Partial information decomposition reveals that synergistic neural integration is greater downstream of recurrent information flow in organotypic cortical cultures.

The directionality of network information flow dictates how networks process information. A central component of information processing in both biological and artificial neural networks is their ability to perform synergistic integration-a type of computation. We established previously that synergistic integration varies directly with the strength of feedforward information flow. However, the relationships between both recurrent and feedback information flow and synergistic integration remain unknown. To address this, we analyzed the spiking activity of hundreds of neurons in organotypic cultures of mouse cortex. We asked how empirically observed synergistic integration-determined from partial information decomposition-varied with local functional network structure that was categorized into motifs with varying recurrent and feedback information flow. We found that synergistic integration was elevated in motifs with greater recurrent information flow beyond that expected from the local feedforward information flow. Feedback information flow was interrelated with feedforward information flow and was associated with decreased synergistic integration. Our results indicate that synergistic integration is distinctly influenced by the directionality of local information flow.

A Method to Present and Analyze Ensembles of Information Sources.

Information theory is a powerful tool for analyzing complex systems. In many areas of neuroscience, it is now possible to gather data from large ensembles of neural variables (e.g., data from many neurons, genes, or voxels). The individual variables can be analyzed with information theory to provide estimates of information shared between variables (forming a network between variables), or between neural variables and other variables (e.g., behavior or sensory stimuli). However, it can be difficult to (1) evaluate if the ensemble is significantly different from what would be expected in a purely noisy system and (2) determine if two ensembles are different. Herein, we introduce relatively simple methods to address these problems by analyzing ensembles of information sources. We demonstrate how an ensemble built of mutual information connections can be compared to null surrogate data to determine if the ensemble is significantly different from noise. Next, we show how two ensembles can be compared using a randomization process to determine if the sources in one contain more information than the other. All code necessary to carry out these analyses and demonstrations are provided.

Rich-Club Organization in Effective Connectivity among Cortical Neurons.

The performance of complex networks, like the brain, depends on how effectively their elements communicate. Despite the importance of communication, it is virtually unknown how information is transferred in local cortical networks, consisting of hundreds of closely spaced neurons. To address this, it is important to record simultaneously from hundreds of neurons at a spacing that matches typical axonal connection distances, and at a temporal resolution that matches synaptic delays. We used a 512-electrode array (60 µm spacing) to record spontaneous activity at 20 kHz from up to 500 neurons simultaneously in slice cultures of mouse somatosensory cortex for 1 h at a time. We applied a previously validated version of transfer entropy to quantify information transfer. Similar to in vivo reports, we found an approximately lognormal distribution of firing rates. Pairwise information transfer strengths also were nearly lognormally distributed, similar to reports of synaptic strengths. Some neurons transferred and received much more information than others, which is consistent with previous predictions. Neurons with the highest outgoing and incoming information transfer were more strongly connected to each other than chance, thus forming a "rich club." We found similar results in networks recorded in vivo from rodent cortex, suggesting the generality of these findings. A rich-club structure has been found previously in large-scale human brain networks and is thought to facilitate communication between cortical regions. The discovery of a small, but information-rich, subset of neurons within cortical regions suggests that this population will play a vital role in communication, learning, and memory. Significance statement: Many studies have focused on communication networks between cortical brain regions. In contrast, very few studies have examined communication networks within a cortical region. This is the first study to combine such a large number of neurons (several hundred at a time) with such high temporal resolution (so we can know the direction of communication between neurons) for mapping networks within cortex. We found that information was not transferred equally through all neurons. Instead, ∼70% of the information passed through only 20% of the neurons. Network models suggest that this highly concentrated pattern of information transfer would be both efficient and robust to damage. Therefore, this work may help in understanding how the cortex processes information and responds to neurodegenerative diseases.

High-Degree Neurons Feed Cortical Computations.

