99 research outputs found
Solitary waves in a model of dendritic cable with active spines
We consider a continuum model of dendritic spines with active membrane dynamics uniformly
distributed along a passive dendritic cable. Byconsidering a systematic reduction of the Hodgkin-Huxleydy namics that is valid on all but very short time-scales we derive 2 dimensional and 1
dimensional systems for excitable tissue, both of which may be used to model the active processes
in spine-heads. In the first case the coupling of the spine head dynamics to a passive dendritic cable
via a direct electrical connection yields a model that may be regarded as a simplification of the Baer
and Rinzel cable theory of excitable spinynerv e tissue [3]. This model is computationally simple
with few free parameters. Importantly, as in the full model, numerical simulation illustrates the
possibilityof a traveling wave. We present a systematic numerical investigation of the speed and
stability of the wave as a function of physiologically important parameters. A further reduction of
this model suggests that active spine-head dynamics mayb e modeled byan all or none type process
which we take to be of the integrate-and-fire (IF) type. The model is analytically tractable allowing
the explicit construction of the shape of traveling waves as well as the calculation of wave speed as a
function of system parameters. In general a slow and fast wave are found to co-exist. The behavior
of the fast wave is found to closely reproduce the behavior of the wave seen in simulations of the
more detailed model. Importantly a linear stability theory is presented showing that it is the faster
of the two solutions that is stable. Beyond a critical value the speed of the stable wave is found to
decrease as a function of spine density. Moreover, the speed of this wave is found to decrease as a
function of the strength of the electrical resistor coupling the spine-head and the cable, such that
beyond some critical value there is propagation failure. Finally we discuss the importance of a model
of passive electrical cable coupled to a system of integrate-and-fire units for physiological studies of
branching dendritic tissue with active spines
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
Travelling waves in a model of quasi-active dendrites with active spines
Dendrites, the major components of neurons, have many different types of branching structures and are involved in receiving and integrating thousands of synaptic inputs from other neurons. Dendritic spines with excitable channels can be present in large densities on the dendrites of many cells. The recently proposed Spike-Diffuse-Spike (SDS) model that is described by a system of point hot-spots (with an integrate-and-fire process) embedded throughout a passive tree has been shown to provide a reasonable caricature of a dendritic tree with supra-threshold dynamics. Interestingly, real dendrites equipped with voltage-gated ion channels can exhibit not only supra-threshold responses, but also sub-threshold dynamics. This sub-threshold resonant-like oscillatory behaviour has already been shown to be adequately described by a quasi-active membrane. In this paper we introduce a mathematical model of a branched dendritic tree based upon a generalisation of the SDS model where the active spines are assumed to be distributed along a quasi-active dendritic structure. We demonstrate how solitary and periodic travelling wave solutions can be constructed for both continuous and discrete spine distributions. In both cases the speed of such waves is calculated as a function of system parameters. We also illustrate that the model can be naturally generalised to an arbitrary branched dendritic geometry whilst remaining computationally simple. The spatio-temporal patterns of neuronal activity are shown to be significantly influenced by the properties of the quasi-active membrane. Active (sub- and supra-threshold) properties of dendrites are known to vary considerably among cell types and animal species, and this theoretical framework can be used in studying the combined role of complex dendritic morphologies and active conductances in rich neuronal dynamics
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 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
From periodic travelling waves to travelling fronts in the spike-diffuse-spike model of dendritic waves
In the vertebrate brain excitatory synaptic contacts typically occur on the tiny
evaginations of neuron dendritic surface known as dendritic spines. There is clear
evidence that spine heads are endowed with voltage dependent excitable channels
and that action potentials invade spines. Computational models are being increasingly
used to gain insight into the functional significance for a spine with excitable
membrane. The spike-diffuse-spike (SDS) model is one such model that admits to
a relatively straightforward mathematical analysis. In this paper we demonstrate
that not only can the SDS model support solitary travelling pulses, already observed
numerically in more detailed biophysical models, but that it has periodic travelling
wave solutions. The exact mathematical treatment of periodic travelling waves in
the SDS model is used, within a kinematic framework, to predict the existence of
connections between two periodic spike trains of different interspike interval. The
associated wave front in the sequence of interspike intervals travels with a constant
velocity without degradation of shape, and might therefore be used for robust
encoding of information
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 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
Traveling waves in the Baer and Rinzel model of spine studded dendritic tissue
The Baer and Rinzel model of dendritic spines uniformly distributed along a dendritic
cable is shown to admit a variety of regular traveling wave solutions including
solitary pulses, multiple pulses and periodic waves. We investigate numerically the
speed of these waves and their propagation failure as functions of the system parameters
by numerical continuation. Multiple pulse waves are shown to occur close to
the primary pulse, except in certain exceptional regions of parameter space, which
we identify. The propagation failure of solitary and multiple pulse waves is shown to
be associated with the destruction of a saddle-node bifurcation of periodic orbits.
The system also supports many types of irregular wave trains. These include waves
which may be regarded as connections to periodics and bursting patterns in which
pulses can cluster together in well-defined packets. The behavior and properties of
both these irregular spike-trains is explained within a kinematic framework that is
based on the times of wave pulses. The dispersion curve for periodic waves is important
for such a description and is obtained in a straightforward manner using the
numerical scheme developed for the study of the speed of a periodic wave. Stability
of periodic waves within the kinematic theory is given in terms of the derivative
of the dispersion curve and provides a weak form of stability that may be applied
to solutions of the traveling wave equations. The kinematic theory correctly predicts
the conditions for period doubling bifurcations and the generation of bursting states. Moreover, it also accurately describes the shape and speed of the traveling
front that connects waves with two different periods
Saltatory waves in the spike-diffuse-spike model of active dendritic spines
In this Letter we present the explicit construction of a saltatory traveling pulse of non-constant
profile in an idealized model of dendritic tissue. Excitable dendritic spine clusters, modeled with
integrate-and-fire (IF) units, are connected to a passive dendritic cable at a discrete set of points.
The saltatory nature of the wave is directly attributed to the breaking of translation symmetry in
the cable. The conditions for propagation failure are presented as a function of cluster separation
and IF threshold
Neural cytoskeleton capabilities for learning and memory
This paper proposes a physical model involving the key structures within the neural cytoskeleton as major players in molecular-level processing of information required for learning and memory storage. In particular, actin filaments and microtubules are macromolecules having highly charged surfaces that enable them to conduct electric signals. The biophysical properties of these filaments relevant to the conduction of ionic current include a condensation of counterions on the filament surface and a nonlinear complex physical structure conducive to the generation of modulated waves. Cytoskeletal filaments are often directly connected with both ionotropic and metabotropic types of membrane-embedded receptors, thereby linking synaptic inputs to intracellular functions. Possible roles for cable-like, conductive filaments in neurons include intracellular information processing, regulating developmental plasticity, and mediating transport. The cytoskeletal proteins form a complex network capable of emergent information processing, and they stand to intervene between inputs to and outputs from neurons. In this manner, the cytoskeletal matrix is proposed to work with neuronal membrane and its intrinsic components (e.g., ion channels, scaffolding proteins, and adaptor proteins), especially at sites of synaptic contacts and spines. An information processing model based on cytoskeletal networks is proposed that may underlie certain types of learning and memory
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