Path Integration of Head Direction: Updating a Packet of Neural Activity at the Correct Speed Using Axonal Conduction Delays

The head direction cell system is capable of accurately updating its current representation of head direction in the absence of visual input. This is known as the path integration of head direction. An important question is how the head direction cell system learns to perform accurate path integration of head direction. In this paper we propose a model of velocity path integration of head direction in which the natural time delay of axonal transmission between a linked continuous attractor network and competitive network acts as a timing mechanism to facilitate the correct speed of path integration. The model effectively learns a “look-up” table for the correct speed of path integration. In simulation, we show that the model is able to successfully learn two different speeds of path integration across two different axonal conduction delays, and without the need to alter any other model parameters. An implication of this model is that, by learning look-up tables for each speed of path integration, the model should exhibit a degree of robustness to damage. In simulations, we show that the speed of path integration is not significantly affected by degrading the network through removing a proportion of the cells that signal rotational velocity.     

Robust path integration in the entorhinal grid cell system with hippocampal feed-back

Animals are able to update their knowledge about their current position solely by integrating the speed and the direction of their movement, which is known as path integration. Recent discoveries suggest that grid cells in the medial entorhinal cortex might perform some of the essential underlying computations of path integration. However, a major concern over path integration is that as the measurement of speed and direction is inaccurate, the representation of the position will become increasingly unreliable. In this paper, we study how allothetic inputs can be used to continually correct the accumulating error in the path integrator system. We set up the model of a mobile agent equipped with the entorhinal representation of idiothetic (grid cell) and allothetic (visual cells) information and simulated its place learning in a virtual environment. Due to competitive learning, a robust hippocampal place code emerges rapidly in the model. At the same time, the hippocampo-entorhinal feed-back connections are modified via Hebbian learning in order to allow hippocampal place cells to influence the attractor dynamics in the entorhinal cortex. We show that the continuous feed-back from the integrated hippocampal place representation is able to stabilize the grid cell code. This research was supported by the EU Framework 6 ICEA project (IST-4-027819-IP).     

Sensory feedback in a bump attractor model of path integration

Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal’s current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal’s knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541–4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.     

Alternative time representation in dopamine models

Dopaminergic neuron activity has been modeled during learning and appetitive behavior, most commonly using the temporal-difference (TD) algorithm. However, a proper representation of elapsed time and of the exact task is usually required for the model to work. Most models use timing elements such as delay-line representations of time that are not biologically realistic for intervals in the range of seconds. The interval-timing literature provides several alternatives. One of them is that timing could emerge from general network dynamics, instead of coming from a dedicated circuit. Here, we present a general rate-based learning model based on long short-term memory (LSTM) networks that learns a time representation when needed. Using a naïve network learning its environment in conjunction with TD, we reproduce dopamine activity in appetitive trace conditioning with a constant CS-US interval, including probe trials with unexpected delays. The proposed model learns a representation of the environment dynamics in an adaptive biologically plausible framework, without recourse to delay lines or other special-purpose circuits. Instead, the model predicts that the task-dependent representation of time is learned by experience, is encoded in ramp-like changes in single-neuron activity distributed across small neural networks, and reflects a temporal integration mechanism resulting from the inherent dynamics of recurrent loops within the network. The model also reproduces the known finding that trace conditioning is more difficult than delay conditioning and that the learned representation of the task can be highly dependent on the types of trials experienced during training. Finally, it suggests that the phasic dopaminergic signal could facilitate learning in the cortex.     

Accurate Path Integration in Continuous Attractor Network Models of Grid Cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal''s position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat''s velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ∼10–100 meters and ∼1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.     

A Controlled Attractor Network Model of Path Integration in the Rat

Cells in several areas of the hippocampal formation show place specific firing patterns, and are thought to form a distributed representation of an animals current location in an environment. Experimental results suggest that this representation is continually updated even in complete darkness, indicating the presence of a path integration mechanism in the rat. Adopting the Neural Engineering Framework (NEF) presented by Eliasmith and Anderson (2003) we derive a novel attractor network model of path integration, using heterogeneous spiking neurons. The network we derive incorporates representation and updating of position into a single layer of neurons, eliminating the need for a large external control population, and without making use of multiplicative synapses. An efficient and biologically plausible control mechanism results directly from applying the principles of the NEF. We simulate the network for a variety of inputs, analyze its performance, and give three testable predictions of our model.     

