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Spatiotemporal dynamics in a model of turtle visual cortex
Neurocomputing 32}33 (2000) 479}486
Spatiotemporal dynamics in a model of turtle visual cortex Zoran Nenadic *, Bijoy Ghosh, Philip Ulinski Department of Systems Science and Mathematics, Washington University, Saint Louis, MO 63130-4899, USA Department of Systems Science and Mathematics, Washington University, Saint Louis, MO 63130, USA Department of Organismal Biology and Anatomy, University of Chicago, Chicago, IL 60637, USA Accepted 13 January 2000
Abstract This paper presents simulations of a small patch of the turtle's visual cortex with 20 pyramidal cells and four smooth stellate cells. Our model captures the basic geometry and temporal structure of the visual cortex and has been shown to generate propagating waves of activity that contain information about a moving stimulus. 2000 Elsevier Science B.V. All rights reserved. Keywords: Turtle visual cortex; Propagating wave of activity; Moving stimulus
1. Introduction The visual cortex of freshwater turtles contains three layers. The intermediate layer 2 principally contains pyramidal cells with dendrites that extend into layers 1 and 3. The outer layer 1 and inner layer 3 contain mainly inhibitory interneurons. Geniculate a!erents make excitatory synapses upon the dendrites and somata of pyramidal cells and the dendrites and somata of layer 1 neurons. Studies using both multiple electrode recording techniques [9] and voltage-sensitive dye techniques [7,8], demonstrate that visual stimuli produce waves of activity that propagate along the rostrocaudal and mediolateral axes of the cortex. These waves have been compared in the literature [3] to the waves generated in a vibrating membrane, such as a `druma [8]. This study uses a minimal, or `toya model of turtle visual cortex to study the cellular origin and properties of these propagating waves. The model is a rectangular array of 20
* Corresponding author. E-mail address: [email protected] (Z. Nenadic). 0925-2312/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 2 3 1 2 ( 0 0 ) 0 0 2 0 2 - 2
480
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
pyramidal neurons and four inhibitory interneurons. Each neuron is a compartmental model with biophysically realistic conductances. The input to the model is an array of "ve geniculate inputs. The study demonstrates that (1) excitatory interactions within the cortex generate a propagating wave in the model that duplicates the general features of the propagating wave in the real cortex, and (2) the cortical dynamics in even this simple model are su$cient to capture the velocity of a drifting square wave grating.
2. Model description The model represents a 2;12 mm, rectangular region of turtle visual cortex. It contains 20 pyramidal neurons, organized in 4;5 matrix array (Fig. 1). Four inhibitory neurons are interspersed between the pyramidal cells. Each pyramidal neuron makes excitatory synapses on each of its nearest neighbors (Fig. 2). These include synapses upon both pyramidal neurons and inhibitory neurons. Inhibitory neurons make inhibitory synapses upon all neurons within their spheres of in#uence (Fig. 3). Five geniculate axons run across the cortex, from medial to lateral, consistent with the known anatomy of the system [5]. Each geniculate a!erent makes excitatory synapses upon each pyramidal neuron and each inhibitory neuron along its trajectory. Each neuron is represented by a 16-compartment model based on the anatomy of real pyramidal neurons and inhibitory interneurons (Fig. 4). Each compartment is represented by a standard membrane equation. All compartments contain a leakage conductance. The soma compartments of both types of neurons contain fast sodium and delayed recti"er conductances which are speci"ed by the Hodgkin}Huxley kinetic schemes. Geniculocortical synapses are known to be glutaminergic and access the
Fig. 1. Topology of the model.
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
481
Fig. 2. Internal structure of the model.
Fig. 3. Sphere of in#uence of the inhibitory neuron.
