Abstract
Prominent models of spike trains assume only one source of variability – stochastic (Poisson) spiking – when stimuli and behavior are fixed. However, spike trains may also reflect variability due to internal processes such as planning. For example, we can plan a movement at one point in time and execute it at some arbitrary later time. Neurons involved in planning may thus share an underlying time course that is not precisely locked to the actual movement. Here we combine the standard Linear-Nonlinear-Poisson (LNP) model with Dynamic Time Warping (DTW) to account for shared temporal variability. When applied to recordings from macaque premotor cortex, we find that time warping considerably improves predictions of neural activity. We suggest that such temporal variability is a widespread phenomenon in the brain which should be modeled.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aldworth, Z.N., Miller, J.P., Gedeon, T., Cummins, G.I., Dimitrov, A.G. (2005). Dejittered spike-conditioned stimulus waveforms yield improved estimates of neuronal feature selectivity and spike-timing precision of sensory interneurons. The Journal of Neuroscience, 25(22), 5323–5332. https://doi.org/10.1523/JNEUROSCI.0359-05.2005.
Aldworth, Z.N., Dimitrov, A.G., Cummins, G.I., Gedeon, T., Miller, J.P. (2011). Temporal encoding in a nervous system. PLoS Computational Biology, 7(5), e1002041–e1002041. https://doi.org/10.1371/journal.pcbi.1002041.
Berndt, D., & Clifford, J. (1994). Using dynamic time warping to find patterns in time series. Workshop on Knowledge Knowledge Discovery in Databases, 398, 359–370.
Buesing, L., Macke, J.H., Sahani, M. (2012). Learning stable, regularised latent models of neural population dynamics. Network: Computation in Neural Systems, 23(1-2), 24–47. https://doi.org/10.3109/0954898X.2012.677095.
Carandini, M. (2004). Amplification of trial-to-trial response variability by neurons in visual cortex. PLoS Biology, 2(9), e264–e264. https://doi.org/10.1371/journal.pbio.0020264.
Chase, S.M., Schwartz, A.B., Kass, R.E. (2010). Latent inputs improve estimates of neural encoding in motor cortex. The Journal of Neuoscience, 30(41), 13,873–13,882. https://doi.org/10.1523/JNEUROSCI.2325-10.2010.
Churchland, M.M., & Shenoy, K.V. (2007). Temporal complexity and heterogeneity of single-neuron activity in premotor and motor cortex. Journal of Neurophysiology, 97(6), 4235–4257. https://doi.org/10.1152/jn.00095.2007.
Cisek, P., & Kalaska, J.F. (2004). Neural correlates of mental rehearsal in dorsal premotor cortex. Nature, 431(7011), 993–996. https://doi.org/10.1038/nature03005.
Cisek, P., & Kalaska, J.F. (2005). Neural correlates of reaching decisions in dorsal premotor cortex: specification of multiple direction choices and final selection of action. Neuron, 45(5), 801–814. https://doi.org/10.1016/j.neuron.2005.01.027.
Cohen, M.R., & Maunsell, J.H.R. (2009). Attention improves performance primarily by reducing interneuronal correlations. Nature Neuroscience, 12(12), 1594–1600. https://doi.org/10.1038/nn.2439.
Crammond, D.J., & Kalaska, J.F. (2000). Prior information in motor and premotor cortex: activity during the delay period and effect on pre-movement activity. Journal of Neurophysiology, 84(2), 986–1005.
de Ruyter van Steveninck, RR, Lewen, G.D., Strong, S.P., Köberle, R., Bialek, W. (1997). Reproducibility and variability in neural spike trains. Science, 275(5307), 1805–1808. https://doi.org/10.1126/science.275.5307.1805.
Dempster, A.P., Laird, N.M., Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 38, 1–38.
Fernandes, H.L., Stevenson, I.H., Phillips, A.N., Segraves, M.A., Kording, K.P. (2013). Saliency and saccade encoding in the frontal eye field during natural scene search. Cerebral cortex (New York NY), 1991, 1–14. https://doi.org/10.1093/cercor/bht179.
Gold, J.I., & Shadlen, M.N. (2007). The neural basis of decision making. Annual Review of Neuroscience, 30, 535–574. https://doi.org/10.1146/annurev.neuro.29.051605.113038.
Gollisch, T. (2006). Estimating receptive fields in the presence of spike-time jitter. Network (Bristol England), 17(2), 103–129. https://doi.org/10.1080/09548980600569670.
