Dynamics of cortical neuronal ensembles transit from decision making to storage for later report

A sticky Poisson Hidden Markov Model for solving the problem of over-segmentation and rapid state switching in cortical datasets

The application of hidden Markov models (HMMs) to neural data has uncovered hidden states and signatures of neural dynamics that are relevant for sensory and cognitive processes. However, training an HMM on cortical data requires a careful handling of model selection, since models with more numerous hidden states generally have a higher likelihood on new (unseen) data. A potentially related problem is the occurrence of very rapid state switching after decoding the data with an HMM. The first problem can lead to overfitting and over-segmentation of the data. The second problem is due to intermediate-to-low self-transition probabilities and is at odds with many reports that hidden states in cortex tend to last from hundred of milliseconds to seconds. Here, we show that we can alleviate both problems by regularizing a Poisson-HMM during training so as to enforce large self-transition probabilities. We call this algorithm the 'sticky Poisson-HMM' (sPHMM). When used together with the Bayesian Information Criterion for model selection, the sPHMM successfully eliminates rapid state switching, outperforming an alternative strategy based on an HMM with a large prior on the self-transition probabilities. The sPHMM also captures the ground truth in surrogate datasets built to resemble the statistical properties of the experimental data.

Co-existence of synaptic plasticity and metastable dynamics in a spiking model of cortical circuits

Evidence for metastable dynamics and its role in brain function is emerging at a fast pace and is changing our understanding of neural coding by putting an emphasis on hidden states of transient activity. Clustered networks of spiking neurons have enhanced synaptic connections among groups of neurons forming structures called cell assemblies; such networks are capable of producing metastable dynamics that is in agreement with many experimental results. However, it is unclear how a clustered network structure producing metastable dynamics may emerge from a fully local plasticity rule, i.e., a plasticity rule where each synapse has only access to the activity of the neurons it connects (as opposed to the activity of other neurons or other synapses). Here, we propose a local plasticity rule producing ongoing metastable dynamics in a deterministic, recurrent network of spiking neurons. The metastable dynamics co-exists with ongoing plasticity and is the consequence of a self-tuning mechanism that keeps the synaptic weights close to the instability line where memories are spontaneously reactivated. In turn, the synaptic structure is stable to ongoing dynamics and random perturbations, yet it remains sufficiently plastic to remap sensory representations to encode new sets of stimuli. Both the plasticity rule and the metastable dynamics scale well with network size, with synaptic stability increasing with the number of neurons. Overall, our results show that it is possible to generate metastable dynamics over meaningful hidden states using a simple but biologically plausible plasticity rule which co-exists with ongoing neural dynamics.

Co-existence of synaptic plasticity and metastable dynamics in a spiking model of cortical circuits

Evidence for metastable dynamics and its role in brain function is emerging at a fast pace and is changing our understanding of neural coding by putting an emphasis on hidden states of transient activity. Clustered networks of spiking neurons have enhanced synaptic connections among groups of neurons forming structures called cell assemblies; such networks are capable of producing metastable dynamics that is in agreement with many experimental results. However, it is unclear how a clustered network structure producing metastable dynamics may emerge from a fully local plasticity rule, i.e., a plasticity rule where each synapse has only access to the activity of the neurons it connects (as opposed to the activity of other neurons or other synapses). Here, we propose a local plasticity rule producing ongoing metastable dynamics in a deterministic, recurrent network of spiking neurons. The metastable dynamics co-exists with ongoing plasticity and is the consequence of a self-tuning mechanism that keeps the synaptic weights close to the instability line where memories are spontaneously reactivated. In turn, the synaptic structure is stable to ongoing dynamics and random perturbations, yet it remains sufficiently plastic to remap sensory representations to encode new sets of stimuli. Both the plasticity rule and the metastable dynamics scale well with network size, with synaptic stability increasing with the number of neurons. Overall, our results show that it is possible to generate metastable dynamics over meaningful hidden states using a simple but biologically plausible plasticity rule which co-exists with ongoing neural dynamics.

Multistability in neural systems with random cross-connections

Neural circuits with multiple discrete attractor states could support a variety of cognitive tasks according to both empirical data and model simulations. We assess the conditions for such multistability in neural systems using a firing rate model framework, in which clusters of similarly responsive neurons are represented as single units, which interact with each other through independent random connections. We explore the range of conditions in which multistability arises via recurrent input from other units while individual units, typically with some degree of self-excitation, lack sufficient self-excitation to become bistable on their own. We find many cases of multistability-defined as the system possessing more than one stable fixed point-in which stable states arise via a network effect, allowing subsets of units to maintain each others' activity because their net input to each other when active is sufficiently positive. In terms of the strength of within-unit self-excitation and standard deviation of random cross-connections, the region of multistability depends on the response function of units. Indeed, multistability can arise with zero self-excitation, purely through zero-mean random cross-connections, if the response function rises supralinearly at low inputs from a value near zero at zero input. We simulate and analyze finite systems, showing that the probability of multistability can peak at intermediate system size, and connect with other literature analyzing similar systems in the infinite-size limit. We find regions of multistability with a bimodal distribution for the number of active units in a stable state. Finally, we find evidence for a log-normal distribution of sizes of attractor basins, which produces Zipf's Law when enumerating the proportion of trials within which random initial conditions lead to a particular stable state of the system.

