Hippocampus-retrosplenial cortex interaction is increased during phasic REM and contributes to memory consolidation

Thalamocortical Dynamics during Rapid Eye Movement Sleep in the Mouse Somatosensory Pathway

Rapid eye movement (REM) sleep, also referred to as paradoxical sleep for the striking resemblance of its electroencephalogram (EEG) to the one observed in wakefulness, is characterized by the occurrence of transient events such as limb twitches or facial and rapid eye movements. Here, we investigated the local activity of the primary somatosensory or barrel cortex (S1) in naturally sleeping head-fixed male mice during REM. Through local field potential recordings, we uncovered local appearances of spindle waves in the barrel cortex during REM concomitant with strong delta power, challenging the view of a wakefulness-like activity in REM. We further performed extra- and intracellular recordings of thalamic cells in head-fixed mice. Our data show high-frequency thalamic bursts of spikes and subthreshold spindle oscillations in approximately half of the neurons of the ventral posterior medial nucleus which further confirmed the thalamic origin of local cortical spindles in S1 in REM. Cortical spindle oscillations were suppressed, while thalamus spike firing increased, associated with rapid mouse whisker movements and S1 cortical activity transitioned to an activated state. During REM, the sensory thalamus and barrel cortex therefore alternate between high (wake-like) and low (non-REM sleep-like) activation states, potentially providing a neuronal substrate for mnemonic processes occurring during this paradoxical sleep stage.

Months-long tracking of neuronal ensembles spanning multiple brain areas with Ultra-Flexible Tentacle Electrodes

We introduce Ultra-Flexible Tentacle Electrodes (UFTEs), packing many independent fibers with the smallest possible footprint without limitation in recording depth using a combination of mechanical and chemical tethering for insertion. We demonstrate a scheme to implant UFTEs simultaneously into many brain areas at arbitrary locations without angle-of-insertion limitations, and a 512-channel wireless logger. Immunostaining reveals no detectable chronic tissue damage even after several months. Mean spike signal-to-noise ratios are 1.5-3x compared to the state-of-the-art, while the highest signal-to-noise ratios reach 89, and average cortical unit yields are ~1.75/channel. UFTEs can track the same neurons across sessions for at least 10 months (longest duration tested). We tracked inter- and intra-areal neuronal ensembles (neurons repeatedly co-activated within 25 ms) simultaneously from hippocampus, retrosplenial cortex, and medial prefrontal cortex in freely moving rodents. Average ensemble lifetimes were shorter than the durations over which we can track individual neurons. We identify two distinct classes of ensembles. Those tuned to sharp-wave ripples display the shortest lifetimes, and the ensemble members are mostly hippocampal. Yet, inter-areal ensembles with members from both hippocampus and cortex have weak tuning to sharp wave ripples, and some have unusual months-long lifetimes. Such inter-areal ensembles occasionally remain inactive for weeks before re-emerging.

Spatial-Temporal Analysis of Neural Desynchronization in Sleeplike States Reveals Critical Dynamics

Sleep is characterized by nonrapid eye movement sleep, originating from widespread neuronal synchrony, and rapid eye movement sleep, with neuronal desynchronization akin to waking behavior. While these were thought to be global brain states, recent research suggests otherwise. Using time-frequency analysis of mesoscopic voltage-sensitive dye recordings of mice in a urethane-anesthetized model of sleep, we find transient neural desynchronization occurring heterogeneously across the cortex within a background of synchronized neural activity, in a manner reminiscent of a critical spreading process and indicative of an "edge-of-synchronization" phase transition.

Infralimbic activity during REM sleep facilitates fear extinction memory

Rapid eye movement (REM) sleep is known to facilitate fear extinction and play a protective role against fearful memories.1,2 Consequently, disruption of REM sleep after a traumatic event may increase the risk for developing PTSD.3,4 However, the underlying mechanisms by which REM sleep promotes extinction of aversive memories remain largely unknown. The infralimbic cortex (IL) is a key brain structure for the consolidation of extinction memory.5 Using calcium imaging, we found in mice that most IL pyramidal neurons are intensively activated during REM sleep. Optogenetically suppressing the IL specifically during REM sleep within a 4-h window after auditory-cued fear conditioning impaired extinction memory consolidation. In contrast, REM-specific IL inhibition after extinction learning did not affect the extinction memory. Whole-cell patch-clamp recordings demonstrated that inactivating IL neurons during REM sleep depresses their excitability. Together, our findings suggest that REM sleep after fear conditioning facilitates fear extinction by enhancing IL excitability and highlight the importance of REM sleep in the aftermath of traumatic events for protecting against traumatic memories.

