Population vector code: a geometric universal as actuator

A population of descending neurons that regulates the flight motor of Drosophila

Like many insect species, Drosophila melanogaster are capable of maintaining a stable flight trajectory for periods lasting up to several hours^1,2. Because aerodynamic torque is roughly proportional to the fifth power of wing length³, even small asymmetries in wing size require the maintenance of subtle bilateral differences in flapping motion to maintain a stable path. Flies can even fly straight after losing half of a wing, a feat they accomplish via very large, sustained kinematic changes to both the damaged and intact wings⁴. Thus, the neural network responsible for stable flight must be capable of sustaining fine-scaled control over wing motion across a large dynamic range. In this paper, we describe an unusual type of descending neuron (DNg02) that projects directly from visual output regions of the brain to the dorsal flight neuropil of the ventral nerve cord. Unlike many descending neurons, which exist as single bilateral pairs with unique morphology, there is a population of at least 15 DNg02 cell pairs with nearly identical shape. By optogenetically activating different numbers of DNg02 cells, we demonstrate that these neurons regulate wingbeat amplitude over a wide dynamic range via a population code. Using 2-photon functional imaging, we show that DNg02 cells are responsive to visual motion during flight in a manner that would make them well suited to continuously regulate bilateral changes in wing kinematics. Collectively, we have identified a critical set of DNs that provide the sensitivity and dynamic range required for flight control.

Using an activation screen in flying flies, Namiki et al. identify a population of descending neurons that regulates wing amplitude over a large dynamic range. Via functional imaging and activation of different numbers of cells, they show that this population is a core component of the flight circuit, allowing the fly to steer and fly straight.

Barn Owl's Auditory Space Map Activity Matching Conditions for a Population Vector Readout to Drive Adaptive Sound-Localizing Behavior

Space-specific neurons in the owl's midbrain form a neural map of auditory space, which supports sound-orienting behavior. Previous work proposed that a population vector (PV) readout of this map, implementing statistical inference, predicts the owl's sound localization behavior. This model also predicts the frontal localization bias normally observed and how sound-localizing behavior changes when the signal-to-noise ratio varies, based on the spread of activity across the map. However, the actual distribution of population activity and whether this pattern is consistent with premises of the PV readout model on a trial-by-trial basis remains unknown. To answer these questions, we investigated whether the population response profile across the midbrain map in the optic tectum of the barn owl matches these predictions using in vivo multielectrode array recordings. We found that response profiles of recorded subpopulations are sufficient for estimating the stimulus interaural time difference using responses from single trials. Furthermore, this decoder matches the expected differences in trial-by-trial variability and frontal bias between stimulus conditions of low and high signal-to-noise ratio. These results support the hypothesis that a PV readout of the midbrain map can mediate statistical inference in sound-localizing behavior of barn owls.SIGNIFICANCE STATEMENT While the tuning of single neurons in the owl's midbrain map of auditory space has been considered predictive of the highly specialized sound-localizing behavior of this species, response properties across the population remain largely unknown. For the first time, this study analyzed the spread of population responses across the map using multielectrode recordings and how it changes with signal-to-noise ratio. The observed responses support the hypothesis concerning the ability of a population vector readout to predict biases in orienting behaviors and mediate uncertainty-dependent behavioral commands. The results are of significance for understanding potential mechanisms for the implementation of optimal behavioral commands across species.

Mathematization of nature: how it is done

Natural phenomena can be quantitatively described by means of mathematics, which is actually the only way of doing so. Physics is a convincing example of the mathematization of nature. This paper gives an answer to the question of how mathematization of nature is done and illustrates the answer. Here nature is to be taken in a wide sense, being a substantial object of study in, among others, large domains of biology, such as epidemiology and neurobiology, chemistry, and physics, the most outspoken example. It is argued that mathematization of natural phenomena needs appropriate core concepts that are intimately connected with the phenomena one wants to describe and explain mathematically. Second, there is a scale on and not beyond which a specific description holds. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis, which has meanwhile been confirmed on many occasions. Furthermore, a mathematical description can, as in physics, but need not be universally valid, as in biology. Finally, the history of science shows that only an intensive gauging of theory, i.e., mathematical description, by experiment leads to progress. That is, appropriate core concepts and appropriate scales are a necessary condition for mathematizing nature, and so is its verification by experiment.

