1. A Neural Signature of Divisive Normalization at the Level of Multisensory Integration in Primate Cortex 
Tomokazu Ohshiro, Dora E. Angelaki, Gregory C. DeAngelis 
Neuron 
Volume 95, Issue 2, Pages e8 (July 2017)
DOI: /j.neuron
Copyright © 2017 Elsevier Inc. Terms and Conditions

2. Figure 1
Multisensory Normalization Model and the Diagnostic Prediction of Cross-modal Suppression
(A) Schematic illustration of the divisive normalization model for visual-vestibular cue integration. Model MSTd neurons (rectangles) perform a weighted sum of heading-tuned inputs from unisensory (vestibular, visual) neurons, with weights given by dvest, dvis. The weighted sum is raised to an exponent and gain-modulated multiplicatively by a function of the total activity of the population of neurons (see STAR Methods).
(B) The diagnostic prediction of the normalization model. When visual and vestibular stimuli are presented at the heading preferences of the model neuron (Δ = 0°), the combined response (black) exceeds the single cue responses (cyan, red) for all stimulus amplitudes (left). When the heading of cue2 is offset from the cell’s heading preference by Δ = 60° (middle), cue2 is activating on its own but suppresses the combined response below that of cue1 (middle). For a larger offset (Δ = 120°), cue2 becomes suppressive on its own and suppression of the combined response is trivial (right). Motion amplitude indicates the total displacement of the body within a trial.
(C) Summary of predictions of the normalization model (circles) and a family of alternative models involving subtractive inhibition (triangles). Responses of model neurons were simulated for heading offsets of cue2 (Δ) ranging from 0° to 180°, in steps of 15°. The response to cue2 (Rcue2) and the combined response (Rcomb) are divided by the response to cue1 (Rcue1), and the ratios (Rcue2/Rcue1, Rcomb/Rcue1) are plotted against each other. Rcue1, Rcue2, and Rcomb denote simulated responses to the largest stimulus amplitude.
Neuron  , e8DOI: ( /j.neuron )
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3. Figure 2 Data from an Example Multisensory MSTd Neuron
(A) Three-dimensional heading tuning functions (left, vestibular; right, visual) are shown as color contour maps. This neuron prefers rightward self-motion (−30° azimuth, 0° elevation; white crosses) for both modalities. White dots indicate visual headings that were tested in the screening protocol.
(B) Screening test. Combined (black), vestibular (cyan), and visual (red) responses are plotted as a function of the offset (Δ°) of the visual heading from the cell’s heading preference. The heading tuning curves were fit with a modified sinusoid (Equation 3). Motion amplitude = 10.0 cm. Error bars denote SEM.
(C) Responses are plotted as a function of stimulus amplitude. Data are shown for Δ = 0° (left), +60° (middle), and −60° (right). Asterisks indicate significant suppression or activation (∗∗p < 0.01; Wilcoxon rank-sum test). Smooth curves show the hyperbolic-ratio functions (Equation 1) that best fit the amplitude-response curves. Error bars indicate SEM.
Neuron  , e8DOI: ( /j.neuron )
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4. Figure 3
Demonstration of Cross-modal Suppression for Three Additional Example Neurons
Format as in Figure 2C.
(A) A second example neuron showing cross-modal suppression by a non-preferred visual heading stimulus. Data are shown for Δ = 0° (left) and Δ = 80° (right). Note that this neuron is an opposite cell; thus, the stimulus headings for Δ = 0° have different directions.
(B and C) Two example neurons showing cross-modal suppression by a non-preferred vestibular stimulus. The non-zero vestibular offsets were Δ = 60° (B, right) and Δ = 180° (C, right). Asterisks indicate significant suppression or activation (∗p < 0.05; ∗∗p < 0.01; Wilcoxon rank-sum test). Smooth curves show the best-fitting hyperbolic-ratio functions.
Error bars indicate SEM.
Neuron  , e8DOI: ( /j.neuron )
Copyright © 2017 Elsevier Inc. Terms and Conditions

5. Figure 4
Quantification and Visualization of Cross-modal Suppression Effects
(A) Amplitude-response functions for an example MSTd neuron, along with best-fitting hyperbolic-ratio functions (Equation 1). Here, both visual (cue1) and vestibular (cue2) stimuli were presented at the preferred headings, and cross-modal enhancement occurs. G(p,p), both cues at respective preferred headings; G(p,0), preferred cue1 only; G(0,p), preferred cue2 only. Error bars indicate SEM.
