The balance between spontaneous and evoked vesicle exocytosis provides control for the rate of Hebbian plasticity.

<p>We use the VTDP model represented by Eqs (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004386#pcbi.1004386.e001" target="_blank">1</a>) to (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004386#pcbi.1004386.e008" target="_blank">8</a>). <b>A</b>: Vesicle exocytosis can occur directly following a presynaptic spike (sEVE), with a high probability after a presynaptic spike (aEVE) or randomly, independent of a presynaptic spike (SVE). <b>B</b>: Each exocytosis mode can coordinate activity across the synapse. When EVE mode dominates the release process, there will be competition between synapses of neurons that have low (left presynaptic neuron) and high (right presynaptic neuron) firing rates, with the former decreasing in strength and the latter increasing in strength (top and middle synapses). There is no such competition for SVE dominated synapses (bottom synapses). <b>C</b>: Vesicle exocytosis is initially dominated by SVE, which maintains the synaptic strength distribution. Following a switch to EVE, the synapses at which many action potentials arrive (upper traces) are potentiated at the expense of synapses for the lower firing rate neurons (lower traces). The (partial) switch to EVE occurs at the dotted line and is either to aEVE or sEVE. The colorbar denotes the SVE-aEVE (green) and SVE-sEVE (red) balance. <b>D</b>: The final difference in weight for the synapses of the low- and high firing rate neurons depends on the SVE-EVE balance. Dots are the mean of the last 100 seconds for the upper (top) and lower (bottom) traces in panel C. Colors represent the same degree of balance as in panel C. <b>E</b>: The divergence factor between the synapses of the high and low firing rate neurons (upper and lower traces in panel C, respectively) increases after the SVE to EVE switch. <b>F</b>: The divergence rate is calculated as the change in divergence factor (panel E) per time unit. The maximal rate of divergence depends on the SVE-EVE balance, where a large fraction of EVE results in faster divergence. The divergence rate for equivalent strength is a bit lower for aEVE compared to sEVE. For purely SVE there is no divergence. The SVE-EVE balance can thus act to control the divergence rate during synaptic competition.</p

The adaptive threshold neuron is more informative for high temporal precision and low noise than the fixed threshold neuron.

<p>Two types of encoding (left) were investigated on the input side, either a classical rate encoding (top), where the number of input spikes carry the information but spike times are drawn randomly from a normal distribution centered at t₀, and a pattern encoding (bottom), where the spatiotemporal pattern of inputs encodes the information and spike times are hence precise across repetitions. In both cases, the temporal precision (σ) according to which the stimuli are drawn is important (bottom). <b>(A)</b> Responses of the adaptive threshold model neurons (red) encode information mostly at low temporal spread σ, while the fixed threshold neurons (blue) possess a wider range of encoding w.r.t. to σ if information is rate-encoded. <b>(B)</b> This relationship holds across a wide range of noise inputs, with adaptive threshold neurons encoding generally better for lower values of σ, and fixed threshold neurons for higher (<b>B3,</b> the differences in mutual information between adaptive and fixed threshold models). Color mapping here represents information. Noise was modeled as independent Poisson spike trains with constant rate for each input neuron; there were 100 input neurons in total. <b>(C)</b> A similar relationship in information encoding between the models is observed when information is decoded from the temporal pattern of incoming spikes. Again the adaptive threshold model performs better for low σ. <b>(D)</b> This relationship holds only for a limited range of noise, after which point the differences between the models becomes fairly small.</p

Additional functional roles of spontaneous vesicle exocytosis (SVE).

