Zebrafish: Neuronal Computation in the Zebrafish Olfactory Bulb
The Zebrafish Olfactory System
The zebrafish (Danio rerio) is a freshwater teleost native in Southeast Asia . Water flow through the nose is laminar and unidirectional. Even when a zebrafish is not moving, water flow is provided by motile cilia such that a constant odourant supply is provided. Hence, a zebrafish constantly screens the odour space by moving through the environment. The first relay station of odour information is the olfactory bulb. Information passing in the olfactory bulb is an extremely complex process which includes multiple steps of transformation performed by the underlying circuitry. For instance, an odour consisting of different molecules activates a specific set of odourant receptors on olfactory sensory neurons, which terminate in the olfactory bulb in an array of glomeruli. Hence, an odour is encoded in a combinatorial fashion of glomerular activation patterns. An adult zebrafish olfactory bulb contains about 140 stereotyped glomeruli . A glomerulus is a functional unit consisting of synaptic connections within three different cell classes(Figure 1).
- The incoming olfactory sensory neurons expressing the same odorant receptor. All synaptic connections are excitatory.
- Inhibitory interneurons responsible for multiple transformations of the odour signal. In Zebrafish, interneurons can be subdivided into periglomerular cells, granule cells and short axon cells, each of which has distinct morphological features.
- Mitral cells, which relay the signal out of the olfactory bulb to higher brain areas. In adult Zebrafish there are about 1’500 mitral cells. 70% of these mitral cells receive input from one distinct glomerulus .
For the olfactory system, the broad concept of receptive fields present in the visual system is only valid in a very general sense. As described above, a glomerulus receives input from olfactory sensory neurons expressing the same odourant receptor. As a result, a rough spatial chemotopic map is spanned across the olfactory bulb. In other words, different classes of natural odours of the Zebrafish (amino acids, bile acids, nucleotides) activate different anatomical domains of the olfactory bulb .
A computational step ongoing in the glomeruli of the zebrafish is pattern decorrelation, which reduces the overlap between activity patterns representing similar odours. Think of two similar fragrances such as cumin seed essential and fennel seed essential. Due to the similar molecular composition, both fragrances initially evoke a similar glomerular activation pattern. Initially, these activation patterns are therefore highly correlated. In other words, odourants with similar molecular features activate overlapping combinations of glomeruli. Subsequently, most of the correlations decrease and the glomerular activity gets redistributed and settles to a steady state. From a computational point of view pattern decorrelation is an useful early step in many pattern classification procedures. It does not increase the information content of an odour representation and it does not increase the performance of an optimal classifier. Rather, it can improve the performance of suboptimal classifiers by increasing the tolerance region(Figure 2) . In nervous systems this process could be important for learning odours and subsequent identification of these odours .
Odour evoked glomerular activity patterns can be measured optically by introducing calcium sensors selectively into the olfactory sensory neurons . This was done in Zebrafishes to analyze the glomerular activity pattern evoked by 16 amino acids, which belong to the natural odour space of zebrafishes. To study pattern decorrelation, responses to highly similar amino acids (Phe, Tyr or Trp) were measured across the mitral cells by multiphoton calcium imaging. Multiphoton calcium imaging revealed that the activity patterns in spatially clustered mitral cells initially overlapped. This overlap subsequently decreased because subsets of these mitral cells became less active or silent, resulting in a local, but not a global, sparsening of MC activity. Concomitantly, the activity of inhibitory interneurons increased and became more dense. Figure 3 shows real data of the activity of Mitral cells before and after a Zebrafish olfactory bulb is exposed to two different odourants.
Other Possible Simulation Approaches of Pattern Decorrelation
- Recurrence-enhanced threshold-induced decorrelation (reTIDe)
Analytical approaches and simulations showed that generic networks of Stochastic networks of rectifying elements (SNOREs) with uniform synaptic weights decorrelate specific input patterns by a mechanism referred to as reTIDe . Thresholding the input pattern is the first step in reTIDe. SNOREs consist of threshold-linear units that are randomly connected by synapses of uniform weight. For any positively correlated and normally distributed input patterns, this nonlinearity always results in decorrelation and that decorrelation monotonically increases with the threshold level . This decorrelation is then amplified by feeding the thresholded output patterns back into the network through recurrent connections until a steady state is reached . For mathematical proof and analysis, refer to ONLINE METHOD of the referenced paper .