Consciousness and sleep

Sleep is a universal, essential biological process. It is also an invaluable window on consciousness. It tells us that consciousness can be lost but also that it can be regained, in all its richness, when we are disconnected from the environment and unable to reflect. By considering the neurophysiological differences between dreaming and dreamless sleep, we can learn about the substrate of consciousness and understand why it vanishes. We also learn that the ongoing state of the substrate of consciousness determines the way each experience feels regardless of how it is triggered-endogenously or exogenously. Dreaming consciousness is also a window on sleep and its functions. Dreams tell us that the sleeping brain is remarkably lively, recombining intrinsic activation patterns from a vast repertoire, freed from the requirements of ongoing behavior and cognitive control.

Which structure generates paradoxical (REM) sleep: The brainstem, the hypothalamus, the amygdala or the cortex?

Paradoxical or Rapid eye movement (REM) sleep (PS) is a state characterized by REMs, EEG activation and muscle atonia. In this review, we discuss the contribution of brainstem, hypothalamic, amygdalar and cortical structures in PS genesis. We propose that muscle atonia during PS is due to activation of glutamatergic neurons localized in the pontine sublaterodorsal tegmental nucleus (SLD) projecting to glycinergic/GABAergic pre-motoneurons localized in the ventro-medial medulla (vmM). The SLD PS-on neurons are inactivated during wakefulness and slow-wave sleep by PS-off GABAergic neurons localized in the ventrolateral periaqueductal gray (vPAG) and the adjacent deep mesencephalic reticular nucleus. Melanin concentrating hormone (MCH) and GABAergic PS-on neurons localized in the posterior hypothalamus would inhibit these PS-off neurons to initiate the state. Finally, the activation of a few limbic cortical structures during PS by the claustrum and the supramammillary nucleus as well as that of the basolateral amygdala would also contribute to PS expression. Accumulating evidence indicates that the activation of these limbic structures plays a role in memory consolidation and would communicate to the PS-generating structures the need for PS to process memory. In summary, PS generation is controlled by structures distributed from the cortex to the medullary level of the brain.

Granular retrosplenial cortex layer 2/3 generates high-frequency oscillations dynamically coupled with hippocampal rhythms across brain states

The granular retrosplenial cortex (gRSC) exhibits high-frequency oscillations (HFOs; ∼150 Hz), which can be driven by a hippocampus-subiculum pathway. How the cellular-synaptic and laminar organization of gRSC facilitates HFOs is unknown. Here, we probe gRSC HFO generation and coupling with hippocampal rhythms using focal optogenetics and silicon-probe recordings in behaving mice. ChR2-mediated excitation of CaMKII-expressing cells in L2/3 or L5 induces HFOs, but spontaneous HFOs are found only in L2/3, where HFO power is highest. HFOs couple to CA1 sharp wave-ripples (SPW-Rs) during rest and the descending phase of theta. gRSC HFO current sources and sinks are the same for events during both SPW-Rs and theta oscillations. Independent component analysis shows that high gamma (50-100 Hz) in CA1 stratum lacunosum moleculare is comodulated with HFO power. HFOs may thus facilitate interregional communication of a multisynaptic loop between the gRSC, hippocampus, and medial entorhinal cortex during distinct brain and behavioral states.

Sleep-wake dependent hippocampal regulation of fear memory

The hippocampus (HPC) plays a pivotal role in fear learning and memory. Our two recent studies suggest that rapid eye movement (REM) sleep via the HPC downregulates fear memory consolidation and promotes fear extinction. However, it is not clear whether and how the dorsal and the ventral HPC regulates fear memory differently; and how the HPC in wake regulates fear memory. By chemogenetic stimulating in the HPC directly and its afferent entorhinal cortex that selectively activated the HPC in REM sleep for 3-6 h post-fear-acquisition, we found that HPC activation in REM sleep consolidated fear extinction memory. In particular, dorsal HPC (dHPC) stimulation in REM sleep virtually eliminated fear memory by enhancing fear extinction and reducing fear memory consolidation. By contrast, chemogenetic stimulating HPC afferent the supramammillary nucleus (SUM) induced 3-hr wake with HPC activation impaired fear extinction. Finally, desipramine (DMI) injection that selectively eliminated REM sleep for >6 h impaired fear extinction. Our results demonstrate that the HPC is critical for fear memory regulation; and wake HPC and REM sleep HPC have an opposite role in fear extinction of respective impairment and consolidation.