<p><b>A</b>: Synaptic weights that are initially heterogeneous, homogenize into a tight synaptic weight distribution in the case of SVE. Black lines are traces of 50 synaptic weights randomly selected from a network of 500 presynaptic neurons that connect to 10 postsynaptic neurons. The neurons fire uncorrelated action potentials at the same mean firing rate. <b>B</b>: Synaptic weights show large fluctuations in the case of EVE. As before, neurons fire uncorrelated action potentials at the same mean firing rate. <b>C</b>: Distribution of synaptic weights for SVE (black line), EVE with uncorrelated spiking activity (4.8 Hz, blue line) and EVE with patterned spiking activity (red line). For the patterned, a subset of the neurons (20%) have higher firing rates (8 Hz) compared to the others (4 Hz). Notice the broadening for uncorrelated and patterned spiking activity in the case of EVE. <b>D</b>: Synaptogenesis creates new synapses with small initial synaptic weights (denoted with a *). SVE incorporates the newly generated synapses into the homogeneous pool of all synaptic weights. <b>E</b>: In the absence of SVE, the synaptic weights increase due to the homeostatic mechanism until they reach the max synapse size. Synaptic weights are heterogeneous when the switch to evoked vesicle exocytosis (EVE) occurs. <b>F</b>: For a gradual increase of EVE, in the absence of SVE, the synaptic weights span a large dynamic range and are heterogeneous distributed.</p

Membrane and threshold time constants influence temporal selectivity similarly.

<p><b>(A-B)</b> For rate encoding, the firing rate of the model neurons was limited by τ_m (A) and τ_θ (B), if either of them were too small. Short τ_m prevent integration, while short τ_θ lead to a threshold that quickly follows the input. <b>(C-D)</b> The limitation in firing rate by τ_m (C) and τ_θ (D) translates to a limitation of represented stimulus information. Only for short values of τ_m and τ_θ the lowpass shape gives way for a bandpass shape, which is a consequence of the decoding bin size chosen here (2ms): for small σ and low τ_m/τ_θ the responses to different stimuli will tend to fall in a small number of bins. <b>(E)</b> We extract the average σ that maximized MI for a combination of τ_m and τ_θ. The resulting dependence is monotonically in τ_m and τ_θ, consistent with a change in the σ edge of the lowpass relationship (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004984#pcbi.1004984.g003" target="_blank">Fig 3A</a>). <b>(F-G)</b> For pattern encoding, the firing rate is limited analogously by τ_m (F) and τ_θ (G). <b>(H-I)</b> The value of σ that leads to highest MI shifts with both τ_m (H) and τ_θ (I), indicating a match between the membrane dynamics and the temporal scale of input patterns that can effectively be encoded. Larger σ values generate temporal patterns that are more distinguishable but the spikes are more dispersed in time,and both τ_m and τ_θ set the temporal limit in which the spikes can be integrated. <b>(J)</b> The best MI is achieved at different average σ across the range of τ_m and τ_θ, monotonically increasing for both parameters.</p

The spike threshold depends on the history of the membrane potential in both real and simulated data.

<p><b>(A)</b> We performed patch-clamp recordings in layer 2/3 pyramidal neurons in vitro, in response to population input from stimulation in layer 4 (left). The pyramidal neuron identity was confirmed in a subset by filling the targeted neuron using biotin (middle). <b>(B)</b> From recorded action potentials (top), the spike threshold is determined as the maximal positive peak of the second derivative of the membrane potential (bottom). <b>(C1)</b> A cortical neuron stimulated with current inputs of different slopes (bottom, different shades of gray) lead to action potentials (top, corresponding grays) with different thresholds for spike initiation (top, red lines in corresponding brightness to grays of voltage traces, inset shows zoom in of spike initiation). The response is delayed w.r.t. to the stimulation due to the propagation delay from L4 to L2/3. The inset shows a magnified view of the threshold region. (<b>C2</b>) As in previous studies, thresholds were found to vary with the slope of the preceding membrane voltage. In the current stimulation settings, only a limited range of input slopes was realized. <b>(D1)</b> Neurons with an adaptive threshold were simulated on the basis of the model by Fontaine et al. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004984#pcbi.1004984.ref002" target="_blank">2</a>], after adapting the parameterization to cortical excitatory neurons (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004984#sec018" target="_blank">Methods</a>). In addition to the voltage traces (grays), the adapting thresholds are also shown (reds, brightness corresponding to the gray traces). (<b>D2</b>) Applying the same analysis as in the in vitro data to measure the threshold, indicates that designed and measured threshold agree. The relationship between EPSP slope and spike threshold is overall captured by an exponential function especially when the wider range of EPSP slopes was used, which could be explored in the model (compare C2 and D2), see also [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004984#pcbi.1004984.ref005" target="_blank">5</a>]. <b>(E1)</b> Neurons with a fixed threshold were also simulated. The threshold was set to equalize firing probability with the adaptive threshold model. (<b>E2</b>) Re-estimating the threshold, we obtain the expected constant threshold.</p

The state dependence of neural data corresponds closely to adaptive threshold behavior.

