Neuronal processing of translational optic flow in the visual system of the shore crab Carcinus maenas

Vision plays a key role in the majority of animals for their survival. However, the variety of eye types and the functions for which they are adapted is huge (Land and Nilsson, 2002). In contrast to the camera eyes of vertebrates, many arthropods have compound eyes, made up of individual units called ommatidia, each of which has its own lens system and photoreceptors. Such compound eyes have two major subtypes, apposition and superposition, that are adapted for vision under high and low light intensities, respectively (Land, 1981). The eyes of crabs are known as parabolic superposition eyes (there are also reflecting and refracting superposition eye types), and each ommatidium uses a mixture of lens and mirror optics to form an image of a small part of the field of view at the tip of the rhabdom, the part of the eye where the visual pigment is located (Nilsson, 1988). Compared with humans, both spatial acuity and colour vision are poor, but the eyes do detect ultraviolet light and are sensitive to the plane of polarisation of light. The latter ability is particularly useful for seeing reflecting surfaces (Zeil and Zanker, 1997) and, at least in insects such as bees, is used for navigation. Crab eyes, though lacking a fovea, have a band of high acuity located around the equator of the eye, which is particularly pronounced in ‘flat-world’ crabs that live on sand or mud flats, though less so in ‘complex-environment’ crabs such as the shore crab Carcinus (Zeil et al., 1986; Zeil et al., 1989), the crab used in this study.

As well as the perception of brightness and colour, eyes detect form and movement, and this motion perception is involved in a multitude of behavioural tasks including finding and/or selecting a mate, avoiding predators and catching prey, as well as more basic tasks such as control of balance and those that contribute to oculomotor reflexes. Motion detection can also be used by animals to detect their own movements (self-motion) in order to navigate through their surroundings. Therefore, the detection of movement plays a very important part in an animal's life and, consequently, has been an active field of research (for reviews, see Land, 1999; Eckert and Zeil, 2001).

Of particular interest is the image motion over the retina of the eye resulting from an animal moving through its surroundings, first described by Gibson over 60 years ago (Gibson, 1950). The term ‘optic flow’ was used by Gibson to describe these images and his studies were aimed at understanding the role of optic flow in visual perception and guidance (Gibson, 1950; Gibson, 1966; Gibson, 1986). The mathematics underlying these studies was described by Koenderink and Van Doorn (Koenderink and Van Doorn, 1987) and has led to rapid advances in computer vision and the development of autonomous robots that can navigate on the basis of optic flow (e.g. Srinivasan et al., 1999; Green et al., 2004; Hyslop et al., 2010). Optic flow can be split into two components, rotational and translational. Active turning results in a rotational optic flow field in which all the vectors (indicating direction of motion and its velocity) at a given elevation have the same length, irrespective of the distance of the objects in the image, and they all point in the opposite direction to the movement. Motion in a straight line, however, produces a translational flow field with a pole or focus of expansion in the direction of travel, and vector length depends on both the angle of the contour relative to the direction of travel and the distance of objects from the eye. Gibson demonstrated that the rotational component could be used to correct deviations from an intended path whereas the translational component provides animals with a large amount of information about their own movement, such as velocity, distance covered and heading (Gibson, 1966). Since this time, evidence has accumulated for the involvement of optic flow in tasks such as distance estimation (David, 1982; Srinivasan et al., 1991), collision avoidance (Holmqvist and Srinivasan, 1991; Tammero and Dickinson, 2002), maintenance of a constant heading (Collett and Land, 1975), course stabilization and oculomotor control (Hassenstein and Reichardt, 1956; Götz, 1975), triggering of landing responses (Wagner, 1982) and control of moth–flower distance in hovering flight (Farina et al., 1994).

Within the vertebrates, optic flow neurones have been recorded from both birds and mammals, including the mammalian vestibulocerebellum (Simpson et al., 1981), primate dorsal medial superior temporal area (Saito et al., 1986; Tanaka and Saito, 1989; Paolini et al., 2000), primate ventral intraparietal area (Bremmer et al., 2002) and avian nucleus rotundus (Wang and Frost, 1992; Wylie and Frost, 1993; Sun and Frost, 1998). Optic flow neurones of insects include neurones in hovering moths that respond to looming or receding stimuli (Wicklein and Strausfeld, 2000), but undoubtedly the best understood system is the lobula plate (third optic neuropil) of blowflies. This contains approximately 60 wide-field directionally selective visual interneurones called tangential neurones (Hausen, 1982a; Hausen, 1982b; Hausen, 1984; Hausen and Egelhaaf, 1989). Elegant experiments by Krapp and Hengstenberg (Krapp and Hengstenberg, 1996) and Krapp et al. (Krapp et al., 1998) [reviewed by Krapp (Krapp, 2000) and extended by Haag and Borst (Haag and Borst, 2004) amongst others], have revealed that many of these neurones have distributions of local preferred directions (LPDs) and local motion sensitivities (LMSs) that show a striking similarity to those of optic flow fields. The findings suggest that each tangential neurone is tuned to process image flow generated by specific movements of the flying insect (for a review, see Taylor and Krapp, 2007).