AMPA subtype of glutamate receptor [4]. Corticocortical synapses are also glutaminergic but access both AMPA and NMDA subtypes of glutamate receptors. In this initial study, only the AMPA conductance is included. Inhibitory interneurons are GABAergic and access both GABAa and GABAb subtypes of GABA receptors, but only GABAa conductances are included in this model. Propagation times between neurons are calculated using the distance between a pair of neurons and conduction velocities. The conduction velocity for geniculate a!erents in turtle visual cortex has been measured at 0.18 m/s [2]. Corticocortical connections are given conduction velocities of 0.05 m/s, consistent with measurements of propagating waves in turtle visual cortex [7] and the conduction velocities for axons of inhibitory interneurons in rat cortex [6]. Visual stimuli have been simulated by activating
482
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
Fig. 4. Compartmental models of pyramidal cell (left) and smooth stellate cell (right).
individual geniculate a!erents or sequences of a!erents in particular temporal patterns.
3. Activation of a single geniculate a4erent produces a propagating wave of activity in the model cortex Presentation of a visual stimulus in a localized region of visual space is simulated by activating a single geniculate a!erent. Activation of a single channel generates several action potentials in all of the cortical neurons postsynaptic to the geniculate a!erent and produces a wave of activity that propagates initially in both rostral and caudal directions. However, the inhibitory interconnections are strong enough to damp the system and limit the extent of the propagation. Sequences of inputs with constant time delays represent stimuli moving with speci"c velocities and produce richer outputs. Fast velocity signals do not produce signi"cant propagating cortical activity because developing cortical activity is damped by intracortical inhibition. Slow velocity
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
483
Fig. 5. Cortical response showing the propagation of activity in both rostrocaudal (horizontal) and mediolateral (vertical) axes.
Fig. 6. Cortical response showing the propagation of activity and re#ection.
signals demonstrate how geniculate inputs and internal cortical inputs interact to produce a wave of activity that travels along the cortex (Fig. 5). Certain sets of parameters cause a secondary wave of activity that travels across the cortex in the opposite direction. This phenomenon is a re#ection, similar to re#ections that have been observed in turtle visual cortex [8] and in the slice preparation of cat and rat cortex [1]. Certain velocities produce large re#ected waves, resulting in a particularly strong response (Fig. 6). Very slow velocity signals produce a network response that equals the sum of the individual responses.
4. The model cortex codes the velocity of moving spatial patterns The response of the model to a moving spatial pattern has been studied using a drifting half-wave-recti"ed square luminance grating (Fig. 7). The small size of the model did not permit the use of sinusoidal gratings as input stimuli. The luminance, spatial frequency and velocity of the square wave grating are given in dimensionless units because the model is not calibrated to units of visual arc. The spectral composition of the stimulus is characterized by taking the absolute value
484
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
Fig. 7. Spatiotemporal input signal.
of its Fourier transform as a function of both spatial and temporal frequencies (Fig. 8). The response of the model to an input stimulus drifting with a certain velocity is represented as absolute value of Fourier transforms of the membrane potentials produced by all of the neurons in the model. Initial simulations indicate that variations in the output signal along the trajectories of the geniculate a!erents are not signi"cant. So responses along each geniculate a!erent have been averaged prior to calculating the Fourier transforms. The Fourier transform shows a signi"cant peak on a line with a slope equal to the velocity of the signal. There is also a DC o!set and other major peaks that result from interactions between neurons within the cortex (Fig. 8).
5. Conclusion This study shows that a very simple model of a cortical structure that captures the basic geometry and temporal structure of visual cortex can generate propagating waves of activity that contain information about the speed of a small moving stimulus or a patterned stimulus, such as a square wave grating. We are now working on building a larger and more complex model of turtle visual cortex that will contain explicit representations of all three layers based on detailed maps of the spatial distributions of neurons in real cortices. The responses of this model can then be compared to propagating waves of activity obtained from real turtle cortices using
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
485
Fig. 8. The Fourier transforms of the input signal (A), and cortical response (B). Top view of the signal from "gure (A), showing that the peak lies on the line u "vu , where v is the drifting velocity of the R V input signal (C). Top view of the signal form "gure (B), showing the secondary peak lying on the same line (D).
