Transmitter release is evoked with low probability predominately by calcium flux through single channel openings at the frog neuromuscular junction.

The quantitative relationship between presynaptic calcium influx and transmitter release critically depends on the spatial coupling of presynaptic calcium channels to synaptic vesicles. When there is a close association between calcium channels and synaptic vesicles, the flux through a single open calcium channel may be sufficient to trigger transmitter release. With increasing spatial distance, however, a larger number of open calcium channels might be required to contribute sufficient calcium ions to trigger vesicle fusion. Here we used a combination of pharmacological calcium channel block, high-resolution calcium imaging, postsynaptic recording, and 3D Monte Carlo reaction-diffusion simulations in the adult frog neuromuscular junction, to show that release of individual synaptic vesicles is predominately triggered by calcium ions entering the nerve terminal through the nearest open calcium channel. Furthermore, calcium ion flux through this channel has a low probability of triggering synaptic vesicle fusion (∼6%), even when multiple channels open in a single active zone. These mechanisms work to control the rare triggering of vesicle fusion in the frog neuromuscular junction from each of the tens of thousands of individual release sites at this large model synapse.

An excess-calcium-binding-site model predicts neurotransmitter release at the neuromuscular junction.

Despite decades of intense experimental studies, we still lack a detailed understanding of synaptic function. Fortunately, using computational approaches, we can obtain important new insights into the inner workings of these important neural systems. Here, we report the development of a spatially realistic computational model of an entire frog active zone in which we constrained model parameters with experimental data, and then used Monte Carlo simulation methods to predict the Ca(2+)-binding stoichiometry and dynamics that underlie neurotransmitter release. Our model reveals that 20-40 independent Ca(2+)-binding sites on synaptic vesicles, only a fraction of which need to bind Ca(2+) to trigger fusion, are sufficient to predict physiological release. Our excess-Ca(2+)-binding-site model has many functional advantages, agrees with recent data on synaptotagmin copy number, and is the first (to our knowledge) to link detailed physiological observations with the molecular machinery of Ca(2+)-triggered exocytosis. In addition, our model provides detailed microscopic insight into the underlying Ca(2+) dynamics during synapse activation.

Single-pixel optical fluctuation analysis of calcium channel function in active zones of motor nerve terminals.

We used high-resolution fluorescence imaging and single-pixel optical fluctuation analysis to estimate the opening probability of individual voltage-gated calcium (Ca(2+)) channels during an action potential and the number of such Ca(2+) channels within active zones of frog neuromuscular junctions. Analysis revealed ∼36 Ca(2+) channels within each active zone, similar to the number of docked synaptic vesicles but far less than the total number of transmembrane particles reported based on freeze-fracture analysis (∼200-250). The probability that each channel opened during an action potential was only ∼0.2. These results suggest why each active zone averages only one quantal release event during every other action potential, despite a substantial number of docked vesicles. With sparse Ca(2+) channels and low opening probability, triggering of fusion for each vesicle is primarily controlled by Ca(2+) influx through individual Ca(2+) channels. In contrast, the entire synapse is highly reliable because it contains hundreds of active zones.

Free-space fluorescence tomography with adaptive sampling based on anatomical information from microCT.

Image reconstruction is one of the main challenges for fluorescence tomography. For in vivo experiments on small animals, in particular, the inhomogeneous optical properties and irregular surface of the animal make free-space image reconstruction challenging because of the difficulties in accurately modeling the forward problem and the finite dynamic range of the photodetector. These two factors are fundamentally limited by the currently available forward models and photonic technologies. Nonetheless, both limitations can be significantly eased using a signal processing approach. We have recently constructed a free-space panoramic fluorescence diffuse optical tomography system to take advantage of co-registered microCT data acquired from the same animal. In this article, we present a data processing strategy that adaptively selects the optical sampling points in the raw 2-D fluorescent CCD images. Specifically, the general sampling area and sampling density are initially specified to create a set of potential sampling points sufficient to cover the region of interest. Based on 3-D anatomical information from the microCT and the fluorescent CCD images, data points are excluded from the set when they are located in an area where either the forward model is known to be problematic (e.g., large wrinkles on the skin) or where the signal is unreliable (e.g., saturated or low signal-to-noise ratio). Parallel Monte Carlo software was implemented to compute the sensitivity function for image reconstruction. Animal experiments were conducted on a mouse cadaver with an artificial fluorescent inclusion. Compared to our previous results using a finite element method, the newly developed parallel Monte Carlo software and the adaptive sampling strategy produced favorable reconstruction results.

