Theoretical analysis of gradient detection by growth cones.

Gradients of diffusible and substrate-bound molecules play an important role in guiding axons to appropriate targets in the developing nervous system. Although some of the molecules involved have recently been identified, little is known about the physical mechanisms by which growth cones sense gradients. This article applies the seminal Berg and Purcell (1977) model of gradient sensing to this problem. The model provides estimates for the statistical fluctuations in the measurement of concentration by a small sensing device. By assuming that gradient detection consists of the comparison of concentrations at two spatially or temporally separated points, the model therefore provides an estimate for the steepness of gradient that can be detected as a function of physiological parameters. The model makes the following specific predictions. (a) It is more likely that growth cones use a spatial rather than temporal sensing strategy. (b) Growth cone sensitivity increases with the concentration of ligand, the speed of ligand diffusion, the size of the growth cone, and the time over which it averages the gradient signal. (c) The minimum detectable gradient steepness for growth cones is roughly in the range 1-10%. (d) This value varies depending on whether a bound or freely diffusing ligand is being sensed, and on whether the sensing occurs in three or two dimensions. The model also makes predictions concerning the role of filopodia in gradient detection.     

A Mechanism for the Polarity Formation of Chemoreceptors at the Growth Cone Membrane for Gradient Amplification during Directional Sensing

Accurate response to external directional signals is essential for many physiological functions such as chemotaxis or axonal guidance. It relies on the detection and amplification of gradients of chemical cues, which, in eukaryotic cells, involves the asymmetric relocalization of signaling molecules. How molecular events coordinate to induce a polarity at the cell level remains however poorly understood, particularly for nerve chemotaxis. Here, we propose a model, inspired by single-molecule experiments, for the membrane dynamics of GABA chemoreceptors in nerve growth cones (GCs) during directional sensing. In our model, transient interactions between the receptors and the microtubules, coupled to GABA-induced signaling, provide a positive-feedback loop that leads to redistribution of the receptors towards the gradient source. Using numerical simulations with parameters derived from experiments, we find that the kinetics of polarization and the steady-state polarized distribution of GABA receptors are in remarkable agreement with experimental observations. Furthermore, we make predictions on the properties of the GC seen as a sensing, amplification and filtering module. In particular, the growth cone acts as a low-pass filter with a time constant ∼10 minutes determined by the Brownian diffusion of chemoreceptors in the membrane. This filtering makes the gradient amplification resistent to rapid fluctuations of the external signals, a beneficial feature to enhance the accuracy of neuronal wiring. Since the model is based on minimal assumptions on the receptor/cytoskeleton interactions, its validity extends to polarity formation beyond the case of GABA gradient sensing. Altogether, it constitutes an original positive-feedback mechanism by which cells can dynamically adapt their internal organization to external signals.     

Growth cones turn and migrate up an immobilized gradient of the laminin IKVAV peptide

Growth cone navigation is guided by extrinsic environmental proteins, called guidance cues. Many in vitro studies have characterized growth cone turning up and down gradients of soluble guidance cues. Although previous studies have shown that axonal elongation rates can be regulated by gradients of surface-bound molecules, there are no convincing demonstrations of growth cones turning to migrate up a surface-bound gradient of an adhesive ligand or guidance cue. In order to test this mode of axonal guidance, we used a photo-immobilization technique to create grids and gradients of an adhesive laminin peptide on polystyrene culture dish surfaces. Chick embryo dorsal root ganglia (DRGs) were placed on peptide grid patterns containing surface-bound gradients of the IKVAV-containing peptide. DRG growth cones followed a path of surface-bound peptide to the middle of a perpendicularly oriented gradient with a 25% concentration difference across 30 microm. The majority of growth cones turned and migrated up the gradient, turning until they were oriented directly up the gradient. Growth cones slowed their migration when they encountered the gradient, but growth cone velocity returned to the previous rate after turning up or down the gradient. This resembles in vivo situations where growth cones slow at a choice point before changing the direction of axonal extension. Thus, these results support the hypothesis that mechanisms of axonal guidance include growth cone orientation by gradients of surface-bound adhesive molecules and guidance cues.     

