The information conveyed to DCN neurons.

<p>The AIP is composed of multiple functional cell groups, each of which forms the output of a cerebellar corticonuclear microcomplex (ucplx). The main mossy fiber input to the DCN cells is derived from spinal motor circuits, which are conveyed to the cerebellum either directly in a spinocerebellar tract (SCT), or via a synaptic relay in the LRN, in a spino-reticulo cerebellar tract (SRCT). These tracts are in turn driven by spinal interneurons, which target specific combinations of muscles or synergies. Pentagons in the ventral horn are alpha-motorneurons encircled by dashed lines to indicate separate spinal motor nuclei, and each spinal interneuron targets a limited number of motor nuclei <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084616#pone.0084616-Jankowska1" target="_blank">[58]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084616#pone.0084616-Takei2" target="_blank">[59]</a> as indicated by example. Hence, the information carried in SCTs/SRCTs informs the DCN cells of the final composition of the motor command, i.e. which muscle synergies that are currently driven. Also the input that drives the CFs is derived from the spinal motor circuitry (indicated by dashed line from the spinal interneurons), via relays at least in the cuneate nucleus and the inferior olive (IO). The spinal motor circuitry is driven by motor commands from the neocortex and the brainstem. The output of the DCN cell represents the cerebellar correction of ongoing motor commands and targets the neocortex and the brainstem. Since the CF receptive field identifies the microcomplex the DCN cell is located in and consequently the muscle synergy it is connected with, comparing the SCT/SRCT input with the location of the CF receptive field is equal to comparing the motor information it receives with the motor information it issues. Accordingly, our findings suggest that the input and the output of the DCN cell are functionally matched. AIP, Anterior interposed nucleus; PC, Purkinje cell; CF, climbing fiber; ucplx, microcomplex; MF, mossy fiber; IO, inferior olive; LRN, lateral reticular nucleus; SRCT, spinoreticulocerebellar tract; SCT, spinocerebellar tract.</p

Responses evoked in DCN cells by microstimulaton in LRN.

<p>(A) Superimposed raw EPSPs recorded from one DCN cell during hyperpolarization to prevent spiking. LRN stimulation, 50 uA. (B) Histogram of spike responses evoked in the same cell but without hyperpolarization. N = 50 stimulations. Bin width 1 ms.</p

Summary of net spike responses evoked from various skin sites.

<p>PFRF, parallel fiber receptive fields of afferent PCs (see text); CFRF, climbing fiber receptive fields of afferent PCs. Kat = category; cFL = contralateral forelimb; Tru. = trunk; iHL = ipsilateral hindlimb.</p

For comparison, responses evoked by a similar stimulation as in Fig. 1 but applied within the CF receptive field of the afferent PCs to the DCN cell (PC-CFRF, see text).

<p>Similar display as in Fig. 1.</p

Approximation error when the number of granule cells is increased.

<p>The figure shows how the RMSE is reduced when the number of GrCs is increased as the functions in the figure legend were approximated using the specified number of projections. To search for the optimal approximations, the approximation directions were also optimized along with the GrC to PC weights. The first equation , is three-dimensional and was approximated using both 4 and 8 projections, while the others are two-dimensional. Note that the last equation was approximated both using 2 and 3 projections to investigate the relatively large differences found using random projections (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002979#pcbi-1002979-g004" target="_blank">Figure 4B</a>).</p

Approximation examples of basic non-linear functions.

