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A Model for the Neuronal Substrate of Dead Reckoning and Memory In Arthropods: a Comparative Computational and Behavioral Study

A Model for the Neuronal Substrate of Dead Reckoning and Memory In Arthropods: a Comparative Computational and Behavioral Study
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  ORIGINAL PAPER A model for the neuronal substrate of dead reckoningand memory in arthropods: a comparative computationaland behavioral study Ulysses Bernardet   Sergi Bermu´dez i Badia   Paul FMJ Verschure Received: 17 October 2007/Accepted: 26 March 2008/Published online: 22 April 2008   Springer-Verlag 2008 Abstract  Returning to the point of departure afterexploring the environment is a key capability for mostanimals. In the absence of landmarks, this task will besolved by integrating direction and distance traveled overtime. This is referred to as path integration or dead reck-oning. An important question is how the nervous systemsof navigating animals such as the 1 mm 3 brain of ants canintegrate local information in order to make global deci-sion. In this article we propose a neurobiologicallyplausible system of storing and retrieving direction anddistance information. The path memory of our modelbuilds on the well established concept of population codes,moreover our system does not rely on trigonometricfunctions or other complex non-linear operations such asmultiplication, but only uses biologically plausible opera-tions such as integration and thresholding. We test ourmodel in two paradigms; in the first paradigm the systemreceives input from a simulated compass, in the secondparadigm, the model is tested against behavioral datarecorded from 17 ants. We were able to show that our pathmemory system was able to reliably encode and computethe angle of the vector pointing to the start location, andthat the system stores the total length of the trajectory in adependable way. From the structure and behavior of ourmodel, we derive testable predictions both at the level of observable behavior as well as on the anatomy and phys-iology of its underlying neuronal substrate. Keywords  Path integration    Dead reckoning   Arthropod    Path memory    Population code   Vector decoding    Neuronal model Introduction Relocating the nest after leaving the dwelling and movingabout in the environment is a basic requirement for anyentity living in the real-world, a task which needs to besolved by human and bug. Two strategies can be used tofind the way back to the point of departure: first, the agentcan memorize its path based on external cues such asvisual, auditory, or olfactory landmarks, or second, theagent can integrate the distance and direction traveled.Commonly, the former is referred to as ‘‘landmark navi-gation’’ (LMN), and the latter is called ‘‘path integration’’(PI) or ‘‘dead reckoning’’ (Fig. 1). Dead reckoning isthought to have been introduced into the scientific dis-course in the 19th century by Darwin (Darwin 1873).Path integration has been studied extensively in insects[for review: (Wehner and Srinivasan 2003)] as well asin mammals [for review: (Etienne and Jeffery 2004)].Experimental research on path integration in insects hasbeen pioneered by the work of von Frisch (von Frisch1993) on bees and of Wehner (Wehner 2003) on ants. Von Frisch, for example, could show already in the 1960s thatbees signal by their waggle-dance the air-line direction to anectar source, irrespective of whether they had to fly adetour to actually get there or not (von Frisch 1993). The U. Bernardet ( & )    S. Bermu´dez i BadiaSynthetic Perceptive, Emotive and Cognitive Systems, IUA,Universitat Pompeu Fabra, Ta`nger, 135, 08018 Barcelona, Spaine-mail: ubernardet@iua.upf.eduS. Bermu´dez i Badiae-mail: sergi.bermudez@upf.eduP. FMJ VerschureSynthetic Perceptive, Emotive and Cognitive Systems, IUA,ICREA, Universitat Pompeu Fabra, Ta`nger, 135,08018 Barcelona, Spaine-mail: paul.verschure@iua.upf.edu  1 3 Theory Biosci. (2008) 127:163–175DOI 10.1007/s12064-008-0038-8  empirical verification of vertebrate path integration strate-gies has been put forward more recently (Mittelstaedt andMittelstaedt 1980).To integrate the path, two signals are required; thetraveling direction and the traveling distance (Fig. 2).While the sources of information for path integration ininsects are well investigated, it is presently not clear whichof the several possible cues mammals are making use of,e.g., vestibular information, proprioceptive information,sensory flow, or efferent copies from movement commands(Wallace et al. 2002).Measuring the traveled distanceWalking insects like ants have been shown to predomi-nantly use proprioception to estimate the distance traveledduring a