Recent work has shown that functional connectivity among cortical neurons is highly varied, with a small percentage of neurons having many more connections than others. Also, recent theoretical developments now make it possible to quantify how neurons modify information from the connections they receive. Therefore, it is now possible to investigate how information modification, or computation, depends on the number of connections a neuron receives (in-degree) or sends out (out-degree). To do this, we recorded the simultaneous spiking activity of hundreds of neurons in cortico-hippocampal slice cultures using a high-density 512-electrode array. This preparation and recording method combination produced large numbers of neurons recorded at temporal and spatial resolutions that are not currently available in any in vivo recording system. We utilized transfer entropy (a well-established method for detecting linear and nonlinear interactions in time series) and the partial information decomposition (a powerful, recently developed tool for dissecting multivariate information processing into distinct parts) to quantify computation between neurons where information flows converged. We found that computations did not occur equally in all neurons throughout the networks. Surprisingly, neurons that computed large amounts of information tended to receive connections from high out-degree neurons. However, the in-degree of a neuron was not related to the amount of information it computed. To gain insight into these findings, we developed a simple feedforward network model. We found that a degree-modified Hebbian wiring rule best reproduced the pattern of computation and degree correlation results seen in the real data. Interestingly, this rule also maximized signal propagation in the presence of network-wide correlations, suggesting a mechanism by which cortex could deal with common random background input. These are the first results to show that the extent to which a neuron modifies incoming information streams depends on its topological location in the surrounding functional network.

Synergy, redundancy, and multivariate information measures: an experimentalist's perspective.

Information theory has long been used to quantify interactions between two variables. With the rise of complex systems research, multivariate information measures have been increasingly used to investigate interactions between groups of three or more variables, often with an emphasis on so called synergistic and redundant interactions. While bivariate information measures are commonly agreed upon, the multivariate information measures in use today have been developed by many different groups, and differ in subtle, yet significant ways. Here, we will review these multivariate information measures with special emphasis paid to their relationship to synergy and redundancy, as well as examine the differences between these measures by applying them to several simple model systems. In addition to these systems, we will illustrate the usefulness of the information measures by analyzing neural spiking data from a dissociated culture through early stages of its development. Our aim is that this work will aid other researchers as they seek the best multivariate information measure for their specific research goals and system. Finally, we have made software available online which allows the user to calculate all of the information measures discussed within this paper.

Non-consummatory behavior signals predict aversion-resistant alcohol drinking in head-fixed mice.

A key facet of alcohol use disorder is continuing to drink alcohol despite negative consequences (so called "aversion-resistant drinking"). In this study, we sought to assess the degree to which head-fixed mice exhibit aversion-resistant drinking and to leverage behavioral analysis techniques available in head-fixture to relate non-consummatory behaviors to aversion-resistant drinking. We assessed aversion-resistant drinking in head-fixed female and male C57BL/6 J mice. We adulterated 20% (v/v) alcohol with varying concentrations of the bitter tastant quinine to measure the degree to which mice would continue to drink despite this aversive stimulus. We recorded high-resolution video of the mice during head-fixed drinking, tracked body parts with machine vision tools, and analyzed body movements in relation to consumption. Female and male head-fixed mice exhibited heterogenous levels of aversion-resistant drinking. Additionally, non-consummatory behaviors, such as paw movement and snout movement, were related to the intensity of aversion-resistant drinking. These studies demonstrate that head-fixed mice exhibit aversion-resistant drinking and that non-consummatory behaviors can be used to assess perceived aversiveness in this paradigm. Furthermore, these studies lay the groundwork for future experiments that will utilize advanced electrophysiological techniques to record from large populations of neurons during aversion-resistant drinking to understand the neurocomputational processes that drive this clinically relevant behavior. This article is part of the Special Issue on "PFC circuit function in psychiatric disease and relevant models".

Non-Consummatory Behavior Signals Predict Aversion-Resistant Alcohol Drinking in Head-Fixed Mice.