Bayesian multilevel hidden Markov models identify stable state dynamics in longitudinal recordings from macaque primary motor cortex

Neural populations, rather than single neurons, may be the fundamental unit of cortical computation. Analysing chronically recorded neural population activity is challenging not only because of the high dimensionality of activity but also because of changes in the signal that may or may not be due to neural plasticity. Hidden Markov models (HMMs) are a promising technique for analysing such data in terms of discrete latent states, but previous approaches have not considered the statistical properties of neural spiking data, have not been adaptable to longitudinal data, or have not modelled condition-specific differences. We present a multilevel Bayesian HMM addresses these shortcomings by incorporating multivariate Poisson log-normal emission probability distributions, multilevel parameter estimation and trial-specific condition covariates. We applied this framework to multi-unit neural spiking data recorded using chronically implanted multi-electrode arrays from macaque primary motor cortex during a cued reaching, grasping and placing task. We show that, in line with previous work, the model identifies latent neural population states which are tightly linked to behavioural events, despite the model being trained without any information about event timing. The association between these states and corresponding behaviour is consistent across multiple days of recording. Notably, this consistency is not observed in the case of a single-level HMM, which fails to generalise across distinct recording sessions. The utility and stability of this approach is demonstrated using a previously learned task, but this multilevel Bayesian HMM framework would be especially suited for future studies of long-term plasticity in neural populations.

Multistability in neural systems with random cross-connections

Neural circuits with multiple discrete attractor states could support a variety of cognitive tasks according to both empirical data and model simulations. We assess the conditions for such multistability in neural systems, using a firing-rate model framework, in which clusters of neurons with net self-excitation are represented as units, which interact with each other through random connections. We focus on conditions in which individual units lack sufficient self-excitation to become bistable on their own. Rather, multistability can arise via recurrent input from other units as a network effect for subsets of units, whose net input to each other when active is sufficiently positive to maintain such activity. In terms of the strength of within-unit self-excitation and standard-deviation of random cross-connections, the region of multistability depends on the firing-rate curve of units. Indeed, bistability can arise with zero self-excitation, purely through zero-mean random cross-connections, if the firing-rate curve rises supralinearly at low inputs from a value near zero at zero input. We simulate and analyze finite systems, showing that the probability of multistability can peak at intermediate system size, and connect with other literature analyzing similar systems in the infinite-size limit. We find regions of multistability with a bimodal distribution for the number of active units in a stable state. Finally, we find evidence for a log-normal distribution of sizes of attractor basins, which can appear as Zipf's Law when sampled as the proportion of trials within which random initial conditions lead to a particular stable state of the system.

Temporal progression along discrete coding states during decision-making in the mouse gustatory cortex

The mouse gustatory cortex (GC) is involved in taste-guided decision-making in addition to sensory processing. Rodent GC exhibits metastable neural dynamics during ongoing and stimulus-evoked activity, but how these dynamics evolve in the context of a taste-based decision-making task remains unclear. Here we employ analytical and modeling approaches to i) extract metastable dynamics in ensemble spiking activity recorded from the GC of mice performing a perceptual decision-making task; ii) investigate the computational mechanisms underlying GC metastability in this task; and iii) establish a relationship between GC dynamics and behavioral performance. Our results show that activity in GC during perceptual decision-making is metastable and that this metastability may serve as a substrate for sequentially encoding sensory, abstract cue, and decision information over time. Perturbations of the model's metastable dynamics indicate that boosting inhibition in different coding epochs differentially impacts network performance, explaining a counterintuitive effect of GC optogenetic silencing on mouse behavior.

Metastable dynamics of neural circuits and networks

Cortical neurons emit seemingly erratic trains of action potentials or "spikes," and neural network dynamics emerge from the coordinated spiking activity within neural circuits. These rich dynamics manifest themselves in a variety of patterns, which emerge spontaneously or in response to incoming activity produced by sensory inputs. In this Review, we focus on neural dynamics that is best understood as a sequence of repeated activations of a number of discrete hidden states. These transiently occupied states are termed "metastable" and have been linked to important sensory and cognitive functions. In the rodent gustatory cortex, for instance, metastable dynamics have been associated with stimulus coding, with states of expectation, and with decision making. In frontal, parietal, and motor areas of macaques, metastable activity has been related to behavioral performance, choice behavior, task difficulty, and attention. In this article, we review the experimental evidence for neural metastable dynamics together with theoretical approaches to the study of metastable activity in neural circuits. These approaches include (i) a theoretical framework based on non-equilibrium statistical physics for network dynamics; (ii) statistical approaches to extract information about metastable states from a variety of neural signals; and (iii) recent neural network approaches, informed by experimental results, to model the emergence of metastable dynamics. By discussing these topics, we aim to provide a cohesive view of how transitions between different states of activity may provide the neural underpinnings for essential functions such as perception, memory, expectation, or decision making, and more generally, how the study of metastable neural activity may advance our understanding of neural circuit function in health and disease.

Metastable attractors explain the variable timing of stable behavioral action sequences

The timing of self-initiated actions shows large variability even when they are executed in stable, well-learned sequences. Could this mix of reliability and stochasticity arise within the same neural circuit? We trained rats to perform a stereotyped sequence of self-initiated actions and recorded neural ensemble activity in secondary motor cortex (M2), which is known to reflect trial-by-trial action-timing fluctuations. Using hidden Markov models, we established a dictionary between activity patterns and actions. We then showed that metastable attractors, representing activity patterns with a reliable sequential structure and large transition timing variability, could be produced by reciprocally coupling a high-dimensional recurrent network and a low-dimensional feedforward one. Transitions between attractors relied on correlated variability in this mesoscale feedback loop, predicting a specific structure of low-dimensional correlations that were empirically verified in M2 recordings. Our results suggest a novel mesoscale network motif based on correlated variability supporting naturalistic animal behavior.

