Neurobiology of Aging · Sep 2011
Robert D. Frisina, Ameet Singh, Matthew Bak, … Xiaoxia Zhu
Abstract
Age-related hearing loss - presbycusis - is the most common communication problem and third most prevalent chronic medical disorder of the aged. The CBA and C57BL/6 mouse strains are useful for studying features of presbycusis. The CBA loses its hearing slowly, like most humans. Because the C57 develops a rapid, high frequency hearing loss by middle age, it has an "old" ear but a relatively young brain, a model that helps separate peripheral (cochlear) from central (brain) etiologies. This field of sensory neuroscience lacks a good mouse model for the 5-10% of aged humans with normal cochlear sensitivity, but who have trouble perceiving speech in background noise. We hypothesized that F1 (CBA×C57) hybrids would have better hearing than either parental strain. Measurements of peripheral auditory sensitivity supported this hypothesis, however, a rapid decline in the auditory efferent feedback system, did not. Therefore, F1s might be an optimal model for studying cases where the peripheral hearing is quite good in old age; thereby allowing isolation of central auditory changes due to brain neurodegeneration.
The Journal of Neuroscience · Aug 2011
Richard A. Felix, Anders Fridberger, Sara Leijon, … Anna K. Magnusson
Abstract
The superior paraolivary nucleus (SPON) is a prominent structure in the auditory brainstem. In contrast to the principal superior olivary nuclei with identified roles in processing binaural sound localization cues, the role of the SPON in hearing is not well understood. A combined in vitro and in vivo approach was used to investigate the cellular properties of SPON neurons in the mouse. Patch-clamp recordings in brain slices revealed that brief and well timed postinhibitory rebound spiking, generated by the interaction of two subthreshold-activated ion currents, is a hallmark of SPON neurons. The I h current determines the timing of the rebound, whereas the T-type Ca 2+ current boosts the rebound to spike threshold. This precisely timed rebound spiking provides a physiological explanation for the sensitivity of SPON neurons to sinusoidally amplitude-modulated (SAM) tones in vivo , where peaks in the sound envelope drive inhibitory inputs and SPON neurons fire action potentials during the waveform troughs. Consistent with this notion, SPON neurons display intrinsic tuning to frequency-modulated sinusoidal currents (1–15Hz) in vitro and discharge with strong synchrony to SAMs with modulation frequencies between 1 and 20 Hz in vivo . The results of this study suggest that the SPON is particularly well suited to encode rhythmic sound patterns. Such temporal periodicity information is likely important for detection of communication cues, such as the acoustic envelopes of animal vocalizations and speech signals.
Cognitive Neurodynamics · Aug 2011
Yoshinori Ide, Takashi Miyazaki, Johan Lauwereyns, … Takeshi Aihara
Abstract
The plastic changes in the auditory cortex induced by a fear conditioning, through pairing a sound (CS) with an electric foot-shock (US), were investigated using an optical recording method with voltage sensitive dye, RH795. In order to investigate the effects of association learning, optical signals in the auditory cortex in response to CS (12 kHz pure tone) and non-CS (4, 8, 16 kHz pure tone) were recorded before and after normal and sham conditioning. As a result, the response area to CS enlarged only in the conditioning group after the conditioning. Additionally, the rise time constant of the auditory response to CS significantly decreased and the relative peak value and the decay time constant of the auditory response to CS significantly increased after the conditioning. This study introduces an optical approach to the investigation of fear conditioning, representational plasticity, and the cholinergic system. The findings are synthesized in a model of the synaptic mechanisms that underlie cortical plasticity.