Path integration — a network model

Path integration is a primary means of navigation for a number of animals. We present a model which performs path integration with a neural network. This model is based on a neural structure called a sinusoidal array, which allows an efficient representation of vector information with neurons. We show that exact path integration can easily be achieved by a neural network. Thus deviations from the direct home trajectory, found previously in experiments with ants, can not be explained by computational limitations of the nervous system. Instead we suggest that the observed deviations are caused by a strategy to simplify landmark navigation.     

A Continuous Attractor Network Model Without Recurrent Excitation: Maintenance and Integration in the Head Direction Cell System

Motivated by experimental observations of the head direction system, we study a three population network model that operates as a continuous attractor network. This network is able to store in a short-term memory an angular variable (the head direction) as a spatial profile of activity across neurons in the absence of selective external inputs, and to accurately update this variable on the basis of angular velocity inputs. The network is composed of one excitatory population and two inhibitory populations, with inter-connections between populations but no connections within the neurons of a same population. In particular, there are no excitatory-to-excitatory connections. Angular velocity signals are represented as inputs in one inhibitory population (clockwise turns) or the other (counterclockwise turns). The system is studied using a combination of analytical and numerical methods. Analysis of a simplified model composed of threshold-linear neurons gives the conditions on the connectivity for (i) the emergence of the spatially selective profile, (ii) reliable integration of angular velocity inputs, and (iii) the range of angular velocities that can be accurately integrated by the model. Numerical simulations allow us to study the proposed scenario in a large network of spiking neurons and compare their dynamics with that of head direction cells recorded in the rat limbic system. In particular, we show that the directional representation encoded by the attractor network can be rapidly updated by external cues, consistent with the very short update latencies observed experimentally by Zugaro et al. (2003) in thalamic head direction cells.     

A computational model of the hippocampus that represents environmental structure and goal location,and guides movement

Hippocampal place cells (PCs) are believed to represent environmental structure. However, it is unclear how and which brain regions represent goals and guide movements. Recently, another type of cells that fire around a goal was found in rat hippocampus (we designate these cells as goal place cells, GPCs). This suggests that the hippocampus is also involved in goal representation. Assuming that the activities of GPCs depend on the distance to a goal, we propose an adaptive navigation model. By monitoring the population activity of GPCs, the model navigates to shorten the distance to the goal. To achieve the distance-dependent activities of GPCs, plastic connections are assumed between PCs and GPCs, which are modified depending on two reward-triggered activities: activity propagation through PC–PC network representing the topological environmental structure, and the activity of GPCs with different durations. The former activity propagation is regarded as a computational interpretation of “reverse replay” phenomenon found in rat hippocampus. Simulation results confirm that after reaching a goal only once, the model can navigate to the goal along almost the shortest path from arbitrary places in the environment. This indicates that the hippocampus might play a primary role in the representation of not only the environmental structure but also the goal, in addition to guiding the movement. This navigation strategy using the population activity of GPCs is equivalent to the taxis strategy, the simplest and most basic for biological systems. Our model is unique because this simple strategy allows the model to follow the shortest path in the topological map of the environment.     

Spatial cognition and neuro-mimetic navigation: a model of hippocampal place cell activity

 A computational model of hippocampal activity during spatial cognition and navigation tasks is presented. The spatial representation in our model of the rat hippocampus is built on-line during exploration via two processing streams. An allothetic vision-based representation is built by unsupervised Hebbian learning extracting spatio-temporal properties of the environment from visual input. An idiothetic representation is learned based on internal movement-related information provided by path integration. On the level of the hippocampus, allothetic and idiothetic representations are integrated to yield a stable representation of the environment by a population of localized overlapping CA3-CA1 place fields. The hippocampal spatial representation is used as a basis for goal-oriented spatial behavior. We focus on the neural pathway connecting the hippocampus to the nucleus accumbens. Place cells drive a population of locomotor action neurons in the nucleus accumbens. Reward-based learning is applied to map place cell activity into action cell activity. The ensemble action cell activity provides navigational maps to support spatial behavior. We present experimental results obtained with a mobile Khepera robot. Received: 02 July 1999 / Accepted in revised form: 20 March 2000     

Finding the way with a noisy brain

Successful navigation is fundamental to the survival of nearly every animal on earth, and achieved by nervous systems of vastly different sizes and characteristics. Yet surprisingly little is known of the detailed neural circuitry from any species which can accurately represent space for navigation. Path integration is one of the oldest and most ubiquitous navigation strategies in the animal kingdom. Despite a plethora of computational models, from equational to neural network form, there is currently no consensus, even in principle, of how this important phenomenon occurs neurally. Recently, all path integration models were examined according to a novel, unifying classification system. Here we combine this theoretical framework with recent insights from directed walk theory, and develop an intuitive yet mathematically rigorous proof that only one class of neural representation of space can tolerate noise during path integration. This result suggests many existing models of path integration are not biologically plausible due to their intolerance to noise. This surprising result imposes significant computational limitations on the neurobiological spatial representation of all successfully navigating animals, irrespective of species. Indeed, noise-tolerance may be an important functional constraint on the evolution of neuroarchitectural plans in the animal kingdom.     

