10,705 research outputs found
Astrocytic Ion Dynamics: Implications for Potassium Buffering and Liquid Flow
We review modeling of astrocyte ion dynamics with a specific focus on the
implications of so-called spatial potassium buffering, where excess potassium
in the extracellular space (ECS) is transported away to prevent pathological
neural spiking. The recently introduced Kirchoff-Nernst-Planck (KNP) scheme for
modeling ion dynamics in astrocytes (and brain tissue in general) is outlined
and used to study such spatial buffering. We next describe how the ion dynamics
of astrocytes may regulate microscopic liquid flow by osmotic effects and how
such microscopic flow can be linked to whole-brain macroscopic flow. We thus
include the key elements in a putative multiscale theory with astrocytes
linking neural activity on a microscopic scale to macroscopic fluid flow.Comment: 27 pages, 7 figure
Dendritic spine geometry and spine apparatus organization govern the spatiotemporal dynamics of calcium.
Dendritic spines are small subcompartments that protrude from the dendrites of neurons and are important for signaling activity and synaptic communication. These subcompartments have been characterized to have different shapes. While it is known that these shapes are associated with spine function, the specific nature of these shape-function relationships is not well understood. In this work, we systematically investigated the relationship between the shape and size of both the spine head and spine apparatus, a specialized endoplasmic reticulum compartment within the spine head, in modulating rapid calcium dynamics using mathematical modeling. We developed a spatial multicompartment reaction-diffusion model of calcium dynamics in three dimensions with various flux sources, including N-methyl-D-aspartate receptors (NMDARs), voltage-sensitive calcium channels (VSCCs), and different ion pumps on the plasma membrane. Using this model, we make several important predictions. First, the volume to surface area ratio of the spine regulates calcium dynamics. Second, membrane fluxes impact calcium dynamics temporally and spatially in a nonlinear fashion. Finally, the spine apparatus can act as a physical buffer for calcium by acting as a sink and rescaling the calcium concentration. These predictions set the stage for future experimental investigations of calcium dynamics in dendritic spines
Nonlinear physics of electrical wave propagation in the heart: a review
The beating of the heart is a synchronized contraction of muscle cells
(myocytes) that are triggered by a periodic sequence of electrical waves (action
potentials) originating in the sino-atrial node and propagating over the atria and
the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF)
or ventricular tachycardia (VT) are caused by disruptions and instabilities of these
electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent
wave patterns (AF,VF). Numerous simulation and experimental studies during the
last 20 years have addressed these topics. In this review we focus on the nonlinear
dynamics of wave propagation in the heart with an emphasis on the theory of pulses,
spirals and scroll waves and their instabilities in excitable media and their application
to cardiac modeling. After an introduction into electrophysiological models for action
potential propagation, the modeling and analysis of spatiotemporal alternans, spiral
and scroll meandering, spiral breakup and scroll wave instabilities like negative line
tension and sproing are reviewed in depth and discussed with emphasis on their impact
in cardiac arrhythmias.Peer ReviewedPreprin
Mapping the spatiotemporal dynamics of calcium signaling in cellular neural networks using optical flow
An optical flow gradient algorithm was applied to spontaneously forming net-
works of neurons and glia in culture imaged by fluorescence optical microscopy
in order to map functional calcium signaling with single pixel resolution.
