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Multiscale modeling by means of co-simulation is a powerful tool to address many vital questions in neuroscience. It can for example be applied in the study of the process of learning and memory formation in the brain. At the same time the co-simulation technique makes it possible to take advantage of interoperability between existing tools and multi-physics models as well as distributed computing. However, the theoretical basis for multiscale modeling is not sufficiently understood. There is, for example, a need of efficient and accurate numerical methods for time integration. When time constants of model components are different by several orders of magnitude, individual dynamics and mathematical definitions of each component all together impose stability, accuracy and efficiency challenges for the time integrator. Following our numerical investigations in Brocke et al. (Frontiers in Computational Neuroscience, 10, 97, 2016), we present a new multirate algorithm that allows us to handle each component of a large system with a step size appropriate to its time scale. We take care of error estimates in a recursive manner allowing individual components to follow their discretization time course while keeping numerical error within acceptable bounds. The method is developed with an ultimate goal of minimizing the communication between the components. Thus it is especially suitable for co-simulations. Our preliminary results support our confidence that the multirate approach can be used in the class of problems we are interested in. We show that the dynamics ofa communication signal as well as an appropriate choice of the discretization order between system components may have a significant impact on the accuracy of the coupled simulation. Although, the ideas presented in the paper have only been tested on a single model, it is likely that they can be applied to other problems without loss of generality. We believe that this work may significantly contribute to the establishment of a firm theoretical basis and to the development of an efficient computational framework for multiscale modeling and simulations. Electronic Supplementary Material The online version of this article (doi:10.1007/s10827-017-0639-7) contains supplementary material, which is available to authorized users.

Connecting MOOSE and NeuroRD through MUSIC : towards a communication framework for multi-scale modeling

The nervous system encompasses structure and phenomena at different spatial and temporal scales from molecule to behavior. In addition, different scales are described by different physical and mathematical formalisms. The dynamics of second messenger pathways can be formulated as stochastic reaction-diffusion systems [1] while the electrical dynamics of the neuronal membrane is often described by compartment models and the Hodgkin-Huxley formalism. In neuroscience, there is an increasing need and interest to study multi-scale phenomena where multiple scales and physical formalisms are covered by a single model. While there exists simulators/frameworks, such as GENESIS and MOOSE [3], which span such scales (kinetikit/HH-models), most software applications are specialized for a given domain. Here, we report about initial steps towards a framework for multi-scale modeling which builds on the concept of multi-simulations [2]. We aim to provide a standard API and communication framework allowing parallel simulators targeted at different scales and/or different physics to communicate on-line in a cluster environment. Specifically, we show prototype work on simulating the effect on receptor induced cascades on membrane excitability. Electrical properties of a compartment model is simulated in MOOSE, while receptor induced cascades are simulated in NeuroRD [4,7] . In a prototype system, the two simulators are connected using PyMOOSE [5] and JPype [6]. The two models with their different physical properties (membrane currents in MOOSE, molecular biophysics in NeuroRD), are joined into a single model system. We demonstrate the interaction of the numerical solvers of two simulators (MOOSE, NeuroRD) targeted at different spatiotemporal scales and different physics while solving a multi-scale problem. We analyze some of the problems that may arise in multi-scale multi-simulations and present requirements for a generic API for parallel solvers. This work represents initial steps towards a flexible modular framework for simulation of large-scale multi-scale multi-physics problems in neuroscience. References 1. Blackwell KT: An efficient stochastic diffusion algorithm for modeling second messengers in dendrites and spines. J Neurosci Meth 2006, 157: 142-153. 2. Djurfeldt M, Hjorth J, Eppler JM, Dudani N, Helias M, Potjans TC, Bhalla US, Diesmann M, Hellgren Kotaleski J, Ekeberg O: Run-Time Interoperability Between Neural Network Simulators Based on the MUSIC Framework. Neurinform 2010, 8: 43-60. 3. Dudani N, Ray S, George S, Bhalla US: Multiscale modeling and interoperability in MOOSE. Neuroscience 2009, 10(Suppl 1): 54. 4. Oliveira RF, Terrin A, Di Benedetto G, Cannon RC, Koh W, Kim M, Zaccolo M, Blacwell KT: The Role of Type 4 Phosphdiesterases in Generating Microdomains of cAMP: Large Scale Stochastic Simulations.

Multiscale modeling and simulations in neuroscience is gaining scientific attention due to its growing importance and unexplored capabilities. For instance, it can help to acquire better understanding of biological phenomena that have important features at multiple scales of time and space. This includes synaptic plasticity, memory formation and modulation, homeostasis. There are several ways to organize multiscale simulations depending on the scientific problem and the system to be modeled. One of the possibilities is to simulate different components of a multiscale system simultaneously and exchange data when required. The latter may become a challenging task for several reasons. First, the components of a multiscale system usually span different spatial and temporal scales, such that rigorous analysis of possible coupling solutions is required. Then, the components can be defined by different mathematical formalisms. For certain classes of problems a number of coupling mechanisms have been proposed and successfully used. However, a strict mathematical theory is missing in many cases. Recent work in the field has not so far investigated artifacts that may arise during coupled integration of different approximation methods. Moreover, in neuroscience, the coupling of widely used numerical fixed step size solvers may lead to unexpected inefficiency. In this paper we address the question of possible numerical artifacts that can arise during the integration of a coupled system. We develop an efficient strategy to couple the components comprising a multiscale test problem in neuroscience. We introduce an efficient coupling method based on the second-order backward differentiation formula (BDF2) numerical approximation. The method uses an adaptive step size integration with an error estimation proposed by Skelboe (2000). The method shows a significant advantage over conventional fixed step size solvers used in neuroscience for similar problems. We explore different coupling strategies that define the organization of computations between system components. We study the importance of an appropriate approximation of exchanged variables during the simulation. The analysis shows a substantial impact of these aspects on the solution accuracy in the application to our multiscale neuroscientific test problem. We believe that the ideas presented in the paper may essentially contribute to the development of a robust and efficient framework for multiscale brain modeling and simulations in neuroscience. QC 20161024