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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.

References

[1] Hernández, Alfredo I., et al. (2011) "Integration of detailed modules in a core model of body fluid homeostasis and blood pressure regulation." Progress in biophysics and molecular biology 107.1: 169-182.

[2] Wils, Stefan, and Erik De Schutter (2009) "STEPS: modeling and simulating complex reaction-diffusion systems with Python." Frontiers in neuroinformatics 3.

[3] Hines, Michael L., and Nicholas T. Carnevale. (1997) "The NEURON simulation environment." Neural computation 9.6: 1179-1209.

[4] Gewaltig, Marc-Oliver, and Markus Diesmann (2007) "NEST (neural simulation tool)." Scholarpedia 2.4: 1430.

[5] Djurfeldt, Mikael, et al. (2010) "Run-time interoperability between neuronal network simulators based on the MUSIC framework." Neuroinformatics 8.1: 43-60.

[6] Bhalla, Upinder S. (2011) "Multiscale interactions between chemical and electric signaling in LTP induction, LTP reversal and dendritic excitability." Neural Networks 24.9: 943-949.

[7] Mattioni, Michele, and Nicolas Le Novère (2013) "Integration of Biochemical and Electrical Signaling-Multiscale Model of the Medium Spiny Neuron of the Striatum." PloS one 8.7: e66811.

[8] Skelboe, Stig (2000) "Accuracy of decoupled implicit integration formulas." SIAM Journal on Scientific Computing 21.6: 2206-2224.

Keywords: Numerical Analysis, Computer-Assisted, Co-simulation, modeling, Multi-scale modeling, Hodgkin-Huxley, MAP Kinase Signaling System

Conference: Neuroinformatics 2014, Leiden, Netherlands, 25 Aug - 27 Aug, 2014.

Presentation Type: Poster, not to be considered for oral presentation

Topic: Large-scale modeling

Citation: Nilsson J, Brocke E, Djurfeldt M, Bhalla US, Hellgren-Kotaleski J and Hanke M (2014). Methods for co-simulation of multi-scale models. Front. Neuroinform. Conference Abstract: Neuroinformatics 2014. doi: 10.3389/conf.fninf.2014.18.00093

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Received: 30 Apr 2014; Published Online: 04 Jun 2014.

* Correspondence: Dr. Mikael Djurfeldt, KTH, PDC, Stockholm, 100 44, Sweden, mikael@djurfeldt.com