Towards the design principles of neural population codes

Energy in functional brain states correlates with cognition in adolescent-onset schizophrenia and healthy persons

Adolescent-onset schizophrenia (AOS) is a relatively rare and under-studied form of schizophrenia with more severe cognitive impairments and poorer outcome compared to adult-onset schizophrenia. Several neuroimaging studies have reported alterations in regional activations that account for activity in individual regions (first-order model) and functional connectivity that reveals pairwise co-activations (second-order model) in AOS compared to controls. The pairwise maximum entropy model, also called the Ising model, can integrate both first-order and second-order terms to elucidate a comprehensive picture of neural dynamics and captures both individual and pairwise activity measures into a single quantity known as energy, which is inversely related to the probability of state occurrence. We applied the MEM framework to task functional MRI data collected on 23 AOS individuals in comparison with 53 healthy control subjects while performing the Penn Conditional Exclusion Test (PCET), which measures executive function that has been repeatedly shown to be more impaired in AOS compared to adult-onset schizophrenia. Accuracy of PCET performance was significantly reduced among AOS compared to controls as expected. Average cumulative energy achieved for a participant over the course of the fMRI negatively correlated with task performance, and the association was stronger than any first-order associations. The AOS subjects spent more time in higher energy states that represent lower probability of occurrence and were associated with impaired executive function and greater severity of psychopathology suggesting that the neural dynamics may be less efficient compared to controls who spent more time in lower energy states occurring with higher probability and hence are more stable and efficient. The energy landscapes in both conditions featured attractors that corresponded to two distinct subnetworks, namely fronto-temporal and parieto-motor. Attractor basins were larger in the controls than in AOS; moreover, fronto-temporal basin size was significantly correlated with cognitive performance in controls but not among the AOS. The single trial trajectories for the AOS group also showed higher variability in concordance with shallow attractor basins among AOS. These findings suggest that the neural dynamics of AOS features more frequent occurrence of less probable states with shallower attractors, which lack the relation to executive function associated with attractors in control subjects suggesting a diminished capacity of AOS to generate task-effective brain states.

Brain Connectivity Signature Extractions from TMS Invoked EEGs

(1) Background: The correlations between brain connectivity abnormality and psychiatric disorders have been continuously investigated and progressively recognized. Brain connectivity signatures are becoming exceedingly useful for identifying patients, monitoring mental health disorders, and treatment. By using electroencephalography (EEG)-based cortical source localization along with energy landscape analysis techniques, we can statistically analyze transcranial magnetic stimulation (TMS)-invoked EEG signals, for obtaining connectivity among different brain regions at a high spatiotemporal resolution. (2) Methods: In this study, we analyze EEG-based source localized alpha wave activity in response to TMS administered to three locations, namely, the left motor cortex (49 subjects), left prefrontal cortex (27 subjects), and the posterior cerebellum, or vermis (27 subjects) by using energy landscape analysis techniques to uncover connectivity signatures. We then perform two sample t-tests and use the (5 × 10^-5) Bonferroni corrected p-valued cases for reporting six reliably stable signatures. (3) Results: Vermis stimulation invoked the highest number of connectivity signatures and the left motor cortex stimulation invoked a sensorimotor network state. In total, six out of 29 reliable, stable connectivity signatures are found and discussed. (4) Conclusions: We extend previous findings to localized cortical connectivity signatures for medical applications that serve as a baseline for future dense electrode studies.

Modelling the neural code in large populations of correlated neurons

Neurons respond selectively to stimuli, and thereby define a code that associates stimuli with population response patterns. Certain correlations within population responses (noise correlations) significantly impact the information content of the code, especially in large populations. Understanding the neural code thus necessitates response models that quantify the coding properties of modelled populations, while fitting large-scale neural recordings and capturing noise correlations. In this paper, we propose a class of response model based on mixture models and exponential families. We show how to fit our models with expectation-maximization, and that they capture diverse variability and covariability in recordings of macaque primary visual cortex. We also show how they facilitate accurate Bayesian decoding, provide a closed-form expression for the Fisher information, and are compatible with theories of probabilistic population coding. Our framework could allow researchers to quantitatively validate the predictions of neural coding theories against both large-scale neural recordings and cognitive performance.

Changes in pairwise correlations during running reshape global network state in the main olfactory bulb

Neural codes for sensory inputs have been hypothesized to reside in a broader space defined by ongoing patterns of spontaneous activity. To understand the structure of this spontaneous activity in the olfactory system, we performed high-density recordings of neural populations in the main olfactory bulb of awake mice. We observed changes in pairwise correlations of spontaneous activity between mitral and tufted (M/T) cells when animals were running, which resulted in an increase in the entropy of the population. Surprisingly, pairwise maximum entropy models that described the population activity using only assumptions about the firing rates and correlations of neurons were better at predicting the global structure of activity when animals were stationary as compared to when they were running, implying that higher order (3rd, 4th order) interactions governed population activity during locomotion. Taken together, we found that locomotion alters the functional interactions that shape spontaneous population activity at the earliest stages of olfactory processing, one synapse away from the sensory receptors in the nasal epithelium. These data suggest that the coding space available for sensory representations responds adaptively to the animal's behavioral state.NEW & NOTEWORTHY The organization and structure of spontaneous population activity in the olfactory system places constraints of how odor information is represented. Using high-density electrophysiological recordings of mitral and tufted cells, we found that running increases the dimensionality of spontaneous activity, implicating higher order interactions among neurons during locomotion. Behavior, thus, flexibly alters neuronal activity at the earliest stages of sensory processing.

