Yulia Timofeeva

Differential triggering of spontaneous glutamate release by P/Q-, N- and R-type Ca2+ channels

The role of voltage-gated Ca2+ channels (VGCCs) in spontaneous miniature neurotransmitter release is incompletely understood. We found that stochastic opening of P/Q-, N- and R-type VGCCs accounts for ∼50% of all spontaneous glutamate release at rat cultured hippocampal synapses, and that R-type channels have a far greater role in spontaneous than in action potential–evoked exocytosis. VGCC-dependent miniature neurotransmitter release (minis) showed similar sensitivity to presynaptic Ca2+ chelation as evoked release, arguing for direct triggering of spontaneous release by transient spatially localized Ca2+ domains. Experimentally constrained three-dimensional diffusion modeling of Ca2+ influx–exocytosis coupling was consistent with clustered distribution of VGCCs in the active zone of small hippocampal synapses and revealed that spontaneous VGCCs openings can account for the experimentally observed VGCC-dependent minis, although single channel openings triggered release with low probability. Uncorrelated stochastic VGCC opening is therefore a major trigger for spontaneous glutamate release, with differential roles for distinct channel subtypes.

Mixed Mode Oscillations in Mouse Spinal Motoneurons Arise from a Low Excitability State

We explain the mechanism that elicits the mixed mode oscillations (MMOs) and the subprimary firing range that we recently discovered in mouse spinal motoneurons. In this firing regime, high-frequency subthreshold oscillations appear a few millivolts below the spike voltage threshold and precede the firing of a full blown spike. By combining intracellular recordings in vivo (including dynamic clamp experiments) in mouse spinal motoneurons and modeling, we show that the subthreshold oscillations are due to the spike currents and that MMOs appear each time the membrane is in a low excitability state. Slow kinetic processes largely contribute to this low excitability. The clockwise hysteresis in the I–F relationship, frequently observed in mouse motoneurons, is mainly due to a substantial slow inactivation of the sodium current. As a consequence, less sodium current is available for spiking. This explains why a large subprimary range with numerous oscillations is present in motoneurons displaying a clockwise hysteresis. In motoneurons whose I–F curve exhibits a counterclockwise hysteresis, it is likely that the slow inactivation operates on a shorter time scale and is substantially reduced by the de-inactivating effect of the afterhyperpolarization (AHP) current, thus resulting in a more excitable state. This accounts for the short subprimary firing range with only a few MMOs seen in these motoneurons. Our study reveals a new role for the AHP current that sets the membrane excitability level by counteracting the slow inactivation of the sodium current and allows or precludes the appearance of MMOs.

Spatio-temporal filtering properties of a dendritic cable with active spines: A modeling study in the spike-diffuse-spike framework

The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modeled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. In this paper we develop a computational framework that allows the study of multiple spiking events in a network of such spines embedded on a simple one-dimensional cable. In the first instance this system is shown to support saltatory waves with the same qualitative features as those observed in a model with Hodgkin-Huxley kinetics in the spine-head. Moreover, there is excellent agreement with the analytically calculated speed for a solitary saltatory pulse. Upon driving the system with time-varying external input we find that the distribution of spines can play a crucial role in determining spatio-temporal filtering properties. In particular, the SDS model in response to periodic pulse train shows a positive correlation between spine density and low-pass temporal filtering that is consistent with the experimental results of Rose and Fortune [1999, ‘Mechanisms for generating temporal filters in the electrosensory system,’ The Journal of Experimental Biology 202: 1281–1289]. Further, we demonstrate the robustness of observed wave properties to natural sources of noise that arise both in the cable and the spine-head, and highlight the possibility of purely noise induced waves and coherent oscillations.

Democratization in a passive dendritic tree: an analytical investigation

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as “dendritic democracy”. Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green’s representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius.

Gap Junctions, Dendrites and Resonances: A Recipe for Tuning Network Dynamics

Gap junctions, also referred to as electrical synapses, are expressed along the entire central nervous system and are important in mediating various brain rhythms in both normal and pathological states. These connections can form between the dendritic trees of individual cells. Many dendrites express membrane channels that confer on them a form of sub-threshold resonant dynamics. To obtain insight into the modulatory role of gap junctions in tuning networks of resonant dendritic trees, we generalise the “sum-over-trips” formalism for calculating the response function of a single branching dendrite to a gap junctionally coupled network. Each cell in the network is modelled by a soma connected to an arbitrary structure of dendrites with resonant membrane. The network is treated as a single extended tree structure with dendro-dendritic gap junction coupling. We present the generalised “sum-over-trips” rules for constructing the network response function in terms of a set of coefficients defined at special branching, somatic and gap-junctional nodes. Applying this framework to a two-cell network, we construct compact closed form solutions for the network response function in the Laplace (frequency) domain and study how a preferred frequency in each soma depends on the location and strength of the gap junction.