<p>(A) Approximated surfaces using a single or two projections (left and middle columns, respectively) compared to the approximated or target function surface (right-hand column) (i.e RMSE = 0). The colors represent the height of the surface ranging from negative values (blue) to positive values (red), comparable to the surface in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002979#pcbi-1002979-g002" target="_blank">Figure 2C</a>. In each row, a different non-linear interaction retrieved from the terms within the inverse dynamics of the planar double joint arm in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002979#pcbi.1002979-Hollerbach1" target="_blank">[79]</a> is used. The illustrated projections had the lowest RMSE of 100 tested projections, each tested projection having a random direction. The actual RMSE values can be found in (B). The approximated surfaces also display the actual projections used as dashed lines above the surfaces. The value of the elbow angle variable, range between and , to capture an entire period of the sin function that is approximated. (B) RMSE of approximations of three two-dimensional non-linear terms in A. The approximations where constructed using random projection directions and a total of 60 GrCs. 100 approximations where constructed for each box. The mean RMSE is shown by the center line of the box, the boxes themselves extend to the 25th and 75th quartile and the whiskers extends to the most extreme RMSE not considered to be outliers, which are instead shown as black crosses. The red markers with an arrow from “raw signal” show the RMSE of approximations using the raw signals as projection directions, i.e. without recombination of inputs and those with an arrow from “in A” show the RMSE of the approximations shown in (A).</p

Responses evoked from various skin sites.

<p>(A) Spike response evoked by electrical skin stimulation of the skin site indicated by an ‘X’ in (C). Bin width of the peristimulus histograms in A and B, 5 ms. (B) Spike response evoked by electrical skin stimulation within PC-CFRF (asterisk marks the location in C). (C) Histograms of net spike responses evoked from various skin sites. Bin width, 10 ms. iH, ipsilateral hindlimb, coFL, contralateral forelimb (both with a distal location).</p

Piecewise-linear (PL) approximations in the cerebellar neuronal network.

<p>(A) Using the excitatory input directly from PF and the inhibitory pathway through molecular layer interneurons, the PC can construct a PL approximation of arbitrary non-linear functions of the input reaching the GrCs. (top) Two PFs innervate the PC directly (3 & 4), while the other two innervate a stellate interneuron (1 & 2). (middle) The four GrCs have slightly different thresholds and varying MF efficacy leading to varying activity slopes. (bottom) The PC modulates its output using the input coming from the GrCs according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002979#pcbi.1002979.e001" target="_blank">Eq. (1)</a>. The path through the inhibitory molecular layer interneurons allows the weight and thus the slope of the curve to be negative. Each GrC threshold corresponds to one knot in the PL PC output. (B) The distribution of GrC thresholds over the input range determines how well the PC can approximate the non-linear regions of the approximated function. (top) Several receptive fields can contribute to measure a single intrinsic dimension. In this case, the skin stretch can be used to deduce the joint angle. (middle) The different receptive fields allow the GrC thresholds to be spread over a larger input range than that using only a varying degree of Golgi cell tonic inhibition. (bottom) Sum of activity of all GrCs activated from the three receptive fields. As the population GrC activity rises over the entire input range, their output could be used to approximate non-linearities over the entire input range. (C) A naïve approach to enable the PC output to approximate functions of two-dimensions. In this example, afferent information from skin stretch and Ib afferents are added separately in the PC, generating an approximated surface. At each point in the input space, the PC output is calculated by adding the contribution from GrCs innervated by the two separate afferent types.</p

Responses of DCN cells to manual skin stimulation.

<p>(A) Location of a recorded, stained DCN neuron in the anterior interposed nucleus. The outlines of the nucleus and the electrode track are indicated with white dotted lines. (B) Sample IC recording illustrating an excitatory response. The neuron was slightly hyperpolarized from resting membrane potential. (C) Strain gauge signal indicating the time course of the force applied during the skin stimulation. (D) Averaged intracellular recording after removing spikes in software from raw data (N = 50 stimulations). (E) Spike responses for the same cell as in (B)–(D) but recorded without hyperpolarization. The bin width of the peristimulus histogram (obtained using N = 50 stimulations) is 10 ms.</p

Net spike responses in DCN cells and LRN cells evoked by manual skin stimulation.

<p>(A) Net spike response of the same cell as illustrated in Fig. 1. (B) Net spike response shown as an average peristimulus histogram of all LRN cells recorded (N = 29). The motivation for pooling the LRN cells in (B) is that DCN cells would be expected to receive multiple LRN MF synaptic inputs. Bin width in both (A) and (B) is 10 ms. (C) Reconstructed electrode track for a stimulation electrode placed in LRN, shown in a histological section and a 3D reconstruction of the brainstem, respectively.</p