{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:29:05Z","timestamp":1760243345669,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2014,11,3]],"date-time":"2014-11-03T00:00:00Z","timestamp":1414972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Information-theory is being increasingly used to analyze complex, self-organizing processes on networks, predominantly in analytical and numerical studies. Perhaps one of the most paradigmatic complex systems is a network of neurons, in which cognition arises from the information storage, transfer, and processing among individual neurons. In this article we review experimental techniques suitable for validating information-theoretical predictions in simple neural networks, as well as generating new hypotheses. Specifically, we focus on techniques that may be used to measure both network (microcircuit) anatomy as well as neuronal activity simultaneously. This is needed to study the role of the network structure on the emergent collective dynamics, which is one of the reasons to study the characteristics of information processing. We discuss in detail two suitable techniques, namely calcium imaging and the application of multi-electrode arrays to simple neural networks in culture, and discuss their advantages and limitations in an accessible manner for non-experts. In particular, we show that each technique induces a qualitatively different type of error on the measured mutual information. The ultimate goal of this work is to bridge the gap between theorists and experimentalists in their shared goal of understanding the behavior of networks of neurons.<\/jats:p>","DOI":"10.3390\/e16115721","type":"journal-article","created":{"date-parts":[[2014,11,3]],"date-time":"2014-11-03T08:52:52Z","timestamp":1415004772000},"page":"5721-5737","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Applying Information Theory to Neuronal Networks: From Theory to Experiments"],"prefix":"10.3390","volume":"16","author":[{"given":"Thijs","family":"Jung","sequence":"first","affiliation":[{"name":"Computational Science, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Filippos","family":"Vogiatzian","sequence":"additional","affiliation":[{"name":"Computational Science, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0876-4457","authenticated-orcid":false,"given":"Omri","family":"Har-Shemesh","sequence":"additional","affiliation":[{"name":"Computational Science, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carlos","family":"Fitzsimons","sequence":"additional","affiliation":[{"name":"Center for Neuroscience, Swammerdam Institute for Life Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rick","family":"Quax","sequence":"additional","affiliation":[{"name":"Computational Science, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,11,3]]},"reference":[{"unstructured":"Penrose, R., and Zenil, H.A. (2012). Computable Universe: Understanding and Exploring Nature as Computation, World Scientific.","key":"ref_1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1063\/1.1530990","article-title":"Regularities unseen, randomness observed: Levels of entropy convergence","volume":"13","author":"Crutchfield","year":"2003","journal-title":"Chaos"},{"doi-asserted-by":"crossref","unstructured":"Crutchfield, J.P., Ellison, C.J., and Mahoney, J.R. (2009). Time\u2019s barbed arrow: Irreversibility, crypticity, and stored information. Phys. Rev. Lett., 103.","key":"ref_3","DOI":"10.1103\/PhysRevLett.103.094101"},{"unstructured":"Williams, P.L., and Beer, R.D. (2010). Nonnegative decomposition of multivariate information, arXiv, 1004.2515.","key":"ref_4"},{"unstructured":"Quax, R., Apolloni, A., and Sloot, P.M.A. (2011). Information processing reveals how microscopic components affect the macroscopic system-state in complex networks, arXiv, 1111.5483.","key":"ref_5"},{"doi-asserted-by":"crossref","unstructured":"James, R.G., Ellison, C.J., and Crutchfield, J.P. (2011). Anatomy of a bit: Information in a time series observation. Chaos Interdiscip. J. Nonlinear Sci., 21.","key":"ref_6","DOI":"10.1063\/1.3637494"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.jocs.2012.07.001","article-title":"Information processing as a paradigm to model and simulate complex systems","volume":"3","author":"Sloot","year":"2012","journal-title":"J. Comput. Sci."