38 research outputs found

    An error-tuned model for sensorimotor learning

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    <div><p>Current models of sensorimotor control posit that motor commands are generated by combining multiple modules which may consist of internal models, motor primitives or motor synergies. The mechanisms which select modules based on task requirements and modify their output during learning are therefore critical to our understanding of sensorimotor control. Here we develop a novel modular architecture for multi-dimensional tasks in which a set of fixed primitives are each able to compensate for errors in a single direction in the task space. The contribution of the primitives to the motor output is determined by both top-down contextual information and bottom-up error information. We implement this model for a task in which subjects learn to manipulate a dynamic object whose orientation can vary. In the model, visual information regarding the context (the orientation of the object) allows the appropriate primitives to be engaged. This top-down module selection is implemented by a Gaussian function tuned for the visual orientation of the object. Second, each module's contribution adapts across trials in proportion to its ability to decrease the current kinematic error. Specifically, adaptation is implemented by cosine tuning of primitives to the current direction of the error, which we show to be theoretically optimal for reducing error. This error-tuned model makes two novel predictions. First, interference should occur between alternating dynamics only when the kinematic errors associated with each oppose one another. In contrast, dynamics which lead to orthogonal errors should not interfere. Second, kinematic errors alone should be sufficient to engage the appropriate modules, even in the absence of contextual information normally provided by vision. We confirm both these predictions experimentally and show that the model can also account for data from previous experiments. Our results suggest that two interacting processes account for module selection during sensorimotor control and learning.</p></div

    Object lifting experiment.

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    <p><b>A</b>. The lifting paradigm used in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005883#pcbi.1005883.ref023" target="_blank">23</a>]. Participants lifted a U-shaped object by alternating between the right-hand and left-hand grasp points in four blocks. <b>B</b>. The peak roll angle (tilt) of the object (top panel), as well as the compensation torque (bottom panel). Perfect compensation required ±550 N.mm depending on the context. Data is plotted in black and the fits for the ETM and CDM are plotted in red and blue, respectively. The best-fit parameters for the models (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005883#sec010" target="_blank">Methods</a> for details) are: <i>α</i><sub>0</sub> = 0.87, <i>β</i><sub>0</sub> = 0.74, <i>β</i><sub>180</sub> = 0.17, <i>c</i><sub>180</sub> = 0.0, <i>x</i>° = 0.66, and <i>k</i> = 15.68 for the ETM, and <i>α</i><sub>0</sub> = 0.92, <i>β</i><sub>0</sub> = 0.79, <i>β</i><sub>180</sub> = 0.00, <i>c</i><sub>180</sub> = 0.49, <i>x</i>° = 1.00 and <i>k</i> = 15.68 for the CDM.</p

    Schematic of the error tuned model (ETM).

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    <p><b>A</b>. Motor output. The modules each have a preferred direction uniformly covering the possible object orientations (here, 16 modules are shown by the grey peripheral objects). On the n<sup>th</sup> trial the modules each have an adaptive state indicated by the length of the vectors (left panel). In this example, the distribution of adapted states is consistent with recent experience of an object at 270°. On the current trial, the object is changed to an orientation of 0° (blue peripheral object). In this case, the visual contextual tuning gives the greatest weight to modules with preferred directions near 0° (middle panel). The motor contribution of each module (black vectors, right panel) is vector summed to produce the final motor output (green vector). The ideal motor output is shown by the blue vector, leading to an error (magenta vector). <b>B</b>. Motor adaptation is driven by two processes. The top row shows error-independent decay in which visual contextual tuning (middle panel) determines the decay of memory across modules. Here the memory decays most for the current context (0°) and less for more distant contexts. This leads to a set of reduced adaptive states (right panel; original states indicated by solid line). The bottom row shows error-dependent adaptation. The left panel shows the error (magenta) as well as its projection onto each module’s preferred direction (i.e. cosine tuning in which red vectors reflect negative magnitudes). This tuning reflects the extent that changing the adaptive state of a module will reduce the error. These projections are modulated by the visual contextual tuning (middle panel) which is greatest for the current context. This determines how each module updates its adaptive state in response to the error (right panel). The adaptive state on the next trial (n+1; far right panel) is the sum of the decayed states and the state updates, leading to a reduced error on the next trial for the same orientation of the object. Note that this schematic is not drawn to scale and exaggerates some of the changes so that they are visible. The ⊙ symbol represents element-wise multiplication across the modules.</p

    Experiments 1 and 2: Context-dependent adaptation and decay.

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    <p><b>A</b>. The paradigm for experiments 1 and 2. After an initial exposure block at 180° (yellow background), subjects performed alternating probe blocks presented at one of five orientations between 0° and 180° (green background) followed by re-exposure blocks at 180° (blue background). <b>B</b>. Experiment 1 in which probe blocks consisted of 20 error-clamp trials. The left plot shows the composite trial-series for PD (all trials) and Adaptation (error-clamp probe blocks only). Grey shading shows ±SE across subjects. Each subject experienced the probe blocks in a pseudorandomized order so the trial-series has been rearranged in order of increasing probe orientation (∆0° to ∆180°). The right plots show the corresponding measures averaged over the different probe blocks and over subjects (error-bars show ±SE across subjects). Adaptation is measured from the probe blocks (right top, green background) and re-exposure PD is measured from the re-exposure blocks (right bottom, blue background). Model fits are shown in all panels for the CDM (blue) and ETM (red). Experimental data from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005883#pcbi.1005883.ref004" target="_blank">4</a>]. <b>C</b>. Experiment 2, plotted as in panel B. In this case, probe blocks consisted of 8 zero-force trials. As in panel B, model fits are shown in all panels. Experimental data from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005883#pcbi.1005883.ref003" target="_blank">3</a>].</p

    Model parameters.