Goris, R.L.T, Movshon, J.A., Simoncelli, E.P. (2014). Partitioning neuronal variability. Nature Neuroscience (April). https://doi.org/10.1038/nn.3711.
Guo, Z.V., Inagaki, H.K., Daie, K., Druckmann, S., Gerfen, C.R., Svoboda, K. (2017). Maintenance of persistent activity in a frontal thalamocortical loop. Nature, 545(7653), 181–186. https://doi.org/10.1038/nature22324. http://www.nature.com/doifinder/10.1038/nature22324.
Haith, A.M., Pakpoor, J., Krakauer, J.W. (2016). Independence of movement preparation and movement initiation. Journal of Neuroscience, 36(10), 3007–3015. https://doi.org/10.1523/JNEUROSCI.3245-15.2016.
Hubel, D.H., & Wiesel, T.N. (1962). Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. The Journal of Physiology, 160, 106–154.
Kisley, M.A., & Gerstein, G.L. (1999). Trial-to-trial variability and state-dependent modulation of auditory-evoked responses in cortex. Journal of Neuroscience, 19(23), 10,451–10,460.
Kollmorgen, S., & Hahnloser, R.H.R. (2014). Dynamic alignment models for neural coding. PLoS Computational Biology, 10(3), e1003508–e1003508. https://doi.org/10.1371/journal.pcbi.1003508.
Lakshmanan, K.C., Sadtler, P.T., Tyler-Kabara, E.C., Batista, A.P., Yu, B.M. (2015). Extracting low-dimensional latent structure from time series in the presence of delays. Neural Computation, 27(9), 1825–1856. https://doi.org/10.1162/NECO_a_00759.
Latimer, K.W., Yates, J.L., Meister, M.L.R., Huk, A.C., Pillow, J.W. (2015). Single-trial spike trains in parietal cortex reveal discrete steps during decision-making. Science, 349(6244), 184–187. https://doi.org/10.1126/science.aaa4056.
Lawhern, V., Wu, W., Hatsopoulos, N., Paninski, L. (2010). Population decoding of motor cortical activity using a generalized linear model with hidden states. Journal of Neuroscience Methods, 189(2), 267–280. https://doi.org/10.1016/j.jneumeth.2010.03.024.
Lin, I.C., Okun, M., Carandini, M., Harris, K. D. (2015). The nature of shared cortical variability. Neuron, 87(3), 1–13. https://doi.org/10.1016/j.neuron.2015.06.035.
Mitchell, J.F., Sundberg, K.A., Reynolds, J.H. (2009). Spatial attention decorrelates intrinsic activity fluctuations in macaque area V4. Neuron, 63(6), 879–888. https://doi.org/10.1016/j.neuron.2009.09.013.
Nelder, J.A., & Baker, R.J. (1972). Generalized linear models. Encyclopedia of Statistical Sciences.
Nordstrom, M., Fuglevand, A., Enoka, R. (1992). Estimating the strength of common input to human motoneurons from the cross-correlogram. The Journal of Physiology, 453, 547–574.
Okun, M., Steinmetz, N.A., Cossell, L., Iacaruso, M.F., Ko, H., Barthó, P., Moore, T., Hofer, S.B., Mrsic-Flogel, T.D., Carandini, M., Harris, K.D. (2015). Diverse coupling of neurons to populations in sensory cortex. Nature. https://doi.org/10.1038/nature14273.
Perez, O., Kass, R.E., Merchant, H. (2013). Trial time warping to discriminate stimulus-related from movement-related neural activity. Journal of Neuroscience Methods, 212(2), 203–210. https://doi.org/10.1016/j.jneumeth.2012.10.019.
Pfau, D., Pnevmatikakis, E.A., Paninski, L. (2013). Robust learning of low-dimensional dynamics from large neural ensembles. In Burges, C.J.C., Bottou, L., Welling, M., Ghahramani, Z., Weinberger, K.Q. (Eds.) Advances in neural information processing systems (Vol. 26, pp. 2391–2399). Red Hook: Curran Associates, Inc.
Pillow, J.W., Shlens, J., Paninski, L., Sher, A., Litke, A.M., Chichilnisky, E.J., Simoncelli, E.P. (2008). Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature, 454(7207), 995–999. https://doi.org/10.1038/nature07140.
