the hyperpolarization equilibrium potential. Such electrogeometrical coupling may form a basis for path-dependent input-output conversion in the dendritic neurons, as the output discharge rate is defined by the net current delivered to the soma. Received: 18 December 1997 / Accepted in revised form: 12 June 1998     

Electro-geometrical coupling in non-uniform branching dendrites

The relationships between somatofugal electronic voltage spread, somatopetal charge transfer and non-uniform geometry of the neuronal dendrites were studied on the basis of the linear cable theory. It is demonstrated that for the dendritic arborization of arbitrary geometry, the path distribution of the relative effectiveness of somatopetal synaptic charge transfer defined as in Barrett and Crill (1974) is identical to that of the somatofugal steady electrotonic voltage normalized to the voltage at the soma. The features of both distributions are determined by breaks in the voltage gradient (the slope of monotonic voltage decay) at the sites of local non-uniformity of the dendritic geometry, such as abrupt change in diameter and asymmetric branching. If the membrane- and cytoplasm-specific electrical parameters are assumed as uniform and the branch diameter as piece-wise uniform, then at any site of step change the square reciprocal ratio of the pre- and poststep diameters determines the ratio of the pre- and poststep electronic gradients. At branching points this ratio is modulated by partition of the core current between the daughter branches in proportion to their input conductances depending on global geometries of the daughter subtrees originating there. Thus, simply computed steady somatofugal voltages provide a physiologically meaningful estimation of the relative influence of synaptic inputs in different parts of the dendritic arborization on the output of the neuron.     

Modeling organelle transport in branching dendrites with a variable cross-sectional area

The purpose of this paper is to develop a method for calculating organelle transport in dendrites with a non-uniform cross-sectional area that depends on the distance from the neuron soma. The model is based on modified Smith–Simmons equations governing molecular motor-assisted organelle transport. The developed method is then applied to simulating organelle transport in branching dendrites with two particular microtubule (MT) orientations reported from experiments. It is found that the rate of organelle transport toward a dendrite’s growth cone heavily depends on the MT orientation, and since there is experimental evidence that the MT orientation in a particular region of a dendrite may depend on the dendrite’s developmental stage, the obtained results suggest that a rearrangement of the MT structure may depend on the amount of organelles needed at the growth cone.     

Synthesis of mathematical models of branching axons and dendrites

A synthesis was made of models of branching neuronal cable structures from a full set of standard basic models. The study aimed to produce an instrument of mathematical modelling making it possible to reflect true life morphological and electrophysiological characteristics of axons and dendrites, discarding some of the restrictions and simplifications characterizing existing models of the structures mentioned. Equivalent electrical circuits of branching axons and dendrites were set up with in-series and node connections of standard four-terminal networks corresponding to basic segments with active or passive membrane. Equations were obtained for electrical processes in branching neuronal neurites, generalized in the case of multiple binary branching with arbitrary symmetry and branching structure. A difference scheme common to the whole class of models contemplated was produced and the algorithm of a numerical solution to the difference equations thus obtained was elaborated. The instrument described makes it possible to synthesize diverse models of branching axons and dendrites, offering considerably greater opportunities for modelling the main electrophysiological processes developing in these structures of electrotonus, propagation of excitation, and interaction between these two factors.State University Commemorating Tricentenary of Russo-Ukrainian Union. Dnepropetrovsk. Translated from Neirofiziologiya, Vol. 20, No. 4, pp. 471–479, July–August, 1988.     

Activity-dependent clustering of functional synaptic inputs on developing hippocampal dendrites

During brain development, before sensory systems become functional, neuronal networks spontaneously generate repetitive bursts of neuronal activity, which are typically synchronized across many neurons. Such activity patterns have been described on the level of networks and cells, but the fine-structure of inputs received by an individual neuron during spontaneous network activity has not been studied. Here, we used calcium imaging to record activity at many synapses of hippocampal pyramidal neurons simultaneously to establish the activity patterns in the majority of synapses of an entire cell. Analysis of the spatiotemporal patterns of synaptic activity revealed a fine-scale connectivity rule: neighboring synapses (<16?μm intersynapse distance) are more likely to be coactive than synapses that are farther away from each other. Blocking spiking activity or NMDA receptor activation revealed that the clustering of synaptic inputs required neuronal activity, demonstrating a role of developmentally expressed spontaneous activity for connecting neurons with subcellular precision.     