Sleep scoring in rodents: Criteria, automatic approaches and outstanding issues

There is nothing we spend as much time on in our lives as we do sleeping, which makes it even more surprising that we currently do not know why we need to sleep. Most of the research addressing this question is performed in rodents to allow for invasive, mechanistic approaches. However, in contrast to human sleep, we currently do not have shared and agreed upon standards on sleep states in rodents. In this article, we present an overview on sleep stages in humans and rodents and a historical perspective on the development of automatic sleep scoring systems in rodents. Further, we highlight specific issues in rodent sleep that also call into question some of the standards used in human sleep research.

Prefrontal Cortical Regulation of REM Sleep

Rapid-eye-movement (REM) sleep is accompanied by intense cortical activity, underlying its wake-like electroencephalogram (EEG). The neural activity inducing REM sleep is thought to originate from subcortical circuits in brainstem and hypothalamus. However, whether cortical neurons can also trigger REM sleep has remained unknown. Here, we show in mice that the medial prefrontal cortex (mPFC) strongly promotes REM sleep. Bidirectional optogenetic manipulations demonstrate that excitatory mPFC neurons promote REM sleep through their projections to the lateral hypothalamus (LH) and regulate phasic events, reflected in accelerated EEG theta oscillations and increased eye-movement density during REM sleep. Calcium imaging reveals that the majority of LH-projecting mPFC neurons are maximally activated during REM sleep and a subpopulation is recruited during phasic theta accelerations. Our results delineate a cortico-hypothalamic circuit for the top-down control of REM sleep and identify a critical role of the mPFC in regulating phasic events during REM sleep.

Prefrontal cortical regulation of REM sleep

Rapid eye movement (REM) sleep is accompanied by intense cortical activity, underlying its wake-like electroencephalogram. The neural activity inducing REM sleep is thought to originate from subcortical circuits in brainstem and hypothalamus. However, whether cortical neurons can also trigger REM sleep has remained unknown. Here we show in mice that the medial prefrontal cortex (mPFC) strongly promotes REM sleep. Bidirectional optogenetic manipulations demonstrate that excitatory mPFC neurons promote REM sleep through their projections to the lateral hypothalamus and regulate phasic events, reflected in accelerated electroencephalogram theta oscillations and increased eye movement density during REM sleep. Calcium imaging reveals that the majority of lateral hypothalamus-projecting mPFC neurons are maximally activated during REM sleep and a subpopulation is recruited during phasic theta accelerations. Our results delineate a cortico-hypothalamic circuit for the top-down control of REM sleep and identify a critical role of the mPFC in regulating phasic events during REM sleep.

Linking temporal coordination of hippocampal activity to memory function

Oscillations in neural activity are widespread throughout the brain and can be observed at the population level through the local field potential. These rhythmic patterns are associated with cycles of excitability and are thought to coordinate networks of neurons, in turn facilitating effective communication both within local circuits and across brain regions. In the hippocampus, theta rhythms (4-12 Hz) could contribute to several key physiological mechanisms including long-range synchrony, plasticity, and at the behavioral scale, support memory encoding and retrieval. While neurons in the hippocampus appear to be temporally coordinated by theta oscillations, they also tend to fire in sequences that are developmentally preconfigured. Although loss of theta rhythmicity impairs memory, these sequences of spatiotemporal representations persist in conditions of altered hippocampal oscillations. The focus of this review is to disentangle the relative contribution of hippocampal oscillations from single-neuron activity in learning and memory. We first review cellular, anatomical, and physiological mechanisms underlying the generation and maintenance of hippocampal rhythms and how they contribute to memory function. We propose candidate hypotheses for how septohippocampal oscillations could support memory function while not contributing directly to hippocampal sequences. In particular, we explore how theta rhythms could coordinate the integration of upstream signals in the hippocampus to form future decisions, the relevance of such integration to downstream regions, as well as setting the stage for behavioral timescale synaptic plasticity. Finally, we leverage stimulation-based treatment in Alzheimer's disease conditions as an opportunity to assess the sufficiency of hippocampal oscillations for memory function.