Theoretical principles for illuminating sensorimotor processing with brain-wide neuronal recordings

Modern recording techniques now permit brain-wide sensorimotor circuits to be observed at single neuron resolution in small animals. Extracting theoretical understanding from these recordings requires principles that organize findings and guide future experiments. Here we review theoretical principles that shed light onto brain-wide sensorimotor processing. We begin with an analogy that conceptualizes principles as streetlamps that illuminate the empirical terrain, and we illustrate the analogy by showing how two familiar principles apply in new ways to brain-wide phenomena. We then focus the bulk of the review on describing three more principles that have wide utility for mapping brain-wide neural activity, making testable predictions from highly parameterized mechanistic models, and investigating the computational determinants of neuronal response patterns across the brain.

Dynamics of social representation in the mouse prefrontal cortex

The prefrontal cortex (PFC) plays an important role in regulating social functions in mammals, and its dysfunction has been linked to social deficits in neurodevelopmental disorders. Yet little is known of how the PFC encodes social information and how social representations may be altered in such disorders. Here, we show that neurons in the medial PFC of freely behaving male mice preferentially respond to socially relevant olfactory cues. Population activity patterns in this region differed between social and nonsocial stimuli and underwent experience-dependent refinement. In mice lacking the autism-associated gene Cntnap2, both the categorization of sensory stimuli and the refinement of social representations were impaired. Noise levels in spontaneous population activity were higher in Cntnap2 knockouts and correlated with the degree to which social representations were disrupted. Our findings elucidate the encoding of social sensory cues in the medial PFC and provide a link between altered prefrontal dynamics and autism-associated social dysfunction.

Sensorimotor integration in Caenorhabditis elegans: a reappraisal towards dynamic and distributed computations

The nematode Caenorhabditis elegans is a tractable model system to study locomotion, sensory navigation and decision-making. In its natural habitat, it is thought to navigate complex multisensory environments in order to find food and mating partners, while avoiding threats like predators or toxic environments. While research in past decades has shed much light on the functions and mechanisms of selected sensory neurons, we are just at the brink of understanding how sensory information is integrated by interneuron circuits for action selection in the worm. Recent technological advances have enabled whole-brain Ca2+ imaging and Ca2+ imaging of neuronal activity in freely moving worms. A common principle emerging across multiple studies is that most interneuron activities are tightly coupled to the worm's instantaneous behaviour; notably, these observations encompass neurons receiving direct sensory neuron inputs. The new findings suggest that in the C. elegans brain, sensory and motor representations are integrated already at the uppermost sensory processing layers. Moreover, these results challenge a perhaps more intuitive view of sequential feed-forward sensory pathways that converge onto premotor interneurons and motor neurons. We propose that sensorimotor integration occurs rather in a distributed dynamical fashion. In this perspective article, we will explore this view, discuss the challenges and implications of these discoveries on the interpretation and design of neural activity experiments, and discuss possible functions. Furthermore, we will discuss the broader context of similar findings in fruit flies and rodents, which suggest generalizable principles that can be learnt from this amenable nematode model organism.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

Discrete Sequential Information Coding: Heteroclinic Cognitive Dynamics

Discrete sequential information coding is a key mechanism that transforms complex cognitive brain activity into a low-dimensional dynamical process based on the sequential switching among finite numbers of patterns. The storage size of the corresponding process is large because of the permutation capacity as a function of control signals in ensembles of these patterns. Extracting low-dimensional functional dynamics from multiple large-scale neural populations is a central problem both in neuro- and cognitive- sciences. Experimental results in the last decade represent a solid base for the creation of low-dimensional models of different cognitive functions and allow moving toward a dynamical theory of consciousness. We discuss here a methodology to build simple kinetic equations that can be the mathematical skeleton of this theory. Models of the corresponding discrete information processing can be designed using the following dynamical principles: (i) clusterization of the neural activity in space and time and formation of information patterns; (ii) robustness of the sequential dynamics based on heteroclinic chains of metastable clusters; and (iii) sensitivity of such sequential dynamics to intrinsic and external informational signals. We analyze sequential discrete coding based on winnerless competition low-frequency dynamics. Under such dynamics, entrainment, and heteroclinic coordination leads to a large variety of coding regimes that are invariant in time.