Much less is known about the visual system of crustaceans. Early work identified response properties of interneurones of the optic nerve to simple stimuli. These included sustaining fibres, dimming fibres and several classes of motion detectors (Waterman et al., 1964; Wiersma, 1966; Wiersma and Yamaguchi, 1966; Wiersma and Yamaguchi, 1967; York and Wiersma, 1975) (reviewed in Wiersma et al., 1982). Subsequent studies based on intracellular recording and Lucifer Yellow injections confirmed the identity of many of the sustaining fibres (Kirk et al., 1982; Kirk et al., 1983). More recent work on the neural integration of motion stimuli of particular relevance to this study examined the properties of neurones responsive to looming stimuli that elicit escape (Tomsic et al., 2003; Medan et al., 2007; Oliva et al., 2007; Sztarker and Tomsic, 2008).

The present study examines the responses of visual neurones sensitive to optic flow in the visual system of the shore crab using Krapp and Hengstenberg's procedure (Krapp and Hengstenberg, 1997) adapted for crabs (Johnson et al., 2002) and other visual stimulation methods. This involves determining the local motion sensitivity at many points within the receptive field. The map of LPDs and LMSs derived in this way then reveals the cell's global motion sensitivity. Using this method, we discovered two families of interneurones sensitive to optic flow, one in the lobula and the other in the medulla. We hypothesise that the lobula and medulla interneurones are representatives of arrays of cells with poles at different azimuth angles, each of which would be optimally activated by self-motion in a different direction. The lobula neurones would be stimulated by the approaching scene, the medulla neurones by the receding scene. Preliminary accounts of these experiments appear in Barnes et al. (Barnes et al., 2001; Barnes et al., 2002).

Experiments were performed on shore crabs Carcinus maenas (Linnaeus 1758) collected from the Firth of Clyde, Scotland (Millport Marine Station). They were maintained for up 2 months in holding tanks of circulating seawater (10°C, 12 h:12 h light:dark regime) before use. They were fed once a week on a diet of fish.

Recordings were made from the right eyestalk of crabs of both sexes (carapace width=5–7 cm). Each crab was first induced to autotomise the chelae, and was mounted horizontally in a clamp. The right eyestalk was then fixed to the carapace with cyanoacrylate cement in a natural ‘raised’ position while the left eye was glued into a position fully withdrawn into its socket. In order to make intracellular recordings from visual interneurones in the optic lobe it was necessary to exchange the blood for oxygenated Ringer's solution. This was done by a method broadly similar to that described for crayfish (Kirk et al., 1982; Glantz and Bartels, 1994). The hypodermis dorsal to the heart was exposed by making a circular cut (ca. 1cm in diameter) through the cardiac region of the carapace using a dental drill. The circular flap of cuticle thus formed was carefully removed without puncturing the skin. A similar area of hypodermis in the left protogastric region of the carapace [nomenclature of Pearson (Pearson, 1908)] was exposed in the same way. The crab was then lowered into a bath of cold (6°C) oxygenated Carcinus Ringer's solution (500 mmol l^–1 NaCl, 12 mmol l^–1 KCl, 12 mmol l^–1 CaCl₂, 20 mmol l^–1 MgCl₂, 10 mmol l^–1 Tris, 2 mmol l^–1 maleic acid, 2 mmol l^–1 glucose; pH 7.3) [modified after Bush and Roberts (Bush and Roberts, 1971)]. The exposed hypodermis above the heart was then cut away, the pericardium was torn and the blood was allowed to exchange with the surrounding Ringer's solution. This process was accelerated by injecting Ringer's solution into the main chamber of the heart (10–15 ml min^–1) via a syringe and hypodermic needle.

After 25 min of exsanguination, the crab was connected to a gravity-fed system to perfuse the circulatory system continuously with oxygenated Ringer's solution. The crab was first raised above the surface of the Ringer's solution. Then a cannula was introduced into the hole in the carapace above the heart and sealed in position with a combination of cyanoacrylate cement and Blu Tack™ (Bostik, Wauwatosa, WI, USA). The flow rate was set to ∼3 ml min^–1. The previously exposed hypodermis in the protogastric region was cut away and the underlying blood sinuses were opened to provide a route for the outflow of Ringer's solution. In some preparations it was necessary to displace the exposed part of the stomach posteriorly and glue it to the carapace to prevent it from ballooning out through the hole and blocking the outflow of Ringer's solution. After re-immersing the crab, the right optic lobe was exposed by whittling away the overlying eyestalk cuticle with a scalpel blade, removing the hypodermis and desheathing the optic ganglia in the region of interest. The crab was removed from the saline bath and transferred to the experimental setup.

