Memory-relevant nap sleep physiology in healthy and pathological aging.

STUDY OBJECTIVES: Aging is associated with detrimental changes in sleep physiology, a process accelerated in Alzheimer's disease. Fine-tuned temporal interactions of non-rapid eye movement slow oscillations and spindles were shown to be particularly important for memory consolidation, and to deteriorate in healthy older adults. Whether this oscillatory interaction further decline in early stages of Alzheimer's disease such as mild cognitive impairment has not been investigated to date, but may have important therapeutic implications. METHODS: Here, we assessed differences in sleep architecture and memory-relevant slow oscillation, sleep spindles and their functional coupling during a 90-min nap between healthy young and older adults, and in older patients with mild cognitive impairment. Furthermore, associations of nap-sleep characteristics with sleep-dependent memory performance change were evaluated. RESULTS: We found significant differences between young and older healthy adults, and between young adults and patients with mild cognitive impairment, but not between healthy older adults and patients for several sleep metrics, including slow oscillation-spindle coupling. Moreover, sleep-dependent retention of verbal memories was significantly higher in young healthy adults versus older adults with and without mild cognitive impairment, but no difference between the two older groups was observed. Associations with sleep metrics were only found for pre-nap memory performances. CONCLUSIONS: In conclusion, our results indicate changes in nap sleep physiology and sleep-related memory consolidation in older adults with and without mild cognitive impairment. Thus, interventions targeted at improving sleep physiology may help to reduce memory decline in both groups, but our study does not indicate additional benefits for patients with mild cognitive impairment. CLINICAL TRAIL REGISTRATION: Effects of Brain Stimulation During Daytime Nap on Memory Consolidation in Younger, Healthy Subjects: https://clinicaltrials.gov/ct2/show/NCT01840865; NCT01840865. Effects of Brain Stimulation During a Daytime Nap on Memory Consolidation in Older Adults; https://clinicaltrials.gov/ct2/show/study/NCT01840839?term=01840839&draw=2&rank=1; NCT01840839. Effects of Brain Stimulation During a Daytime Nap on Memory Consolidation in Patients With Mild Cognitive Impairment; https://clinicaltrials.gov/ct2/show/NCT01782365?term=01782365&draw=2&rank=1; NCT01782365.

Inferring and validating mechanistic models of neural microcircuits based on spike-train data.

The interpretation of neuronal spike train recordings often relies on abstract statistical models that allow for principled parameter estimation and model selection but provide only limited insights into underlying microcircuits. In contrast, mechanistic models are useful to interpret microcircuit dynamics, but are rarely quantitatively matched to experimental data due to methodological challenges. Here we present analytical methods to efficiently fit spiking circuit models to single-trial spike trains. Using derived likelihood functions, we statistically infer the mean and variance of hidden inputs, neuronal adaptation properties and connectivity for coupled integrate-and-fire neurons. Comprehensive evaluations on synthetic data, validations using ground truth in-vitro and in-vivo recordings, and comparisons with existing techniques demonstrate that parameter estimation is very accurate and efficient, even for highly subsampled networks. Our methods bridge statistical, data-driven and theoretical, model-based neurosciences at the level of spiking circuits, for the purpose of a quantitative, mechanistic interpretation of recorded neuronal population activity.

Weak electric fields promote resonance in neuronal spiking activity: Analytical results from two-compartment cell and network models.

Transcranial brain stimulation and evidence of ephaptic coupling have sparked strong interests in understanding the effects of weak electric fields on the dynamics of neuronal populations. While their influence on the subthreshold membrane voltage can be biophysically well explained using spatially extended neuron models, mechanistic analyses of neuronal spiking and network activity have remained a methodological challenge. More generally, this challenge applies to phenomena for which single-compartment (point) neuron models are oversimplified. Here we employ a pyramidal neuron model that comprises two compartments, allowing to distinguish basal-somatic from apical dendritic inputs and accounting for an extracellular field in a biophysically minimalistic way. Using an analytical approach we fit its parameters to reproduce the response properties of a canonical, spatial model neuron and dissect the stochastic spiking dynamics of single cells and large networks. We show that oscillatory weak fields effectively mimic anti-correlated inputs at the soma and dendrite and strongly modulate neuronal spiking activity in a rather narrow frequency band. This effect carries over to coupled populations of pyramidal cells and inhibitory interneurons, boosting network-induced resonance in the beta and gamma frequency bands. Our work contributes a useful theoretical framework for mechanistic analyses of population dynamics going beyond point neuron models, and provides insights on modulation effects of extracellular fields due to the morphology of pyramidal cells.