A key facet of alcohol use disorder is continuing to drink alcohol despite negative consequences (so called "aversion-resistant drinking"). In this study, we sought to assess the degree to which head-fixed mice exhibit aversion-resistant drinking and to leverage behavioral analysis techniques available in head-fixture to relate non-consummatory behaviors to aversion-resistant drinking. We assessed aversion-resistant drinking in head-fixed female and male C57BL/6J mice. We adulterated 20% (v/v) alcohol with varying concentrations of the bitter tastant quinine to measure the degree to which mice would continue to drink despite this aversive stimulus. We recorded high-resolution video of the mice during head-fixed drinking, tracked body parts with machine vision tools, and analyzed body movements in relation to consumption. Female and male head-fixed mice exhibited heterogenous levels of aversion-resistant drinking. Additionally, non-consummatory behaviors, such as paw movement and snout movement, were related to the intensity of aversion-resistant drinking. These studies demonstrate that head-fixed mice exhibit aversion-resistant drinking and that non-consummatory behaviors can be used to assess perceived aversiveness in this paradigm. Furthermore, these studies lay the groundwork for future experiments that will utilize advanced electrophysiological techniques to record from large populations of neurons during aversion-resistant drinking to understand the neurocomputational processes that drive this clinically relevant behavior.

Compulsive alcohol drinking in rodents is associated with altered representations of behavioral control and seeking in dorsal medial prefrontal cortex.

A key feature of compulsive alcohol drinking is continuing to drink despite negative consequences. To examine the changes in neural activity that underlie this behavior, compulsive alcohol drinking was assessed in a validated rodent model of heritable risk for excessive drinking (alcohol preferring (P) rats). Neural activity was measured in dorsal medial prefrontal cortex (dmPFC-a brain region involved in maladaptive decision-making) and assessed via change point analyses and novel principal component analyses. Neural population representations of specific decision-making variables were measured to determine how they were altered in animals that drink alcohol compulsively. Compulsive animals showed weakened representations of behavioral control signals, but strengthened representations of alcohol seeking-related signals. Finally, chemogenetic-based excitation of dmPFC prevented escalation of compulsive alcohol drinking. Collectively, these data indicate that compulsive alcohol drinking in rats is associated with alterations in dmPFC neural activity that underlie diminished behavioral control and enhanced seeking.

Correlated activity favors synergistic processing in local cortical networks in vitro at synaptically relevant timescales.

Neural information processing is widely understood to depend on correlations in neuronal activity. However, whether correlation is favorable or not is contentious. Here, we sought to determine how correlated activity and information processing are related in cortical circuits. Using recordings of hundreds of spiking neurons in organotypic cultures of mouse neocortex, we asked whether mutual information between neurons that feed into a common third neuron increased synergistic information processing by the receiving neuron. We found that mutual information and synergistic processing were positively related at synaptic timescales (0.05-14 ms), where mutual information values were low. This effect was mediated by the increase in information transmission-of which synergistic processing is a component-that resulted as mutual information grew. However, at extrasynaptic windows (up to 3,000 ms), where mutual information values were high, the relationship between mutual information and synergistic processing became negative. In this regime, greater mutual information resulted in a disproportionate increase in redundancy relative to information transmission. These results indicate that the emergence of synergistic processing from correlated activity differs according to timescale and correlation regime. In a low-correlation regime, synergistic processing increases with greater correlation, and in a high-correlation regime, synergistic processing decreases with greater correlation.

Alcohol-preferring P rats exhibit aversion-resistant drinking of alcohol adulterated with quinine.