Visual stimuli were back-projected onto two flat screens (38×32 cm) that formed two sides of an equilateral triangle (Fig. 1). The crab was positioned midway between the two screens, facing the apex, with the right eye at the midpoint of the triangle. In this way, images could be projected over an angular range relative to the eye of 240 deg in azimuth (0 to 120 deg on the right screen, 0 to –120 deg on the left) and ∼100 deg in elevation (typically –40 to +60 deg relative to the crab's horizon).

The test stimuli were generated by computer programs written in the Turbo Pascal or Borland Delphi languages, and running on PCs. They were projected via angled plane mirrors onto each screen with LCD computer projectors (Panasonic PT-L291EG, resolution 640×480 pixels, contrast ratio 150:1; Panasonic Corp., Osaka, Japan). Using a light meter placed at the position normally occupied by the crab, we measured maximum (I_max) and minimum (I_min) luminance of our stimuli (using a ‘completely white’ and ‘completely dark’ screen, respectively) of 42.2 and 0.33 cd m^–2, respectively. The Michelson contrast [(I_max–I_min)/(I_max+I_min)] was therefore 0.98. The main stimuli used in this study were: a moving white disc (Fig. 2B), a flashing white disc (Fig. 2C), small-field straight line motion (Fig. 2D), small-field circular motion (Fig. 2E) and small-field circular motion compensated for distortions due to perspective (Fig. 2F), as described previously (Johnson et al., 2002). Responses to local motion stimuli were tested at fixed angular intervals, typically of 15 deg azimuth and elevation at the intersections of the grid shown in Fig. 2A.

As Barnes et al. (Barnes et al., 2002) have shown, our computer-generated stimuli are entirely suitable for crab visual system research. In particular, the refresh rate of our computer projectors, 70 Hz, was significantly higher than crab flicker fusion rates (50 Hz light-adapted and 32 Hz dark-adapted) measured in the fiddler crab, Uca pugilator (Layne et al., 1997). Secondly, the spatial resolution of our experimental setup (0.1875 deg pixel^–1) was over 10 times greater than the best spatial resolution of the Carcinus eye [2 deg (Zeil et al., 1986)].

Intracellular recordings were made using either thin-walled (1 mm outer diameter, 0.22 mm wall, impedance 40 MΩ) or thick-walled (1 mm outer diameter, 0.42 mm wall, impedance 110 MΩ) borosilicate glass microelectrodes, filled with 4% Lucifer Yellow in the tip and 1 mol l^–1 lithium chloride in the barrel. Neural responses and monitors of intracellular current injection and the visual stimulus were amplified conventionally and recorded online using a CED1401 Plus interface and Spike 2 (both Cambridge Electronic Design, Cambridge, UK) software running on a PC. Subsequent data analysis was performed using Spike 2 scripts. Raw data and analysed results were stored on the hard drive and recordable compact discs.

Neuronal morphology was investigated using Lucifer Yellow dye injection (Stewart, 1978). Cells were dye-filled using approximately –4 nA continuous current injection for as long as possible. In practice, this varied from 5 to 90 min. As soon as the recording was over, a drop of fixative was applied to the eyestalk to initiate the fixation process. Then the whole eyestalk was removed from the crab and dissected in fixative. The fixative consisted of 3.7% formaldehyde with added sucrose (15 g per 100 ml) in a phosphate buffer (5 g NaCl, 14 g Na₂HPO₄·2H₂O and 3.2 g NaH₂PO₄·2H₂O, dissolved in 1 l of distilled water). Both fixative and buffer were adjusted to pH 7.3 with 1 mol l^–1 NaOH. It was found that the fixative did not penetrate properly unless the optic ganglia were dissected out of the eyestalk. Preparations were then left to fixate overnight in a refrigerator. Reconstructions of neuronal morphology were carried out on whole mounts viewed under a fluorescence microscope.