voltage sensitive dyes. This large-scale model will also be used to study the responses of the cortex to more complex visual stimuli. References [1] Y. Chagnac-amitai, B.W. Connors, Horizontal spread of synchronized activity in neocortex and its control by GABA mediated inhibition, J. Neurophysiol. 61 (1989) 747}758. [2] J. F. Colombe, P.S. Ulinski, Temporal dispersion windows in cortical neurons, J. Comput. Neurosci. 7 (1999) 71}87. [3] D.A. Glaser, D. Barch, Motion detection and characterization by an excitable membrane: The `bow wavea model, Neurocomputing 26&27 (1999) 137}146. [4] L.J. Larson-Prior, P.S. Ulinski, N.T. Slater, Excitatory amino acid receptory-mediated transmission in geniculocortical and intracortical pathways within visual cortex, J. Neurophysiol. 66 (1991) 293}306. [5] K.A. Mulligan, P.S. Ulinski, Organization of geniculocortical projections in turtles: isoazimuth lamellae in the visual cortex, J. Comput. Neurol. 296 (1990) 531}547.
486
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
[6] P.A. Salin, D.A. Prince, Electrophysiological mapping of GABAa receptor-mediated inhibition in adult rat somatosensory cortex, J. Neurophysiol. 75 (1991) 293}306. [7] D.M. Senseman, Correspondence between visually evoked voltage sensitive dye signals and synaptic activity recorded in cortical pyramidal cells with intracellular microelectrodes, Vis. Neurosci. 13 (1996) 963}977. [8] D.M. Senseman, Spatiotemporal structure of depolarization spread in cortical pyramidal cell populations evoked by di!use retinal light #ashes, Visual Neurosci. 16 (1999) 65}79. [9] J.C. Prechtl, Visual motion induces synchronous oscillations in turtle visual cortex, Proc. Natl. Acad. Sci. USA 91, 12 467}12 471.
Spatiotemporal dynamics in a model of turtle visual cortex Zoran Nenadic *, Bijoy Ghosh, Philip Ulinski Department of Systems Science and Mathematics, Washington University, Saint Louis, MO 63130-4899, USA Department of Systems Science and Mathematics, Washington University, Saint Louis, MO 63130, USA Department of Organismal Biology and Anatomy, University of Chicago, Chicago, IL 60637, USA Accepted 13 January 2000
Abstract This paper presents simulations of a small patch of the turtle's visual cortex with 20 pyramidal cells and four smooth stellate cells. Our model captures the basic geometry and temporal structure of the visual cortex and has been shown to generate propagating waves of activity that contain information about a moving stimulus. 2000 Elsevier Science B.V. All rights reserved. Keywords: Turtle visual cortex; Propagating wave of activity; Moving stimulus
1. Introduction The visual cortex of freshwater turtles contains three layers. The intermediate layer 2 principally contains pyramidal cells with dendrites that extend into layers 1 and 3. The outer layer 1 and inner layer 3 contain mainly inhibitory interneurons. Geniculate a!erents make excitatory synapses upon the dendrites and somata of pyramidal cells and the dendrites and somata of layer 1 neurons. Studies using both multiple electrode recording techniques [9] and voltage-sensitive dye techniques [7,8], demonstrate that visual stimuli produce waves of activity that propagate along the rostrocaudal and mediolateral axes of the cortex. These waves have been compared in the literature [3] to the waves generated in a vibrating membrane, such as a `druma [8]. This study uses a minimal, or `toya model of turtle visual cortex to study the cellular origin and properties of these propagating waves. The model is a rectangular array of 20
* Corresponding author. E-mail address: [email protected] (Z. Nenadic). 0925-2312/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 2 3 1 2 ( 0 0 ) 0 0 2 0 2 - 2
480
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
pyramidal neurons and four inhibitory interneurons. Each neuron is a compartmental model with biophysically realistic conductances. The input to the model is an array of "ve geniculate inputs. The study demonstrates that (1) excitatory interactions within the cortex generate a propagating wave in the model that duplicates the general features of the propagating wave in the real cortex, and (2) the cortical dynamics in even this simple model are su$cient to capture the velocity of a drifting square wave grating.
