Klinotaxis as a basic form of navigation.

Abstract

In their article, Gomez-Marin and Louis (2014) found that runs in Drosophila larval chemotaxis bend toward the direction of higher concentration. This steering process called weathervaning or klinotaxis was previously discovered in the worm C. elegans (Ward, 1973; Iino and Yoshida, 2009) and raises the question: how is it performed? Although Gomez-Marin and Louis (2014) found that run orientation relies on the detection of the lateral gradient component, the underlying control mechanism is largely unknown. Two alternative strategies might be employed, direct error correction and proportional navigation (Figure ​(Figure1A).1A). In direct error correction, the animal would turn proportionally to the error; that is, the local bearing angle between the current heading and the desired direction to the goal (intensity peak). In proportional navigation (Murtaugh and Criel, 1966; Zarchan, 2012), the objective is to maintain a constant line of sight (LOS) angle during motion (Figure ​(Figure1A).1A). This tactic has been known by sailors for many years as a mean to detect collision courses and is currently implemented in guided missiles. Thus, in proportional navigation, the animal would turn proportionally to the derivative of the LOS angle. Here we argue that klinotaxis, as observed in Gomez-Marin and Louis (2014), does not result from direct error correction. Instead, klinotaxis is directed through proportional navigation that is a basic form of navigation (where the goal direction is estimated using gradient sensing rather than spatial memory) involving indirect error correction through an attempt to keep the LOS angle constant. Our claim is supported by theoretical analyses as well as computer simulations. Figure 1 (A) Error correction vs. proportional navigation. The turning rate is proportional to the local bearing angle in error correction and to the rate of change of the LOS angle in proportional navigation. See text for the details. (B) Dependency of the turning ...