Rapid creation, Monte Carlo simulation, and visualization of realistic 3D cell models.

Spatially realistic diffusion-reaction simulations supplement traditional experiments and provide testable hypotheses for complex physiological systems. To date, however, the creation of realistic 3D cell models has been difficult and time-consuming, typically involving hand reconstruction from electron microscopic images. Here, we present a complementary approach that is much simpler and faster, because the cell architecture (geometry) is created directly in silico using 3D modeling software like that used for commercial film animations. We show how a freely available open source program (Blender) can be used to create the model geometry, which then can be read by our Monte Carlo simulation and visualization softwares (MCell and DReAMM, respectively). This new workflow allows rapid prototyping and development of realistic computational models, and thus should dramatically accelerate their use by a wide variety of computational and experimental investigators. Using two self-contained examples based on synaptic transmission, we illustrate the creation of 3D cellular geometry with Blender, addition of molecules, reactions, and other run-time conditions using MCell's Model Description Language (MDL), and subsequent MCell simulations and DReAMM visualizations. In the first example, we simulate calcium influx through voltage-gated channels localized on a presynaptic bouton, with subsequent intracellular calcium diffusion and binding to sites on synaptic vesicles. In the second example, we simulate neurotransmitter release from synaptic vesicles as they fuse with the presynaptic membrane, subsequent transmitter diffusion into the synaptic cleft, and binding to postsynaptic receptors on a dendritic spine.

FAST MONTE CARLO SIMULATION METHODS FOR BIOLOGICAL REACTION-DIFFUSION SYSTEMS IN SOLUTION AND ON SURFACES.

Many important physiological processes operate at time and space scales far beyond those accessible to atom-realistic simulations, and yet discrete stochastic rather than continuum methods may best represent finite numbers of molecules interacting in complex cellular spaces. We describe and validate new tools and algorithms developed for a new version of the MCell simulation program (MCell3), which supports generalized Monte Carlo modeling of diffusion and chemical reaction in solution, on surfaces representing membranes, and combinations thereof. A new syntax for describing the spatial directionality of surface reactions is introduced, along with optimizations and algorithms that can substantially reduce computational costs (e.g., event scheduling, variable time and space steps). Examples for simple reactions in simple spaces are validated by comparison to analytic solutions. Thus we show how spatially realistic Monte Carlo simulations of biological systems can be far more cost-effective than often is assumed, and provide a level of accuracy and insight beyond that of continuum methods.

Interoperability of neuroscience modeling software: current status and future directions.

Neuroscience increasingly uses computational models to assist in the exploration and interpretation of complex phenomena. As a result, considerable effort is invested in the development of software tools and technologies for numerical simulations and for the creation and publication of models. The diversity of related tools leads to the duplication of effort and hinders model reuse. Development practices and technologies that support interoperability between software systems therefore play an important role in making the modeling process more efficient and in ensuring that published models can be reliably and easily reused. Various forms of interoperability are possible including the development of portable model description standards, the adoption of common simulation languages or the use of standardized middleware. Each of these approaches finds applications within the broad range of current modeling activity. However more effort is required in many areas to enable new scientific questions to be addressed. Here we present the conclusions of the "Neuro-IT Interoperability of Simulators" workshop, held at the 11th computational neuroscience meeting in Edinburgh ( July 19-20 2006; http://www.cnsorg.org ). We assess the current state of interoperability of neural simulation software and explore the future directions that will enable the field to advance.

An introduction to simulation and visualization of biological systems at multiple scales: a summer training program for interdisciplinary research.

