Microsaccade characterization using the continuous wavelet transform and principal component analysis

During visual fixation on a target, humans perform miniature (or fixational) eye movements consisting of three components, i.e., tremor, drift, and microsaccades. Microsaccades are high velocity components with small amplitudes within fixational eye movements. However, microsaccade shapes and statistical properties vary between individual observers. Here we show that microsaccades can be formally represented with two significant shapes which we identfied using the mathematical definition of singularities for the detection of the former in real data with the continuous wavelet transform. For character-ization and model selection, we carried out a principal component analysis, which identified a step shape with an overshoot as first and a bump which regulates the overshoot as second component. We conclude that microsaccades are singular events with an overshoot component which can be detected by the continuous wavelet transform

Spatial separation of two different pathways accounting for the generation of calcium signals in astrocytes

<div><p>Astrocytes integrate and process synaptic information and exhibit calcium (Ca²⁺) signals in response to incoming information from neighboring synapses. The generation of Ca²⁺ signals is mostly attributed to Ca²⁺ release from internal Ca²⁺ stores evoked by an elevated metabotropic glutamate receptor (mGluR) activity. Different experimental results associated the generation of Ca²⁺ signals to the activity of the glutamate transporter (GluT). The GluT itself does not influence the intracellular Ca²⁺ concentration, but it indirectly activates Ca²⁺ entry over the membrane. A closer look into Ca²⁺ signaling in different astrocytic compartments revealed a spatial separation of those two pathways. Ca²⁺ signals in the soma are mainly generated by Ca²⁺ release from internal Ca²⁺ stores (mGluR-dependent pathway). In astrocytic compartments close to the synapse most Ca²⁺ signals are evoked by Ca²⁺ entry over the plasma membrane (GluT-dependent pathway). This assumption is supported by the finding, that the volume ratio between the internal Ca²⁺ store and the intracellular space decreases from the soma towards the synapse. We extended a model for mGluR-dependent Ca²⁺ signals in astrocytes with the GluT-dependent pathway. Additionally, we included the volume ratio between the internal Ca²⁺ store and the intracellular compartment into the model in order to analyze Ca²⁺ signals either in the soma or close to the synapse. Our model results confirm the spatial separation of the mGluR- and GluT-dependent pathways along the astrocytic process. The model allows to study the binary Ca²⁺ response during a block of either of both pathways. Moreover, the model contributes to a better understanding of the impact of channel densities on the interaction of both pathways and on the Ca²⁺ signal.</p></div

Ca²⁺ oscillation frequency and amplitude for different values of the volume ratio between the internal Ca²⁺ store and the intracellular space (ratio_ER), as well as the maximal pump currents of the Na⁺/Ca²⁺ exchanger (I_{NCX_max}) and the glutamate transporter (I_{GluT_max}).

<p>The astrocytic compartment was stimulated for 200 seconds with a Poisson spike train of 100 Hz. <b>a</b> Ca²⁺ oscillation frequency for three different values of ratio_ER (0.08, 0.1 and 0.15), as a function of I_{GluT_max} and I_{NCX_max}. The colored lines correspond to I_{NCX_max} equal to 0.0001 (blue), 0.001 (yellow), 0.01 (gray), 0.1 (green) and 1 (red). The dashed line corresponds to I_{GluT_max} equal to 0.68. <b>b</b> Ca²⁺ oscillation frequencies for three different values of ratio_ER (0.08 0.1 and 0.15), as a function of I_{GluT_max} and I_{NCX_max}. The colored symbols denote the values of I_{NCX_max} shown in <b>a</b>. <b>c</b> Ca²⁺ oscillation amplitudes for four different values of ratio_ER (0.05, 0.06, 0.1 and 0.15), and as a function of I_{GluT_max} and I_{NCX_max}.</p

Model parameters for the production and degradation of IP₃.

<p>IP₃ production is mediated by PLC<i>β</i> and PLC<i>δ</i> and IP₃ degradation is mediated by IP₃—3K and IP—5P.</p

Parameters for the Tsodyks and Markram model.

<p>Parameters for the Tsodyks and Markram model.</p

Increase of the Na⁺ concentration in the intracellular compartment, [Na⁺]_i, during a constant extracellular glutamate concentration for different values of the maximal pump currents of the Na⁺/Ca²⁺ exchanger (I_NCX_max), the glutamate transporter (I_GluT_max), the Na⁺/K⁺-ATPase (I_NKA_max).

<p>The astrocytic compartment was stimulated for 200 seconds with a constant extracellular glutamate concentration of 100 <i>μ</i>M. The surface volume ratio (SVR) was set equal to 1 <i>μ</i>m^-1, which corresponds to astrocytic compartments close to the soma. <b>a</b> [Na⁺]_i after 200 seconds with respect to its resting concentration ([Na⁺]_rest = 15 mM, Δ Na⁺ = [Na⁺]_End—[Na⁺]_rest) for a maximal pump current of the Na⁺/Ca²⁺ exchanger (I_NCX_max) equal to 0 (left) or equal to 1 (right) and different values of the maximal pump current of the glutamate transporter (I_GluT_max) and the Na⁺/K⁺-ATPase (I_NKA_max). <b>b</b> Time to reach saturation for a maximal pump current of the Na⁺/Ca²⁺ exchanger (I_NCX_max) equal to 0 (left) or equal to 1 (right) and different values of the maximal pump current of the glutamate transporter (I_GluT_max) and the Na⁺/K⁺-ATPase (I_NKA_max). The time to saturation was defined as the time required for the intracellular Na⁺ concentration to remain on a constant concentration.</p

Dynamics of the Ca²⁺ concentration in the intracellular compartment during synaptic activation.

<p><b>a</b> Sample stimulus (spikes). The astrocytic compartment was stimulated for 200 seconds with a Poisson spike train of 100 Hz. The corresponding glutamate concentration in the extracellular compartment as a function of time was calculated using the Tsodyks-Markram model. <b>b</b> [Ca²⁺]_i for different values of the volume ratio (ratio_ER) between the internal Ca²⁺ store and the intracellular compartments. The upper and lower symbols for ratio_ER>0.06 denote the average height of peaks and troughs of the emerging Ca²⁺ oscillations (in [<i>μ</i>M]). For ratio_ER≤0.06 no Ca²⁺ oscillations were present and symbols denote the average concentration of Ca²⁺ over the stimulation period. <b>c</b> Frequency of Ca²⁺ oscillations as a function of ratio_ER.</p