Decoding Kinematic Information From Primary Motor Cortex Ensemble Activities Using a Deep Canonical Correlation Analysis

The control of arm movements through intracortical brain–machine interfaces (BMIs) mainly relies on the activities of the primary motor cortex (M1) neurons and mathematical models that decode their activities. Recent research on decoding process attempts to not only improve the performance but also simultaneously understand neural and behavioral relationships. In this study, we propose an efficient decoding algorithm using a deep canonical correlation analysis (DCCA), which maximizes correlations between canonical variables with the non-linear approximation of mappings from neuronal to canonical variables via deep learning. We investigate the effectiveness of using DCCA for finding a relationship between M1 activities and kinematic information when non-human primates performed a reaching task with one arm. Then, we examine whether using neural activity representations from DCCA improves the decoding performance through linear and non-linear decoders: a linear Kalman filter (LKF) and a long short-term memory in recurrent neural networks (LSTM-RNN). We found that neural representations of M1 activities estimated by DCCA resulted in more accurate decoding of velocity than those estimated by linear canonical correlation analysis, principal component analysis, factor analysis, and linear dynamical system. Decoding with DCCA yielded better performance than decoding the original FRs using LSTM-RNN (6.6 and 16.0% improvement on average for each velocity and position, respectively; Wilcoxon rank sum test, p < 0.05). Thus, DCCA can identify the kinematics-related canonical variables of M1 activities, thus improving the decoding performance. Our results may help advance the design of decoding models for intracortical BMIs.

Activity in Primary Motor Cortex Related to Visual Feedback

Neural modulation in primate motor cortex exhibits complex patterns. We found that modulation during reaching could be separated into discrete temporal epochs. To determine if these epochs are driven by behavioral events, monkeys performed variations of a center-out reaching task. Monkeys viewed a computer cursor matched to hand position and a radial target at 1 of 16 locations. In some trials, they performed a visuomotor rotation (the cursor moved at an angle to the hand). After adaptation, encoding changes for single units are temporally structured: adaptation could affect one temporal component of a unit's response but not another. In half the normal and perturbed trials, we removed visual feedback before movement. Adaptation-sensitive firing components toward the end of movement are often weak or absent during reaches without feedback. These results show that temporal structure in motor cortical activity is driven by behavior, with a discrete component related to visual feedback.

Temporally Segmented Directionality in the Motor Cortex

Developing models of the dynamic and complex patterns of information processing that take place during behavior is a major thrust of systems neuroscience. An underlying assumption of many models is that the same set of rules applies across different conditions. This has been the case for directional tuning during volitional movement; a single cosine function has been remarkably robust for describing the encoding of movement direction in different types of neurons, in many locations of the nervous system, and even across species. However, detailed examination of the tuning time course in motor cortex suggests that direction coding may be labile. Here, we show that there are discrete time epochs within single reaches, between which individual neurons change their tuning. Our findings suggest that motor cortical activity patterns may reflect consistent changes in the state of the control system during center-out reaching. These transitions are likely linked to different behavioral components, suggesting that the task defines changes in the operational structure of the control system.

Decoding arm speed during reaching

Neural prostheses decode intention from cortical activity to restore upper extremity movement. Typical decoding algorithms extract velocity—a vector quantity with direction and magnitude (speed) —from neuronal firing rates. Standard decoding algorithms accurately recover arm direction, but the extraction of speed has proven more difficult. We show that this difficulty is due to the way speed is encoded by individual neurons and demonstrate how standard encoding-decoding procedures produce characteristic errors. These problems are addressed using alternative brain–computer interface (BCI) algorithms that accommodate nonlinear encoding of speed and direction. Our BCI approach leads to skillful control of both direction and speed as demonstrated by stereotypic bell-shaped speed profiles, straight trajectories, and steady cursor positions before and after the movement.

Brain–machine interfaces typically decode arm velocity from motor cortical neurons to move neuroprostheses, but performance of these devices is degraded by erroneous extraction of speed from the neuronal firing patterns. Here, the authors show that this error can be corrected by using a hybrid artificial neural network approach.

Periodic population codes: From a single circular variable to higher dimensions, multiple nested scales, and conceptual spaces

Across the nervous system, neurons often encode circular stimuli using tuning curves that are not sine or cosine functions, but that belong to the richer class of von Mises functions, which are periodic variants of Gaussians. For a population of neurons encoding a single circular variable with such canonical tuning curves, computing a simple population vector is the optimal read-out of the most likely stimulus. We argue that the advantages of population vector read-outs are so compelling that even the neural representation of the outside world's flat Euclidean geometry is curled up into a torus (a circle times a circle), creating the hexagonal activity patterns of mammalian grid cells. Here, the circular scale is not set a priori, so the nervous system can use multiple scales and gain fields to overcome the ambiguity inherent in periodic representations of linear variables. We review the experimental evidence for this framework and discuss its testable predictions and generalizations to more abstract grid-like neural representations.

