This paper presents Integrated Information Theory (IIT) 4.0. IIT aims to account for the properties of experience in physical (operational) terms. It identifies the essential properties of experience (axioms), infers the necessary and sufficient properties that its substrate must satisfy (postulates), and expresses them in mathematical terms. In principle, the postulates can be applied to any system of units in a state to determine whether it is conscious, to what degree, and in what way. IIT offers a parsimonious explanation of empirical evidence, makes testable predictions concerning both the presence and the quality of experience, and permits inferences and extrapolations. IIT 4.0 incorporates several developments of the past ten years, including a more accurate formulation of the axioms as postulates and mathematical expressions, the introduction of a unique measure of intrinsic information that is consistent with the postulates, and an explicit assessment of causal relations. By fully unfolding a system’s irreducible cause–effect power, the distinctions and relations specified by a substrate can account for the quality of experience.

During non-rapid eye-movement (NREM) sleep, cortical and thalamic neurons oscillate every second or so between ON periods, characterized by membrane depolarization and wake-like tonic firing, and OFF periods, characterized by membrane hyperpolarization and neuronal silence. Cortical slow waves, the hallmark of NREM sleep, reflect near-synchronous OFF periods in cortical neurons. However, the mechanisms triggering such OFF periods are unclear, as there is little evidence for somatic inhibition. We studied cortical inhibitory interneurons that express somatostatin (SOM), because ∼70% of them are Martinotti cells that target diffusely layer I and can block excitatory transmission presynaptically, at glutamatergic terminals, and postsynaptically, at apical dendrites, without inhibiting the soma. In freely moving male mice, we show that SOM+ cells can fire immediately before slow waves and their optogenetic stimulation during ON periods of NREM sleep triggers long OFF periods. Next, we show that chemogenetic activation of SOM+ cells increases slow-wave activity (SWA), slope of individual slow waves, and NREM sleep duration; whereas their chemogenetic inhibition decreases SWA and slow-wave incidence without changing time spent in NREM sleep. By contrast, activation of parvalbumin+ (PV+) cells, the most numerous population of cortical inhibitory neurons, greatly decreases SWA and cortical firing, triggers short OFF periods in NREM sleep, and increases NREM sleep duration. Thus SOM+ cells, but not PV+ cells, are involved in the generation of sleep slow waves. Whether Martinotti cells are solely responsible for this effect, or are complemented by other classes of inhibitory neurons, remains to be investigated.SIGNIFICANCE STATEMENTCortical slow waves are a defining feature of non-rapid eye-movement (NREM) sleep and are thought to be important for many of its restorative benefits. Yet, the mechanism by which cortical neurons abruptly and synchronously cease firing, the neuronal basis of the slow wave, remains unknown. Using chemogenetic and optogenetic approaches, we provide the first evidence that links a specific class of inhibitory interneurons—somatostatin-positive cells—to the generation of slow waves during NREM sleep in freely moving mice.

Integrated information theory provides a mathematical framework to fully characterize the cause-effect structure of a physical system. Here, we introduce PyPhi, a Python software package that implements this framework for causal analysis and unfolds the full cause-effect structure of discrete dynamical systems of binary elements. The software allows users to easily study these structures, serves as an up-to-date reference implementation of the formalisms of integrated information theory, and has been applied in research on complexity, emergence, and certain biological questions. We first provide an overview of the main algorithm and demonstrate PyPhi’s functionality in the course of analyzing an example system, and then describe details of the algorithm’s design and implementation. PyPhi can be installed with Python’s package manager via the command ‘pip install pyphi’ on Linux and macOS systems equipped with Python 3.4 or higher. PyPhi is open-source and licensed under the GPLv3; the source code is hosted on GitHub at https://github.com/wmayner/pyphi. Comprehensive and continually-updated documentation is available at https://pyphi.readthedocs.io. The pyphi-users mailing list can be joined at https://groups.google.com/forum/#!forum/pyphi-users. A web-based graphical interface to the software is available at http://integratedinformationtheory.org/calculate.html.

