Impact of Network Structure and Cellular Response on Spike Time Correlations

Abstract

Novel experimental techniques reveal the simultaneous activity of larger and larger numbers of neurons. As a result there is increasing interest in the structure of cooperative--or correlated--activity in neural populations, and in the possible impact of such correlations on the neural code. A fundamental theoretical challenge is to understand how the architecture of network connectivity along with the dynamical properties of single cells shape the magnitude and timescale of correlations. We provide a general approach to this problem by extending prior techniques based on linear response theory. We consider networks of general integrate-and-fire cells with arbitrary architecture, and provide explicit expressions for the approximate cross-correlation between constituent cells. These correlations depend strongly on the operating point (input mean and variance) of the neurons, even when connectivity is fixed. Moreover, the approximations admit an expansion in powers of the matrices that describe the network architecture. This expansion can be readily interpreted in terms of paths between different cells. We apply our results to large excitatory-inhibitory networks, and demonstrate first how precise balance--or lack thereof--between the strengths and timescales of excitatory and inhibitory synapses is reflected in the overall correlation structure of the network. We then derive explicit expressions for the average correlation structure in randomly connected networks. These expressions help to identify the important factors that shape coordinated neural activity in such networks.

Full text

Its licence does not allow us to show the full text. Read it at PubMed Central:

References 69

1. 1.

   Cohen M, Kohn A. Measuring and interpreting neuronal correlations. Nat Neurosci. 2011;14:811-819.

   Not in our library10.1038/nn.2842

2. 2.

   Ohki K, Chung S, Ch'ng Y, Kara P, Reid R. Functional imaging with cellular resolution reveals precise micro-architecture in visual cortex. Nature. 2005;433:597-603.

   Not in our library10.1038/nature03274

3. 3.

   Field G, Gauthier J, Sher A, Greschner M, Machado T, et al. Functional connectivity in the retina at the resolution of photoreceptors. Nature. 2010;467:673-677.

   Not in our library10.1038/nature09424

4. 4.

   Jia H, Rochefort N, Chen X, Konnerth A. In vivo two-photon imaging of sensory-evoked dendritic calcium signals in cortical neurons. Nat Protoc. 2010;6:28-35.

   Not in our library10.1038/nprot.2010.169

5. 5.

   Brown EN, Kass RE, Mitra P. Multiple neural spike train data analysis: state-of-the-art and future challenges. Nat Neurosci. 2004;7:456-61.

   Not in our library10.1038/nn1228

6. 6.

   Averbeck B, Latham P, Pouget A. Neural correlations, population coding and computation. Nat Rev Neurosci. 2006;7:358-366.

   Not in our library10.1038/nrn1888

7. 7.

   Shadlen M, Newsome W. The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J Neurosci. 1998;18:3870-3896.

   Not in our library10.1523/jneurosci.18-10-03870.1998

8. 8.

   Panzeri S, Schultz S, Treves A, Rolls E. Correlations and encoding of information in the nervous system. P Roy Soc Lond B Bio. 1999;266:1001-1012.

   Not in our library10.1098/rspb.1999.0736

9. 9.

   Zohary E, Shadlen MN, Newsome WT. Correlated neuronal discharge rate and its implication for psychophysical performance. Nature. 1994;370:140-143.

   Not in our library10.1038/370140a0

10. 10.

    Abbott LF, Dayan P. The effect of correlated variability on the accuracy of a population code. Neural Comput. 1999;11:91-101.

    Not in our library10.1162/089976699300016827

11. 11.

    Sompolinsky H, Yoon H, Kang K, Shamir M. Population coding in neuronal systems with correlated noise. Phys Rev E. 2001;64:051904.

    Not in our library10.1103/physreve.64.051904

12. 12.

    Panzeri S, Petersen R, Schultz S, Lebedev M, Diamond M. The role of spike timing in the coding of stimulus location in rat somatosensory cortex. Neuron. 2001;29:769-777.

    Not in our library10.1016/s0896-6273(01)00251-3

13. 13.

    Beck J, Bejjanki V, Pouget A. Insights from a simple expression for linear fisher information in a recurrently connected population of spiking neurons. Neural Comput. 2011;23:1484-1502.

