Fixed point topology and robustness to perturbations between pairs of coupled neurons
© Norman et al; licensee BioMed Central Ltd. 2012
Published: 16 July 2012
Synchronization of neural firing plays an important role in nervous system function. Synchronized and phase locked relationships have been implicated in the creation and retrieval of memories [1, 2], while the disruption of normal synchrony and phase locking appears to be a factor in disorders like schizophrenia [3, 4]. Here we explore synchronization mechanisms in small two-cell networks and the robustness of these networks to perturbations.
Phase response curves (PRCs) describe how neurons respond to perturbations applied at specific times during the interspike interval. The PRC can be plotted in terms of the time to next spike as a function of when the spike arrived; this curve describes the dynamics of a single neuron, and the intersection points of two of these interaction curves represent the fixed points of the coupled system [5, 6].
Achuthan and colleagues have recently shown (manuscript submitted) that interaction curves with 0, 1, or 2 fixed points can exist in hybrid circuits of one biological and one model neuron. In this work, we use two reciprocally coupled Wang Buzsaki  model neurons to investigate how different numbers of coupled system fixed points affect the network robustness against perturbation. In addition, we investigate the effect of interaction curve shape on network robustness. The perturbation applied to test robustness is a delay or advance of a single spike of one model neuron.
Like Achuthan et al, we show that systems with 1 or 2 fixed points exhibit phase locking, while a system with 0 fixed points, but interaction curves in close proximity, shows temporary locking with some phase walkthrough. We are currently quantifying the effects of perturbation strength and timing on transient disturbances to the phase locking of the coupled system as well as convergence time back to the pre-perturbation phase relationship. In addition, we are exploring how the proximity of interaction curves affects robustness of the coupled system to perturbation. Preliminary results show that interaction curves that are closer together take a longer amount of time and more cycles to recover from perturbation than interaction curves that are further apart. Experimental validation of these modeling results will be shown.
- Jutras MJ, Buffalo EA: Synchronous neural activity and memory formation. Curr Opin Neurobiol. 2010, 20: 150-155. 10.1016/j.conb.2010.02.006.PubMed CentralView ArticlePubMedGoogle Scholar
- Liebe S, Hoerzer GM, Logothetis NK, Rainer G: Theta coupling between V4 and prefrontal cortex predicts visual short-term memory performance. Nat Neurosci. 2012, published online, doi:10.1038/nn.3038Google Scholar
- Sigurdsson T, Stark KL, Karayiorgou M, Gogos JA, Gordon JA: Impaired hippocampal-prefrontal synchrony in a genetic mouse model of schizophrenia. Nature. 2010, 464: 763-767. 10.1038/nature08855.PubMed CentralView ArticlePubMedGoogle Scholar
- Uhlaas PJ, Singer W: Neural synchrony in brain disorders: relevance for cognitive dysfunctions and pathophysiology. Neuron. 2006, 52: 155-168. 10.1016/j.neuron.2006.09.020.View ArticleGoogle Scholar
- Canavier CC, Achuthan S: Pulse coupled oscillators and the phase resetting curve. Math Biosci. 2010, 226 (2): 77-96. 10.1016/j.mbs.2010.05.001.PubMed CentralView ArticlePubMedGoogle Scholar
- Maran SK, Canavier CC: Using phase resetting to predict 1:1 and 2:2 locking in two neuron networks in which firing order is not always preserved. J Comput Neurosci. 2008, 24: 37-55. 10.1007/s10827-007-0040-z.PubMed CentralView ArticlePubMedGoogle Scholar
- Wang XJ, Buzsaki G: Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J Neurosci. 1996, 16 (20): 6402-6413.PubMedGoogle Scholar
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