Computational model of the cockroach escape behavior: winner and losers in a population code

 I present a comprehensive biologically oriented computational model to account for the escape response of the cockroach on the ground. This model is an expansion of previous work that accounted only for discriminating left from right wind directions [Ezrachi et al. (1999) Biol Cybern 81: 89–99]. The model is composed of computational elements describing the biological processes taking place in the various neurons and includes input which emulates empirical data. With this model it is possible to obtain escape behavior that resembles natural behavior. The model is used to address an ongoing debate as to whether the cockroach's turn direction is determined by computations carried out by the entire neuronal population (PC) or rather by a “winner-take-all” (WTA) mechanism. I suggest that the computation mechanism that underlies the cockroach escape response is composed of both PC and WTA principles. Based on the properties of the suggested new mechanism I denote it a “Darwinian population code.” Received: 26 March 2002 / Accepted in revised form: 24 June 2002 Acknowledgements. I thank H. Parnas for her advice and assistance, J. M. Camhi for helpful comments, and D. Lipson for developing the simulation tools. Correspondence to: E. A. Ezrachi (e-mail: erez@piano.ls.huji.ac.il, Tel.: +972-2-6585818, Fax: +972-2-6585569)     

Wide-field, motion-sensitive neurons and matched filters for optic flow fields

 The receptive field organization of a class of visual interneurons in the fly brain (vertical system, or VS neurons) shows a striking similarity to certain self-motion-induced optic flow fields. The present study compares the measured motion sensitivities of the VS neurons (Krapp et al. 1998) to a matched filter model for optic flow fields generated by rotation or translation. The model minimizes the variance of the filter output caused by noise and distance variability between different scenes. To that end, prior knowledge about distance and self-motion statistics is incorporated in the form of a “world model”. We show that a special case of the matched filter model is able to predict the local motion sensitivities observed in some VS neurons. This suggests that their receptive field organization enables the VS neurons to maintain a consistent output when the same type of self-motion occurs in different situations. Received: 14 June 1999 / Accepted in revised form: 20 March 2000     

Dynamics of two electrically coupled chaotic neurons: Experimental observations and model analysis

Conductance-based models of neurons from the lobster stomatogastric ganglion (STG) have been developed to understand the observed chaotic behavior of individual STG neurons. These models identify an additional slow dynamical process – calcium exchange and storage in the endoplasmic reticulum – as a biologically plausible source for the observed chaos in the oscillations of these cells. In this paper we test these ideas further by exploring the dynamical behavior when two model neurons are coupled by electrical or gap junction connections. We compare in detail the model results to the laboratory measurements of electrically-coupled neurons that we reported earlier. The experiments on the biological neurons varied the strength of the effective coupling by applying a parallel, artificial synapse, which changed both the magnitude and polarity of the conductance between the neurons. We observed a sequence of bifurcations that took the neurons from strongly synchronized in-phase behavior, through uncorrelated chaotic oscillations to strongly synchronized – and now regular – out-of-phase behavior. The model calculations reproduce these observations quantitatively, indicating that slow subcellular processes could account for the mechanisms involved in the synchronization and regularization of the otherwise individual chaotic activities. Received: 28 June 1999 / Accepted in revised form: 30 June 2000     

Computational model of dot-pattern selective cells

A computational model of a dot-pattern selective neuron is proposed. This type of neuron is found in the inferotemporal cortex of monkeys. It responds strongly to groups of dots and spots of light intensity variation but very weakly or not at all to single dots and spots that are not part of a pattern. This non-linear behaviour is quite different from the spatial frequency filtering behaviour exhibited by other neurons that react to spot-shaped stimuli, such as neurons with centre-surround receptive field profiles found in the lateral geniculate nuclei and layer 4Cβ of V1. It is implemented in the proposed computational model by using an AND-type non-linearity to combine the responses of centre-surround cells. The proposed model is capable of explaining the results of neurophysiological experiments as well as certain psychophysical observations. Received: 20 December 1999 / Accepted in revised form: 3 March 2000     