Some pre-treatment of the data was necessary, e.g. using Spike 2 peak detection or threshold facilities to generate an event channel for nerve impulses based on the waveform of an intracellular recording. However, after this the analysis was semi-automatic. Examples of the stages involved in deriving the directional motion sensitivity of a neurone to small-field circular motion at an individual screen locus (Krapp and Hengstenberg, 1997) are shown in Fig. 3. The first stage was to generate a phase diagram of the response to anticlockwise motion (Fig. 3A), based either on impulse activity or a signal mean of non-spiking responses (Fig. 3C). The mean preferred direction was derived by circular statistics (Batschelet, 1981). A similar phase diagram of the response to clockwise rotation (Fig. 3D) is not directly comparable because the sequence of motion directions tested is different. However, the clockwise plot can be made comparable to the anticlockwise response by reversing it (i.e. rotating it about its x-axis) and then phase-shifting it by 180 deg (Fig. 3E). Clearly, the curves for anticlockwise and clockwise motion still do not match. This is because the anticlockwise distribution is subject to an unknown phase lag whereas in the clockwise distribution, this has been converted to an equal phase lead because of the flip and shift transformation of the data. Thus, the two distributions are separated by two times the phase shift. The true preferred direction is derived by shifting the anticlockwise distribution clockwise (to eliminate phase lag), and the clockwise distribution anticlockwise (to eliminate phase lead), until the mean vectors are aligned. The true mean vector is obtained by averaging the two distributions and recalculating the circular statistics (Fig. 3F). During the analysis, a provisional response map is built up progressively as each response at a new screen position is analysed on a Mercator map of visual space. A vector is drawn at each position tested, the angle indicating the local preferred direction of motion. The vector length is r, indicating the local strength of this direction preference; r=1 means that all events fall within the same directional bin whereas r=0 means that they are equally distributed over the full 360 deg angular range. Once all the data are analysed, an LMS response map can be generated. Here, local motion sensitivity is defined as mean response in a 90 deg sector that is centred on the LPD minus the response in the 90 deg sector centred on the opposite direction. Vector lengths can be normalised relative to the largest to generate a map that facilitates comparison of sensitivity patterns between individuals.

A second method of generating the polar plots from which the LPDs and LMSs are calculated used straight-line motion (Fig. 4). In these linear motion tests, the same target disc moved, at constant speed, back and forth across the diameter of the circular path followed in the rotating disc paradigm (Fig. 4A). The target remained stationary for a fixed time at the end of each sweep so that the unknown response latency did not lead to ambiguity between responses to motion in opposite directions (Fig. 4B). After a fixed number of sweeps, the ‘diameter’ tested was advanced by 30 deg and the process repeated until all 12 directions had been tested. The initial pair of directions was then repeated as a control for adaptation of motion sensitivity during the sequence. Polar directional plots were based on accumulated spike counts for each motion direction (Fig. 4C), and the LPD was derived from this using circular statistics (Batschelet, 1981). In practice, this method was generally applied at relatively few screen loci in order to corroborate the analysis based on rotational motion. This was because the linear motion stimulus was more time consuming and has a much lower resolution.

Our analysis of the properties of wide-field motion-detecting neurones that might be involved in the detection of optic flow involved a two-stage process. First, the direction of local motion sensitivity was analysed at many different points within the neurone's receptive field. Then the resulting vectors, representing the direction and strength of motion sensitivity at each analysed position, were used to compile a map of the cell's global motion sensitivity.

The initial stimulus used to search for motion-sensitive neurones and estimate their receptive fields was a white disc moved over a black background using the computer mouse (Fig. 2B). Receptive fields were further characterised from responses to a flashing white disc at each test locus (Fig. 2C). Only motion-sensitive neurones with large receptive fields (>90 deg of arc) were studied further. Neurones with the above properties were found in both the medulla and lobula neuropils of the optic tract [terminology of Sztarker et al. (Sztarker et al., 2005)].

LPDs of motion sensitivity were analysed from the responses to the rotation of a white disc moved in a circle, first anticlockwise for a number of cycles and then clockwise for the same number of cycles (Fig. 2E,F). As Fig. 3 illustrates, most of these neurones responded with bursts of nerve impulses to these local stimuli whenever the movement was in the preferred direction for this location within the receptive field, though we have also analysed subthreshold responses (data not shown). Polar phase diagrams were separately compiled for clockwise and anticlockwise responses (Fig. 3C,D) and then, after appropriate transformations (see figure legend and Fig. 3E), combined to give the final polar plot (Fig. 3F).

LPDs were also calculated from responses to straight-line motion rather than rotation (Fig. 2D). Fig. 4 shows a typical example of the responses obtained from a neurone in the medulla. The response is phasotonic, the firing frequency remaining high for a period after the end of the movement (Fig. 4B). Note that movement in the opposite direction produces inhibition. Exactly the same screen positions could be tested with the two different methods to provide a check of the directional selectivity. Polar directional plots (e.g. Fig. 4C) were based on accumulated spike counts for each motion direction. Resulting LPDs usually had smaller concentration parameter values than when circular motion stimuli were used (see below).

