LINEAR AND NONLINEAR DYNAMICS OF RECEPTIVE FIELDS IN PRIMARY VISUAL CORTEX A thesis presented to the faculty of Weill Graduate School of Medical Science of Cornell University in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Michael Anthony Repucci Weill Graduate School of Medical Science of Cornell University 1300 York Avenue, Room LC-811, New York, NY 10021 January 19, 2005 © 2005 Michael Anthony Repucci ABSTRACT We investigated the linear and nonlinear spatiotemporal dynamics of receptive fields in the primary visual cortex (a.k.a V1, striate cortex, or area 17) in cats and monkeys We examined the spatial processing of V1 neurons and, at the same time, the dynamics of the visual receptive field, in a manner which could distinguish between the linear and nonlinear parts of the neuronal response, and would permit characterization of the heterogeneous responses of V1 neurons To achieve these goals, we designed a pseudorandom stimulus with multiple spatial regions and strong orientation signals, and used it to investigate first- and second-order response kernels, and to characterize the V1 receptive field under a rigorous mathematical framework The parameters of the stimulus were varied across orientation, spatial phase, or spatial frequency The linear dynamics described by the first-order response kernels of V1 neurons, while relatively heterogeneous, are largely in agreement with reports in the literature The nonlinear dynamics described by the second-order response kernels of V1 neurons are significant in most neurons, and include gain controls and nonlinearities in both orientation and spatial frequency tuning that cannot be described by feedforward inputs or simple static nonlinearity models Moreover, the nonlinear dynamics of spatial phase are intricately linked to the processing of motion and direction selectivity However, the nonlinear dynamic responses of V1 neurons are very heterogeneous, and many issues remain unanswered regarding how the different stimulus attributes are represented and bound together by cortical networks i ACKNOWLEDGMENTS I am indebted to a great many people for their help in preparing, performing, and completing this research Firstly, I would like to thank my thesis advisor Jonathan Victor, whose intelligence is only exceeded by his patience and a true dedication to his work and his students I sincerely thank Keith Purpura, who has been a voice of reason and a source of many valuable conversations, both scientific and otherwise What I owe to Ferenc Mechler, for his help and encouragement, I can never repay, and so I offer my deepest thanks From other lab members, past and present, I have received much help and advice over the years, to which I am eternally thankful The words of Steve Kalik were especially helpful: “Do not wait until the end to start your analyses!” While I would have been well served to start even earlier than I did, I thank him immensely for these words of wisdom To all my friends and family, who have little or no idea exactly what it is I (even if I explained it more than once), I thank you for your love, support, and encouragement To have a sense, as I do, that one is surrounded by people who care for and respect you is invaluable But I owe special thanks to my parents for having encouraged me from birth to always ask “Why?” Lastly, I would like to thank Sarah, my “love” and my wife, who made this all possible Without her love and presence, through good times and through bad, none of the struggle would have been worthwhile I would be half of what I am without her—she makes my life complete For me, she is the answer to that question that I always ask ii TABLE OF CONTENTS ACKNOWLEDGMENTS i LIST OF FIGURES iv LIST OF EQUATIONS ix CHAPTER 1: INTRODUCTION ORGANIZATION OF THE THESIS BASIC CHARACTERISTICS AND MODELS OF THE V1 RECEPTIVE FIELD SPATIAL DYNAMICS AND NONLINEARITIES IN V1 RECEPTIVE FIELDS DYNAMICS OF ATTRIBUTE TUNING IN THE V1 RECEPTIVE FIELD CLASSICAL/NON-CLASSICAL V1 RECEPTIVE FIELD NONLINEARITIES MOTIVATIONS AND GOALS FOR THIS THESIS WORK 12 CHAPTER 2: METHODS 14 SURGERY AND PHYSIOLOGICAL MAINTENANCE LESIONS, EUTHANASIA, AND HISTOLOGY ELECTROPHYSIOLOGY AND RECEPTIVE FIELD CHARACTERIZATION M-SEQUENCE STIMULUS PARADIGM M-SEQUENCE ANALYSIS AND RESPONSE KERNEL ESTIMATION RECEPTIVE FIELD MODELS DATA PROCESSING 14 15 16 19 21 24 26 CHAPTER 3: DYNAMICS OF ORIENTATION TUNING 32 METHODS 32 RESULTS 33 Linear Dynamics 36 Nonlinear Dynamics 48 Interactions between the CRF and NCRF .49 Interactions within the CRF 68 Static Nonlinearity Models 79 CHAPTER 4: DYNAMICS OF SPATIAL FREQUENCY TUNING .90 METHODS 90 RESULTS 92 Linear Dynamics 93 Nonlinear Dynamics 99 Interactions between the CRF and NCRF 100 Interactions within the CRF 103 Static Nonlinearity Models .108 CHAPTER 5: DYNAMICS OF SPATIAL PHASE TUNING 109 METHODS 109 RESULTS 110 Linear Dynamics .111 Nonlinear Dynamics 117 Interactions between the CRF and NCRF 119 Interactions within the CRF 120 Static Nonlinearity Models .127 CHAPTER 6: DISCUSSION 128 LINEAR DYNAMICS 129 Orientation Tuning 130 Spatial Frequency Tuning 132 iii Spatial Phase Tuning 134 Implications of Attribute Tuning .135 NONLINEAR DYNAMICS 136 Interactions Between the CRF and NCRF 137 Interactions Within the CRF .138 Orientation Tuning 138 Spatial Frequency Tuning 140 Spatial Phase Tuning 141 Implications of Attribute Tuning 144 STATIC NONLINEARITY MODELS 145 APPENDIX: NON-BINARY M-SEQUENCES 150 REFERENCES .153 iv LIST OF FIGURES Figure Data flow diagram for visual stimulus generation, electrophysiological recording, and online data collection 18 Figure Patch size tuning (area-summation) curve overlaid with annulus size tuning curve shows a close correspondence between the size of the receptive field as measured with patches or annuli (“B” is a blank stimulus of mean luminance; error bars are +/-SEM) .19 Figure A few frames of the m-sequence stimulus, which highlight the spatial and temporal aspects of the stimulus 20 Figure Static nonlinearities used in models of the CRF 26 Figure Examples of difference-of-Gaussians (DOG) fits to size tuning curves (error bars are +/SEM) 35 Figure Distribution of the suppression index (SI) versus CRF size shows a weak but significant negative correlation 36 Figure Distribution of the suppression index (SI) versus F1/F0 shows a weak but significant positive correlation 36 Figure First-order kernels from a typical neuron in response to the standard orientation space msequence demonstrate separable dynamics of orientation tuning in the CRF (left), and lack orientation-dependent spike rate modulations in the NCRF (right) 38 Figure Population analysis of enhancement/suppression relative to the blank response shows an early enhancement of responses to oriented gratings (about 10 ms before the peak response, tpeak), followed by a rapid suppression that is stronger at orientations less than 90 degrees from the preferred orientation At is the peak-to-trough height derived from a dynamic orientation tuning curve (see Figure 8), Rtmin is the blank-to-trough distance (where Rtmin