Event Abstract Back to Event Methods for co-simulation of multi-scale models Jerker Nilsson1, Ekaterina Brocke1, Mikael Djurfeldt2, 3*, Upinder S. Bhalla4, Jeanette Hellgren-Kotaleski1, 5 and Michael Hanke6 1 KTH, CB/CSC, Sweden 2 KTH, PDC, Sweden 3 INCF, Sweden 4 NCBS, India 5 Karolinska Institute, Nobel Institute for Neurophysiology, Sweden 6 KTH, Dept. Mathematics, Sweden In multi-scale models, multiple scales, and even physical formalisms, are used in a single model [1] while simulation tools in computational neuroscience are usually specialized for a single scale and formalism [2, 3, 4]. One possibility when solving such models is to use a co-simulation methodology. Co-simulation allows model components to be simulated by different tools, running simultaneously while exchanging data. However, a naive coupling of numerical methods for different models may lead to unexpected numerical problems going far beyond those which could be expected from the individual components. With the ultimate goal of extending the MUSIC API [5] for multi-scale modeling through co-simulation by integration of numerical solvers, we have examined ways of moving beyond trial-and-error and ad-hoc methods [6, 7] when coupling solvers. We show techniques for how synchronization in bi-directional communication as well as error control [8] can be achieved in a framework motivated by waveform relaxation methods. We apply these techniques when simulating a reduced MAPK model [6] in a spine in the context of the electrical activity of the whole neuron. The model exhibits bistability. It switches from the inactive to the active stable state after current injection to the soma. In our model, the stimulus of 0.09 nA causes a Ca2+ elevation of 1 uM in the spine during the stimulation period of 5 s. This condition is sufficient to switch on P-MAPK and phosphorylate potassium channels. The electrical part of the model is formulated using Hodgkin-Huxley formalism while biochemistry is formulated by the reaction-rate equations. This model gives us a stiff problem with a coupling strength varying along the integration. We compare different techniques for achieving a balance between efficiency of coupling and accuracy of integration. This analysis will be used to set up the requirements for a generic API to perform co-simulation and, in particular, identify the signals which need to be propagated by a multi-scale API.
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