Fig 1.
SNARE Complex Structure and Dynamics.
(A) SNAREpins prior to vesicle fusion. (B) Binding of Ca2+ to synaptotagmin (Syt-1 here, Syt-7 attaches to target membrane [6,7]) triggers full zippering of SNARE complex and, in turn, vesicle fusion [8,9].
Fig 2.
Spatial Modeling of Spike-Evoked Ca2+ Transients.
(A) Ca2+ sensors (dark yellow through dark blue filled circles) at vesicle cluster centers, displaced linearly from cluster of Ca2+ channels (blue half-disk on the left); distance in μm, dn = 0.160+0.105n for n∈{0,…,16}. (B) [Ca2+]i measured over time in MCell (dark yellow through dark blue) and in the deterministic well-mixed model (maroon). MCell traces averaged from 2000 trials of MCell simulations with Δt = 0.1 ms. Color transitions from yellow for vesicles proximal to the VDCC Ca2+ source to blue for vesicles far away, as in A. Proximally (distally) measured [Ca2+]i displays more (fewer) components of decay than are evident in the deterministic model. (C) Logarithmic plots of peak [Ca2+]i (blue) and peak time (red) as a function of distance from Ca2+ source; peak [Ca2+]i drops off exponentially with distance from VDCC cluster; amplitude of latent Ca2+ dominates over the initial action-potential-evoked influx after 1.4 μm.
Fig 3.
Model of Ca2+-Evoked, Synaptotagmin-Mediated Neurotransmitter Release.
(A,B) Model adapted from Sun et al. [5]. γS and γA represent rates of vesicle fusion from the releasable states of the synchronous and asynchronous mechanisms, respectively. (A) Ca2+-bound states for Syt-1 (synchronous release); Sn indicates n Ca2+ ions bound to the synchronous release mechanism. (B) Ca2+-bound states for Syt-7 (asynchronous release); An indicates n Ca2+ ions bound to the asynchronous release mechanism. (C,D) Action-potential-like stimulus delivered to model axon starting at 0 ms. Diffusion is assumed to be instantaneous, and molecular state probabilities are tracked deterministically over time. (C) Free [Ca2+]i in response to single action potential. (D) Instantaneous vesicle release rate in response to buffered Ca2+ from both synaptotagmin-mediated release mechanisms.
Table 1.
SNARE Release State Transition Parameters.
Fig 4.
Synchronous and Asynchronous Release in MCell.
Color indicates distance from VDCC source, with yellow representing a nearby Ca2+ sensor and dark blue a distant one (as in Fig 2A and 2B). Action-potential-like stimulus delivered at 0 ms (left), followed by another at 20 ms (center) and 100 ms (right). (A) Spike-evoked Ca2+ traces that drive release. (B) Synchronous release raster. (C) Asynchronous release raster. (D) Synchronous (tall, thin bars) and asynchronous (short, wide bars) release stacked histogram. Most synchronous releases happen close to the Ca2+ source; asynchronous releases distributed across all distances.
Fig 5.
Multi-Exponential Shape of Ca2+-Driven Vesicle Release Rate.
(A,B) Plots given as semi-log to highlight exponential decay components (straight line segments of profiles). (A) A single, spike-evoked [Ca2+]i transient, which drives (B) the synchronous and asynchronous release rates. (C) Instantaneous time constants for Ca2+, synchronous, and asynchronous curves, calculated from the well-mixed model (see Eq (2)). Long release rate time constants (around 80 ms and 1000 ms; dashed lines) follow Ca2+ curve due to slow un-buffering of latent Ca2+. Asynchronous starts high because fast and slow components have comparable magnitude and become conflated; it goes up to infinity where additive effects cause the curve to flatten.
Fig 6.
Synchronous and Asynchronous Release Rates in Response to Ca2+ Impulse at Different Resting Concentrations.
Instantaneous impulse of Ca2+ delivered at 10 ms. Solid lines represent true release rate; dotted lines have spontaneous rates subtracted off to show secondary exponential components. Black lines show release rate decaying with a single exponential component with no baseline [Ca2+]i. For other curves, [Ca2+]i0 ranges from 0.001 μM to 10 μM. (A) Synchronous release rate over time: S(t). (B) Asynchronous release rate over time: A(t). (C) Instantaneous release rate decay time constants for synchronous and asynchronous mechanisms. Fast components (lower blue and red lines) determined from profiles with [Ca2+]i0 = 0 (black lines in A and B). Slower components (upper blue and red curves) determined from cases with small [Ca2+]i0.
Fig 7.
Fitted Release Rate Histogram Profiles for a Single Spike.
Parameter values given in Table 2. (A) Synchronous release rate: true histogram (blue) with estimated histogram (black). (B) Asynchronous release rate: true histogram (red) with estimated histogram (black).
Table 2.
Spike-Evoked Release Rate Parameters.
Fig 8.
Convolutional Filter Applied to a Component of a Release Rate Function.
Toy model with P = 5, τ = 10 ms, k = 0.5 ms–1, μ = 5 ms, and σ = 1 ms. (A) Unfiltered release rate component. (B) MCMC ex-Gaussian filter shape. (C) Filtered release profile produced by convolving the release rate profile with the temporal delay filter. (D-F) Release rates in response to spike trains without applying delay filter. (G-I) Release rates in response to spike trains with delay filter applied. (D,G) Response to one spike. (E,H) Response to two spikes. (F,I) Response to multiple spikes. Dotted lines show how the histogram of response to one spike falls off with interference from the response to the following spike. Spike times at 0, 15, 20, 30, and 50 ms.
Fig 9.
Empirical Facilitation in Synchronous and Asynchronous Release Rates.
Release rate profiles facilitate in response to single spikes (A) or to spike ramps (B,C). Probe spikes of increasing ISI reveal how facilitation then decays back toward baseline after a delay. Each rise in release rate is triggered by a spike event. Synchronous release rate profiles shown in blue. Asynchronous profiles shown in red. Profiles from multiple runs are overlaid in each panel. Dark colors represent response to initial spike or spike ramp (common to all traces on a plot). Light colors represent profiles from different runs in response to single probe spikes at different ISIs following the initial spike or ramp. (A) After single spike, paired-pulse facilitation decays with increasing ISI (probe ISIs of 2, 5, 10, 20, 50, 100, 200 ms). (B) 5-spike ramp with a 5-ms ISI shows strong facilitation in release rate (dark colors) followed by rapid decay seen at the probe spikes (light colors). (C) 5-spike ramp with a 20-ms ISI shows weaker facilitation in the ramp phase but a similar rate of decay at the probe spikes. Note the orders of magnitude difference in scale between synchronous and asynchronous release rates, as well as the change in scale from (A) to (B,C).
Fig 10.
Release Rate Parameters and Facilitation Metaparameters Fitted to Empirical Histogram Profiles.
(A) Synchronous and asynchronous profiles fitted for baseline (un-facilitated) case, and for highly facilitated case (probe spike 5 ms after 5-spike ramp of 5-ms ISIs). (B,C) Release fidelity values fitted case-by-case (dark colors) overlaid with predictions from best-fit facilitation functions (light colors) for synchronous (B) and asynchronous (C) components.
Table 3.
Metaparameters for Facilitation of Release Fidelity.