Multiple-Timescale Neural Networks: Generation of History-Dependent Sequences and Inference Through Autonomous Bifurcations

Sequential transitions between metastable states are ubiquitously observed in the neural system and underlying various cognitive functions such as perception and decision making. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences are generated, the focused sequences are simple Markov ones. On the other hand, fine recurrent neural networks trained with supervised machine learning methods can generate complex non-Markov sequences, but these sequences are vulnerable against perturbations and such learning methods are biologically implausible. How stable and complex sequences are generated in the neural system still remains unclear. We have developed a neural network with fast and slow dynamics, which are inspired by the hierarchy of timescales on neural activities in the cortex. The slow dynamics store the history of inputs and outputs and affect the fast dynamics depending on the stored history. We show that the learning rule that requires only local information can form the network generating the complex and robust sequences in the fast dynamics. The slow dynamics work as bifurcation parameters for the fast one, wherein they stabilize the next pattern of the sequence before the current pattern is destabilized depending on the previous patterns. This co-existence period leads to the stable transition between the current and the next pattern in the non-Markov sequence. We further find that timescale balance is critical to the co-existence period. Our study provides a novel mechanism generating robust complex sequences with multiple timescales. Considering the multiple timescales are widely observed, the mechanism advances our understanding of temporal processing in the neural system.

Binocular rivalry reveals an out-of-equilibrium neural dynamics suited for decision-making

In ambiguous or conflicting sensory situations, perception is often 'multistable' in that it perpetually changes at irregular intervals, shifting abruptly between distinct alternatives. The interval statistics of these alternations exhibits quasi-universal characteristics, suggesting a general mechanism. Using binocular rivalry, we show that many aspects of this perceptual dynamics are reproduced by a hierarchical model operating out of equilibrium. The constitutive elements of this model idealize the metastability of cortical networks. Independent elements accumulate visual evidence at one level, while groups of coupled elements compete for dominance at another level. As soon as one group dominates perception, feedback inhibition suppresses supporting evidence. Previously unreported features in the serial dependencies of perceptual alternations compellingly corroborate this mechanism. Moreover, the proposed out-of-equilibrium dynamics satisfies normative constraints of continuous decision-making. Thus, multistable perception may reflect decision-making in a volatile world: integrating evidence over space and time, choosing categorically between hypotheses, while concurrently evaluating alternatives.

State-Dependent Regulation of Cortical Processing Speed via Gain Modulation

To thrive in dynamic environments, animals must be capable of rapidly and flexibly adapting behavioral responses to a changing context and internal state. Examples of behavioral flexibility include faster stimulus responses when attentive and slower responses when distracted. Contextual or state-dependent modulations may occur early in the cortical hierarchy and may be implemented via top-down projections from corticocortical or neuromodulatory pathways. However, the computational mechanisms mediating the effects of such projections are not known. Here, we introduce a theoretical framework to classify the effects of cell type-specific top-down perturbations on the information processing speed of cortical circuits. Our theory demonstrates that perturbation effects on stimulus processing can be predicted by intrinsic gain modulation, which controls the timescale of the circuit dynamics. Our theory leads to counterintuitive effects, such as improved performance with increased input variance. We tested the model predictions using large-scale electrophysiological recordings from the visual hierarchy in freely running mice, where we found that a decrease in single-cell intrinsic gain during locomotion led to an acceleration of visual processing. Our results establish a novel theory of cell type-specific perturbations, applicable to top-down modulation as well as optogenetic and pharmacological manipulations. Our theory links connectivity, dynamics, and information processing via gain modulation.SIGNIFICANCE STATEMENT To thrive in dynamic environments, animals adapt their behavior to changing circumstances and different internal states. Examples of behavioral flexibility include faster responses to sensory stimuli when attentive and slower responses when distracted. Previous work suggested that contextual modulations may be implemented via top-down inputs to sensory cortex coming from higher brain areas or neuromodulatory pathways. Here, we introduce a theory explaining how the speed at which sensory cortex processes incoming information is adjusted by changes in these top-down projections, which control the timescale of neural activity. We tested our model predictions in freely running mice, revealing that locomotion accelerates visual processing. Our theory is applicable to internal modulation as well as optogenetic and pharmacological manipulations and links circuit connectivity, dynamics, and information processing.

Slower prefrontal metastable dynamics during deliberation predicts error trials in a distance discrimination task

Cortical activity related to erroneous behavior in discrimination or decision-making tasks is rarely analyzed, yet it can help clarify which computations are essential during a specific task. Here, we use a hidden Markov model (HMM) to perform a trial-by-trial analysis of the ensemble activity of dorsolateral prefrontal cortex (PFdl) neurons of rhesus monkeys performing a distance discrimination task. By segmenting the neural activity into sequences of metastable states, HMM allows us to uncover modulations of the neural dynamics related to internal computations. We find that metastable dynamics slow down during error trials, while state transitions at a pivotal point during the trial take longer in difficult correct trials. Both these phenomena occur during the decision interval, with errors occurring in both easy and difficult trials. Our results provide further support for the emerging role of metastable cortical dynamics in mediating complex cognitive functions and behavior.

Approaches to inferring multi-regional interactions from simultaneous population recordings: Inferring multi-regional interactions from simultaneous population recordings

Most past studies of neural representations and dynamics have focused on recordings from single brain areas. However, growing evidence of brain-wide, parallel representations of cognitive variables suggests that analyzing neural representations and dynamics in individual brain areas can benefit from understanding the context of multi-regional interactions that support them. Moreover, perturbation experiments revealed that the manner in which these parallel representations interact with each other can differ dramatically across different pairs of brain areas. Recent advances in recording technology offer a potentially powerful substrate to study how multi-regional interactions coordinate neural representations in individual brain areas and dictate behavior on a single-trial basis through simultaneous recordings of multiple brain areas. We review pragmatic approaches to studying multi-regional interactions and illustrate them in the concrete context of a rodent delayed response task paradigm.