Advances in biomedical research require a new generation of researchers having a strong background in both the life and physical sciences and a knowledge of computational, mathematical, and engineering tools for tackling biological problems. The NIH-NSF Bioengineering and Bioinformatics Summer Institute at the University of Pittsburgh (BBSI @ Pitt; www.ccbb.pitt.edu/bbsi) is a multi-institutional 10-week summer program hosted by the University of Pittsburgh, Duquesne University, the Pittsburgh Supercomputing Center, and Carnegie Mellon University, and is one of nine Institutes throughout the nation currently participating in the NIH-NSF program. Each BBSI focuses on a different area; the BBSI @ Pitt, entitled "Simulation and Computer Visualization of Biological Systems at Multiple Scales", focuses on computational and mathematical approaches to understanding the complex machinery of molecular-to-cellular systems at three levels, namely, molecular, subcellular (microphysiological), and cellular. We present here an overview of the BBSI @ Pitt, the objectives and focus of the program, and a description of the didactic training activities that distinguish it from other traditional summer research programs. Furthermore, we also report several challenges that have been identified in implementing such an interdisciplinary program that brings together students from diverse academic programs for a limited period of time. These challenges notwithstanding, presenting an integrative view of molecular-to-system analytical models has introduced these students to the field of computational biology and has allowed them to make an informed decision regarding their future career prospects.

Evidence for ectopic neurotransmission at a neuronal synapse.

Neurotransmitter release is well known to occur at specialized synaptic regions that include presynaptic active zones and postsynaptic densities. At cholinergic synapses in the chick ciliary ganglion, however, membrane formations and physiological measurements suggest that release distant from postsynaptic densities can activate the predominantly extrasynaptic alpha7 nicotinic receptor subtype. We explored such ectopic neurotransmission with a novel model synapse that combines Monte Carlo simulations with high-resolution serial electron microscopic tomography. Simulated synaptic activity is consistent with experimental recordings of miniature excitatory postsynaptic currents only when ectopic transmission is included in the model, broadening the possibilities for mechanisms of neuronal communication.

Spatial Distribution of Calcium Entry Evoked by Single Action Potentials within the Presynaptic Active Zone.

The nature of presynaptic calcium (Ca(2+)) signals that initiate neurotransmitter release makes these signals difficult to study, in part because of the small size of specialized active zones within most nerve terminals. Using the frog motor nerve terminal, which contains especially large active zones, we show that increases in intracellular Ca(2+) concentration within 1 msec of action potential invasion are attributable to Ca(2+) entry through N-type Ca(2+) channels and are not uniformly distributed throughout active zone regions. Furthermore, changes in the location and magnitude of Ca(2+) signals recorded before and after experimental manipulations (omega-conotoxin GVIA, diaminopyridine, and lowered extracellular Ca(2+)) support the hypothesis that there is a remarkably low probability of a single Ca(2+) channel opening within an active zone after an action potential. The trial-to-trial variability observed in the spatial distribution of presynaptic Ca(2+) entry also supports this conclusion, which differs from the conclusions of previous work in other synapses.

Novel delta subunit mutation in slow-channel syndrome causes severe weakness by novel mechanisms.

We investigated the basis for a novel form of the slow-channel congenital myasthenic syndrome presenting in infancy in a single individual as progressive weakness and impaired neuromuscular transmission without overt degeneration of the motor endplate. Prolonged low-amplitude synaptic currents in biopsied anconeus muscle at 9 years of age suggested a kinetic disorder of the muscle acetylcholine receptor. Ultrastructural studies at 16 months, at 9 years, and at 15 years of age showed none of the typical degenerative changes of the endplate associated with the slow-channel congenital myasthenic syndrome, and acetylcholine receptor numbers were not significantly reduced. We identified a novel C-to-T substitution in exon 8 of the delta-subunit that results in a serine to phenylalanine mutation in the region encoding the second transmembrane domain that lines the ion channel. Using Xenopus oocyte in vitro expression studies we confirmed that the deltaS268F mutation, as with other slow-channel congenital myasthenic syndrome mutations, causes delayed closure of acetylcholine receptor ion channels. In addition, unlike other mutations in slow-channel congenital myasthenic syndrome, this mutation also causes delayed opening of the channel, a finding that readily explains the marked congenital weakness in the absence of endplate degeneration. Finally, we used serial morphometric analysis of electron micrographs to explore the basis for the progressive weakness and decline of amplitude of endplate currents over a period of 14 years. We demonstrated a progressive widening and accumulation of debris in the synaptic cleft, resulting in loss of efficacy of released neurotransmitter and reduced safety factor. These studies demonstrate the role of previously unrecognized mechanisms of impairment of synaptic transmission caused by a novel mutation and show the importance of serial in vitro studies to elucidate novel disease mechanisms.