Bifurcation points were observed in model simulations for amplitudes at which the spike count changed.

<p>We show the (A) R-reliability (sigma = 1 ms) and (B) rastergram as a function of amplitude obtained from simulations of the Wang-Buzsaki model neuron <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002615#pcbi.1002615-Tiesinga2" target="_blank">[22]</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002615#pcbi.1002615-Wang2" target="_blank">[47]</a>, using the same injected current as in the recordings from neurons. The dip in reliability indicated by the black and gray arrow in (A) corresponds to the bifurcation in the black and gray circle in (B), respectively. The inset in B is the close up of the rastergram shown in the black circle. We plot (C) mean spike count and (D) standard deviation of the spike count across trials versus the amplitude. The gray curve is the R-reliability replotted from panel A, the full range for R, 0 to 1, is represented in the graph. Peaks in the reliability, indicated by the double-headed arrows, correspond to (C) plateaus in the spike count, for which (D) the trial-to-trial variability in the spike count was small.</p

Bifurcation points led to multiple spike patterns that persisted across multiple amplitudes.

<p>(A) The rastergram for the data shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002615#pcbi-1002615-g002" target="_blank">Figure 2A</a> for amplitudes between 60% and 100% and during the time segment between 650 ms and 850 ms. (B) The analysis procedure suggested that there were four clusters, each corresponding to a spike pattern. We show the rastergram with the trials sorted according to their cluster membership. The numbers on the right side are the cluster index. The gray vertical bands show the detected events that remained after applying a procedure to merge events common to multiple clusters. We used the value <i>t_ISI</i> = 3 ms to detect the events using the interval method and the value <i>t_ROC</i> = 0.50 to find and merge common events. (C) Rastergram of the clustered data shown in panel A. Each block (separated by thick black lines) corresponds to a different amplitude, with the lowest amplitude at the bottom and the highest amplitude at the top. Within each block, the trials are ordered based on their cluster membership. The clusters are separated by thin dashed lines. Two events are highlighted: the ones in the black ellipses, whose reliability increased with amplitude and the ones in the gray ellipses, whose reliability decreased with amplitude. (D) The pattern occupation (or probability) for a given amplitude is the fraction of trials on which that pattern is obtained. We show the pattern occupation as a function of amplitude for the four patterns that were detected, as indicated by the numbers in the graph. (E) The diversity of patterns observed for a given value of the amplitude is quantified as the entropy of the pattern distribution. The entropy as a function of amplitude has a peak at 80% (arrow), indicating that the pattern diversity is largest for that amplitude. The error bars represent the standard deviation of the entropy determined using a resampling procedure (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002615#s4" target="_blank">Methods</a>). There is no correction for the bias, which took values between 0.02 and 0.05 bits.</p

Spike timing in response to a fluctuating current is robust against changes in amplitude and offset.

<p>Responses of two Layer 5 pyramidal cells in a slice preparation of rat prefrontal cortex. In (A) the amplitude of the fluctuating current was varied, whereas in another cell (B) the current offset was varied. For each panel: (a) the rastergram, (b) the R-reliability (Schreiber measure with sigma = 3 ms, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002615#s4" target="_blank">Methods</a>) versus amplitude or current offset and (c) the average spike time histogram across all values of either the amplitude or offset. In subpanel (Ab), the gray curve is the R-reliability based on only spikes in the time interval between 700 ms and 900 ms. The stimulus waveform is shown for reference at the bottom of subpanels (a) and (c). Each line in the rastergram represents a spike train obtained on a trial, with the ordinate of each tick representing a spike time. The spike trains are ordered in blocks (delineated by horizontal lines) based on the amplitude or offset of the injected current, expressed as a percentage, with the highest amplitude or offset on top. In (A) the amplitude ranges from 0% to 100% of maximum amplitude. In (B) the current offset ranges from 0.05 nA to 0.3 nA; indicated as a percentage (0.05/0.3 = 13% of maximum; 0.3/0.3 = 100% of maximum). Within each block the trials are in the order they were recorded, with the earliest trial at the bottom. The arrows in subpanels (b) indicates the dip in the R-reliability, which is related to the spike train dynamics highlighted by the corresponding gray box in subpanels (a). This behavior is related to the presence of so-called bifurcation points.</p

Conceptual foundation for the in vitro experiment.

