Skip to main content
SpringerLink
Log in

Improved dimensionally-reduced visual cortical network using stochastic noise modeling

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

In this paper, we extend our framework for constructing low-dimensional dynamical system models of large-scale neuronal networks of mammalian primary visual cortex. Our dimensional reduction procedure consists of performing a suitable linear change of variables and then systematically truncating the new set of equations. The extended framework includes modeling the effect of neglected modes as a stochastic process. By parametrizing and including stochasticity in one of two ways we show that we can improve the systems-level characterization of our dimensionally reduced neuronal network model. We examined orientation selectivity maps calculated from the firing rate distribution of large-scale simulations and stochastic dimensionally reduced models and found that by using stochastic processes to model the neglected modes, we were able to better reproduce the mean and variance of firing rates in the original large-scale simulations while still accurately predicting the orientation preference distribution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Antoulas, T. C. (2005). Approximation of large-scale dynamical systems. Philadelphia: SIAM.

    Book  Google Scholar 

  • Badel, L., Lefort, S., Brette, R., Petersen, C. C., Gerstner, W., & Richardson, M. J. (2008a). Dynamic I–V curves are reliable predictors of naturalistic pyramidal-neuron voltage traces. Journal of Neurophysiology, 99, 656–666.

    Article  Google Scholar 

  • Badel, L., Lefort, S., Berger, T. K., Petersen, C. C., Gerstner, W., & Richardson, M. J. (2008b). Extracting non-linear integrate-and-fire models from experimental data using dynamic I–V curves. Biological Cybernetics, 99, 361–370.

    Article  Google Scholar 

  • Broder, J., Majumder, A., Porter, E., Srinivasamoorthy, G., Keith, C., Lauderdale, J., et al. (2007). Estimating weak ratiometric signals in imaging data. I. Dual-channel data. Journal of the Optical Society of America. A Optics, Image Science and Vision, 24, 2921–2931.

    Article  Google Scholar 

  • Cai, D., Rangan, A. V., & McLaughlin, D. W. (2005). Architectural and synaptic mechanisms underlying coherent spontaneous activity in V1. Proceedings of the National Academy of Sciences of the United States of America, 102, 5868–5873.

    Article  PubMed  CAS  Google Scholar 

  • De Valois, R. L., Albrecht, D. G., & Thorell, L. G. (1982). Spatial frequency selectivity of cells in macaque visual cortex. Vision Research, 22, 545–559.

    Article  PubMed  Google Scholar 

  • Eckart, C., & Young, G. (1936). The approximation of one matrix by another of lower rank. Psychometrika, 1, 211–218.

    Article  Google Scholar 

  • Everson, R. M., Prashanth, A. K., Gabbay, M., Knight, B. W., Sirovich, L., & Kaplan, E. (1998). Representation of spatial frequency and orientation in the visual cortex. Proceedings of the National Academy of Sciences of the United States of America, 95, 8334–8338.

    Article  PubMed  CAS  Google Scholar 

  • FitzHugh, R. (1961). Impulses and Physiological States in Theoretical Models of Nerve Membrane. Biophysical Journal, 1, 445–466.

    Article  PubMed  CAS  Google Scholar 

  • Hodgkin, A., & Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117, 500–544.

    PubMed  CAS  Google Scholar 

  • 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.

    PubMed  CAS  Google Scholar 

  • Huys, Q. J., & Paninski, L. (2009). Smoothing of, and parameter estimation from, noisy biophysical recordings. PLoS Computational Biology, 5, e1000379.

    Article  PubMed  Google Scholar 

  • Huys, Q. J., Ahrens, M. B., & Paninski, L. (2006). Efficient estimation of detailed single-neuron models. Journal of Neurophysiology, 96, 872–890.

    Article  PubMed  Google Scholar 

  • Ikeda, S., & Toyama, K. (2000). Independent component analysis for noisy data—MEG data analysis. Neural Networks, 13, 1063–1074.

    Article  PubMed  CAS  Google Scholar 

  • Jolivet, R., Lewis, T. J., & Gerstner, W. (2004). Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. Journal of Neurophysiology, 92, 959–976.