    Not in our library10.1162/neco_a_00125

14. 14.

    Josić K, Shea-Brown E, Doiron B, de La Rocha J. Stimulus-dependent correlations and population codes. Neural Comput. 2009;21:2774-2804.

    Not in our library10.1162/neco.2009.10-08-879

15. 15.

    Schneidman E, Bialek W, Berry M. Synergy, Redundancy, and Independence in Population Codes. J Neurosci. 2003;23:11539-11553.

    Not in our library10.1523/jneurosci.23-37-11539.2003

16. 16.

    Latham PE, Nirenberg S. Synergy, Redundancy, and Independence in Population Codes, Revisited. J Neurosci. 2005;25:5195-5206.

    Not in our library10.1523/jneurosci.5319-04.2005

17. 17.

    Nirenberg S, Carcieri SM, Jacobs AL, Latham PE. Retinal ganglion cells act largely as independent encoders. Nature. 2001;411:698-701.

    Not in our library10.1038/35079612

18. 18.

    Cohen M, Newsome W. Estimates of the contribution of single neurons to perception depend on timescale and noise correlation. J Neurosci. 2009;29:6635-6648.

    Not in our library10.1523/jneurosci.5179-08.2009

19. 19.

    Romo R, Hernandez A, Zainos A, Salinas E. Correlated neuronal discharges that increase coding efficiency during perceptual discrimination. Neuron. 2003;38:649-657.

    Not in our library10.1016/s0896-6273(03)00287-3

20. 20.

    Renart A, de la Rocha J, Bartho P, Hollender L, Parga N, et al. The asynchronous state in cortical circuits. Science. 2010;327:587-590.

    Not in our library10.1126/science.1179850

21. 21.

    Ecker A, Berens P, Keliris G, Bethge M, Logothetis N, et al. Decorrelated neuronal firing in cortical microcircuits. Science. 2010;327:584-587.

    Not in our library10.1126/science.1179867

22. 22.

    Paninski L, Ahmadian Y, Ferreira D, Koyama S, Rahnama Rad K, et al. A new look at state-space models for neural data. J Comput Neurosci. 2010;29:107-126.

    Not in our library10.1007/s10827-009-0179-x

23. 23.

    Nykamp D. A mathematical framework for inferring connectivity in probabilistic neuronal networks. Math Biosci. 2007;205:204-251.

    Not in our library10.1016/j.mbs.2006.08.020

24. 24.

    Ostojic S, Brunel N, Hakim V. How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains. J Neurosci. 2009;29:10234-10253.

    Not in our library10.1523/jneurosci.1275-09.2009

25. 25.

    Fourcaud-Trocmé N, Hansel D, Van Vreeswijk C, Brunel N. How spike generation mechanisms determine the neuronal response to uctuating inputs. J Neurosci. 2003;23:11628-11640.

    Not in our library10.1523/jneurosci.23-37-11628.2003

26. 26.

    Lindner B, Doiron B, Longtin A. Theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback. Phys Rev E. 2005;72:061919.

    Not in our library10.1103/physreve.72.061919

27. 27.

    Brunel N, Hakim V. Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput. 1999;11:1621-1671.

    Not in our library10.1162/089976699300016179

28. 28.

    Lindner B, Schimansky-Geier L. Transmission of noise coded versus additive signals through a neuronal ensemble. Phys Rev Lett. 2001;86:2934-2937.

    Not in our library10.1103/physrevlett.86.2934

29. 29.

    Richardson M. Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive. Phys Rev E. 2007;76:021919.

    Not in our library10.1103/physreve.76.021919

30. 30.

    Gabbiani F, Koch C, Segev I, Koch C. Principles of spike train analysis. Methods in Neuronal Modeling. 1998;313-360.

    Not in our library

31. 31.
    How Structure Determines Correlations in Neuronal Networks · 2011

    No notice
32. 32.

    Rangan A. Diagrammatic expansion of pulse-coupled network dynamics. Phys Rev Lett. 2009;102:158101.

    Not in our library10.1103/physrevlett.102.158101

33. 33.

    Rangan A. Diagrammatic expansion of pulse-coupled network dynamics in terms of subnetworks. Phys Rev E. 2009;80:036101.

