Integration time, modulation frequency and communication accuracy.

<p>(A–D) Fisher information as a function of integration time. Target modulation frequency is indicated by line color (see key). For incoherent distractors (A) and phase separation (D) conditions, distractor frequency was the same as target frequency. For frequency separation condition (C), distractor frequency is indicated by line style (see key). The duration of one period of the target input modulation is indicated by the vertical dashed lines, color coded by target modulation frequency.</p

Oscillation structure determines communication accuracy.

<p>(<i>A</i>–<i>D</i>) Example firing rate modulation of the target (red) and distracting inputs (gray) over the 100 ms integration time. Gain modulation (blue) produced by the optimized receiving network. (<i>E</i>) Firing rate as a function of oscillation phase for synchronization strengths from 0.1–0.9. (<i>F</i>) Fisher information as a function of the synchronization strength of the target input for stimulus estimates decoded from receiving network output integrated over 100 ms. Distractor condition indicated by color as shown in key. (<i>G</i>) Comparison of Fisher information for asynchronous and incoherently oscillating distracting inputs as functions of firing rate of input networks. (<i>H</i>) Separation of target and distractors in frequency. Fisher information as function of oscillation frequency of distractor networks for narrowband (purple) and broadband (orange) sinusoidal oscillations and narrowband Von Mises oscillations (blue). Frequency of target input modulation (50 Hz) is indicated by black arrow. (<i>I</i>) Amplitude spectrum of oscillatory modulations for narrowband Von Mises modulation and narrow and broadband sinusoidal oscillations (F₀ is oscillation center frequency).</p

Bottom-up coherence.

<p>(<i>A</i>) Diagram illustrating receiving network in which gain modulation is a filtered version of the summed combined spike input. (<i>B</i>–<i>E</i>) Comparison of Fisher information of decoded stimulus estimates for original ‘top-down’ model (solid lines) and ‘bottom-up’ model (dashed lines).</p

Filtering with arbitrary gain modulations.

<p>(A–D) Example input firing rate modulations, gain modulations generated by optimized linear filter (blue trace), and gain modulations found to optimize decoding accuracy for specific examples of target firing rate modulation (green traces). (E) Effect of synchronization strength on decoding accuracy for asynchronous distractors (blue), distractors oscillating incoherently in the same frequency band as the target (red) and distractors oscillating coherently with the target but equally space in phase (yellow). (F) Effect of distractor frequency on decoding accuracy. (G) Comparison of decoding accuracy for different distractor conditions indicated by color as above for synchronization strength of 0.5 and average neuronal firing rate of 5 Hz.</p

Inter-synaptic variability of Ca²⁺ cooperativity of AP-evoked vesicular release.

<p>(A) Dependency of the average AP-evoked de-staining rate on . Data are mean ± SEM from six independent experiments for each . (B) Cumulative distributions of at different (1 mM, 620 boutons; 2 mM, 550 boutons, and 4 mM, 555 boutons). (C) Ca²⁺ cooperativity of vesicular release is higher in boutons with slow SRC1 de-staining (blue) than in boutons with fast SRC1 de-staining (red): values at different corresponding to cumulative probabilities 0.75 (Fast boutons) and 0.25 (Slow boutons) were normalized to the corresponding de-staining rates at 1 mM and then plotted against the relative amplitude of Ca²⁺ influx (determined as in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio-1001396-g007" target="_blank">Figure 7</a>), which was also normalized to its value at 1 mM . Numbers next to the dotted lines connecting the data points correspond to differential Ca²⁺ cooperativity of vesicular release calculated using the equation <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio.1001396-Matveev1" target="_blank">[63]</a> (blue, slow boutons; red, fast boutons).</p

Consecutive imaging of vesicular exocytosis and presynaptic Ca²⁺ dynamics in individual synaptic boutons supplied by the same axon.