Computational Convergence of the Path Integral for Real Dendritic Morphologies

Neurons are characterised by a morphological structure unique amongst biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties of the cell membrane, continue to challenge scientists in predicting neuronal input-output relationships, even in the case of sub-threshold dendritic currents. The Green’s function obtained for a given dendritic geometry provides this functional relationship for passive or quasi-active dendrites and can be constructed by a sum-over-trips approach based on a path integral formalism. In this paper, we introduce a number of efficient algorithms for realisation of the sum-over-trips framework and investigate the convergence of these algorithms on different dendritic geometries. We demonstrate that the convergence of the trip sampling methods strongly depends on dendritic morphology as well as the biophysical properties of the cell membrane. For real morphologies, the number of trips to guarantee a small convergence error might become very large and strongly affect computational efficiency. As an alternative, we introduce a highly-efficient matrix method which can be applied to arbitrary branching structures.

Dendritic cable with active spines: A modelling study in the spike-diffuse-spike framework

The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modelled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. Here we develop a computational framework that allows the study of multiple spiking events in a network of such spines embedded in a simple one-dimensional cable. This system is shown to support saltatory waves as a result of the discrete distribution of spines. Moreover, we demonstrate one of the ways to incorporate noise into the spine-head whilst retaining computational tractability of the model. The SDS model sustains a variety of propagating patterns.

Calmodulin as a major calcium buffer shaping vesicular release and short-term synaptic plasticity: facilitation through buffer dislocation

Action potential-dependent release of synaptic vesicles and short-term synaptic plasticity are dynamically regulated by the endogenous Ca2+ buffers that shape [Ca2+] profiles within a presynaptic bouton. Calmodulin is one of the most abundant presynaptic proteins and it binds Ca2+ faster than any other characterized endogenous neuronal Ca2+ buffer. Direct effects of calmodulin on fast presynaptic Ca2+ dynamics and vesicular release however have not been studied in detail. Using experimentally constrained three-dimensional diffusion modeling of Ca2+ influx–exocytosis coupling at small excitatory synapses we show that, at physiologically relevant concentrations, Ca2+ buffering by calmodulin plays a dominant role in inhibiting vesicular release and in modulating short-term synaptic plasticity. We also propose a novel and potentially powerful mechanism for short-term facilitation based on Ca2+-dependent dynamic dislocation of calmodulin molecules from the plasma membrane within the active zone.

Response of Gap Junction-Coupled Dendrites: A Sum-Over-Trips Approach

Dendrites form the major components of neurons. They are complex branching structures that receive and process thousands of synaptic inputs from other neurons. The impulse response function for branched dendritic trees can be calculated using a so-called sum-over-trips approach. In this chapter we extend this formalism to treat networks of dendritic trees connected via dendro-dendritic gap junctions. To illustrate the usefulness of this extended formalism for understanding how gap junctions can contribute to signal integration in neural networks, we consider how they affect somatic voltages in a simple two neuron network with gap junction coupling between distal dendrites. We find that proximal input on one cell can strongly innervate the soma of that cell though the spread of charge to the gap junction-coupled cell is weak. In contrast distal inputs on one cell weakly innervate the soma of that cell though charge can spread effectively to the gap junction-coupled cell.

Response functions for electrically coupled neuronal network: a method of local point matching and its applications

Neuronal networks connected by electrical synapses, also referred to as gap junctions, are present throughout the entire central nervous system. Many instances of gap-junctional coupling are formed between dendritic arbours of individual cells, and these dendro-dendritic gap junctions are known to play an important role in mediating various brain rhythms in both normal and pathological states. The dynamics of such neuronal networks modelled by passive or quasi-active (resonant) membranes can be described by the Green’s function which provides the fundamental input-output relationships of the entire network. One of the methods for calculating this response function is the so-called ‘sum-over-trips’ framework which enables the construction of the Green’s function for an arbitrary network as a convergent infinite series solution. Here we propose an alternative and computationally efficient approach for constructing the Green’s functions on dendro-dendritic gap junction-coupled neuronal networks which avoids any infinite terms in the solutions. Instead, the Green’s function is constructed from the solution of a system of linear algebraic equations. We apply this new method to a number of systems including a simple single cell model and two-cell neuronal networks. We also demonstrate that the application of this novel approach allows one to reduce a model with complex dendritic formations to an equivalent model with a much simpler morphological structure.