Abstract
Investigation of cellular and network dynamics in the brain by means of modeling and simulation has evolved into a highly interdisciplinary field, that uses sophisticated modeling and simulation approaches to understand distinct areas of brain function. Depending on the underlying complexity, these models vary in their level of detail, in order to cope with the attached computational cost. Hence for large network simulations, single neurons are typically reduced to time-dependent signal processors, dismissing the spatial aspect of each cell. For single cell or networks with relatively small numbers of neurons, general purpose simulators allow for space and time-dependent simulations of electrical signal processing, based on the cable equation theory. An emerging field in Computational Neuroscience encompasses a new level of detail by incorporating the full three-dimensional morphology of cells and organelles into three-dimensional, space and time-dependent, simulations. While every approach has its advantages and limitations, such as computational cost, integrated and methods-spanning simulation approaches, depending on the network size could establish new ways to investigate the brain. In this paper we present a hybrid simulation approach, that makes use of reduced 1D-models using e.g., the NEURON simulator—which couples to fully resolved models for simulating cellular and sub-cellular dynamics, including the detailed three-dimensional morphology of neurons and organelles. In order to couple 1D- and 3D-simulations, we present a geometry-, membrane potential- and intracellular concentration mapping framework, with which graph- based morphologies, e.g., in the swc- or hoc-format, are mapped to full surface and volume representations of the neuron and computational data from 1D-simulations can be used as boundary conditions for full 3D simulations and vice versa. Thus, established models and data, based on general purpose 1D-simulators, can be directly coupled to the emerging field of fully resolved, highly detailed 3D-modeling approaches. We present the developed general framework for 1D/3D hybrid modeling and apply it to investigate electrically active neurons and their intracellular spatio-temporal calcium dynamics.
Highlights
The level of detail, that can be achieved with experimental techniques in Neuroscience is ever increasing
In addition to projects focussing on the coupling of existing simulators for parallel computing architectures (Djurfeldt et al, 2010), the influence of spatial channel distribution on the electrical properties (Cannon et al, 2010) or integrating reduced intra-cellular approximations of reaction-diffusion processes, (Resasco et al, 2012; Anwar et al, 2013; McDougal et al, 2013a), we focus on the topic of how the three-dimensional intracellular architecture of neurons influences intra-cellular signals and how the resulting models can be efficiently solved on different computing scales
Since intra-cellular processes are strongly regulated by calcium, e.g., (Milner et al, 1998; Bading, 1998; West et al, 2002; Clapham, 2007; Tai et al, 2008), we chose calcium dynamics regulated by plasma membrane-located calcium channels with a given density, modeling effectively a channel conductance density, and a diffusion-reaction process in the neuronal cytosol as a representative of three-dimensional, intracellular signaling in neurons. 3D simulations were carried out in uG, Bastian et al (1997); Vogel et al
Summary
The level of detail, that can be achieved with experimental techniques in Neuroscience is ever increasing. Simulators for the electrical signaling in neurons, e.g., NEURON (Hines and Carnevale, 2003) or Genesis (Bower and Beeman, 1997), solve a one-dimensional numerical problem in space. While this has great advantages in many applications, foremost the computational speed of the methods that allows the simulation of large network activity, the drawback is the loss of modeling the intra- and extra-cellular space of neurons, and being able to include intracellular processes in a full three-dimensional resolution. The three-dimensional organization of neurons, e.g., the filigreed geometry of the endoplasmic reticulum, (Spacek and Harris, 1997) or the intra- and inter-cellular organization of spines, (Murase and Schuman, 1999; Arellano et al, 2007; Chen et al, 2008; Tai et al, 2008; Popov et al, 2011), demonstrates the Frontiers in Neuroinformatics www.frontiersin.org
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