Optical flow estimates the direction and speed of motion of objects in an image
between subsequent frames in a recorded digital sequence of images (i.e. a
movie). Computed vector field outputs by the algorithm were able to track the
spatiotemporal dynamics of calcium signaling pat- terns. We begin by briefly
reviewing the mathematics of the optical flow algorithm, and then describe how
to solve for the displacement vectors and how to measure their reliability. We
then compare computed flow vectors with manually estimated vectors for the
progression of a calcium signal recorded from representative astrocyte
cultures. Finally, we applied the algorithm to preparations of primary
astrocytes and hippocampal neurons and to the rMC-1 Muller glial cell line in
order to illustrate the capability of the algorithm for capturing different
types of spatiotemporal calcium activity. We discuss the imaging requirements,
parameter selection and threshold selection for reliable measurements, and
offer perspectives on uses of the vector data.Comment: 23 pages, 5 figures. Peer reviewed accepted version in press in
Annals of Biomedical Engineerin
Disentangling astroglial physiology with a realistic cell model in silico
Electrically non-excitable astroglia take up neurotransmitters, buffer extracellular K+ and generate Ca2+ signals that release molecular regulators of neural circuitry. The underlying machinery remains enigmatic, mainly because the sponge-like astrocyte morphology has been difficult to access experimentally or explore theoretically. Here, we systematically incorporate multi-scale, tri-dimensional astroglial architecture into a realistic multi-compartmental cell model, which we constrain by empirical tests and integrate into the NEURON computational biophysical environment. This approach is implemented as a flexible astrocyte-model builder ASTRO. As a proof-of-concept, we explore an in silico astrocyte to evaluate basic cell physiology features inaccessible experimentally. Our simulations suggest that currents generated by glutamate transporters or K+ channels have negligible distant effects on membrane voltage and that individual astrocytes can successfully handle extracellular K+ hotspots. We show how intracellular Ca2+ buffers affect Ca2+ waves and why the classical Ca2+ sparks-and-puffs mechanism is theoretically compatible with common readouts of astroglial Ca2+ imaging
Quantitative Analysis Linking Inner Hair Cell Voltage Changes and Postsynaptic Conductance Change: A Modelling Study
This paper presents a computational model which estimates the postsynaptic conductance change of mammalian Type I afferent peripheral process when airborne acoustic waves impact on the tympanic membrane. A model of the human auditory periphery is used to estimate the inner hair cell potential change in response to airborne sound. A generic and tunable topology of the mammalian synaptic ribbon is generated and the voltage dependence of its substructures is used to calculate discrete and probabilistic neurotransmitter vesicle release. Results suggest an almost linear relationship between increasing sound level (in dB SPL) and the postsynaptic conductance for frequencies considered too high for neurons to phase lock with (i.e., a few kHz). Furthermore coordinated vesicle release is shown for up to 300–400 Hz and a mechanism of phase shifting the subharmonic content of a stimulating signal is suggested. Model outputs suggest that strong onset response and highly synchronised multivesicular release rely on compound fusion of ribbon tethered vesicles
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A unified theory of calcium alternans in ventricular myocytes.
Intracellular calcium (Ca2+) alternans is a dynamical phenomenon in ventricular myocytes, which is linked to the genesis of lethal arrhythmias. Iterated map models of intracellular Ca2+ cycling dynamics in ventricular myocytes under periodic pacing have been developed to study the mechanisms of Ca2+ alternans. Two mechanisms of Ca2+ alternans have been demonstrated in these models: one relies mainly on fractional sarcoplasmic reticulum Ca2+ release and uptake, and the other on refractoriness and other properties of Ca2+ sparks. Each of the two mechanisms can partially explain the experimental observations, but both have their inconsistencies with the experimental results. Here we developed an iterated map model that is composed of two coupled iterated maps, which unifies the two mechanisms into a single cohesive mathematical framework. The unified theory can consistently explain the seemingly contradictory experimental observations and shows that the two mechanisms work synergistically to promote Ca2+ alternans. Predictions of the theory were examined in a physiologically-detailed spatial Ca2+ cycling model of ventricular myocytes
An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum
Motivated by recent experimental studies, we derive and analyze a
twodimensional model for the contraction patterns observed in protoplasmic
droplets of Physarum polycephalum. The model couples a model of an active
poroelastic two-phase medium with equations describing the spatiotemporal
dynamics of the intracellular free calcium concentration. The poroelastic
medium is assumed to consist of an active viscoelastic solid representing the
cytoskeleton and a viscous fluid describing the cytosol. The model equations
for the poroelastic medium are obtained from continuum force-balance equations
that include the relevant mechanical fields and an incompressibility relation
for the two-phase medium. The reaction-diffusion equations for the calcium
dynamics in the protoplasm of Physarum are extended by advective transport due
to the flow of the cytosol generated by mechanical stresses. Moreover, we
assume that the active tension in the solid cytoskeleton is regulated by the
calcium concentration in the fluid phase at the same location, which introduces
a chemomechanical feedback. A linear stability analysis of the homogeneous
state without deformation and cytosolic flows exhibits an oscillatory Turing
instability for a large enough mechanochemical coupling strength. Numerical
simulations of the model equations reproduce a large variety of wave patterns,
including traveling and standing waves, turbulent patterns, rotating spirals
and antiphase oscillations in line with experimental observations of
contraction patterns in the protoplasmic droplets.Comment: Additional supplemental material is supplie
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