(B) Data and fits from the same neuron when the vestibular stimulus (cue2) was offset by 90° from the vestibular heading preference. G(p,n), preferred cue1 and non-preferred cue2; G(0,n), non-preferred cue2 only. Error bars indicate SEM.
(C) Combined response gains for the preferred-preferred (purple, G(p,p)) and preferred-non-preferred (green, G(p,n)) stimulus combinations are plotted against the corresponding response gains for cue2 (G(0,p) or G(0,n)). Values on both axes are normalized by the response gain for cue1, G(p,0). Multiple data points are plotted for each neuron: one for the preferred-preferred combination (purple) and one or more for preferred-non-preferred heading combinations (green). Filled green symbols represent cases with significant cross-modal suppression and significant activation by the non-preferred cue2. Filled purple symbols indicate the preferred-preferred stimulus combinations that correspond to the filled green symbols. Purple and green stars correspond to the data shown in (A) and (B), respectively. Solid black curve, second-order polynomial fit. Data points for a few cases with outlier values are plotted at the maximum values on the x and y axes.
Neuron  , e8DOI: ( /j.neuron )
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6. Figure 5
Cross-modal Suppression Is Exhibited by Unisensory MSTd Neurons, but Not MT Neurons
(A) Data from a unisensory (visual only) MSTd neuron, along with best-fitting hyperbolic ratio functions. Format as in Figure 3, except that data are superimposed for two values of Δ: 135° (solid curves) and 160° (dashed curves). Significant cross-modal suppression occurs for the largest stimulus amplitude (∗p < 0.05; ∗∗p < 0.01; Wilcoxon rank-sum test). Error bars indicate SEM.
(B) Data from a typical MT neuron tested with Δ values of 0° and 90°. Smooth curves show the best-fitting hyperbolic-ratio functions. Error bars indicate SEM.
(C) The ratio of combined:visual response gains is plotted against the ratio of vestibular:visual response gains. Data are shown for unisensory MSTd neurons (orange symbols; 56 observations from 33 neurons) and MT neurons (green symbols; 127 observations from 43 neurons). Multiple data points may be plotted for each neuron, corresponding to the multiple vestibular headings tested. Filled symbols indicate cases for which Gcombined/Gvisual is significantly different from 1.0. A histogram of the ratio, Gcombined/Gvisual, is shown on the right margin.
Neuron  , e8DOI: ( /j.neuron )
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7. Figure 6 Summary of Model Fits to the Population of MSTd Neurons
(A and B) Amplitude-response functions for an example MSTd neuron, along with best-fitting curves based on the normalization model (A), or the alternative (subtractive) model (B). The vestibular stimulus (Cue2) was presented at both preferred and non-preferred headings. Note that the diagnostic cross-modal suppression effect is captured well in the normalization model fit (green curve below black curve), but not in the alternative model fit. The partial correlation coefficient between data and model fit is 0.76 for the normalization model and 0.30 for the alternative model. Error bars indicate SEM.
(C) Fisher z-transformed partial correlation coefficient for the normalization model (ordinate) is plotted against that for the alternative model (abscissa). Data from multisensory MSTd neurons are shown. Filled symbols correspond to cases that exhibit the diagnostic form of cross-modal suppression as defined in Figure 4. The red filled symbol corresponds to the data shown in (A) and (B). The plot is divided into three areas by the dashed lines; data points in the top-left region are significantly better fit by the normalization model, and those in the bottom-right region are significantly better fit by the alternative model.
Neuron  , e8DOI: ( /j.neuron )
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8. Figure 7
Summary of Cross-modal Suppression in Fits of the Normalization and Alternative Models
Response gains were obtained from model fits to the data from each neuron and are plotted in the same format as Figure 4C.
(A) Results for the normalization model.
(B) Results for the alternative (subtractive) model.
In each panel, combined response gains are plotted against the corresponding response gains for cue2. Values on both axes are normalized by the response gain for cue1. Filled green symbols represent cases with significant cross-modal suppression and significant activation by the non-preferred cue2, as identified by the analysis of actual firing rate data shown in Figure 4. Solid black curve, third-order polynomial fit to the data.
Neuron  , e8DOI: ( /j.neuron )
Copyright © 2017 Elsevier Inc. Terms and Conditions