Neural activity and branching of embryonic retinal ganglion cell dendrites

The shape of a neuron's dendritic arbor is critical for its function as it determines the number of inputs the neuron can receive and how those inputs are processed. During development, a neuron initiates primary dendrites that branch to form a simple arbor. Subsequently, growth occurs by a process that combines the extension and retraction of existing dendrites, and the addition of new branches. The loss and addition of the fine terminal branches of retinal ganglion cells (RGCs) is dependent on afferent inputs from its synaptic partners, the amacrine and bipolar cells. It is unknown, however, whether neural activity regulates the initiation of primary dendrites and their initial branching. To investigate this, Xenopus laevis RGCs developing in vivo were made to express either a delayed rectifier type voltage-gated potassium (KV) channel, Xenopus Kv1.1, or a human inward rectifying channel, Kir2.1, shown previously to modulate the electrical activity of Xenopus spinal cord neurons. Misexpression of either potassium channel increased the number of branch points and the total length of all the branches. As a result, the total dendritic arbor was bigger than for control green fluorescent protein-expressing RGCs and those ectopically expressing a highly related mutant non-functional Kv1.1 channel. Our data indicate that membrane excitability regulates the earliest differentiation of RGC dendritic arbors.     

Conditions of dominant effectiveness of distal sites of active uniform dendrites with distributed tonic inputs

This simulation study aimed at assessing linkage between the membrane properties and the effectiveness of somatopetal current transfer from activated tonic excitatory inputs homogeneously distributed along uniform dendrites. It was shown that in the dendrites having anN-shaped steady current-voltage membrane characteristic due to the negative slope within a certain range of potentials, distal sites can be more effective than proximal sites in somatopetal current transfer from tonically activated excitatory synaptic inputs. Inhomogeneous dendritic depolarization produced by these inputs should be found everywhere within a range of the negative slope. In simulated dendrites receiving, as in rat abducens motoneurons, voltage-sensitive synaptic inputs of anN-methyl-D-aspartate (NMDA) type, such spatial effects occurred at low depolarization produced by subcritical excitation. At supercritical excitation, depolarization increased and left the range of the negative slope, and proximal sites became much more effective than distal ones. It is suggested that persistent inward currents (including other than of NMDA nature) can provide similar effects.     

Barriers to diffusion in dendrites and estimation of calcium spread following synaptic inputs

The motion of ions, molecules or proteins in dendrites is restricted by cytoplasmic obstacles such as organelles, microtubules and actin network. To account for molecular crowding, we study the effect of diffusion barriers on local calcium spread in a dendrite. We first present a model based on a dimension reduction approach to approximate a three dimensional diffusion in a cylindrical dendrite by a one-dimensional effective diffusion process. By comparing uncaging experiments of an inert dye in a spiny dendrite and in a thin glass tube, we quantify the change in diffusion constants due to molecular crowding as D_cyto/D_water = 1/20. We validate our approach by reconstructing the uncaging experiments using Brownian simulations in a realistic 3D model dendrite. Finally, we construct a reduced reaction-diffusion equation to model calcium spread in a dendrite under the presence of additional buffers, pumps and synaptic input. We find that for moderate crowding, calcium dynamics is mainly regulated by the buffer concentration, but not by the cytoplasmic crowding, dendritic spines or synaptic inputs. Following high frequency stimulations, we predict that calcium spread in dendrites is limited to small microdomains of the order of a few microns (<5 μm).     

A role for synaptic inputs at distal dendrites: instructive signals for hippocampal long-term plasticity

Synaptic potentials originating at distal dendritic locations are severely attenuated when they reach the soma and, thus, are poor at driving somatic spikes. Nonetheless, distal inputs convey essential information, suggesting that such inputs may be important for compartmentalized dendritic signaling. Here we report a new plasticity rule in which stimulation of distal perforant path inputs to hippocampal CA1 pyramidal neurons induces long-term potentiation at the CA1 proximal Schaffer collateral synapses when the two inputs are paired at a precise interval. This subthreshold form of heterosynaptic plasticity occurs in the absence of somatic spiking but requires activation of both NMDA receptors and IP(3) receptor-dependent release of Ca(2+) from internal stores. Our results suggest that direct sensory information arriving at distal CA1 synapses through the perforant path provide compartmentalized, instructive signals that assess the saliency of mnemonic information propagated through the hippocampal circuit to proximal synapses.     

Mother rotor anchoring in branching tissue with heterogeneous membrane properties.

Abstract Current understanding of atrial fibrillation is based on the co-existence of multiple re-entrant waves propagating randomly throughout the tissue. However, recent experimental results indicate that in many cases one or a small number of periodic, high-frequency re-entrant sources (mother rotors) can drive the arrhythmia. Owing to the high activation rate, mother rotors seem to be located in regions of shortened action potential duration. In this study a computer model of cardiac propagation was applied to investigate mechanisms leading to the formation and maintenance of such mother rotors. For this purpose, a region of short action potential duration was generated by varying the acetylcholine concentration across the tissue. A mother rotor initiated in the center of this region drifts away, and the activation terminates. If an additional heterogeneity such as a bundle is included into the model, a further drift mechanism directed to the bundle is observed and the rotor can be stabilized. Therefore, bundle insertions may play an important role in the maintenance of mother rotors. The influence of the driving rotor on the activation pattern was studied in a three-dimensional model of rectangular shape and a monolayer model of anatomically correct atrial geometry.     