Invariant association of ecdysis with increases in cyclic 3′,5′-guanosine monophosphate immunoreactivity in a small network of peptidergic neurons in the hornworm, Manduca sexta

At the end of each molt insects shed their old cuticle by performing the stereotyped behavior of ecdysis. In the moth, Manduca sexta, this behavior is triggered by the neuropeptide eclosion hormone (EH). Insights into the mechanism of action of EH have come from the identification of a small network of peptidergic neurons that shows increased cyclic 3′,5′-guanosine monophosphate (cGMP) immunoreactivity at ecdysis in insects from many different orders. Here we present further evidence that strengthens the association between ecdysis and the occurrence of this cGMP response in Manduca. We found that the cGMP increases occurred at every ecdysis, although some of the neurons that showed a response at larval ecdysis did not participate at pupal and adult ecdysis. Both ecdysis and the cGMP increases only required an intact connection with the brain for the first 30 min after EH injection. Interestingly, ecdysis in debrained animals only occurred if the cGMP response had been initiated, suggesting that the onset of this response marks the time at which the central nervous system is first able to drive ecdysis. Finally, we found that the appearance of sensitivity to EH for triggering the cGMP response coincided with the time at which EH first triggers ecdysis. Accepted: 6 May 1997     

Maturation of escape circuit function during the early adulthood of cockroaches Periplaneta americana

During postembryonic development of insects, sensorimotor pathways, which generate specific behaviors, undergo maturational changes. It is less clear whether such pathways are typically stable, or undergo further maturation, during the adult stage. In the present study, we have examined this issue by multilevel analysis of a simple model system, the escape behavior of the cockroach, from identified synapses to behavior. We show that the escape system is highly responsive immediately after the molt to adulthood, but that the latency of escape responses was not at its typical value immediately after the molt to adult. The latency of escape behavior increased over the first 30 days of adult life, perhaps indicating maturational adjustments of the escape sensorimotor pathway. The first station in the escape circuitry is the synaptic connections between the cercal wind receptors and the giant interneurons. We measured unitary excitatory synaptic potentials between single sensory neurons and an identified giant interneuron (GI(2)). We found a decrease in the synaptic strength between identified cercal hairs from a single column and GI(2) over the first month after the adult molt. Consequently, the latency and the number of action potentials of GI(2) in response to natural stimuli increased and decreased respectively during this time. Thus, we show that both behavioral performance and the wind sensitivity of GI(2) decreased over the first month after molt. We conclude that the cockroach escape system undergoes further sensorimotor maturation over a period of 1 month, and that cellular changes correlate with, or predict, some changes in behavioral performance.     

A neural mechanism of hyperaccurate detection of phase advance and delay in the jamming avoidance response of weakly electric fish

 The weakly electric fish Eigenmannia can detect the phase difference between a jamming signal and its own signal down to 1 s. To clarify the neuronal mechanism of this hyperaccurate detection of phase difference, we present a neural network model of the torus of the midbrain which plays an essential role in the detection of phase advances and delays. The small-cell model functions as a coincidence detector and can discriminate a time difference of more than 100 s. The torus model consists of laminae 6 and 8. The model of lamina 6 is made with multiple encoding units, each of which consists of a single linear array of small cells and a single giant cell. The encoding unit encodes the phase difference into its spatio-temporal firing pattern. The spatially random distribution of small cells in each encoding unit improves the encoding ability of phase modulation. The neurons in lamina 8 can discriminate the phase advance and delay of jamming electric organ discharges (EODs) compared with the phase of the fish's own EOD by integrating simultaneously the outputs from multiple encoding units in lamina 6. The discrimination accuracy of the feature-detection neurons is of the order of 1 s. The neuronal mechanism generating this hyperacuity arises from the spatial feature of the system that the innervation sites of small cells in different encoding units are distributed randomly and differently on the dendrites of single feature-detection neurons. The mechanism is similar to that of noise-enhanced information transmission. Received: 10 July 2000 / Accepted in revised form: 19 January 2001     