No need for a cognitive map: decentralized memory for insect navigation

In many animals the ability to navigate over long distances is an important prerequisite for foraging. For example, it is widely accepted that desert ants and honey bees, but also mammals, use path integration for finding the way back to their home site. It is however a matter of a long standing debate whether animals in addition are able to acquire and use so called cognitive maps. Such a 'map', a global spatial representation of the foraging area, is generally assumed to allow the animal to find shortcuts between two sites although the direct connection has never been travelled before. Using the artificial neural network approach, here we develop an artificial memory system which is based on path integration and various landmark guidance mechanisms (a bank of individual and independent landmark-defined memory elements). Activation of the individual memory elements depends on a separate motivation network and an, in part, asymmetrical lateral inhibition network. The information concerning the absolute position of the agent is present, but resides in a separate memory that can only be used by the path integration subsystem to control the behaviour, but cannot be used for computational purposes with other memory elements of the system. Thus, in this simulation there is no neural basis of a cognitive map. Nevertheless, an agent controlled by this network is able to accomplish various navigational tasks known from ants and bees and often discussed as being dependent on a cognitive map. For example, map-like behaviour as observed in honey bees arises as an emergent property from a decentralized system. This behaviour thus can be explained without referring to the assumption that a cognitive map, a coherent representation of foraging space, must exist. We hypothesize that the proposed network essentially resides in the mushroom bodies of the insect brain.     

Multisensory integration in the superior colliculus: a neural network model

Neurons in the superior colliculus (SC) are known to integrate stimuli of different modalities (e.g., visual and auditory) following specific properties. In this work, we present a mathematical model of the integrative response of SC neurons, in order to suggest a possible physiological mechanism underlying multisensory integration in SC. The model includes three distinct neural areas: two unimodal areas (auditory and visual) are devoted to a topological representation of external stimuli, and communicate via synaptic connections with a third downstream area (in the SC) responsible for multisensory integration. The present simulations show that the model, with a single set of parameters, can mimic various responses to different combinations of external stimuli including the inverse effectiveness, both in terms of multisensory enhancement and contrast, the existence of within- and cross-modality suppression between spatially disparate stimuli, a reduction of network settling time in response to cross-modal stimuli compared with individual stimuli. The model suggests that non-linearities in neural responses and synaptic (excitatory and inhibitory) connections can explain several aspects of multisensory integration.     

Spatial inference without a cognitive map: the role of higher-order path integration

The cognitive map has been taken as the standard model for how agents infer the most efficient route to a goal location. Alternatively, path integration – maintaining a homing vector during navigation – constitutes a primitive and presumably less-flexible strategy than cognitive mapping because path integration relies primarily on vestibular stimuli and pace counting. The historical debate as to whether complex spatial navigation is ruled by associative learning or cognitive map mechanisms has been challenged by experimental difficulties in successfully neutralizing path integration. To our knowledge, there are only three studies that have succeeded in resolving this issue, all showing clear evidence of novel route taking, a behaviour outside the scope of traditional associative learning accounts. Nevertheless, there is no mechanistic explanation as to how animals perform novel route taking. We propose here a new model of spatial learning that combines path integration with higher-order associative learning, and demonstrate how it can account for novel route taking without a cognitive map, thus resolving this long-standing debate. We show how our higher-order path integration (HOPI) model can explain spatial inferences, such as novel detours and shortcuts. Our analysis suggests that a phylogenetically ancient, vector-based navigational strategy utilizing associative processes is powerful enough to support complex spatial inferences.     