Resting-State Neural Firing Rate Is Linked to Cardiac-Cycle Duration in the Human Cingulate and Parahippocampal Cortices.

Stimulation and functional imaging studies have revealed the existence of a large network of cortical regions involved in the regulation of heart rate. However, very little is known about the link between cortical neural firing and cardiac-cycle duration (CCD). Here, we analyze single-unit and multiunit data obtained in humans at rest, and show that firing rate covaries with CCD in 16.7% of the sample (25 of 150). The link between firing rate and CCD was most prevalent in the anterior medial temporal lobe (entorhinal and perirhinal cortices, anterior hippocampus, and amygdala), where 36% (18 of 50) of the units show the effect, and to a lesser extent in the mid-to-anterior cingulate cortex (11.1%, 5 of 45). The variance in firing rate explained by CCD ranged from 0.5 to 11%. Several lines of analysis indicate that neural firing influences CCD, rather than the other way around, and that neural firing affects CCD through vagally mediated mechanisms in most cases. These results show that part of the spontaneous fluctuations in firing rate can be attributed to the cortical control of the cardiac cycle. The fine tuning of the regulation of CCD represents a novel physiological factor accounting for spontaneous variance in firing rate. It remains to be determined whether the "noise" introduced in firing rate by the regulation of CCD is detrimental or beneficial to the cognitive information processing carried out in the parahippocampal and cingulate regions.SIGNIFICANCE STATEMENT Fluctuations in heart rate are known to be under the control of cortical structures, but spontaneous fluctuations in cortical firing rate, or "noise," have seldom been related to heart rate. Here, we analyze unit activity in humans at rest and show that spontaneous fluctuations in neural firing in the medial temporal lobe, as well as in the mid-to-anterior cingulate cortex, influence heart rate. This phenomenon was particularly pronounced in the entorhinal and perirhinal cortices, where it could be observed in one of three neurons. Our results show that part of spontaneous firing rate variability in regions best known for their cognitive role in spatial navigation and memory corresponds to precise physiological regulations.

Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation.

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models.

Promoting Sleep Oscillations and Their Functional Coupling by Transcranial Stimulation Enhances Memory Consolidation in Mild Cognitive Impairment.

Alzheimer's disease (AD) not only involves loss of memory functions, but also prominent deterioration of sleep physiology, which is already evident at the stage of mild cognitive impairment (MCI). Cortical slow oscillations (SO; 0.5-1 Hz) and thalamocortical spindle activity (12-15 Hz) during sleep, and their temporal coordination, are considered critical for memory formation. We investigated the potential of slow oscillatory transcranial direct current stimulation (so-tDCS), applied during a daytime nap in a sleep-state-dependent manner, to modulate these activity patterns and sleep-related memory consolidation in nine male and seven female human patients with MCI. Stimulation significantly increased overall SO and spindle power, amplified spindle power during SO up-phases, and led to stronger synchronization between SO and spindle power fluctuations in EEG recordings. Moreover, visual declarative memory was improved by so-tDCS compared with sham stimulation and was associated with stronger synchronization. These findings indicate a well-tolerated therapeutic approach for disordered sleep physiology and memory deficits in MCI patients and advance our understanding of offline memory consolidation.SIGNIFICANCE STATEMENT In the light of increasing evidence that sleep disruption is crucially involved in the progression of Alzheimer's disease (AD), sleep appears as a promising treatment target in this pathology, particularly to counteract memory decline. This study demonstrates the potential of a noninvasive brain stimulation method during sleep in patients with mild cognitive impairment (MCI), a precursor of AD, and advances our understanding of its mechanism. We provide first time evidence that slow oscillatory transcranial stimulation amplifies the functional cross-frequency coupling between memory-relevant brain oscillations and improves visual memory consolidation in patients with MCI.

The Influence of Mexican Hat Recurrent Connectivity on Noise Correlations and Stimulus Encoding.

Noise correlations are a common feature of neural responses and have been observed in many cortical areas across different species. These correlations can influence information processing by enhancing or diminishing the quality of the neural code, but the origin of these correlations is still a matter of controversy. In this computational study we explore the hypothesis that noise correlations are the result of local recurrent excitatory and inhibitory connections. We simulated two-dimensional networks of adaptive spiking neurons with local connection patterns following Gaussian kernels. Noise correlations decay with distance between neurons but are only observed if the range of excitatory connections is smaller than the range of inhibitory connections ("Mexican hat" connectivity) and if the connection strengths are sufficiently strong. These correlations arise from a moving blob-like structure of evoked activity, which is absent if inhibitory interactions have a smaller range ("inverse Mexican hat" connectivity). Spatially structured external inputs fixate these blobs to certain locations and thus effectively reduce noise correlations. We further investigated the influence of these network configurations on stimulus encoding. On the one hand, the observed correlations diminish information about a stimulus encoded by a network. On the other hand, correlated activity allows for more precise encoding of stimulus information if the decoder has only access to a limited amount of neurons.

