Interfaces in multiscale reaction-diffusion models in the NEURON simulator

The rapid parallel growth in computational systems biology (CSB), with a focus on modeling of signaling cascades and other molecular details, and Computational Neuroscience, with its focus on the spread of electrical activity in the cell, has led to a growing need for integrated tools that provide access to both types of modeling. Development of these linkages in multiscale modeling will also be critical in better understanding the functioning of neuronal networks. Recurring difficulties in producing multiscale simulations arise at interfaces which are not only the interfaces between the traditionally defined scales but also interfaces across techniques that must be made to work in concert. We describe our approach to 5 interface problems: cytoplasm & membrane, cytoplasm & internal membranes, 1D & 3D, stochastic & deterministic diffusion, and stylized & mechanistic descriptions. 1. Ion concentrations near the surface, as determined by reactions, diffusion, pumps, and channels produce localized variations in the driving force for selective channels, whether calculated as a Nernst potential or via Goldman-Hodgkin-Katz. 2. Potential gradients also arise across internal membranes, such as those separating the cytosol from the ER, mitochondria, or the nucleus. When needed, membrane potential may be calculated for these regions and used to modulate ion flow through channels. 3. We typically use a 1D approximation to study reaction-diffusion across the lengthy dendritic processes, while 3D is more appropriate at the soma and in dendritic regions of special interest. We conserve mass at the boundaries by integrating the flux leaving the 3D region and distributing the flux leaving the 1D region. For 3D simulations, watertight surfaces are generated from Neurolucida point-diameter data. 4. The small volumes of dendritic spines house very few of each molecular species. In this setting small numbers of molecules require that this region be handled with a stochastic simulation algorithm. In the larger volumes of the dendrites, noise is damped by the sheer number of molecules, so deterministic diffusion is appropriate. We are adapting algorithms to conserve mass across the stochastic-deterministic interface. 5. Reaction schemes may be specified via full kinetic descriptions (via Python or imported from SBML) or abstract representations such as Boolean networks (BNs), where each variable is represented as a switch. We allowed BNs and RxD variables to interact bidirectionally via flexible, user-defined callback functions, triggered when a BN switch was set, or when an RxD variable passed a criterion.