- Optimizing a weight matrix to model activities of interneurons
W is a weight matrix which represents activity of interneurons between Mitral cells. For instance, its element represents connectivity strength from Mitral cell to Mitral cell. X(t) is a matrix representing firing rates to stimulus 1 and 2 of each individual Mitral cell at time t. Given more data set of X in time, it is probable that the weight matrix W can be optimized.
Pattern decorrelation in the olfactory bulb is a computational step which has been observed in the zebrafish. However, there has not been proposed a mathematical model to explain pattern decorrelation on a mechanistic basis. A model of how excitatory and inhibitory neurons interact together in the olfactory bulb will help to understand how pattern decorrelation is performed on a neurons level. But even so, such a model implies a full connectivity map of the olfactory bulb. This goal mainly depends on the achievements of the acquisition of large datasets with scanning electron microscopy techniques and dense EM-based reconstruction of this data in the next years.
We express our special gratitude to Prof. Rainer Friedrich for his advice on this work.
 Friedrich, R. W. (2013). Neuronal Computations in the Olfactory System of Zebrafish. The annual Review of Neuroscience.
 Braubach, O. R., (2012). Distribution and Functional Organization of Glomeruli in the Olfactory Bulbs of Zebrafish (Danio rerio). The Journal of Comparative Neurology.
 Figure 1 is adapted from: Friedrich, R. W., & Wiechert, M. T. (2014). Neuronal circuits and computations: Pattern decorrelation in the olfactory bulb. Elsevier.
 Fuller C. L., (2006). Mitral cells in the olfactory bulb of adult zebrafish (Danio rerio): morphology and distribution. J. Neurophysiology.
 Figure 2 is adapted from: Friedrich, R. W. (2013). Neuronal Computations in the Olfactory System of Zebrafish. The annual Review of Neuroscience.
 Friedrich, R. W., & Wiechert, M. T. (2014). Neuronal circuits and computations: Pattern decorrelation in the olfactory bulb. Elsevier.
 Wiechert, M. T. et. al (2010). Mechanism of pattern decorrelation by recurrent neuronal circuits.
Toothed Whales: Echolocation
Marine mammals such as whales, dolphins and porpoises have developed sensing abilities that have allowed them to go into deep sea and spread across the world’s oceans. These mammals belong to the order of Cetacea. Toothed whales (Odontocetes), a parvorder of Cetacea which consists of at least 71 species, including sperm whales, killer whales, porpoises and dolphins, have acquired an astonishing type of sensing mechanism, called echolocation or bio sonar. It allows them to successfully navigate and hunt prey at places where vision is limited due to great depth or turbulences. Research has shown that it provides them with a three-dimensional view of their environment and further gives them the ability to differentiate and recognize characteristics of objects, which is a key biological benefit. Echolocation has therefore played a major role in the evolutionary success of toothed whales, which have emerged 34 million years ago. However, it is not only used by toothed whales, but can be found in all sorts of other animals as well. Microchiropteran bats, for example, have a highly-developed bio sonar system, but also shrews, two genera of birds and megachiropteran bats make use of this sensing ability.
Principle of Echolocation
The basic principle of echolocation is to obtain information about the environment from the received echoes of emitted sound waves (see Figure_Echolocation). Odontocetes produce pulse-like clicking sounds in a high-frequency range of 10kHz to 200kHz. These clicks are mostly in the ultrasonic range (>22.1kHz) and thus not perceivable by humans. The duration, frequency, interval and source level of the created pulses vary between different species and depend on environmental conditions such as ambient noise, reverberation, target distance and target characteristics. For example, sperm whales use a range of 10-30kHz to echolocate, while porpoises and many dolphins broadcast signals greater than 100kHz. Once a reflected sound wave is detected, time delay and intensity are used to gain information about distance and orientation of the incoming signal. Odontocetes can dynamically control the interval and source level of the transmitted signals. Usually, the clicks are transmitted at a rate that enables the signal to return before the next click is sent out. Thus, the repetition rate increases as a target gets closer. Furthermore, the output level of the click is usually higher when a target is further away and lower when it is closer.
Echolocation in toothed whales is used for orientation and hence navigating the oceans. Further, it allows them to find prey and avoid predators. This is achieved by the active detection, localization, discrimination and recognition of objects in the surrounding environment. Research suggests that in some species, e.g. Hector's Dolphins, the produced sounds are also used in social context.
