Abstract
Lateral-line encoding is diffuse, needing at least a large part of the fish body and several detectors to measure the information contained in the velocity or pressure field surrounding a fish or an aquatic frog such as Xenopus. This paper presents a careful analysis of the mathematical mechanisms and algorithms underlying neuronal information processing as it is performed by the lateral-line system both in the perception ensuing from neuromasts and in the resulting neuronal representations, the maps. The goal is to explicitly show how the lateral line can simultaneously perceive several objects, e.g., identical ones, which role fish geometry plays in lateral-line detection, and why its direct range is short, about one fish length. A lateral-line ‘object’ in the outside world has both position and shape and the lateral line can handle both, at the price of having a restricted range. Detection of vortex wakes as hydrodynamic entities exhibiting the consequence of conservation of angular momentum is also analyzed and contrasted with the instantaneous momentum transfer studied as the usual lateral-line stimulus. Finally, it is shown how lateral-line ‘objects’ may arise neuronally both separately and in the context of a multimodal integration of the lateral-line system and vision, and a concrete theory of map formation in the torus on the basis of neuroanatomy and spike-timing-dependent plasticity (STDP) in conjunction with local excitation and global inhibition is presented. An appendix gives a full and simple mathematical account of surface-wave hydrodynamics, including surface tension.
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- 1.
Great care is needed in the case of shallow baths with a depth h of only a few cm. On the other hand, the experimental setup of, e.g., Elepfandt et al. (2000) is a nearly optimal.
References
Acheson DJ (1990) Elementary fluid dynamics. Oxford University Press, Oxford
Bachman G, Narici L (1966) Functional analysis. Academic, New York; (2000) Dover, Mineola
Bastian J (1982) Vision and electroreception: integration of sensory information in the optic tectum of the weakly electric fish Apteronotus albifrons. J Comp Physiol A 147:287–297
Bi G-Q, Poo M-M (2001) Synaptic modification by correlated activity: HebbÕs postulate revisited. Annu Rev Neurosci 24:139–166
Bleckmann H (1994) Reception of hydrodynamic stimuli in aquatic and semiaquatic animals. Fischer, Stuttgart
Bleckmann H, Schwarz E (1982) The functional significance of frequency modulation within a wave train for prey localization in the surface-feeding fish Aplocheilus lineatus (Cyprinodontidae). J Comp Physiol A 145:331–339
Billingham J, King AC (2000) Wave motion. Cambridge University Press, Cambridge
Blickhan R, Krick C, Zehren D, Nachtigall W, Breithaupt T (1992) Generation of a vortex chain in the wake of a subundulatory swimmer. Naturw 79:220–221
Bürck M, Friedel P, Sichert AB, Vossen C, van Hemmen JL (2010) Optimality in mono- and multi-sensory map formation. Biol Cybern 103:1–20
Calvert G, Spence C, Stein BE (eds) (2004) The handbook of multisensory processes. MIT Press, Cambridge
von Campenhausen C, Riess I, Weissert R (1981) Detection of stationary objects by the blind cave fish Anoptichthys jordani (Characidae). J Comp Physiol A 143:369–374
Chagnaud BP, Bleckmann H, Engelmann J (2006) Neural responses of goldfish lateral line afferents to vortex motions. J Exp Biol 209:327–342
Chung SH, Stirling RV, Gazei RM (1975) The structural and functional development of the retina in larval Xenopus. J Embryol Exp Morph (now: Development) 33(4):915–940. The Appendix Optics of Xenopus eyes during development by M. Land and R. V. Stirling appears on pp 934–940. The author thanks Susan Udin (SUNY at Buffalo) for drawing his attention to this wonderful piece of work
Claas B, Münz H (1996) Analysis of surface wave direction by the lateral line system of Xenopus: source localization before and after inactivation of different parts of the lateral line. J Comp Physiol A 178:253–268
Clegg JG (1968) Calculus of variations. Oliver and Boyd, Edinburgh
Coombs S (1994) Nearfield detection of dipole sources by the goldfish (Carassius auratus) and the mottled sculpin (Cottus bairdi). J Exp Biol 190:109–129
