[Dynamical electrical states of heterogeneous populations of ion channels in the membranes of excitable cells].

In computer models, we studied instantaneous (time-varying) current-voltage relationships (iIVs) of populations of ion channels characteristic of the membrane of different type excitable cells, of which the responses to electrical stimuli essentially differ: giant squid axon (Hodgkin-Huxley model), cardiomyocyte, dendrites of CA3 hippocampal pyramidal neurons and Purkinje neurons of the cerebellum. The membrane potential was stepped from the rest level to a certain depolarization test level that was clamped for a certain time, and the total current was measured at different moments after the step onset. For each iIV zero-current points (potentials) were determined. A set of such points, which were situated on the limb of iIV positive slop and corresponded to the state of high membrane depolarization (excitation state, upstate) at different time moments, were used to characterize the dynamics of the excitation state in time. With these indicators the axon membrane was characterized by a single excitation state that rapidly occurred (0.25 ms) and was short-lasting (decayed from -45 to 40 mV during life-time of 5.5 ms). There were two such states of the membrane of cardiomyocyte. The first one was early, rapidly occurring and short-living (rapidly relaxing). It occurred shortly after the depolarization start and lasted for 14.5 ms. The second one was late, slowly rising and long-lasting (occurred with a 7.5-ms delay, increased from 11 to 46 mV in 39 ms and then relaxed lasting for 623 ms in total). The dendritic membrane ofCA3 neurons had one long-lasting excitation state that occurred shortly after the depolarization shift, first rapidly relaxed during 3 ms from initial 30 mV level to -10 mV and then slowly, in 80 ms, stabilized at the level of -20 mV. In the Purkinje neuron membrane two short-lasting and one very long-lasting excitation states were revealed. The first state of very high (>100 mV) depolarization relaxed to 4 mV in 0.8 ms. Shortly before its vanishing, at 0.7 ms, the second short-lasting state emerged, which relaxed in 1 ms from -22 mV to -48 mV. At 1.8 ms a new excitation state emerged, which after a transient relaxation stabilized at -29.65 mV starting from 88 ms. Thus, iIVs allowed disclosing a fine organization of the states of electrical excitation of the membrane and revealing, in populations of ion channels of different content, existence of different number of the mentioned states, which differ from each other in occurrence time and life-time.

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

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

Spatial reconfiguration of charge transfer effectiveness in active bistable dendritic arborizations.

The aim of this work was to explore the electrical spatial profile of the dendritic arborization during membrane potential oscillations of a bistable motoneuron. Computational simulations provided the spatial counterparts of the temporal dynamics of bistability and allowed simultaneous depiction the electrical states of any sites in the arborization. We assumed that the dendritic membrane had homogeneously distributed specific electrical properties and was equipped with a cocktail of passive extrasynaptic and NMDA synaptic conductances. The electrical conditions for evoking bistability in a single isopotential compartment and in a whole dendritic arborization were computed and showed differences, revealing a crucial effect of dendritic geometry. Snapshots of the whole arborization during bistability revealed the spatial distribution of the density of the transmembrane current generated at the synapses and the effectiveness of the current transfer from any dendritic site to the soma. These functional maps changed dynamically according to the phase of the oscillatory cycle. In the low depolarization state, the current density was low in the proximal dendrites and higher in the distal parts of the arborization while the transfer effectiveness varied in a narrow range with small differences between proximal and distal dendritic segments. When the neuron switched to high depolarization state, the current density was high in the proximal dendrites and low in the distal branches while a large domain of the dendritic field became electrically disconnected beyond 200 micro m from the soma with a null transfer efficiency. These spatial reconfigurations affected dynamically the size and shape of the functional dendritic field and were strongly geometry-dependent.

Activity-dependent reconfiguration of the effective dendritic field of motoneurons.

A neuron in vivo receives a continuous bombardment of synaptic inputs that modify the integrative properties of dendritic arborizations by changing the specific membrane resistance (R(m)). To address the mechanisms by which the synaptic background activity transforms the charge transfer effectiveness (T(x)) of a dendritic arborization, the authors simulated a neuron at rest and a highly excited neuron. After in vivo identification of the motoneurons recorded and stained intracellularly, the motoneuron arborizations were reconstructed at high spatial resolution. The neuronal model was constrained by the geometric data describing the numerized arborization. The electrotonic structure and T(x) were computed under different R(m) values to mimic a highly excited neuron (1 kOhm x cm(2)) and a neuron at rest (100 kOhm x cm(2)). The authors found that the shape and the size of the effective dendritic fields varied in the function of R(m). In the highly excited neuron, the effective dendritic field was reduced spatially by switching off most of the distal dendritic branches, which were disconnected functionally from the somata. At rest, the entire dendritic field was highly efficient in transferring current to the somata, but there was a lack of spatial discrimination. Because the large motoneurons are more sensitive to variations in the upper range of R(m), they switch off their distal dendrites before the small motoneurons. Thus, the same anatomic structure that shrinks or expands according to the background synaptic activity can select the types of its synaptic inputs. The results of this study demonstrate that these reconfigurations of the effective dendritic field of the motoneurons are activity-dependent and geometry-dependent.

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.