    Not in our library10.1103/physreve.80.036101

34. 34.

    Risken H. The Fokker-Planck equation: Methods of solution and applications. 1996.

    Not in our library

35. 35.

    Brunel N, Chance F, Fourcaud N, Abbott L. Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys Rev Lett. 2001;86:2186-2189.

    Not in our library10.1103/physrevlett.86.2186

36. 36.

    White JA, Rubinstein JT, Kay AR. Channel noise in neurons. Trends Neurosci. 2000;23:131-137.

    Not in our library10.1016/s0166-2236(99)01521-0

37. 37.

    Renart A, Brunel N, Wang X, Feng J. Mean-field theory of irregularly spiking neuronal populations and working memory in recurrent cortical networks. Computational Neuroscience: A Comprehensive Approach. 2004;431-490.

    Not in our library

38. 38.

    Burkitt A. A review of the integrate-and-fire neuron model: I. homogeneous synaptic input. Biol Cybern. 2006;95:1-19.

    Not in our library10.1007/s00422-006-0068-6

39. 39.

    Gabbiani F, Cox S. Mathematics for Neuroscientists. 2010.

    Not in our library

40. 40.

    Barreiro A, Shea-Brown E, Thilo E. Time scales of spike-train correlation for neural oscillators with common drive. Phys Rev E. 2010;81:011916.

    Not in our library10.1103/physreve.81.011916

41. 41.

    Roxin A. The role of degree distribution in shaping the dynamics in networks of sparsely connected spiking neurons. Front Comput Neurosci. 2011;5:1-15.

    Not in our library10.3389/fncom.2011.00008

42. 42.

    Zhao L, Beverlin B, Netoff T, Nykamp DQ. Synchronization from second order network connectivity statistics. Front Comput Neurosci. 2011;5:1-16.

    Not in our library10.3389/fncom.2011.00028

43. 43.

    Bullmore E, Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci. 2009;10:186-198.

    Not in our library10.1038/nrn2575

44. 44.
    Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits · 2005

    Corrected
45. 45.

    Oswald A, Doiron B, Rinzel J, Reyes A. Spatial profile and differential recruitment of gabab modulate oscillatory activity in auditory cortex. J Neurosci. 2009;29:10321.

    Not in our library10.1523/jneurosci.1703-09.2009

46. 46.

    Perin R, Berger T, Markram H. A synaptic organizing principle for cortical neuronal groups. Proc Natl Acad Sci U S A. 2011;108:5419-5424.

    Not in our library10.1073/pnas.1016051108

47. 47.

    Katō T. Perturbation Theory for Linear Operators. 1995.

    Not in our library

48. 48.

    Horn R, Johnson C. Matrix Analysis. 1990.

    Not in our library

49. 49.

    de la Rocha J, Doiron B, Shea-Brown E, Josić K, Reyes A. Correlation between neural spike trains increases with firing rate. Nature. 2007;448:802-806.

    Not in our library10.1038/nature06028

50. 50.

    Vilela R, Lindner B. Comparative study of different integrate-and-fire neurons: Spontaneous activity, dynamical response, and stimulus-induced correlation. Phys Rev E. 2009;80:031909.

    Not in our library10.1103/physreve.80.031909

51. 51.

    Kremkow J, Perrinet L, Masson G, Aertsen A. Functional consequences of correlated excitatory and inhibitory conductances in cortical networks. J Comp Neurosci. 2010;28:579-594.

    Not in our library10.1007/s10827-010-0240-9

52. 52.

    Veredas F, Vico F, Alonso J. Factors determining the precision of the correlated firing generated by a monosynaptic connection in the cat visual pathway. J Physiol. 2005;567:1057.

    Not in our library10.1113/jphysiol.2005.092882

53. 53.

    Kirkwood P. On the use and interpretation of cross-correlations measurements in the mammalian central nervous system. J Neurosci Meth. 1979;1:107.

    Not in our library10.1016/0165-0270(79)90009-8

54. 54.

    Fetz E, Gustafsson B. Relation between shapes of post-synaptic potentials and changes in firing probability of cat motoneurones. J Physiol. 1983;341:387.

