Skip to main content
  • Poster presentation
  • Open access
  • Published:

Optimal signal detection with neuronal diversity: balancing the gullible and the prudent neurons

Network connectivity have been shown to play an important role in shaping the neuronal dynamics [15]. A complementary remarkable feature of neuronal systems is the large degree of morphological and functional diversity. Despite some recent efforts in understanding the role of neuronal diversity embedded in a network [69], the benefits of cellular variability to distinguish input varying over orders of magnitude remain elusive. We utilize a simple quiescent-active-refractory-quiescent model, which is amenable to mathematical analysis [10], interacting in a (non-structured) random network with diversity in the parameter that controls the propensity of the neurons to fire in response to input from their neighbors. We consider a simple binomial distribution, a uniform distribution, and a more realistic gamma distribution. As depicted in Figure 1, we show that the capability of the network to distinguish the amount of external input can be improved by two orders of magnitude (20 dB) in the presence of diversity. We explain how diversity enhances the network capabilities, and identify the cases in which one specialized sub-population outperforms the rest of the network and the cases in which the average network outperforms any sub-population. Finally, we show the robustness of our results in a balanced cortical network of excitatory and inhibitory neurons.

Figure 1
figure 1

Top: Illustrative random networks with neuronal diversity in the threshold parameter θ. Bottom: Maximal dynamic range Δmax (as defined in ref. [6]) reached by networks with binomial (left), uniform (center), and gamma (right) distributions (bottom). Networks with binomial distribution have a proportion of integrator neurons with θ=2, whereas the remainders are non-integrator neurons (θ=1). The threshold In the uniform distribution varies from 1 to θmax. Network size is 5000 neurons.


  1. Gollo LL, Zalesky A, Hutchison RM, van den Heuvel M, Breakspear M: Dwelling quietly in the rich club: brain network determinants of slow cortical fluctuations. Phil Trans R Soc B. 2015, 370 (1668):

  2. Matias FS, Gollo LL, Carelli PV, Bressler SL, Copelli M, Mirasso CR: Modeling positive Granger causality and negative phase lag between cortical areas. NeuroImage. 2014, 99: 411-418.

    Article  PubMed  Google Scholar 

  3. Gollo LL, Mirasso C, Sporns O, Breakspear M: Mechanisms of zero-lag synchronization in cortical motifs. PLoS Comput Biol. 2014, 10 (4): e1003548-

    Article  PubMed  PubMed Central  Google Scholar 

  4. Gollo LL, Breakspear M: The frustrated brain: from dynamics on motifs to communities and networks. Phil Trans R Soc B. 2014, 369 (1653): 20130532-

    Article  PubMed  PubMed Central  Google Scholar 

  5. Moretti P, Muñoz MA: Griffiths phases and the stretching of criticality in brain networks. Nat Commun. 2013, 4:

    Google Scholar 

  6. Gollo LL, Mirasso C, Eguíluz VM: Signal integration enhances the dynamic range in neuronal systems. Phys Rev E. 2012, 85 (4): 040902-

    Article  Google Scholar 

  7. Mejias JF, Longtin A: Optimal heterogeneity for coding in spiking neural networks. Phys Rev Lett. 2012, 108 (22): 228102-

    Article  PubMed  CAS  Google Scholar 

  8. Vladimirski BB, Tabak J, O'Donovan MJ, Rinzel J: Episodic activity in a heterogeneous excitatory network, from spiking neurons to mean field. J Comput Neurosci. 2008, 25 (1): 39-63.

    Article  PubMed  Google Scholar 

  9. Tessone CJ, Mirasso CR, Toral R, Gunton JD: Diversity-induced resonance. Phys Rev Lett. 2006, 97 (19): 194101-

    Article  PubMed  Google Scholar 

  10. Gollo LL, Kinouchi O, Copelli M: Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation. Phys Rev E. 2012, 85 (1): 011911-

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Leonardo L Gollo.

Rights and permissions

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gollo, L.L., Copelli, M. & Roberts, J.A. Optimal signal detection with neuronal diversity: balancing the gullible and the prudent neurons. BMC Neurosci 16 (Suppl 1), P208 (2015).

Download citation

  • Published:

  • DOI: