Compositionality of arm movements can be realized by propagating synchrony.
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Here, we map the propagation of activity in a chain to a linearly evolving preferred velocity, which results in parabolic segments that fulfill the two-thirds power law.The model provides an explanation for the segmentation of the trajectory and the experimentally observed deviations of the trajectory from the parabolic shape at primitive transition sites.Furthermore, the model predicts low frequency oscillations (<10 Hz) of the motor cortex local field potential during ongoing movements and increasing firing rates of non-specific motor cortex neurons before movement onset.
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Affiliation: Functional Neural Circuits Group, Faculty of Biology, Schänzlestrasse 1, 79104, Freiburg, Germany. hanuschkin@bccn.uni-freiburg.de
ABSTRACT
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We present a biologically plausible spiking neuronal network model of free monkey scribbling that reproduces experimental findings on cortical activity and the properties of the scribbling trajectory. The model is based on the idea that synfire chains can encode movement primitives. Here, we map the propagation of activity in a chain to a linearly evolving preferred velocity, which results in parabolic segments that fulfill the two-thirds power law. Connections between chains that match the final velocity of one encoded primitive to the initial velocity of the next allow the composition of random sequences of primitives with smooth transitions. The model provides an explanation for the segmentation of the trajectory and the experimentally observed deviations of the trajectory from the parabolic shape at primitive transition sites. Furthermore, the model predicts low frequency oscillations (<10 Hz) of the motor cortex local field potential during ongoing movements and increasing firing rates of non-specific motor cortex neurons before movement onset. Related in: MedlinePlus |
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Mentions: The activity of single cells in the motor cortex has been shown to be directionally tuned to arm movements (Georgopoulos et al. 1982). The arm trajectory can be estimated by calculating the population average over all neurons (Georgopoulos et al. 1986a, 1988). Similarly, we use population coding to generate a trajectory from simulated neuronal activity:4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{rll} \mathbf{v} & = & \sum\limits_{k}^{\mathrm{all}\,\,\mathrm{neurons}}w_{k}a_{k}(t)\mathbf{p}_{k} \\ & = & \sum\limits_{j}^{\mathrm{chain}}\sum\limits_{i}^{\mathrm{pool}}w_{i}^{j}a_{i}^{j}(t)\mathbf{p}_{i}^{j}, \end{array}$$\end{document}where v is the instantaneous velocity, is the activity in the ith group of the jth chain and its preferred velocity. The weights are set to ∀ i,j resulting in velocities comparable to the monkey experiments (median 300 mm/s as given by Polyakov et al. 2009b). The propagation speed of the activity volley in a synfire chain from one pool to the next is constant as described in Section 2.2. We can therefore map a synfire chain to an arrow in velocity space. Each pool of the synfire chain is assigned its preferred velocity pi according to its position along the arrow, i.e. for a chain consisting of n pools mapped to an arrow starting at v0 and ending at v1,5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbf{p}_{i}=\frac{i-1}{n-1}\left(\mathbf{v}_{1}-\mathbf{v}_{0}\right)+\mathbf{v}_{0}. $$\end{document}This is illustrated in Fig. 3(a); the activity of the corresponding synfire chain is given in Fig. 3(b). As the preferred velocity for each chain j changes linearly with the pool index i and the propagation speed from one pool to the next is constant, the instantaneous velocity vector also evolves linearly resulting in parabolic motion as derived in Section 2.1. Figure 3(c) shows the parabolic trajectory in position space generated by the synfire activity in Fig. 3(b). To extract the trajectory from the simulated neuronal activity, we bin the activity in 1 ms intervals and reconstruct the motion according to the population coding scheme given by Eqs. 4 and 5.Fig. 3 |
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Affiliation: Functional Neural Circuits Group, Faculty of Biology, Schänzlestrasse 1, 79104, Freiburg, Germany. hanuschkin@bccn.uni-freiburg.de