Binding characteristics of chondroitin sulfate proteoglycans and laminin‐1, and correlative neurite outgrowth behaviors in a standard tissue culture choice assay

Neuronal growth cones are capable of sophisticated discrimination of environmental cues, on cell surfaces and in the extracellular matrix, to accomplish navigation during development (generation) and following nervous system injury (regeneration). Choices made by growth cones are commonly examined using tissue culture paradigms in which molecules of interest are purified and substratum‐bound. From observations of growth cone behaviors using these paradigms, assertions are made about choices neuronal growth cones may make in vivo. However, in many cases, the binding, interactions, and conformations of these molecules have not been determined. In the present study, we investigated the binding characteristics of two commonly studied outgrowth regulatory molecules: chondroitin sulfate proteoglycans (CSPGs), which are typically inhibitory to neurite outgrowth during development and following nervous system injury, and laminin, which is typically outgrowth promoting for many neuronal types. Using a novel combination of radiolabeling and quantitative fluorescence, we determined the precise concentrations of CSPGs and laminin‐1 that were bound separately and together in a variety of choice assays. For identically prepared cultures, we correlated neurite outgrowth behaviors with binding characteristics. The data support our working hypothesis that neuronal growth cones are guided by the ratio of outgrowth‐promoting to outgrowth‐inhibiting influences in their environment, i.e., they summate local molecular cues. The response of growth cones to these molecular combinations is most likely mediated by integrins and subsequent activation of signal transduction cascades in growth cones. © 2002 Wiley Periodicals, Inc. J Neurobiol 51: 285–301, 2002     

B‐type Eph receptors and ephrins induce growth cone collapse through distinct intracellular pathways

Forward and reverse signaling mediated by EphB tyrosine kinase receptors and their transmembrane ephrin‐B ligands play important roles in axon pathfinding, yet little is known about the intracellular pathways involved. Here we have used growth cones from the ventral (EphB receptor‐bearing) and dorsal (ephrin‐B‐bearing) embryonic Xenopus retina to investigate the signaling mechanisms in both forward and reverse directions. We report that unclustered, but not clustered, EphB2 ectodomains trigger fast (5–10 min) transient collapse responses in growth cones. This collapse response is mediated by low levels of intracellular cyclic GMP and requires proteasome function. In contrast, clustered, but not unclustered, ephrin‐B1 ectodomains cause slow (30–60 min) growth cone collapse that depends on high cGMP levels and is insensitive to inhibition of the proteasomal pathway. Upon receptor‐ligand binding, endocytosis occurs in the reverse direction (EphB2‐Fc into dorsal retinal growth cones), but not the forward direction, and is also sensitive to proteasomal inhibition. Endocytosis is functionally important because blocking of EphB2 internalization inhibits growth cone collapse. Our data reveal that distinct signaling mechanisms exist for B‐type Eph/ephrin‐mediated growth cone guidance and suggest that endocytosis provides a fast mechanism for switching off signaling in the reverse direction. © 2003 Wiley Periodicals, Inc. J Neurobiol 57: 323–336, 2003     

Integration of Shallow Gradients of Shh and Netrin-1 Guides Commissural Axons

During nervous system development, gradients of Sonic Hedgehog (Shh) and Netrin-1 attract growth cones of commissural axons toward the floor plate of the embryonic spinal cord. Mice defective for either Shh or Netrin-1 signaling have commissural axon guidance defects, suggesting that both Shh and Netrin-1 are required for correct axon guidance. However, how Shh and Netrin-1 collaborate to guide axons is not known. We first quantified the steepness of the Shh gradient in the spinal cord and found that it is mostly very shallow. We then developed an in vitro microfluidic guidance assay to simulate these shallow gradients. We found that axons of dissociated commissural neurons respond to steep but not shallow gradients of Shh or Netrin-1. However, when we presented axons with combined Shh and Netrin-1 gradients, they had heightened sensitivity to the guidance cues, turning in response to shallower gradients that were unable to guide axons when only one cue was present. Furthermore, these shallow gradients polarized growth cone Src-family kinase (SFK) activity only when Shh and Netrin-1 were combined, indicating that SFKs can integrate the two guidance cues. Together, our results indicate that Shh and Netrin-1 synergize to enable growth cones to sense shallow gradients in regions of the spinal cord where the steepness of a single guidance cue is insufficient to guide axons, and we identify a novel type of synergy that occurs when the steepness (and not the concentration) of a guidance cue is limiting.     