Cortical Observation by Synchronous Multifocal Optical Sampling Reveals Widespread Population Encoding of Actions

To advance the measurement of distributed neuronal population representations of targeted motor actions on single trials, we developed an optical method (COSMOS) for tracking neural activity in a largely uncharacterized spatiotemporal regime. COSMOS allowed simultaneous recording of neural dynamics at ∼30 Hz from over a thousand near-cellular resolution neuronal sources spread across the entire dorsal neocortex of awake, behaving mice during a three-option lick-to-target task. We identified spatially distributed neuronal population representations spanning the dorsal cortex that precisely encoded ongoing motor actions on single trials. Neuronal correlations measured at video rate using unaveraged, whole-session data had localized spatial structure, whereas trial-averaged data exhibited widespread correlations. Separable modes of neural activity encoded history-guided motor plans, with similar population dynamics in individual areas throughout cortex. These initial experiments illustrate how COSMOS enables investigation of large-scale cortical dynamics and that information about motor actions is widely shared between areas, potentially underlying distributed computations.

Memory reactivation in rat medial prefrontal cortex occurs in a subtype of cortical UP state during slow-wave sleep

Interaction between hippocampal sharp-wave ripples (SWRs) and UP states, possibly by coordinated reactivation of memory traces, is conjectured to play an important role in memory consolidation. Recently, it was reported that SWRs were differentiated into multiple subtypes. However, whether cortical UP states can also be classified into subtypes is not known. Here, we analysed neural ensemble activity from the medial prefrontal cortex from rats trained to run a spatial sequence-memory task. Application of the hidden Markov model (HMM) with three states to epochs of UP-DOWN oscillations identified DOWN states and two subtypes of UP state (UP-1 and UP-2). The two UP subtypes were distinguished by differences in duration, with UP-1 having a longer duration than UP-2, as well as differences in the speed of population vector (PV) decorrelation, with UP-1 decorrelating more slowly than UP-2. Reactivation of recent memory sequences predominantly occurred in UP-2. Short-duration reactivating UP states were dominated by UP-2 whereas long-duration ones exhibit transitions from UP-1 to UP-2. Thus, recent memory reactivation, if it occurred within long-duration UP states, typically was preceded by a period of slow PV evolution not related to recent experience, and which we speculate may be related to previously encoded information. If that is the case, then the transition from UP-1 to UP-2 subtypes may help gradual integration of recent experience with pre-existing cortical memories by interleaving the two in the same UP state. This article is part of the Theo Murphy meeting issue 'Memory reactivation: replaying events past, present and future'.

Hidden Markov Models Predict the Future Choice Better Than a PSTH-Based Method

Beyond average firing rate, other measurable signals of neuronal activity are fundamental to an understanding of behavior. Recently, hidden Markov models (HMMs) have been applied to neural recordings and have described how neuronal ensembles process information by going through sequences of different states. Such collective dynamics are impossible to capture by just looking at the average firing rate. To estimate how well HMMs can decode information contained in single trials, we compared HMMs with a recently developed classification method based on the peristimulus time histogram (PSTH). The accuracy of the two methods was tested by using the activity of prefrontal neurons recorded while two monkeys were engaged in a strategy task. In this task, the monkeys had to select one of three spatial targets based on an instruction cue and on their previous choice. We show that by using the single trial's neural activity in a period preceding action execution, both models were able to classify the monkeys' choice with an accuracy higher than by chance. Moreover, the HMM was significantly more accurate than the PSTH-based method, even in cases in which the HMM performance was low, although always above chance. Furthermore, the accuracy of both methods was related to the number of neurons exhibiting spatial selectivity within an experimental session. Overall, our study shows that neural activity is better described when not only the mean activity of individual neurons is considered and that therefore, the study of other signals rather than only the average firing rate is fundamental to an understanding of the dynamics of neuronal ensembles.

Cortical computations via metastable activity

Metastable brain dynamics are characterized by abrupt, jump-like modulations so that the neural activity in single trials appears to unfold as a sequence of discrete, quasi-stationary 'states'. Evidence that cortical neural activity unfolds as a sequence of metastable states is accumulating at fast pace. Metastable activity occurs both in response to an external stimulus and during ongoing, self-generated activity. These spontaneous metastable states are increasingly found to subserve internal representations that are not locked to external triggers, including states of deliberations, attention and expectation. Moreover, decoding stimuli or decisions via metastable states can be carried out trial-by-trial. Focusing on metastability will allow us to shift our perspective on neural coding from traditional concepts based on trial-averaging to models based on dynamic ensemble representations. Recent theoretical work has started to characterize the mechanistic origin and potential roles of metastable representations. In this article we review recent findings on metastable activity, how it may arise in biologically realistic models, and its potential role for representing internal states as well as relevant task variables.

Expectation-induced modulation of metastable activity underlies faster coding of sensory stimuli

Sensory stimuli can be recognized more rapidly when they are expected. This phenomenon depends on expectation affecting the cortical processing of sensory information. However, the mechanisms responsible for the effects of expectation on sensory circuits remain elusive. Here, we report a novel computational mechanism underlying the expectation-dependent acceleration of coding observed in the gustatory cortex of alert rats. We use a recurrent spiking network model with a clustered architecture capturing essential features of cortical activity, such as its intrinsically generated metastable dynamics. Relying on network theory and computer simulations, we propose that expectation exerts its function by modulating the intrinsically generated dynamics preceding taste delivery. Our model’s predictions were confirmed in the experimental data, demonstrating how the modulation of ongoing activity can shape sensory coding. Altogether, these results provide a biologically plausible theory of expectation and ascribe a new functional role to intrinsically generated, metastable activity.