2. Model description The model represents a 2;12 mm, rectangular region of turtle visual cortex. It contains 20 pyramidal neurons, organized in 4;5 matrix array (Fig. 1). Four inhibitory neurons are interspersed between the pyramidal cells. Each pyramidal neuron makes excitatory synapses on each of its nearest neighbors (Fig. 2). These include synapses upon both pyramidal neurons and inhibitory neurons. Inhibitory neurons make inhibitory synapses upon all neurons within their spheres of in#uence (Fig. 3). Five geniculate axons run across the cortex, from medial to lateral, consistent with the known anatomy of the system [5]. Each geniculate a!erent makes excitatory synapses upon each pyramidal neuron and each inhibitory neuron along its trajectory. Each neuron is represented by a 16-compartment model based on the anatomy of real pyramidal neurons and inhibitory interneurons (Fig. 4). Each compartment is represented by a standard membrane equation. All compartments contain a leakage conductance. The soma compartments of both types of neurons contain fast sodium and delayed recti"er conductances which are speci"ed by the Hodgkin}Huxley kinetic schemes. Geniculocortical synapses are known to be glutaminergic and access the
Fig. 1. Topology of the model.
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
481
Fig. 2. Internal structure of the model.
Fig. 3. Sphere of in#uence of the inhibitory neuron.
AMPA subtype of glutamate receptor [4]. Corticocortical synapses are also glutaminergic but access both AMPA and NMDA subtypes of glutamate receptors. In this initial study, only the AMPA conductance is included. Inhibitory interneurons are GABAergic and access both GABAa and GABAb subtypes of GABA receptors, but only GABAa conductances are included in this model. Propagation times between neurons are calculated using the distance between a pair of neurons and conduction velocities. The conduction velocity for geniculate a!erents in turtle visual cortex has been measured at 0.18 m/s [2]. Corticocortical connections are given conduction velocities of 0.05 m/s, consistent with measurements of propagating waves in turtle visual cortex [7] and the conduction velocities for axons of inhibitory interneurons in rat cortex [6]. Visual stimuli have been simulated by activating
482
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
Fig. 4. Compartmental models of pyramidal cell (left) and smooth stellate cell (right).
individual geniculate a!erents or sequences of a!erents in particular temporal patterns.
3. Activation of a single geniculate a4erent produces a propagating wave of activity in the model cortex Presentation of a visual stimulus in a localized region of visual space is simulated by activating a single geniculate a!erent. Activation of a single channel generates several action potentials in all of the cortical neurons postsynaptic to the geniculate a!erent and produces a wave of activity that propagates initially in both rostral and caudal directions. However, the inhibitory interconnections are strong enough to damp the system and limit the extent of the propagation. Sequences of inputs with constant time delays represent stimuli moving with speci"c velocities and produce richer outputs. Fast velocity signals do not produce signi"cant propagating cortical activity because developing cortical activity is damped by intracortical inhibition. Slow velocity
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
483
Fig. 5. Cortical response showing the propagation of activity in both rostrocaudal (horizontal) and mediolateral (vertical) axes.
Fig. 6. Cortical response showing the propagation of activity and re#ection.
signals demonstrate how geniculate inputs and internal cortical inputs interact to produce a wave of activity that travels along the cortex (Fig. 5). Certain sets of parameters cause a secondary wave of activity that travels across the cortex in the opposite direction. This phenomenon is a re#ection, similar to re#ections that have been observed in turtle visual cortex [8] and in the slice preparation of cat and rat cortex [1]. Certain velocities produce large re#ected waves, resulting in a particularly strong response (Fig. 6). Very slow velocity signals produce a network response that equals the sum of the individual responses.