The Role of the Escape Swim Motor Network in the Organization of Behavioral Hierarchy and Arousal in Pleurobranchaea

The escape swimming pattern generator of the notaspid opisthobranchPleurobranchaea drives a high threshold, override behavior.The pattern generator is integrated with neural networks ofother behaviors so as to coordinate unitary behavioral expressionand to promote general behavioral arousal. These functions areseparately produced by different swim network elements. Oneset of swim premotor neurons, the A1/A10 ensemble, A3 and I_VS,generate the swim pattern and, through corollary activity, suppresspotentially conflicting feeding behavior by exerting broad inhibitionat major feeding network interneurons. A second set of swimneurons, the serotonergic As1–4 neurons, provides intrinsicneuromodulatory excitation to the swim pattern generator thatsustains the escape swim episode through multiple cycles. TheAs1–4 also provide neuromodulatory excitation to importantmodulatory, serotonergic cells in the feeding motor networkand locomotor network, and may have a general regulatory rolein the distributed serotonergic arousal network of the mollusk.The As1–4 appear to be also necessary to both avoidanceand orienting turning, and are therefore likely to be critical,multi-functional components upon which much of the organizationof the animal's behavior rests.     

A Brownian simulation model of glutamate synaptic diffusion in the femtosecond time scale

 To gain a better understanding of the elementary unit of synaptic communication between hippocampal neurons, we simulated the release of glutamate from a single pre-synaptic vesicle and its diffusion into the synaptic cleft. Diffusion of glutamate was simulated by a Brownian model based on Langevin equations. The model was implemented for parallel computer simulation and tested under different conditions of glutamate release and different geometrical and physical characteristics of the synaptic cleft. All the tested parameters have shown to be important for the synaptic responses. The results show that the synaptic transmission efficacy is influenced by many different geometrical parameters and, as a consequence, the quality of the excitatory post-synaptic response can be very different in the same synapse. The variability in the quantal response found by several authors can also be explained by physical parameters other than by variations in the quantal content of the synaptic vesicle as proposed by these authors. Received: 6 October 1999 / Accepted: 29 February 2000     

Learning a grating discrimination task broadens human spatial frequency tuning

 The effect of spatial frequency discrimination learning on spatial frequency detection tuning curves, obtained by a summation to threshold paradigm, has been investigated. Three human observers were exposed to a grating discrimination task for longer than two weeks, and their detection thresholds for compound Gabor gratings were measured before and after this time interval. Discrimination thresholds decreased continuously and substantially during the course of learning, while the spatial frequency detection tuning curves show significant broadening in the posttest. Calculating the discrimination resolution of an ensemble of sensory coding units shows that larger bandwidths lead to better spatial frequency discrimination performance if pattern discrimination rests on multidimensional comparison or one-dimensional scaling of the spatial frequency parameter. Further, it is shown that a multiple-mechanism nonlinear pooling model is capable of explaining the results if plasticity of coding unit bandwidth or adaptive weights of the coding unit responses at the stage of response integration is assumed. The alternative sources of plasticity and the consequences of the findings for psychophysical modeling are discussed. Received: 8 September 1999 / Accepted in revised form: 16 October 2000     

Self-organization and competition in the immune response to cancer invasion: a phase-orientated computational model of oncogenesis

Motivation: Recent studies indicate that fractal dimensionscan uncover aspects of cellular dynamics prior to pathological manifestation. In this respect we are interested in buildinga computational model of oncogenesis able to generate patternswith the same fractal dimension spectrum as the in vivo tumor. Results: A new theoretical model incorporating a systemic viewof oncogenesis in a computational model was proposed. Thetumor growth is viewed as competition for resources betweenthe two self-organizing subsystems: the neoplastic and theimmune. Numerical simulations revealed that tumor escape canbe uncovered in some earlier stage of the immune-system–tumorinteraction using multifractal measures. The described computationalmodel is able to simulate also the case of immune, surgical,chemical and radiotherapeutical treatment, as well as theireffects. Availability: The software used is available on request fromthe authors. Contact: Sorinel Oprisan, University of New Orleans, Department of Psychology, New Orleans, LA 70148, USA. soprisan{at}uno.edu Received on July 6, 1999 ; revised on September 15, 1999 ; accepted on September 17, 1999     

