The effect of rectifying gap junctions on phase-locking in neuronal networks
1
BioMed Central Page 1 of 1 (page number not for citation purposes) BMC Neuroscience Open Access Poster presentation The effect of rectifying gap junctions on phase-locking in neuronal networks Donald French 1 , Tamara J Schlichter 2 and Timothy J Lewis* 2 Address: 1 Department of Mathematics, University of Cincinnati, Cincinnati, Ohio, 45221, USA and 2 Department of Mathematics, University of California, Davis, CA, 95616, USA Email: Timothy J Lewis* - [email protected] * Corresponding author Introduction Gap junction mediated electrical coupling is ubiquitous in neuronal systems. Electrical coupling is almost always modeled as a linear ohmic resistance between cells, where the coupling current is proportional to the transjunctional potential. However, many gap junctions exhibit rectifica- tion with transjunctional voltage [1]. That is, the coupling conductance attenuates for increased voltage differences between cells. This rectification process can evolve at dif- ferent time scales. Because gap junction rectification alters the strength of coupling between cells in a way that depends on the intrinsic states of the cells, it may affect the dynamics in neuronal networks. However, the effects of rectification on network dynamics are largely unstudied. Methods We explore the effects of gap junction rectification on phase-locking in model neuronal networks. Using an extension of the theory of weak coupling, phase plane arguments, and numerical simulations, we examine both fast and slow rectification and their effects on the dynam- ics of networks of spiking neurons and networks of burst- ing neurons. Results In the slow rectification case, we show that the rectifica- tion always promotes synchronous activity. Because it decreases the coupling strength only, slow rectification has no effect on the existence of phase-locked states in homogeneous, noiseless networks. However, it alters the robustness of these states. The synchronous state is rela- tively unaffected by the rectification, but the coupling strength can decrease substantially during asynchronous activity (especially anti-phase activity). Thus, the effective robustness of the synchronous state increases in the pres- ence of noise and heterogeneity. In the case of fast rectification, we find a wide variety of effects that depend on degree of rectification and the intrinsic dynamics of the cells. The effects include both stabilization and destabilization of the anti-phase state. The effect of rectification is most prevalent in networks with bursting neurons, but it can also be of considerable magnitude in networks of spiking neurons. Summary Our theoretical and computational study shows that recti- fication of gap junctions can affect neuronal network dynamics in a significant and complex manner. Acknowledgements This research supported in part by the NSF Grant DMS-0518022 to TJL. DF was supported in part by the University of Cincinnati Taft Memorial Fund and NSF Grants DMS-0207145 and NSF-051589. References 1. Bukauskas FF, Verselis VK: Gap junction channel gating. Biochim- ica et Biophysica Acta 2004, 1662:42-60. from Seventeenth Annual Computational Neuroscience Meeting: CNS*2008 Portland, OR, USA. 19–24 July 2008 Published: 11 July 2008 BMC Neuroscience 2008, 9(Suppl 1):P132 doi:10.1186/1471-2202-9-S1-P132 This abstract is available from: http://www.biomedcentral.com/1471-2202/9/S1/P132 © 2008 French et al; licensee BioMed Central Ltd.
-
Upload
donald-french -
Category
Documents
-
view
212 -
download
0
Transcript of The effect of rectifying gap junctions on phase-locking in neuronal networks
BioMed Central
Page 1 of 1(page number not for citation purposes)
BMC Neuroscience
Open AccessPoster presentationThe effect of rectifying gap junctions on phase-locking in neuronal networksDonald French1, Tamara J Schlichter2 and Timothy J Lewis*2
Address: 1Department of Mathematics, University of Cincinnati, Cincinnati, Ohio, 45221, USA and 2Department of Mathematics, University of California, Davis, CA, 95616, USA
Email: Timothy J Lewis* - [email protected]
* Corresponding author
IntroductionGap junction mediated electrical coupling is ubiquitousin neuronal systems. Electrical coupling is almost alwaysmodeled as a linear ohmic resistance between cells, wherethe coupling current is proportional to the transjunctionalpotential. However, many gap junctions exhibit rectifica-tion with transjunctional voltage [1]. That is, the couplingconductance attenuates for increased voltage differencesbetween cells. This rectification process can evolve at dif-ferent time scales. Because gap junction rectification altersthe strength of coupling between cells in a way thatdepends on the intrinsic states of the cells, it may affect thedynamics in neuronal networks. However, the effects ofrectification on network dynamics are largely unstudied.
MethodsWe explore the effects of gap junction rectification onphase-locking in model neuronal networks. Using anextension of the theory of weak coupling, phase planearguments, and numerical simulations, we examine bothfast and slow rectification and their effects on the dynam-ics of networks of spiking neurons and networks of burst-ing neurons.
ResultsIn the slow rectification case, we show that the rectifica-tion always promotes synchronous activity. Because itdecreases the coupling strength only, slow rectificationhas no effect on the existence of phase-locked states inhomogeneous, noiseless networks. However, it alters therobustness of these states. The synchronous state is rela-
tively unaffected by the rectification, but the couplingstrength can decrease substantially during asynchronousactivity (especially anti-phase activity). Thus, the effectiverobustness of the synchronous state increases in the pres-ence of noise and heterogeneity.
In the case of fast rectification, we find a wide variety ofeffects that depend on degree of rectification and theintrinsic dynamics of the cells. The effects include bothstabilization and destabilization of the anti-phase state.
The effect of rectification is most prevalent in networkswith bursting neurons, but it can also be of considerablemagnitude in networks of spiking neurons.
SummaryOur theoretical and computational study shows that recti-fication of gap junctions can affect neuronal networkdynamics in a significant and complex manner.
AcknowledgementsThis research supported in part by the NSF Grant DMS-0518022 to TJL. DF was supported in part by the University of Cincinnati Taft Memorial Fund and NSF Grants DMS-0207145 and NSF-051589.
References1. Bukauskas FF, Verselis VK: Gap junction channel gating. Biochim-
ica et Biophysica Acta 2004, 1662:42-60.
from Seventeenth Annual Computational Neuroscience Meeting: CNS*2008Portland, OR, USA. 19–24 July 2008
Published: 11 July 2008
BMC Neuroscience 2008, 9(Suppl 1):P132 doi:10.1186/1471-2202-9-S1-P132
This abstract is available from: http://www.biomedcentral.com/1471-2202/9/S1/P132
© 2008 French et al; licensee BioMed Central Ltd.
