Inhibition stabilized network model in the primary visual cortex Studies on conditions to achieve surround suppression and properties of spontaneous and sensory-driven activities Jun Zhao Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2012 © 2012 Jun Zhao All Rights Reserved Abstract Inhibition stabilized network model in the primary visual cortex Jun Zhao In this paper, we studied neural networks of both excitatory and inhibitory populations with inhibition stabilized network (ISN) models. In ISN models, the recurrent excitatory connections are so strong that the excitatory sub-network is unstable if the inhibitory firing rate is fixed; however, the entire network is stable due to inhibitory connections. In such networks, external input to inhibitory neurons reduced their responses due to the withdrawal of network excitation (Tsodyks et al., 1997). This paradoxical effect of the ISN was observed in recent surround suppression experiments in the primary visual cortex with direct membrane conductance measurements (Ozeki et al., 2009). In our work, we used a linearized rate model of both excitatory and inhibitory populations with weight matrices dependent on the locations of the neurons. We applied this model to study surround suppression effects and searched for networks with appropriated parameters. The same model was also applied in the study of spontaneous activities in awake ferrets. Both studies led to network solutions in the ISN regime, suggesting that ISN mechanisms might play an important role in the neural circuitry in the primary visual cortex. Table of Contents Table of Contents ............................................................................................................................. i List of Figures ................................................................................................................................ iv Acknowledgements ........................................................................................................................ vi Chapter I: Introduction and Literature Review ............................................................................... 1 1. Surround suppression effects in the primary visual cortex (V1) .......................................... 1 2. Spontaneous and sensory-driven activities in the primary visual cortex of awake ferrets ... 6 3. Properties of Inhibition Stabilized Networks (ISN) .............................................................. 8 Chapter II: Conditions to achieve surround suppression in the primary visual cortex ................. 12 1. Linear rate model with spatially invariant weight matrix ................................................... 12 2. Surround suppression constraints on the response curve .................................................... 15 3. Analytic solutions with surround suppression boundary conditions .................................. 18 4. General numerical solutions with parameter space search ................................................. 19 5. Amplification at critical filter frequency ............................................................................ 23 6. Strong surround suppression generated by stable sparse networks .................................... 25 7. Effects of different input functions with different blurring widths..................................... 27 8. Spatial oscillations in population activity ........................................................................... 29 9. Summary ............................................................................................................................. 31 ~ i ~ Chapter III: Properties of spontaneous and sensory-driven activities in the primary visual cortex of awake ferret ........................................................................................................................... 34 1. Experimental procedure and data acquisition ..................................................................... 34 2. Principal Component Analysis of the spike trains and the dominance of a spatially long- ranged principal component ................................................................................................. 35 3. Development of spontaneous oscillation ............................................................................ 39 4. Spontaneous oscillation in networks with surround suppression ....................................... 41 5. Modulations of the auto-covariance by sensory stimuli ..................................................... 44 6. Absence of orientation map structure in both spontaneous and sensory-driven activities . 46 7. Summary ............................................................................................................................. 50 Chapter IV: Conclusions and Discussions .................................................................................... 53 Figures in the main text................................................................................................................. 61 References ................................................................................................................................... 123 Appendix A: Structures and Functions of the Visual System..................................................... 129 1. Cortical and sub-cortical structures in the central visual pathway ................................... 129 2. Receptive field structures of neurons in the visual system. .............................................. 131 3. Columnar organization of the visual cortex ...................................................................... 134 Appendix B: Supplemental Information ..................................................................................... 136 1. Properties of Inhibition Stabilized Networks .................................................................... 136 a. Stability of the fixed point........................................................................................... 136 ~ ii ~ b. Effects of increased inhibitory input ........................................................................... 138 2. Linear rate model with spatial dependency ...................................................................... 138 a. Derivation of the steady state solution ........................................................................ 138 b. Steady state solution of 2D model with circular symmetry ........................................ 140 c. Analytic solutions with surround suppression boundary conditions........................... 141 d. Expansion of the connectivity filter in the Fourier space when the network approaches instability...................................................................................................................... 147 e. Relationship between the maximal response stimulus size and the critical stimulus size ...................................................................................................................................... 149 3. Experimental procedure and data acquisition for spontaneous and sensory-driven activity in awake ferret V1 .............................................................................................................. 152 4. Principal Component Analysis of the activity pattern under Dark, Movie and Noise viewing conditions ............................................................................................................. 153 a. The 1st PC mode under Movie and Noise viewing conditions ................................... 153 b. Nested model test ........................................................................................................ 155 5. Mechanisms of Hebbian amplification and properties of normal and non-normal matrices ............................................................................................................................................ 158 a. Hebbian amplification for translation-invariant linear rate models ............................ 158 b. Properties of normal and non-normal matrices ........................................................... 159 Supplemental figures .................................................................................................................. 161 ~ iii ~ List of Figures Figure 1. Typical stimulus configurations for surround suppression experiments. ...................... 62 Figure 2. Mechanisms of the Difference of Gaussian model ........................................................ 63 Figure 3. The Inhibition Stabilized Network model. .................................................................... 65 Figure 4. 휍 subspace of numerical solutions with Gaussian input function ................................. 67 Figure 5. 푊 subspace of numerical solutions with Gaussian input function ................................ 72 Figure 6. Histogram of the amplitude of the 퐸 ← 퐸 connection .................................................. 75 Figure 7. Histogram of the real part of the leading eigenvalue 휆퐿 ................................................ 76 Figure 8. Amplification at network critical filter frequency 푘퐹.................................................... 77 Figure 9. Resonance effects around the critical stimulus size 휍퐹 ................................................. 79 Figure 10. Simulation results of sparse networks. .......................................................................