<p>(A) Experimental paradigm (sequence of loading and imaging protocols) and (B–H) a detailed illustration of a typical experiment. (B,C) Cultured hippocampal neurons (DIC and fluorescence images) showing SRC1 staining (red) before (B) and after (C) the de-staining experiment. (D) The area shown in (B) and (C), imaged after (i) re-staining with SRC1 and (ii) whole-cell patch-loading of a presynaptic cell with Fluo-4 and Alexa Fluor 568 (yellow). A single axon with two branches is clearly seen. Arrows in (B–D) depict boutons (1, 2, and 3) in which both SRC1 de-staining and Ca²⁺ dynamics have been recorded. (E) Details of SRC1 and Fluo-4 imaging in individual boutons. Left, SRC1 stained presynaptic boutons during 0.5-Hz stimulation, after the high-frequency (HF) de-staining, and after re-staining with SRC1 and patch-loading with Fluo-4 and Alexa Fluor 568. Line-scan positions used for Ca²⁺ recordings are shown with red dotted lines on the Alexa image. Right, line-scan recordings of Ca²⁺ responses in selected boutons; brightness is color-coded, red arrow, single spike onset; red segment above, a saturating 100-Hz train of APs. (F) Analysis of SRC1 de-staining in recorded boutons; fluorescence traces were normalized to the initial SRC1 fluorescence at the beginning of 0.5-Hz stimulation (marked by dotted vertical lines), dashed lines depict single-exponent fits in the absence of stimulation () and during 0.5-Hz stimulation (). The specific AP-evoked de-staining rate in each bouton was calculated as . (G) Analysis of presynaptic Ca²⁺ dynamics in recorded boutons. Line-scan fluorescence time courses corresponding to stimulation paradigms shown in (E), average of five traces. Dashed lines: maximal value of Fluo-4 fluorescence <i>F_m</i>, resting Ca²⁺ fluorescence <i>F₀</i>, background fluorescence <i>F_BG</i>, and peak amplitude of AP-evoked fluorescence integrated over 10 ms Δ<i>F.</i> (H) AP-evoked SRC1 de-staining rate (top) and vesicular release rate (bottom) plotted against the amplitude of AP-evoked presynaptic Ca²⁺ fluorescence <i>ΔF/F_m</i>. Boutons are color coded as in (F) and (G). RFU, relative fluorescence units. Spearman rank correlation coefficients ρ are indicated. Dashed lines show data fits with a power function. Scale bars, 10 µm (B), 2 µm (E, top left), and 200 ms (E, bottom right).</p

Linear relationship between ΔF/F_m and total magnitude of presynaptic Ca²⁺ influx.

<p>(A, B) Typical Ca²⁺ fluorescence responses to a single AP followed by a saturating train of 100 APs in individual synaptic boutons recorded at two different : 1 mM and 2 mM (A), and 2 mM and 4 mM (B). [Mg²⁺]_ext was adjusted to keep the total divalent cation concentration constant (4 mM). Whilst <i>F_m</i> measured at the end of a 100-Hz AP train was not affected by changing , both the amplitude Δ<i>F</i> of Fluo-4 responses to a single AP and the rate of rise in fluorescence during 100-Hz stimulation were increased at higher. (C, D) Fractional change of peak AP-evoked fluorescence response was similar in all recorded boutons irrespective of the initial Δ<i>F/F_m</i> value when was changed from 1 mM to 2 mM (C, <i>n</i> = 24 boutons from four axons) or from 2 mM to 4 mM (D, <i>n</i> = 21 bouton from five axons). Dashed lines <i>y</i> = 1.33×(C) and <i>y</i> = 1.38×(D).</p

Synaptic boutons located on the same axon have similar endogenous Ca²⁺ buffering capacity.

<p>(A, B) Theoretical effects of the major endogenous neuronal Ca²⁺ buffers calbindin-D_28K (A) and parvalbumin (B) on presynaptic Ca²⁺ Fluo-4 fluorescence transients calculated using a non-stationary model of presynaptic Ca²⁺ dynamics (<a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio.1001396.s011" target="_blank">Text S3</a>). Left, the effect of increasing concentrations of endogenous Ca²⁺ binding sites on the amplitude and the shape of fluorescence Ca²⁺ transients. Right, peak-scaled Ca²⁺ fluorescence traces illustrating an increase of the fast fluorescence decay component and a decrease of the slow fluorescence decay component with the increase of the endogenous Ca²⁺ buffer concentration. (C, D) Theoretical dependences of changes in the amplitude of AP-evoked Ca²⁺ fluorescence Δ<i>F/F_m</i> (black) and the fast fluorescence decay time constant <i>τ_fast</i> (grey) on intracellular concentration of calbindin-D_28K (C) and parvalbumin (D): <i>τ_fast</i> is more sensitive then Δ<i>F/F_m</i> to changes in endogenous Ca²⁺ buffering. (E) Scaled average responses to a single AP reveal heterogeneity of fast decay rates of Ca²⁺ fluorescence transients recorded in different axons (<i>n</i> = 10 experiments, the same dataset as in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio-1001396-g004" target="_blank">Figure 4E–4F</a>). Black trace, the average response recorded in boutons 1, 2, and 3 from experiment illustrated in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio-1001396-g003" target="_blank">Figures 3C</a> and <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio-1001396-g004" target="_blank">4C</a>. (F, G) Detailed comparison of presynaptic Ca²⁺ dynamics in boutons 1, 2, and 3. (F) Superimposed original traces (color coded as in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio-1001396-g004" target="_blank">Figure 4C</a>) showing variability of Δ<i>F/F_m</i> and the resting Ca²⁺ fluorescence <i>F</i>₀ among the three boutons. (G) Scaled responses from the same boutons showing similar fluorescence decay rates (black shows the average of three traces). (H) To test how the fast fluorescence decay rate (τ₅₀, calculated by fitting the Ca²⁺ transient over 50 ms with a mono-exponential function) depends on the amplitude of presynaptic Ca²⁺ fluorescence transient, boutons recorded in each axon were divided into two groups according to the Δ<i>F/F_m</i> value: above the median (high Ca²⁺) and below the median value (low Ca²⁺). Next, the average amplitude Δ<i>F/F_m</i> and the average τ₅₀ were calculated for each group followed by calculation of and . Because the ratio was not significantly different from 1 we conclude that fast fluorescence decay rate is the same in boutons with high and low Δ<i>F/F_m</i>. Bars are mean ± SEM; <i>n</i> = 10 experiments, **<i>p</i><0.01, non-significant (NS) <i>p</i> = 0.70, Wilcoxon singed rank test for single group median.</p

Simultaneous measurements of ratio and AP-evoked SRC1 de-staining rate demonstrate heterogeneity of among synapses supplied by single axons.