Sleep has been hypothesized to rebalance overall synaptic strength after ongoing learning during waking leads to net synaptic potentiation. If so, because synaptic strength and size are correlated, synapses on average should be larger after wake and smaller after sleep. This prediction was recently confirmed in mouse cerebral cortex using serial block-face electron microscopy (SBEM). However, whether these findings extend to other brain regions is unknown. Moreover, sleep deprivation by gentle handling was reported to produce hippocampal spine loss, raising the question of whether synapse size and number are differentially affected by sleep and waking. Here we applied SBEM to measure axon–spine interface (ASI), the contact area between pre-synapse and post-synapse, and synapse density in CA1 stratum radiatum. Adolescent YFP-H mice were studied after 6–8 h of sleep (S = 6), spontaneous wake at night (W = 4) or wake enforced during the day by novelty exposure (EW = 4; males/females balanced). In each animal ≥425 ASIs were measured and synaptic vesicles were counted in ~100 synapses/mouse. Reconstructed dendrites included many small, nonperforated synapses and fewer large, perforated synapses. Relative to S, ASI sizes in perforated synapses shifted toward higher values after W and more so after EW. ASI sizes in nonperforated synapses grew after EW relative to S and W, and so did their density. ASI size correlated with presynaptic vesicle number but the proportion of readily available vesicles decreased after EW, suggesting presynaptic fatigue. Thus, CA1 synapses undergo changes consistent with sleep-dependent synaptic renormalization and their number increases after extended wake. SIGNIFICANCE STATEMENT Sleep benefits learning, memory consolidation, and the integration of new with old memories, but the underlying mechanisms remain highly debated. One hypothesis suggests that sleep9s cognitive benefits stem from its ability to renormalize total synaptic strength, after ongoing learning during wake leads to net synaptic potentiation. Supporting evidence for this hypothesis mainly comes from the cerebral cortex, including the observation that cortical synapses are larger after wake and smaller after sleep. Using serial electron microscopy, we find here that sleep/wake synaptic changes consistent with sleep-dependent synaptic renormalization also occur in the CA1 region. Thus, the role of sleep in maintaining synaptic homeostasis may extend to the hippocampus, a key area for learning and synaptic plasticity.

Reductionism assumes that causation in the physical world occurs at the micro level, excluding the emergence of macro-level causation. We challenge this reductionist assumption by employing a principled, well-defined measure of intrinsic cause-effect power–integrated information (Φ), and showing that, according to this measure, it is possible for a macro level to “beat” the micro level. Simple systems were evaluated for Φ across different spatial and temporal scales by systematically considering all possible black boxes. These are macro elements that consist of one or more micro elements over one or more micro updates. Cause-effect power was evaluated based on the inputs and outputs of the black boxes, ignoring the internal micro elements that support their input-output function. We show how black-box elements can have more common inputs and outputs than the corresponding micro elements, revealing the emergence of high-order mechanisms and joint constraints that are not apparent at the micro level. As a consequence, a macro, black-box system can have higher Φ than its micro constituents by having more mechanisms (higher composition) that are more interconnected (higher integration). We also show that, for a given micro system, one can identify local maxima of Φ across several spatiotemporal scales. The framework is demonstrated on a simple biological system, the Boolean network model of the fission-yeast cell-cycle, for which we identify stable local maxima during the course of its simulated biological function. These local maxima correspond to macro levels of organization at which emergent cause-effect properties of physical systems come into focus, and provide a natural vantage point for scientific inquiries. We challenge the reductionist assumption by studying causal properties of physical systems across different spatiotemporal scales. The result is that–contrary to reductionist views–causal power can emerge at macro scales. Rather than relying on the traditional notion of coarse-grains (averages), we introduce the notion of functional black boxes that are defined based on their input-output relationship. Using a sequence of examples, our work demonstrates that black boxes are particularly well suited to capture the heterogeneous and specialized nature of components in biological systems. While the emergence of coarse-grained systems relies on increased specificity, black-boxing reveals the importance of structure and integration. Our framework is mathematically rigorous and fully general, hence applicable across many disciplines; it is particularly useful in objectively identifying informative perspectives on complex systems in the physical sciences.

The Integrated Information Theory (IIT) of consciousness starts from essential phenomenological properties, which are then translated into postulates that any physical system must satisfy in order to specify the physical substrate of consciousness. We recently introduced an information measure (Barbosa et al., 2020) that captures three postulates of IIT—existence, intrinsicality and information—and is unique. Here we show that the new measure also satisfies the remaining postulates of IIT—integration and exclusion—and create the framework that identifies maximally irreducible mechanisms. These mechanisms can then form maximally irreducible systems, which in turn will specify the physical substrate of conscious experience.