An example of such a check of directional selectivity appears in Fig. 5. It shows that LPDs are reassuringly robust and relatively insensitive to changes in speed of movement. Estimates of LPD for a single point in the neurone's receptive field are hardly affected by changing the velocity at which the disc is rotated for cycle periods between 0.5 and 3 s (Fig. 5A), though there is a halving of the value of the concentration parameter r for a fourfold increase in cycle period. These periods translate into angular velocities covering the range 35–200 deg s^–1. LPDs are also unaffected by the method used to compile them. When linear motion stimuli are used instead of a rotating disc (Fig. 5B–D shows three different points in the visual field), the LPDs remain closely matched, though again the value of r is affected; it is lower for straight-line stimuli. The reduction in r for straight-line movements is, however, mostly a property of the way in which the polar plot was compiled for such movements, for they include the tonic as well as the phasic response to the movement (Fig. 4C). In Fig. 5E, we looked at one point in space, and used circular motion to assess the mean vector (plotted on the y-axis of the graph). This is affected by neither the period of the motion (x-axis of graph) nor the shape of the object moved, whether it be a spot, bar, annulus or lattice. The line of best fit is not significantly different from the horizontal (t-test, P>0.10). Together, these three tests make us confident that LPDs represent real properties of the neurones' receptive fields, rather than artifacts of the experimental method.

Fig. 6A–D shows recordings from a wide-field motion-detecting neurone with its dendritic arborization in the medulla, and phase plots resulting from stimulating positions in space 20 deg apart in azimuth. There is a clear reversal of directional selectivity between the two points (mean ± s.d. phase shift=170±34 deg, N=47). Such a result makes it clear that we are dealing with a neurone with a complex receptive field. Local motion sensitivity was therefore analysed over the whole receptive field of the neurone, at all 56 standardised grid coordinates, and the resulting LPDs were then plotted onto a Mercator projection map of visual space. This map is shown in Fig. 6E (green vectors). It has a clear focus of contraction (FOC) at ∼45 deg to the right of the midline at an elevation of approximately –20 deg (horizon=0 deg) and all vectors are directed approximately towards this point. The illustrated polar plots are situated on either side of the FOC in columns three and five of row four (asterisks). As a test of whether response maps depended on the type of visual stimulus, we used three different methods to calculate the LPDs in Fig. 6E: flat-screen rotational stimuli (Fig. 2E), pre-distorted rotational stimuli (Fig. 2F) and straight-line motion (Fig. 2D). The response maps resulting from these different procedures are coloured green, black and red, respectively in Fig. 6E. Clearly there is a good match between the results obtained using the three different methods, an indication that such maps truly represent the cell's global motion sensitivity.

Variability of responses within crabs was tested on a number of occasions by repeating the compilation of the map of local motion sensitivity after an interval of approximately 30 min with the microelectrode still within the neurone. Consistent values were invariably obtained (data not shown).

Of the 18 preparations (out of a total of 27) where we have good data and have been able to compile response maps from up to three wide-field motion-sensitive neurones per preparation, we have successful Lucifer Yellow fills from 13 neurones. The majority of these have their dendritic arborisations in the lobula and their somata ventrally located between the lobula and the lateral protocerebrum. A smaller percentage has their dendritic arborisations in the medulla and their somata at the edge of the lobula near the sinus gland. All neurones anatomically identified as medulla neurones (Fig. 7A) had response maps characterised by an FOC (Fig. 7B) whereas all neurones anatomically identified as lobula neurones (Fig. 7C,E) had response maps characterised by a focus of expansion (FOE) (Fig. 7D,F). We conclude that we recorded from two arrays of neurones with opposite properties. Neurones receiving their inputs in the medulla have receptive fields characterised by an FOC and so would be stimulated by receding objects, whereas neurones receiving their inputs in the lobula have receptive fields characterized by an FOE and so would be stimulated by approaching objects. Surprisingly, in view of the fact that high-gain optokinetic responses occur in crabs such as Carcinus (Horridge and Sandeman, 1964; Horridge, 1966; Barnes and Horridge, 1969), we did not record from neurones sensitive to rotational optic flow.

From experiments where we recorded from more than one neurone in a preparation (Fig. 8), it is clear that different neurones have poles at different azimuths. As far as medulla neurones are concerned, we recorded from cells where the azimuths of the FOCs were located 0 (frontal), 50–55, 90 and 120 deg to the right of frontal (N=10). For lobula neurones, the azimuths of the FOEs were located 30–40, 60–75 and 90–100 deg to the right of frontal (N=17). Presumably, the left optic lobe will include cells covering the area to the left of the midline. Examples of these are illustrated in Fig. 8. Whether the foci also have different elevations is less certain, because of possible errors (±10 deg) in the positioning of the eye. For medulla neurones, the range was –25 to +30 deg (horizon=0 deg) with a mean value of –5 deg (N=10), whereas for lobula neurones, the range was 0 to +48 deg with a mean of +22 deg (N=17). It certainly appears that the FOEs of lobula neurones are, in general, centred above the horizon.