},{"doi-asserted-by":"crossref","unstructured":"Lizier, J.T. (2012). The Local Information Dynamics of Distributed Computation in Complex Systems, Springer.","key":"ref_8","DOI":"10.1007\/978-3-642-32952-4"},{"doi-asserted-by":"crossref","unstructured":"Bertschinger, N., Rauh, J., Olbrich, E., and Jost, J. (2012, January 3\u20137). Shared information\u2014New insights and problems in decomposing information in complex systems, Brussels, Belgium.","key":"ref_9","DOI":"10.1007\/978-3-319-00395-5_35"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.3390\/e16041985","article-title":"Intersection information based on common randomness","volume":"16","author":"Griffith","year":"2014","journal-title":"Entropy"},{"doi-asserted-by":"crossref","unstructured":"Beer, R.D., and Williams, P.L. (2014). Information processing and dynamics in minimally cognitive agents. Cogn. Sci.","key":"ref_11","DOI":"10.1111\/cogs.12142"},{"unstructured":"Shannon, C.E., and Weaver, W. (1963). Mathematical Theory of Communication, University of Illinois Press.","key":"ref_12"},{"unstructured":"Cover, T.M., and Thomas, J.A. (1991). Elements of Information Theory, John Wiley & Sons.","key":"ref_13"},{"doi-asserted-by":"crossref","unstructured":"Quax, R., Apolloni, A., and Sloot, P.M. (2013). The diminishing role of hubs in dynamical processes on complex networks. J. R. Soc. Interface, 10.","key":"ref_14","DOI":"10.1098\/rsif.2013.0568"},{"doi-asserted-by":"crossref","unstructured":"Lizier, J.T., Prokopenko, M., and Zomaya, A.Y. (2010). Information modification and particle collisions in distributed computation. Chaos Interdiscip. J. Nonlinear Sci., 20.","key":"ref_15","DOI":"10.1063\/1.3486801"},{"unstructured":"Lizier, J.T., Prokopenko, M., and Zomaya, A.Y. (2008, January 5\u20138). The information dynamics of phase transitions in random Boolean networks, Winchester, UK.","key":"ref_16"},{"doi-asserted-by":"crossref","unstructured":"Barnett, L., Lizier, J.T., Harr\u00e9, M., Seth, A.K., and Bossomaier, T. (2013). Information flow in a kinetic Ising model peaks in the disordered phase. Phys. Rev. Lett., 111.","key":"ref_17","DOI":"10.1103\/PhysRevLett.111.177203"},{"doi-asserted-by":"crossref","unstructured":"Lizier, J.T., Flecker, B., and Williams, P.L. (2013, January 16\u201319). Towards a synergy-based approach to measuring information modification, Singapore, Singapore.","key":"ref_18","DOI":"10.1109\/ALIFE.2013.6602430"},{"doi-asserted-by":"crossref","unstructured":"Schreiber, T. (2000). Measuring information transfer. Phys. Rev. Lett., 85.","key":"ref_19","DOI":"10.1103\/PhysRevLett.85.461"},{"doi-asserted-by":"crossref","unstructured":"Lizier, J.T., Prokopenko, M., and Zomaya, A.Y. (2008). Local information transfer as a spatiotemporal filter for complex systems. Phys. Rev. E, 77.","key":"ref_20","DOI":"10.1103\/PhysRevE.77.026110"},{"doi-asserted-by":"crossref","unstructured":"Quax, R., Kandhai, D., and Sloot, P.M. (2013). Information dissipation as an early-warning signal for the Lehman Brothers collapse in financial time series. Sci. Rep., 3.","key":"ref_21","DOI":"10.1038\/srep01898"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1038\/nrn2575","article-title":"Complex brain networks: Graph theoretical analysis of structural and functional systems","volume":"10","author":"Bullmore","year":"2009","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1113\/jphysiol.1997.sp022031","article-title":"Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex","volume":"500","author":"Markram","year":"1997","journal-title":"J. Physiol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1006\/meth.1999.0774","article-title":"Detecting action potentials in neuronal populations with calcium imaging","volume":"18","author":"Smetters","year":"1999","journal-title":"Methods"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"7319","DOI":"10.1073\/pnas.1232232100","article-title":"In vivo two-photon calcium imaging of neuronal networks","volume":"100","author":"Stosiek","year":"2003","journal-title":"Proc. Natl. Acad. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1113\/expphysiol.2009.051953","article-title":"Optical reporters of synaptic activity in neural circuits","volume":"96","author":"Dreosti","year":"2011","journal-title":"Exp. Physiol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1038\/nmeth.1453","article-title":"High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision","volume":"7","author":"Grewe","year":"2010","journal-title":"Nat. Methods"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1152\/physiol.00032.2007","article-title":"In vivo calcium imaging of neural network function","volume":"22","author":"Gobel","year":"2007","journal-title":"Physiology"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/s00424-006-0150-x","article-title":"Optical monitoring of brain function in vivo: From neurons to networks","volume":"453","author":"Garaschuk","year":"2006","journal-title":"Pfl\u00fcg. Arch."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1016\/j.neuron.2008.01.002","article-title":"Genetic dissection of neural circuits","volume":"57","author":"Luo","year":"2008","journal-title":"Neuron"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/978-1-61779-170-3_2","article-title":"Primary neurons in culture and neuronal cell lines for in vitro neurotoxicological studies","volume":"758","author":"Giordano","year":"2011","journal-title":"Methods Mol. Biol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1038\/nbt.2738","article-title":"Genetically encoded voltage sensor goes live","volume":"31","author":"Marshel","year":"2013","journal-title":"Nat. Biotechnol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1038\/nature12354","article-title":"Ultrasensitive fluorescent proteins for imaging neuronal activity","volume":"499","author":"Chen","year":"2013","journal-title":"Nature"},{"doi-asserted-by":"crossref","unstructured":"Stetter, O., Battaglia, D., Soriano, J., and Geisel, T. (2012). Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals. Comput. Biol., 8.","key":"ref_34","DOI":"10.1371\/journal.pcbi.1002653"},{"doi-asserted-by":"crossref","unstructured":"Cousin, M.A. (2008). Use of FM1-43 and other derivatives to investigate neuronal function. Curr. Protoc. Neurosci., 43.","key":"ref_35","DOI":"10.1002\/0471142301.ns0206s43"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1640","DOI":"10.1109\/TBME.2004.827252","article-title":"Extracellular recordings from patterned neuronal networks using planar microelectrode arrays","volume":"51","author":"James","year":"2004","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0165-0270(94)90030-2","article-title":"Multi-neuronal signals from the retina: Acquisition and analysis","volume":"51","author":"Meister","year":"1994","journal-title":"J. Neurosci. Methods"},{"doi-asserted-by":"crossref","unstructured":"Frega, M., Tedesco, M., Massobrio, P., Pesce, M., and Martinoia, S. (2014). Network dynamics of 3D engineered neuronal cultures: A new experimental model for in-vitro electrophysiology. Sci. Rep., 30.","key":"ref_38","DOI":"10.1038\/srep05489"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.conb.2011.10.001","article-title":"Towards reliable spike-train recordings from thousands of neurons with multielectrodes","volume":"22","author":"Einevoll","year":"2012","journal-title":"Curr. Opin. Neurobiol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.cub.2011.11.005","article-title":"Spike sorting","volume":"22","author":"Quiroga","year":"2012","journal-title":"Curr. Biol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1038\/nrn2578","article-title":"Extracting information from neuronal populations: Information theory and decoding approaches","volume":"10","author":"Quiroga","year":"2009","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1783","DOI":"10.1016\/j.bios.2006.08.035","article-title":"Flexible polyimide microelectrode array for in vivo recordings and current source density analysis","volume":"22","author":"Cheung","year":"2007","journal-title":"Biosens. Bioelectron."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1038\/nnano.2012.265","article-title":"Multi-electrode array technologies for neuroscience and cardiology","volume":"8","author":"Spira","year":"2013","journal-title":"Nat. Nanotechnol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.ceca.2005.01.013","article-title":"Calcium imaging of cortical networks dynamics","volume":"37","author":"Cossart","year":"2005","journal-title":"Cell Calcium"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.neuroimage.2011.12.018","article-title":"Reliable optical detection of coherent neuronal activity in fast oscillating networks in vitro","volume":"60","author":"Reichinnek","year":"2012","journal-title":"NeuroImage"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1152\/jn.2000.84.1.401","article-title":"Accuracy of tetrode spike separation as determined by simultaneous intracellular and extracellular measurements","volume":"84","author":"Harris","year":"2000","journal-title":"J. Neurophysiol."},{"doi-asserted-by":"crossref","unstructured":"Kim, D.-J., Kent, J.S., Bolbecker, A.R., Sporns, O., Cheng, H., Newman, S.D., Puce, A., O\u2019Donnell, B.F., and Hetrick, W.P. (2014). Disrupted modular architecture of cerebellum in schizophrenia: A graph theoretic analysis. Schizophr. Bull., 40.","key":"ref_47","DOI":"10.1093\/schbul\/sbu059"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.schres.2014.04.012","article-title":"Disruptions in small-world cortical functional connectivity network during an auditory oddball paradigm task in patients with schizophrenia","volume":"156","author":"Shim","year":"2014","journal-title":"Schizophr. Res."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/B978-0-444-52898-8.00003-3","article-title":"Epilepsy as a dynamic disease of neuronal networks","volume":"107","author":"Gorter","year":"2012","journal-title":"Handb. Clin. Neurol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/11\/5721\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:17:43Z","timestamp":1760217463000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/11\/5721"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,3]]},"references-count":49,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2014,11]]}},"alternative-id":["e16115721"],"URL":"https:\/\/doi.org\/10.3390\/e16115721","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2014,11,3]]}}}