First published online December 2, 2005
Journal of Experimental Biology 208, 4727-4733 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01933
Analysis of the effects of turning bias on chemotaxis in C. elegans
Jonathan T. Pierce-Shimomura1,2,*,
Michael Dores2 and
Shawn R. Lockery2
1 Ernest Gallo Clinic and Research Center, Department of Neurology, Programs
in Neuroscience and Biomedical Science, University of California, San
Francisco, 5858 Horton Street, Suite 200, Emeryville, CA 94608, USA
2 Institute of Neuroscience, University of Oregon, Eugene, OR 97403-1254,
USA
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Fig. 1. Effect of the unc-23 bent-head phenotype on movement. (A)
Morphology of typical wild-type and unc-23 worms. The bend in the
head of the unc-23 mutant is indicated by an arrow. (B) Comparison of
dispersion and chemotaxis behavior for wild-type (Biii,Biv) and
unc-23 mutant (Bi,Bii) animals. Shown are representative tracks made
by individual unc-23 mutants and wild-type animals in the absence of
a gradient (Bi,Biii) and in the presence of a radial gradient of chemical
attractant (NH4Cl; Bii,Biv). The unc-23 track comprises a
series of curls visible in the expanded inset. Note that the handedness of the
curls, indicative of turning bias (clockwise), is opposite to the handedness
of the spiral track (counterclockwise). Pirouette initiation events are
indicated by orange crosses superimposed on the magnified track within the
inset. Animals were started near asterisks; the gradient peak is indicated by
the plus sign. Color represents time, as shown in the key. Elapsed time was 20
min for tracks Bi, Biii and Biv, and 90 min for the track in Bii. (C,D)
Distributions of turning bias and instantaneous speed for wild-type (black
lines) and unc-23 mutant (solid gray bars) animals. Arrowheads
indicate the average for each distribution.
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Fig. 2. Analysis of pirouette initiation and execution. (A) Instantaneous pirouette
rate as a function of the value of dC/dt for wild-type and
mutant animals in NH4Cl gradients. The data have been smoothed with
a box filter (4001 points long). The gray line represents unc-23 data
(21 293 points); the black line represents wild-type data (29 171 points).
Spontaneous or basal pirouette rates measured in the absence of a gradient are
represented by horizontal lines (black broken line, wild-type; gray dotted,
unc-23). (B–D) Histograms of bearings immediately before
pirouettes (B), immediately after pirouettes (C), and changes in bearing (D)
for the animals in A. The wild-type distributions (black lines) contain 1129
pirouettes; the unc-23 distributions (solid gray bars) contain 816
pirouettes. Arrowheads indicate the angle of the vector average for each
distribution; numbers indicate the corresponding vector magnitude.
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Fig. 3. Mathematical model of unc-23 behavior. (A) Representative track of
a simulated unc-23 mutant in a radial gradient. Note that the
simulated worm had a clockwise turning bias (7 deg. s–1) and
made a counterclockwise spiral, as do real unc-23 mutants
(Fig. 1Bii). The gradient peak
is indicated by the plus sign. Color represents time (see color scale).
Pirouette initiation events are indicated by orange crosses superimposed on
the magnified track within the inset. (B) Population behavior of simulated
unc-23 worms in a radial gradient. The track of one simulated worm is
highlighted in black; all other tracks are gray (N=50). Each
simulated worm had a right-handed turning bias and made a left-handed spiral.
The gradient peak is indicated by intersection of dotted lines. Simulations in
A and B were started near the asterisks.
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Fig. 4. Geometric analysis of the interaction between unc-23 pirouette
behavior and turning bias. An idealized unc-23 mutant animal moves
with a constant clockwise turning bias and produces pirouettes with either a
180° or 0° change in bearing. The animal moves in a radial gradient
from the starting position indicated by asterisks; the gradient peak is at the
plus sign. Shown are four cases in which the animal initiates pirouettes in
only one quadrant (I, II, III or IV) that is defined relative to direction of
the gradient peak (see diagrams adjacent to each track). (A) Quadrant IV
pirouettes produce a clockwise spiral track. This type of track corresponds to
the unc-23 tracks reported in the original study
(Ward, 1973 ). (B) Quadrant I
pirouettes produce a counterclockwise spiral track centered on the radial
gradient peak. This type of track corresponds to the real unc-23
track shown in Fig. 1Bii. (C,D)
Quadrants II or III pirouettes produce spiral tracks leading down the gradient
away from the gradient peak.
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Fig. 5. The variability of pirouette latency within curls and its affect on the
unc-23 model. (A) Pirouette probability by quadrant in real
unc-23 worms. Quadrants I–IV are defined as in
Fig. 4. Total number of
pirouettes was 216. (B) Population behavior of simulated unc-23 worms
that initiate pirouettes according to the probabilities in A. Imposing the
probabilities in A on the model was sufficient to produce spiral tracks with
opposite spiral-bias handedness. Simulated worms had a constant clockwise
turning bias of 7 deg. s–1. Each simulated worm was started
near asterisks and allowed to move for the equivalent of 90 min. The gradient
peak is indicated by intersection of dotted lines. The track of one simulated
worm is highlighted in black; all other tracks are gray (N=50).
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© The Company of Biologists Ltd 2005
