Abstract
We record spontaneous activity from a developing culture of dissociated rat hippocampal neurons in vitro using a multi electrode array. To statistically characterize activity, we look at the time intervals between recorded spikes, which, unlike neuronal avalanche sizes, do not require the selection of a time bin. The distribution of inter event intervals in our data approximate power laws at all recorded stages of development, with exponents that can be used to characterize the development of the culture. Synchronized bursting emerges as the culture matures, and these bursts show activity that decays approximately exponentially. From this, we propose a model for neuronal activity within bursts based on the consumption of a shared resource. Our model produces power law distributed avalanches in simulations, and is analytically demonstrated to produce power law distributed inter event intervals with an exponent close to that observed in our data. This indicates that power law distributions in neuronal avalanche size and other observables, can be also an artefact of exponentially decaying activity within synchronized bursts.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Stanley, H.E.: Introduction to Phase Transitions and Critical Phenomena. Oxford University Press, Oxford (1987)
Beggs, J.M., Plenz, D.: Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177 (2003)
Beggs, J.M., Plenz, D.: Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures. J. Neurosci. 24, 5216–5229 (2004)
Corral, A., Perez, C.J., Diaz-Guilera, A., Arenas, A.: Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators. Phys. Rev Lett. 74, 118–121 (1995)
Herz, A.V., Hopfield, J.J.: Earthquake cycles and neural reverberations: collective oscillations in systems with pulse-coupled threshold elements. Phys. Rev. Lett. 96, 1222–1225 (1995)
Orlandi, J.G., Soriano, J., Alvarez-Lacalle, E., Teller, S., Casademunt, J.: Noise focusing and the emergence of coherent activity in neuronal cultures. Nat. Phys. 9, 582–590 (2013)
Pasquale, V., Massobrio, P., Bologna, L.L., Chippalone, M., Martinoia, S.: Self-organization and neuronal avalanches in networks of dissociated cortical neurons. Neuroscience 153, 1354 (2008)
Shew, W.L., Yang, H., Petermann, T., Roy, R., Plenz, D.: Neuronal avalanches imply maximum dynamic range in cortical networks at criticality. J. Neurosci. 29, 15595 (2009)
Lorimer, T., Gomez, F., Stoop, R.: Two universal physical principles shape the power-law statistics of real-world networks. Sci. Rep. 5, 12353 (2015)
Haldeman, C., Beggs, J.M.: Critical branching captures activity in living neural networks and maximizes the number of metastable states. Phys. Rev. Lett. 94, 058101 (2005)
Breskin, I., Soriano, J., Moses, E., Tlusty, T.: Percolation in living neural networks. Phys. Rev. Lett 97, 188102 (2006)
Deluca, A., Corral, A.: Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions. Acta Geophys. 61, 1351–1394 (2013)
Marlinski, V., Beloozerova, I.N.: Burst firing of neurons in the thalamic reticular nucleus during locomotion. J. Neurophysiol. 112, 181–192 (2014)
Reed, W.J., Hughes, B.D.: From gene families and genera to incomes and internet file sizes: Why power laws are so common in nature. Phys. Rev. E 66, 067103 (2002)
Newman, M.E.J.: Power laws, Pareto distributions, and Zipf’s law. Contemp. Phys. 46, 323–351 (2005)
Chialvo, D.: Emergent complex neural dynamics. Nat. Phys. 6, 744–450 (2010)
Friedman, N., Ito, S., Brinkman, B.A.W., Shimono, M., DeVille, R.E.L., Dahmen, K.A., Beggs, J.M., Butler, T.C.: Universal critical dynamics in high resolution neuronal avalanche data. Phys. Rev. Lett. 108, 208102 (2012)
Beggs, J.M., Timme, N.: Being critical of criticality in the brain. Front. Physiol. 3, 163 (2012)
Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality: an explanation of the 1/f noise. Phys. Rev. Lett. 59, 381 (1987)
Acknowledgements
This work was supported by a joint Swiss-South Korea collaboration grant (IZKS2_162190).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Berger, D., Joo, S., Lorimer, T., Nam, Y., Stoop, R. (2017). Power Laws in Neuronal Culture Activity from Limited Availability of a Shared Resource. In: Mantica, G., Stoop, R., Stramaglia, S. (eds) Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences. Springer Proceedings in Physics, vol 191. Springer, Cham. https://doi.org/10.1007/978-3-319-47810-4_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-47810-4_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47808-1
Online ISBN: 978-3-319-47810-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)