## Abstract

Multi-scale models in neuroscience integrate detailed neurobiological phenomena from molecular level up to network and system levels. such models are very challenging to simulate despite the availability of massively parallel

computing systems. model order reduction (mor) is an established method in

engineering sciences, such as control theory. mor is used in improving

computational efficiency of simulations of complex nonlinear mathematical

models. in this study the dimension of a nonlinear mathematical model of

plasticity in the brain is reduced using mathematical mor methods.

Traditionally, models are simplified by eliminating variables, such as

molecular entities and ionic currents, from the system. additionally,

assumptions of the system behavior can be made, for example regarding the

steady state of the chemical reactions. however, comprehensive models with full

system dynamics are needed in order to increase understanding of different

mechanisms in one brain area. thus the elimination approach is not suitable for

the consequent analysis of neural phenomena.

The loss of information induced by eliminating variables of the system can be

avoided by mathematical mor methods that approximate the entire system with a smaller number of dimensions compared to the original system. here,

mathematical MOR is applied in the context of an experimentally verified

signaling pathway model of plasticity (Kim et al., PLoS Comp. Biol., 2013).

This nonlinear chemical equation based model describes the biochemical calcium signaling steps required for plasticity and learning in the subcortical area of the brain. By applying these methods, the simulation time of the model is radically shortened.

computing systems. model order reduction (mor) is an established method in

engineering sciences, such as control theory. mor is used in improving

computational efficiency of simulations of complex nonlinear mathematical

models. in this study the dimension of a nonlinear mathematical model of

plasticity in the brain is reduced using mathematical mor methods.

Traditionally, models are simplified by eliminating variables, such as

molecular entities and ionic currents, from the system. additionally,

assumptions of the system behavior can be made, for example regarding the

steady state of the chemical reactions. however, comprehensive models with full

system dynamics are needed in order to increase understanding of different

mechanisms in one brain area. thus the elimination approach is not suitable for

the consequent analysis of neural phenomena.

The loss of information induced by eliminating variables of the system can be

avoided by mathematical mor methods that approximate the entire system with a smaller number of dimensions compared to the original system. here,

mathematical MOR is applied in the context of an experimentally verified

signaling pathway model of plasticity (Kim et al., PLoS Comp. Biol., 2013).

This nonlinear chemical equation based model describes the biochemical calcium signaling steps required for plasticity and learning in the subcortical area of the brain. By applying these methods, the simulation time of the model is radically shortened.

Original language | English |
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Publication status | Published - 20 Sep 2018 |

Event | Brain and Mind Symposium 2018 - University of Helsinki, Helsinki, Finland Duration: 20 Oct 2018 → 21 Oct 2018 |

### Conference

Conference | Brain and Mind Symposium 2018 |
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Country/Territory | Finland |

City | Helsinki |

Period | 20/10/18 → 21/10/18 |

## Keywords

- Neuroscience
- Computational Neuroscience
- Control theory