Joel R. Stiles

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.

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

The nature of presynaptic calcium (Ca2+) 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 Ca2+ concentration within 1 msec of action potential invasion are attributable to Ca2+ entry through N-type Ca2+ channels and are not uniformly distributed throughout active zone regions. Furthermore, changes in the location and magnitude of Ca2+ signals recorded before and after experimental manipulations (ω-conotoxin GVIA, diaminopyridine, and lowered extracellular Ca2+) support the hypothesis that there is a remarkably low probability of a single Ca2+ channel opening within an active zone after an action potential. The trial-to-trial variability observed in the spatial distribution of presynaptic Ca2+ entry also supports this conclusion, which differs from the conclusions of previous work in other synapses.

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.

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 δ‐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 δS268F 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.

Distributing MCell Simulations on the Grid

The computational Grid is a promising platform for the deployment of large-scale scientific and engineering applications. Parameter sweep applications (PSAs) arise in many fields of science and engineering and are structured as sets of “experiments,” each of which is executed with a distinct set of parameters. Given that structure, PSAs are particularly well suited to the Grid infrastructure and can be deployed on very large scales. However, deployment is not easy to achieve for the domain scientist given the complexity and multiplicity of the Grid software infrastructure, the heterogeneity of the resources, and the dynamic resource availabilities. It is therefore necessary to provide user-level middleware that acts as an intermediate layer between the application and the Grid. That middleware must address all deployment, data movements, and scheduling issues to provide the user with a transparent way of running his or her simulation on the Grid. In this paper, the authors focus on such middleware specifically targeted to a biology application: MCell. After describing the application and its structure, they describe desired usage scenarios on the Grid and identify user requirements, discuss relevant computer science issues, and propose suitable solutions given currently available Grid technologies. The authors then describe a general-purpose user-level middleware project for PSAs—AppLes Parameter Sweep Template—explain how it can be extended to accommodate MCell’s specific requirements, and introduce current work in that direction.

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 (Ca2+) channels during an action potential and the number of such Ca2+ channels within active zones of frog neuromuscular junctions. Analysis revealed ∼36 Ca2+ 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 Ca2+ channels and low opening probability, triggering of fusion for each vesicle is primarily controlled by Ca2+ influx through individual Ca2+ channels. In contrast, the entire synapse is highly reliable because it contains hundreds of active zones.

The Virtual Instrument: Support for Grid-Enabled Mcell Simulations

Ensembles of widely distributed, heterogeneous resources, or Grids, have emerged as popular platforms for largescale scientific applications. In this paper we present the Virtual Instrument project, which provides an integrated application execution environment that enables end-users to run and interact with running scientific simulations on Grids. This work is performed in the specific context of MCell, a computational biology application. While MCell provides the basis for running simulations, its capabilities are currently limited in terms of scale, ease-of-use, and interactivity. These limitations preclude usage scenarios that are critical for scientific advances. Our goal is to create a scientific “Virtual Instrument” from MCell by allowing its users to transparently access Grid resources while being able to steer running simulations. In this paper, we motivate the Virtual Instrument project and discuss a number of relevant issues and accomplishments in the area of Grid software development and application scheduling. We then describe our software design and report on the current implementation. We verify and evaluate our design via experiments with MCell on a real-world Grid testbed.

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.

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.

Spatially realistic computational physiology: Past, present and future

Publisher Summary Physiological function depends on the spatial and temporal dynamics of specific genes, proteins, signaling molecules, and metabolites, within and between cells. Realistic physiological simulations present a grand challenge, because of the wide range of underlying space and time scales, as well as the widely disparate organization and properties of different cells. This chapter describes unique methods developed for spatially realistic physiological simulations and illustrates their use with simulations of synaptic transmission. The simulation of synaptic transmission at the nerve-muscle synapse is discussed. Synaptic transmission exemplifies cellular interactions in which stochastic behaviors and spatial complexity are very important. Changes in synaptic signal size and time course (plasticity) may underlie high-level cognitive functions, such as learning and memory, and can also be an integral component of many neurological disorders. The computational cost of a MCell simulation is mostly dependent on the number of tests for ray/polygon intersections. In a naive algorithm, every mesh element would have to be checked for a potential intersection every time each diffusing molecule moves. Future extensions to MCells present capabilities include simulation of arbitrary chemical interactions between diffusing molecules in solution as well as in membrane environments, and also incorporation of volume meshes with embedded surfaces. The needs for algorithm design and efficient large-scale parallel computing is discussed.