Growth cone behavior on gradients of substratum bound laminin

We have tested the ability of a gentle gradient of neurite-promoting activity to orient the extension of embryonic growth cones. Gradients of neurite-promoting activity were made with biologically active, tritium-labeled laminin. The distributions of laminin bound to glass substrata were visualized by autoradiography and quantified with an image processing system. Embryonic chick sympathetic ganglia were explanted onto laminin gradients and cultured. No tendency for neurites to be oriented up-gradient was detected by examining the morphology of explants. Time-lapse studies of individual growth cones detected no up- or down-gradient bias in growth cone motility. These results suggest that growth cone orientation is relatively insensitive to a graded distribution of a naturally occurring neurite-promoting molecule.     

Modulation of growth cone morphology by substrate-bound adhesion molecules.

The growth cone, a terminal structure on developing and regenerating axons, is specialized for motility and guidance functions. In vivo the growth cone responds to environmental cues to guide the axon to its appropriate target. These cues are thought to be responsible for position-specific morphological changes in the growth cone, but the molecules that control growth cone behavior are poorly characterized. We used scanning electron microscopy to analyze the morphology of retinal ganglion cell growth cones in vitro on different adhesion molecules that axons normally encounter in vivo. L1/8D9, N-cadherin, and laminin each induced distinctive morphological characteristics in growth cones. Growth cones elaborated lamellipodial structures in response to the cell adhesion molecules L1/8D9 and N-cadherin, whereas laminin supported filopodial growth cones with small veils. On L1/8D9, the growth cones were larger and produced more filopodia. Filopodial associations between adjacent growth cones and neurites were frequent on L1/8D9 but were uncommon on laminin or N-cadherin. These results demonstrate that different adhesion molecules have profoundly different effects on growth cone morphology. This is consistent with previous reports suggesting that changes in growth cone morphology in vivo occur in response to changes in substrate composition.     

Mechanisms of growth cone guidance and motility in the developing grasshopper embryo

During neuronal pathfinding in vivo, growth cones must reorient their direction of migration in response to extracellular guidance cues. The developing grasshopper limb bud has proved to be a model system in which to examine mechanisms of growth cone guidance and motility in vivo. In this review we examine the contributions of adhesion and multiple guidance cues (semaphorins 1 and 2) in directing a growth cone steering event. Recent observations have suggested that the tibial pioneer growth cones are not directed via mechanisms of differential adhesivity. We present a model of growth cone steering that suggests a combination of adhesive and guidance receptors are important for a correct steering event and that guidance molecules may be important regulators of adhesive interactions with the actin cytoskeleton.     

On the turning of Xenopus retinal axons induced by ephrin-A5

The Eph family of receptor tyrosine kinases and their ligands, the ephrins, play important roles during development of the nervous system. Frequently they exert their functions through a repellent mechanism, so that, for example, an axon expressing an Eph receptor does not invade a territory in which an ephrin is expressed. Eph receptor activation requires membrane-associated ligands. This feature discriminates ephrins from other molecules sculpturing the nervous system such as netrins, slits and class 3 semaphorins, which are secreted molecules. While the ability of secreted molecules to guide axons, i.e. to change their growth direction, is well established in vitro, little is known about this for the membrane-bound ephrins. Here we set out to investigate--using Xenopus laevis retinal axons--the properties of substratum-bound and (artificially) soluble forms of ephrin-A5 (ephrin-A5-Fc) to guide axons. We find--as expected on the basis of chick experiments - that, when immobilised in the stripe assay, ephrin-A5 has a repellent effect such that retinal axons avoid ephrin-A5-Fc-containing lanes. Also, retinal axons react with repulsive turning or growth cone collapse when confronted with ephrin-A5-Fc bound to beads. However, when added in soluble form to the medium, ephrin-A5 induces growth cone collapse, comparable to data from chick. The analysis of growth cone behaviour in a gradient of soluble ephrin-A5 in the 'turning assay' revealed a substratum-dependent reaction of Xenopus retinal axons. On fibronectin, we observed a repulsive response, with the turning of growth cones away from higher concentrations of ephrin-A5. On laminin, retinal axons turned towards higher concentrations, indicating an attractive effect. In both cases the turning response occurred at a high background level of growth cone collapse. In sum, our data indicate that ephrin-As are able to guide axons in immobilised bound form as well as in the form of soluble molecules. To what degree this type of guidance is relevant for the in vivo situation remains to be shown.     