Eye movements during phasic versus tonic rapid eye movement sleep are biomarkers of dissociable electroencephalogram processes for the consolidation of novel problem-solving skills

The hallmark eye movement (EM) bursts that occur during rapid eye movement (REM) sleep are markers of consolidation for procedural memory involving novel cognitive strategies and problem-solving skills. Examination of the brain activity associated with EMs during REM sleep might elucidate the processes involved in memory consolidation, and may uncover the functional significance of REM sleep and EMs themselves. Participants performed a REM-dependent, novel procedural problem-solving task (i.e. the Tower of Hanoi; ToH) before and after intervals of either overnight sleep (n = 20) or a daytime 8-hour wake period (n = 20). In addition, event-related spectral perturbation of the electroencephalogram (EEG) time-locked to EMs occurring either in bursts (i.e. phasic REM), or in isolation (i.e. tonic REM), were compared to sleep on a non-learning control night. ToH improvement was greater following sleep compared to wakefulness. During sleep, prefrontal theta (~2-8 Hz) and central-parietal-occipital sensorimotor rhythm (SMR) activity (~8-16 Hz) time-locked to EMs, were greater on the ToH night versus control night, and during phasic REM sleep, were both positively correlated with overnight memory improvements. Furthermore, SMR power during tonic REM increased significantly from the control night to ToH night, but was relatively stable from night to night during phasic REM. These results suggest that EMs are markers of learning-related increases in theta and SMR during phasic and tonic REM sleep. Phasic and tonic REM sleep may be functionally distinct in terms of their contribution to procedural memory consolidation.

A medullary hub for controlling REM sleep and pontine waves

Rapid-eye-movement (REM) sleep is a distinct behavioral state associated with vivid dreaming and memory processing. Phasic bursts of electrical activity, measurable as spike-like pontine (P)-waves, are a hallmark of REM sleep implicated in memory consolidation. However, the brainstem circuits regulating P-waves, and their interactions with circuits generating REM sleep, remain largely unknown. Here, we show that an excitatory population of dorsomedial medulla (dmM) neurons expressing corticotropin-releasing-hormone (CRH) regulates both REM sleep and P-waves in mice. Calcium imaging showed that dmM CRH neurons are selectively activated during REM sleep and recruited during P-waves, and opto- and chemogenetic experiments revealed that this population promotes REM sleep. Chemogenetic manipulation also induced prolonged changes in P-wave frequency, while brief optogenetic activation reliably triggered P-waves along with transiently accelerated theta oscillations in the electroencephalogram (EEG). Together, these findings anatomically and functionally delineate a common medullary hub for the regulation of both REM sleep and P-waves.

Sleep-A brain-state serving systems memory consolidation

Although long-term memory consolidation is supported by sleep, it is unclear how it differs from that during wakefulness. Our review, focusing on recent advances in the field, identifies the repeated replay of neuronal firing patterns as a basic mechanism triggering consolidation during sleep and wakefulness. During sleep, memory replay occurs during slow-wave sleep (SWS) in hippocampal assemblies together with ripples, thalamic spindles, neocortical slow oscillations, and noradrenergic activity. Here, hippocampal replay likely favors the transformation of hippocampus-dependent episodic memory into schema-like neocortical memory. REM sleep following SWS might balance local synaptic rescaling accompanying memory transformation with a sleep-dependent homeostatic process of global synaptic renormalization. Sleep-dependent memory transformation is intensified during early development despite the immaturity of the hippocampus. Overall, beyond its greater efficacy, sleep consolidation differs from wake consolidation mainly in that it is supported, rather than impaired, by spontaneous hippocampal replay activity possibly gating memory formation in neocortex.

Memory reactivations during sleep: a neural basis of dream experiences?

Newly encoded memory traces are spontaneously reactivated during sleep. Since their discovery in the 1990s, these memory reactivations have been discussed as a potential neural basis for dream experiences. New results from animal and human research, as well as from the rapidly growing field of sleep and dream engineering, provide essential insights into this question, and reveal both strong parallels and disparities between the two phenomena. We suggest that, although memory reactivations may contribute to subjective experiences across different states of consciousness, they are not likely to be the primary neural basis of dreaming. We identify important limitations in current research paradigms and suggest novel strategies to address this question empirically.

