Abstract
Is the information transmitted by an ensemble of neurons determined solely by the number of spikes fired by each cell, or do correlations in the emission of action potentials also play a significant role? We derive a simple formula which enables this question to be answered rigorously for short time-scales. The formula quantifies the corrections to the instantaneous information rate which result from correlations in spike emission between pairs of neurons. The mutual information that the ensemble of neurons conveys about external stimuli can thus be broken down into firing rate and correlation components. This analysis provides fundamental constraints upon the nature of information coding, showing that over short time-scales correlations cannot dominate information representation, that stimulus-independent correlations may lead to synergy (where the neurons together convey more information than they would if they were considered independently), but that only certain combinations of the different sources of correlation result in significant synergy rather than in redundancy or in negligible effects. This analysis leads to a new quantification procedure which is directly applicable to simultaneous multiple neuron recordings.
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- Aertsen A. M., Gerstein G. L., Habib M. K., Palm G. Dynamics of neuronal firing correlation: modulation of "effective connectivity". J Neurophysiol. 1989 May;61(5):900–917. doi: 10.1152/jn.1989.61.5.900. [DOI] [PubMed] [Google Scholar]
- Arieli A., Sterkin A., Grinvald A., Aertsen A. Dynamics of ongoing activity: explanation of the large variability in evoked cortical responses. Science. 1996 Sep 27;273(5283):1868–1871. doi: 10.1126/science.273.5283.1868. [DOI] [PubMed] [Google Scholar]
- Bialek W., Rieke F., de Ruyter van Steveninck R. R., Warland D. Reading a neural code. Science. 1991 Jun 28;252(5014):1854–1857. doi: 10.1126/science.2063199. [DOI] [PubMed] [Google Scholar]
- Carr C. E., Konishi M. A circuit for detection of interaural time differences in the brain stem of the barn owl. J Neurosci. 1990 Oct;10(10):3227–3246. doi: 10.1523/JNEUROSCI.10-10-03227.1990. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Carr C. E. Processing of temporal information in the brain. Annu Rev Neurosci. 1993;16:223–243. doi: 10.1146/annurev.ne.16.030193.001255. [DOI] [PubMed] [Google Scholar]
- Donoghue J. P., Sanes J. N., Hatsopoulos N. G., Gaál G. Neural discharge and local field potential oscillations in primate motor cortex during voluntary movements. J Neurophysiol. 1998 Jan;79(1):159–173. doi: 10.1152/jn.1998.79.1.159. [DOI] [PubMed] [Google Scholar]
- Gawne T. J., Kjaer T. W., Hertz J. A., Richmond B. J. Adjacent visual cortical complex cells share about 20% of their stimulus-related information. Cereb Cortex. 1996 May-Jun;6(3):482–489. doi: 10.1093/cercor/6.3.482. [DOI] [PubMed] [Google Scholar]
- Gawne T. J., Richmond B. J. How independent are the messages carried by adjacent inferior temporal cortical neurons? J Neurosci. 1993 Jul;13(7):2758–2771. doi: 10.1523/JNEUROSCI.13-07-02758.1993. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Golledge H. D., Hilgetag C. C., Tovée M. J. A solution to the binding problem? Information processing. Curr Biol. 1996 Sep 1;6(9):1092–1095. doi: 10.1016/s0960-9822(02)70675-1. [DOI] [PubMed] [Google Scholar]
- Gray C. M., Engel A. K., König P., Singer W. Synchronization of oscillatory neuronal responses in cat striate cortex: temporal properties. Vis Neurosci. 1992 Apr;8(4):337–347. doi: 10.1017/s0952523800005071. [DOI] [PubMed] [Google Scholar]
- Heller J., Hertz J. A., Kjaer T. W., Richmond B. J. Information flow and temporal coding in primate pattern vision. J Comput Neurosci. 1995 Sep;2(3):175–193. doi: 10.1007/BF00961433. [DOI] [PubMed] [Google Scholar]
- Kitazawa S., Kimura T., Yin P. B. Cerebellar complex spikes encode both destinations and errors in arm movements. Nature. 1998 Apr 2;392(6675):494–497. doi: 10.1038/33141. [DOI] [PubMed] [Google Scholar]
- Macknik S. L., Livingstone M. S. Neuronal correlates of visibility and invisibility in the primate visual system. Nat Neurosci. 1998 Jun;1(2):144–149. doi: 10.1038/393. [DOI] [PubMed] [Google Scholar]