    Not in our library10.1113/jphysiol.1983.sp014812

55. 55.

    Herrmann A, Gerstner W. Noise and the PSTH response to current transients: I. general theory and application to the integrate-and-fire neuron. J Comput Neurosci. 2001;11:135-151.

    Not in our library10.1023/a:1012841516004

56. 56.

    Vreeswijk C, Abbott L, Bard Ermentrout G. When inhibition not excitation synchronizes neural firing. J Comput Neurosci. 1994;1:313-321.

    Not in our library10.1007/bf00961879

57. 57.

    Shepherd G. Foundations of the Neuron Doctrine. 1991.

    Not in our library

58. 58.

    Hawkes A. Spectra of some self-exciting and mutually exciting point processes. Biometrika. 1971;58:83-90.

    Not in our library

59. 59.

    Hawkes A. Point spectra of some mutually exciting point processes. J Roy Stat Soc B Met. 1971;33:438-443.

    Not in our library

60. 60.

    Marinazzo D, Kappen H, Gielen S. Input-driven oscillations in networks with excitatory and inhibitory neurons with dynamic synapses. Neural Comput. 2007;19:1739-1765.

    Not in our library10.1162/neco.2007.19.7.1739

61. 61.

    Chacron M, Longtin A, Maler L. Delayed excitatory and inhibitory feedback shape neural information transmission. Phys Rev E. 2005;72:051917.

    Not in our library10.1103/physreve.72.051917

62. 62.

    Åkerberg O, Chacron M. Noise shaping in neural populations. Phys Rev E. 2009;79:011914.

    Not in our library10.1103/physreve.79.011914

63. 63.

    Shea-Brown E, Josić K, de La Rocha J, Doiron B. Correlation and synchrony transfer in integrate-and-fire neurons: Basic properties and consequences for coding. Phys Rev Lett. 2008;100:108102.

    Not in our library10.1103/physrevlett.100.108102

64. 64.

    Toyoizumi T, Rad K, Paninski L. Mean-field approximations for coupled populations of generalized linear model spiking neurons with markov refractoriness. Neural Comput. 2009;21:1203-1243.

    Not in our library10.1162/neco.2008.04-08-757

65. 65.

    Alijani A, Richardson M. Rate response of neurons subject to fast or frozen noise: From stochastic and homogeneous to deterministic and heterogeneous populations. Phys Rev E. 2011;84:011919.

    Not in our library10.1103/physreve.84.011919

66. 66.
    From Spiking Neuron Models to Linear-Nonlinear Models · 2011

    No notice
67. 67.

    Richardson M. Dynamics of populations and networks of neurons with voltage-activated and calcium-activated currents. Phys Rev E. 2009;80:021928.

    Not in our library10.1103/physreve.80.021928

68. 68.

    Bair W, Zohary E, Newsome W. Correlated firing in macaque visual area mt: time scales and relationship to behavior. J Neurosci. 2001;21:1676-1697.

    Not in our library10.1523/jneurosci.21-05-01676.2001

69. 69.

    Ricciardi L, Sacerdote L. The ornstein-uhlenbeck process as a model for neuronal activity. Biol Cybern. 1979;35:1-9.

    Not in our library10.1007/bf01845839

Cited by papers we hold 9

• Synaptic Plasticity Shapes Brain Connectivity: Implications for Network Topology · 2019
  No notice
• A stochastic-field description of finite-size spiking neural networks. · 2017
  Not checked
• Bistability, non-ergodicity, and inhibition in pairwise maximum-entropy models. · 2017
  Not checked
• Linking structure and activity in nonlinear spiking networks. · 2017
  Not checked
• Estimation of Directed Effective Connectivity from fMRI Functional Connectivity Hints at Asymmetries of Cortical Connectome · 2016
  No notice
• Small modifications to network topology can induce stochastic bistable spiking dynamics in a balanced cortical model. · 2014
  Not checked
• Self-consistent determination of the spike-train power spectrum in a neural network with sparse connectivity · 2014
  Not checked
• Mechanisms of Zero-Lag Synchronization in Cortical Motifs · 2014
  No notice
• Decorrelation of Neural-Network Activity by Inhibitory Feedback · 2012
  No notice

Reads

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.