The majority of response maps had a receptive field 90–120 deg in width and extending vertically from ∼40 deg below to ∼60 deg above the horizon (Fig. 7D and Fig. 8). A small minority were much wider in extent. For instance, the medulla neurone whose response map is shown in Fig. 7B extended from –65 to +65 deg, whereas the lobula neurone whose response map is illustrated in Fig. 7F extended from –115 to +115 deg. For all neurones where we both dye-filled the neurone and mapped its response field, there was a good correlation between the extent of the dendritic tree and the width of the response map (Fig. 7). Response maps of medulla neurones were relatively variable in shape. Fig. 8C shows a map where there is an extended vertical area around the FOC, whereas those in Fig. 7B and Fig. 8D show extended horizontal areas. A common feature of lobula neurone response maps, illustrated in Fig. 8A,B (but not in Fig. 7B), is for the response map to be extended horizontally, perhaps providing a template for the horizontal skylines that dominate most seascapes (Barnes et al., 2001; Eckert and Zeil, 2001).

The class of interneurone in which the dendritic arborisations occur in the medulla respond vigorously to the preferred direction of motion and are strongly inhibited by movements in the opposite direction (Fig. 6A,B). They also respond phasotonically to ‘light on’ and are momentarily hyperpolarised following ‘light off’ (Fig. 9A). Lobula neurones, however, showed ‘on’ and ‘off’ responses to a stationary light stimulus in addition to their response to movement (Fig. 9B). In a few experiments their distribution was mapped. Both ‘on’ and ‘off’ responses occurred in the central area of the receptive field, with ‘off’ responses extending towards the periphery of the receptive field more widely than ‘on’ responses (Fig. 8A).

A number of different classes of visually responsive neurone, including sustaining fibres, dimming fibres and several different types of movement fibres, have been identified within the optic nerves of a variety of decapod crustaceans (for a review, see Wiersma et al., 1982). Each of these categories can be subdivided on the basis of the size and location of the neurone's excitatory receptive field, in some cases down to the level of individual physiologically identifiable neurones. Subsequent work on crayfish, based on intracellular recordings, has begun to give us insights into the neural circuitry of the optic tract (reviewed by Glantz and Miller, 2001). A more complete picture is emerging from recent work on the crab Chasmagnathus. This includes a thorough histological study based on silver staining of neurones (Sztarker et al., 2005; Sztarker et al., 2009) and a detailed analysis of the different properties of lobular neurones involved in escape responses to looming stimuli (Berón de Astrada and Tomsic, 2002; Medan et al., 2007; Oliva et al., 2007; Sztarker and Tomsic, 2008), several of which show a form of learning related to habituation (Tomsic et al., 2003). Yet none of this work refers to the term ‘optic flow’, nor have stimuli appropriate for the identification of neurones tuned to optic flow been used. It is clearly of interest to see how our work fits into this picture.

In crayfish, a class of visual interneurones known as sustaining fibres, initially called tonic ‘on’ neurones by Wiersma and Yamaguchi (Wiersma and Yamaguchi, 1966; Wiersma and Yamaguchi, 1967), have their main dendritic tree in the medulla (Kirk et al., 1982) and respond to a light pulse with a phasotonic discharge that persists for the duration of the stimulus and is followed by an inhibitory ‘off’ response (Kirk et al., 1983; Pfeiffer and Glantz, 1989). They are additionally directionally selective to movement (Glantz et al., 1995). Similar responses to light have been recorded from sustaining fibres in crabs (Berón de Astrada et al., 2001; Berón de Astrada et al., 2009). It seems quite clear that the class of neurones we have been recording from that have their dendritic arborisations in the medulla are sustaining fibres. The location of the dendritic tree (Fig. 7A) and the response to light pulses (Fig. 9A) are identical to those described above for such fibres. Additionally, our evidence that there are a number of these neurones, with receptive fields that together cover the whole visual field of the crab, is compatible with the 14 members of the sustaining fibre ensemble identified by Kirk et al. (Kirk et al., 1983).

We can be equally sure of the identity of the second group of optic flow sensitive neurones, those having their main dendritic arborisation in the lobula (or internal medulla to use the older nomenclature). From their responses to movement, it is clear that these neurones belong to the class of fibres called movement fibres by Wiersma et al. (Wiersma et al., 1982). In their early work, the Tomsic group called such fibres movement detector neurones (MDNs) (Berón de Astrada and Tomsic, 2002; Tomsic et al., 2003). The histological work of Sztarker et al. (Sztarker et al., 2005) demonstrated that MDNs were not a single morphological cell type; intracellular staining revealed two morphological subtypes, with dendrites restricted to a single stratum of the lobula (monostratified) or spread over two strata (bistratified). Each of these types can be further subdivided according to the size of their receptive fields, ∼90 deg (type 1) or >180 deg (type 2). We thus end up with four morphological types (M1, M2, B1 and B2) according to Oliva et al. (Oliva et al., 2007), but renamed monostratified and bistratified lobular giants 1 and 2 (MLG1, MLG2, BLG1 and BLG2) by Medan et al. (Medan et al., 2007). As well as their strong responses to small moving stimuli, they are characterised by brief excitatory responses (often just a single spike) to a light pulse at ‘on’ and ‘off’ (Medan et al., 2007). The response to movement, the location of the main dendritic arborisations in the lobula and the characteristic response to a light pulse (Fig. 9B) indicate that the lobular neurones we have been recording from are lobular giant neurones. Because we see dendrites restricted to a single plane (Fig. 7C,E), they are monostratified lobular giants. The majority of our recordings are from MLG1 neurones, as they have receptive fields covering approximately 90 deg of arc (Fig. 7D), with different neurones covering different parts of the visual field. Medan et al. identified 14 neurones in this category (Medan et al., 2007). On a few occasions, we recorded from neurones with much larger receptive fields (Fig. 7F), where the dendrites covered the full width of the lobula (Fig. 7E). These are clearly MLG2 neurones. Medan et al. suspect that there is only one neurone of this type (Medan et al., 2007), a conclusion with which we concur.