<p>(A,B) Currents with the same temporal waveform are injected multiple times, but either (A) the offset <i>a</i> or (B) the amplitude <i>b</i> is varied systematically. (C, left) Exactly the same input (including amplitude and offset) is repeatedly injected into the neuron on different trials. (C, right) Under some circumstances the recordings can be interpreted as the response of an ensemble of similar neurons. (D, right) Within an assembly of neurons receiving common input, cells could differ in their membrane properties such as input resistance, level of depolarization, etc. Cells with different input resistances, for instance, would have different gains, represented schematically by bars of different heights. (D, left) The resulting ensemble activity can be approximately reconstructed by repeatedly injecting a common fluctuating current waveform with different amplitude and offset in the same neuron. Hence, the amplitude/offset combinations represent groups of neurons with different intrinsic properties.</p

Information about the time course of the stimulus waveform is increased at bifurcation points because of the presence of multiple spike patterns.

<p>Data from an example model neuron as described in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002615#pcbi-1002615-g005" target="_blank">Figure 5</a>. (A) Rastergram for a short time segment across 100 trials for a (bottom) low-noise and (top) medium-noise model neuron. The noise level refers to the magnitude of a white noise current that varied from trial-to-trial relative to the amplitude of the repeated fluctuating current waveform (shown as a thin solid line on top of each rastergram). For low noise, the neuron spiked only at six events, whereas for medium noise there were additional events. (B) We calculated the reliability and jitter for each event for the entire stimulus duration (1100 ms). The open circles represent the low-noise, and the asterisks represent the medium-noise result. The gray-filled region schematically represents the combination of jitter and reliability for which a putative postsynaptic neuron would generate a spike. (C) The spike-triggered average obtained across the entire stimulus period for (solid line) the medium-noise neuron and (dotted line) the low-noise neuron. (D) The stimulus waveform reconstructed using the low-noise (dotted line) and medium-noise (solid line) spike trains was compared to the actual stimulus waveform (gray solid line). We used an event-based reconstruction, where each extracted event contributed equally to the reconstruction regardless of reliability and jitter, as long as the reliability exceeded 5%. The three curves are offset from each other for clarity.</p

Enzyme-Modified Carbon-Fiber Microelectrode for the Quantification of Dynamic Fluctuations of Nonelectroactive Analytes Using Fast-Scan Cyclic Voltammetry

Neurotransmission occurs on a millisecond time scale, but conventional methods for monitoring nonelectroactive neurochemicals are limited by slow sampling rates. Despite a significant global market, a sensor capable of measuring the dynamics of rapidly fluctuating, nonelectroactive molecules at a single recording site with high sensitivity, electrochemical selectivity, and a subsecond response time is still lacking. To address this need, we have enabled the real-time detection of dynamic glucose fluctuations in live brain tissue using background-subtracted, fast-scan cyclic voltammetry. The novel microbiosensor consists of a simple carbon fiber surface modified with an electrodeposited chitosan hydrogel encapsulating glucose oxidase. The selectivity afforded by voltammetry enables quantitative and qualitative measurements of enzymatically generated H₂O₂ without the need for additional strategies to eliminate interfering agents. The microbiosensors possess a sensitivity and limit of detection for glucose of 19.4 ± 0.2 nA mM^–1 and 13.1 ± 0.7 μM, respectively. They are stable, even under deviations from physiological normoxic conditions, and show minimal interference from endogenous electroactive substances. Using this approach, we have quantitatively and selectively monitored pharmacologically evoked glucose fluctuations with unprecedented chemical and spatial resolution. Furthermore, this novel biosensing strategy is widely applicable to the immobilization of any H₂O₂ producing enzyme, enabling rapid monitoring of many nonelectroactive enzyme substrates