Toxicological Sciences · Aug 2011
Emily Poon, Brian E. Powers, Ruth M. McAlonan, … Susan L. Schantz
Abstract
Developmental exposure to polychlorinated biphenyls (PCBs) causes hearing loss that may be due to reduced thyroxine during cochlear development. Polybrominated diphenyl ethers (PBDEs) are structurally similar to PCBs and reduce thyroxine. This study utilized an environmental PCB mixture and a commercial PBDE mixture, DE-71, that represents the PBDEs found in humans to assess the potential for additive effects of PCBs and PBDEs on cochlear function. Female Long-Evans rats were dosed with corn oil vehicle, PCBs (3 or 6 mg/kg), molar equivalent doses of PBDEs (5.7 or 11.4 mg/kg), 3 mg/kg PCBs + 5.7 mg/kg PBDEs, or 6 mg/kg PCBs + 11.4 mg/kg PBDEs throughout gestation and lactation. At weaning, pup blood was taken to assess thyroxine concentrations. One male and one female from each litter were maintained until adulthood for distortion product otoacoustic emission (DPOAE) measurements of cochlear function. DPOAE amplitudes were decreased and thresholds were elevated in the 6 mg/kg PCB group. Exposure to PBDEs did not cause DPOAE deficits. There was an interactive effect from combined exposure such that the individual low doses of PCBs and PBDEs did not result in DPOAE deficits, but the two combined produced a deficit similar to that in the high-dose PCB group. Serum thyroxine concentrations of all groups were reduced compared with controls, but PBDEs produced a less dramatic reduction than PCBs, which could explain the lack of DPOAE effects. Importantly, there was evidence that the co-exposure to subthreshold doses of PCBs and PBDEs can have an additive effect on cochlear function.
The Journal of Neuroscience · Aug 2011
Katherine A. Steigelman, Andrea Lelli, Xudong Wu, … Jian Zuo
Abstract
The polycystic kidney disease-1 ( Pkd1 ) gene encodes a large transmembrane protein (polycystin-1, or PC-1) that is reported to function as a fluid flow sensor in the kidney. As a member of the transient receptor potential family, PC-1 has also been hypothesized to play a role in the elusive mechanoelectrical transduction (MET) channel in inner ear hair cells. Here, we analyze two independent mouse models of PC-1, a knock-in (KI) mutant line and a hair cell-specific inducible Cre-mediated knock-out line. Both models exhibit normal MET channel function at neonatal ages despite hearing loss and ultrastructural abnormalities of sterecilia that remain properly polarized at adult ages. These findings demonstrate that PC-1 plays an essential role in stereocilia structure and maintenance but not directly in MET channel function or planar cell polarity. We also demonstrate that PC-1 is colocalized with F-actin in hair cell stereocilia in vivo , using a hemagglutinin-tagged PC-1 KI mouse model, and in renal epithelial cell microvilli in vitro . These results not only demonstrate a novel role for PC-1 in the cochlea, but also suggest insight into the development of polycystic kidney disease.
PLoS ONE · Aug 2011
Giulia Crispino, Giovanni Di Pasquale, Pietro Scimemi, … Fabio Mammano
Abstract
The deafness locus DFNB1 contains GJB2, the gene encoding connexin26 and GJB6, encoding connexin30, which appear to be coordinately regulated in the inner ear. In this work, we investigated the expression and function of connexin26 and connexin30 from postnatal day 5 to adult age in double transgenic Cx26(Sox10Cre) mice, which we obtained by crossing connexin26 floxed mice with a deleter Sox10-Cre line. Cx26(Sox10Cre) mice presented with complete connexin26 ablation in the epithelial gap junction network of the cochlea, whereas connexin30 expression was developmentally delayed; immunolabeling patterns for both connexins were normal in the cochlear lateral wall. In vivo electrophysiological measurements in Cx26(Sox10Cre) mice revealed profound hearing loss accompanied by reduction of endocochlear potential, and functional experiments performed in postnatal cochlear organotypic cultures showed impaired gap junction coupling. Transduction of these cultures with a bovine adeno associated virus vector restored connexin26 protein expression and rescued gap junction coupling. These results suggest that restoration of normal connexin levels by gene delivery via recombinant adeno associated virus could be a way to rescue hearing function in DFNB1 mouse models and, in future, lead to the development of therapeutic interventions in humans.
Physiological Research · Aug 2011
Y. ZHANG, L. HAN, X. XIAO, … Y. XIONG
Abstract
Spontaneous activity of cortical neurons exhibits alternative fluctuations of membrane potential consisting of phased depolarization called "up-state" and persistent hyperpolarization called "down-state" during slow wave sleep and anesthesia. Here, we examined the effects of sound stimuli (noise bursts) on neuronal activity by intracellular recording in vivo from the rat auditory cortex (AC). Noise bursts increased the average time in the up-state by 0.81±0.65 s (range, 0.27-1.74 s) related to a 10 s recording duration. The rise times of the spontaneous up-events averaged 69.41±18.04 ms (range, 40.10-119.21 ms), while those of the sound-evoked up-events were significantly shorter (p<0.001) averaging only 22.54±8.81 ms (range, 9.31-45.74 ms). Sound stimulation did not influence ongoing spontaneous up-events. Our data suggest that a sound stimulus does not interfere with ongoing spontaneous neuronal activity in auditory cortex but can evoke new depolarizations in addition to the spontaneous ones.