Conditional transitions in gaze dynamics: role of vestibular nuclei in eye-only and eye/head gaze behaviors

 The gaze control system governs distinct gaze behaviors, including visual fixation and gaze reorientations. Transitions between these gaze behaviors are frequent and smooth in healthy individuals. This study models these gaze-behavior transitions for different numbers of gaze degrees of freedom. Eye/head gaze behaviors have twice the number of degrees of freedom as eye-only gaze behaviors. Each gaze behavior is observable in the system dynamics and is correlated with neuronal behaviors in several, coordinated neural centers, including the vestibular nuclei. The coordination among the neural centers establishes a sensorimotor state which maintains each gaze behavior. This study develops a mathematical framework for synthesizing the coordination among neural centers in gaze sensorimotor states and focuses on the role of vestibular nuclei neurons in gaze sensorimotor state transitions. Received: 17 December 1999 / Accepted in revised form: 3 May 2001     

Biomechanical properties and a kinetic simulation model of the smooth muscle I2 in the buccal mass of Aplysia

The muscle I2 is a smooth muscle from the buccal mass of the marine mollusc Aplysia californica whose neural control, in vivo kinematics, and behavioral role have been extensively analyzed. In this study, we measured the activation and contractile dynamics of the muscle in order to construct a Hill-type kinetic model of the muscle. This is the first study to our knowledge, of Aplysia muscle contractile dynamics. The isometric force-frequency relationship of I2 had a frequency threshold of about 6–8 Hz, and its force output saturated at 20–25 Hz, properties that match the high frequency (20 Hz) bursts generated by the B31/B32 neurons that innervate it. Peak isometric force was generated at about 118% of the in situ relaxed length. These results and I2's estimated in vivo kinematics suggest that it generates maximum force at the onset of protraction. The muscle tension during iso-velocity lengthening and shortening was an asymmetric function of velocity. Short range stiffness and yielding responses were observed in lengthening, whereas muscle tension decreased smoothly in shortening. These visco-elastic properties suggest that the I2 muscle can serve to brake forceful retraction movements. A Hill-type model, parameterized from the measurements, captured many of the mechanical properties of I2. Our results provide a quantitative understanding of the biomechanical significance of the muscle's neural control and provide a basis for simulation studies of the control of feeding behavior. Received: 5 February 1999 / Accepted in revised form: 18 May 1999     

Life and death near a windy oasis

We propose a simple experiment to study delocalization and extinction in inhomogeneous biological systems. The nonlinear steady state for, say, a bacteria colony living on and near a patch of nutrient or favorable illumination (“oasis”) in the presence of a drift term (“wind”) is computed. The bacteria, described by a simple generalization of the Fisher equation, diffuse, divide A→A + A, die A→ 0, and annihilate A + A→ 0. At high wind velocities all bacteria are blown into an unfavorable region (“desert”), and the colony dies out. At low velocity a steady state concentration survives near the oasis. In between these two regimes there is a critical velocity at which bacteria first survive. If the “desert” supports a small nonzero population, this extinction transition is replaced by a delocalization transition with increasing velocity. Predictions for the behavior as a function of wind velocity are made for one and two dimensions. Received: 3 August 1998 / Revised version: 17 July 1999 / Published online: 4 July 2000     

Visual channels, Hebbian assemblies and the effect of Hebb's rule

 A model of sensory learning is proposed that is based upon Hebb's rule, where Hebb's rule has been generalised by introducing a stabilising function representing some feedback process within or at the adapting (cortical) neuron, preventing synaptic weights from increasing without limit. It will be shown that neurons adapting according to this stabilised Hebb rule will turn into a matched filter for that part of the stimulus pattern that covers the receptive field of a neuron. It follows that the presentation of a stimulus pattern may imply the formation of a set of neurons with overlapping receptive fields, where each neuron has adapted to a certain part of the stimulus. Making simplifying assumptions about the detection process, the model will be illustrated, fitting it to data from Meinhardt and Mortensen [Meinhardt G, Mortensen U (1998) Biol Cybern 79:413–425] which are not compatible with the classical matched filter model introduced by Hauske et al. [Hauske G, Wolf W, Lupp U (1976) Biol Cybern 22:181–188]. Received: 10 May 1999 / Accepted in revised form: 22 October 1999     

