Learning-induced bidirectional enhancement of inhibitory synaptic metaplasticity

Training rodents in a particularly difficult olfactory-discrimination (OD) task results in the acquisition of the ability to perform the task well, termed 'rule learning'. In addition to enhanced intrinsic excitability and synaptic excitation in piriform cortex pyramidal neurons, rule learning results in increased synaptic inhibition across the whole cortical network to the point where it precisely maintains the balance between inhibition and excitation. The mechanism underlying such precise inhibitory enhancement remains to be explored. Here, we use brain slices from transgenic mice (VGAT-ChR2-EYFP), enabling optogenetic stimulation of single GABAergic neurons and recordings of unitary synaptic events in pyramidal neurons. Quantal analysis revealed that learning-induced enhanced inhibition is mediated by increased quantal size of the evoked inhibitory events. Next, we examined the plasticity of synaptic inhibition induced by long-lasting, intrinsically evoked spike firing in post-synaptic neurons. Repetitive depolarizing current pulses from depolarized (-70 mV) or hyperpolarized (-90 mV) membrane potentials induced long-term depression (LTD) and long-term potentiation (LTP) of synaptic inhibition, respectively. We found a profound bidirectional increase in the ability to induce both LTD, mediated by L-type calcium channels, and LTP, mediated by R-type calcium channels after rule learning. Blocking the GABAB receptor reversed the effect of intrinsic stimulation at -90 mV from LTP to LTD. We suggest that learning greatly enhances the ability to modify the strength of synaptic inhibition of principal neurons in both directions. Such plasticity of synaptic plasticity allows fine-tuning of inhibition on each particular neuron, thereby stabilizing the network while maintaining the memory of the rule. KEY POINTS: Olfactory discrimination rule learning results in long-lasting enhancement of synaptic inhibition on piriform cortex pyramidal neurons. Quantal analysis of unitary inhibitory synaptic events, evoked by optogenetic minimal stimulation, revealed that enhanced synaptic inhibition is mediated by increased quantal size. Surprisingly, metaplasticity of synaptic inhibition, induced by intrinsically evoked repetitive spike firing, is increased bidirectionally. The susceptibility to both long-term depression (LTD) and long-term potentiation (LTP) of inhibition is enhanced after learning. LTD of synaptic inhibition is mediated by L-type calcium channels and LTP by R-type calcium channels. LTP is also dependent on activation of GABAB receptors. We suggest that learning-induced changes in the metaplasticity of synaptic inhibition enable the fine-tuning of inhibition on each particular neuron, thereby stabilizing the network while maintaining the memory of the rule.

Reversing Aging: Decline in Complex Olfactory Learning Can be Rectified by Restoring Intrinsic Plasticity of Hippocampal CA1 Pyramidal Neurons

The acquisition of complex rules requires modifications in intrinsic plasticity of excitatory neurons within relevant brain areas. Olfactory discrimination (OD) rule learning occludes slow calcium-dependent potassium current (sIAHP ) in piriform cortex (PC) pyramidal neurons, which increases their intrinsic neuronal excitability. Similar learning-induced sIAHP changes are demonstrated in hippocampal CA1. The shutdown of sIAHP is mediated by the metabotropic activation of the kainate subtype glutamatergic receptor, GluK2. Here, the duration of training required for OD rule learning increased significantly as the mice matured and aged is first shown, which appears earlier in 5xFAD mice. At the cellular biophysical level, aging is accompanied by reduction in the post-burst AHP in these neurons, while neuronal excitability remains stable. This is in contrast to aging CA1 neurons that exhibit enhanced post-burst AHPs in previous reports. Kainate reduces post-burst AHP in adults, but not in aged PC neurons, whereas it reduces post-burst AHPs in hippocampal CA1 pyramidal neurons of both young and aged mice. Overexpression of GluK2 in CA1 neurons restores OD learning capabilities in aged wild-type and 5xFAD mice, to a level comparable to young adults. Activation of GluK2 receptors in selectively vulnerable neurons can prevent aging-related cognitive decline is suggested.

Ergodic properties of Brownian motion under stochastic resetting

We study the ergodic properties of one-dimensional Brownian motion with resetting. Using generic classes of statistics of times between resets, we find respectively for thin- or fat-tailed distributions the normalized or non-normalized invariant density of this process. The former case corresponds to known results in the resetting literature and the latter to infinite ergodic theory. Two types of ergodic transitions are found in this system. The first is when the mean waiting time between resets diverges, when standard ergodic theory switches to infinite ergodic theory. The second is when the mean of the square root of time between resets diverges and the properties of the invariant density are drastically modified. We then find a fractional integral equation describing the density of particles. This finite time tool is particularly useful close to the ergodic transition where convergence to asymptotic limits is logarithmically slow. Our study implies rich ergodic behaviors for this nonequilibrium process which should hold far beyond the case of Brownian motion analyzed here.

Restart Expedites Quantum Walk Hitting Times

Classical first-passage times under restart are used in a wide variety of models, yet the quantum version of the problem still misses key concepts. We study the quantum hitting time with restart using a monitored quantum walk. The restart strategy eliminates the problem of dark states, i.e., cases where the particle evades detection, while maintaining the ballistic propagation which is important for a fast search. We find profound effects of quantum oscillations on the restart problem, namely, a type of instability of the mean detection time, and optimal restart times that form staircases, with sudden drops as the rate of sampling is modified. In the absence of restart and in the Zeno limit, the detection of the walker is not possible, and we examine how restart overcomes this well-known problem, showing that the optimal restart time becomes insensitive to the sampling period.