Probabilistic models for neural populations that naturally capture global coupling and criticality

Advances in multi-unit recordings pave the way for statistical modeling of activity patterns in large neural populations. Recent studies have shown that the summed activity of all neurons strongly shapes the population response. A separate recent finding has been that neural populations also exhibit criticality, an anomalously large dynamic range for the probabilities of different population activity patterns. Motivated by these two observations, we introduce a class of probabilistic models which takes into account the prior knowledge that the neural population could be globally coupled and close to critical. These models consist of an energy function which parametrizes interactions between small groups of neurons, and an arbitrary positive, strictly increasing, and twice differentiable function which maps the energy of a population pattern to its probability. We show that: 1) augmenting a pairwise Ising model with a nonlinearity yields an accurate description of the activity of retinal ganglion cells which outperforms previous models based on the summed activity of neurons; 2) prior knowledge that the population is critical translates to prior expectations about the shape of the nonlinearity; 3) the nonlinearity admits an interpretation in terms of a continuous latent variable globally coupling the system whose distribution we can infer from data. Our method is independent of the underlying system’s state space; hence, it can be applied to other systems such as natural scenes or amino acid sequences of proteins which are also known to exhibit criticality.

Populations of sensory neurons represent information about the outside environment in a collective fashion. A salient property of this distributed neural code is criticality. Yet most models used to date to analyze recordings from large neural populations do not take this observation explicitly into account. Here we aim to bridge this gap by designing probabilistic models whose structure reflects the expectation that the population is close to critical. We show that such principled approach improves previously considered models, and we demonstrate a connection between our models and the presence of continuous latent variables which is a recently proposed mechanism underlying criticality in many natural systems.

Energy landscape analysis of neuroimaging data

Computational neuroscience models have been used for understanding neural dynamics in the brain and how they may be altered when physiological or other conditions change. We review and develop a data-driven approach to neuroimaging data called the energy landscape analysis. The methods are rooted in statistical physics theory, in particular the Ising model, also known as the (pairwise) maximum entropy model and Boltzmann machine. The methods have been applied to fitting electrophysiological data in neuroscience for a decade, but their use in neuroimaging data is still in its infancy. We first review the methods and discuss some algorithms and technical aspects. Then, we apply the methods to functional magnetic resonance imaging data recorded from healthy individuals to inspect the relationship between the accuracy of fitting, the size of the brain system to be analysed and the data length.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

Optimizing for generalization in the decoding of internally generated activity in the hippocampus

The decoding of a sensory or motor variable from neural activity benefits from a known ground truth against which decoding performance can be compared. In contrast, the decoding of covert, cognitive neural activity, such as occurs in memory recall or planning, typically cannot be compared to a known ground truth. As a result, it is unclear how decoders of such internally generated activity should be configured in practice. We suggest that if the true code for covert activity is unknown, decoders should be optimized for generalization performance using cross-validation. Using ensemble recording data from hippocampal place cells, we show that this cross-validation approach results in different decoding error, different optimal decoding parameters, and different distributions of error across the decoded variable space. In addition, we show that a minor modification to the commonly used Bayesian decoding procedure, which enables the use of spike density functions, results in substantially lower decoding errors. These results have implications for the interpretation of covert neural activity, and suggest easy-to-implement changes to commonly used procedures across domains, with applications to hippocampal place cells in particular. © 2017 Wiley Periodicals, Inc.

512-Channel and 13-Region Simultaneous Recordings Coupled with Optogenetic Manipulation in Freely Behaving Mice

The development of technologies capable of recording both single-unit activity and local field potentials (LFPs) over a wide range of brain circuits in freely behaving animals is the key to constructing brain activity maps. Although mice are the most popular mammalian genetic model, in vivo neural recording has been traditionally limited to smaller channel count and fewer brain structures because of the mouse’s small size and thin skull. Here, we describe a 512-channel tetrode system that allows us to record simultaneously over a dozen cortical and subcortical structures in behaving mice. This new technique offers two major advantages – namely, the ultra-low cost and the do-it-yourself flexibility for targeting any combination of many brain areas. We show the successful recordings of both single units and LFPs from 13 distinct neural circuits of the mouse brain, including subregions of the anterior cingulate cortices, retrosplenial cortices, somatosensory cortices, secondary auditory cortex, hippocampal CA1, dentate gyrus, subiculum, lateral entorhinal cortex, perirhinal cortex, and prelimbic cortex. This 512-channel system can also be combined with Cre-lox neurogenetics and optogenetics to further examine interactions between genes, cell types, and circuit dynamics across a wide range of brain structures. Finally, we demonstrate that complex stimuli – such as an earthquake and fear-inducing foot-shock – trigger firing changes in all of the 13 brain regions recorded, supporting the notion that neural code is highly distributed. In addition, we show that localized optogenetic manipulation in any given brain region could disrupt network oscillations and caused changes in single-unit firing patterns in a brain-wide manner, thereby raising the cautionary note of the interpretation of optogenetically manipulated behaviors.