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    <p>Parameters for the CDM and ETM when fit to datasets obtained from the different experiments. In the first dataset (top 2 rows for CDM and ETM), experiments 1, 2 and 3 were concurrently fit with all free model parameters. In the second dataset (bottom 2 rows for CDM and ETM), experiments 4 and 5 were concurrently fit with the Gaussian tuning function widths fixed to values obtained from fitting the first dataset (grey backgrounds indicate the fixed tuning-width values). BICs are relative to the best model within the fits for each dataset (the ETM in both cases). See Supporting <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005883#pcbi.1005883.s001" target="_blank">S1 Table</a> for 95% confidence limits.</p

    Experiment 5: Visually ambiguous object.

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    <p><b>A.</b> The paradigm consisted of initial exposure to a visually ambiguous object with dynamics at 180° (yellow background), after which subjects perform alternating probe blocks (20 error-clamp trials) at one of two orientations (0° or 180°; green background) followed by re-exposure to the visually ambiguous object with dynamics at 180°. <b>B.</b> The right plot shows the composite trial-series for PD (all trials) and Adaptation (error-clamp probe blocks only). Grey shading shows ±SE across subjects. Each subject experienced the probe blocks in a pseudorandomized order. The trial-series has been rearranged in order of probe orientation (∆0° and ∆180°). The right plots show the corresponding measures averaged over the different probe blocks and over subjects (error-bars show SE across subjects; p-values are for two-tailed paired t-tests as indicated). Adaptation is taken from the probe blocks (right top, green background) and re-exposure PD is taken from the re-exposure blocks (right bottom, blue background). The model fits are shown in all panels for the CDM (blue) and ETM (red). <b>C.</b> A second group of subjects was exposed to the visually ambiguous object with dynamics at 0°. Results are plotted as in panel B.</p

    Object manipulation task.

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    <p><b>A.</b> Subjects grasped the handle of a robotic manipulandum (the WristBOT) that could generate forces in the horizontal plane and torques around the vertical handle. A mirror-monitor system projected an image of the object and the task into the plane of the movement. <b>B.</b> Subjects rotated the object (green) clockwise and counter-clockwise (top inset) between visually presented targets (purple) and were required to keep the handle (grasp point) as still as possible within the central home region (grey). On exposure trials, the dynamics of the object (forces and torques) were consistent with rotating a mass (<i>m</i>) on the end of an 8 cm rod (<i>r</i>). Rotation of the object generates forces at the handle (<b>F</b>) that are approximately orthogonal to the orientation (θ) of the rod. In order to maintain the handle stationary while rotating the object, the subject must counteract these forces. The visual orientation of the object could be made ambiguous by presenting an ambiguous object (bottom inset). The rotation and translation of the visual object (normal or ambiguous) always tracked the rotation and translation of the WristBOT handle.</p

    Experiment 3: Opposing dynamics.

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    <p><b>A.</b> The paradigm consisted of alternating exposure blocks at 180° and 0° followed by two final blocks of zero-force trials (all blocks consist of 24 trials). <b>B.</b> Trial-series averaged across subjects (grey shading shows ±SE across subjects). Performance was stable from the 5th exposure cycle onwards so we omit exposure blocks after this for clarity. The fits of the models are shown in all panels for the CDM (blue) and ETM (red). <b>C.</b> The PD averaged over each of the first four 180° exposure blocks for the experimental data (error-bars are SE across subjects; p-values are for two-tailed paired t-tests as indicated) and CDM and ETM fits. Experimental data from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005883#pcbi.1005883.ref003" target="_blank">3</a>].</p

    Experiment 4: Opposing versus orthogonal dynamics.

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    <p><b>A.</b> The paradigm consisted of the first five blocks alternating between exposure at 180° and exposure at either 0° or 270° (opposing or orthogonal conditions; here shown as 270°). Interference was assessed by comparing PD on the 3rd and 5th block (purple comparison). The sixth block was either exposure (E6) or zero-force (Z6). Facilitation was assessed by comparing PD on the 7th block (Z180°) between E6 and Z6 conditions (dark green comparison). <b>B.</b> The trial-series for the four conditions (grey shading shows ±SE across subjects). Rows are opposing versus orthogonal dynamics and columns are E6 (exposure trials on 6th block) or Z6 (zero-force trials on 6th block). The model fits are shown in all panels for the CDM (blue) and ETM (red). Purple and dark green arrows test for interference and facilitation, respectively. <b>C.</b> Interference for the opposing and orthogonal conditions for the experimental data (black; error-bars show SE across subjects; p-values are for two-tailed paired t-tests) and the two models (CDM in blue; ETM in red). <b>D.</b> Facilitation, plotted as in panel C.</p

    A functional assay to test nanobarcoded proteins.

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    Cells expressing different nanobarcoded proteins were pulsed with transferrin conjugated to Alexa488 and with EGF conjugated to Alexa647, for 10 minutes, allowing the cells to endocytose these ligands. Afterwards, they were immediately fixed or were chased (washed off) in a minimal buffer at 37°C, for 10 or 20 minutes. Finally, all cells were fixed and immunolabeled for the ALFA tag, to identify the nanobarcoded proteins. (A, B) The behavior of transferrin and EGF, respectively. Transferrin recycles, as expected, being released during the chase period (Kruskal–Wallis test followed by Tukey post hoc test, p N = 17–18 independent experiments. (C, D) Same data as above, but indicating the nature of the nanobarcoded protein in each of the independent experiments. The data underlying this Figure can be found in the following Sheets of the “S1 Data file: “Tf_SFig 6A,” “EGF_SFig 6B,” “Tf_SFig 6C,” and “EGF_SFig 6D.” The S1 Data file is available from http://dx.doi.org/10.17169/refubium-40101. (TIF)</p
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