Modulation of social investigation by anterior hypothalamic nucleus rhythmic neural activity

Social interactions involve both approach and avoidance toward specific individuals. Currently, the brain regions subserving these behaviors are not fully recognized. The anterior hypothalamic nucleus (AHN) is a poorly defined brain area, and recent studies have yielded contradicting conclusions regarding its behavioral role. Here we explored the role of AHN neuronal activity in regulating approach and avoidance actions during social interactions. Using electrophysiological recordings from behaving mice, we revealed that theta rhythmicity in the AHN is enhanced during affiliative interactions, but decreases during aversive ones. Moreover, the spiking activity of AHN neurons increased during the investigation of social stimuli, as compared to objects, and was modulated by theta rhythmicity. Finally, AHN optogenetic stimulation during social interactions augmented the approach toward stimuli associated with the stimulation. These results suggest the role for AHN neural activity in regulating approach behavior during social interactions, and for theta rhythmicity in mediating the valence of social stimuli.

Nck1 activity in lateral amygdala regulates long-term fear memory formation

Fear conditioning leads to long-term fear memory formation and is a model for studying fear-related psychopathological conditions such as phobias and post-traumatic stress disorder. Long-term fear memory formation is believed to involve alterations of synaptic efficacy mediated by changes in synaptic transmission and morphology in lateral amygdala (LA). Nck1 is a key neuronal adaptor protein involved in the regulation of the actin cytoskeleton and the neuronal processes believed to be involved in memory formation. However, the role of Nck1 in memory formation is not known. Here we explored the role of Nck1 in fear memory formation in lateral amygdala (LA). Reduction of Nck1 in excitatory neurons in LA enhanced long-term, but not short-term, auditory fear conditioning memory. Activation of Nck1, by using a photoactivatable Nck1 (PA-Nck1), during auditory fear conditioning in excitatory neurons in LA impaired long-term, but not short-term, fear memory. Activation of Nck1 immediately or a day after fear conditioning did not affect fear memory. The hippocampal-mediated contextual fear memory was not affected by the reduction or activation of Nck1 in LA. We show that Nck1 is localized to the presynapses in LA. Nck1 activation in LA excitatory neurons decreased the frequency of AMPA receptors-mediated miniature excitatory synaptic currents (mEPSCs). Nck1 activation did not affect GABA receptor-mediated inhibitory synaptic currents (mIPSCs). These results show that Nck1 activity in excitatory neurons in LA regulates glutamate release and sets the threshold for fear memory formation. Moreover, our research shows that Nck1 may serve as a target for pharmacological treatment of fear and anxiety disorders.

Olfactory rule learning-induced enhancement in intrinsic neuronal excitability is maintained by shutdown of the cholinergic M-current

Training rats in a particularly difficult olfactory discrimination task initiates a period of accelerated learning, manifested as a dramatic increase in the rats' capacity to discriminate between pairs of odors once they have learned the discrimination task, implying that rule learning has taken place. At the cellular biophysical level, rule learning is maintained by reduction in the conductance of the slow current (sI_AHP) simultaneously in most piriform cortex layer II pyramidal neurons. Such sI_AHP reduction is expressed in attenuation of the post-burst afterhyperpolarization (AHP) potential and thus in enhanced repetitive action potential firing. Previous studies have shown that a causal relationship exists between long-lasting post-burst AHP reduction and rule learning. A specific channel through which the sI_AHP flows has not been identified. The sI_AHP in pyramidal cells is critically dependent on membrane phosphatidylinositol 4,5-bisphosphate [PtdIns(4,5)P(2)]. PtdIns(4,5)P(2) regulates the calcium sensitivity of the sI_AHP by acting downstream from the rise in intracellular calcium. These findings led to the interesting hypothesis that PtdIns(4,5)P(2) activates a variety of potassium channels. Thus, the sI_AHP would not represent a unitary ionic current but the embodiment of a generalized potassium channel gating mechanism. We thus hypothesized that the learning-induced increase in intrinsic excitability is mediated by reduced conductance of one or more of the currents that contribute to the sI_AHP. Here we first show, using current-clamp recordings, that the post-burst AHP in piriform cortex pyramidal neurons is also mediated by the I_h, and the contribution of this current to the post-burst AHP is also affected by learning. We also show, using whole-cell patch-clamp recordings, that the sI_AHP in neurons from trained rats is not sensitive to blocking membrane phosphatidylinositol 4,5-bisphosphate [PtdIns(4,5)P(2)], and to the blocking of the current mediated by the cholinergic muscarinic acetylcholine receptor (M-current). Further current-clamp recordings also show that blocking PtdIns(4,5)P(2) synthesis and application of a specific IKCa blocker have no effect on the post-burst AHP in neurons from trained as well as control rats. Taken together with results from our previous studies, these data suggest that rule learning-induced long-lasting enhancement in intrinsic neuronal excitability results from reduced conductance of the M-current and thus the slow potassium currents, which control repetitive spike firing.

Measurement-induced quantum walks

We investigate a tight-binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory," and a combination of classical and quantum mechanical properties for the walk are observed. We explore the effects of the measurements on the spreading of the packet on a one-dimensional line, showing that except for the Zeno limit, the system converges to Gaussian statistics similarly to a classical random walk. A large deviation analysis and an Edgeworth expansion yield quantum corrections to this normal behavior. We then explore the first passage time to a target state using a generating function method, yielding properties like the quantization of the mean first return time. In particular, we study the effects of certain sampling rates that cause remarkable changes in the behavior in the system, such as divergence of the mean detection time in finite systems and decomposition of the phase space into mutually exclusive regions, an effect that mimics ergodicity breaking, whose origin here is the destructive interference in quantum mechanics. For a quantum walk on a line, we show that in our system the first detection probability decays classically like (time)^{-3/2}. This is dramatically different compared to local measurements, which yield a decay rate of (time)^{-3}, indicating that the exponents of the first passage time depend on the type of measurements used.