In Vivo Imaging Reveals Composite Coding for Diagonal Motion in the Drosophila Visual System

Understanding information coding is important for resolving the functions of visual neural circuits. The motion vision system is a classic model for studying information coding as it contains a concise and complete information-processing circuit. In Drosophila, the axon terminals of motion-detection neurons (T4 and T5) project to the lobula plate, which comprises four regions that respond to the four cardinal directions of motion. The lobula plate thus represents a topographic map on a transverse plane. This enables us to study the coding of diagonal motion by investigating its response pattern. By using in vivo two-photon calcium imaging, we found that the axon terminals of T4 and T5 cells in the lobula plate were activated during diagonal motion. Further experiments showed that the response to diagonal motion is distributed over the following two regions compared to the cardinal directions of motion—a diagonal motion selective response region and a non-selective response region—which overlap with the response regions of the two vector-correlated cardinal directions of motion. Interestingly, the sizes of the non-selective response regions are linearly correlated with the angle of the diagonal motion. These results revealed that the Drosophila visual system employs a composite coding for diagonal motion that includes both independent coding and vector decomposition coding.

Movement: How the Brain Communicates with the World

Voluntary movement is a result of signals transmitted through a communication channel that links the internal world in our minds to the physical world around us. Intention can be considered the desire to effect change on our environment, and this is contained in the signals from the brain, passed through the nervous system to converge on muscles that generate displacements and forces on our surroundings. The resulting changes in the world act to generate sensations that feed back to the nervous system, closing the control loop. This Perspective discusses the experimental and theoretical underpinnings of current models of movement generation and the way they are modulated by external information. Movement systems embody intentionality and prediction, two factors that are propelling a revolution in engineering. Development of movement models that include the complexities of the external world may allow a better understanding of the neuronal populations regulating these processes, as well as the development of solutions for autonomous vehicles and robots, and neural prostheses for those who are motor impaired.

Neuroscience from a mathematical perspective: key concepts, scales and scaling hypothesis, universality

This article analyzes the question of whether neuroscience allows for mathematical descriptions and whether an interaction between experimental and theoretical neuroscience can be expected to benefit both of them. It is argued that a mathematization of natural phenomena never happens by itself. First, appropriate key concepts must be found that are intimately connected with the phenomena one wishes to describe and explain mathematically. Second, the scale on, and not beyond, which a specific description can hold must be specified. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis. Third, can a mathematical description be universally valid and, if so, how? Here we put forth the argument that universals also exist in theoretical neuroscience, that evolution proves the rule, and that theoretical neuroscience is a domain with still lots of space for new developments initiated by an intensive interaction with experiment. Finally, major insight is provided by a careful analysis of the way in which particular brain structures respond to perceptual input and in so doing induce action in an animal's surroundings.

Current challenges to the clinical translation of brain machine interface technology

Development of neural prostheses over the past few decades has produced a number of clinically relevant brain-machine interfaces (BMIs), such as the cochlear prostheses and deep brain stimulators. Current research pursues the restoration of communication or motor function to individuals with neurological disorders. Efforts in the field, such as the BrainGate trials, have already demonstrated that such interfaces can enable humans to effectively control external devices with neural signals. However, a number of significant issues regarding BMI performance, device capabilities, and surgery must be resolved before clinical use of BMI technology can become widespread. This chapter reviews challenges to clinical translation and discusses potential solutions that have been reported in recent literature, with focuses on hardware reliability, state-of-the-art decoding algorithms, and surgical considerations during implantation.

Eight pairs of descending visual neurons in the dragonfly give wing motor centers accurate population vector of prey direction

Intercepting a moving object requires prediction of its future location. This complex task has been solved by dragonflies, who intercept their prey in midair with a 95% success rate. In this study, we show that a group of 16 neurons, called target-selective descending neurons (TSDNs), code a population vector that reflects the direction of the target with high accuracy and reliability across 360°. The TSDN spatial (receptive field) and temporal (latency) properties matched the area of the retina where the prey is focused and the reaction time, respectively, during predatory flights. The directional tuning curves and morphological traits (3D tracings) for each TSDN type were consistent among animals, but spike rates were not. Our results emphasize that a successful neural circuit for target tracking and interception can be achieved with few neurons and that in dragonflies this information is relayed from the brain to the wing motor centers in population vector form.

Facilitation and restoration of cognitive function in primate prefrontal cortex by a neuroprosthesis that utilizes minicolumn-specific neural firing

OBJECTIVE

Maintenance of cognitive control is a major concern for many human disease conditions; therefore, a major goal of human neuroprosthetics is to facilitate and/or recover the cognitive function when such circumstances impair appropriate decision making.

APPROACH

Minicolumnar activity from the prefrontal cortex (PFC) was recorded from nonhuman primates trained to perform a delayed match to sample (DMS), via custom-designed conformal multielectrode arrays that provided inter-laminar recordings from neurons in the PFC layer 2/3 and layer 5. Such recordings were analyzed via a previously demonstrated nonlinear multi-input-multi-output (MIMO) neuroprosthesis in rodents, which extracted and characterized multicolumnar firing patterns during DMS performance.