4. The model cortex codes the velocity of moving spatial patterns The response of the model to a moving spatial pattern has been studied using a drifting half-wave-recti"ed square luminance grating (Fig. 7). The small size of the model did not permit the use of sinusoidal gratings as input stimuli. The luminance, spatial frequency and velocity of the square wave grating are given in dimensionless units because the model is not calibrated to units of visual arc. The spectral composition of the stimulus is characterized by taking the absolute value
484
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
Fig. 7. Spatiotemporal input signal.
of its Fourier transform as a function of both spatial and temporal frequencies (Fig. 8). The response of the model to an input stimulus drifting with a certain velocity is represented as absolute value of Fourier transforms of the membrane potentials produced by all of the neurons in the model. Initial simulations indicate that variations in the output signal along the trajectories of the geniculate a!erents are not signi"cant. So responses along each geniculate a!erent have been averaged prior to calculating the Fourier transforms. The Fourier transform shows a signi"cant peak on a line with a slope equal to the velocity of the signal. There is also a DC o!set and other major peaks that result from interactions between neurons within the cortex (Fig. 8).
5. Conclusion This study shows that a very simple model of a cortical structure that captures the basic geometry and temporal structure of visual cortex can generate propagating waves of activity that contain information about the speed of a small moving stimulus or a patterned stimulus, such as a square wave grating. We are now working on building a larger and more complex model of turtle visual cortex that will contain explicit representations of all three layers based on detailed maps of the spatial distributions of neurons in real cortices. The responses of this model can then be compared to propagating waves of activity obtained from real turtle cortices using
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
485
Fig. 8. The Fourier transforms of the input signal (A), and cortical response (B). Top view of the signal from "gure (A), showing that the peak lies on the line u "vu , where v is the drifting velocity of the R V input signal (C). Top view of the signal form "gure (B), showing the secondary peak lying on the same line (D).
voltage sensitive dyes. This large-scale model will also be used to study the responses of the cortex to more complex visual stimuli. References [1] Y. Chagnac-amitai, B.W. Connors, Horizontal spread of synchronized activity in neocortex and its control by GABA mediated inhibition, J. Neurophysiol. 61 (1989) 747}758. [2] J. F. Colombe, P.S. Ulinski, Temporal dispersion windows in cortical neurons, J. Comput. Neurosci. 7 (1999) 71}87. [3] D.A. Glaser, D. Barch, Motion detection and characterization by an excitable membrane: The `bow wavea model, Neurocomputing 26&27 (1999) 137}146. [4] L.J. Larson-Prior, P.S. Ulinski, N.T. Slater, Excitatory amino acid receptory-mediated transmission in geniculocortical and intracortical pathways within visual cortex, J. Neurophysiol. 66 (1991) 293}306. [5] K.A. Mulligan, P.S. Ulinski, Organization of geniculocortical projections in turtles: isoazimuth lamellae in the visual cortex, J. Comput. Neurol. 296 (1990) 531}547.
486
Z. Nenadic et al. / Neurocomputing 32}33 (2000) 479}486
[6] P.A. Salin, D.A. Prince, Electrophysiological mapping of GABAa receptor-mediated inhibition in adult rat somatosensory cortex, J. Neurophysiol. 75 (1991) 293}306. [7] D.M. Senseman, Correspondence between visually evoked voltage sensitive dye signals and synaptic activity recorded in cortical pyramidal cells with intracellular microelectrodes, Vis. Neurosci. 13 (1996) 963}977. [8] D.M. Senseman, Spatiotemporal structure of depolarization spread in cortical pyramidal cell populations evoked by di!use retinal light #ashes, Visual Neurosci. 16 (1999) 65}79. [9] J.C. Prechtl, Visual motion induces synchronous oscillations in turtle visual cortex, Proc. Natl. Acad. Sci. USA 91, 12 467}12 471.