Plasticity of olfactory bulb inputs mediated by dendritic NMDA-spikes in rodent piriform cortex

The piriform cortex (PCx) is essential for learning of odor information. The current view postulates that odor learning in the PCx is mainly due to plasticity in intracortical (IC) synapses, while odor information from the olfactory bulb carried via the lateral olfactory tract (LOT) is ‘hardwired.’ Here, we revisit this notion by studying location- and pathway-dependent plasticity rules. We find that in contrast to the prevailing view, synaptic and optogenetically activated LOT synapses undergo strong and robust long-term potentiation (LTP) mediated by only a few local NMDA-spikes delivered at theta frequency, while global spike timing-dependent plasticity (STDP) protocols failed to induce LTP in these distal synapses. In contrast, IC synapses in apical and basal dendrites undergo plasticity with both NMDA-spikes and STDP protocols but to a smaller extent compared with LOT synapses. These results are consistent with a self-potentiating mechanism of odor information via NMDA-spikes that can form branch-specific memory traces of odors that can further associate with contextual IC information via STDP mechanisms to provide cognitive and emotional value to odors.

Cusp of Non-Gaussian Density of Particles for a Diffusing Diffusivity Model

We study a two state "jumping diffusivity" model for a Brownian process alternating between two different diffusion constants, D+>D-, with random waiting times in both states whose distribution is rather general. In the limit of long measurement times, Gaussian behavior with an effective diffusion coefficient is recovered. We show that, for equilibrium initial conditions and when the limit of the diffusion coefficient D-⟶0 is taken, the short time behavior leads to a cusp, namely a non-analytical behavior, in the distribution of the displacements P(x,t) for x⟶0. Visually this cusp, or tent-like shape, resembles similar behavior found in many experiments of diffusing particles in disordered environments, such as glassy systems and intracellular media. This general result depends only on the existence of finite mean values of the waiting times at the different states of the model. Gaussian statistics in the long time limit is achieved due to ergodicity and convergence of the distribution of the temporal occupation fraction in state D+ to a δ-function. The short time behavior of the same quantity converges to a uniform distribution, which leads to the non-analyticity in P(x,t). We demonstrate how super-statistical framework is a zeroth order short time expansion of P(x,t), in the number of transitions, that does not yield the cusp like shape. The latter, considered as the key feature of experiments in the field, is found with the first correction in perturbation theory.

The role of p21-activated kinase in maintaining the fear learning-induced modulation of excitation/inhibition ratio in lateral amygdala

We study the relations between different learning paradigms and enduring changes in excitatory synaptic transmission. Here we show that auditory fear conditioning (AFC), but not olfactory fear conditioning (OFC) training, led to enduring enhancement in AMPA-mediated miniature EPSCs (mEPSCs). Moreover, olfactory unpaired training led to a stable significant reduction in excitatory synaptic transmission. However, olfactory discrimination learning (OD) did not modulate postsynaptic AMPA-mediated mEPSCs in LA. The p21-activated kinase (PAK) activity, previously shown to have a key role in maintaining persistent long-lasting enhancement in synaptic inhibition after OFC, has an opposing effect on excitatory synaptic transmission. PAK maintained the level of excitatory synaptic transmission in the amygdala in all experimental groups, except in neurons in the OFC trained rats. PAK also maintained excitatory synaptic transmission in all neurons of auditory fear conditioning and naïve training groups except in neurons of the auditory safety learning. Safety learning was previously shown in our study to enhance synaptic inhibition. We thus suggest that PAK maintains inhibitory synaptic transmission in a learning-dependent manner and on the other hand affects excitatory synaptic transmission only in groups where learning has not affected inhibitory transmission. Thus, PAK controls learning-induced changes in the excitation/inhibition balance.

Hitchhiker model for Laplace diffusion processes

Brownian motion is a Gaussian process describing normal diffusion with a variance increasing linearly with time. Recently, intracellular single-molecule tracking experiments have recorded exponentially decaying propagators, a phenomenon called Laplace diffusion. Inspired by these developments we study a many-body approach, called the Hitchhiker model, providing a microscopic description of the widely observed behavior. Our model explains how Laplace diffusion is controlled by size fluctuations of single molecules, independently of the diffusion law which they follow. By means of numerical simulations Laplace diffusion is recovered and we show how single-molecule tracking and data analysis, in a many-body system, is highly nontrivial as tracking of a single particle or many in parallel yields vastly different estimates for the diffusivity. We quantify the differences between these two commonly used approaches, showing how the single-molecule estimate of diffusivity is larger if compared to the full tagging method.

A Cellular Mechanism of Learning-Induced Enhancement of Synaptic Inhibition: PKC-Dependent Upregulation of KCC2 Activation

Long-term memory of complex olfactory learning is expressed by wide spread enhancement in excitatory and inhibitory synaptic transmission onto piriform cortex pyramidal neurons. A particularly interesting modification in synaptic inhibition is the hyperpolarization of the reversal potential of the fast post synaptic inhibitory potential (fIPSP). Here we study the mechanism underlying the maintenance of such a shift in the fIPSP. Blocking of the neuronal specific K+-Cl- co-transporter (KCC2) in neurons of trained rats significantly depolarized the averaged fIPSP reversal potential of the spontaneous miniature inhibitory post synaptic currents (mIPSCs), to the averaged pre-training level. A similar effect was obtained by blocking PKC, which was previously shown to upregulate KCC2. Accordingly, the level of PKC-dependent phosphorylation of KCC2, at the serine 940 site, was significantly increased after learning. In contrast, blocking two other key second messenger systems CaMKII and PKA, which have no phosphorylation sites on KCC2, had no effect on the fIPSP reversal potential. Importantly, the PKC inhibitor also reduced the averaged amplitude of the spontaneous miniature excitatory synaptic currents (mEPSCs) in neurons of trained rats only, to the pre-training level. We conclude that learning-induced hyper-polarization of the fIPSP reversal potential is mediated by PKC-dependent increase of KCC2 phosphorylation.