Sound Production Mechanisms
The high-frequency sound generation in Odontocetes happens in a structure called monkey lips/dorsal bursae (MLDB), which is located in the upper nasal passage. The MLDB complex is built up of the fatty dorsal bursae, the monkey lips, the bursal cartilages, and the blowhole ligament. By moving air between the monkey lips, the MLDB complex starts to vibrate and hence sounds are generated. These sounds are sent out through a fatty-filled area in the upper forehead called the melon, which acts as an acoustic lens to focus the directional sound beams ahead of the animal (see Figure_SoundMechanisms). The melon contains fats that are composed of lipids very rich in oil. These lipids are also called acoustic tissue, since they conduct sound well and may also play a role in focusing the outgoing beam. A study by Aroyan has shown that not only the melon, but also the skull and the dorsal bursae (air sacs) play important roles in forming the forward beam that is transmitted into water. The air sacs reflect any upward or downward directed sound, while the nasal passage and cranium reflect any backward directed sound. It has to be noted that although these mechanisms account for almost all Odontocetes, sperm whales pose an exception. Their head structure and hence the sound production and hearing mechanisms are different to those of dolphins and other toothed whales and are still subject to ongoing research.
Sound Reception Mechanisms
Odontocetes have the astonishing ability to hear over a broad range of frequencies, even ranging beyond 100kHz. The apparatus for the reception of acoustic signals is located in the lower mandible (see Figure_SoundMechanisms). The rear portion of the mandible consists of a thin pan bone, which is directly connected to the auditory bulla through a fatty-filled channel. Sound waves are conducted from the mandible to the bulla through this low-density channel. The auditory bulla, properly called “tympano-periotic complex”, consists of the middle ear (tympanic bulla) and the inner ear (periotic bulla). Except for the connection to the mandible, the tympano-periotic complex is completely separated from the skull, which is an important factor in underwater sound localization. From the middle ear, which is filled with acoustic tissue, signals travel to the inner ear. In the inner ear, hair cells located in the cochlea are stimulated and convert the acoustic signal into electrical nerve signals. These hair cells are connected to ganglion cells that transmit the electrical signals to the brain via the auditory nerve. Compared to humans and other mammals, there are quite some differences in the structure of the inner ear. The major differences are a larger auditory nerve, a longer basilar membrane, a small semi-circular canal and a higher ratio of ganglion to hair cells. The time between emitted clicks and auditory response, also called latency of response, can be as short as 7-10μsec. This auditory nervous response is faster than that of a rat, even though a rat's head is a lot smaller.
Sound localization, i.e. the ability to spot the direction and distance of an incoming sound, depends highly on the medium. In land mammals, binaural cues, i.e. differences in arrival time and differences in intensity, help the localization process. Research suggests that odontocete also make use of this technique. It is assumed that the large spread between the ears and the functional separation from the skull are the reason for accurate underwater sound localization in toothed whales. By receiving sounds through tissue in the mandible and not through an eardrum as in terrestrial mammals, hearing loss due to increasing pressure in deeper waters is avoided. An interesting characteristic of the emitted sound beam is that it is inhomogeneous, i.e. only signals traveling along the straight axis of the beam are undistorted. Thus, objects lying in the direction of the major axis of the emitted beam are most likely to be recognized.
Sound Transmission and Characteristics of Signals
The sounds produced by toothed whales are some of the loudest in all animals with peak-to-peak amplitudes up to 225dB. There is a distinction of the echolocation signals in Odontocetes. One group, whistling Odontocetes (most dolphins) project shorter clicking sounds of 40-70μsec and bandwidths over 100kHz, while non-whistling Odontocetes (sperm whale, Hector’s dolphin) produce longer sounds of 120-200μsec with a bandwidth of around 10kHz. The maximum detection range varies between species. Experiments have shown ranges of 113m for bottlenose dolphins and 26m for harbor porpoises. Sperm whales can detect objects as far away as 500m. These numbers should be considered with caution, however, since measurements are hard to compare and also depend on environmental aspects such as background noise and turbulences.