- Meister M., Lagnado L., Baylor D. A. Concerted signaling by retinal ganglion cells. Science. 1995 Nov 17;270(5239):1207–1210. doi: 10.1126/science.270.5239.1207. [DOI] [PubMed] [Google Scholar]
- Murthy V. N., Fetz E. E. Synchronization of neurons during local field potential oscillations in sensorimotor cortex of awake monkeys. J Neurophysiol. 1996 Dec;76(6):3968–3982. doi: 10.1152/jn.1996.76.6.3968. [DOI] [PubMed] [Google Scholar]
- Optican L. M., Richmond B. J. Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. III. Information theoretic analysis. J Neurophysiol. 1987 Jan;57(1):162–178. doi: 10.1152/jn.1987.57.1.162. [DOI] [PubMed] [Google Scholar]
- Oram M. W., Földiák P., Perrett D. I., Sengpiel F. The 'Ideal Homunculus': decoding neural population signals. Trends Neurosci. 1998 Jun;21(6):259–265. doi: 10.1016/s0166-2236(97)01216-2. [DOI] [PubMed] [Google Scholar]
- Oram M. W., Perrett D. I. Time course of neural responses discriminating different views of the face and head. J Neurophysiol. 1992 Jul;68(1):70–84. doi: 10.1152/jn.1992.68.1.70. [DOI] [PubMed] [Google Scholar]
- Parker A. J., Newsome W. T. Sense and the single neuron: probing the physiology of perception. Annu Rev Neurosci. 1998;21:227–277. doi: 10.1146/annurev.neuro.21.1.227. [DOI] [PubMed] [Google Scholar]
- Riehle A., Grün S., Diesmann M., Aertsen A. Spike synchronization and rate modulation differentially involved in motor cortical function. Science. 1997 Dec 12;278(5345):1950–1953. doi: 10.1126/science.278.5345.1950. [DOI] [PubMed] [Google Scholar]
- Rolls E. T., Robertson R. G., Georges-François P. Spatial view cells in the primate hippocampus. Eur J Neurosci. 1997 Aug;9(8):1789–1794. doi: 10.1111/j.1460-9568.1997.tb01538.x. [DOI] [PubMed] [Google Scholar]
- Rolls E. T., Tovee M. J. Processing speed in the cerebral cortex and the neurophysiology of visual masking. Proc Biol Sci. 1994 Jul 22;257(1348):9–15. doi: 10.1098/rspb.1994.0087. [DOI] [PubMed] [Google Scholar]
- Rolls E. T., Treves A., Tovee M. J. The representational capacity of the distributed encoding of information provided by populations of neurons in primate temporal visual cortex. Exp Brain Res. 1997 Mar;114(1):149–162. doi: 10.1007/pl00005615. [DOI] [PubMed] [Google Scholar]
- Shadlen M. N., Newsome W. T. The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J Neurosci. 1998 May 15;18(10):3870–3896. doi: 10.1523/JNEUROSCI.18-10-03870.1998. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Thorpe S., Fize D., Marlot C. Speed of processing in the human visual system. Nature. 1996 Jun 6;381(6582):520–522. doi: 10.1038/381520a0. [DOI] [PubMed] [Google Scholar]
- Tovée M. J., Rolls E. T., Treves A., Bellis R. P. Information encoding and the responses of single neurons in the primate temporal visual cortex. J Neurophysiol. 1993 Aug;70(2):640–654. doi: 10.1152/jn.1993.70.2.640. [DOI] [PubMed] [Google Scholar]
- Treisman A. M., Gelade G. A feature-integration theory of attention. Cogn Psychol. 1980 Jan;12(1):97–136. doi: 10.1016/0010-0285(80)90005-5. [DOI] [PubMed] [Google Scholar]
- Treisman A. The binding problem. Curr Opin Neurobiol. 1996 Apr;6(2):171–178. doi: 10.1016/s0959-4388(96)80070-5. [DOI] [PubMed] [Google Scholar]
- Vaadia E., Haalman I., Abeles M., Bergman H., Prut Y., Slovin H., Aertsen A. Dynamics of neuronal interactions in monkey cortex in relation to behavioural events. Nature. 1995 Feb 9;373(6514):515–518. doi: 10.1038/373515a0. [DOI] [PubMed] [Google Scholar]
- WERNER G., MOUNTCASTLE V. B. NEURAL ACTIVITY IN MECHANORECEPTIVE CUTANEOUS AFFERENTS: STIMULUS-RESPONSE RELATIONS, WEBER FUNCTIONS, AND INFORMATION TRANSMISSION. J Neurophysiol. 1965 Mar;28:359–397. doi: 10.1152/jn.1965.28.2.359. [DOI] [PubMed] [Google Scholar]
- Zohary E., Shadlen M. N., Newsome W. T. Correlated neuronal discharge rate and its implications for psychophysical performance. Nature. 1994 Jul 14;370(6485):140–143. doi: 10.1038/370140a0. [DOI] [PubMed] [Google Scholar]
- deCharms R. C., Merzenich M. M. Primary cortical representation of sounds by the coordination of action-potential timing. Nature. 1996 Jun 13;381(6583):610–613. doi: 10.1038/381610a0. [DOI] [PubMed] [Google Scholar]
- von der Malsburg C. Binding in models of perception and brain function. Curr Opin Neurobiol. 1995 Aug;5(4):520–526. doi: 10.1016/0959-4388(95)80014-x. [DOI] [PubMed] [Google Scholar]
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