采用Reichardt运动检测器和Boltzmann Machine神经网络的运动计算

建立了一个探讨灵长类视皮层从Ｖ１区到ＭＴ区的运动信息加工原理的计算模型,这个过程的突出特征是视觉运动信息经过了从局部检测进步到整体感知。模型的第一层由用于抽提运动模式的局部速度以及结构性质的Ｒｅｉｃｈａｒｄｔ运动检测器组成,进一步的加工是通过Ｂｏｌｔｚｍａｎｎ Ｍａｃｈｉｎｅ神经网络来实现的。这种网络的学习算法具有局部更新的显著性质,在学习阶段,网络不断地修改联结权重以形成对于记录在网络的显单元上     

ISYMOD: a knowledge warehouse for the identification, assembly and analysis of bacterial integrated systems

MOTIVATION: Complex biological functions emerge from interactions between proteins in stable supra-molecular assemblies and/or through transitory contacts. Most of the time protein partners of the assemblies are composed of one or several domains which exhibit different biochemical functions. Thus the study of cellular process requires the identification of different functional units and their integration in an interaction network; such complexes are referred to as integrated systems. In order to exploit with optimum efficiency the increased release of data, automated bioinformatics strategies are needed to identify, reconstruct and model such systems. For that purpose, we have developed a knowledge warehouse dedicated to the representation and acquisition of bacterial integrated systems involved in the exchange of the bacterial cell with its environment. RESULTS: ISYMOD is a knowledge warehouse that consistently integrates in the same environment the data and the methods used for their acquisition. This is achieved through the construction of (1) a domain knowledge base (DKB) devoted to the storage of the knowledge about the systems, their functional specificities, their partners and how they are related and (2) a methodological knowledge base (MKB) which depicts the task layout used to identify and reconstruct functional integrated systems. Instantiation of the DKB is obtained by solving the tasks of the MKB, whereas some tasks need instances of the DKB to be solved. AROM, an object-based knowledge representation system, has been used to design the DKB, and its task manager, AROMTasks, for developing the MKB. In this study two integrated systems, ABC transporters and two component systems, both involved in adaptation processes of a bacterial cell to its biotope, have been used to evaluate the feasibility of the approach.     

Adaptive Learning Networks: Developing Resource Management Knowledge through Social Learning Forums

The purpose of this paper is to explore adaptive learning networks as a contemporary means by which new resource management knowledge can develop through social learning forums. The paper draws upon recent discussions within two disparate literatures on indigenous knowledge and network theory and is grounded in fieldwork with two Anishinaabe First Nations in northwestern Ontario. The paper has three objectives. First, problematize the principle of representation as a basic way of including the knowledge of indigenous peoples within natural resource and environmental management. Second, utilize network theory as a way to weave together adaptive learning by individuals into a cross-cultural social learning process. Finally, propose an adaptive natural resources and environmental framework that brings together, through a social learning process, the different ways individuals, indigenous peoples and resource managers, perceive environmental change.     

Representing where along with what information in a model of a cortical patch

Behaving in the real world requires flexibly combining and maintaining information about both continuous and discrete variables. In the visual domain, several lines of evidence show that neurons in some cortical networks can simultaneously represent information about the position and identity of objects, and maintain this combined representation when the object is no longer present. The underlying network mechanism for this combined representation is, however, unknown. In this paper, we approach this issue through a theoretical analysis of recurrent networks. We present a model of a cortical network that can retrieve information about the identity of objects from incomplete transient cues, while simultaneously representing their spatial position. Our results show that two factors are important in making this possible: A) a metric organisation of the recurrent connections, and B) a spatially localised change in the linear gain of neurons. Metric connectivity enables a localised retrieval of information about object identity, while gain modulation ensures localisation in the correct position. Importantly, we find that the amount of information that the network can retrieve and retain about identity is strongly affected by the amount of information it maintains about position. This balance can be controlled by global signals that change the neuronal gain. These results show that anatomical and physiological properties, which have long been known to characterise cortical networks, naturally endow them with the ability to maintain a conjunctive representation of the identity and location of objects.     

Multimodal integration for the representation of space in the posterior parietal cortex.

The posterior parietal cortex has long been considered an ''association'' area that combines information from different sensory modalities to form a cognitive representation of space. However, until recently little has been known about the neural mechanisms responsible for this important cognitive process. Recent experiments from the author''s laboratory indicate that visual, somatosensory, auditory and vestibular signals are combined in areas LIP and 7a of the posterior parietal cortex. The integration of these signals can represent the locations of stimuli with respect to the observer and within the environment. Area MSTd combines visual motion signals, similar to those generated during an observer''s movement through the environment, with eye-movement and vestibular signals. This integration appears to play a role in specifying the path on which the observer is moving. All three cortical areas combine different modalities into common spatial frames by using a gain-field mechanism. The spatial representations in areas LIP and 7a appear to be important for specifying the locations of targets for actions such as eye movements or reaching; the spatial representation within area MSTd appears to be important for navigation and the perceptual stability of motion signals.