Coding and decoding with dendrites

Since the discovery of complex, voltage dependent mechanisms in the dendrites of multiple neuron types, great effort has been devoted in search of a direct link between dendritic properties and specific neuronal functions. Over the last few years, new experimental techniques have allowed the visualization and probing of dendritic anatomy, plasticity and integrative schemes with unprecedented detail. This vast amount of information has caused a paradigm shift in the study of memory, one of the most important pursuits in Neuroscience, and calls for the development of novel theories and models that will unify the available data according to some basic principles. Traditional models of memory considered neural cells as the fundamental processing units in the brain. Recent studies however are proposing new theories in which memory is not only formed by modifying the synaptic connections between neurons, but also by modifications of intrinsic and anatomical dendritic properties as well as fine tuning of the wiring diagram. In this review paper we present previous studies along with recent findings from our group that support a key role of dendrites in information processing, including the encoding and decoding of new memories, both at the single cell and the network level.     

Discharge patterns of tonically firing human motoneurones

We have attempted to reconcile the different patterns of distribution of interspike intervals that are found in motoneurones made to discharge by intracellular injection of constant current in reduced animal preparations and by voluntary control in human subjects. We recorded long spike trains from single motor units in three human muscles made to discharge at constant mean frequencies with the help of auditory and visual feedback. The distribution of interspike intervals in each spike train was analysed quantitatively. We found that the different pattern of discharge of the human motor units could be accounted for when due allowance was made for the variability of the drive to the human motoneurone which arose because of the feedback process used to maintain the target frequency. A model testing this hypothesis gave results that were qualitatively consistent with the human data.     

Intrinsic properties of and thalamocortical inputs onto identified corticothalamic-VPM neurons

Corticothalamic (CT) feedback plays an important role in regulating the sensory information that the cortex receives. Within the somatosensory cortex layer VI originates the feedback to the ventral posterior medial (VPM) nucleus of the thalamus, which in turn receives sensory information from the contralateral whiskers. We examined the physiology and morphology of CT neurons in rat somatosensory cortex, focusing on the physiological characteristics of the monosynaptic inputs that they receive from the thalamus. To identify CT neurons, rhodamine microspheres were injected into VPM and allowed to retrogradely transport to the soma of CT neurons. Thalamocortical slices were prepared at least 3 days post injection. Whole-cell recordings from labeled CT cells in layer VI demonstrated that they are regular spiking neurons and exhibit little spike frequency adaption. Two anatomical classes were identified based on their apical dendrites that either terminated by layer V (compact cells) or layer IV (elaborate cells). Thalamic inputs onto identified CT-VPM neurons demonstrated paired pulse depression over a wide frequency range (2–20?Hz). Stimulus trains also resulted in significant synaptic depression above 10?Hz. Our results suggest that thalamic inputs differentially impact CT-VPM neurons in layer VI. This characteristic may allow them to differentiate a wide range of stimulation frequencies which in turn further tune the feedback signals to the thalamus.     

Fibrinolytic properties of activated FXII.

Activated factor XII (FXIIa), the initiator of the contact activation system, has been shown to activate plasminogen in a purified system. However, the quantitative role of FXIIa as a plasminogen activator in contact activation-dependent fibrinolysis in plasma is still unclear. In this study, the plasminogen activator (PA) activity of FXIIa was examined both in a purified system and in a dextran sulfate euglobulin fraction of plasma by measuring fibrinolysis in a fibrin microtiter plate assay. FXIIa was found to have low PA activity in a purified system. Dextran sulfate potentiated the PA activity of FXIIa about sixfold, but had no effect on the PA activity of smaller fragments of FXIIa, missing the binding domain for negatively charged surfaces. The addition of small amounts of factor XII (FXII) to FXII-deficient plasma induced a large increase in contact activation-dependent PA activity, as measured in a dextran sulfate euglobulin fraction, which may be ascribed to FXII-dependent activation of plasminogen activators like prekallikrein. When more FXII was added, PA activity continued to increase but to a lesser extent. In normal plasma, the addition of FXII also resulted in an increase of contact activation-dependent PA activity. These findings suggested a significant contribution of FXIIa as a direct plasminogen activator. Indeed, at least 20% of contact activation-dependent PA activity could be extracted from a dextran sulfate euglobulin fraction prepared from normal plasma by immunodepletion of FXIIa and therefore be ascribed to direct PA activity of FXIIa. PA activity of endogenous FXIIa immunoadsorped from plasma could only be detected in the presence of dextran sulfate. From these results it is concluded that FXIIa can contribute significantly to fibrinolysis as a plasminogen activator in the presence of a potentiating surface.