### General

I am interested in applying biophysical and quantitative methods to the analysis of learning and behavior in simple organisms. Our approach is to develop instrumentation and methods that allow us to measure and analyze behavioral responses at the motor output level. We hope this bottom up approach will help us detail the molecular, cellular, and neuronal components involved in these pathways, and also allow us to ask questions that span a number of traditional scientific boundaries such as sensory biology, systems neuroscience, theoretical neuroscience, and sensory ecology.

### Measuring patterns of motion in *C. elegans* (work with Bill Bialek and Greg Stephens)

We are interested in developing a quantitative and principled analysis of motor behavior of *C. elegans*as it freely crawls on an agar plate. Behavioral data come from a custom built tracking microscope that allows us to capture and follow the motions of single worms crawling on agar for long time periods. While previous work has described worm movements with ad hoc collections of metrics (e.g. oscillation frequency, center of mass, orientation, etc.), we extract the skeleton of the shape as a head-to-tail ordered array of tangent angles sampled along the curve to explore the full space of shapes, making no

*a priori*assumptions about what aspects of shape are important. Using principal components analysis we show that the shape space is remarkably low dimensional, with four dimensions accounting for ~95% of the shape variance. Given this low dimensional description we can analyze the dynamics of movement as a time series for a small number of variables. Two dimensions exhibit a limit cycle oscillation, which corresponds to sinuous crawling movements. The displacements along the other two dimensions corresponds stereotyped movements such as turns, reversals, and omega turns.

*C. elegans* thermotaxis

The nematode, *C. elegans*is thermotactic and prefers the temperature at which it was cultivated. When placed on agar plates in thermal gradients, worms will migrate toward their preferred temperature and near this temperature they will track isotherms with surprising accuracy (with 0.1C). The thermal preference of worms is plastic. If placed at a different temperature in the presence of food, worms will acquire a new thermal preference in about 4 hours. By applying defined thermal stimuli to single worms using an IR laser and then following the behavior of the worm in time with the worm tracker, we are studying various components of the thermosensory behavior of C. elegans, including the impulse response, isothermal behavior, and general computational strategy.

*C. elegans* foraging

What is the statistical foraging strategy of *C. elegans*? A common model to describe the foraging movements of organisms is the random walk, in which the duration and direction of the forward movement of the organism is chosen randomly. A variation on this strategy allows for taxis. For example, an organism can perform chemotaxis - biasing its motion along a chemical gradient towards an attractant or away from a repellant - by correlating the duration of forward movements with the changes in sensory input. In the absence of any such sensory stimuli, an important question is what statistical strategy will be the most efficient? Or more specifically, from what distribution should the organism choose the duration of its forward movements? It has been suggested that for randomly distributed targets it is more efficient to perform a Levy walk than a Brownian walk. A Levy walk is a random walk in which the run lengths have a power-law distribution ( P(

*l*) µ

*l*-

*μ*, for large

*l*, 1 <

*μ*< 3 ), and a Brownian walk is a random walk in which the run lengths have an normal distribution (μ > 3). More specifically it has been shown that for sparsely distributed targets, the optimal value of μ is 2. It is known that the turning frequency of

*C. elegans*decreases as a function of time away from food. In order to quantify this behavior we are using the tracking microscope to measure trajectories of worms freely crawling on agar plates. We can show that

*C. elegans*in the absence of food performs a Brownian walk initially (μ > 3) and shifts to a Levy walk (μ ~ 2) after a period of about 15 minutes. Through Monte Carlo simulations, we show that this behavior is in fact more efficient than either a Brownian walk or Levy walk alone. We also show that the statistical strategy is under genetic control. Dopamine receptor mutants,

*dop-2*, show Brownian behavior at early and late times, while

*dop-3*mutants show Levy walk behavior at early and late times. We are continuing to explore how this statistical control of strategy is controlled through hormonal neurotransmitter systems of the worm.

*E. coli* thermotaxis

*E. coli*also is thermotactic and prefers a temperature around 30C (in a gradient from 10C to 40C). Using a tethered cell assay where the bacterium is tethered to a glass coverslip by a single flagellar motor, we can measure the behavioral state of single bacteria in time. By apply defined thermal stimuli we can measure the thermal responses of single bacteria. What is the thermotaxis strategy of E. coli? What does the thermosensory system of E. coli tell us about the evolution of early thermal sensation? How does the this system remain robust across such a wide range of temperatures? We are just starting experiments to ask these questions.