Learning-induced enduring changes in inhibitory synaptic transmission in lateral amygdala are mediated by p21-activated kinase

In this study we explored whether learning leads to enduring changes in inhibitory synaptic transmission in lateral amygdala (LA). We revealed that olfactory discrimination (OD) learning in rats led to a long-lasting increase in postsynaptic GABAA channel-mediated miniature inhibitory postsynaptic currents (mIPSCs) in LA. Olfactory fear conditioning, but not auditory fear conditioning, also led to enduring enhancement in GABAA-mediated mIPSCs. Auditory fear conditioning, but not olfactory fear conditioning or OD learning, induced an enduring reduction in the frequency but not the current of mIPSC events. We found that p21-activated kinase (PAK) activity is needed to maintain OD and olfactory fear conditioning learning-induced enduring enhancement of mIPSCs. Further analysis revealed that OD led to an increase in GABAA channel conductance whereas olfactory fear conditioning increased the number of GABAA channels. These alterations in GABAA channels conductance and level are controlled by PAK activity. Our study shows that the learning-induced increase in postsynaptic inhibitory transmission in LA is specific to the sensory modality. However, the mechanism that mediates the increase in inhibitory transmission, namely the increase in the conductance or in the level of GABAA channel, is learning specific.

NEW & NOTEWORTHY Here we studied whether learning leads to long-lasting alterations in inhibitory synaptic transmission in lateral amygdala (LA). We revealed that learning led to enduring changes in inhibitory synaptic transmission in LA that are affected by the sensory modality (auditory or olfaction) used during learning. However, the mechanism that mediated the changes in inhibitory transmission (alterations in GABAA channel level or conductance) depended on the type of learning. These long-lasting alterations are maintained by p21-activated kinase.

Infinite ergodic theory for heterogeneous diffusion processes

We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as D(x)∼|x-x[over ̃]|^{2-2/α} in the vicinity of a point x[over ̃], where α can be either positive or negative. We find that a nonnormalized state, also called an infinite density, describes statistical properties of the system. For processes under investigation, the time averages of a wide class of observables are obtained using an ensemble average with respect to the nonnormalized density. A Langevin equation which involves multiplicative noise may take different interpretation, Itô, Stratonovich, or Hänggi-Klimontovich, so the existence of an infinite density and the density's shape are both related to the considered interpretation and the structure of D(x).

A Cellular Mechanism Underlying Enhanced Capability for Complex Olfactory Discrimination Learning

The biological mechanisms underlying complex forms of learning requiring the understanding of rules based on previous experience are not yet known. Previous studies have raised the intriguing possibility that improvement in complex learning tasks requires the long-term modulation of intrinsic neuronal excitability, induced by reducing the conductance of the slow calcium-dependent potassium current (sIAHP) simultaneously in most neurons in the relevant neuronal networks in several key brain areas. Such sIAHP reduction is expressed in attenuation of the postburst afterhyperpolarization (AHP) potential, and thus in enhanced repetitive action potential firing. Using complex olfactory discrimination (OD) learning as a model for complex learning, we show that brief activation of the GluK2 subtype glutamate receptor results in long-lasting enhancement of neuronal excitability in neurons from controls, but not from trained rats. Such an effect can be obtained by a brief tetanic synaptic stimulation or by direct application of kainate, both of which reduce the postburst AHP in pyramidal neurons. Induction of long-lasting enhancement of neuronal excitability is mediated via a metabotropic process that requires PKC and ERK activation. Intrinsic neuronal excitability cannot be modulated by synaptic activation in neurons from GluK2 knock-out mice. Accordingly, these mice are incapable of learning the complex OD task. Moreover, viral-induced overexpression of Gluk2 in piriform cortex pyramidal neurons results in remarkable enhancement of complex OD learning. Thus, signaling via kainate receptors has a central functional role in higher cognitive abilities.

NMDA spikes mediate amplification of inputs in the rat piriform cortex

The piriform cortex (PCx) receives direct input from the olfactory bulb (OB) and is the brain's main station for odor recognition and memory. The transformation of the odor code from OB to PCx is profound: mitral and tufted cells in olfactory glomeruli respond to individual odorant molecules, whereas pyramidal neurons (PNs) in the PCx responds to multiple, apparently random combinations of activated glomeruli. How these 'discontinuous' receptive fields are formed from OB inputs remains unknown. Counter to the prevailing view that olfactory PNs sum their inputs passively, we show for the first time that NMDA spikes within individual dendrites can both amplify OB inputs and impose combination selectivity upon them, while their ability to compartmentalize voltage signals allows different dendrites to represent different odorant combinations. Thus, the 2-layer integrative behavior of olfactory PN dendrites provides a parsimonious account for the nonlinear remapping of the odor code from bulb to cortex.

Tune it in: mechanisms and computational significance of neuron-autonomous plasticity

The activity of a neural network is a result of synaptic signals that convey the communication between neurons and neuron-based intrinsic currents that determine the neuron’s input-output transfer function. Ample studies have demonstrated that cell-based excitability, and in particular intrinsic excitability, is modulated by learning and that these modifications play a key role in learning-related behavioral changes. The field of cell-based plasticity is largely growing, and it entails numerous experimental findings that demonstrate a large diversity of currents that are affected by learning. The diverse effect of learning on the neuron’s excitability emphasizes the need for a framework under which cell-based plasticity can be categorized to enable the assessment of the computational roles of the intrinsic modifications. We divide the domain of cell-based plasticity into three main categories, where the first category entails the currents that mediate the passive properties and single-spike generation, the second category entails the currents that mediate spike frequency adaptation, and the third category entails a novel learning-induced mechanism where all excitatory and inhibitory synapses double their strength. Curiously, this elementary division enables a natural categorization of the computational roles of these learning-induced plasticities. The computational roles are diverse and include modification of the neuronal mode of action, such as bursting, prolonged, and fast responsive; attention-like effect where the signal detection is improved; transfer of the network into an active state; biasing the competition for memory allocation; and transforming an environmental cue into a dominant cue and enabling a quicker formation of new memories.