Understanding why some people continue to drink alcohol despite negative consequences and others do not is a central problem in the study of alcohol use disorder (AUD). In this study, we used alcohol-preferring P rats (a strain bred to prefer to drink alcohol, a model for genetic risk for AUD) and Wistar rats (control) to examine drinking despite negative consequences in the form of an aversive bitter taste stimulus produced by quinine. Animals were trained to consume 10% ethanol in a simple Pavlovian conditioning task that paired alcohol access with an auditory stimulus. When the alcohol was adulterated with quinine (0.1 g/L), P rats continued to consume alcohol + quinine at the same rate as unadulterated alcohol, despite a demonstrated aversion to quinine-adulterated alcohol when given a choice between adulterated and unadulterated alcohol in the home cage. Conversely, Wistar rats decreased consumption of quinine-adulterated alcohol in the task, but continued to try the alcohol + quinine solution at similar rates to unadulterated alcohol. These results indicate that following about 8 weeks of alcohol consumption, P rats exhibit aversion-resistant drinking. This model could be used in future work to explore how the biological basis of alcohol consumption and genetic risk for excessive drinking lead to drinking that is resistant to devaluation.

The mode shapes of a tennis racket and the effects of vibration dampers on those mode shapes.

The vibrational behavior of a tennis racket was studied using a speckle-pattern interferometry system. Specifically, the first 12 mode shapes of a racket are shown and discussed. In addition, the speckle-pattern interferometry system was used to compare the effects of four commercially available vibration damping systems. It was found that these vibration dampers produce a variety of effects on the vibrational behavior of the racket, though these effects may not be noticeable during play.

Encoding of the Intent to Drink Alcohol by the Prefrontal Cortex Is Blunted in Rats with a Family History of Excessive Drinking.

The prefrontal cortex (PFC) plays a central role in guiding decision making, and its function is altered by alcohol use and an individual's innate risk for excessive alcohol drinking. The primary goal of this work was to determine how neural activity in the PFC guides the decision to drink. Towards this goal, the within-session changes in neural activity were measured from medial PFC (mPFC) of rats performing a drinking procedure that allowed them to consume or abstain from alcohol in a self-paced manner. Recordings were obtained from rats that either lacked or expressed an innate risk for excessive alcohol intake, Wistar or alcohol-preferring (P) rats, respectively. Wistar rats exhibited patterns of neural activity consistent with the intention to drink or abstain from drinking, whereas these patterns were blunted or absent in P rats. Collectively, these data indicate that neural activity patterns in mPFC associated with the intention to drink alcohol are influenced by innate risk for excessive alcohol drinking. This observation may indicate a lack of control over the decision to drink by this otherwise well-validated supervisory brain region.

Computation is concentrated in rich clubs of local cortical networks.

To understand how neural circuits process information, it is essential to identify the relationship between computation and circuit organization. Rich clubs, highly interconnected sets of neurons, are known to propagate a disproportionate amount of information within cortical circuits. Here, we test the hypothesis that rich clubs also perform a disproportionate amount of computation. To do so, we recorded the spiking activity of on average ∼300 well-isolated individual neurons from organotypic cortical cultures. We then constructed weighted, directed networks reflecting the effective connectivity between the neurons. For each neuron, we quantified the amount of computation it performed based on its inputs. We found that rich-club neurons compute ∼160% more information than neurons outside of the rich club. The amount of computation performed in the rich club was proportional to the amount of information propagation by the same neurons. This suggests that in these circuits, information propagation drives computation. In total, our findings indicate that rich-club organization in effective cortical circuits supports not only information propagation but also neural computation.

A Tutorial for Information Theory in Neuroscience.

Understanding how neural systems integrate, encode, and compute information is central to understanding brain function. Frequently, data from neuroscience experiments are multivariate, the interactions between the variables are nonlinear, and the landscape of hypothesized or possible interactions between variables is extremely broad. Information theory is well suited to address these types of data, as it possesses multivariate analysis tools, it can be applied to many different types of data, it can capture nonlinear interactions, and it does not require assumptions about the structure of the underlying data (i.e., it is model independent). In this article, we walk through the mathematics of information theory along with common logistical problems associated with data type, data binning, data quantity requirements, bias, and significance testing. Next, we analyze models inspired by canonical neuroscience experiments to improve understanding and demonstrate the strengths of information theory analyses. To facilitate the use of information theory analyses, and an understanding of how these analyses are implemented, we also provide a free MATLAB software package that can be applied to a wide range of data from neuroscience experiments, as well as from other fields of study.

