TTS relative frequency histogram and overlaid inverse Gaussian distribution with the same mean and variance.

<p>(A) is generated by a current-step of 0.67 nA, the mean TTS is 13.38 ms (vertical line) and the variance is 0.022 ms². (B) is generated by Poisson synaptic activation (λ = 55.8 events/ms), the mean TTS is 14.46 ms (vertical line) and the variance is 1.25 ms². One thousand simulations produce each of the histograms. Current and synaptic activations begin at TTS = 0. Notice the x-axis scale difference.</p

Inverse TTS approximates a linear function of excitation.

<p>Excitation is either (A) a point dendritic current-step or (B) a spatially dispersed, synaptic activation. Lines are best linear fits (see text). Each point is an average of 120 excitations from rest. The error bars (SEM) for the current-step are within the plot points. All points but the highest intensities always had spike initiation at the AIS. At the largest intensity on each curve, the spike originated in the dendrite 20 percent of the time.</p

Comparison of a stochastic- and a deterministic-based action potential.

<p>The deterministic action potential (blue dashed line) reproduces the result of Hu et al; their action potential initiates at the AIS and spreads to the soma and apical dendrite. Aligned, peaked to peak, is a second action potential (solid red line) using stochastic Na-channels (both Nav 1.2 and Nav 1.6). Both action potentials are generated by the same somatic current-step of 1 nA. Inset y-axis goes from -55 mV to -48 mV (increments of 1 mV); inset x-axis goes from 4.8 ms to 5.2 ms (increments of.05 ms).</p

Distributions for Λ and associated mutual information values.

<p>Distributions for Λ and associated mutual information values.</p

TTS relative frequency histogram and overlaid inverse Gaussian distribution with the same mean and variance.

<p>(A) is generated by a current-step of 0.67 nA, the mean TTS is 13.38 ms (vertical line) and the variance is 0.022 ms². (B) is generated by Poisson synaptic activation (λ = 55.8 events/ms), the mean TTS is 14.46 ms (vertical line) and the variance is 1.25 ms². One thousand simulations produce each of the histograms. Current and synaptic activations begin at TTS = 0. Notice the x-axis scale difference.</p

Synaptic shot-noise far exceeds Na-channel shot-noise.

<p>Random synaptic activation greatly increases the variation in TTS. (A) The only variation in TTS using a current-step is due to the stochastic nature of Na-channel activation. TTS variance increases as individual Na-channel conductance events get larger while keeping constant. By comparison in (B), the synaptic conductance events create much more variance. Note the y-axis scale differences. A current-step of 0.7 nA generates the data of (A). In (B), stochastic activation for each point is on average the same with a total conductance of 16.6 nS. Error bars are SEM. Lines are best linear fits (see text).</p

A transient overproduction in the number of synapses is more prominent in fast developing neurons.

<p>Faster developing neurons have larger overproductions in synapse number as well as more synapses at stability. The overproduction is calculated as the difference between each average maximum (black, circle) and the corresponding average final number of synapses per neuron (red, upside-down triangle). (A) As SSN is increased, overproduction becomes more prominent. For simulations manipulating SSN, the values of γ and ε are fixed at 0.001 for all points, and the values of SSN for the points from left to right are 50, 100, 150, 200, and 250 out of 1,000 total possible synapses. (B) As γ is increased, neurons converge faster, and overproduction (red, circle) is more prominent. These simulations manipulating γ use values of ε that are fastest for the given value of γ (See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005750#sec013" target="_blank">Methods</a> for how such values of ε are found), and the values of γ for the points from left to right are 0.0003, 0.001, 0.002, 0.003, and 0.004. Each point is a mean of 1,000 postsynaptic neurons.</p

Input datasets single blocks of the datasets.

<p>Patterns are grouped together by category to aid visualization of the categories, but in simulations, the presentation order of the patterns is randomized for each block. (A) and (B) show 100-pattern blocks of Datasets A1 and A2, respectively. There are five orthogonal categories. Dataset A1 has categories with probabilities of 0.1, 0.15, 0.2, 0.25, and 0.3, and Dataset A2 has categories with the same probability of 0.2. (C) and (D) show 100-pattern blocks of the Datasets C1 and C3, respectively. Datasets C2 and C4 are not shown. The datasets mimic environments of orientation neurons in the visual system. The circular illustrations are qualitative visualizations of the orientation biases that each C dataset represents. Dataset C1 and C2 simulate experimentally manipulated environments with contours of a single orientation. Dataset C3 simulates a retinal wave-generated environment with no bias in orientation, and Dataset C4 simulates a normal visual environment with slight biases for horizontal and vertical orientations. The circular illustrations are qualitative visualizations of the datasets. See text for more details, including references to the empirical motivations.</p

A neuron overproduces and subsequently sheds synapses.

<p>An individual example of the overproduction phenomenon. The neuron develops in a simulation with a γ value of 0.0003 and an ε value of 0.0015 and is representative of the amount of overproduction for neurons with these settings. It obtains a maximum total synapse number of 30 at block 101, but eventually stabilizes with 14 synapses by block 235. The simulation continues for 1,088 more blocks with connections remaining unchanged. Note that the example neuron shown here (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005750#pcbi.1005750.g007" target="_blank">Fig 7B</a>) is chosen from the 1,000 neurons used to produce the single data point where γ equals 0.0003.</p

Assumptions and simplifications.

<p>Assumptions and simplifications.</p