Growth cone form, behavior, and interactions in vivo: retinal axon pathfinding as a model

Studies in vitro have revealed a great deal about growth cone behaviors, especially responses to guidance molecules, both positive and negative, and the signaling systems mediating these responses. Little, however, is known about these events as they take place in vivo. With new imaging methods, growth cone behaviors can be chronicled in the complex settings of intact or semi-intact systems. With the retinal projection through the optic chiasm as a model, we examined the hypothesis previously drawn from static material that growth cone form is position-specific: growth cone form in fact reflects specific behaviors, including rate and tempo of extension, that are more or less prominent in different locales in which growth cones are situated. Other studies show that growth cones interact with cells along the pathway, both specialized nonneuronal cells and other neurons, some expressing known guidance molecules. The present challenge is to bridge dynamic imaging with electron microscopy and molecular localization, in order to link growth cone behaviors with cell and molecular interactions in the natural setting in which growth cones extend.     

Binding characteristics of chondroitin sulfate proteoglycans and laminin-1, and correlative neurite outgrowth behaviors in a standard tissue culture choice assay

Neuronal growth cones are capable of sophisticated discrimination of environmental cues, on cell surfaces and in the extracellular matrix, to accomplish navigation during development (generation) and following nervous system injury (regeneration). Choices made by growth cones are commonly examined using tissue culture paradigms in which molecules of interest are purified and substratum-bound. From observations of growth cone behaviors using these paradigms, assertions are made about choices neuronal growth cones may make in vivo. However, in many cases, the binding, interactions, and conformations of these molecules have not been determined. In the present study, we investigated the binding characteristics of two commonly studied outgrowth regulatory molecules: chondroitin sulfate proteoglycans (CSPGs), which are typically inhibitory to neurite outgrowth during development and following nervous system injury, and laminin, which is typically outgrowth promoting for many neuronal types. Using a novel combination of radiolabeling and quantitative fluorescence, we determined the precise concentrations of CSPGs and laminin-1 that were bound separately and together in a variety of choice assays. For identically prepared cultures, we correlated neurite outgrowth behaviors with binding characteristics. The data support-our working hypothesis that neuronal growth cones are guided by the ratio of outgrowth-promoting to outgrowth-inhibiting influences in their environment, i.e., they summate local molecular cues. The response of growth cones to these molecular combinations is most likely mediated by integrins and subsequent activation of signal transduction cascades in growth cones.     

Autonomous regulation of growth cone filopodia

The fan-shaped array of filopodia is the first site of contact of a neuronal growth cone with molecules encountered during neuronal pathfinding. Filopodia are highly dynamic structures, and the “action radius” of a growth cone is strongly determined by the length and number of its filopodia. Since interactions of filopodia with instructive cues in the vicinity of the growth cone can have effects on growth cone morphology within minutes, it has to be assumed that a large part of the signaling underlying such morphological changes resides locally within the growth cone proper. In this study, we tested the hypothesis that two important growth cone parameters namely, the length and number of its filopodiaare regulated autonomously in the growth cone. We previously demonstrated in identified neurons from the snail Helisoma trivolvis that filopodial length and number are regulated by intracellular calcium. Here, we investigated filopodial dynamics and their regulation by the second-messenger calcium in growth cones which were physically isolated from their parent neuron by neurite transection. Our results show that isolated growth cones have longer but fewer filopodia than growth cones attached to their parent cell. These isolated growth cones, however, are fully capable of undergoing calcium-induced cytoskeletal changes, suggesting that the machinery necessary to perform changes in filopodial length and number is fully intrinsic to the growth cone proper. © 1998 John Wiley & Sons, Inc. J Neurobiol 34: 179–192, 1998     

Growth cone navigation in substrate-bound ephrin gradients

Graded distributions of ephrin ligands are involved in the formation of topographic maps. However, it is still poorly understood how growth cones read gradients of membrane-bound guidance molecules. We used microcontact printing to produce discontinuous gradients of substrate-bound ephrinA5. These consist of submicron-sized protein-covered spots, which vary with respect to their sizes and spacings. Growth cones of chick temporal retinal axons are able to integrate these discontinuous ephrin distributions and stop at a distinct zone in the gradient while still undergoing filopodial activity. The position of this stop zone depends on both the steepness of the gradient and on the amount of substrate-bound ephrin per unit surface area. Quantitative analysis of axon outgrowth shows that the stop reaction is controlled by a combination of the local ephrin concentration and the total amount of encountered ephrin, but cannot be attributed to one of these parameters alone.     