Extending Integrate-and-Fire Model Neurons to Account for the Effects of Weak Electric Fields and Input Filtering Mediated by the Dendrite.

Transcranial brain stimulation and evidence of ephaptic coupling have recently sparked strong interests in understanding the effects of weak electric fields on the dynamics of brain networks and of coupled populations of neurons. The collective dynamics of large neuronal populations can be efficiently studied using single-compartment (point) model neurons of the integrate-and-fire (IF) type as their elements. These models, however, lack the dendritic morphology required to biophysically describe the effect of an extracellular electric field on the neuronal membrane voltage. Here, we extend the IF point neuron models to accurately reflect morphology dependent electric field effects extracted from a canonical spatial "ball-and-stick" (BS) neuron model. Even in the absence of an extracellular field, neuronal morphology by itself strongly affects the cellular response properties. We, therefore, derive additional components for leaky and nonlinear IF neuron models to reproduce the subthreshold voltage and spiking dynamics of the BS model exposed to both fluctuating somatic and dendritic inputs and an extracellular electric field. We show that an oscillatory electric field causes spike rate resonance, or equivalently, pronounced spike to field coherence. Its resonance frequency depends on the location of the synaptic background inputs. For somatic inputs the resonance appears in the beta and gamma frequency range, whereas for distal dendritic inputs it is shifted to even higher frequencies. Irrespective of an external electric field, the presence of a dendritic cable attenuates the subthreshold response at the soma to slowly-varying somatic inputs while implementing a low-pass filter for distal dendritic inputs. Our point neuron model extension is straightforward to implement and is computationally much more efficient compared to the original BS model. It is well suited for studying the dynamics of large populations of neurons with heterogeneous dendritic morphology with (and without) the influence of weak external electric fields.

Controlling statistical moments of stochastic dynamical networks.

We consider a general class of stochastic networks and ask which network nodes need to be controlled, and how, to stabilize and switch between desired metastable (target) states in terms of the first and second statistical moments of the system. We first show that it is sufficient to directly interfere with a subset of nodes which can be identified using information about the graph of the network only. Then we develop a suitable method for feedback control which acts on that subset of nodes and preserves the covariance structure of the desired target state. Finally, we demonstrate our theoretical results using a stochastic Hopfield network and a global brain model. Our results are applicable to a variety of (model) networks and further our understanding of the relationship between network structure and collective dynamics for the benefit of effective control.

How adaptation currents change threshold, gain, and variability of neuronal spiking.

Many types of neurons exhibit spike rate adaptation, mediated by intrinsic slow K(+) currents, which effectively inhibit neuronal responses. How these adaptation currents change the relationship between in vivo like fluctuating synaptic input, spike rate output, and the spike train statistics, however, is not well understood. In this computational study we show that an adaptation current that primarily depends on the subthreshold membrane voltage changes the neuronal input-output relationship (I-O curve) subtractively, thereby increasing the response threshold, and decreases its slope (response gain) for low spike rates. A spike-dependent adaptation current alters the I-O curve divisively, thus reducing the response gain. Both types of an adaptation current naturally increase the mean interspike interval (ISI), but they can affect ISI variability in opposite ways. A subthreshold current always causes an increase of variability while a spike-triggered current decreases high variability caused by fluctuation-dominated inputs and increases low variability when the average input is large. The effects on I-O curves match those caused by synaptic inhibition in networks with asynchronous irregular activity, for which we find subtractive and divisive changes caused by external and recurrent inhibition, respectively. Synaptic inhibition, however, always increases the ISI variability. We analytically derive expressions for the I-O curve and ISI variability, which demonstrate the robustness of our results. Furthermore, we show how the biophysical parameters of slow K(+) conductances contribute to the two different types of an adaptation current and find that Ca(2+)-activated K(+) currents are effectively captured by a simple spike-dependent description, while muscarine-sensitive or Na(+)-activated K(+) currents show a dominant subthreshold component.

Adaptation controls synchrony and cluster states of coupled threshold-model neurons.