Journal of Experimental Biology · Aug 2011
Eric Parmentier, Kenneth Mann, David Mann
Abstract
The air-filled swimbladder acts as an acoustic amplifier for some fish by converting sound pressure into particle motion, which is transmitted to the inner ear. Here, we describe in detail the specialized connection between the swimbladder and ear in the mojarra, as well as a modified cone on the anal fin in which the posterior end of the swimbladder sits. Hearing tests show the mojarra has better hearing sensitivity than other species of fish without a connection. However, mojarras do not seem to use this adaptation for communication. Furthermore, the inclined position of the swimbladder may help the fish to catch their prey more easily, as the swimbladder will be horizontal when they are picking up benthic prey.
PLoS ONE · Aug 2011
Nevo Taaseh, Amit Yaron, Israel Nelken
Abstract
Stimulus-specific adaptation (SSA) is the specific decrease in the response to a frequent ('standard') stimulus, which does not generalize, or generalizes only partially, to another, rare stimulus ('deviant'). Stimulus-specific adaptation could result simply from the depression of the responses to the standard. Alternatively, there may be an increase in the responses to the deviant stimulus due to the violation of expectations set by the standard, indicating the presence of true deviance detection. We studied SSA in the auditory cortex of halothane-anesthetized rats, recording local field potentials and multi-unit activity. We tested the responses to pure tones of one frequency when embedded in sequences that differed from each other in the frequency and probability of the tones composing them. The responses to tones of the same frequency were larger when deviant than when standard, even with inter-stimulus time intervals of almost 2 seconds. Thus, SSA is present and strong in rat auditory cortex. SSA was present even when the frequency difference between deviants and standards was as small as 10%, substantially smaller than the typical width of cortical tuning curves, revealing hyper-resolution in frequency. Strong responses were evoked also by a rare tone presented by itself, and by rare tones presented as part of a sequence of many widely spaced frequencies. On the other hand, when presented within a sequence of narrowly spaced frequencies, the responses to a tone, even when rare, were smaller. A model of SSA that included only adaptation of the responses in narrow frequency channels predicted responses to the deviants that were substantially smaller than the observed ones. Thus, the response to a deviant is at least partially due to the change it represents relative to the regularity set by the standard tone, indicating the presence of true deviance detection in rat auditory cortex.
PLoS ONE · Aug 2011
Jose A. Garcia-Lazaro, Bashir Ahmed, Jan W. H. Schnupp
Abstract
We have previously shown that neurons in primary auditory cortex (A1) of anaesthetized (ketamine/medetomidine) ferrets respond more strongly and reliably to dynamic stimuli whose statistics follow "natural" 1/f dynamics than to stimuli exhibiting pitch and amplitude modulations that are faster (1/f(0.5)) or slower (1/f(2)) than 1/f. To investigate where along the central auditory pathway this 1/f-modulation tuning arises, we have now characterized responses of neurons in the central nucleus of the inferior colliculus (ICC) and the ventral division of the mediate geniculate nucleus of the thalamus (MGV) to 1/f(γ) distributed stimuli with γ varying between 0.5 and 2.8. We found that, while the great majority of neurons recorded from the ICC showed a strong preference for the most rapidly varying (1/f(0.5) distributed) stimuli, responses from MGV neurons did not exhibit marked or systematic preferences for any particular γ exponent. Only in A1 did a majority of neurons respond with higher firing rates to stimuli in which γ takes values near 1. These results indicate that 1/f tuning emerges at forebrain levels of the ascending auditory pathway.