Rabinowitz, N.C., Goris, R.L., Cohen, M., Simoncelli, E. (2015). Attention stabilizes the shared gain of V4 populations. eLife, 4, e08998–e08998. https://doi.org/10.7554/eLife.08998.
Ramkumar, P., Lawlor, P.N., Glaser, J.I., Wood, D.K., Phillips, A.N., Segraves, M.A., Kording, K.P. (2016). Feature-based attention and spatial selection in frontal eye fields during natural scene search. Journal of Neurophysiology, 116 (3), 1328–1343. https://doi.org/10.1152/jn.01044.2015. http://jn.physiology.org/lookup/doi/10.1152/jn.01044.2015.
Reich, D.S., Victor, J.D., Knight, B.W., Ozaki, T., Kaplan, E. (1997). Response variability and timing precision of neuronal spike trains in vivo. Journal of Neurophysiology, 77(5), 2836–2841.
Sakoe, H., & Chiba, S. (1978). Dynamic programming algorithm optimization for spoken word recognition. ASSP-26, 26(1), 43–49. https://doi.org/10.1109/TASSP.1978.1163055.
Shenoy, K.V., Sahani, M., Churchland, M.M. (2013). Cortical control of arm movements: a dynamical systems perspective. Annual Review of Neuroscience, 36(1), 337–359. https://doi.org/10.1146/annurev-neuro-062111-150509.
Siegel, M., Buschman, T.J., Miller, E.K. (2015). Cortical information flow during flexible sensorimotor decisions. Science, 348(6241), 1352–1355. https://doi.org/10.1126/science.aab0551.
Stevenson, I.H., Rebesco, J.M., Miller, L.E., Körding, K.P. (2008). Inferring functional connections between neurons. Current Opinion in Neurobiology, 18(6), 582–588. https://doi.org/10.1016/j.conb.2008.11.005.
Stevenson, I.H., London, B.M., Oby, E.R., Sachs, N.A., Reimer, J., Englitz, B., David, S.V., Shamma, S.A., Blanche, T.J., Mizuseki, K., Zandvakili, A., Hatsopoulos, N.G., Miller, L.E., Kording, K.P. (2012). Functional connectivity and tuning curves in populations of simultaneously recorded neurons . PLoS Computational Biology, 8(11), e1002775–e1002775. https://doi.org/10.1371/journal.pcbi.1002775.
Ventura, V., Cai, C., Kass, R.E. (2005). Trial-to-trial variability and its effect on time-varying dependency between two neurons. Journal of Neurophysiology, 94(4), 2928–2939.
Victor, J.D. (2005). Spike train metrics. Current Opinion in Neurobiology, 15(5), 585–592. https://doi.org/10.1016/j.conb.2005.08.002.
Victor, J.D., & Purpura, K.P. (1996). Nature and precision of temporal coding in visual cortex: a metric-space analysis. Journal of Neurophysiology, 76(2), 1310–1326.
Vidne, M., Ahmadian, Y., Shlens, J., Pillow, J.W., Kulkarni, J., Litke, A.M., Chichilnisky, E.J., Simoncelli, E., Paninski, L. (2012). Modeling the impact of common noise inputs on the network activity of retinal ganglion cells. Journal of Computational Neuroscience, 33(1), 97–121. https://doi.org/10.1007/s10827-011-0376-2.
Weinrich, M., Wise, S.P., Mauritz, K.H. (1984). A neurophysiological study of the premotor cortex in the rhesus monkey. Brain: A Journal of Neurology, 2, 385–414. https://doi.org/10.1093/brain/107.2.385.
Wurtz, R.H. (1969a). Comparison of effects of eye movements and stimulus movements on striate cortex neurons of the monkey. Journal of Neurophysiology, 32(98), 994–994.
Wurtz, R.H. (1969b). Visual receptive fields of striate cortex neurons in awake monkeys. Journal of Neurophysiology, 32(5), 727– 742.
Yu, B.M., Cunningham, J.P., Santhanam, G., Ryu, S.I., Shenoy, K.V., Sahani, M. (2009). Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity. Journal of Neurophysiology, 102(1), 614–635. https://doi.org/10.1152/jn.90941.2008.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interests
The authors declare that they have no conflict of interest.
Additional information
Action Editor: Simon R Schultz
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Lawlor, P.N., Perich, M.G., Miller, L.E. et al. Linear-nonlinear-time-warp-poisson models of neural activity. J Comput Neurosci 45, 173–191 (2018). https://doi.org/10.1007/s10827-018-0696-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10827-018-0696-6