Model of change in information rates as a function of transmission jitter and expansive non-linearity.

<p>A surface depicting the percentage change in mutual information between encoding and decoding sites is shown in greyscale for model parametrized by the magnitude of the transmission jitter (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030115#pone-0030115-g001" target="_blank">Fig. 1C</a>) and the time constant of the expansive nonlinearity (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030115#pone-0030115-g002" target="_blank">Fig. 2A</a>). The parameter combinations measured in 8 neurons are shown with grey x's.</p

Measurement of jitter and information rates.

<p><i>A</i>, Comparison of jitter at encoding end (light grey portion of bar) assessed over repeated presentations of stimulus, and transmission jitter (black portion of bar), measured in three different neurons. <i>B</i>, Mutual information rates for the three neurons in <i>A</i>, calculated at the encoding (light grey) and decoding (black) sites. Error bars represent Bayesian 95% confidence interval from CTW calculation.</p

Transmission jitter and fit parameters for all 8 intra-intra and intra-extra experiments.

<p>Transmission jitter and fit parameters for all 8 intra-intra and intra-extra experiments.</p

Change in ISI Distribution and Relation to Stimulus Coding.

<p><i>A</i>, Percentage change in probability of ISI at decoding site relative to encoding site, same data as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030115#pone-0030115-g002" target="_blank">figure 2D</a>. The shaded region indicates ISIs that occur more frequently at the decoding site than at the encoding site. <i>B</i>, The correlation between first and second spikes of ISIs reliably elicited by repeated presentations of identical stimuli (“frozen noise”). <i>C</i>, The linearity of stimuli associated with doublet patterns of spikes with various ISIs, as assessed with log likelihood ratios. Data in <i>B</i> & <i>C</i> are from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030115#pone.0030115-Aldworth2" target="_blank">[28]</a>, reprinted with permission.</p

Conduction failures.

<p><i>A</i>, Simultaneous intracellular recording from encoding (lower trace) and decoding (upper trace) sites in a single 10-2a neuron, showing an instance of an action potential which failed to propagate the length of the axon (red arrows). <i>B</i>, Distribution of spike propagation time as a function of ISI, along with exponential fit (dashed red line), as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030115#pone-0030115-g002" target="_blank">figure 2</a>. Also shown is the length of the preceding ISI for 32 action potentials that failed to propagate (blue circles, arbitrary ordinate position). <i>C</i>, Data are presented as in <i>B</i>, but for a different cell (class 10-3a). Scale bars: <i>A</i>, horizontal, 20 ms; vertical, 5 mV.</p

A Model of Filiform Hair Distribution on the Cricket Cercus

<div><p>Crickets and other orthopteran insects sense air currents with a pair of abdominal appendages resembling antennae, called cerci. Each cercus in the common house cricket <em>Acheta domesticus</em> is covered with between 500 to 750 filiform mechanosensory hairs. The distribution of the hairs on the cerci, as well as the global patterns of their movement axes, are very stereotypical across different animals in this species, and the development of this system has been studied extensively. Although hypotheses regarding the mechanisms underlying pattern development of the hair array have been proposed in previous studies, no quantitative modeling studies have been published that test these hypotheses. We demonstrate that several aspects of the global pattern of mechanosensory hairs can be predicted with considerable accuracy using a simple model based on two independent morphogen systems. One system constrains inter-hair spacing, and the second system determines the directional movement axes of the hairs.</p> </div

Histograms showing the distribution of hair movement angles.

<p>A: Summed distribution for experimental measurements from three cerci. B: Summed distributions for three simulation runs using different initial hair positions, using 1×10⁵ iterations to minimize the functional. C: Summed distributions for three simulation runs using different initial hair positions, using 2×10⁶ iterations to minimize the functional. The agreement between the simulations and the experimental distribution were acceptable for P>10⁵. Note the differences in <i>Y</i>-axis scales between the panels.</p

Spatial autocorrelation comparisons.

<p>Value of the Ripley L function of the inter-hair spacing for the model hair distribution (solid line) and experimentally measured hair distribution (circular symbols) for different circular window diameters (in mm). A distribution following a Poisson process would fall on the straight thin diagonal line. Values above the diagonal line indicate spatial clustering, and values below the line indicate spatial segregation. For circular window sizes of 1 mm or larger, the model prediction and experimental measurements show spatial segregation for the filiform hairs. The hairs are observed to be more uniformly distributed than would be observed in a random process indicating the existence of some mechanism (hypothesized as morphogen S) that prevents hairs from being located near one another.</p

Filiform mechanosensory hairs on the cerci of <i>Acheta domesticus</i>.

<p>A: An adult female <i>Acheta domesticus</i> cricket. Scale bar is 1 cm. The cerci are the two antenna-like appendages extending from the rear of the abdomen. B: An enlarged view of a single cercus. Total length of the cercus is 1 cm. Each cercus is covered with approximately 500–750 filiform mechanosensory hairs, which can be seen in this image like bristles on a bottle brush. C: The locations and excitatory movement directions of all filiform hairs on the basal 50% of the right cercus of a typical cricket. This conical segment of the cercus had been cut along its long axis and flattened out onto a plane. All data is from our previous study <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0046588#pone.0046588-Miller1" target="_blank">[2]</a>. The X and Y axis labels of the bounding box are in millimeters. The image has been oriented within the box so that the lateral longitudinal axis of the cercus is defined as the <i>X</i> axis, indicated with a solid red line. That axis corresponds to the <i>lateral lineage restriction line</i> used as one of the sources for morphogen M in the model. The origin at X = 0 corresponds to the base of the cercus at its point of attachment to the abdomen. The medial longitudinal axis is indicated with the dashed red lines near the top and bottom edges of the filet preparation: these lines both represent the same axis, and would wrap around to superimpose on one another to form the conical segment of the cercus. That (fused) dashed axis would correspond to the <i>medial lineage restriction line</i> used as the other source for morphogen M in the model. The 300 arrows in the plot correspond to the array of mechanosensory hairs observed in this section of the cercus. Each arrow corresponds to anatomical measurements from a single hair socket. The center point of each vector corresponds to the location of the corresponding filiform hair socket, and the length of the vector is proportional to the length of the hair. The direction of each arrow indicates the hair’s excitatory direction of hair movement along its movement plane.</p

The distribution and movement directions of filiform mechanosensory hairs.

<p>A, B: Experimental measurements of filiform hair positions and movement directions in two different cricket preparations. C, D: Model predictions for an equivalent segment of the cercus for two different simulations using different initial hair positions. As indicated in the text, filiform hairs are excluded from a small region near the base of cricket cerci containing the clavate sensor array, corresponding to the “scooped-out” regions in panels A and B. We did not attempt to model those restrictions in our simulations, and so the computed arrays in panels C and D show the vectors extending all the way to the medial restriction lines. All labels on the bounding boxes are in mm.</p