Correction: Maternal deprivation induces alterations in cognitive and cortical function in adulthood.

The original version of this Article omitted the author Maureen M. Timm from the Department of Psychology, Indiana University-Purdue University Indianapolis, Indianapolis, IN, USA.

Maternal deprivation induces alterations in cognitive and cortical function in adulthood.

Early life trauma is a risk factor for a number of neuropsychiatric disorders, including schizophrenia (SZ). The current study assessed how an early life traumatic event, maternal deprivation (MD), alters cognition and brain function in rodents. Rats were maternally deprived in the early postnatal period and then recognition memory (RM) was tested in adulthood using the novel object recognition task. The expression of catechol-o-methyl transferase (COMT) and glutamic acid decarboxylase (GAD67) were quantified in the medial prefrontal cortex (mPFC), ventral striatum, and temporal cortex (TC). In addition, depth EEG recordings were obtained from the mPFC, vertex, and TC during a paired-click paradigm to assess the effects of MD on sensory gating. MD animals exhibited impaired RM, lower expression of COMT in the mPFC and TC, and lower expression of GAD67 in the TC. Increased bioelectric noise was observed at each recording site of MD animals. MD animals also exhibited altered information theoretic measures of stimulus encoding. These data indicate that a neurodevelopmental perturbation yields persistent alterations in cognition and brain function, and are consistent with human studies that identified relationships between allelic differences in COMT and GAD67 and bioelectric noise. These changes evoked by MD also lead to alterations in shared information between cognitive and primary sensory processing areas, which provides insight into how early life trauma confers a risk for neurodevelopmental disorders, such as SZ, later in life.

Analysis of Power Laws, Shape Collapses, and Neural Complexity: New Techniques and MATLAB Support via the NCC Toolbox.

Neural systems include interactions that occur across many scales. Two divergent methods for characterizing such interactions have drawn on the physical analysis of critical phenomena and the mathematical study of information. Inferring criticality in neural systems has traditionally rested on fitting power laws to the property distributions of "neural avalanches" (contiguous bursts of activity), but the fractal nature of avalanche shapes has recently emerged as another signature of criticality. On the other hand, neural complexity, an information theoretic measure, has been used to capture the interplay between the functional localization of brain regions and their integration for higher cognitive functions. Unfortunately, treatments of all three methods-power-law fitting, avalanche shape collapse, and neural complexity-have suffered from shortcomings. Empirical data often contain biases that introduce deviations from true power law in the tail and head of the distribution, but deviations in the tail have often been unconsidered; avalanche shape collapse has required manual parameter tuning; and the estimation of neural complexity has relied on small data sets or statistical assumptions for the sake of computational efficiency. In this paper we present technical advancements in the analysis of criticality and complexity in neural systems. We use maximum-likelihood estimation to automatically fit power laws with left and right cutoffs, present the first automated shape collapse algorithm, and describe new techniques to account for large numbers of neural variables and small data sets in the calculation of neural complexity. In order to facilitate future research in criticality and complexity, we have made the software utilized in this analysis freely available online in the MATLAB NCC (Neural Complexity and Criticality) Toolbox.

Criticality Maximizes Complexity in Neural Tissue.

