Abstract
Recent studies have shown that gamma-band oscillations are directly related to pain intensity. Pain can be exacerbated or diminished via deactivation or activation of inhibitory interneurons in the dorsal horn. We consider a biologically plausible network model with different proportion of inhibitory neurons to emulate gamma elicited activity during pain processes. We perform an analysis using graph theory to gain further insight in the functional state of the circuitry underlying nociceptive process, considering all the possible gamma elicited configurations of pain when changing the number of inhibitory neurons. The probability distribution of the signal associated with each node or neuron is estimated through the Bandt and Pompe approach. We evaluate the Jensen–Shannon distance between all the possible pairs of nodes/neurons, characterizing the different network configurations by calculating the closeness centrality. Thus, by building the graph properties through the node strength distributions and using an information theoretical approach, we characterize the dynamics of the network configurations of pain. This allows us to identify the nonlinear dynamical structure underlying the nociceptive process. Importantly, our findings show that a network configuration with a \(20\%\) of inhibitory neurons boosts information transmission of the complex network circuitry associated with the pain processing.
Graphic abstract
Similar content being viewed by others
Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical study and no experimental data has been listed.]
References
G. Castellani, N. Intrator, D. Remondini, Front. Genet. 5 (2014)
M. Rubinov, O. Sporns, Neuroimage 52, 1059 (2010)
M.P. Van Den Heuvel, H.E. Hulshoff Pol, Eur. Neuropsychopharmacol. 20, 519 (2010)
E.W. Lang, A. Tomé, I.R. Keck, J. Górriz-Sáez, C. Puntonet, Comput. Intell. Neurosci. 2012, 8 (2012)
F. Montani, A. Oliynyk, L. Fadiga, Int. J. Neural Syst. 27, 1650009 (2017)
J. Wang, X. Zuo, Y. He, Front. Syst. Neurosci. 4, 1 (2010)
Ja Braz, C. Solorzano, X. Wang, A.I. Basbaum, Neuron 82, 522 (2014)
A. Franois, S.A. Low, E.I. Sypek, A.J. Christensen, C. Sotoudeh, K.T. Beier, C. Ramakrishnan, K.D. Ritola, R. Sharif-Naeini, K. Deisseroth et al., Neuron 93, 822 (2017)
A.J. Todd, Nat. Rev. Neurosci. 11, 823 (2010)
H.C. Johannssen, F. Helmchen, J. Physiol. 588, 3397 (2010)
T. Takazawa, A.B. MacDermott, Ann. N. Y. Acad. Sci. 1198, 153 (2010)
W. Ren, V. Neugebauer, Mol. Pain 6, 93 (2010)
F. Montani, E.B. Deleglise, O.A. Rosso, Phys. A Stat. Mech. Appl. 401, 58 (2014)
R. Bardoni, K.F. Shen, H. Li, J. Jeffry, D.M. Barry, A. Comitato, Y.Q. Li, Z.F. Chen, Sci. Rep. 9, 15804 (2019)
L.L. Tan, M.J. Oswald, C. Heinl, O.A.R. Romero, S.K. Kaushalya, H. Monyer, R. Kuner, Sci. Rep. 10, 983 (2019)
G. Buzsaki, Rhythms of the Brain (Oxford University Press, Oxford, 2009)
M. Hauck, J. Lorenz, A.K. Engel, J. Neurosci. 27, 9270 (2007)
M.N. Baliki, A.T. Baria, A.V. Apkarian, J. Neurosci. 31, 13981 (2011)
M. Ploner, C. Sorg, J. Gross, Trends Cogn. Sci. 21, 100 (2017)
J. Gross, A. Schnitzler, L. Timmermann, M. Ploner, PLoS Biol. 5, e133 (2007)
Z. Zhang, L. Hu, Y. Hung, A. Mouraux, G. Iannetti, J. Neurosci. 32, 7429 (2012)
E.S. May, M.M. Nickel, S.T. Dinh, L. Tiemann, H. Heitmann, I. Voth, T.R. Tölle, J. Gross, M. Ploner, Hum. Brain Mapp. 40, 293 (2019)
E.M. Izhikevich, IEEE Trans. Neural Netw. 14, 1569 (2003)
E.M. Izhikevich, Neural Comput. 18, 245 (2006)
R. Baravalle, N. Guisande, M. Granado, O.A. Rosso, F. Montani, Front. Phys. 7, 115 (2019)
O. Rosso, C. Masoller, Phys. Rev. E 79, 040106(R) (2009)
O. Rosso, C. Masoller, Eur. Phys. J. B 69, 37 (2009)
O. Rosso, F. Olivares, A. Plastino, Paper Phys. 7, 070006 (2015)
F. Montani, O.A. Rosso, Entropy 16, 4677 (2014)
E.M. Izhikevich, Dynamical Systems in Neuroscience (MIT Press, Cambridge, 2007)