<p>Identical analyses were carried out as for the model data in the preceding figures. (<b>A</b>) Across three initial states of voltage (-80, -70, -60mV) a correlation between threshold and the EPSP slope was observed, i.e. a negative dependence between spike threshold and EPSP slope. Red lines, least-square linear fit to the data. (<b>B</b>) All recorded neurons (N = 11) exhibited this behavior. The average slopes across the different states were across the three states, i.e. -0.99 (0.27), -0.92 (0.19), and 0.90 (0.23) ms, respectively. Numbers in () are s.d. Red lines, average across all the neurons. (<b>C</b>) For small state differences, both the response patterns (<b>C1</b>), the decoded information (<b>D1</b> top) and the robustness (<b>D1</b> bottom, measured as robustness index RI) remain comparable across stimulus-centered (orange) and response-centered (red) decoding. N.S., non-spiking trials. (<b>D</b>) For larger state differences the advantage of decoding with an adaptive threshold becomes evident (<b>D2</b>). Stim. cent., stimulus-centered; Resp. cent., response-centered. (<b>E</b>) The similarity of PSTHs as a function of state difference reflects the behavior of the adaptive threshold model (Figs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004984#pcbi.1004984.g005" target="_blank">5C</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004984#pcbi.1004984.g006" target="_blank">6C</a>, red) exhibiting a slow decay, based on a similar robustness in mean and variance of the spike-timing. (<b>F</b>) Robustness in decoding across states shows a similar dependence on the correlation coefficient as for the model data (compare orange to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004984#pcbi.1004984.g005" target="_blank">Fig 5D</a>, and red to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004984#pcbi.1004984.g006" target="_blank">Fig 6D</a>), validating the analysis across real and model data. (<b>G</b>) Robustness across states of the cortical neurons exhibits a shape closer to the adaptive threshold model, characterized by a slower and later decay (for static decoding especially) than for the fixed threshold model (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004984#pcbi.1004984.g005" target="_blank">Fig 5E</a>).</p

Predictions for the role of the SVE to EVE switch in refinement of cortical neural circuits.

<p><b>A</b>: During early development arborization of barrel cortical neurons is sparse, and does not respect the columnar boundaries. Neurite outgrowth occurs during the intermediate developmental period and in late development, as synapses mature, the extensive arborizations outside the column are pruned in an activity dependent manner (illustration based on the results from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004386#pcbi.1004386.ref001" target="_blank">1</a>], using the Trees Toolbox [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004386#pcbi.1004386.ref037" target="_blank">37</a>]). <b>B</b>: Whisker deflection induces synaptic responses in layer 2/3 of the barrel cortex. The input to L2/3 is largely uncorrelated at P12, with a rapid switch to stimulus-driven responses during development [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004386#pcbi.1004386.ref002" target="_blank">2</a>]. At P12-P14 the stimulus-induced activity is typically prolonged and with high variability, whereas at a later stage (P20) the responses are more precisely time-locked to the stimulus [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004386#pcbi.1004386.ref002" target="_blank">2</a>]. <b>C</b>: By modeling changes in the release probability from SVE to highly time-locked release during development, Hebbian plasticity behavior changes from an immature to mature STDP rule. The maturation process of the STDP rule is described <i>in vitro</i> for layer 4 –layer 2/3 synapses during these critical developmental stages [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004386#pcbi.1004386.ref019" target="_blank">19</a>]. The calcium time constant (Eq (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004386#pcbi.1004386.e004" target="_blank">4</a>)) was 1 second (top), 7 millisecond (middle) and 2 millisecond (bottom), and 50 stimuli were given for each t_pre - t_post bin.</p

An adaptive threshold neuron represents information more robustly across membrane states for a ‘response-centered’ time reference.