Smell and Taste
There are no olfactory lobes as well as no vomeronasal organ in toothed whales, thus they are lacking the sense of smell. Taste buds are found on tongues of some Odontocetes such as bottlenose dolphins, but have atrophied in most species. It is thus assumed that they only have a very weak sense of taste if any at all. There are, however, some indications that toothed whales have developed additional sensory organs to substitute for the sense of taste, as they do respond to certain substances in surrounding water.
Vision persists and works relatively well underwater and above water, although Odontocetes do not rely on their sight as much. Their eyes are especially adapted to the different conditions underwater: The eyeballs and corneas are flatter than in terrestrial mammals in order to allow as much light as possible to enter. To achieve maximum vision, they have enlarged pupils and the incoming light is reflected twice through a reflective layer called tapetum lucidum. The receptive layer predominantly consists of rods with far fewer cone cells. Hence, colour vision in toothed whales is limited. As toothed whales rise to the surface, the pupils shrink in order to prevent damage from direct sunlight. For further protection of the eyeballs, glands that produce a secrete which cleans the eyes exist. Toothed whales can see roughly 10.7m ahead underwater, a little less above the surface.
The skin of toothed whales consists of a thin layer that is very sensitive. The most sensitive areas include the head, the belly, the genital organs and the flippers. The sense of touch plays an important role in communication, e.g. touching bodies as a way of greeting, and other social contexts.
Another sense that toothed whales seem to be making use of is geomagnetism. Besides using echolocation, they may navigate by sensing the earth's magnetic field for longer distance journeys. When following their movements, scientists have discovered that they often travel along lines of the earth's magnetic field. They suggest that Odontocetes use the flux of the magnetic field in two ways: Whales travel parallel to contours of a map provided by the topography of the local magnetic field. To monitor position and progress on this map, they use regular fluctuations in this field. Live strandings seem to be connected to this sensory ability and are explained by irregular field fluctuations, e.g. caused by military sonar or solar storms, or when the route crosses land.
Tactile Sensation with Lateral Line Organs
Fish are aquatic animals with great diversity. There are over 32’000 species of fish, making it the largest group of vertebrates.
Most fish possess highly developed sense organs. The eyes of most daylight dwelling fish are capable of color vision. Some can even see ultra violet light. Fish also have a very good sense of smell. Trout for example have special holes called “nares” in their head that they use to register tiny amounts of chemicals in the water. Migrating salmon coming from the ocean use this sense to find their way back to their home streams, because they remember what they smell like. Especially ground dwelling fish have a very strong tactile sense in their lips and barbels. Their taste buds are also located there. They use these senses to search for food on the ground and in murky waters.
Fish also have a lateral line system, also known as the lateralis system. It is a system of tactile sense organs located in the head and along both sides of the body. It is used to detect movement and vibration in the surrounding water.
Fish use the lateral line sense organ to sense prey and predators, changes in the current and its orientation and they use it to avoid collision in schooling.
Coombs et al. have shown  that the lateral line sensory organ is necessary for fish to detect their prey and orient towards it. The fish detect and orient themselves towards movements created by prey or a vibrating metal sphere even when they are blinded. When signal transduction in the lateral lines is inhibited by cobalt chloride application, the ability to target the prey is greatly diminished.
The dependency of fish on the lateral line organ to avoid collisions in schooling fish was demonstrated by Pitcher et al. in 1976, where they show that optically blinded fish can swim in a school of fish, while those with a disabled lateral line organ cannot .
The lateral lines are visible as two faint lines that run along either side of the fish body, from its head to its tail. They are made up of a series of mechanoreceptor cells called neuromasts. These are either located on the surface of the skin or are, more frequently, embedded within the lateral line canal. The lateral line canal is a mucus filled structure that lies just beneath the skin and transduces the external water displacement through openings from the outside to the neuromasts on the inside. The neuromasts themselves are made up of sensory cells with fine hair cells that are encapsulated by a cylindrical gelatinous cupula. These reach either directly into the open water (common in deep sea fish) or into the lymph fluid of the lateral line canal. The changing water pressures bend the cupula, and in turn the hair cells inside. Similar to the hair cells in all vertebrate ears, a deflection towards the shorter cilia leads to a hyperpolarization (decrease of firing rate) and a deflection in the opposite direction leads to depolarization (increase of firing rate) of the sensory cells. Therefore the pressure information is transduced to digital information using rate coding that is then passed along the lateral line nerve to the brain. By integrating many neuromasts through their afferent and efferent connections, complex circuits can be formed. This can make them respond to different stimulation frequencies and consequently coding for different parameters, like acceleration or velocity .