PLoS ONE · Aug 2011
Rosalyn J. Moran, Fabienne Jung, Tetsuya Kumagai, … Marc Tittgemeyer
Abstract
Generative models of neuroimaging and electrophysiological data present new opportunities for accessing hidden or latent brain states. Dynamic causal modeling (DCM) uses Bayesian model inversion and selection to infer the synaptic mechanisms underlying empirically observed brain responses. DCM for electrophysiological data, in particular, aims to estimate the relative strength of synaptic transmission at different cell types and via specific neurotransmitters. Here, we report a DCM validation study concerning inference on excitatory and inhibitory synaptic transmission, using different doses of a volatile anaesthetic agent (isoflurane) to parametrically modify excitatory and inhibitory synaptic processing while recording local field potentials (LFPs) from primary auditory cortex (A1) and the posterior auditory field (PAF) in the auditory belt region in rodents. We test whether DCM can infer, from the LFP measurements, the expected drug-induced changes in synaptic transmission mediated via fast ionotropic receptors; i.e., excitatory (glutamatergic) AMPA and inhibitory GABA(A) receptors. Cross- and auto-spectra from the two regions were used to optimise three DCMs based on biologically plausible neural mass models and specific network architectures. Consistent with known extrinsic connectivity patterns in sensory hierarchies, we found that a model comprising forward connections from A1 to PAF and backward connections from PAF to A1 outperformed a model with forward connections from PAF to A1 and backward connections from A1 to PAF and a model with reciprocal lateral connections. The parameter estimates from the most plausible model indicated that the amplitude of fast glutamatergic excitatory postsynaptic potentials (EPSPs) and inhibitory postsynaptic potentials (IPSPs) behaved as predicted by previous neurophysiological studies. Specifically, with increasing levels of anaesthesia, glutamatergic EPSPs decreased linearly, whereas fast GABAergic IPSPs displayed a nonlinear (saturating) increase. The consistency of our model-based in vivo results with experimental in vitro results lends further validity to the capacity of DCM to infer on synaptic processes using macroscopic neurophysiological data.
The Journal of the Acoustical Society of America · Aug 2011
Carol L. Mackersie, James Dewey, Lesli A. Guthrie
Abstract
The purpose was to determine the effect of hearing loss on the ability to separate competing talkers using talker differences in fundamental frequency (F0) and apparent vocal-tract length (VTL). Performance of 13 adults with hearing loss and 6 adults with normal hearing was measured using the Coordinate Response Measure. For listeners with hearing loss, the speech was amplified and filtered according to the NAL-RP hearing aid prescription. Target-to-competition ratios varied from 0 to 9 dB. The target sentence was randomly assigned to the higher or lower values of F0 or VTL on each trial. Performance improved for F0 differences up to 9 and 6 semitones for people with normal hearing and hearing loss, respectively, but only when the target talker had the higher F0. Recognition for the lower F0 target improved when trial-to-trial uncertainty was removed (9-semitone condition). Scores improved with increasing differences in VTL for the normal-hearing group. On average, hearing-impaired listeners did not benefit from VTL cues, but substantial inter-subject variability was observed. The amount of benefit from VTL cues was related to the average hearing loss in the 1–3-kHz region when the target talker had the shorter VTL.
The Journal of the Acoustical Society of America · Aug 2011
Jing Xia, Barbara Shinn-Cunningham
Abstract
This study tests how peripheral auditory processing and spectral dominance impact lateralization of precedence effect (PE) stimuli consisting of a pair of leading and lagging clicks. Predictions from a model whose parameters were set from established physiological results were tested with specific behavioral experiments. To generate predictions, an auditory nerve model drove a binaural, cross correlation computation whose outputs were summed across frequency using weightings derived from past physiological studies. The model predicted that lateralization (1) depends on stimulus center frequency and the inter-stimulus delay (ISD) between leading and lagging clicks for narrowband clicks and (2) changes differently with lead click level for different ISDs. Behaviorally, subjects lateralized narrowband and wideband click pairs whose stimulus parameters were chosen based on modeling results to test how peripheral processing and frequency dominance contribute to lateralization of PE stimuli. Behavioral results (including unique measures with the lead attenuated relative to the lag) suggest that peripheral interactions between leading and lagging clicks on the basilar membrane and strong weighting of cues around 750 Hz influence lateralization of paired clicks with short ISDs. When combined with auditory nerve adaptation, which emphasizes onset information, lateralization of PE click pairs with a short ISD can be well predicted.