Neurocognitive, mood changes, and sleepiness in patients with REM-predominant obstructive sleep apnea

PURPOSE

This article focuses on recent evidence linking rapid eye movement (REM) obstructive sleep apnea (OSA) (REM-OSA) to neurocognitive dysfunction and mood changes; the proposed mechanisms for increased risk of neurocognitive dysfunction in REM-OSA, and future research prospects.

METHODS

PubMed and Google Scholar records were examined for articles utilizing pre-defined keywords. In this work, we mainly included studies published after 2017; nevertheless, critical studies published prior to 2017 were considered.

RESULTS

REM-OSA is an under-recognized stage-related sleep-disordered breathing in which obstructive respiratory events happen chiefly in stage REM. The disorder is commonly seen amongst younger patients and females and has recently been linked to cardiometabolic complications. Although less symptomatic than non-REM-OSA and non-stage-specific OSA, current findings indicate that REM-OSA may have neurocognitive repercussions and mood changes and could be linked to insomnia, increased dreams, and nightmares.

CONCLUSION

Currently available evidence indicates that REM-OSA may present with insomnia and nightmares and could affect cognitive function and mood.

Offline neuronal activity and synaptic plasticity during sleep and memory consolidation

After initial formation during learning, memories are further processed in the brain during subsequent days for long-term consolidation, with sleep playing a key role in this process. Studies have shown that neuronal activity patterns during the awake period are repeated in the hippocampus during sleep, which may coordinate brain-wide reactivation leading to memory consolidation. Consistently, perturbation of this activity blocks the formation of long-term memory. This 'replay' of activity during sleep likely triggers plastic changes in synaptic transmission, a cellular substrate of memory, in multiple brain regions, which likely plays a critical role in long-term memory. Two forms of synaptic plasticity, potentiation and depression of synaptic transmission, are induced in parallel during sleep and is termed "offline synaptic plasticity", as opposed to the "online synaptic plasticity" that occurs immediately following a memory event.

Functional roles of REM sleep

Rapid eye movement (REM) sleep is an enigmatic and intriguing sleep state. REM sleep differs from non-REM sleep by its characteristic brain activity and from wakefulness by a reduced anti-gravity muscle tone. In addition to these key traits, diverse physiological phenomena appear across the whole body during REM sleep. However, it remains unclear whether these phenomena are the causes or the consequences of REM sleep. Experimental approaches using humans and animal models have gradually revealed the functional roles of REM sleep. Extensive efforts have been made to interpret the characteristic brain activity in the context of memory functions. Numerous physical and psychological functions of REM sleep have also been proposed. Moreover, REM sleep has been implicated in aspects of brain development. Here, we review the variety of functional roles of REM sleep, mainly as revealed by animal models. In addition, we discuss controversies regarding the functional roles of REM sleep.

Cortical regulation of two-stage rapid eye movement sleep

Rapid eye movement (REM) sleep is a sleep state characterized by skeletal muscle paralysis and cerebral cortical activation. Yet, global cortical dynamics and their role in regulating REM sleep remain unclear. Here we show that in mice, REM sleep is accompanied by highly patterned cortical activity waves, with the retrosplenial cortex (RSC) as a major initiation site. Two-photon imaging of layer 2/3 pyramidal neurons of the RSC revealed two distinct patterns of population activities during REM sleep. These activities encoded two sequential REM sleep substages, characterized by contrasting facial movement and autonomic activity and by distinguishable electroencephalogram theta oscillations. Closed-loop optogenetic inactivation of RSC during REM sleep altered cortical activity dynamics and shortened REM sleep duration via inhibition of the REM substage transition. These results highlight an important role for the RSC in dictating cortical dynamics and regulating REM sleep progression.