Controlling seizure propagation in large-scale brain networks

Information transmission in the human brain is a fundamentally dynamic network process. In partial epilepsy, this process is perturbed and highly synchronous seizures originate in a local network, the so-called epileptogenic zone (EZ), before recruiting other close or distant brain regions. We studied patient-specific brain network models of 15 drug-resistant epilepsy patients with implanted stereotactic electroencephalography (SEEG) electrodes. Each personalized brain model was derived from structural data of magnetic resonance imaging (MRI) and diffusion tensor weighted imaging (DTI), comprising 88 nodes equipped with region specific neural mass models capable of demonstrating a range of epileptiform discharges. Each patient's virtual brain was further personalized through the integration of the clinically hypothesized EZ. Subsequent simulations and connectivity modulations were performed and uncovered a finite repertoire of seizure propagation patterns. Across patients, we found that (i) patient-specific network connectivity is predictive for the subsequent seizure propagation pattern; (ii) seizure propagation is characterized by a systematic sequence of brain states; (iii) propagation can be controlled by an optimal intervention on the connectivity matrix; (iv) the degree of invasiveness can be significantly reduced via the proposed seizure control as compared to traditional resective surgery. To stop seizures, neurosurgeons typically resect the EZ completely. We showed that stability analysis of the network dynamics, employing structural and dynamical information, estimates reliably the spatiotemporal properties of seizure propagation. This suggests novel less invasive paradigms of surgical interventions to treat and manage partial epilepsy.

Decoding a Decision Process in the Neuronal Population of Dorsal Premotor Cortex

When trained monkeys discriminate the temporal structure of two sequential vibrotactile stimuli, dorsal premotor cortex (DPC) showed high heterogeneity among its neuronal responses. Notably, DPC neurons coded stimulus patterns as broader categories and signaled them during working memory, comparison, and postponed decision periods. Here, we show that such population activity can be condensed into two major coding components: one that persistently represented in working memory both the first stimulus identity and the postponed informed choice and another that transiently coded the initial sensory information and the result of the comparison between the two stimuli. Additionally, we identified relevant signals that coded the timing of task events. These temporal and task-parameter readouts were shown to be strongly linked to the monkeys' behavior when contrasted to those obtained in a non-demanding cognitive control task and during error trials. These signals, hidden in the heterogeneity, were prominently represented by the DPC population response.

What can neuronal populations tell us about cognition?

Nowadays, it is possible to record the activity of hundreds of cells at the same time in behaving animals. However, these data are often treated and analyzed as if they consisted of many independently recorded neurons. How can neuronal populations be uniquely used to learn about cognition? We describe recent work that shows that populations of simultaneously recorded neurons are fundamental to understand the basis of decision-making, including processes such as ongoing deliberations and decision confidence, which generally fall outside the reach of single-cell analysis. Thus, neuronal population data allow addressing novel questions, but they also come with so far unsolved challenges.

A mathematical and biological plausible model of decision-execution regulation in "Go/No-Go" tasks: Focusing on the fronto-striatal-thalamic pathway

Discovering factors influencing the speed and accuracy of responses in tasks such as "Go/No-Go" is one of issues which have been raised in neurocognitive studies. Mathematical models are considered as tools to identify and to study decision making procedure from different aspects. In this paper, a mathematical model has been presented to show several factors can alter the output of decision making procedure before execution in a "Go/No-Go" task. The dynamic of this model has two stable fixed points, each of them corresponds to the "Press" and "Not-press" responses. This model that focuses on the fronto-striatal-thalamic direct and indirect pathways, receives planned decisions from frontal cortex and sends a regulated output to motor cortex for execution. The state-space analysis showed that several factors could affect the regulation procedure such as the input strength, noise value, initial condition, and the values of involved neurotransmitters. Some probable analytical reasons that may lead to changes in decision-execution regulation have been suggested as well. Bifurcation diagram analysis demonstrates that an optimal interaction between these factors can compensate the weaknesses of some others. It is predicted that abnormalities of response control in different brain disorders such as attention deficit hyperactivity disorder may be resolved by providing treatment techniques that target the regulation of the interaction. The model also suggests a possible justification to show why so many studies insist on the important role of dopamine in some brain disorders.

Closed-loop neuromodulation systems: next-generation treatments for psychiatric illness

Despite deep brain stimulation's positive early results in psychiatric disorders, well-designed clinical trials have yielded inconsistent clinical outcomes. One path to more reliable benefit is closed-loop therapy: stimulation that is automatically adjusted by a device or algorithm in response to changes in the patient's electrical brain activity. These interventions may provide more precise and patient-specific treatments. This article first introduces the available closed-loop neuromodulation platforms, which have shown clinical efficacy in epilepsy and strong early results in movement disorders. It discusses the strengths and limitations of these devices in the context of psychiatric illness. It then describes emerging technologies to address these limitations, including pre-clinical developments such as wireless deep neurostimulation and genetically targeted neuromodulation. Finally, ongoing challenges and limitations for closed-loop psychiatric brain stimulation development, most notably the difficulty of identifying meaningful biomarkers for titration, are discussed. This is considered in the recently-released Research Domain Criteria (RDoC) framework, and how neuromodulation and RDoC are jointly very well suited to address the problem of treatment-resistant illness is described.

