Biological Cybernetics

, Volume 108, Issue 4, pp 475–493 | Cite as

Estimating latency from inhibitory input

  • Marie Levakova
  • Susanne Ditlevsen
  • Petr Lansky
Original Paper


Stimulus response latency is the time period between the presentation of a stimulus and the occurrence of a change in the neural firing evoked by the stimulation. The response latency has been explored and estimation methods proposed mostly for excitatory stimuli, which means that the neuron reacts to the stimulus by an increase in the firing rate. We focus on the estimation of the response latency in the case of inhibitory stimuli. Models used in this paper represent two different descriptions of response latency. We consider either the latency to be constant across trials or to be a random variable. In the case of random latency, special attention is given to models with selective interaction. The aim is to propose methods for estimation of the latency or the parameters of its distribution. Parameters are estimated by four different methods: method of moments, maximum-likelihood method, a method comparing an empirical and a theoretical cumulative distribution function and a method based on the Laplace transform of a probability density function. All four methods are applied on simulated data and compared.


Response latency Selective interaction Neuronal firing Inhibition Maximum likelihood  Laplace transform 



M.L. and P.L. were supported by the Grant Agency of the Czech Republic, project P304/12/G069, and by RVO:67985823. S.D. was supported by the Danish Council for Independent Research | Natural Sciences. The work is part of the Dynamical Systems Interdisciplinary Network, University of Copenhagen.

Supplementary material

422_2014_614_MOESM1_ESM.txt (22 kb)
Supplementary material 1 (txt 22 KB)