In sharks and rays, some neuromasts have undergone an interesting evolution. They have evolved into electroreceptors called ampullae of Lorenzini. They are mostly concentrated around the head of the fish and can detect a change of electrical stimuli as small as 0.01 microvolt . With this sensitive instrument these fish are able to detect tiny electrical potentials generated by muscle contractions and can thus find their prey over large distances, in murky waters or even hidden under the sand. It has been suggested that sharks also use this sense for migration and orientation, since the ampullae of Lorenzini are sensitive enough to detect the earth’s electromagnetic field.
Cephalopods such as squids, octopuses and cuttlefish have lines of ciliated epidermal cells on head and arms that resemble the lateral lines of fish. Electrophysiological recordings from these lines in the common cuttlefish (Sepia officinalis) and the brief squid (Lolliguncula brevis) have identified them as an invertebrate analogue to the mechanoreceptive lateral lines of fish and aquatic amphibians .
Another convergence to the fish lateral line is found in some crustaceans. Contrary to fish, they don’t have the mechanosensory cells on their body, but have them spaced at regular intervals on long trailing antennae. These are held parallel to the body. This forms two ‘lateral lines’ parallel to the body that have similar properties to those of fish lateral lines and are mechanically independent of the body .
In aquatic manatees the postcranial body bears tactile hairs. They resemble the mechanosensory hairs of naked mole rats. This arrangement of hair has been compared to the fish lateral line and complement the poor visual capacities of the manatees. Similarly, the whiskers of harbor seals are known to detect minute water movements and serve as a hydrodynamic receptor system. This system is far less sensitive than the fish equivalent. 
Sharks are some of the most ancient animals on our planet (the earliest known sharks date back more than 420 million years ago). They belong to the elasmobranchii, a subclass of Chondrichthyes (cartilaginous fish) which further includes rays and skates. Among some other features, elasmobranchii are characterized by the fact that they have - in contrast to most other fish - no swim bladder. Another unusual feature is that they are able to perceive electric fields with organs called ampullae of Lorenzini (see 2. Ampullae of Lorenzini) . The number of sensory nerves is comparable with the ones from the eye, ear, nose and lateral line. This sensory perception allows elasmobranchs to detect electric fields of prey, conspecifics and predators. To following paragraphs will only focus on sharks.
Electric fields can be generated by bioelectric activity in other fish or by induction during the movement of charges in earth’s magnetic field.
In the surrounding of fish, three kinds of electric fields, so called bioelectric fields, were detected by Kalmijn :
- dc fields up to 500 μV in the head and gill region and in proximity to wounds
- low frequency ac fields (< 20Hz) up to 500 μV, strongest in the head and the gill region, synchronous with the respiratory movements
- weak high frequency ac fields during trunk and tail muscle contractions
The low frequency ac fields were caused by the periodic fluctuations of the resistance ratio due to the respiratory movement in the existing dc field.
The bioelectric fields of 60 vertebrate and invertebrate were measured which proofs that these fields occur in many animals. In any cases the dc fields were independent of muscle activity and would be a reliable stimulus for sharks to detect their prey. Prey fishes or conspecifics generate a dipole field which can be estimated with following formula :
ε_0 is the permeability coefficient, p ⃗ the dipole vector, r ̂= r ⃗/|r ⃗| a unit vector in direction r ⃗ and |r ⃗ | the distance to the dipole source.
In order to detect electric phenomena sharks can use their electroreceptors in an active (see 1.2. Induced electric potential) or passive mode . In the passive mode the shark detects fields in its environment like the bioelectric fields of prey or geoelectric fields present in the sea water (see 1.2. Induced electric potential). Kalmijn reported that lemon sharks follow straight paths when crossing the wide bay between North and South Bimini in the Bahamas . They could orient on the ambient electric field induced by ocean currents.
Induced electric potential
Due to earth’s magnetic field a stream of sea water or a shark can induce a dc field  (see Figure 1 and Figure 2).
A particle with charge q experiences a Lorentz force F perpendicular to the magnetic field B, if it moves with a velocity v through the field:
Free charges in an object get deflected due to their movement through a magnetic field according to the formula above. This leads to a separation of positive and negative charges resulting in an induced electric field.