Activation of ADF/cofilin mediates attractive growth cone turning toward nerve growth factor and netrin‐1

Proper neural circuitry requires that growth cones, motile tips of extending axons, respond to molecular guidance cues expressed in the developing organism. However, it is unclear how guidance cues modify the cytoskeleton to guide growth cone pathfinding. Here, we show acute treatment with two attractive guidance cues, nerve growth factor (NGF) and netrin‐1, for embryonic dorsal root ganglion and temporal retinal neurons, respectively, results in increased growth cone membrane protrusion, actin polymerization, and filamentous actin (F‐actin). ADF/cofilin (AC) family proteins facilitate F‐actin dynamics, and we found the inactive phosphorylated form of AC is decreased in NGF‐ or netrin‐1‐treated growth cones. Directly increasing AC activity mimics addition of NGF or netrin‐1 to increase growth cone protrusion and F‐actin levels. Extracellular gradients of NGF, netrin‐1, and a cell‐permeable AC elicit attractive growth cone turning and increased F‐actin barbed ends, F‐actin accumulation, and active AC in growth cone regions proximal to the gradient source. Reducing AC activity blunts turning responses to NGF and netrin. Our results suggest that gradients of NGF and netrin‐1 locally activate AC to promote actin polymerization and subsequent growth cone turning toward the side containing higher AC activity. © 2010 Wiley Periodicals, Inc. Develop Neurobiol 70: 565–588, 2010     

Long-range signaling in growing neurons after local elevation of cyclic AMP-dependent activity

Cyclic AMP-dependent activity at the growth cone or the soma of cultured Xenopus spinal neurons was elevated by local extracellular perfusion of the neuron with culture medium containing 8-bromoadenosine 3',5'-cyclic monophosphate (8-br-cAMP) or forskolin. During local perfusion of one of the growth cones of multipolar neurons with these drugs, the perfused growth cone showed further extension, while the distant, unperfused growth cones were inhibited in their growth. Local perfusion of the growth cone with culture medium or local perfusion with 8-br-cAMP at a cell-free region 100 microns away from the growth cone did not produce any effect on the extension of the growth cone. Reduced extension of all growth cones was observed when the perfusion with 8-br-cAMP was restricted to the soma. The distant inhibitory effect does not depend on the growth of the perfused growth cone since local coperfusion of the growth cone with 8-br-cAMP and colchicine inhibited growth on both perfused and unperfused growth cones, while local perfusion with colchicine alone inhibited only the perfused growth cone. The distant inhibitory effect was abolished when the perfusion of 8-br-cAMP was carried out together with kinase inhibitor H- 8, suggesting the involvement of cAMP-dependent protein kinase and/or its downstream factors in the long-range inhibitory signaling. Uniform exposure of the entire neuron to bath-applied 8-br-cAMP, however, led to enhanced growth activity at all growth cones. Thus, local elevation of cAMP-dependent activity produces long-range and opposite effects on distant parts of the neuron, and a cytosolic gradient of second messengers may produce effects distinctly different from those following uniform global elevation of the messenger, leading to differential growth regulation at different regions of the same neuron.     

Cortical neurite outgrowth and growth cone behaviors reveal developmentally regulated cues in spinal cord membranes

Corticospinal axon outgrowth in vivo and the ability to sprout or regenerate after injury decline with age. This developmental decline in growth potential has been correlated with an increase in inhibitory myelin‐associated proteins in older spinal cord. However, previous results have shown that sprouting of corticospinal fibers after contralateral lesions begins to diminish prior to myelination, suggesting that a decrease in growth promoting and/or an increase in inhibitory molecules in spinal gray matter may also regulate corticospinal axon outgrowth. To address this possibility, we carried out in vitro experiments to measure neurite outgrowth from explants of 1‐day‐old hamster forelimb sensorimotor cortex that were plated onto membrane carpets or membrane stripe assays prepared from white or gray matter of 1‐to 22‐day‐old cervical spinal cord. On uniform carpets and in the stripe assays cortical neurites grew robustly on young but not older membranes from both white and gray matter. Mixtures of membranes from 1‐ and 15‐day spinal cord inhibited neurite outgrowth, suggesting that the presence of inhibitory molecules in the 15‐day cord overwhelmed permissive or growth promoting molecules in membranes from 1‐day cord. Video microscopic observations of growth cone behaviors on membrane stripe assays transferred to glass coverslips supported this view. Cortical growth cones repeatedly collapsed at borders between permissive substrates (laminin or young membrane stripes) and nonpermissive substrates (older membrane stripes). Growth cones either turned away from the older membranes or reduced their growth rates. These results suggest that molecules in both the gray and white matter of the developing spinal cord can inhibit cortical neurite outgrowth. © 1999 John Wiley & Sons, Inc. J Neurobiol 39: 393–406, 1999     