journey (Ronacher et al. 2000; Wohlgemuth et al.2001; Sommer and Wehner 2004; Wittlinger et al. 2006). In flying insects, the consumption of energy was thought tobe used as a means to measure distance. This is referred toas the ‘‘energy hypothesis’’ (von Frisch 1993). Yet researchhas shown that this hypothesis cannot be upheld [reviewedin Esch and Burns (1996)]. Bees have been shown in both,laboratory (Srinivasan et al. 2000; Si et al. 2003; Hrncir et al. 2003) and natural settings (Tautz et al. 2004), to rely on optic flow to gauge distance.Measuring the heading directionA large variety of terrestrial and aquatic animals are usingthe so called ‘‘solar compass’’ for navigation. The solarcompass derives heading information from the polarizationpattern of the sky and possibly the luminance distributionof the sunlight. In the class of insects this has been shownfor the desert ant ( Cataglyphis ) (Wehner 1997), the cricket( Gryllus campestris ) (Labhart 1988), the locust ( Schistoc-erca gregaria ) (Homberg and Wu¨rden 1997), the honeybee(  Apis mellifera ) (von Frisch 1993; Rossel and Wehner1986), the cockchafer beetle (  Melolontha melolontha )(Labhart et al. 1992), the cockroach (  Leucophaeamaderae ) (Loesel and Homberg 2001), the fly (  Muscadomestica ) (von Philipsborn and Labhart 1990) and themonarch butterflies (  Danaus plexippus ) (Reppert et al.2004; Stalleicken et al. 2005). At the behavioral level, ants have been studied most extensively, whereas in the domainof physiology, the best investigated animals are cricketsand locusts.The solar compass fulfills functions similar to the socalled head direction cells (HDCs) found in mammals(Knierim et al. 1995). These head direction cells show anincrease in firing rate that is specific to the animal’s ori-entation, but not to the location in space and can be foundin various brain areas, e.g., in the rat including but notlimited to the postsubiculum, anterior dorsal nucleus of theanterior thalamus, and lateral mammillary nucleus (Taube2007).Path memory modelsResearch on the memory of bees is predominantly phe-nomenological, and has shown that the working memory of bees is plastic and robust and is organized to work at dif-ferent temporal scales (Menzel et al. 2005; Reinhard et al.2006; Zhang et al. 2005). Looking for the underlying mechanism, we have to turn to research on the fruit fly. Inthe  Drosophila , neuronal structures for memory areshowing a high degree of domain specificity, i.e., there isno central all-purpose memory structure. The mushroombodies are the location of odor related short-term (Zarset al. 2000a, b) and long-term memories (Pascual and Pre ´at2001). Visual memory traces can be found in the centralcomplex, a neuronal structure with repetitive and regularorganization (Liu et al. 2006). The role of the medianbundle is not entirely clear. Recent investigations areflagging it as a candidate for a kind of place memory, as itis the integration site for sensory information, e.g., from theantennae, and path information from the ventral ganglion(Zars et al. 2000a, b). Hence, although the actual location of the path integrator and memory has not yet been iden-tified, the ventral ganglion seems to be a good candidate(Zars et al. 2000a, b). Many of the above mentioned mechanisms are in therealms of long-term memory, and would seem to requiresynaptic changes. The question is, what mechanisms of working and short-term memory could support path inte-gration and dead reckoning. Here we will investigate twoscenarios on such a memory system based on a populationcoding of heading direction. The standard way of  Fig. 1  An Example of path integration based navigation. Theoutbound journey is marked with a  solid line , and the return pathwith a  dashed line .  Diamonds  mark the location of landmarks. h a ! ; h b ! ;  h c ! indicate vectors pointing to the departure location,  b a , b a , b a indicate the corresponding angles of the homewards pointing vectors164 Theory Biosci. (2008) 127:163–175  1 3  calculating the homing vector is the linear summation of all memorized vectors. This procedure heavily relies onmultiplicative and trigonometric operations. Though it isargued that multiplicative operations are occurring in ner-vous systems (Gabbiani et al. 2002), this issue is still underactive investigation. A nervous system performing trigo-nometric operations, possibly relying on some kind of lookup table, seems highly improbable.The memory subsystem of our model is built on twoconcepts; neurons exhibiting persistent activity and thepopulation code.The persistent activity of tonically firing neurons istriggered by a short excitatory input and shunted by a brief inhibitory input. Neurons showing these properties can befound in a wide variety of