Error-Robust Modes of the Retinal Population Code

Across the nervous system, certain population spiking patterns are observed far more frequently than others. A hypothesis about this structure is that these collective activity patterns function as population codewords–collective modes–carrying information distinct from that of any single cell. We investigate this phenomenon in recordings of ∼150 retinal ganglion cells, the retina’s output. We develop a novel statistical model that decomposes the population response into modes; it predicts the distribution of spiking activity in the ganglion cell population with high accuracy. We found that the modes represent localized features of the visual stimulus that are distinct from the features represented by single neurons. Modes form clusters of activity states that are readily discriminated from one another. When we repeated the same visual stimulus, we found that the same mode was robustly elicited. These results suggest that retinal ganglion cells’ collective signaling is endowed with a form of error-correcting code–a principle that may hold in brain areas beyond retina.

Neurons in most parts of the nervous system represent and process information in a collective fashion, yet the nature of this collective code is poorly understood. An important constraint placed on any such collective processing comes from the fact that individual neurons’ signaling is prone to corruption by noise. The information theory and engineering literatures have studied error-correcting codes that allow individual noise-prone coding units to “check” each other, forming an overall representation that is robust to errors. In this paper, we have analyzed the population code of one of the best-studied neural systems, the retina, and found that it is structured in a manner analogous to error-correcting schemes. Indeed, we found that the complex activity patterns over ~150 retinal ganglion cells, the output neurons of the retina, could be mapped onto collective code words, and that these code words represented precise visual information while suppressing noise. In order to analyze this coding scheme, we introduced a novel quantitative model of the retinal output that predicted neural activity patterns more accurately than existing state-of-the-art approaches.

Three challenges for connecting model to mechanism in decision-making

Recent years have seen a growing interest in understanding the neural mechanisms that support decision-making. The advent of new tools for measuring and manipulating neurons, alongside the inclusion of multiple new animal models and sensory systems has led to the generation of many novel datasets. The potential for these new approaches to constrain decision-making models is unprecedented. Here, we argue that to fully leverage these new approaches, three challenges must be met. First, experimenters must design well-controlled behavioral experiments that make it possible to distinguish competing behavioral strategies. Second, analyses of neural responses should think beyond single neurons, taking into account tradeoffs of single-trial versus trial-averaged approaches. Finally, quantitative model comparisons should be used, but must consider common obstacles.

Itinerancy between attractor states in neural systems

Converging evidence from neural, perceptual and simulated data suggests that discrete attractor states form within neural circuits through learning and development. External stimuli may bias neural activity to one attractor state or cause activity to transition between several discrete states. Evidence for such transitions, whose timing can vary across trials, is best accrued through analyses that avoid any trial-averaging of data. One such method, hidden Markov modeling, has been effective in this context, revealing state transitions in many neural circuits during many tasks. Concurrently, modeling efforts have revealed computational benefits of stimulus processing via transitions between attractor states. This review describes the current state of the field, with comments on how its perceived limitations have been addressed.

The Behavioral Relevance of Cortical Neural Ensemble Responses Emerges Suddenly

Whereas many laboratory-studied decisions involve a highly trained animal identifying an ambiguous stimulus, many naturalistic decisions do not. Consumption decisions, for instance, involve determining whether to eject or consume an already identified stimulus in the mouth and are decisions that can be made without training. By standard analyses, rodent cortical single-neuron taste responses come to predict such consumption decisions across the 500 ms preceding the consumption or rejection itself; decision-related firing emerges well after stimulus identification. Analyzing single-trial ensemble activity using hidden Markov models, we show these decision-related cortical responses to be part of a reliable sequence of states (each defined by the firing rates within the ensemble) separated by brief state-to-state transitions, the latencies of which vary widely between trials. When we aligned data to the onset of the (late-appearing) state that dominates during the time period in which single-neuron firing is correlated to taste palatability, the apparent ramp in stimulus-aligned choice-related firing was shown to be a much more precipitous coherent jump. This jump in choice-related firing resembled a step function more than it did the output of a standard (ramping) decision-making model, and provided a robust prediction of decision latency in single trials. Together, these results demonstrate that activity related to naturalistic consumption decisions emerges nearly instantaneously in cortical ensembles. Significance statement: This paper provides a description of how the brain makes evaluative decisions. The majority of work on the neurobiology of decision making deals with "what is it?" decisions; out of this work has emerged a model whereby neurons accumulate information about the stimulus in the form of slowly increasing firing rates and reach a decision when those firing rates reach a threshold. Here, we study a different kind of more naturalistic decision--a decision to evaluate "what shall I do with it?" after the identity of a taste in the mouth has been identified--and show that this decision is not made through the gradual increasing of stimulus-related firing, but rather that this decision appears to be made in a sudden moment of "insight."

Stimuli Reduce the Dimensionality of Cortical Activity

The activity of ensembles of simultaneously recorded neurons can be represented as a set of points in the space of firing rates. Even though the dimension of this space is equal to the ensemble size, neural activity can be effectively localized on smaller subspaces. The dimensionality of the neural space is an important determinant of the computational tasks supported by the neural activity. Here, we investigate the dimensionality of neural ensembles from the sensory cortex of alert rats during periods of ongoing (inter-trial) and stimulus-evoked activity. We find that dimensionality grows linearly with ensemble size, and grows significantly faster during ongoing activity compared to evoked activity. We explain these results using a spiking network model based on a clustered architecture. The model captures the difference in growth rate between ongoing and evoked activity and predicts a characteristic scaling with ensemble size that could be tested in high-density multi-electrode recordings. Moreover, we present a simple theory that predicts the existence of an upper bound on dimensionality. This upper bound is inversely proportional to the amount of pair-wise correlations and, compared to a homogeneous network without clusters, it is larger by a factor equal to the number of clusters. The empirical estimation of such bounds depends on the number and duration of trials and is well predicted by the theory. Together, these results provide a framework to analyze neural dimensionality in alert animals, its behavior under stimulus presentation, and its theoretical dependence on ensemble size, number of clusters, and correlations in spiking network models.