Neuroscience · Aug 2011
J. Lu, E. Lobarinas, A. Deng, … W. Sun
Abstract
Although high doses of sodium salicylate impair cochlear function, it paradoxically enhances sound-evoked activity in the auditory cortex (AC) and augments acoustic startle reflex responses, neural and behavioral metrics associated with hyperexcitability and hyperacusis. To explore the neural mechanisms underlying salicylate (SS)-induced hyperexcitability and "increased central gain," we examined the effects of GABA receptor agonists and antagonists on SS-induced hyperexcitability in the AC and startle reflex responses. Consistent with our previous findings, local or systemic application of SS significantly increased the amplitude of sound-evoked AC neural activity, but generally reduced spontaneous activity in the AC. Systemic injection of SS also significantly increased the acoustic startle reflex. S-baclofen or R-baclofen, GABA-B agonists, which suppressed sound-evoked AC neural firing rate and local field potentials, also suppressed the SS-induced enhancement of the AC field potential and the acoustic startle reflex. Local application of vigabatrin, which enhances GABA concentration in the brain, suppressed the SS-induced enhancement of AC firing rate. Systemic injection of vigabatrin also reduced the SS-induced enhancement of acoustic startle reflex. Collectively, these results suggest that the sound-evoked behavioral and neural hyperactivity induced by SS may arise from a SS-induced suppression of GABAergic inhibition in the AC.
Journal of Neurophysiology · Aug 2011
Sean J. Slee, Eric D. Young
Abstract
Previous studies have demonstrated that single neurons in the central nucleus of the inferior colliculus (ICC) are sensitive to multiple sound localization cues. We investigated the hypothesis that ICC neurons are specialized to encode multiple sound localization cues that are aligned in space (as would naturally occur from a single broadband sound source). Sound localization cues including interaural time differences (ITDs), interaural level differences (ILDs), and spectral shapes (SSs) were measured in a marmoset monkey. Virtual space methods were used to generate stimuli with aligned and misaligned combinations of cues while recording in the ICC of the same monkey. Mutual information (MI) between spike rates and stimuli for aligned versus misaligned cues were compared. Neurons with best frequencies (BFs) less than ∼11 kHz mostly encoded information about a single sound localization cue, ITD or ILD depending on frequency, consistent with the dominance of ear acoustics by either ITD or ILD at those frequencies. Most neurons with BFs >11 kHz encoded information about multiple sound localization cues, usually ILD and SS, and were sensitive to their alignment. In some neurons MI between stimuli and spike responses was greater for aligned cues, while in others it was greater for misaligned cues. If SS cues were shifted to lower frequencies in the virtual space stimuli, a similar result was found for neurons with BFs <11 kHz, showing that the cue interaction reflects the spectra of the stimuli and not a specialization for representing SS cues. In general the results show that ICC neurons are sensitive to multiple localization cues if they are simultaneously present in the frequency response area of the neuron. However, the representation is diffuse in that there is not a specialization in the ICC for encoding aligned sound localization cues.
Neuroscience Research · Aug 2011
Yoshinao Kajikawa, Corrie R. Camalier, Lisa A. de la Mothe, … Troy A. Hackett
Abstract
We examined multiunit responses to tones and to 1/3 and 2/3 octave band-pass noise (BPN) in the marmoset primary auditory cortex (A1) and the caudomedial belt (CM). In both areas, BPN was more effective than tones, evoking multiunit responses at lower intensity and across a wider frequency range. Typically, the best responses to BPN remained at the characteristic frequency. Additionally, in both areas responses to BPN tended to be of greater magnitude and shorter latency than responses to tones. These effects are consistent with the integration of more excitatory inputs driven by BPN than by tones. While it is generally thought that single units in A1 prefer narrow band sounds such as tones, we found that best responses for multi units in both A1 and CM were obtained with noises of narrow spectral bandwidths.
Nature Neuroscience · Jul 2011
Tania Rinaldi Barkat, Daniel B Polley, Takao K Hensch
Abstract
Neural circuits are shaped by experience during periods of heightened brain plasticity in early postnatal life. Exposure to acoustic features produces age-dependent changes through largely unresolved cellular mechanisms and sites of origin. We isolated the refinement of auditory thalamocortical connectivity by in vivo recordings and day-by-day voltage-sensitive dye imaging in an acute brain slice preparation. Passive tone-rearing modified response strength and topography in mouse primary auditory cortex (A1) during a brief, 3-d window, but did not alter tonotopic maps in the thalamus. Gene-targeted deletion of a forebrain-specific cell-adhesion molecule (Icam5) accelerated plasticity in this critical period. Consistent with its normal role of slowing spinogenesis, loss of Icam5 induced precocious stubby spine maturation on pyramidal cell dendrites in neocortical layer 4 (L4), identifying a primary locus of change for the tonotopic plasticity. The evolving postnatal connectivity between thalamus and cortex in the days following hearing onset may therefore determine a critical period for auditory processing.