The methodology used here involved determining local motion sensitivity at 56 different points in the visual field. The resulting LPDs were then used to compile a response map representing the neurone's global motion sensitivity. The overriding advantage of this method over other stimuli that stimulate the whole receptive field at once is that the experimenter does not have to pre-judge the neurone's response pattern in order to provide an appropriate stimulus. The response pattern, whether it results from translational optic flow, rotational optic flow, looming or any other kind of motion sensitivity, makes itself apparent when compilation of the map of LPDs and LMSs is complete. This method has successfully been used to analyse neurones sensitive to optic flow in the blowfly's lobula plate (Krapp and Hengtstenberg, 1996; Krapp et al., 1998). These blowfly neurones also respond to global stimuli (Karmeier et al., 2003) and, when viewing panoramic virtual reality stimuli that take into account the saccadic head movements of the fly during flight, show responses to translational optic flow (Kern et al., 2005). On the basis of the performance of a simple model, the cyberfly, they may even play a role in obstacle avoidance (Lindemann et al., 2008).

The response maps we have obtained by the use of this analysis are just what you would expect of neurones responsive to optic flow (Fig. 10). Although we have not recorded from neurones sensitive to rotational optic flow (Fig. 10A), such neurones must exist as crabs show powerful optokinetic responses to rotation of a striped drum around the animal and to body turns (Barnes, 1990; Paul et al., 1998). The response maps of our populations of lobula and medulla neurones are, however, excellent matches to the patterns expected from neurones sensitive to translational optic flow. The maps of our population of lamina neurones are a good match to the pattern of vectors of an approaching scene (compare Fig. 8A,B with Fig. 10B), whereas the maps of medulla neurones are a similarly good match to the vector pattern of a receding scene (compare Fig. 8C,D with Fig. 10C). In each case there is a central pole, which is an FOE in the case of neurones sensitive to the approaching scene and an FOC in the case of neurones sensitive to the receding scene. Such poles would provide the crab with good visual information about its direction of travel.

LPDs are robust, as they are relatively insensitive to changes in the velocity of movement, changes in the method used to compile them (circular or linear motion) and changes in the shape of the stimulus object. Response maps are similarly robust (Fig. 6E). We are thus confident that the response maps of these populations of medulla and lobula neurones are truly representative of the neurones' global motion sensitivity. However, before we can be sure that they are indeed optic flow neurones, it is necessary to show that they respond to the appropriate global stimuli. Our preliminary experiments have failed to do this (data not shown). Perhaps this is not surprising. All the data analysis was carried out off-line, so that the properties of the neurone, its receptive field and the pole of the flow field only revealed themselves long after the experiment was over. Thus the likelihood of presenting the correct global stimulus at the right location within the eye's field of view was relatively low.

An alternative possibility, for the lobula neurones only, is that they are neurones sensitive to looming and would trigger the crab's escape response, as has been shown in the crab Chasmagnathus (e.g. Sztarker and Tomsic, 2008). This possibility cannot be excluded, because looming neurones might be expected to produce response maps rather similar to those of translational optic flow. However, C. maenas has a lifestyle that is very different to that of Chasmagnathus. It remains hidden when the tide is low, and so would not be subject to the same predation risks as Chasmagnathus, a semi-terrestrial crab at constant risk from predation by seabirds (Bachmann and Martinez, 1999; Copello and Favero, 2001). Unlike Chasmagnathus lobula neurones, those of C. maenas do not show strong habituation, which is an important feature of neurones that elicit escape. Indeed, there is good evidence that, although different crab species (and, to a lesser extent, different decapods) do have homologous neurones, such neurones may become specialised for different functions according to the lifestyle of the species (Sztarker et al., 2005; Sztarker et al., 2009). It is also worth pointing out that a well-studied looming neurone in locusts, the lobula giant movement detector (LGMD) is not directionally selective (Krapp and Gabbiani, 2005); therefore, looming detection and optic flow processing are not necessarily linked.