MAIN RESULTS

The MIMO model verified that the conformal recorded individual PFC minicolumns responded to entrained target selections in patterns critical for successful DMS performance. This allowed the substitution of task-related layer 5 neuron firing patterns with electrical stimulation in the same recording regions during columnar transmission from layer 2/3 at the time of target selection. Such stimulation improved normal task performance, but more importantly, recovered performance when applied as a neuroprosthesis following the pharmacological disruption of decision making in the same task.

SIGNIFICANCE

These findings provide the first successful application of neuroprosthesis in the primate brain designed specifically to restore or repair the disrupted cognitive function.

Models of grid cell spatial firing published 2005-2011

Since the discovery of grid cells in rat entorhinal cortex, many models of their hexagonally arrayed spatial firing fields have been suggested. We review the models and organize them according to the mechanisms they use to encode position, update the positional code, read it out in the spatial grid pattern, and learn any patterned synaptic connections needed. We mention biological implementations of the models, but focus on the models on Marr’s algorithmic level, where they are not things to individually prove or disprove, but rather are a valuable collection of metaphors of the grid cell system for guiding research that are all likely true to some degree, with each simply emphasizing different aspects of the system. For the convenience of interested researchers, MATLAB implementations of the discussed grid cell models are provided at ModelDB accession 144006 or http://people.bu.edu/zilli/gridmodels.html.

Revealing non-analytic kinematic shifts in smooth goal-directed behaviour

How do biological agents plan and organise a smooth accurate path to shift from one smooth mode of behaviour to another as part of graceful movement that is both plastic and controlled? This paper addresses the question in conducting a novel shape analysis of approach and adjustment phases in rapid voluntary target aiming and 2-D reaching hand actions. A number of mode changing experiments are reported that investigate these actions under a range of goals and conditions. After a typically roughly aimed approach, regular projective adjustment is observed that has height and velocity kinematic profiles that are scaled copies of one another. This empirical property is encapsulated as a novel self-similar shift function. The mathematics shows that the biological shifts consist of continual deviation from their full Taylor series everywhere throughout their interval, which is a deep form of plasticity not described before. The experimental results find the same approach and adjustment strategy to occur with behavioural trajectories over the full and varied range of tested goals and conditions. The trajectory shapes have a large degree of predictability through using the shift function to handle extensive variation in the trajectories' adjustment across individual behaviours and subjects. We provide connections between the behavioural features and results and various neural studies to show how the methodology may be exploited. The conclusion is that a roughly aimed approach followed by a specific highly plastic shift adjustment can provide a regular basis for fast and accurate goal-directed motion in a simple and generalisable way.

Owl's behavior and neural representation predicted by Bayesian inference

The owl captures prey using sound localization. In the classical model, the owl infers sound direction from the position of greatest activity in a brain map of auditory space. However, this model fails to describe the actual behavior. Although owls accurately localize sources near the center of gaze, they systematically underestimate peripheral source directions. We found that this behavior is predicted by statistical inference, formulated as a Bayesian model that emphasizes central directions. We propose that there is a bias in the neural coding of auditory space, which, at the expense of inducing errors in the periphery, achieves high behavioral accuracy at the ethologically relevant range. We found that the owl's map of auditory space decoded by a population vector is consistent with the behavioral model. Thus, a probabilistic model describes both how the map of auditory space supports behavior and why this representation is optimal.

Decoding center-out hand velocity from MEG signals during visuomotor adaptation

During reaching or drawing, the primate cortex carries information about the current and upcoming position of the hand. Researchers have decoded hand position, velocity, and acceleration during center-out reaching or drawing tasks from neural recordings acquired invasively at the microscale and mesoscale levels. Here we report that we can continuously decode information about hand velocity at the macroscale level from magnetoencephalography (MEG) data acquired from the scalp during a center-out drawing task with an imposed hand-cursor rotation. The grand mean (n=5) correlation coefficients (CCs) between measured and decoded velocity profiles were 0.48, 0.40, 0.38, and 0.28 for the horizontal dimension of movement and 0.32, 0.49, 0.56, and 0.23 for the vertical dimension of movement where the order of the CCs indicates pre-exposure, early-exposure, late-exposure, and post-exposure to the hand-cursor rotation. By projecting the sensor contributions to decoding onto whole-head scalp maps, we found that a macroscale sensorimotor network carries information about detailed hand velocity and that contributions from sensors over central and parietal scalp areas change due to adaptation to the rotated environment. Moreover, a 3-D linear estimation of distributed current sources using standardized low-resolution brain electromagnetic tomography (sLORETA) permitted a more detailed investigation into the cortical network that encodes for hand velocity in each of the adaptation phases. Beneficial implications of these findings include a non-invasive methodology to examine the neural correlates of behavior on a macroscale with high temporal resolution and the potential to provide continuous, complex control of a non-invasive neuromotor prosthesis for movement-impaired individuals.