neuronal systems in a number of species that have also been associated with spatial navi-gation [(Major and Tank  2004) for review]. Examplesinclude the entorhinal cortex of rats (Egorov et al. 2002),cultured Retzius cells of the leech (Angstadt 1999), respi-ratory and flight system inter- and motoneurones in thelocust (Ramirez and Pearson 1991), and cells in theantenna lobe of the moth (Mercer et al. 2005).The concept of a ‘‘population code’’ was pioneered byGeorgopoulos’ work on the motor cortex (Georgopouloset al. 1986; Georgopoulos 1994). Systems employing this mechanism can be found in a wide range of biologicalneuronal systems (Salinas and Abbott 1994), including thecricket’s cercal sensory system (Jacobs and Theunissen1996). The driving idea of the population code is the rep-resentation of a single vector as the sum of multiplevectors. Each of the single vectors is in turn represented byneurons. The angle of the vector is given by the direction-dependent tuning curve of the neuron, whereas the lengthof the vector is represented by the spiking frequency.Hence in a vector population each neuron can be under-stood as vector  v ! with norm || v || proportional to the firingrate and an angle  a  given by the neuron’s preferreddirection (Fig. 3). Methods Path memory modelOur path memory model consists of three main stages:input, memory, and memory decoding (Fig. 4). Subse-quently we will elaborate the function and implementationof these different stages. For ease of explanation we willstart with the memory storage mechanism before explain-ing the input to the memory.  Memory storage mechanism The task of the memory is to store the direction and thedistance traveled. In the  ‘‘Memory’’  group, every neuron isassociate with a specific direction. Each neuron has anarrow tuning curve of 10  . Neurons with the same Fig. 2  Diagram of the embedding of the path memory in a model of aforaging agent. The computation of the heading direction is providedby, e.g., a solar compass system, whereas the distance information canstem, e.g., from the optic flow, or proprioceptive information. Bothsignals are fed into the path memory system which in turn providesthe behavior regulation system with the homing vector 1 2 3 4 5 6 7 805101520253035404550 neuron number    f   i  r   i  n  g  r  a   t  e   [  a  r   b   i   t  r  a  r  y  u  n   i   t   ] 302106024090270120300150330180 0 neuron #1neuron #2neuron #3neuron #4neuron #5neuron #6neuron #7neuron #8 −60 −50 −40 −30 −20 −10 0 10−70−60−50−40−30−20−10010 sum vectorneuron #1neuron #2neuron #3neuron #4neuron #5neuron #6neuron #7neuron #8 (a) (b) (c) Fig. 3  Illustration of the population code concept.  a  A group of cells(8 in this case) can be understood as vector field, where each cell inthe group represents a vector  v ! with norm || v  || proportional to thefiring rate and an angle  a  given by the neuron’s preferred direction( b ).  c  The sum vector  s ! of all vectors  v ! is indicated by a  red arrow Theory Biosci. (2008) 127:163–175 165  1 3  preferred direction are organized into columns within thegroup (Fig. 5). This is not a conceptual requirement, but isuseful to make the handling easier.The neuron type used is of the type ‘‘Integrate and Fire’’with a high membrane persistence. This means, that asingle excitatory input spike to this cell suffices to trigger asustained firing, whereas a single inhibitory input spike willpull the neuron back to the resting state. The persistentfiring of the cells in the  ‘‘Memory’’  group constitutes themid-term memory mechanism. The schema of persistentfiring is consistent with neurobiological findings in a widerange of neuronal systems (Major and Tank  2004). Binaryneurons are used in order make the system immune topossible fluctuations of the spiking frequency of a singleneuron, and to increase the redundancy. In principlethe system could also be implemented using neuronsexhibiting graded persistent activity (Egorov et al. 2002),which would increase the memory capacity, but make thememory more susceptible to the fluctuation of activity of single neurons.In total the  ‘‘Memory’’  group consists of 3,600 neurons,organized into 36 columns. The length of the vectorspointing in the 36 different directions can be visualized bysumming up the activity of all neurons in one column.  Input to the memory system The heading direction information is provided via a ‘‘Gater’’  group (Fig. 4). In this group, only one cell isactive at any given time, and its identity determines theagent’s heading direction (Fig. 6). The velocity informa-tion is provided by the odometry subsystem and is Fig. 4  Architecture of the pathmemory model.  