Coombs S, Conley RA (1997) Dipole source localization by mottled sculpin I: approach strategies. J Comp Physiol A 180:387–399
Coombs S, van Netten S (2006) The hydrodynamics and structural mechanics of the lateral line system. Chapter 4 in: fish physiology. In: Shadwick RE, Lauder GV (eds) Fish biomechanics, vol 23. Academic
Coombs S, Hastings M, Finneran J (1996) Modeling and measuring lateral line excitation patterns to changing dipole source locations. J Comp Physiol A 178:359–371
Coombs S, New JG, Nelson M (2002) Information-processing demands in electrosensory and mechanosensory lateral line systems. J Physiol (Paris) 96:341–354
Ćurčić-Blake B, van Netten SM (2006) Source location encoding in the fish lateral line canal. J Exp Biol 209:1548–1559
Denton E, Gray JAB (1982) The rigidity of fish and patterns of lateral line stimulation. Nature 297:679–681
Denton E, Gray JAB (1983) Mechanical factors in the excitation of clupeid lateral lines. Proc R Soc Lond B 218:1–26
Dickinson M (2003) How to walk on water. Nature 424:621–622
Dijksterhuis EJ (1969) The mechanization of the world picture. Oxford University Press, Oxford
Dijkgraaf S (1963) The functioning and significance of the lateral-line organs. Biol Rev 38:51–105
Drucker EG, Lauder GV (2002) Experimental hydrodynamics of fish locomotion: Functional insights from wake visualization. Integr Comp Biol 42(2):243–257
Dym H, McKean HP (1972) Fourier series and integrals. Academic, New York
Elepfandt A (1982) Accuracy of taxis response to water waves in the clawed toad (Xenopus laevis Daudin) with intact or with lesioned lateral line system. J Comp Physiol A 148:535–545
Elepfandt A (1984) The role of ventral lateral line organs in water wave localization in the clawed toad (Xenopus laevis). J Comp Physiol A 154:773–780
Elepfandt A (1986) Detection of individual waves in an interference pattern by the clawed frog Xenopus laevis Daudin. Neurosci Lett 26:S380
Elepfandt A (2012) private communication
Elepfandt A, Wiedemer L (1986) Lateral-line responses to water surface waves in the clawed frog, Xenopus laevis. J Comp Physiol A 160:667–682
Elepfandt A, Seiler B, Aicher B (1985) Water wave frequency discrimination in the clawed frog, Xenopus laevis. J Comp Physiol A 157:255–261
Elepfandt A, Kroese ABA, van Netten SM, private communications. The latter two have performed their experiments independently of Elepfandt; their lateral-line object was a passing zebrafish
Elepfandt A, Lebrecht A, Schroedter K, Brudermanns B (2004) Discrimination of two water waves presented simultaneously in the clawed frog, Xenopus laevis laevis. In: Abstract 7th congress of the international society for neuroethology; Schroedter K, Staatsexamensarbeit, Humboldt Universität zu Berlin, (2002) under the direction of A. Elepfandt
Elepfandt A, Eistetter I, Fleig A, Günther E, Hainich M, Hepperle S, Traub B (2000) Hearing threshold and frequency discrimination in the purely aquatic frog Xenopus laevis (Pipidae): measurement by means of conditioning. J Exp Biol 203:3621–3629; see in particular Fig. 1
von der Emde G, Engelmann J (2011) Active electrolocation. In: Farrell AP (ed) Encyclopedia of fish physiology: from genome to environment, vol 1. Elsevier, Amsterdam, pp 375–386
Engelmann J, Bleckmann H (2004) Coding of lateral line stimuli in the goldfish midbrain in still and running water. Zoology 107(2):135–151
Faucher K, Parmentier E, Becco C, Vandewalle N, Vandewalle P (2010) Fish lateral system is required for accurate control of shoaling behaviour. Animal Behav 79:679–687
Flanders M (2011) What is the biological basis of sensorimotor integration? Biol Cybern 104:1–8
Franosch J-MP, Sobotka MC, Elepfandt E, van Hemmen JL (2003) Minimal model of prey localization through the lateral-line system. Phys Rev Lett 91:158101
Franosch J-MP, Lingenheil M, van Hemmen JL (2005a) How a frog learns what is where in the dark. Phys Rev Lett 95:078106
Franosch J-MP, Sichert AB, Sobotka MC, Elepfandt A, van Hemmen JL (2005b) Model of amphibian prey localization through the lateral-line system. Physik Department T35, Technische Universität München, internal report
