Thomas M. Bartol

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.

Monte Carlo simulation of miniature endplate current generation in the vertebrate neuromuscular junction

A Monte Carlo method for modeling the neuromuscular junction is described in which the three-dimensional structure of the synapse can be specified. Complexities can be introduced into the acetylcholine kinetic model used with only a small increase in computing time. The Monte Carlo technique is shown to be superior to differential equation modeling methods (although less accurate) if a three-dimensional representation of synaptic geometry is desired. The conceptual development of the model is presented and the accuracy estimated. The consequences of manipulations such as varying the spacing of secondary synaptic folds or that between the release of multiple quantal packets of acetylcholine, are also presented. Increasing the spacing between folds increases peak current. Decreased spacing of adjacent quantal release sites increases the potentiation of peak current.

A Monte Carlo Model Reveals Independent Signaling at Central Glutamatergic Synapses

We have developed a biophysically realistic model of receptor activation at an idealized central glutamatergic synapse that uses Monte Carlo techniques to simulate the stochastic nature of transmission following release of a single synaptic vesicle. For the a synapse with 80 AMPA and 20 NMDA receptors, a single quantum, with 3000 glutamate molecules, opened approximately 3 NMDARs and 20 AMPARs. The number of open receptors varied directly with the total number of receptors, and the fraction of open receptors did not depend on the ratio of co-localized AMPARs and NMDARs. Variability decreased with increases in either total receptor number or quantal size, and differences between the variability of AMPAR and NMDAR responses were due solely to unequal numbers of receptors at the synapse. Despite NMDARs having a much higher affinity for glutamate than AMPARs, quantal release resulted in similar occupancy levels in both receptor types. Receptor activation increased with number of transmitter molecules released or total receptor number, whereas occupancy levels were only dependent on quantal size. Tortuous diffusion spaces reduced the extent of spillover and the activation of extrasynaptic receptors. These results support the conclusion that signaling is spatially independent within and between central glutamatergic synapses.

Calmodulin Activation by Calcium Transients in the Postsynaptic Density of Dendritic Spines

The entry of calcium into dendritic spines can trigger a sequence of biochemical reactions that begins with the activation of calmodulin (CaM) and ends with long-term changes to synaptic strengths. The degree of activation of CaM can depend on highly local elevations in the concentration of calcium and the duration of transient increases in calcium concentration. Accurate measurement of these local changes in calcium is difficult because the spaces are so small and the numbers of molecules are so low. We have therefore developed a Monte Carlo model of intracellular calcium dynamics within the spine that included calcium binding proteins, calcium transporters and ion channels activated by voltage and glutamate binding. The model reproduced optical recordings using calcium indicator dyes and showed that without the dye the free intracellular calcium concentration transient was much higher than predicted from the fluorescent signal. Excitatory postsynaptic potentials induced large, long-lasting calcium gradients across the postsynaptic density, which activated CaM. When glutamate was released at the synapse 10 ms before an action potential occurred, simulating activity patterns that strengthen hippocampal synapses, the calcium gradient and activation of CaM in the postsynaptic density were much greater than when the order was reversed, a condition that decreases synaptic strengths, suggesting a possible mechanism underlying the induction of long-term changes in synaptic strength. The spatial and temporal mechanisms for selectivity in CaM activation demonstrated here could be used in other signaling pathways.

Monte Carlo simulation of neuro-transmitter release using MCell, a general simulator of cellular physiological processes

Issues surrounding synaptic current efficacy, variability, plasticity, and possible crosstalk are presently of great interest and lend themselves well to computational investigations. One important factor that impacts on all of these issues is the time course of neurotransmitter exocytosis from a synaptic vesicle.1 We have recently reported excellent quantitative agreement between highly accurate recordings of the fast rising phase of miniature endplate currents (mEPCs), and Monte Carlo simulations of vesicular acetylcholine release and postsynaptic mEPC generation.2 The simulations were performed using an early version of our program MCell, * a generalized and highly optimized outgrowth of our original Monte Carlo programs specifically tailored to simulation of mEPC generation.3,4 In this paper we first briefly introduce the present version of MCell and its capabilities, and then next discuss simulation of neurotransmitter exocytosis. We focus on: (1) the theoretical and computational factors underlying simulation accuracy: (2) how inadvertent use of seemingly appropriate input parameters can lead to orders-of- magnitude errors; and (3) how some of MCell’s features can reduce the computation time required for simulations by orders of magnitude.

