Fig 1.
Illustration of mechanistic model.
A dense and evenly distributed layer of retinal ganglion cells with identical response properties are activated by the visual stimulus according to their receptive fields. This creates a pattern of neural activity for the layer of ganglion cells, acting as input for a similar layer of dLGN relay cells. Relay cells are connected to the ganglion cells via a spatiotemporal coupling-kernel function KRG which is assumed to only depend on the relative distance between the retinal ganglion cell and relay cell. the subscript in the coupling kernel function reflects the direct synaptic input dLGN relay cells (R) receive from the retinal ganglion cells (G).
Fig 2.
Schematic overview of the present eDOG model.
Cell types are: retinal ganglion cells (G), dLGN relay cells (R), and cortical cells (C). Each cell type corresponds to a two-dimensional layer (or population) of identical cells (see Fig 1). Note that only one cortical population is shown for each pathway even though an arbitrary number of cortical populations is considered. Unlike the feedforward projection, the feedback is cross-symmetry, i.e., the activity of ON-center relay cells are affected both by ON and OFF-center cortical cells. The OFF-center dLGN relay cells are assumed to receive the same input as the corresponding ON-center dLGN relay cells with opposite sign. Solid lines represent explicitly included connections in the eDOG model, while dashed lines represent connections included implicitly.
Fig 3.
Illustration of spatial and temporal features of retinal input and coupling kernels.
Panel A: receptive-field function for the retinal input (left) and the connectivity kernels (right). The spatial functions are shown as one-dimensional plots, although they are (circularly symmetric) two-dimensional functions. Panel B, top: spatial connectivity patterns between presynaptic neurons in the top layer and a single postsynaptic neuron (red circle) in the bottom layer for Gaussian width parameters (a). The Gaussian curves superimposed on top layers illustrate the spatial extent of the input to the neuron in the bottom layer. Bottom: different scenarios for the temporal connectivity pattern. The time constant τ in the exponential decay function describes the duration, while Δ is the delay parameter. In the present example applications we have kept the time constant τ fixed at 5 ms. Panel C: spatial feedback configurations investigated in present study. The ON and OFF cells are marked with red and blue color, respectively. The spatial connectivity kernels are shown as one-dimensional plots where the fill color corresponds to the sign of the input (excitatory: red, inhibitory: blue).
Table 1.
WG is the impulse-response function of ganglion cells, KRG and KRIG are the excitatory and inhibitory feedforward kernels, respectively. and
are ON-ON excitatory and inhibitory thalamo-cortico-thalamic kernels, respectively.
denotes the mixed ON-ON feedback kernel, consisting of an excitatory and an inhibitory term. The subscript ‘RIG’ refers to the indirect inhibitory input from retinal ganglion cells onto relay cells via intrageniculate interneurons (ganglion → interneuron → relay), while the subscript ‘RCR’ refers to the complete thalamo-cortico-thalamic loop (relay → cortex → relay). F represents the DOG function, f represents the Gaussian function, H represents the biphasic temporal function, and h represents the delayed decaying exponential function. The width parameters in spatial functions are given in units of degree, while the temporal parameters are in units of ms. In the present example applications we have kept the time constant τ fixed at 5 ms (comparable to what, e.g., was found in [74]), while the temporal delay parameters Δ have been varied in a range of 5–30 ms. † denotes the default values for parameters that have been varied.
Fig 4.
Cortical feedback modulates the center-surround receptive fields of relay cells.
Upper left: the two dimensional spatial structure of the impulse-response function. Bottom left: one-dimensional plot of the impulse-response function. Center excitation and surround inhibition correspond to the maximum and minimum value of (r), respectively, while where the zero-crossing occurs is used as an indication for the receptive field size. Right: spatial impulse-response function for different circuit configurations. In each case all other contributions are removed, except feedforward excitation. Default parameters from Table 1 have been used.
Fig 5.
Effects on relay-cell spatial impulse-response function characteristics from excitatory and inhibitory inputs are opposite.
Top row: dependence on the feedforward inhibition weight wRIG and width aRIG. Middle row: dependence on the feedback inhibition weight and width
. Bottom row: dependence on the feedback excitation weight
and width
. All values are normalized with respect to the case where relay cells only receive feedforward excitation from retinal ganglion cells. The parameters in WG and KRG are kept fixed (see Table 1).
Fig 6.
Effects on relay-cell spatial impulse-response function from mixed excitatory and inhibitory feedback.
Top row: dependence on cortical feedback widths and
with weights kept fixed:
and
. Bottom row: dependence on cortical feedback weights
and
with widths kept fixed:
, and
. All values are normalized with respect to the case where relay cells only receive feedforward excitation from retinal ganglion cells. The parameters in WG and KRG are kept fixed (see Table 1).
Fig 7.
Mixed feedback may enhance both excitatory response to stimuli within the receptive-field center (unlike inhibitory feedback alone), and suppressive effects of stimuli in the surround (unlike excitatory feedback alone).
