Axonal chemotaxis is believed to be important in wiring up the developing and regenerating nervous system, but little is known about how axons actually respond to molecular gradients. We report a new quantitative assay that allows the long-term response of axons to gradients of known and controllable shape to be examined in a three-dimensional gel. Using this assay, we show that axons may be nature’s most-sensitive gradient detectors, but this sensitivity exists only within a narrow range of ligand concentrations. This assay should also be applicable to other biological processes that are controlled by molecular gradients, such as cell migration and morphogenesis. A key hypothesis in developmental neuroscience is that axons are often guided to their targets by sensing molecular gradients 1–4 . Precise measurements of axonal sensitivity to gradients in physiologically rel- evant environments are essential for understanding how gradients direct axons along particular trajectories in vivo, and for designing effective therapeutic interventions using guidance factors. Several quantitative gradient assays have greatly aided the study of chemotaxis in fibroblasts, leukocytes and neutrophils 5–8 . These assays, however, are generally unsuitable for studying axonal guidance, and previous approaches to quantifying axonal sensitivity to gradients have so far provided only limited information 9–14 . Here we present a new technol- ogy that is compatible with the demands of long-term neuronal cell culturing and that allows for the efficient generation of precise, repro- ducible and arbitrarily shaped gradients of diffusible molecules. Using this technology, we show that growth cones, the motile sensing struc- tures at the tips of developing axons, are capable of detecting a concen- tration difference as small as about one molecule across their spatial extent. Furthermore, we show that this sensitivity exists across only a relatively small range of ligand concentrations, indicating that adapta- tion in these growth cones is limited. RESULTS Gradient generation We established gradients by ‘printing’ drops of solution in a a series of ten lines 1 mm apart with increasing amounts of chemotropic molecules onto the surface of a thin collagen gel (Fig. 1a). After a relatively short time, molecules diffuse to fill in the gaps between the printed lines and to create a profile that is independent of the depth. The resulting smooth gradient can be quite stable, as in general the time τ required for significant diffusion over a distance L scales as the square of distance, τ≈ L 2 /D, where D is the diffusion coeffi- cient 15 . For nerve growth factor (NGF), the guidance factor used in these experiments, we have measured D = 8 × 10 –7 cm 2 /s in collagen (see Methods), which gives τ≈ 52 min for L = 0.5 mm, the distance over which molecules must diffuse to fill in the space in between the lines or to reach the midplane of the gel (where the axons are grow- ing), but τ≈ 3.6 d for L = 5 mm, the horizontal distance from the center to the end of the printed pattern. The time-dependent con- centration profile can be calculated using finite element modeling of the diffusion equation. Figure 1b,c shows the result of a two-dimen- sional simulation of an exponential gradient applied to a gel, appro- priate to the situation depicted in Figure 1a, assuming no significant variation in the direction parallel to the printed lines. The printed molecules diffused quickly into the thin gel, and the concentration rapidly became independent of depth (Fig. 1b). The initial oscilla- tions along the length of the block quickly died away, followed by a long period of a relatively stable gradient, particularly at the low- concentration end (Fig. 1c). The actual concentration gradients produced by this method can be measured with quantitative fluorescence imaging. Concentration profiles of fluorescently labeled casein for exponential and linear patterns are shown (Fig. 2a,b; casein is of similar molecular weight to NGF but is relatively inexpensive and easy to label). The actual time- dependent concentration profiles of casein that were extracted from the fluorescence imaging show a good match with the results of the finite element modeling using an independently determined value of D = 6 × 10 –7 cm 2 /s (Fig. 2c). This gradient generation method has several important advantages over previous approaches: large num- bers of identical gradients can be generated quickly, the often pre- cious chemotropic molecules are required in only very limited quantities, the gradients are established in a short time but can remain stable for a day or more, nonlinear gradient shapes can be used and gradients of multiple factors with different shapes and arbi- trary spatial relationships can be generated. This technique could also be used to provide a source of factor while axons are growing, as no direct contact is made with the gel. 1 Department of Neuroscience, Georgetown University Medical Center, Washington, DC, 20007, USA. 2 Department of Physics, Georgetown University, Washington, DC 20057, USA. 3 Department of Anatomy and Neurobiology, and The Program in Neuroscience, University of Maryland School of Medicine, Baltimore, Maryland 21201, USA. 4 These authors contributed equally to this work. Correspondence should be addressed to G.J.G. (geoff@georgetown.edu). Published online: 25 May 2004; doi:10.1038/nn1259 A new chemotaxis assay shows the extreme sensitivity of axons to molecular gradients William J Rosoff 1,4 , Jeffrey S Urbach 2,4 , Mark A Esrick 2 , Ryan G McAllister 2 , Linda J Richards 3 & Geoffrey J Goodhill 1 TECHNICAL REPORT 678 VOLUME 7 | NUMBER 6 | JUNE 2004 NATURE NEUROSCIENCE © 2004 Nature Publishing Group http://www.nature.com/natureneuroscience