Gray boxes stand for sub-systems. A sub-system can consist of a singlecell group, or of multiple,connected groups. Excitatoryconnections are symbolized by solid red  , inhibitory connectionsby  dashed blue arrows . The ‘‘Velocity’’  group provides thevelocity input from theodometry subsystem. In the ‘‘Gater’’  group the velocityinput is combined with theheading direction.  ‘‘Memory’’  isthe main memory grouporganized into 36 columns of 100 neurons. Each neuron inone column of the  ‘‘Memory’’ group projects onto the ‘‘Memory sum’’  group (36neurons). Hence each neuron inthe  ‘‘Memory sum’’  group has anactivity proportional to thenumber of active neurons in acolumn of the  ‘‘Memory’’  group.Each neuron in the  ‘‘Memorysum’’  represents a vector  v ! with norm ||  v  || proportional tothe firing rate and an angle  a corresponding to the angle of acolumn of the  ‘‘Memory’’  group(Fig. 5)166 Theory Biosci. (2008) 127:163–175  1 3  represented by the spiking frequency of the active cell inthe  ‘‘Gater’’  group. The activity of this group is linearlydependent on the traveling velocity.All cells within one column of the  ‘‘Memory’’  groupreceive excitatory input from the corresponding cell in the ‘‘Gater’’  group, hence the position of the active cell in the ‘‘Gater’’  group defines which column within the memorygroup is activated.The synapses between the  ‘‘Gater’’  and the  ‘‘Memory’’ groups are of type ‘‘probabilistic fixed weight’’. Thisprobabilistic synapse type transfers the synaptic input  synIn to the post-synaptic potential  psp  with transmission prob-ability  Prob  and the synaptic weight  w  [ [ - 1,1] (Eq. 1).  psp i ð t   þ  1 Þ ¼  synIn i ð t  Þ   w  with probability Prob0 otherwise  ð 1 Þ The transmission probability for the synapses between the ‘‘Gater’’  and the  ‘‘Memory’’  group is relatively small(0.05) therefore each excitatory/inhibitory pre-synapticspike will only ‘‘kick’’ a relatively small number of post-synaptic cells above threshold. This probabilistic mecha-nism represents a sub-sampling of the actual headingdirection input. Taken together, the number of currentlyspiking neurons in a column of the  ‘‘Memory’’  group isproportional to the total distance traveled in a specificdirection.  Memory readout mechanism Having the path stored in memory is useful only if theinformation can be subsequently retrieved. The goal of thememory readout is therefore to calculate the sum vector s ! :  s !¼ P 1  i  n  v ! i :  For ease of illustration, we add agroup  ‘‘Memory sum’’  where each cell receives input fromall cells of one column of the  ‘‘Memory’’  group (Fig. 4).Hence, each neuron in the  ‘‘Memory sum’’  has an activityproportional to the number of active neurons in a column of the  ‘‘Memory’’  group, and represents a vector  v ! with norm|| v || proportional to the firing rate and an angle  a  corre-sponding to the angle of a column of the  ‘‘Memory’’  group.This intermediate step is not a requirement, but helps inconstructing the system.The solution we employ to approximate  s ! is a two-stepprocess. In a first operation we project the vectors  v !  j represented by the neurons in the group  ‘‘Memory sum’’ onto a set of projection neurons  p !  j  (Fig. 7). Fig. 5  The basic concept of the path memory is the representation of the distance traveled in different directions by a population code.Each column in the  ‘‘Memory’’  group ( reddish columns  at the bottom)represents a vector  v ! in a direction  j .  Red stripes  in the columnsindicate tonically firing neurons, whereas in the  black parts  noneurons are active. The length of the vector component is given by thenumber of spiking neurons within a column. For illustration the figureshows a memory for 16 directions, as opposed to 36 directions used inthe model Fig. 6  Illustration of the memory system input mechanism. Thespeed information represented by the group ‘‘ Velocity ’’ is projectedonto each cell of the ‘‘ Gater  ’’ group, but only the cell representing thecurrent heading direction (‘‘  Heading ’’) is active, all other cells areinhibited. For illustration, the figure the input mechanism 8 directions,as opposed to 36 direction used in the model Fig. 7  Illustration of the memory readout mechanism. The figureshows a single projection neuron, which receives input from the ‘‘Memory sum’’  group. Excitatory connections are symbolized by  red  ,inhibitory connections by  blue arrows . The synaptic weights aredistributed in a Gaussian fashion, approximating a cosine distribution.The  top panel  shown the weight of the excitatory and inhibitoryconnection. In the  bottom panel  the weight of the connection isrepresented by the width of the connection. In total the ‘‘ Vector decode ’’ group (Fig. 4) consists of 36 projection neuronsTheory Biosci. (2008) 127:163–175 167  1 3
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