From view cells and place cells to cognitive map learning: processing stages of the hippocampal system

 The goal of this paper is to propose a model of the hippocampal system that reconciles the presence of neurons that look like “place cells” with the implication of the hippocampus (Hs) in other cognitive tasks (e.g., complex conditioning acquisition and memory tasks). In the proposed model, “place cells” or “view cells” are learned in the perirhinal and entorhinal cortex. The role of the Hs is not fundamentally dedicated to navigation or map building, the Hs is used to learn, store, and predict transitions between multimodal states. This transition prediction mechanism could be important for novelty detection but, above all, it is crucial to merge planning and sensory–motor functions in a single and coherent system. A neural architecture embedding this model has been successfully tested on an autonomous robot, during navigation and planning in an open environment. Received: 28 June 1999 / Accepted in revised form: 26 April 2001     

Different effects of α- and γ-glycine on the aberrant activity of pyramidal neurons of hippocampal slices

Experiments in vitro on hippocampal slices of mouse have shown that solutions prepared from polymorphic modifications α- and γ-glycine have different effect on the aberrant activity of neurons. In the presence of α-glycine the excitability of these neurons decreased more slowly, prolonging its modulating effect on NMDA type glutamate receptors. This effect agrees with higher biological activity of α-polymorphic modifications (as compared with that of the α-form) that previously observed with respect to behavior of mice from the line with genetic diathesis to catalepsy, which were used as a biological model for investigation of some pathological behavior forms.     

Networks of Causal Linkage Between Eigenmodes Characterize Behavioral Dynamics of Caenorhabditis elegans

Behavioral phenotyping of model organisms has played an important role in unravelling the complexities of animal behavior. Techniques for classifying behavior often rely on easily identified changes in posture and motion. However, such approaches are likely to miss complex behaviors that cannot be readily distinguished by eye (e.g., behaviors produced by high dimensional dynamics). To explore this issue, we focus on the model organism Caenorhabditis elegans, where behaviors have been extensively recorded and classified. Using a dynamical systems lens, we identify high dimensional, nonlinear causal relationships between four basic shapes that describe worm motion (eigenmodes, also called “eigenworms”). We find relationships between all pairs of eigenmodes, but the timescales of the interactions vary between pairs and across individuals. Using these varying timescales, we create “interaction profiles” to represent an individual’s behavioral dynamics. As desired, these profiles are able to distinguish well-known behavioral states: i.e., the profiles for foraging individuals are distinct from those of individuals exhibiting an escape response. More importantly, we find that interaction profiles can distinguish high dimensional behaviors among divergent mutant strains that were previously classified as phenotypically similar. Specifically, we find it is able to detect phenotypic behavioral differences not previously identified in strains related to dysfunction of hermaphrodite-specific neurons.     

Lyapunov functions for Lotka–Volterra predator–prey models with optimal foraging behavior

 The theory of optimal foraging predicts abrupt changes in consumer behavior which lead to discontinuities in the functional response. Therefore population dynamical models with optimal foraging behavior can be appropriately described by differential equations with discontinuous right-hand sides. In this paper we analyze the behavior of three different Lotka–Volterra predator–prey systems with optimal foraging behavior. We examine a predator–prey model with alternative food, a two-patch model with mobile predators and resident prey, and a two-patch model with both predators and prey mobile. We show that in the studied examples, optimal foraging behavior changes the neutral stability intrinsic to Lotka–Volterra systems to the existence of a bounded global attractor. The analysis is based on the construction and use of appropriate Lyapunov functions for models described by discontinuous differential equations. Received: 23 March 1999