    Article  PubMed  Google Scholar 

  • Kistler, W., Gerstner, W., & van Hemmen, J. L. (1997). Reduction of the Hogkin-Huxley equations to a single-variable threshold model. Journal of Neural Computation, 9, 1015–1045.

    Article  Google Scholar 

  • Knight, B. W., Omurtag, A., & Sirovich, L. (2000). The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result. Journal of Neural Computation, 12, 1045–1055.

    Article  CAS  Google Scholar 

  • Lorenz, E. N. (1956). Empirical orthogonal functions and statistical weather prediction. In: Scientific Report. Cambridge, MA: Statistical Forecasting Project, MIT.

  • Lumley, J. L. (1967). The structure of inhomogeneous turbulent flows. In A. M. Yaglom & V. I. Tatrski (Eds.), Atmospheric turbulence and radio wave propagation. Moscow: Nauka.

    Google Scholar 

  • Makeig, S., Bell, A. J., Jung, T.-P., & Sejnowski, T. J. (1996). Independent component analysis of electroencephalographic data. Advances in Neural Information Processing Systems, 8, 145–151.

    Google Scholar 

  • McKeown, M. J., & Sejnowski, T. J. (1998). Independent component analysis of fMRI data: examining the assumptions. Human Brain Mapping, 6, 368–372.

    Article  PubMed  CAS  Google Scholar 

  • McLaughlin, D., Shapley, R., Shelley, M., & Wielaard, D. J. (2000). A neuronal network model of macaque primary visual cortex (V1): orientation selectivity and dynamics in the input layer 4Calpha. Proceedings of the National Academy of Sciences of the United States of America, 97, 8087–8092.

    Article  PubMed  CAS  Google Scholar 

  • Mitra, P. P., & Pesaran, B. (1999). Analysis of dynamic brain imaging data. Biophysical Journal, 76, 691–708.

    Article  PubMed  CAS  Google Scholar 

  • Nagumo, J. S., Arimoto, S., & Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axons. Proceedings of the IRE, 50, 2061–2070.

    Article  Google Scholar 

  • Percival, D., Walden, A. (1993) Spectral analysis for physical applications. Cambridge University Press.

  • Pillow, J. W., Shlens, J., Paninski, L., Sher, A., Litke, A. M., Chichilnisky, E. J., et al. (2008). Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature, 454, 995–999.

    Article  PubMed  CAS  Google Scholar 

  • Rangan, A. V., Cai, D., & McLaughlin, D. W. (2005). Modeling the spatiotemporal cortical activity associated with the line-motion illusion in primary visual cortex. Proceedings of the National Academy of Sciences of the United States of America, 102, 18793–18800.

    Article  PubMed  CAS  Google Scholar 

  • Rudolph, M., & Destexhe, A. (2003). Characterization of subthreshold voltage fluctuations in neuronal membranes. Neural Computation, 15, 2577–2618.

    Article  PubMed  CAS  Google Scholar 

  • Rudolph, M., & Destexhe, A. (2004). Inferring network activity from synaptic noise. Journal of Physiology, Paris, 98, 452–466.

    Article  PubMed  Google Scholar 

  • Salinas, E., & Sejnowski, T. J. (2000). Impact of correlated synaptic input on output firing rate and variability in simple neuronal models. Journal of Neuroscience, 20, 6193–6209.

    PubMed  CAS  Google Scholar 

  • Shelley, M., & McLaughlin, D. (2002). Coarse-grained reduction and analysis of a network model of cortical response: I. Drifting grating stimuli. Journal of Computational Neuroscience, 12, 97–122.

    Article  PubMed  Google Scholar 

  • Shelley, M., McLaughlin, D., Shapley, R., & Wielaard, J. (2002). States of high conductance in a large-scale model of the visual cortex. Journal of Computational Neuroscience, 13, 93–109.

    Article  PubMed  Google Scholar 

  • Sirovich, L. (1987). Turbulence and the dynamics of coherent structures, Parts I–III. Quarterly of Applied Mathematics, 45, 561–590.