The analysis of neural systems leverages tools from many different fields. Drawing on techniques from the study of critical phenomena in statistical mechanics, several studies have reported signatures of criticality in neural systems, including power-law distributions, shape collapses, and optimized quantities under tuning. Independently, neural complexity-an information theoretic measure-has been introduced in an effort to quantify the strength of correlations across multiple scales in a neural system. This measure represents an important tool in complex systems research because it allows for the quantification of the complexity of a neural system. In this analysis, we studied the relationships between neural complexity and criticality in neural culture data. We analyzed neural avalanches in 435 recordings from dissociated hippocampal cultures produced from rats, as well as neural avalanches from a cortical branching model. We utilized recently developed maximum likelihood estimation power-law fitting methods that account for doubly truncated power-laws, an automated shape collapse algorithm, and neural complexity and branching ratio calculation methods that account for sub-sampling, all of which are implemented in the freely available Neural Complexity and Criticality MATLAB toolbox. We found evidence that neural systems operate at or near a critical point and that neural complexity is optimized in these neural systems at or near the critical point. Surprisingly, we found evidence that complexity in neural systems is dependent upon avalanche profiles and neuron firing rate, but not precise spiking relationships between neurons. In order to facilitate future research, we made all of the culture data utilized in this analysis freely available online.

Multiplex networks of cortical and hippocampal neurons revealed at different timescales.

Recent studies have emphasized the importance of multiplex networks--interdependent networks with shared nodes and different types of connections--in systems primarily outside of neuroscience. Though the multiplex properties of networks are frequently not considered, most networks are actually multiplex networks and the multiplex specific features of networks can greatly affect network behavior (e.g. fault tolerance). Thus, the study of networks of neurons could potentially be greatly enhanced using a multiplex perspective. Given the wide range of temporally dependent rhythms and phenomena present in neural systems, we chose to examine multiplex networks of individual neurons with time scale dependent connections. To study these networks, we used transfer entropy--an information theoretic quantity that can be used to measure linear and nonlinear interactions--to systematically measure the connectivity between individual neurons at different time scales in cortical and hippocampal slice cultures. We recorded the spiking activity of almost 12,000 neurons across 60 tissue samples using a 512-electrode array with 60 micrometer inter-electrode spacing and 50 microsecond temporal resolution. To the best of our knowledge, this preparation and recording method represents a superior combination of number of recorded neurons and temporal and spatial recording resolutions to any currently available in vivo system. We found that highly connected neurons ("hubs") were localized to certain time scales, which, we hypothesize, increases the fault tolerance of the network. Conversely, a large proportion of non-hub neurons were not localized to certain time scales. In addition, we found that long and short time scale connectivity was uncorrelated. Finally, we found that long time scale networks were significantly less modular and more disassortative than short time scale networks in both tissue types. As far as we are aware, this analysis represents the first systematic study of temporally dependent multiplex networks among individual neurons.

Large-scale, high-resolution multielectrode-array recording depicts functional network differences of cortical and hippocampal cultures.

Understanding the detailed circuitry of functioning neuronal networks is one of the major goals of neuroscience. Recent improvements in neuronal recording techniques have made it possible to record the spiking activity from hundreds of neurons simultaneously with sub-millisecond temporal resolution. Here we used a 512-channel multielectrode array system to record the activity from hundreds of neurons in organotypic cultures of cortico-hippocampal brain slices from mice. To probe the network structure, we employed a wavelet transform of the cross-correlogram to categorize the functional connectivity in different frequency ranges. With this method we directly compare, for the first time, in any preparation, the neuronal network structures of cortex and hippocampus, on the scale of hundreds of neurons, with sub-millisecond time resolution. Among the three frequency ranges that we investigated, the lower two frequency ranges (gamma (30-80 Hz) and beta (12-30 Hz) range) showed similar network structure between cortex and hippocampus, but there were many significant differences between these structures in the high frequency range (100-1000 Hz). The high frequency networks in cortex showed short tailed degree-distributions, shorter decay length of connectivity density, smaller clustering coefficients, and positive assortativity. Our results suggest that our method can characterize frequency dependent differences of network architecture from different brain regions. Crucially, because these differences between brain regions require millisecond temporal scales to be observed and characterized, these results underscore the importance of high temporal resolution recordings for the understanding of functional networks in neuronal systems.