<p>Since stimulus onset is not known internally, a population-based decoding reference has been suggested to serve a biologically relevant surrogate for stimulus timing [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004984#pcbi.1004984.ref025" target="_blank">25</a>]. With this reference, spike-timing is measured relative to the peak-time of the population response, i.e. local maxima of the population peristimulus time histogram (PSTH). <b>(A1)</b> For small differences in state, adaptive and fixed threshold models show little difference in their relative-time response and consequently the contribution of the knowledge about the state becomes negligible (<b>B1</b>). All colors are as in the preceding figure. (<b>A2</b>) For larger state differences, the response time distributions now differ significantly in their variance, with the fixed threshold model exhibiting a much larger increase in spread for the more hyperpolarized membrane state. Consequently, decoding across states becomes less robust for the fixed model than for the adaptive threshold model (<b>B2</b>). (<b>C</b>) While the ‘response-centered’ time reference increases the similarity of the PSTH across states for both the fixed and the adaptive threshold model, the latter profits more, widening the gap between the models for larger state differences. (<b>D</b>) As before, the correlation coefficient between the PSTHs remains a good predictor for the RI values. (<b>E</b>) In the case of the moving decoding reference, the adaptive model is generally more robust than the fixed threshold model across all state differences investigated, as indicated by a higher RI value. Error bars indicate SEMs across all state differences of a given size.</p

Information decoding across different membrane states and spike threshold types for a ‘stimulus-centered’ time reference.

<p><b>(A)</b> For small differences in state (<b>A1</b>: -62mV vs. -65mV) both adaptive (red) and fixed (blue) threshold models show a shallow dependence on stimulus strength (different rates, range [50:2:60] inputs, total stimulus entropy ~ 2.58 bit, dark color = 60, light color = 50 EPSPs). The adaptive threshold model compensates partly for the difference in initial voltage, and thus exhibits smaller differences in spiking behavior across states. During larger fluctuations in membrane potential (<b>A2</b>: -62mV vs. -72mV) this behavior is qualitatively retained. The different states also scale the slope (average spike times vs. input strength) and spike time variability for each model, with the fixed model being influenced more strongly in both cases. NS, non-spiking trials. <b>(B)</b> Mutual information is estimated across all states with the state known (light colors) or unknown (dark colors) to the decoder. For small state differences (<b>B1</b>) the adaptive model’s MI is independent of state knowledge (RI close to 1, bottom), while the fixed model shows a strong dependence to membrane state (RI around 0.6, indicating ~40% of MI added by state knowledge). For larger state differences, this relationship inverts (<b>B2</b>). Note that in <b>B2</b> upper panel the dark blue curve almost fully overlaps with the light blue curve. <b>(C)</b> To understand this inversion, we relate the response distributions to state difference. The correlation coefficient between response PSTHs measures similarity across state differences. The adaptive threshold neuron (red) retains similar responses for larger state differences than the fixed threshold neuron (blue). <b>(D)</b> The correlation coefficient of response distributions predicts qualitatively the RI values, which indicates the advantage of knowing state during decoding. <b>(E)</b> The adaptive model encodes information in a state-independent manner for small state differences, while the fixed threshold model becomes more state-independent only for larger state differences. This switch is caused by a shift from overlapping to non-overlapping temporal decoding ranges, as indicated by the correlation coefficients of the PSTHs across different states (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004984#pcbi.1004984.g005" target="_blank">Fig 5C</a>, where a vanishing correlation indicates a lack of overlap between the responses across states). Hence, the adaptive threshold model compensates for a part of the initial state, however, does not encode more information independently if a stimulus-based, fixed-time decoding reference is used. Error bars indicate SEMs across all state differences of a given size.</p

Parameters for the VTDP model.

<p>Parameters for the VTDP model.</p