Electrical Double Layer at Various Electrode Potentials: A Modification by Vibration

This paper proposes a vibration model of ions as an improvement over the conventional Gouy–Chapman–Stern theory, which is used to model the electrical double layer capacitance and to study the ionic dynamics at electrode/electrolyte interfaces. Although the Gouy–Chapman–Stern model is successful for small applied potentials, it fails to explain the observed behavior at larger potentials, which are becoming increasingly important as materials with high charge injection capacities are developed. A time-dependent study on ionic transport indicates that ions vibrate near the electrode surface in response to the applied electric field. This vibration allows us to correctly predict the experimentally observed decreasing differential capacitance at high electrode potential. This new model elucidates the mechanism behind the ionic dynamics at solid–electrolyte interfaces, providing useful insight that may be applied to many electrochemical systems in energy storage, photoelectrochemical cells, and biosensing

Electrical receptive field properties.

<p>A) Proportions of cells with up to three excitatory components. B) Proportions of cells with up to three suppressive components. C). The temporal windows over which suppressive and excitatory ERFs affected cell responses, thus indicating duration of stimulus integration time. Excitatory ERFs tended to occur within a short latency from the response (blue circles). Suppressive ERFs tended to extend over a long duration, which was variable from cell to cell (orange circles). The squares represent the means for all cells. D) RGC preference to cathodic-first or anodic-first stimulation. Squares represent means and lines indicate ±1 standard deviation. Stars denote significant differences (<i>p</i> < 0.05).</p

Electrical receptive fields of retinal ganglion cells: Influence of presynaptic neurons - Fig 7

<p>Number of excitatory (A) and suppressive (B) components before and after application of synaptic transmission blockers (CdCl₂).</p

Dendritic and electrical receptive fields.

<p>a-b) Sample cells depicting the stimulating array (large black discs) and the patch-clamp recording electrode (denoted by a *). Overlaid on the images are the morphological reconstructions of the cells. The sample cell in (a) is also shown in (c) 16. The sample cell in (b) is also shown in (c) 20. Note that the stimulating electrodes appear large, but the exposed area is only 400 μm. Also visible are the lycra threads used to keep the retina affixed and the stimulating electrode tracks. c) The electrical receptive fields shown together with the dendritic receptive field estimates. The electrodes with stars above them show the approximate location of the optic disc for each preparation.</p

Model validation for a sample cell.

<p>A) The predicted response was compared to the average responses (black dots with SEM bars). Each point represents the mean response to 200 stimuli. B) The variance of each point in (A) was compared to the prediction. Both values were normalized to the maximum prediction (~3 spikes). For a Poisson-like process, the values should be equal (indicated by the dashed line). C) The contours of fixed response expectation (dotted black) were computed using the predicted model parameters (Eq (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005997#pcbi.1005997.e101" target="_blank">6</a>)). These contours were compared to the contours generated from the experimental data (solid black) when projected onto the principal excitatory component and the second excitatory component (left), third excitatory component (middle), or a suppressive component (right). The contours denote the expectations of 1 and 2 spikes.</p

Model comparison with non-Gaussian stimuli.

<p>A) Distribution of electrode amplitudes for Gaussian and non-Gaussian image stimuli. The amplitudes in both cases have been divided by the variance of the Gaussian stimuli (i.e., the Gaussian distribution has unit variance). B) The model prediction for a sample cell is shown for Gaussian stimuli (round) and images (square). C) Coefficient of determination (R²) of the model prediction when validated with noise and with images for eleven cells. The x denotes the mean R² for noise (0.86) and images (0.70). Dashed line represents line of equality. D) A comparison of the coefficients of determination for the general quadratic model (GQM), non-linear input model (NIM), a two-dimensional spike-triggered covariance analysis (STC₂), and a one-dimension model (STC₁). Squares denote the mean and lines denote ±1 standard deviation.</p

<i>In vitro</i> stimulation and recording.

<p>The retina was placed on a multi-electrode array (large black circles) and held in place with a perfusion chamber and lycra threads. A) Two extracellular electrodes were used to obtain recordings from the retinal surface. B) A hole was made in the inner limiting membrane to expose the RGCs. Once exposed, an intracellular glass electrode was used to obtain whole cell recordings of RGCs.</p

The effect of synaptic blockers.

<p>A) A raster plot of spike times for a sample cell prior to application of CdCl₂. B) The eigenvalues produced from STC analysis showing three significant eigenvalues (arrows). C) A raster plot of spike times for the same cell as in (A) after application of CdCl₂. While spontaneous spikes can be seen at times, long-latency activity was mostly abolished. D) The eigenvalues produced from STC analysis showing only one significant eigenvalue. E) The ERFs corresponding to before (left) and after (right) application of CdCl₂. F) A comparison of the electrode amplitudes making up the ERFs of , before and after application of CdCl₂.</p

Model applied to long-latency responses.

<p>(a) The positive electrical receptive field for long-latency responses of the same cell as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004849#pcbi.1004849.g007" target="_blank">Fig 7</a>. This cell is largely influenced by electrode 9, which in this preparation was below the optic disc. (b) The predicted response vs. the actual response probability for the cell in (a). The root mean square error between prediction and actual response probability was 0.07. (c) The eigenvalues of the long-latency spike-triggered stimuli with one large excitatory and suppressive component evident. (d) An example of a cell with a suppressive response for long-latency (LL) responses. This cell fired with fewer spikes when the stimulus was stronger along the first or second principal component. Also shown is the short-latency (SL) response for comparison. (e) The corresponding eigenvalues for the long-latency responses in (d). (f) An example of a cell with a preferred stimulus polarity for long-latency responses. This cell responded with a greater number of spikes when the stimulus was cathodic-first, and very few spikes when the stimulus was anodic-first. Also shown is the short-latency response for comparison. (g) The corresponding eigenvalues for the long-latency responses in (f).</p

Model validation.

<p>(a) The predicted probability compared to the actual probability from the validation data for all cells (gray). For clarity this data is shown without error bars. The validation of the sample cell from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004849#pcbi.1004849.g007" target="_blank">Fig 7</a> with standard error bars (black solid line) is also shown. The root mean square error for this cell was 0.056. (b) The 2-dimensional model error (<i>E</i>^<i>RMS</i>2) is compared to the 1-dimensional model error (<i>E</i>^<i>RMS</i>1) for all cells where the hypothesis test recovered 2 or more significant components.</p