One liter of sea water contains roughly 35 g dissolved salts (mainly Na+ and Cl-) . Water movements such as ocean currents lead therefore to a movement of electric charges. Positive and negative charges get deflected in opposite directions, which leads to a charge separation. An electric field is induced which is high enough to stimulate the electroreceptors of a shark. Fluids within fish contain many free ions such as Na+, K+, Ca2+, Cl- and HCO3-. By analogy with ocean currents, the movement of a shark itself through earth’s magnetic field induces an electric field.
If a shark uses his electroreceptors in the active mode, electric fields induced by their own activity such as motional induced fields are used . Caray and Scharold  observed that migrating blue sharks keep a constant course in the ocean for several days. The only possibility to follow such a long straight path is the orientation on earth’s magnetic field. Sharks use the magnetic field in the active mode for steady compass headings, whereas the ambient electric field is used in the passive mode to orient to the flow of water . The two operation modes guaranty a complete electromagnetic orientation system.
Ampullae of Lorenzini
The ampullae of Lorenzini are sensing organs to perceive electric fields, so called electroreceptors. They consist of a system of jelly filled, grouped canals . One end of the canal forms a pore through the dermis and epidermis and can be seen as black dots on the skin of the shark (see Figure 3:Head of a tiger shark. The small black dots are the pores of the ampullae of Lorenzini). The other side of the canal ends in an ampulla, a group of bulges lined by the sensory epithelium (Figure 4). The ampullary nerve is a bundle of afferent nerves leaving each ampulla. There are no efferent nerves entering the ampulla. A group of ampullae is enclosed in capsules of tight connective tissue. The distribution pattern is specific for different species.
The sensory epithelium consists of pear shaped receptor cells, supporting cells and a basement membrane (see figure 5). The receptor cell reaches the lumen of the ampulla only at one point where the kinocilium is located. The supporting cells fill the space between the different receptor cells. The synapse which contacts nerve endings are placed on the bases of the receptor cells. This side is attached to the basement membrane. The inside walls of the jelly filled canals consist of two layers of flattened pavement epithelium. The cells in the inner layer are connected by tight junctions, which explain the high resistance. Since the resistance of the jelly is very low, the canals therefore act as excellent low-frequency cables . Sharks are therefore only sensitive to dc field gradients or low frequency ac fields. The outside is made of two layers of well-orientated circular and one layer of longitudinal collagenous fibers.
Distribution over the head
The pores which form the beginning of the jelly-filled canals are predominantly found on the dorsal and ventral surface of the head. The canals point in many different directions. Kim  used the original data from Dijkgraaf and Kalmijn  to identify 15 ampullary clusters of the small-spotted catshark (see figure 6). 14 of them are symmetrically aligned pairwise on each side. One is located dorsal around the symmetry axis.
In rays the ampullary electroreceptors are mapped somatotopically , suggesting that sharks use a similar mapping. Different neurons are tuned to one particular orientation of the electric field. The curve firing rate versus the angle of the electric field line is bell-shaped with a maximum at one specific field direction. Therefore each neuron responds strongest to one field direction.
A single canal with an ampulla only answers to changes in the electric fields with a frequency in the range of 0.1-10Hz . A stationary prey emits an electric field (see 1.1. Bioelectric fields) which quickly drops with distance. If the shark approaches the prey he therefore perceives a changing field . The changing field induces a current in the jelly filled canals of the ampullae of Lorenzini which changes the electrical potential in the ampulla . The voltage is amplified in the ampulla due to ion-channel mediated interactions between the apical and the basal membrane . The apical membrane is the side of the membrane which confines the lumen and the basal membrane forms the surface that is faced towards the outside of the cell. The ampullary epithelium can be regarded as a linear amplifier within a voltage < 100 μV. The voltage across the ampullary organ gets amplified according to following formula :
R_a, R_b and R_c are the apical, basal and canal resistances. V_b and V_c are the voltages across the basal membrane and the ampullary organs. Due to the voltage dependent negative conductance of the ion channels in the apical membrane〖,R〗_a<0. Therefore V_b>V_c and the output voltage is amplified. The voltage across the basal membrane is a graded receptor potential which changes gradually with the physically adequate stimuli, the bioelectric field of prey for example . The receptor potential is therefore an analogue representation of the received stimuli.
