Dominant ionic mechanisms explored in spiking and bursting using local low-dimensional reductions of a biophysically realistic model neuron

  • Robert Clewley
  • Cristina Soto-Treviño
  • Farzan Nadim


The large number of variables involved in many biophysical models can conceal potentially simple dynamical mechanisms governing the properties of its solutions and the transitions between them as parameters are varied. To address this issue, we extend a novel model reduction method, based on “scales of dominance,” to multi-compartment models. We use this method to systematically reduce the dimension of a two-compartment conductance-based model of a crustacean pyloric dilator (PD) neuron that exhibits distinct modes of oscillation—tonic spiking, intermediate bursting and strong bursting. We divide trajectories into intervals dominated by a smaller number of variables, resulting in a locally reduced hybrid model whose dimension varies between two and six in different temporal regimes. The reduced model exhibits the same modes of oscillation as the 16 dimensional model over a comparable parameter range, and requires fewer ad hoc simplifications than a more traditional reduction to a single, globally valid model. The hybrid model highlights low-dimensional organizing structure in the dynamics of the PD neuron, and the dependence of its oscillations on parameters such as the maximal conductances of calcium currents. Our technique could be used to build hybrid low-dimensional models from any large multi-compartment conductance-based model in order to analyze the interactions between different modes of activity.


Model reduction Compartmental modeling Oscillations Stomatogastric Hybrid dynamical system 



National Institute of Health Grant MH-60605 (FN), National Science Foundation Grant FIBR 0425878 (RC). We would like to thank the reviewers for their helpful comments.


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Robert Clewley
    • 1
  • Cristina Soto-Treviño
    • 2
  • Farzan Nadim
    • 2
    • 3
  1. 1.Department of Mathematics and StatisticsGeorgia State UniversityAtlantaUSA
  2. 2.Department of Mathematical SciencesNew Jersey Institute of TechnologyNewarkUSA
  3. 3.Department of Biological SciencesRutgers UniversityNewarkUSA

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