Franosch J-MP, Hagedorn HJA, Goulet J, Engelmann J, van Hemmen JL (2009) Wake tracking and the detection of vortex rings by the canal lateral line of fish. Phys Rev Lett 103:078102
Friedel P, van Hemmen JL (2008) Inhibition, not excitation, is the key to multimodal sensory integration. Biol Cybern 98:597–618
Geer J (1975) Uniform asymptotic solutions for potential flow around a slender body of revolution. J Fluid Mech 67:817–827
Gelfand IM, Fomin SV (1963) Calculus of variations. Prentice-Hall, Englewood Cliffs
Gerstner W, van Hemmen JL (1994) Coding and information processing in neural networks. In: Do-many E, van Hemmen JL, Schulten K (eds) Models of neural networks II. Springer, New York, pp 39–47
Gerstner W, Kempter R, van Hemmen JL, Wagner H (1996) A neuronal learning rule for sub-millisecond temporal coding. Nature 383:76–78
Görner P (1963) Untersuchungen zur Morphologie und Elektrophysiologie des Seitenlinienorgans vom Krallenfrosch (Xenopus laevis Daudin). Z vergl Physiol 47:316–338
Goulet J (2010) Information processing in the lateral-line system of fish. Doctoral Dissertation, Physik Department T35, Technische Universität München. http://mediatum2.ub.tum.de/node?id=959089
Goulet J, Engelmann J, Chagnaud BP, Franosch J-MP, Suttner MD, van Hemmen JL (2008) Object localization through the lateral line system of fish: theory and experiment. J Comp Physiol A 194:1–17
Goulet J, van Hemmen JL, Jung SN, Chagnaud BP, Scholze B, Engelmann J (2012) Temporal precision and reliability in the velocity regime of a hair-cell sensory system: the mechanosensory lateral-line of goldfish, Carassius auratus. J Neurophysiol 107:2581–2593
Grothe B, Pecka M, McAlpine D (2010) Mechanisms of sound localization in mammals. Physiol Rev 90:983–1012
Gutfreund Y, Knudsen EI (2007) Visual instruction of the auditory space map in the midbrain. In: Calvert et al. (2004) Chapter 38
Gutfreund Y, Zheng W, Knudsen EI (2002) Gated visual input to the central auditory system. Science 297:1556–1559
Gutfreund Y, King A (2012) What is the role of vision in the development of the auditory space map? Chapter 32. In: Stein BE (ed) The new handbook of multisensory processes. Cambridge, MIT Press
Guyon E, Hulin J-P, Petit L, Mitescu CD (2001) Physical hydrodynamics. Oxford University Press, Oxford
Hanke W, Brücker C, Bleckmann H (2000) The ageing of the low-frequency water disturbances caused by swimming goldfish and its possible relevance to prey detection. J Exp Biol 203:1193–1200
Hanke W, Bleckmann H (2004) The hydrodynamic trails of Lepomis gibbosus (Centrarchidae), Colomesus psittacus (Tetraodontidae) and Thysochromis ansorgii (Cichlidae) investigated with scanning particle image velocimetry. J Exp Biol 207:1585–1596
Harris GG, van Bergeijk WA (1962) Evidence that the lateral-line organ responds to near-field displacements of sound sources in water. J Acoust Soc Am 34(12):1834–1841
Hassan El-S (1985) Mathematical analysis of the stimulus for the lateral line organ. Biol Cybern 52:23–36
Hassan EI-S (1992a) Mathematical description of the stimuli to the lateral line system of fish derived from a three-dimensional flow field analysis: I The cases of moving in open water and of gliding towards a plane surface. Biol Cybern 66:443–452
Hassan EI-S (1992b) Mathematical description of the stimuli to the lateral line system of fish derived from a three-dimensional flow field analysis: II The case of gliding alongside or above a plane surface. Biol Cybern 66:453–461
Hassan El-S (1993) Mathematical description of the stimuli to the lateral line system of fish, derived from a three-dimensional flow field analysis: III The case of an oscillating sphere near the fish. Biol Cybern 69:525–538
van Hemmen JL (2001) Theory of synaptic plasticity In: Moss F, Gielen S (eds) Handbook of biophysics, vol 4; see in particular §2 and Appendices A and B. Elsevier, Amsterdam, pp 771–823
van Hemmen JL (2006) What is a neuronal map, how does it arise, and what is it good for? In: van Hemmen JL, Sejnowski TJ (eds) 23 Problems in systems neuroscience. Oxford University Press, New York, pp 83–102
van Hemmen JL (2010) Lateral-line detection of underwater objects: from goldfish to submarines. Bull Am Phys Soc 55(2):V10.00008. See also TUM Faszination Forschung 7(10):70–75