Is paradoxical sleep setting up innate and acquired complex sensorimotor and adaptive behaviours?: A proposed function based on literature review

We summarize here the progress in identifying the neuronal network as well as the function of paradoxical sleep and the gaps of knowledge that should be filled in priority. The core system generating paradoxical sleep localized in the brainstem is now well identified, and the next step is to clarify the role of the forebrain in particular that of the hypothalamus including the melanin-concentrating hormone neurons and of the basolateral amygdala. We discuss these two options, and also the discovery that cortical activation during paradoxical sleep is restricted to a few limbic cortices activated by the lateral supramammillary nucleus and the claustrum. Such activation nicely supports the findings recently obtained showing that neuronal reactivation occurs during paradoxical sleep in these structures, and induces both memory consolidation of important memory and forgetting of less relevant ones. The question that still remains to be answered is whether paradoxical sleep is playing more crucial roles in processing emotional and procedural than other types of memories. One attractive hypothesis is that paradoxical sleep is responsible for erasing negative emotional memories, and that this function is not properly functioning in depressed patients. On the other hand, the presence of a muscle atonia during paradoxical sleep is in favour of a role in procedural memory as new types of motor behaviours can be tried without harm during the state. In a way, it also fits with the proposed role of paradoxical sleep in setting up the sensorimotor system during development.

Orexin 2 receptor (OX2R) protein distribution measured by autoradiography using radiolabeled OX2R-selective antagonist EMPA in rodent brain and peripheral tissues

Orexin, a neuropeptide, performs various physiological functions, including the regulation of emotion, feeding, metabolism, respiration, and sleep/wakefulness, by activating the orexin 1 receptor and orexin 2 receptor (OX2R). Owing to the pivotal role of OX2R in wakefulness and other biological functions, OX2R agonists are being developed. A detailed understanding of OX2R protein distribution is essential for determining the mechanisms of action of OX2R agonists; however, this has been hindered by the lack of selective antibodies. In this study, we first confirmed the OX2R-selective binding of [³H]-EMPA in in vitro autoradiography studies, using brain slices from OX2R knockout mice and their wild-type littermates. Subsequently, OX2R protein distribution in rats was comprehensively assessed in 51 brain regions and 10 peripheral tissues using in vitro autoradiography with [³H]-EMPA. The widespread distribution of OX2R protein, including that in previously unrecognized regions of the retrosplenial cortex, was identified. In contrast, OX2R protein expression was negligible/very low in peripheral tissues, suggesting that orexin exerts OX2R-dependent physiological functions primarily through activation of the central nervous system. These findings will be useful for understanding the wide range of biological functions of OX2R and the application of OX2R agonists in various disorders.

Predicting Math Performance of Middle Eastern Students: The Role of Dispositions

The present research examines the contribution of individual differences in chronotype and self-efficacy to the math performance of male and female students in STEM and no-STEM majors. Questionnaires assessing the selected individual differences were distributed to students of Middle Eastern descent enrolled in math courses of the general education curriculum. Summative assessment indices were used to measure performance comprehensively across the entire semester (course grades) and as a one-time occurrence (final test grades). The contribution of morningness and self-efficacy to both course and test performance of STEM students was sensitive to the interaction of gender and major. Instead, neither factor contributed to no-STEM students’ course and test performance. These findings were used to plan improvements in the instruction and advising of students in STEM majors, thereby complying with a key tenet of action research.

Correlation between Alteration of Sharp-wave Ripple Coupled Cortical Oscillation and Long-term Memory Deficit in Alzheimer Disease Model Mice

Alzheimer’s disease (AD) is the most common cause of dementia, characterized by prominent episodic memory dysfunction. Recent studies have suggested that there is a sequential mechanism in the memory deficit, with long-term ones preceding short-term ones. However, there is lack of explanation for these symptoms. Interaction between the hippocampus and retrosplenial cortex (RSC) during slow-wave sleep (SWS) is a crucial step for successful long-term memory formation. In particular, sharp-wave ripple (SWR) is a principal hippocampus oscillation that coordinates with RSC activity. To determine the relationship between memory dysfunction and SWR-related oscillation changes in AD, we implanted local field potential electrodes in the hippocampus and RSC of AD model mice (APP/PS1). We found that the SWR-coupled ripple wave increased in the RSC, while the amplitude of the SWR was preserved. In addition, the corresponding delta power in hippocampus and RSC was elevated, together with altered delta synchrony in AD mice. All these findings showed a significant correlation with long-term memory deficits measured in contextual fear conditions. Our study suggests that altered SWR-coupled oscillations are a possible underlying mechanism of episodic memory dysfunction in AD mice.

Brain neural patterns and the memory function of sleep

[Figure: see text].