Studies of the eye movements of freely moving crabs (Barnes, 1990; Paul et al., 1990; Paul et al., 1998) also lead us to expect that neurones sensitive to translational optic flow should exist, as crabs separate the rotational and translational components of their optic flow field as they move about their environment. They do this by using eye movements to compensate for the rotational component of their path by a variety of mechanisms (for details, see Barnes and Nalbach, 1993; Kern et al., 1993; Blanke et al., 1997). Because combinations of translation and rotation defy easy analysis, viewing only the translational component of optic flow makes available the information it contains, including locomotor performance and the relative positions and distances of objects in the external world (Eckert and Zeil, 2001).

Given that crabs have 360 deg vision and predominantly walk sideways, having two classes of neurone – one responding to the approaching world and the other to the receding world – makes good sense. It doubles the amount of information that they receive and can use in a variety of ways. Indeed, as discussed in mathematical terms by Dahmen et al. (Dahmen et al., 2001), the best estimates of egomotion are obtained with wide field neurones with opposite directions of view. As hypothesized by Gibson (Gibson, 1986), the information can be used to estimate velocity and distance travelled, to give distance information by motion parallax and assist in maintaining a heading. Which of these possibilities are likely to be of relevance to crabs? Recent research has demonstrated the importance of translational optic flow in estimating distance flown in flying insects (Srinivasan et al., 2000; Esch et al., 2001; Dacke and Srinivasan, 2008; Shafir and Barron, 2010), but there is little evidence that land arthropods estimate distance travelled using optic flow (Ronacher et al., 2000). Desert ants, whose homing behaviour has been intensively studied in recent years (e.g. Merkle and Wehner, 2010), use stride integration (summing of individual stride lengths) to estimate distance covered (Wittlinger et al., 2006; Wittlinger et al., 2007). Turning to crustaceans, fiddler crabs certainly use optomotor responses (generated by rotational optic flow) to compensate for deviations from their intended path (Layne et al., 1999) but, like ants, judge distance travelled by flexible stride integration (Layne et al., 2003a; Layne et al., 2003b; Walls and Layne, 2009a; Walls and Layne, 2009b). Homing, however, requires that the individual knows direction as well as distance, and recent evidence suggests that maintenance of the angle between the eye and the burrow (even when the actual burrow is no longer visible to the crab) is crucial to this (Layne, 2008) (J. E. Layne, W.J.P.B. and A. Dzwonczyk, unpublished observations). By maintaining this angle, the directional component of the home vector becomes a retinal location. If this angle is maintained during an excursion from the burrow, then keeping the retinal location of the home vector at the FOE during homing will ensure that home is reached. Retinal location is also key to both predator identification (Layne, 1998) and burrow defence (Hemmi and Zeil, 2003a; Hemmi and Zeil, 2003b). A possible role for this sophisticated system for the detection of translatory optic flow might thus be in the maintenance of a heading. Having the largest vectors near the pole of the flow field, as exhibited by the response maps illustrated in Fig. 8C,D, would help in this, though it must be remembered that the highest velocities of apparent movement lie at right angles to the direction of travel (at least for objects equidistant from the eye). Indeed, our results are the opposite of what has been found in the blowfly (Krapp et al., 1998), where FOEs are surrounded by small vectors. Could it be that the slower image motion (walking rather than flying) is compensated for by increased motion sensitivity? This strategy relies on a high signal to noise ratio, i.e. that the flow vectors are small but reliable. This is reasonable because compensatory eye movements effectively counteract the small rotational components inherent in the somewhat lurching gait of crabs (Barnes, 1990).

These experiments were difficult to perform, and much work still is required. But, with the benefit of hindsight, we suspect that our C. maenas preparation, involving exsanguination and a significant amount of dissection, was not the best preparation to have chosen. The Tomsic group (Berón de Astrada and Tomsic, 2001) has clearly identified a much better method for carrying out such experiments, but whether it works as well for C. maenas as it does for Chasmagnathus remains to be investigated. An obvious gap in our knowledge is the way in which the neurones respond to global stimuli. However, if online data analysis were possible so that the response map was constructed while still having a microelectrode in the cell, it would be much easier to choose an appropriate global stimulus. A second knowledge gap is the extent to which our two populations of neurones consist of arrays of cells with poles at different azimuth angles. Sztarker et al. have now done the anatomy (Sztarker et al., 2005; Sztarker et al., 2009), so future work can build up a picture of the arrays of cells specialized for sensing translational optic flow and the extent to which they interact with each other, perhaps by electrical synapses, as do neurones with similar properties in flies (Haag and Borst, 2005). Finally, we have yet to determine the properties of neurones in the lobula plate of crabs – which may be homologous to that of insects (Strausfeld, 2005) – the area where insect optic flow neurones are found (Krapp et al., 1998).