Learning-induced modulation of the effect of neuroglial transmission on synaptic plasticity

Training rats in a complex olfactory discrimination task results in acquisition of "rule learning" (learning how to learn), a term describing the capability to perform the task superbly. Such rule learning results in strengthening of both excitatory and inhibitory synaptic connections between neurons in the piriform cortex. Moreover, intrinsic excitability is also enhanced throughout the pyramidal neuron population. Surprisingly, the cortical network retains its stability under these long-term modifications. In particular, the susceptibility for long-term potentiation (LTP) induction, while decreased for a short time window, returns to almost its pretraining value, although significant strengthening of AMPA receptor-mediated glutamatergic transmission remains. Such network balance is essential for maintaining the single-cell modifications that underlie long-term memory while preventing hyperexcitability that would result in runaway synaptic activity. However, the mechanisms underlying the long-term maintenance of such balance have yet to be described. In this study, we explored the role of astrocyte-mediated gliotransmission in long-term maintenance of learning-induced modifications in susceptibility for LTP induction and control of the strength of synaptic inhibition. We show that blocking connexin 43 hemichannels, which form gap junctions between astrocytes, decreases significantly the ability to induce LTP by stimulating the excitatory connections between piriform cortex pyramidal neurons after learning only. In parallel, spontaneous miniature inhibitory postsynaptic current amplitude is reduced in neurons from trained rats only, to the level of prelearning. Thus gliotransmission has a key role in maintaining learning-induced cortical stability by a wide-ranged control on synaptic transmission and plasticity. NEW & NOTEWORTHY We explore the role of astrocyte-mediated gliotransmission in maintenance of olfactory discrimination learning-induced modifications. We show that blocking gap junctions between astrocytes decreases significantly the ability to induce long-term potentiation in the piriform cortex after learning only. In parallel, synaptic inhibition is reduced in neurons from trained rats only, to the level of prelearning. Thus gliotransmission has a key role in maintaining learning-induced cortical stability by a wide-ranged control on synaptic transmission and plasticity.

Learning-induced modulation of the effect of endocannabinoids on inhibitory synaptic transmission

Endocannabinoids are key modulators that regulate central brain functions and behaviors, including learning and memory. At the cellular and molecular levels, endocannabinoids are potent modulators of excitatory and inhibitory synaptic function. Most effects of cannabinoids are thought to be mediated via G protein-coupled cannabinoid receptors. In particular, cannabinoids released from postsynaptic neurons are suggested to act as retrograde messengers, activating presynaptic type-1 cannabinoid receptors (CB1Rs), thereby inducing suppression of synaptic release. Another central mechanism of cannabinoid-induced action requires activation of astroglial CB1Rs. CB1Rs are also implicated in self-modulation of cortical neurons. Rats that are trained in a particularly difficult olfactory-discrimination task show a dramatic increased ability to acquire memories of new odors. The memory of the acquired high-skill acquisition, termed “rule learning” or “learning set,” lasts for many months. Using this behavioral paradigm, we show a novel function of action for CB1Rs, supporting long-term memory by maintaining persistent enhancement of inhibitory synaptic transmission. Long-lasting enhancement of inhibitory synaptic transmission is blocked by a CB1R inverse agonist. This effect is mediated by a novel purely postsynaptic mechanism, obtained by enhancing the single GABAA channel conductance that is PKA dependent. The significant role that CB1R has in maintaining learning-induced long-term strengthening of synaptic inhibition suggests that endocannabinoids have a key role in maintaining long-term memory by enhancing synaptic inhibition.

NEW & NOTEWORTHY In this study we show a novel function and mechanism of action for cannabinoids in neurons, mediated by activation of type-1 cannabinoid receptors, supporting long-term memory by maintaining persistent enhancement of inhibitory synaptic transmission on excitatory neurons. This effect is mediated by a novel purely postsynaptic mechanism, obtained by enhancing the single GABAA channel conductance that is PKA dependent. Thus we report for the first time that endocannabinoids have a key role maintaining learning-induced synaptic modification.

Erratum: Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise [Phys. Rev. E 94, 052130 (2016)]

This corrects the article DOI: 10.1103/PhysRevE.94.052130.

Conditional 1/f^{α} noise: From single molecules to macroscopic measurement

We demonstrate that the measurement of 1/f^{α} noise at the single molecule or nano-object limit is remarkably distinct from the macroscopic measurement over a large sample. The single-particle measurements yield a conditional time-dependent spectrum. However, the number of units fluctuating on the time scale of the experiment is increasing in such a way that the macroscopic measurements appear perfectly stationary. The single-particle power spectrum is a conditional spectrum, in the sense that we must make a distinction between idler and nonidler units on the time scale of the experiment. We demonstrate our results based on stochastic and deterministic models, in particular the well-known approach of superimposed Lorentzians, the blinking quantum dot model, and deterministic dynamics generated by a nonlinear mapping. Our results show that the 1/f^{α} spectrum is inherently nonstationary even if the macroscopic measurement completely obscures the underlying time dependence of the phenomena.

Quantum walks: The first detected passage time problem

Even after decades of research, the problem of first passage time statistics for quantum dynamics remains a challenging topic of fundamental and practical importance. Using a projective measurement approach, with a sampling time τ, we obtain the statistics of first detection events for quantum dynamics on a lattice, with the detector located at the origin. A quantum renewal equation for a first detection wave function, in terms of which the first detection probability can be calculated, is derived. This formula gives the relation between first detection statistics and the solution of the corresponding Schrödinger equation in the absence of measurement. We illustrate our results with tight-binding quantum walk models. We examine a closed system, i.e., a ring, and reveal the intricate influence of the sampling time τ on the statistics of detection, discussing the quantum Zeno effect, half dark states, revivals, and optimal detection. The initial condition modifies the statistics of a quantum walk on a finite ring in surprising ways. In some cases, the average detection time is independent of the sampling time while in others the average exhibits multiple divergences as the sampling time is modified. For an unbounded one-dimensional quantum walk, the probability of first detection decays like (time)^{(-3)} with superimposed oscillations, with exceptional behavior when the sampling period τ times the tunneling rate γ is a multiple of π/2. The amplitude of the power-law decay is suppressed as τ→0 due to the Zeno effect. Our work, an extended version of our previously published paper, predicts rich physical behaviors compared with classical Brownian motion, for which the first passage probability density decays monotonically like (time)^{-3/2}, as elucidated by Schrödinger in 1915.