Heiligenberg W, Rose GJ (1987) The optic tectum of the gymnotiform electric fish, Eigenmannia: labeling of physiologically identified cells. Neuroscience 22:331–340
Hopkins CD (2009) Electrical perception and communication. In: Squire LR (ed) Encyclopedia of neuroscience, vol 3. Academic Press, Oxford, pp 813–831
Isakov V (2006) Inverse problems for partial differential equations, 2nd edn. Springer, New York
Isenberg C (1992) The science of soap films and soap bubbles. Dover, Mineola
Janssen J, Coombs S, Pride S (1990) Feeding and orientation of mottled sculpin, Cottus bairdi, to water jets. Environ Biol Fishes 29:43–50
Jazayeri M, Movshon JA (2006) Optimal representation of sensory information by neural populations. Nat Neurosci 9:690–696
Jielof R, Spoor A, de Vries Hl (1952) The microphonic activity of the lateral line. J Physiol 116:137–157
Käse RH, Bleckmann H (1987) Prey localization by surface wave ray-tracing: fish track bugs like oceanographers track storms. Experientia 43:290–293
Kalmijn AJ (1988) Hydrodynamic and acoustic field detection. In: Atema J, Fay RR, Popper AN, Tavolga WN (eds) Sensory biology of aquatic animals. Springer, New York, pp 83–130
Keller CH, Takahaski TT (1996) Binaural cross-correlation predicts the responses of neurons in the owl’s auditory space map under conditions simulating summing localization. J Neurosci 16(13):4300–4309
Kuiper JW (1956) The microphonic effect of the lateral line organ. Ph. D. Thesis, Natuurkundig Laboratorium, University of Groningen, The Netherlands
Knudsen EI (2002) Instructed learning in the auditory localization pathway of the barn owl. Nature 417:322–328
Knudsen EI, Knudsen PF (1989) Vision calibrates sound localization in developing barn owls. J Neurosci 9(9):3306–3313
Knudsen EI, du Lac S, Esterly SD (1987) Computational maps in the brain. Annu Rev Neurosci 10:41–65
Krippner M (2012) Multimodales Lernen im blinden Mexikanischen Hohlenfisch. Diploma thesis, Physik Department T35, Technische Universität München
Kühn R, van Hemmen JL (1995) Temporal association. In: Domany E, van Hemmen JL, Schulten K (eds) Models of neural networks, 2nd edn. Springer, Berlin, pp 213–280 (particularly, §7.4)
Lamb H (1932) Hydrodynamics, 6th edn. Cambridge University Press, Cambridge. See in particular Sects. 92, 226 ff., 246, 331, and Chaps. 5 and 7
Lamperti J (1966) Probability. Benjamin, New York; 2nd edn. (1996) Wiley, New York
Lingenheil M (2005) Theorie der Beuteortung beim Krallenfrosch. Diploma thesis, Physik Department T35, Technische Universität München
Lowe DA (1987) Single-unit study of lateral line cells in the optic tectum of Xenopus laevis: evidence for bimodal lateral line/optic units. J Comp Neurol 257:396–404
Meyer G, Klein A, Mogdans J, Bleckmann H (2012) Toral lateral line units of goldfish, Carassius auratus, are sensitive to the position and vibration direction of a vibrating sphere. J Comp Neurol 198:639–653
Mostowski A, Stark M (1964) Introduction to higher algebra. Pergamon, Oxford. Particularly, Chap. 7, §4. This book is a mine of useful information and clear exposition
van Netten SM (2006) Hydrodynamic detection by cupulae in a lateral-line canal: functional relations between physics and physiology. Biol Cybern 94:67–85
Pandya S, Yang Y, Jones DL, Engel J, Liu C (2006) Multisensor processing algorithms for underwater dipole localization and tracking using MEMS artificial lateral-line sensors. EURASIP J Appl Signal Proc 076593
Pfister J-P, Toyoizumi T, Barber D, Gerstner W (2006) Optimal spike-timing-dependent plasticity for precise action potential firing in supervised learning. Neural Comput 18:1318–1348
Pitcher TJ, Patridge TL, Wardle CS (1976) A blind fish can school. Science 194:963–965
Plachta DTT, Hanke W, Bleckmann H (2003) A hydrodynamic topographic map in the midbrain of goldfish Carassius auratus. J Exp Biol 206:3479–3486
Pohlmann K, Grasso FW, Breithaupt T (2001) Tracking wakes: the nocturnal predatory strategy of piscivorous catfish. Proc Natl Acad Sci USA 98:7371–7374
Press WH, Teukolsky SA, Vetterling WT, Flanery BP (1995) Numerical recipes in C, 2nd edn. Cambridge University Press, Cambridge; see in particular p. 34 for an explanation of the pseudo-inverse