    Google Scholar 

  • Sirovich, L., & Rodriguez, J. D. (1987). Coherent structures and chaos: A model problem. Physics Letters A, 120, 211–214.

    Article  CAS  Google Scholar 

  • Sornborger, A., Sirovich, L., & Morley, G. (2003). Extraction of periodic multivariate signals: mapping of voltage-dependent dye fluorescence in the mouse heart. IEEE Transactions on Medical Imaging, 22, 1537–1549.

    Article  PubMed  Google Scholar 

  • Sornborger, A., Yokoo, T., Delorme, A., Sailstad, C., & Sirovich, L. (2005). Extraction of the average and differential dynamical response in stimulus-locked experimental data. Journal of Neuroscience Methods, 141, 223–229.

    Article  PubMed  CAS  Google Scholar 

  • Spitzer, H., & Hochstein, S. (1985). Simple- and complex-cell response dependences on stimulation parameters. Journal of Neurophysiology, 53, 1244–1265.

    PubMed  CAS  Google Scholar 

  • Tao, L., & Sornborger, A. T. (2010). Dimensionally-reduced visual cortical network model predicts network response and connects system- and cellular-level descriptions. Journal of Computational Neuroscience, 28, 91–106.

    Article  PubMed  Google Scholar 

  • Tao, L., Shelley, M., McLaughlin, D., & Shapley, R. (2004). An egalitarian network model for the emergence of simple and complex cells in visual cortex. Proceedings of the National Academy of Sciences of the United States of America, 101, 366–371.

    Article  PubMed  CAS  Google Scholar 

  • Tao, L., Cai, D., McLaughlin, D. W., Shelley, M. J., & Shapley, R. (2006). Orientation selectivity in visual cortex by fluctuation-controlled criticality. Proceedings of the National Academy of Sciences of the United States of America, 103, 12911–12916.

    Article  PubMed  CAS  Google Scholar 

  • Wang, X. J., & Buzsaki, G. (1996). Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. Journal of Neuroscience, 16, 6402–6413.

    PubMed  CAS  Google Scholar 

  • Wielaard, D. J., Shelley, M., McLaughlin, D., & Shapley, R. (2001). How simple cells are made in a nonlinear network model of the visual cortex. Journal of Neuroscience, 21, 5203–5211.

    PubMed  CAS  Google Scholar 

  • Xu, J., Sornborger, A. T., Lee, J. K., & Shen, P. (2008). Drosophila TRPA channel modulates sugar-stimulated neural excitation, avoidance and social response. Nature Neuroscience, 11, 676–682.

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

Louis Tao would like to acknowledge the hospitality of the University of Georgia Department of Mathematics and Andrew Sornborger would like to acknowledge the hospitality and support of the Center for Bioinformatics of the College of Life Sciences of Peking University.

This work was supported by NIH NIBIB 005432 (ATS), NIH NINDS 070159 (ATS) and the National Basic Research Program of China (973 Program 2011CB809105) (LT).

Author information

Authors and Affiliations

  1. Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetics Engineering, College of Life Sciences, Peking University, Number 5 Summer Palace Road, Beijing, 100871, People’s Republic of China

    Louis Tao

  2. Department of Biochemistry and Molecular Biology, University of Georgia, B122 Life Sciences Building, Green Street, Athens, GA, 30602, USA

    Jeremy Praissman

  3. Department of Mathematics and Faculty of Engineering, University of Georgia, 500 D.W. Brooks Drive, Athens, GA, 30602, USA

    Andrew T. Sornborger

  4. Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, 323 Martin Luther King, Jr. Blvd., Newark, NJ, 07102, USA

    Louis Tao

Authors
  1. Louis Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeremy Praissman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrew T. Sornborger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Louis Tao or Andrew T. Sornborger.

Additional information

Action Editor: David Golomb

Electronic supplementary material

Below is the link to the electronic supplementary material.

ESM 1

(DOC 17 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tao, L., Praissman, J. & Sornborger, A.T. Improved dimensionally-reduced visual cortical network using stochastic noise modeling. J Comput Neurosci 32, 367–376 (2012). https://doi.org/10.1007/s10827-011-0359-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-011-0359-3

Keywords

Search

Navigation