Superdiffusive Dispersals Impart the Geometry of Underlying Random Walks

It is recognized now that a variety of real-life phenomena ranging from diffusion of cold atoms to the motion of humans exhibit dispersal faster than normal diffusion. Lévy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive Lévy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise

The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

Physiological expression of olfactory discrimination rule learning balances whole-population modulation and circuit stability in the piriform cortex network

Once trained, rats are able to execute particularly difficult olfactory discrimination tasks with exceptional accuracy. Such skill acquisition, termed "rule learning", is accompanied by a series of long-lasting modifications to three cellular properties which modulate pyramidal neuron activity in piriform cortex; intrinsic excitability, synaptic excitation, and synaptic inhibition. Here, we explore how these changes, which are seemingly contradictory at the single-cell level in terms of their effect on neuronal excitation, are manifested within the piriform cortical neuronal network to store the memory of the rule, while maintaining network stability. To this end, we monitored network activity via multisite extracellular recordings of field postsynaptic potentials (fPSPS) and with single-cell recordings of miniature inhibitory and excitatory synaptic events in piriform cortex slices. We show that although 5 days after rule learning the cortical network maintains its basic activity patterns, synaptic connectivity is strengthened specifically between spatially proximal cells. Moreover, while the enhancement of inhibitory and excitatory synaptic connectivity is nearly identical, strengthening of synaptic inhibition is equally distributed between neurons while synaptic excitation is particularly strengthened within a specific subgroup of cells. We suggest that memory for the acquired rule is stored mainly by strengthening excitatory synaptic connection between close pyramidal neurons and runaway synaptic activity arising from this change is prevented by a nonspecific enhancement of synaptic inhibition.

Aging Wiener-Khinchin Theorem

The Wiener-Khinchin theorem shows how the power spectrum of a stationary random signal I(t) is related to its correlation function ⟨I(t)I(t+τ)⟩. We consider nonstationary processes with the widely observed aging correlation function ⟨I(t)I(t+τ)⟩∼t(γ)ϕ(EA)(τ/t) and relate it to the sample spectrum. We formulate two aging Wiener-Khinchin theorems relating the power spectrum to the time- and ensemble-averaged correlation functions, discussing briefly the advantages of each. When the scaling function ϕ(EA)(x) exhibits a nonanalytical behavior in the vicinity of its small argument we obtain the aging 1/f-type of spectrum. We demonstrate our results with three examples: blinking quantum dots, single-file diffusion, and Brownian motion in a logarithmic potential, showing that our approach is valid for a wide range of physical mechanisms.

Asymptotic densities of ballistic Lévy walks

We propose an analytical method to determine the shape of density profiles in the asymptotic long-time limit for a broad class of coupled continuous-time random walks which operate in the ballistic regime. In particular, we show that different scenarios of performing a random-walk step, via making an instantaneous jump penalized by a proper waiting time or via moving with a constant speed, dramatically effect the corresponding propagators, despite the fact that the end points of the steps are identical. Furthermore, if the speed during each step of the random walk is itself a random variable, its distribution gets clearly reflected in the asymptotic density of random walkers. These features are in contrast with more standard nonballistic random walks.

Infinite densities for Lévy walks

Motion of particles in many systems exhibits a mixture between periods of random diffusive-like events and ballistic-like motion. In many cases, such systems exhibit strong anomalous diffusion, where low-order moments 〈|x(t)|(q)〉 with q below a critical value q(c) exhibit diffusive scaling while for q>q(c) a ballistic scaling emerges. The mixed dynamics constitutes a theoretical challenge since it does not fall into a unique category of motion, e.g., the known diffusion equations and central limit theorems fail to describe both aspects. In this paper we resolve this problem by resorting to the concept of infinite density. Using the widely applicable Lévy walk model, we find a general expression for the corresponding non-normalized density which is fully determined by the particles velocity distribution, the anomalous diffusion exponent α, and the diffusion coefficient K(α). We explain how infinite densities play a central role in the description of dynamics of a large class of physical processes and discuss how they can be evaluated from experimental or numerical data.

Learning-induced modulation of the GABAB-mediated inhibitory synaptic transmission: mechanisms and functional significance

Complex olfactory-discrimination (OD) learning results in a series of intrinsic and excitatory synaptic modifications in piriform cortex pyramidal neurons that enhance the circuit excitability. Such overexcitation must be balanced to prevent runway activity while maintaining the efficient ability to store memories. We showed previously that OD learning is accompanied by enhancement of the GABAA-mediated inhibition. Here we show that GABAB-mediated inhibition is also enhanced after learning and study the mechanism underlying such enhancement and explore its functional role. We show that presynaptic, GABAB-mediated synaptic inhibition is enhanced after learning. In contrast, the population-average postsynaptic GABAB-mediated synaptic inhibition is unchanged, but its standard deviation is enhanced. Learning-induced reduction in paired pulse facilitation in the glutamatergic synapses interconnecting pyramidal neurons was abolished by application of the GABAB antagonist CGP55845 but not by blocking G protein-gated inwardly rectifying potassium channels only, indicating enhanced suppression of excitatory synaptic release via presynaptic GABAB-receptor activation. In addition, the correlation between the strengths of the early (GABAA-mediated) and late (GABAB-mediated) synaptic inhibition was much stronger for each particular neuron after learning. Consequently, GABAB-mediated inhibition was also more efficient in controlling epileptic-like activity induced by blocking GABAA receptors. We suggest that complex OD learning is accompanied by enhancement of the GABAB-mediated inhibition that enables the cortical network to store memories, while preventing uncontrolled activity.

Occupation times on a comb with ramified teeth

We investigate occupation time statistics for random walks on a comb with ramified teeth. This is achieved through the relation between the occupation time and the first passage times. Statistics of occupation times in half space follows Lamperti's distribution, i.e., the generalized arcsine law holds. Transitions between different behaviors are observed, which are controlled by the size of the backbone and teeth of the comb, as well as bias. Occupation time on a nonsimply connected domain is analyzed with a mean-field theory and numerical simulations. In that case, the generalized arcsine law is not valid.