Patch dynamics and local succession in a sandstone area with frequent disturbance

Abstract. A system of sand talus cones in a small forested rocky sandstone area was investigated to determine the importance of disturbance‐related dynamics and mesoclimate to vegetation differentiation. These cones (usually 3–12 m long) are formed by the accumulation of sand at the foot of sandstone rocks and are subject to frequent disturbance by the transport of sand. Vegetation was recorded both at the whole‐cone level and at the within‐cone level; the latter was approached by means of a transect of small squares along each cone. Soil profiles were recorded at the upper, centre and bottom parts of the cones. To express mesoclimatic differentiation among the cones within the rocky area, the potential insolation was calculated from the horizon angular height and the likelihood of thermal inversions was estimated by the height of the cones above the valley bottom. The major environmental factor correlated with variation in cone vegetation is the disturbance dynamics as determined by the structure of the soil profile; active cones (with sand at the surface) are colonized by different species as compared with non‐active cones (with surface covered by humus sediments). There is a clear primary succession gradient from plants able to cope with continuous sand transport to stands of tall bryophytes, small shrubs and herbs. Quite often the same gradient is found within cones, with late successional vegetation confined to the lower, stabilized parts of the cones, while the upper part is still being affected by sand transport. The differentiation along the gradient of disturbance is much stronger than the differentiation due to climatic or other gradients. Indirect data indicate that the long‐term average rate of sand accumulation is ca. 1 mm/yr. If sand transport ceases, Sphagnum peat accumulates on some of the cones; the depth of accumulated Sphagnum remains may reach 50 cm. The development of the peat layer is but weakly correlated with the measured variables suggesting that random processes at the beginning of Sphagnum establishment may be a driving force. By measuring Sphagnum growth and decomposition, and the peat density, we estimated the time needed for their development to be several hundreds of years.     

Response of retinal ganglion cell axons to striped linear gradients of repellent guidance molecules

Although molecular gradients have long been postulated to play a role in the development of topographic projections in the nervous system, relatively little is known about how axons evaluate gradients. Do growth cones respond to concentration or to slope? Do they react suddenly or gradually? Is there adaptation? In the developing retinotectal system, temporal retinal ganglion cell axons have previously been shown to avoid repellent cell-surface activities distributed in gradients across the optic tectum. We confronted temporal retinal axons with precisely formed striped linear gradients of repellent tectal membranes and of two candidate repellent molecules, ephrin-A2 and -A5. Axons entered gradient stripes independently of their slope and extended unhindered in the uphill direction until they suddenly avoided an apparent threshold concentration of repellent material that was independent of slope. This critical concentration was similar in both linear and nonlinear gradients, and hence independent of gradient shape. When gradients of identical slope were formed on different basal levels of repellent material, axons grew uphill for a fixed increment of concentration, possibly measured from the lowest point of the gradient, rather than up to a fixed absolute concentration. The speed of growth cones was not affected by repellent unstriped gradients below the critical concentration level. Similar results were found with membranes from cell lines stably transfected with either ephrin-A5 or ephrin-A2, two previously identified growth cone repellent cell-surface proteins. These data suggest that growth cones or axons can integrate guidance information over large distances, probably by a combined memory and adaptation mechanism. © 1998 John Wiley & Sons, Inc. J Neurobiol 37: 541–562, 1998     

A stochastic model of neuronal growth cone guidance regulated by multiple sensors

Neuronal growth cones migrate directionally under the control of axon guidance molecules, thereby forming synapses in the developing brain. The signal transduction system by which a growth cone detects surrounding guidance molecules, analyzes the detected signals, and then determines the overall behavior remains undetermined. In this study, we describe a novel stochastic model of this behavior that utilizes multiple sensors on filopodia to respond to guidance molecules. Overall growth cone behavior is determined by using only the concentration gradients of guidance molecules in the immediate vicinity of each sensor. The detected signal at each sensor, which is treated as a vector quantity, is sent to the growth cone center and then integrated to determine axonal growth in the next step by means of a simple vector operation. We compared the results of computer simulations of axonal growth with observations of actual axonal growth from co-culture experiments using olfactory bulb and septum. The probabilistic distributions of axonal growth generated by the computer simulation were consistent with those obtained from the culture experiments, indicating that our model accurately simulates growth cone behavior. We believe that this model will be useful for elucidating the as yet unknown mechanisms responsible for axonal growth in vivo.