We analyze zero-lag and cluster synchrony of delay-coupled nonsmooth dynamical systems by extending the master stability approach, and apply this to networks of adaptive threshold-model neurons. For a homogeneous population of excitatory and inhibitory neurons we find (i) that subthreshold adaptation stabilizes or destabilizes synchrony depending on whether the recurrent synaptic excitatory or inhibitory couplings dominate, and (ii) that synchrony is always unstable for networks with balanced recurrent synaptic inputs. If couplings are not too strong, synchronization properties are similar for very different coupling topologies, i.e., random connections or spatial networks with localized connectivity. We generalize our approach for two subpopulations of neurons with nonidentical local dynamics, including bursting, for which activity-based adaptation controls the stability of cluster states, independent of a specific coupling topology.

How adaptation shapes spike rate oscillations in recurrent neuronal networks.

Neural mass signals from in-vivo recordings often show oscillations with frequencies ranging from <1 to 100 Hz. Fast rhythmic activity in the beta and gamma range can be generated by network-based mechanisms such as recurrent synaptic excitation-inhibition loops. Slower oscillations might instead depend on neuronal adaptation currents whose timescales range from tens of milliseconds to seconds. Here we investigate how the dynamics of such adaptation currents contribute to spike rate oscillations and resonance properties in recurrent networks of excitatory and inhibitory neurons. Based on a network of sparsely coupled spiking model neurons with two types of adaptation current and conductance-based synapses with heterogeneous strengths and delays we use a mean-field approach to analyze oscillatory network activity. For constant external input, we find that spike-triggered adaptation currents provide a mechanism to generate slow oscillations over a wide range of adaptation timescales as long as recurrent synaptic excitation is sufficiently strong. Faster rhythms occur when recurrent inhibition is slower than excitation and oscillation frequency increases with the strength of inhibition. Adaptation facilitates such network-based oscillations for fast synaptic inhibition and leads to decreased frequencies. For oscillatory external input, adaptation currents amplify a narrow band of frequencies and cause phase advances for low frequencies in addition to phase delays at higher frequencies. Our results therefore identify the different key roles of neuronal adaptation dynamics for rhythmogenesis and selective signal propagation in recurrent networks.

Impact of adaptation currents on synchronization of coupled exponential integrate-and-fire neurons.

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.

Can the human lumbar posterior columns be stimulated by transcutaneous spinal cord stimulation? A modeling study.

Stimulation of different spinal cord segments in humans is a widely developed clinical practice for modification of pain, altered sensation, and movement. The human lumbar cord has become a target for modification of motor control by epidural and, more recently, by transcutaneous spinal cord stimulation. Posterior columns of the lumbar spinal cord represent a vertical system of axons and when activated can add other inputs to the motor control of the spinal cord than stimulated posterior roots. We used a detailed three-dimensional volume conductor model of the torso and the McIntyre-Richard-Grill axon model to calculate the thresholds of axons within the posterior columns in response to transcutaneous lumbar spinal cord stimulation. Superficially located large-diameter posterior column fibers with multiple collaterals have a threshold of 45.4 V, three times higher than posterior root fibers (14.1 V). With the stimulation strength needed to activate posterior column axons, posterior root fibers of large and small diameters as well as anterior root fibers are coactivated. The reported results inform on these threshold differences, when stimulation is applied to the posterior structures of the lumbar cord at intensities above the threshold of large-diameter posterior root fibers.

Stimulation of the human lumbar spinal cord with implanted and surface electrodes: a computer simulation study.

Human lumbar spinal cord networks controlling stepping and standing can be activated through posterior root stimulation using implanted electrodes. A new stimulation method utilizing surface electrodes has been shown to excite lumbar posterior root fibers similarly as with implants, an unexpected finding considering the distance to these target neurons. In the present study we apply computer modeling to compare the depolarization of posterior root fibers by both stimulation techniques. We further examine the potential for additional direct activation of motoneurons within the anterior roots. Using an implant, action potentials are initiated in the posterior root fibers at their entry into the spinal cord or along the longitudinal portions of the fiber trajectories, depending on the cathode position. For transcutaneous stimulation low threshold sites of the same fibers are identified at their exits from the spinal canal in addition to their spinal cord entries. In these exit regions anterior root fibers can also be activated. The simulation results provide a biophysical explanation for the electrophysiological findings of lower limb muscle responses induced by posterior root stimulation. Efficient excitation of afferent spinal cord structures with a simple noninvasive method can become a promising modality in the rehabilitation of people with motor disorders.