If the voltage in the ampullae is changed, the firing pattern of the afferent nerve is changed . A quick voltage drop within the jelly leads to an increased firing rate whereas an increase leads to a decrease in the firing rate. The voltage gradient in the ampullae of Lorenzini and therefore the firing rate is maximal when the canal axis is parallel to the electric field lines . Sharks are able to detect voltage gradients of 1-2 nV/cm .
Neural signal processing
Combination of the electric an olfactory sense
Most of the electric fields generated by prey or conspecifics are dipole like (see 1.1. Bioelectric fields) . The electric field lines are curved and the dipole source is not predictable from a local electric field, which is perceived by sharks . Not even the distance to the source can be estimated, since the intensity of the electric field is not a direct measurement of the distance to the dipole source. The electric field of the dipole adds as one over the third power of the distance to the potential difference in the ampullae of Lorenzini. The processing of the electric field information and the sensorimotor mechanism producing the approach style is still unexplained.
Since the electric field decays quickly with distance, the sharks are only able to detect the field of the prey fish, if they are relatively close . More distant signals are detected by pressure (add wikibook link) and smell: for example sharks get attracted by an odor field of injured fish over large distances. The odor fields are easily distorted by local water currents and not suitable to identify the exact location of the wounded fish. If the shark is close enough his electric sense effectively identifies the location of the target fish even if it is burrowed in the sand.
Kalmijn  used electrodes to mimic a bioelectric field of a prey fish. The sharks bit only in the electrodes, although there was an odor source close to the electrode. The electrode triggered a feeding response of large dogfish sharks of about 90-120 cm from a distance of at least 40 cm. The electric gradients were around 5 nV/cm at this distance. The sharks must have detected the field from a greater distance than from the location where the attack was triggered. An attack from a large distance might not be the best strategy since it would alert the prey fish and enable an easy escape. The big advantage lies not in attacking distance but in the penetration power of the electric sense which allows detecting prey buried in sand.
Detection of the electric field direction
In order to be able to detect bioelectric fields of a prey, sharks might subtract, by analogy with other sensory modalities, the anticipated signals produced by environmental fields or fields induced by the movement through earth’s magnetic field . An analysis of the instantaneous potential distribution over the skin or the changes in the field directions over time would be one possibility. The electric field is close to uniform at the distance where the feeding response is triggered and barely distinguishable from the noise in the receptor system. The attack algorithm proposed by Kalmijn (see figure 7) would allow sharks to detect the dipole produced by their prey without knowing the exact location: When the shark first perceives the electric field of prey he keeps a constant angle between his body axis and the local field direction. Every deviation from this angle is nullified by feedback. Following the electric field lines would ultimately guide the shark to the source of the dipole. This algorithm is insensitive to the angle of approach, polarity of the field, temporal changes in the strength or direction of the field and therefore the movement of a prey fish.
In proximity of the dipole the field gets more complicated and difficult to analyze. Sharks might completely ignore that part, since they bit at the original location of the dipole source, which was electrically moved away just after the attack has been initiated . Additional cues from the field nonuniformity, such as curvature or gradient of the field lines could inform sharks to ignore the momentary field information. However in three dimensional situations or if the path of the prey fish is not confined to the plane containing the dipole the algorithm needs further information or leaves some uncertainty.
Distinction between passive and active mode
The question remains how sharks can distinguish between the ambient electric field (passive mode) and the field induced by their motion through earth’s magnetic field (active mode). Since the electroreceptors operate in a frequency range from less than 0.125 – 8 Hz Kalmijn  proposed a possible procedure: The shark might probe its magnetic orientation by temporal acceleration and explore the direction of an ambient field (prey or due to ocean currents) by transiently turning.
Kim  proposed that each lateral symmetric pair of ampullary clusters (see 2.1.1. Distribution over the head) has a contralateral inhibition to localize the dipole source. It can be modeled by taking the intensity difference between the cluster pairs. The shark may turn its head towards the direction of higher intensity to localize dipole source. The highest sensitivity of the ampullae of Lorenzini lies within a frequency range of 1-8 Hz and covers the normal period of the swaying head movement of a shark. The simulation results of Kim show that the larger the sweeping angle of the head swaying motion the better the direction of the electric field can be estimated since the swaying head cancels out noisy signals. The signal is easier distinguishable from noise. This supports the strategy for the detection of an ambient electric field proposed by Kalmijn .
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