Top row: predicted area-response curves of relay cells for different arrangements of cortical feedback using static spot stimuli. Bottom row: optimal size and suppression index (αs) are shown as a function of cortical feedback weight for different feedback configurations. These are extracted from the size tuning curve using static spot (solid lines, top row) and patch grating (dashed lines, |kg| ≈ 1/deg) as stimulus (bottom left figure). The values on the x-axis represent factors multiplied with the default values for and
listed in Table 1. Default values for fixed parameters are also listed in this table.
Fig 8.
Shift from low-pass to band-pass characteristics is seen in spatial frequency tuning of relay cells when increasing stimulus patch size.
Wavenumber (|kpg|) tuning of relay cells, using patch grating at two different patch sizes (rows), is shown for different feedback configurations (columns). the patch diameters are 1.5 deg (top row) and 10 deg (bottom row), respectively. Default values from Table 1 have been used for fixed parameters.
Fig 9.
Mixed feedback has different effect on low and high frequency components of natural scenes in contrast to pure excitatory or inhibitory feedback.
Each subfigure shows activation of a layer of relay cells in response to the input image, shown as a logarithmic color map from blue to red (from reduced to increased response). the responses are normalized with respect to the maximum response in the case without cortical feedback. The red and blue circles mark representative parts of the image with high and low spatial frequency, respectively. Default values from Table 1 have been used except for the feedback weights which have been set at 1.8 times the listed default values to more clearly demonstrate qualitative effects.
Fig 10.
Spatiotemporal impulse-response function of relay cell.
Top: panels showing spatial receptive field at different times. Curves below panels are one-dimensional plots of the receptive fields as a function of x alone. Bottom left: x-t plot of receptive field. ON regions are shown in red (solid lines) while OFF regions are shown in blue (dashed lines). Bottom right: curve showing temporal evolution of ON region of the receptive field. The biphasic index IBP is defined as the ratio between the peak magnitude of the (negative) rebound phase and the peak magnitude of the first (positive) phase. tpeak is the peak response latency. Note that only feedforward excitation from retinal ganglion cells to relay cells is included.
Fig 11.
Inhibitory feedback can increase the biphasic index and reduce the peak response latency, while the opposite is seen for excitatory feedback.
Left panels: temporal evolution of the relay-cell impulse-response function (ON region) for different circuit configurations, i.e., feedforward inhibition only (top), feedback inhibition only (middle), feedback excitation only (bottom). The feedforward excitation is fixed in all cases. Right panel: parameter dependence of two impulse-response measures tpeak and biphasic index IBP. The biphasic index is normalized with respect to the value for the case with feedforward excitation only (IBP = 0.35), while the tpeak plots show the difference in peak time in milliseconds compared to the corresponding value for feedforward excitation only (tpeak = 29 ms). Default parameters have been used for the fixed parameters (see Table 1).
Fig 12.
Mixed feedback: Delayed inhibitory feedback gives oscillatory responses, delayed excitatory feedback more monophasic responses.
Two leftmost panels: temporal impulse-response function with mixed excitatory and inhibitory feedback, where feedforward inhibition also is included. Two rightmost panels: parameter dependence of two impulse-response measures tpeak and biphasic index IBP. See Fig 11 caption for details. Default parameters have been used for fixed parameters (see Table 1).
Fig 13.
Delayed inhibitory feedback sharpens the temporal frequency tuning of relay cells, while delayed excitatory feedback blunts the temporal frequency tuning of relay cells.
Effect of cortical feedback on temporal frequency tuning of relay cells are shown for different values of thalamocortical delay. Panel A: inhibitory feedback only. Panel B: excitatory feedback only. Panel C, left: delayed inhibition, i.e., rapid excitatory feedback combined with long-delay inhibitory feedback ( ms,
ms). Panel C, center: synchronized feedback, i.e., excitatory and inhibitory feedback arrive simultaneously (
ms). Panel C, right: delayed excitation, i.e., long-delay excitatory feedback combined with rapid inhibitory feedback (
ms,
ms). Full-field grating is used as stimulus (|kg| ≈ 1deg−1) and default values from Table 1 is used for fixed parameters.
Fig 14.
Cortical feedback may control the degree of temporal decorrelation in relay cells.
Left: Autocorrelation function of stimulus and relay cell response for different circuit configurations: no feedback, long-delay inhibitory feedback combined with short-delay excitatory feedback, long-delay excitatory feedback combined with short-delay inhibitory feedback, synchronized feedback. In each case the average autocorrelation from 40 × 40 neurons at the center is shown with corresponding standard deviation. Default values from Table 1 have been used for fixed parameters, and the temporal feedback parameters are the same as in Fig 13 (bottom row). Right: Frames from the complex naturalistic movie used as stimulus. This movie was recorded by a camera mounted on the head of a cat exploring the environment (forest) [94, 95]. The red circle marks the receptive-field center size for the relay cell at the center.