Scheich H, Ebbesson SOE (1983) Multimodal torus in the weakly electric fish Eigenmannia. Springer, Berlin
Schlichting H, Gertsen K (2003) Boundary layer theory. Springer, Berlin
Schmitz A, Bleckmann H, Mogdans J (2008) Organization of the superficial neuromast system in goldfish, Carassius auratus. J Morphol 269:751–761
Schnupp JWH, Carr CE (2009) On hearing with more than one ear: lessons from evolution. Nat Neurosci 12(6):692–697
Schwartz E, Hasler AD (1966) Superficial lateral line sense organs of the mudminnow. Z vergl Physiol 53:317–327
Schwarz JS, Reichenbach T, Hudspeth AJ (2011) A hydrodynamic sensory antenna used by killifish for nocturnal hunting. J Exp Biol 214:1857–1866
Sichert AB, van Hemmen JL (2010) How stimulus shape affects lateral-line perception: analytical approach to analyzing natural stimulus characteristics. Biol Cybern 102:177–180
Sichert AB, Bamler R, van Hemmen JL (2009) Hydrodynamic object recognition: When multipoles count. Phys Rev Lett 102:058104
Soares D (2002) An ancient sensory organ in crocodilians. Nature 417:241–242
Song J, Fan C, Wang X, Zhang X (2011) A phylogenetic survey of morphological patterns of superficial neuromasts in teleost fish. Brain Behav Evol 78:190
Stein BE (ed) (2012) The new handbook of multisensory processing. MIT Press, Cambridge
Strelioff D, Honrubia V (1978) Neural transduction in Xenopus laevis lateral-line system. J Neurophysiol 41:432–444
Thomas GB (1972) Calculus and analytic geometry, 3rd edn. Addison-Wesley, Reading (§12.6)
Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. Winston, Washington
Tinsley RC, Kobel HR (eds) (1996) The biology of Xenopus. Oxford University Press, Oxford
Udin SB (2007) The instructive role of binocular vision in the Xenopus tectum. Biol Cybern 97:493–503
Urban S, Vollmayr AN, van Hemmen JL (2014) Hydrodynamic imaging on a 1-dimensional manifold and its inversion in 2-dimensional potential flow. TUM preprint
Vanegas H, Ebbeson SOE, Laufer M (1984a) Morphological aspects of the teleostean optic tectum. In: Vanegas H (ed) Comparative neurology of the optic tectum. Plenum, New York, pp 93–120
Vanegas H, Williams B, Essayac E (1984b) Electrophysiological and behavioral aspects of the teleostean optic tectum. In: Vanegas H (ed) Comparative neurology of the optic tectum. Plenum, New York, pp 121–162
van der Waerden BL (1969) Mathematical statistics. Springer, Berlin. See Jazayeri and Movshon (2006) for a comprehensive explanation of how references like van der Waerden’s classic may serve theoretical neuroscience
Watson GN (1922) A treatise on the theory of Bessel functions (Chaps. 2, 3). Cambridge University Press, Cambridge
Yang Y, Chen J, Engel J, Pandya S, Chen N, Tucker C, Coombs S, Jones DL, Liu C (2006) Distant touch hydrodynamic imaging with an artificial lateral line. Proc Natl Acad Sci USA 103:18891–18895
Yang Y, Nguyen N, Chen N, Lockwood M, Tucker C, Hu H, Bleckmann H, Liu C, Jones DL (2010) Artificial lateral line with biomimetic neuromasts to emulate fish sensing. Bioinsp Biomim 5:016001
Yang Y, Klein A, Bleckmann H, Liu C (2011) Artificial lateral line canal for hydrodynamic detection. Appl Phys Lett 99:023701
Zittlau KE, Claas B, Münz H (1986) Directional sensitivity of lateral line units in the clawed toad Xenopus laevis Daudin. J Comp Physiol A 158:469–477
Acknowledgments
The author sincerely thanks his collaborators over the years on many lateral-line issues: His colleagues, Professors Horst Bleckmann, Jacob Engelmann, and Andreas Elepfandt as well as his former graduate students who have been involved in several projects discussed here; particularly, Drs. Moritz Franosch, Paul Friedel, Julie Goulet, Andy Sichert, and Andreas Vollmayr. Financial support from the BMBF through BCCN—Munich is gratefully acknowledged.
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van Hemmen, J.L. (2014). Hydrodynamic Object Formation: Perception, Neuronal Representation, and Multimodal Integration. In: Bleckmann, H., Mogdans, J., Coombs, S. (eds) Flow Sensing in Air and Water. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41446-6_16
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