The Encoding of Decision Difficulty and Movement Time in the Primate Premotor Cortex

Estimating the difficulty of a decision is a fundamental process to elaborate complex and adaptive behaviour. In this paper, we show that the movement time of behaving monkeys performing a decision-making task is correlated with decision difficulty and that the activity of a population of neurons in ventral Premotor cortex correlates with the movement time. Moreover, we found another population of neurons that encodes the discriminability of the stimulus, thereby supplying another source of information about the difficulty of the decision. The activity of neurons encoding the difficulty can be produced by very different computations. Therefore, we show that decision difficulty can be encoded through three different mechanisms: 1. Switch time coding, 2. rate coding and 3. binary coding. This rich representation reflects the basis of different functional aspects of difficulty in the making of a decision and the possible role of difficulty estimation in complex decision scenarios.

Understanding how the brain produces complex cognitive functions has been a crucial question since ancient philosophical inquiries. The encoding of decision difficulty in the brain is fundamental for complex and adaptive behaviour, and can provide valuable information in uncertain environments where the future outcome of a choice must be evaluated beforehand. Here we show that neurons in premotor cortex represent the difficulty of a decision using at least three different variables: 1) the time of the neuronal response, 2) the intensity of the neuronal response, 3) the probability of switching from a low activity to a high activity profile. Moreover, we show that, by encoding the time elapsed from the end of the stimulus and commitment to a choice, another set of premotor neurons is able to provide information about the difficulty of the decision. These results show that the brain is implementing heterogeneous neural mechanisms to fulfill a complex cognitive function.

Functional neuroimaging of visuospatial working memory tasks enables accurate detection of attention deficit and hyperactivity disorder

Finding neurobiological markers for neurodevelopmental disorders, such as attention deficit and hyperactivity disorder (ADHD), is a major objective of clinicians and neuroscientists. We examined if functional Magnetic Resonance Imaging (fMRI) data from a few distinct visuospatial working memory (VSWM) tasks enables accurately detecting cases with ADHD. We tested 20 boys with ADHD combined type and 20 typically developed (TD) boys in four VSWM tasks that differed in feedback availability (feedback, no-feedback) and reward size (large, small). We used a multimodal analysis based on brain activity in 16 regions of interest, significantly activated or deactivated in the four VSWM tasks (based on the entire participants' sample). Dimensionality of the data was reduced into 10 principal components that were used as the input variables to a logistic regression classifier. fMRI data from the four VSWM tasks enabled a classification accuracy of 92.5%, with high predicted ADHD probability values for most clinical cases, and low predicted ADHD probabilities for most TDs. This accuracy level was higher than those achieved by using the fMRI data of any single task, or the respective behavioral data. This indicates that task-based fMRI data acquired while participants perform a few distinct VSWM tasks enables improved detection of clinical cases.

Dynamics of multistable states during ongoing and evoked cortical activity

Single-trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory, and decision-making. Yet, very little is known about the network mechanisms responsible for its genesis. It is often assumed that the onset of state sequences is triggered by an external stimulus. Here we show that state sequences can be observed also in the absence of overt sensory stimulation. Analysis of multielectrode recordings from the gustatory cortex of alert rats revealed ongoing sequences of states, where single neurons spontaneously attain several firing rates across different states. This single-neuron multistability represents a challenge to existing spiking network models, where typically each neuron is at most bistable. We present a recurrent spiking network model that accounts for both the spontaneous generation of state sequences and the multistability in single-neuron firing rates. Each state results from the activation of neural clusters with potentiated intracluster connections, with the firing rate in each cluster depending on the number of active clusters. Simulations show that the model's ensemble activity hops among the different states, reproducing the ongoing dynamics observed in the data. When probed with external stimuli, the model predicts the quenching of single-neuron multistability into bistability and the reduction of trial-by-trial variability. Both predictions were confirmed in the data. Together, these results provide a theoretical framework that captures both ongoing and evoked network dynamics in a single mechanistic model.

A hierarchy of intrinsic timescales across primate cortex

Specialization and hierarchy are organizing principles for primate cortex, yet there is little direct evidence for how cortical areas are specialized in the temporal domain. We measured timescales of intrinsic fluctuations in spiking activity across areas and found a hierarchical ordering, with sensory and prefrontal areas exhibiting shorter and longer timescales, respectively. On the basis of our findings, we suggest that intrinsic timescales reflect areal specialization for task-relevant computations over multiple temporal ranges.

Dimensionality reduction for large-scale neural recordings

Most sensory, cognitive and motor functions depend on the interactions of many neurons. In recent years, there has been rapid development and increasing use of technologies for recording from large numbers of neurons, either sequentially or simultaneously. A key question is what scientific insight can be gained by studying a population of recorded neurons beyond studying each neuron individually. Here, we examine three important motivations for population studies: single-trial hypotheses requiring statistical power, hypotheses of population response structure and exploratory analyses of large data sets. Many recent studies have adopted dimensionality reduction to analyze these populations and to find features that are not apparent at the level of individual neurons. We describe the dimensionality reduction methods commonly applied to population activity and offer practical advice about selecting methods and interpreting their outputs. This review is intended for experimental and computational researchers who seek to understand the role dimensionality reduction has had and can have in systems neuroscience, and who seek to apply these methods to their own data.