Everlasting effect of initial conditions on single-file diffusion

We study the dynamics of a tagged particle in an environment of point Brownian particles with hard-core interactions in an infinite one-dimensional channel (a single-file model). In particular, we examine the influence of initial conditions on the dynamics of the tagged particle. We compare two initial conditions: equal distances between particles and uniform density distribution. The effect is shown by the differences of mean-square-displacement and correlation function for the two ensembles of initial conditions. We discuss the violation of Einstein relation, and its dependence on the initial condition, and the difference between time and ensemble averaging. More specifically, using the Jepsen line, we will discuss how transport coefficients, like diffusivity, depend on the initial state. Our work shows that initial conditions determine the long time limit of the dynamics, and in this sense the system never forgets its initial state in complete contrast with thermal systems (i.e., a closed system that attains equilibrium independent of the initial state).

Differential modifications of synaptic weights during odor rule learning: dynamics of interaction between the piriform cortex with lower and higher brain areas

Learning of a complex olfactory discrimination (OD) task results in acquisition of rule learning after prolonged training. Previously, we demonstrated enhanced synaptic connectivity between the piriform cortex (PC) and its ascending and descending inputs from the olfactory bulb (OB) and orbitofrontal cortex (OFC) following OD rule learning. Here, using recordings of evoked field postsynaptic potentials in behaving animals, we examined the dynamics by which these synaptic pathways are modified during rule acquisition. We show profound differences in synaptic connectivity modulation between the 2 input sources. During rule acquisition, the ascending synaptic connectivity from the OB to the anterior and posterior PC is simultaneously enhanced. Furthermore, post-training stimulation of the OB enhanced learning rate dramatically. In sharp contrast, the synaptic input in the descending pathway from the OFC was significantly reduced until training completion. Once rule learning was established, the strength of synaptic connectivity in the 2 pathways resumed its pretraining values. We suggest that acquisition of olfactory rule learning requires a transient enhancement of ascending inputs to the PC, synchronized with a parallel decrease in the descending inputs. This combined short-lived modulation enables the PC network to reorganize in a manner that enables it to first acquire and then maintain the rule.

No-go theorem for ergodicity and an Einstein relation

We provide a simple no-go theorem for ergodicity and the generalized Einstein relation for anomalous diffusion processes. The theorem states that either ergodicity in the sense of equal time and ensemble averaged mean squared displacements (MSD) is broken, and/or the generalized Einstein relation for time averaged diffusivity and mobility is invalid, which is in complete contrast to normal diffusion processes. We also give a general relation for the time averages of drift and MSD for ergodic (in the MSD sense) anomalous diffusion processes, showing that the ratio of these quantities depends on the measurement time. The Lévy walk model is used to exemplify the no-go theorem.

Weak subordination breaking for the quenched trap model

We map the problem of diffusion in the quenched trap model onto a different stochastic process: Brownian motion that is terminated at the coverage time S(α)=∑(x=-∞)(∞)(n(x))(α), with n(x) being the number of visits to site x. Here 0<α=T/T(g)<1 is a measure of the disorder in the original model. This mapping allows us to treat the intricate correlations in the underlying random walk in the random environment. The operational time S(α) is changed to laboratory time t with a Lévy time transformation. Investigation of Brownian motion stopped at time S(α) yields the diffusion front of the quenched trap model, which is favorably compared with numerical simulations. In the zero-temperature limit of α→0 we recover the renormalization group solution obtained by Monthus [Phys. Rev. E 68, 036114 (2003)]. Our theory surmounts the critical slowing down that is found when α→1. Above the critical dimension 2, mapping the problem to a continuous time random walk becomes feasible, though still not trivial.

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and we support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the superaging behavior.

Mechanisms underlying rule learning-induced enhancement of excitatory and inhibitory synaptic transmission

Training rats to perform rapidly and efficiently in an olfactory discrimination task results in robust enhancement of excitatory and inhibitory synaptic connectivity in the rat piriform cortex, which is maintained for days after training. To explore the mechanisms by which such synaptic enhancement occurs, we recorded spontaneous miniature excitatory and inhibitory synaptic events in identified piriform cortex neurons from odor-trained, pseudo-trained, and naive rats. We show that olfactory discrimination learning induces profound enhancement in the averaged amplitude of AMPA receptor-mediated miniature synaptic events in piriform cortex pyramidal neurons. Such physiological modifications are apparent at least 4 days after learning completion and outlast learning-induced modifications in the number of spines on these neurons. Also, the averaged amplitude of GABAA receptor-mediated miniature inhibitory synaptic events was significantly enhanced following odor discrimination training. For both excitatory and inhibitory transmission, an increase in miniature postsynaptic current amplitude was evident in most of the recorded neurons; however, some neurons showed an exceptionally great increase in the amplitude of miniature events. For both excitatory and inhibitory transmission, the frequency of spontaneous synaptic events was not modified after learning. These results suggest that olfactory discrimination learning-induced enhancement of synaptic transmission in cortical neurons is mediated by postsynaptic modulation of AMPA receptor-dependent currents and balanced by long-lasting modulation of postsynaptic GABAA receptor-mediated currents.

Infinite invariant density determines statistics of time averages for weak chaos

Weakly chaotic nonlinear maps with marginal fixed points have an infinite invariant measure. Time averages of integrable and nonintegrable observables remain random even in the long time limit. Temporal averages of integrable observables are described by the Aaronson-Darling-Kac theorem. We find the distribution of time averages of nonintegrable observables, for example, the time average position of the particle, x[over ¯]. We show how this distribution is related to the infinite invariant density. We establish four identities between amplitude ratios controlling the statistics of the problem.

Fluctuations of time averages for Langevin dynamics in a binding force field

We derive a simple formula for the fluctuations of the time average x(t) around the thermal mean <x>(eq) for overdamped brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, Schulten, and Schulten in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large nonergodic fluctuations and show how they are related to a superaging correlation function.

