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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