Nanoconnectomic upper bound on the variability of synaptic plasticity

Information in a computer is quantified by the number of bits that can be stored and recovered. An important question about the brain is how much information can be stored at a synapse through synaptic plasticity, which depends on the history of probabilistic synaptic activity. The strong correlation between size and efficacy of a synapse allowed us to estimate the variability of synaptic plasticity. In an EM reconstruction of hippocampal neuropil we found single axons making two or more synaptic contacts onto the same dendrites, having shared histories of presynaptic and postsynaptic activity. The spine heads and neck diameters, but not neck lengths, of these pairs were nearly identical in size. We found that there is a minimum of 26 distinguishable synaptic strengths, corresponding to storing 4.7 bits of information at each synapse. Because of stochastic variability of synaptic activation the observed precision requires averaging activity over several minutes. DOI: http://dx.doi.org/10.7554/eLife.10778.001

Extracellular sheets and tunnels modulate glutamate diffusion in hippocampal neuropil.

Although the extracellular space in the neuropil of the brain is an important channel for volume communication between cells and has other important functions, its morphology on the micron scale has not been analyzed quantitatively owing to experimental limitations. We used manual and computational techniques to reconstruct the 3D geometry of 180 μm3 of rat CA1 hippocampal neuropil from serial electron microscopy and corrected for tissue shrinkage to reflect the in vivo state. The reconstruction revealed an interconnected network of 40–80 nm diameter tunnels, formed at the junction of three or more cellular processes, spanned by sheets between pairs of cell surfaces with 10–40 nm width. The tunnels tended to occur around synapses and axons, and the sheets were enriched around astrocytes. Monte Carlo simulations of diffusion within the reconstructed neuropil demonstrate that the rate of diffusion of neurotransmitter and other small molecules was slower in sheets than in tunnels. Thus, the non‐uniformity found in the extracellular space may have specialized functions for signaling (sheets) and volume transmission (tunnels). J. Comp. Neurol. 521:448–464, 2013.

Computational Modeling of Three-Dimensional Electrodiffusion in Biological Systems: Application to the Node of Ranvier

A computational model is presented for the simulation of three-dimensional electrodiffusion of ions. Finite volume techniques were used to solve the Poisson-Nernst-Planck equation, and a dual Delaunay-Voronoi mesh was constructed to evaluate fluxes of ions, as well as resulting electric potentials. The algorithm has been validated and applied to a generalized node of Ranvier, where numerical results for computed action potentials agree well with cable model predictions for large clusters of voltage-gated ion channels. At smaller channel clusters, however, the three-dimensional electrodiffusion predictions diverge from the cable model predictions and show a broadening of the action potential, indicating a significant effect due to each channels own local electric field. The node of Ranvier complex is an elaborate organization of membrane-bound aqueous compartments, and the model presented here represents what we believe is a significant first step in simulating electrophysiological events with combined realistic structural and physiological data.

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.

Anomalous Diffusion of Single Particles in Cytoplasm

The crowded intracellular environment poses a formidable challenge to experimental and theoretical analyses of intracellular transport mechanisms. Our measurements of single-particle trajectories in cytoplasm and their random-walk interpretations elucidate two of these mechanisms: molecular diffusion in crowded environments and cytoskeletal transport along microtubules. We employed acousto-optic deflector microscopy to map out the three-dimensional trajectories of microspheres migrating in the cytosolic fraction of a cellular extract. Classical Brownian motion (BM), continuous time random walk, and fractional BM were alternatively used to represent these trajectories. The comparison of the experimental and numerical data demonstrates that cytoskeletal transport along microtubules and diffusion in the cytosolic fraction exhibit anomalous (nonFickian) behavior and posses statistically distinct signatures. Among the three random-walk models used, continuous time random walk provides the best representation of diffusion, whereas microtubular transport is accurately modeled with fractional BM.