Linking perception, cognition, and action: psychophysical observations and neural network modelling

It has been argued that perception, decision making, and movement planning are in reality tightly interwoven brain processes. However, how they are implemented in neural circuits is still a matter of debate. We tested human subjects in a temporal categorization task in which intervals had to be categorized as short or long. Subjects communicated their decision by moving a cursor into one of two possible targets, which appeared separated by different angles from trial to trial. Even though there was a 1 second-long delay between interval presentation and decision communication, categorization difficulty affected subjects’ performance, reaction (RT) and movement time (MT). In addition, reaction and movement times were also influenced by the distance between the targets. This implies that not only perceptual, but also movement-related considerations were incorporated into the decision process. Therefore, we searched for a model that could use categorization difficulty and target separation to describe subjects’ performance, RT, and MT. We developed a network consisting of two mutually inhibiting neural populations, each tuned to one of the possible categories and composed of an accumulation and a memory node. This network sequentially acquired interval information, maintained it in working memory and was then attracted to one of two possible states, corresponding to a categorical decision. It faithfully replicated subjects’ RT and MT as a function of categorization difficulty and target distance; it also replicated performance as a function of categorization difficulty. Furthermore, this model was used to make new predictions about the effect of untested durations, target distances and delay durations. To our knowledge, this is the first biologically plausible model that has been proposed to account for decision making and communication by integrating both sensory and motor planning information.

The influence of spatiotemporal structure of noisy stimuli in decision making

Decision making is a process of utmost importance in our daily lives, the study of which has been receiving notable attention for decades. Nevertheless, the neural mechanisms underlying decision making are still not fully understood. Computational modeling has revealed itself as a valuable asset to address some of the fundamental questions. Biophysically plausible models, in particular, are useful in bridging the different levels of description that experimental studies provide, from the neural spiking activity recorded at the cellular level to the performance reported at the behavioral level. In this article, we have reviewed some of the recent progress made in the understanding of the neural mechanisms that underlie decision making. We have performed a critical evaluation of the available results and address, from a computational perspective, aspects of both experimentation and modeling that so far have eluded comprehension. To guide the discussion, we have selected a central theme which revolves around the following question: how does the spatiotemporal structure of sensory stimuli affect the perceptual decision-making process? This question is a timely one as several issues that still remain unresolved stem from this central theme. These include: (i) the role of spatiotemporal input fluctuations in perceptual decision making, (ii) how to extend the current results and models derived from two-alternative choice studies to scenarios with multiple competing evidences, and (iii) to establish whether different types of spatiotemporal input fluctuations affect decision-making outcomes in distinctive ways. And although we have restricted our discussion mostly to visual decisions, our main conclusions are arguably generalizable; hence, their possible extension to other sensory modalities is one of the points in our discussion.

Sensory cortical population dynamics uniquely track behavior across learning and extinction

Neural responses in many cortical regions encode information relevant to behavior: information that necessarily changes as that behavior changes with learning. Although such responses are reasonably theorized to be related to behavior causation, the true nature of that relationship cannot be clarified by simple learning studies, which show primarily that responses change with experience. Neural activity that truly tracks behavior (as opposed to simply changing with experience) will not only change with learning but also change back when that learning is extinguished. Here, we directly probed for this pattern, recording the activity of ensembles of gustatory cortical single neurons as rats that normally consumed sucrose avidly were trained first to reject it (i.e., conditioned taste aversion learning) and then to enjoy it again (i.e., extinction), all within 49 h. Both learning and extinction altered cortical responses, consistent with the suggestion (based on indirect evidence) that extinction is a novel form of learning. But despite the fact that, as expected, postextinction single-neuron responses did not resemble "naive responses," ensemble response dynamics changed with learning and reverted with extinction: both the speed of stimulus processing and the relationships among ensemble responses to the different stimuli tracked behavioral relevance. These data suggest that population coding is linked to behavior with a fidelity that single-neuron coding is not.

Neural circuits as computational dynamical systems

Many recent studies of neurons recorded from cortex reveal complex temporal dynamics. How such dynamics embody the computations that ultimately lead to behavior remains a mystery. Approaching this issue requires developing plausible hypotheses couched in terms of neural dynamics. A tool ideally suited to aid in this question is the recurrent neural network (RNN). RNNs straddle the fields of nonlinear dynamical systems and machine learning and have recently seen great advances in both theory and application. I summarize recent theoretical and technological advances and highlight an example of how RNNs helped to explain perplexing high-dimensional neurophysiological data in the prefrontal cortex.

Accuracy and response-time distributions for decision-making: linear perfect integrators versus nonlinear attractor-based neural circuits

Animals choose actions based on imperfect, ambiguous data. “Noise” inherent in neural processing adds further variability to this already-noisy input signal. Mathematical analysis has suggested that the optimal apparatus (in terms of the speed/accuracy trade-off) for reaching decisions about such noisy inputs is perfect accumulation of the inputs by a temporal integrator. Thus, most highly cited models of neural circuitry underlying decision-making have been instantiations of a perfect integrator. Here, in accordance with a growing mathematical and empirical literature, we describe circumstances in which perfect integration is rendered suboptimal. In particular we highlight the impact of three biological constraints: (1) significant noise arising within the decision-making circuitry itself; (2) bounding of integration by maximal neural firing rates; and (3) time limitations on making a decision. Under conditions (1) and (2), an attractor system with stable attractor states can easily best an integrator when accuracy is more important than speed. Moreover, under conditions in which such stable attractor networks do not best the perfect integrator, a system with unstable initial states can do so if readout of the system’s final state is imperfect. Ubiquitously, an attractor system with a nonselective time-dependent input current is both more accurate and more robust to imprecise tuning of parameters than an integrator with such input. Given that neural responses that switch stochastically between discrete states can “masquerade” as integration in single-neuron and trial-averaged data, our results suggest that such networks should be considered as plausible alternatives to the integrator model.