International Journal of Developmental Neuroscience · Jul 2011
C.A. Hill, S.W. Threlkeld, R.H. Fitch
Abstract
Hypoxia ischemia (HI; reduced blood oxygenation and/or flow to the brain) represents one of the most common injuries for both term and preterm/very low birth weight (VLBW) infants. These children experience elevated incidence of cognitive and/or sensory processing disabilities, including language based learning disabilities. Clinical data also indicate more substantial long‐term deficits for HI injured male babies as compared to HI injured females. Previously, we reported significant deficits in rapid auditory processing and spatial learning in male rats with postnatal day 1 (P1), P7, or P10 HI injury. We also showed sex differences in HI injured animals, with more severe deficits in males as compared to females. Given these findings, combined with extant clinical data, the current study sought to assess a putative role for perinatal testosterone in modulating behavioral outcome following early hypoxic‐ischemic injury in rats. Male, female, and testosterone‐propionate (TP) treated females were subjected to P7 HI or sham surgery, and subsequently (P30+) underwent a battery of auditory testing and water maze assessment. Results confirm previous reports of sex differences following HI, and add new findings of significantly worse performance in TP‐treated HI females compared to vehicle treated HI females. Post mortem anatomic analyses showed consistent effects, with significant brain weight decreases seen in HI male and TP‐treated HI females but not female HI or sham groups. Further neuromorphometric analysis of brain structures showed that HI male animals exhibited increased pathology relative to HI females as reflected in ventricular enlargement. Findings suggest that neonatal testosterone may act to enhance the deleterious consequences of early HI brain injury, as measured by both neuropathology and behavior.
Journal of Neuroscience · Jul 2011
L. Khouri, N. A. Lesica, B. Grothe
Abstract
Aged humans show severe difficulties in temporal auditory processing tasks (e.g., speech recognition in noise, low-frequency sound localization, gap detection). A degradation of auditory function with age is also evident in experimental animals. To investigate age-related changes in temporal processing, we compared extracellular responses to temporally variable pulse trains and human speech in the inferior colliculus of young adult (3 month) and aged (3 years) Mongolian gerbils. We observed a significant decrease of selectivity to the pulse trains in neuronal responses from aged animals. This decrease in selectivity led, on the population level, to an increase in signal correlations and therefore a decrease in heterogeneity of temporal receptive fields and a decreased efficiency in encoding of speech signals. A decrease in selectivity to temporal modulations is consistent with a downregulation of the inhibitory transmitter system in aged animals. These alterations in temporal processing could underlie declines in the aging auditory system, which are unrelated to peripheral hearing loss. These declines cannot be compensated by traditional hearing aids (that rely on amplification of sound) but may rather require pharmacological treatment.
The Journal of The Acoustical Society of America · Jul 2011
Daniel Fogerty
Abstract
Listeners often only have fragments of speech available to understand the intended message due to competing background noise. In order to maximize successful speech recognition, listeners must allocate their perceptual resources to the most informative acoustic properties. The speech signal contains temporally-varying acoustics in the envelope and fine structure that are present across the frequency spectrum. Understanding how listeners perceptually weigh these acoustic properties in different frequency regions during interrupted speech is essential for the design of assistive listening devices. This study measured the perceptual weighting of young normal-hearing listeners for the envelope and fine structure in each of three frequency bands for interrupted sentence materials. Perceptual weights were obtained during interruption at the syllabic rate (i.e., 4 Hz) and the periodic rate (i.e., 128 Hz) of speech. Potential interruption interactions with fundamental frequency information were investigated by shifting the natural pitch contour higher relative to the interruption rate. The availability of each acoustic property was varied independently by adding noise at different levels. Perceptual weights were determined by correlating a listener’s performance with the availability of each acoustic property on a trial-by-trial basis. Results demonstrated similar relative weights across the interruption conditions, with emphasis on the envelope in high-frequencies.