  1. Baker SN, Gerstein GL (2001) Determination of response latency and its application to normalization of cross-correlation measures. Neural Comput 13:1351–1377PubMedCrossRefGoogle Scholar
  2. Bonnasse-Gahot L, Nadal JP (2012) Perception of categories: from coding efficiency to reaction times. Brain Res 1434:47–61PubMedCrossRefGoogle Scholar
  3. Chase SM, Young ED (2007) First-spike latency information in single neurons increases when referenced to population onset. Proc Natl Acad Sci USA 104:5175–5180PubMedCentralPubMedCrossRefGoogle Scholar
  4. Chow CC, White JA (1996) Spontaneous action potentials due to channel fluctuations. Biophys J 71:3013–3021PubMedCentralPubMedCrossRefGoogle Scholar
  5. Commenges D, Seal J, Pinatel F (1986) Inference about a change point in experimental neurophysiology. Math Biosci 80:81–108CrossRefGoogle Scholar
  6. Ditlevsen S, Lansky P (2005) Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model. Phys Rev E 71:011907CrossRefGoogle Scholar
  7. Ditlevsen S, Lansky P (2006) Estimation of the input parameters in the Feller neuronal model. Phys Rev E 73:061910CrossRefGoogle Scholar
  8. Dorval AD (2008) Probability distributions of the logarithm of inter-spike intervals yield accurate entropy estimates from small datasets. J Neurosci Meth 173:129–139CrossRefGoogle Scholar
  9. Duchamp-Viret P, Palouzier-Paulignan B, Duchamp A (1996) Odor coding properties of frog olfactory cortical neurons. Neuroscience 74:885–895PubMedCrossRefGoogle Scholar
  10. Epps TW, Pulley LB (1985) Parameter estimates and test of fit for infinite mixture distributions. Commun Stat Theory Methods 14:3125–3145CrossRefGoogle Scholar
  11. Farkhooi F, Strube-Bloss MF, Nawrot MP (2009) Serial correlation in neural spike trains: experimental evidence, stochastic modeling, and single neuron variability. Phys Rev E 79:021905CrossRefGoogle Scholar
  12. Fienberg SE (1974) Stochastic models for single neuron firing trains: a survey. Biometrics 30:399–427PubMedCrossRefGoogle Scholar
  13. Friedman HS, Priebe CE (1998) Estimating stimulus response latency. J Neurosci Methods 83:185–194PubMedCrossRefGoogle Scholar
  14. Gautrais J, Thorpe S (1997) Rate coding versus temporal order coding: a theoretical approach. Biosystems 48:57–65CrossRefGoogle Scholar
  15. Hentall I (2000) Interactions between brainstem and trigeminal neurons detected by cross-spectral analysis. Neuroscience 96:601–610PubMedCrossRefGoogle Scholar
  16. Kang K, Amari S (2008) Discrimination with spike times and ISI distributions. Neural Comput 20:1411–1426PubMedCrossRefGoogle Scholar
  17. Koutrouvelis IA, Canavos GC (1997) Estimation in the three parameter gamma distribution based on the empirical moment generating function. J Stat Comput Simul 59:47–62CrossRefGoogle Scholar
  18. Koutrouvelis IA, Meintainis S (2002) Estimating the parameters of Poisson-exponential models. Aust NZ J Stat 44:233–245CrossRefGoogle Scholar
  19. Koutrouvelis IA, Canavos GC, Meintanis SG (2005) Estimation in the three-parameter inverse Gaussian distribution. Comput Stat Data An 49:1132–1147CrossRefGoogle Scholar
  20. Krofczik S, Menzel R, Nawrot MP (2009) Rapid odor processing in the honeybee antennal lobe network. Front Comput Neurosci 2:9PubMedCentralPubMedGoogle Scholar
  21. Mandl G (1993) Coding for stimulus velocity by temporal patterning of spike discharges in visual cells of cat superior colliculus. Vis Res 33:1451–1475PubMedCrossRefGoogle Scholar
  22. McKeegan D (2002) Spontaneous and odour evoked activity in single avian olfactory bulb neurons. Brain Res 929:48–58PubMedCrossRefGoogle Scholar
  23. Miura K, Okada M, Amari SI (2006) Estimating spiking irregularities under changing environments. Neural Comput 18:2359–2386PubMedCrossRefGoogle Scholar
  24. Nawrot M, Boucsein C, Molina V, Riehle A, Aertsen A, Rotter S (2008) Measurement of variability dynamics in cortical spike trains. J Neurosci Methods 169:374–390PubMedCrossRefGoogle Scholar
  25. Nawrot MP, Aertsen A, Rotter S (2003) Elimination of response variability in neuronal spike trains. Biol Cybern 88:321–334PubMedCrossRefGoogle Scholar
  26. Pawlas Z, Klebanov LB, Beneš V, Prokešová M, Popelář J, Lánský P (2010) First-spike latency in the presence of spontaneous activity. Neural Comput 22:1675–1697PubMedCrossRefGoogle Scholar
  27. Quandt RE, Ramsey JB (1978) Estimating mixtures of normals and switching regressions. J Am Stat Assoc 73:730–738CrossRefGoogle Scholar
  28. R Core Team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
  29. Reisenman CE, Heinbockel T, Hildebrand JG (2008) Inhibitory interactions among olfactory glomeruli do not necessarily reflect spatial proximity. J Neurophysiol 100:554–564PubMedCentralPubMedCrossRefGoogle Scholar
  30. Rospars JP, Lánský P, Duchamp-Viret P, Duchamp A (2000) Spiking frequency versus odorant concentration in olfactory receptor neurons. Biosystems 58:133–141PubMedCrossRefGoogle Scholar
  31. Shimokawa T, Shinomoto S (2009) Estimating instantaneous irregularity of neuronal firing. Neural Comput 21:1931–1951PubMedCrossRefGoogle Scholar
  32. Tamborrino M, Ditlevsen S, Lansky P (2012) Identification of noisy response latency. Phys Rev E 86:021128CrossRefGoogle Scholar
  33. Tamborrino M, Ditlevsen S, Lansky P (2013) Parametric inference of neuronal response latency in presence of a background signal. BioSystems 112:249–257 PubMedCrossRefGoogle Scholar
  34. Van Rullen R, Gautrais J, Delorme A, Thorpe S (1998) Face processing using one spike per neurone. Biosystems 48:229–239PubMedCrossRefGoogle Scholar
  35. Van Rullen R, Guyonneau R, Thorpe S (2005) Spike times make sense. Trends Neurosci 28:1–4CrossRefGoogle Scholar
  36. Wainrib G, Thieullen M, Pakdaman K (2010) Intrinsic variability of latency to first-spike. Biol Cybern 103:43–56PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Marie Levakova
    • 1
    • 3
  • Susanne Ditlevsen
    • 2
  • Petr Lansky
    • 3
  1. 1.Department of Mathematics and Statistics, Faculty of ScienceMasaryk UniversityBrnoCzech Republic
  2. 2.Department of Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark
  3. 3.Institute of PhysiologyAcademy of Sciences of the Czech RepublicPrague 4Czech Republic

Personalised recommendations