<p>(A) Experimental paradigm. A presynaptic cell was filled with the morphological tracer Alexa Fluor 568 using whole-cell patch-clamp. Recycling synaptic vesicles in all boutons in the field of view were labeled with SRC1 using high-frequency field stimulation. After dye washout the ratio in individual boutons was estimated using 30-Hz 60 AP train (see main text and <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio.1001396.s010" target="_blank">Text S2</a> for details). This was followed by measurements of SRC1 de-staining kinetics () during low-frequency 0.5-Hz stimulation. (B) Fluorescence image from a typical experiment showing SRC1 labeled boutons (red) and axodentritic tree of a single neuron filled with Alexa Fluor 568 (blue). White boxes depict regions of interest containing synaptic boutons analyzed in (C). (C) High resolution images and de-staining profiles in three typical synaptic boutons (depicted by arrows) supplied by the Alexa Fluo 568 loaded neuron. (D and E) Frequency histograms of (D) and (E) from the experiment illustrated in (B and C). Blue histogram, boutons supplied by the Alexa loaded axon; grey histogram, all boutons in the field of view. (F) Comparison of and variability. Blue bars, average CVs for and recorded in synaptic boutons located on single axons; gray bars, average CVs for the same parameters for all boutons recorded in the same experiments. Data are mean ± standard error of the mean (SEM) from 11 independent experiments, **<i>p</i><0.01 and ***<i>p</i><0.001, Wilcoxon signed rank test. (G) Relationship between and . Blue, data points from boutons supplied by the Alexa loaded axon shown in (B); grey data points from all boutons in the field of view. Dotted line shows linear regression for all boutons in the field of view. Pearson's correlation coefficient <i>r</i> and significance levels <i>P</i> (Pearson product correlation test) are indicated. (H) Frequency histogram of calculated for the same set of boutons as in (D, E, and G) using . Scale bars 20 µm (B) and 2 µm (C).</p

Co-variation of and volume averaged AP-evoked presynaptic Ca²⁺ fluorescent transient.

<p>(A) Fluorescence image (Alexa channel) of the same neuron as in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio-1001396-g003" target="_blank">Figure 3B</a> after completion of the SRC1 de-staining experiment and subsequent re-patch-loading with Fluo-4 and Alexa Fluor 568. (B) Experimental paradigm. Ca²⁺ fluorescence responses in each bouton were recorded during a single sweep consisting of five APs delivered at 0.5 Hz followed by a saturating 100-Hz train of APs. The laser was turned on only during 100-ms intervals synchronized with single AP stimulation (brown arrows) and at the very end of the 100-Hz 100 AP train (brown horizontal bar) when Fluo-4 signal was already saturated (e.g., <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio-1001396-g001" target="_blank">Figure 1G</a>). (C) Line-scan recordings of Ca²⁺ dynamics in three typical boutons (prior to these recordings vesicular release in these boutons was measured as illustrated in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio-1001396-g003" target="_blank">Figure 3C</a>). The morphology of each bouton (Alexa channel) and the position of line scans are shown on the left. The aspect ratio in line-scan images has been adjusted to optimize figure layout. (D) Amplitude of AP-evoked presynaptic Ca²⁺ influx does not change during 0.5-Hz stimulation. In each recorded bouton Ca²⁺ fluorescence response at every AP of the 0.5-Hz train (Δ<i>F</i>(AP)) was normalized to the average amplitude calculated for all five APs (<Δ<i>F</i>>) in the same train. The bars are the mean ± SEM values of Δ<i>F</i>(<i>AP</i>)/<Δ<i>F</i>> in all recorded boutons (<i>n</i> = 42 from ten independent experiments). Δ<i>F</i>(<i>AP</i>)/<Δ<i>F</i>> did not vary systematically with the AP number (<i>p</i> = 0.2, one-way ANOVA). (E–G) AP-evoked SRC1 de-staining rate (D), the average release probability of individual RRP vesicles (E), and the ratio (F), plotted against the amplitude of AP-evoked presynaptic Ca²⁺ fluorescence Δ<i>F/F_m</i>. All parameters are normalized to the respective mean value in each experiment (<i>n</i> = 42 boutons from ten independent experiments). Correlation coefficients ρ and significance levels <i>p</i> (Spearman rank correlation test) are indicated. Dashed lines show data fits with a power function. Color-coded data points correspond to boutons 1, 2, and 3 from the experiment analyzed in (C) and also in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1001396#pbio-1001396-g003" target="_blank">Figure 3B and 3C</a>. Scale bars 20 µm (A) and 2 µm (C).</p