L. Risinger, K. Kaikhah, Innovations in Applied Artificial Intelligence (Springer, Berlin, 2004), pp. 1033–1042
T. Schwalger, L. Schimansky-Geier, Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 77, 031914 (2008)
K.S. Kravtsov, M.P. Fok, P.R. Prucnal, D. Rosenbluth, Opt. Express 19, 2133 (2011)
C. Bandt, B. Pompe, Phys. Rev. Lett. 88, 174102 (2002)
F. Olivares, A. Plastino, O. Rosso, Phys. A 391, 2518 (2012)
F. Olivares, A. Plastino, O. Rosso, Phys. Lett. A 376, 1577 (2012)
F. Montani, O.A. Rosso, F.S. Matias, S.L. Bressler, C.R. Mirasso, Philos. Trans. R. Soc. Lond. Ser. A 373, 20150110 (2015)
F. Montani, R. Baravalle, L. Montangie, O.A. Rosso, Philos. Trans. R. Soc. Lond. Ser. A 373, 20150109 (2015)
C. Shannon, W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Champaign, 1949)
T.M. Cover, J.A. Thomas, Elements of Information Theory (Wiley-Interscience, New York, 2012)
B. Frieden, Science from Fisher Information: A Unification (Cambridge University Press, Cambridge, 2004)
R. Lopez-Ruiz, H.L. Mancini, X. Calbet, Phys. Lett. A 209, 321 (1995)
C. Tsallis, Introduction to Nonextensive Statistical Mechanics (Springer, Berlin, 2009)
A. Renyi, On measures of entropy and information, in Fourth Berkeley Symposium on Mathematical Statistics and Probability, pp. 547–561 (1961)
W.K. Wootters, Phys. Rev. D 23, 357 (1981)
S. Kullback, R.A. Leibler, Ann. Math. Stat. 22, 79–86 (1951)
I. Grosse, P. Bernaola-Galván, P. Carpena, R. Román-Roldán, J. Oliver, H.E. Stanley, Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 65, 041905 (2002)
F. Montani, O.A. Rosso, S.R. Schultz, AIP Conf. Proc. 913, 184 (2007)
M. Martín, A. Plastino, O. Rosso, Phys. A 369, 439 (2006)
O. Rosso, H. Larrondo, M. Martín, A. Plastino, M. Fuentes, Phys. Rev. Lett. 99, 154102 (2007)
L.C. Freeman, Soc. Netw. 1, 215 (1979)
L.C. Freeman, D. Roeder, R.R. Mulholland, Soc. Netw. 2, 119 (1979/1980)
D.S. Bassett, E.T. Bullmore, Curr. Opin. Neurol. 22, 340 (2009)
E.T. Bullmore, O. Sporns, Nat. Rev. Neurosci. 10, 186 (2009)
C.J. Stam, J.C. Reijneveld, Nonlinear Biomed. Phys. 1, 3 (2007)
M. Newman, Networks: An Introduction (Oxford University Press, Oxford, 2010)
E. Brigham, R. Morrow, Spectr. IEEE 4, 63 (1967)
S. Ross, Introduction to Probability Models (Academic Press, New York, 2009)
R. Baravalle, O. Rosso, F. Montani, Chaos Interdiscip. J. Nonlinear Sci. 28, 075513 (2018)
I. Nemenman, W. Bialek, RdR van Steveninck, Phys. Rev. E 69, 056111 (2004)
M. Prokopenko, J.T. Lizier, O. Obst, X.R. Wang, Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 84, 041116 (2011)
M. Prokopenko, J.T. Lizier, Sci. Rep. 4 (2014)
M. Prokopenko, L. Barnett, M. Harr, J.T. Lizier, O. Obst, X.R. Wang, Proc. R. Soc. A 471, 20150610 (2015)
O. Rosso, F. Olivares, L. Zunino, L. De Micco, A. Aquino, A. Plastino, H. Larrondo, Eur. Phys. J. B 86 (2012)
H. Paugam-Moisya, R. Martineza, S. Bengio, Nat. Rev. Neurosci. 71, 1143 (2008)
R. Wang, G. Cohen, K. Stiefel, T. Hamilton, J. Tapson, A. van Schaik, Front. Neurosci. 7, 14 (2013)
A. Eguchi, J.B. Isbister, N. Ahmad, S. Stringer, Psychol. Rev. 125, 545 (2018)
M.N. Economo, J.A. White, PLoS Comput. Biol. 8, e1002354 (2018)
Acknowledgements
We gratefully acknowledge funding from PUE 22920170100066CO IFLP-CONICET Argentina, PIP 11220130100327CO (2014/2016) CONICET, Argentina (F.M.), and project 80120190100127LP Universidad Nacional de La Plata, Argentina.
Author information
Authors and Affiliations
Contributions
All the authors were involved in the preparation of the manuscript. All the authors have read and approved the final manuscript.
Corresponding author
Rights and permissions
About this article
Cite this article
De Luise, R., Baravalle, R., Rosso, O.A. et al. Network configurations of pain: an efficiency characterization of information transmission. Eur. Phys. J. B 94, 34 (2021). https://doi.org/10.1140/epjb/s10051-021-00046-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjb/s10051-021-00046-6