Residence time statistics for N renewal processes

We present a study of residence time statistics for N renewal processes with a long tailed distribution of the waiting time. Such processes describe many nonequilibrium systems ranging from the intensity of N blinking quantum dots to the residence time of N Brownian particles. With numerical simulations and exact calculations, we show sharp transitions for a critical number of degrees of freedom N. In contrast to the expectation, the fluctuations in the limit of N→∞ are nontrivial. We briefly discuss how our approach can be used to detect nonergodic kinetics from the measurements of many blinking chromophores, without the need to reach the single molecule limit.

Olfactory learning-induced enhancement of the predisposition for LTP induction

Learning of a particularly difficult olfactory-discrimination (OD) task results in acquisition of rule learning. This enhancement in learning capability is accompanied by the long-term enhancement of synaptic connectivity between piriform cortex pyramidal neurons. In this study we examined whether olfactory rule learning would modify the predisposition to induce long-term potentiation (LTP) in the pathway projecting from the piriform cortex to the olfactory bulb. We report that OD learning was associated with enhancement in the predisposition to induce LTP. This learning-related effect may be affected by process generation of new granule cells located in the olfactory bulb.

Time transformation for random walks in the quenched trap model

We investigate subdiffusion in the quenched trap model by mapping the problem onto a new stochastic process: Brownian motion stopped at the operational time S(α) = ∑(x=-∞)(∞) (n(x))(α) where n(x) is the visitation number at site x and α is a measure of the disorder. In the limit of zero temperature we recover the renormalization group solution found by Monthus. Our approach is an alternative to the renormalization group and is capable of dealing with any disorder strength.

Diffusion of tagged particle in an exclusion process

We study the diffusion of tagged hard-core interacting Brownian point particles under the influence of an external force field in one dimension. Using the Jepsen line we map this many-particle problem onto a single particle one. We obtain general equations for the distribution and the mean-square displacement <(xT)2> of the tagged center particle valid for rather general external force fields and initial conditions. The case of symmetric distribution of initial conditions around the initial position of the tagged particle on x=0 and symmetric potential fields V(x)=V(-x) yields zero drift <xT>=0 and is investigated in detail. We find <(xT)2>=R(1-R)/2Nr2 where 2N is the (large) number of particles in the system. R is a single particle reflection coefficient, i.e., the probability that a particle free of collisions starts on x0>0 and remains in x>0 while r is the probability density of noninteracting particles on the origin. We show that this equation is related to the mathematical theory of order statistics and it can be used to find <(xT)2> even when the motion between collision events is not Brownian (e.g., it might be ballistic or anomalous diffusion). As an example we derive the Percus relation for non-Gaussian diffusion. A wide range of physical behaviors emerge which are very different than the classical single file subdiffusion <(xT)2> approximately t1/2 found for uniformly distributed particles in an infinite space and in the absence of force fields.

Olfactory-learning abilities are correlated with the rate by which intrinsic neuronal excitability is modulated in the piriform cortex

Long-lasting modulation of intrinsic neuronal excitability in cortical neurons underlies distinct stages of skill learning. However, whether individual differences in learning capabilities are dependent on the rate by which such learning-induced modifications occur has yet to be explored. Here we show that training rats in a simple olfactory-discrimination task results in the same enhanced excitability in piriform cortex neurons as previously shown after training in a much more complex olfactory-discrimination task. Based on their learning capabilities in the simple task, rats could be divided to two groups: fast performers and slow performers. The rate at which rats accomplished the skill to perform the simple task was correlated with the time course at which piriform cortex neurons increased their repetitive spike firing. Twelve hours after learning, neurons from fast performers had reduced spike frequency adaptation as compared with neurons from slow performers and controls. Three days after learning, spike frequency adaptation was reduced in neurons from SP, while neurons from fast performers increased their spike firing adaptation to the level of controls. Accordingly, the post-burst AHP was reduced in neurons from fast performers 12 h after learning and in neurons from slow performers 3 days after learning. Moreover, the differences in learning capabilities between fast performers and slow performers were maintained when examined in a different, complex olfactory-discrimination task. We suggest that the rate at which neuronal excitability is modified during learning may affect the behavioral flexibility of the animal.

Multiplicative noise induces zero critical frequency

Stochastic Bloch equations which model the fluorescence of two-level molecules and atoms, NMR experiments, and Josephson junctions are investigated to illustrate the profound effect of multiplicative noise on the critical frequency of a dynamical system. Using exact solutions and the cumulant expansion we find two main effects: (i) even very weak noise may double or triple the number of critical frequencies, which is related to an instability of the system, and (ii) strong multiplicative noise may induce a nontrivial zero critical frequency thus wiping out the overdamped phase.

Einstein relation and effective temperature for systems with quenched disorder

According to the Einstein relation the ratio between independent measurements of fluctuations (e.g., diffusivity) and the response to a weak external field (e.g., mobility) is equal to the thermal temperature when the system is kept close to thermal equilibrium. For strongly disordered systems, which are not self-averaging this ratio is a random variable and hence in this sense the Einstein relation is not valid. Thus effective temperatures found using the fluctuation dissipation ratio are at least in some cases stochastic variables. This scenario is tested with the quenched trap model. An average over an ensemble of systems yields an averaged effective temperature, which is compared with results obtained from the mean-field continuous-time random-walk model.

Transient anomalous diffusion of telomeres in the nucleus of mammalian cells

We measured individual trajectories of fluorescently labeled telomeres in the nucleus of eukaryotic cells in the time range of 10(-2)-10(4)sec by combining a few acquisition methods. At short times the motion is subdiffusive with r2 approximately talpha and it changes to normal diffusion at longer times. The short times diffusion may be explained by the reptation model and the transient diffusion is consistent with a model of telomeres that are subject to a local binding mechanism with a wide but finite distribution of waiting times. These findings have important biological implications with respect to the genome organization in the nucleus.