Cycle Histograms Research Articles

Second-order fatigue of intrinsic mean stress under random loadings

A fatigue process due to random loading that is progressively damaging a certain structural detail will vary in the presence of mean stresses. The variations are already considered in crack propagation laws and by applying equivalent 0-mean stress ranges from the Palmgren–Miner linear rule. Nevertheless, if the mean stress is intrinsic, instead of a direct consequence of the random loading, other second-order effects will have to be taken into account. Those effects are cycle quasi-ordering, histogram variations, and apparent mean tension, which are identified and defined in this study and, finally, developed in a case study for demonstrative purposes.

주파수 영역 피로해석에서 PSD 분석 방식 비교

If fatigue failure occurs during aircraft operation, it can cause catastrophic injuries. So, it is necessary to study fatigue failure at the design stage. Frequency domain fatigue analysis is used to predict fatigue failure. During frequency domain fatigue analysis, results can be calibrated by PSD analysis. In this study, fatigue failure is predicted by the Dirlik method, Lalanne method and Steinberg method. Regarding results, life determined by the Dirlik method, Lalanne method and Steinberg method were 8.737, 8.314, and 7.901 times the standard life, respectively. The Steinberg method is the most conservative but the difference with other methods was approximately 10%. In the cycle histogram, the Dirlik method had more counts than the Lalanne method in lower stress range. However, it does not affect the life of material used in this study. However, if material has a lower fatigue limit or stronger PSD data is used, life difference will occur.

Measuring DNA content in live cells by fluorescence microscopy

BackgroundLive-cell fluorescence microscopy (LCFM) is a powerful tool used to investigate cellular dynamics in real time. However, the capacity to simultaneously measure DNA content in cells being tracked over time remains challenged by dye-associated toxicities. The ability to measure DNA content in single cells by means of LCFM would allow cellular stage and ploidy to be coupled with a variety of imaging directed analyses. Here we describe a widely applicable nontoxic approach for measuring DNA content in live cells by fluorescence microscopy. This method relies on introducing a live-cell membrane-permeant DNA fluorophore, such as Hoechst 33342, into the culture medium of cells at the end of any live-cell imaging experiment and measuring each cell’s integrated nuclear fluorescence to quantify DNA content. Importantly, our method overcomes the toxicity and induction of DNA damage typically caused by live-cell dyes through strategic timing of adding the dye to the cultures; allowing unperturbed cells to be imaged for any interval of time before quantifying their DNA content. We assess the performance of our method empirically and discuss adaptations that can be implemented using this technique.ResultsPresented in conjunction with cells expressing a histone 2B-GFP fusion protein (H2B-GFP), we demonstrated how this method enabled chromosomal segregation errors to be tracked in cells as they progressed through cellular division that were later identified as either diploid or polyploid. We also describe and provide an automated Matlab-derived algorithm that measures the integrated nuclear fluorescence in each cell and subsequently plots these measurements into a cell cycle histogram for each frame imaged. The algorithm’s accurate assessment of DNA content was validated by parallel flow cytometric studies.ConclusionsThis method allows the examination of single-cell dynamics to be correlated with cellular stage and ploidy in a high-throughput fashion. The approach is suitable for any standard epifluorescence microscope equipped with a stable illumination source and either a stage-top incubator or an enclosed live-cell incubation chamber. Collectively, we anticipate that this method will allow high-resolution microscopic analysis of cellular processes involving cell cycle progression, such as checkpoint activation, DNA replication, and cellular division.

A Model-Based Approach for Separating the Cochlear Microphonic from the Auditory Nerve Neurophonic in the Ongoing Response Using Electrocochleography.

Electrocochleography (ECochG) is a potential clinically valuable technique for predicting speech perception outcomes in cochlear implant (CI) recipients, among other uses. Current analysis is limited by an inability to quantify hair cell and neural contributions which are mixed in the ongoing part of the response to low frequency tones. Here, we used a model based on source properties to account for recorded waveform shapes and to separate the combined signal into its components. The model for the cochlear microphonic (CM) was a sinusoid with parameters for independent saturation of the peaks and the troughs of the responses. The model for the auditory nerve neurophonic (ANN) was the convolution of a unit potential and population cycle histogram with a parameter for spread of excitation. Phases of the ANN and CM were additional parameters. The average cycle from the ongoing response was the input, and adaptive fitting identified CM and ANN parameters that best reproduced the waveform shape. Test datasets were responses recorded from the round windows of CI recipients, from the round window of gerbils before and after application of neurotoxins, and with simulated signals where each parameter could be manipulated in isolation. Waveforms recorded from 284 CI recipients had a variety of morphologies that the model fit with an average r2 of 0.97 ± 0.058 (standard deviation). With simulated signals, small systematic differences between outputs and inputs were seen with some variable combinations, but in general there were limited interactions among the parameters. In gerbils, the CM reported was relatively unaffected by the neurotoxins. In contrast, the ANN was strongly reduced and the reduction was limited to frequencies of 1,000 Hz and lower, consistent with the range of strong neural phase-locking. Across human CI subjects, the ANN contribution was variable, ranging from nearly none to larger than the CM. Development of this model could provide a means to isolate hair cell and neural activity that are mixed in the ongoing response to low-frequency tones. This tool can help characterize the residual physiology across CI subjects, and can be useful in other clinical settings where a description of the cochlear physiology is desirable.

Long term simulation of wind-induced fatigue loadings

This paper deals with the fatigue analysis of slender structures subjected to the wind action. A 50-year conditioned Monte Carlo simulation of the bending moment at the base of a steel lighting pole is performed. Long-term simulations of the static part of the bending moment, related to the mean wind speed, are combined with short-term fluctuations due to the turbulence. Multiple time series of the stress at the base of the pole, with length ranging between 10min and 3days, are generated and processed by means of the Rainflow counting algorithm. The resulting large size data set of the fatigue damage is analyzed in order to clarify some cloudy issues related to the fatigue analysis: the contribution to the damage of the low-frequency, large-amplitude cycles in the stress-time series; the contribution of the transition cycles between consecutive wind states; the length of the stress-time series necessary to get a reliable stress cycle histogram in the framework of the classical state approach; the variability of the damage resulting from a given mean wind speed; the variability of the annual damage.

Analysis of Chaotic Resonance in Izhikevich Neuron Model.

In stochastic resonance (SR), the presence of noise helps a nonlinear system amplify a weak (sub-threshold) signal. Chaotic resonance (CR) is a phenomenon similar to SR but without stochastic noise, which has been observed in neural systems. However, no study to date has investigated and compared the characteristics and performance of the signal responses of a spiking neural system in some chaotic states in CR. In this paper, we focus on the Izhikevich neuron model, which can reproduce major spike patterns that have been experimentally observed. We examine and classify the chaotic characteristics of this model by using Lyapunov exponents with a saltation matrix and Poincaré section methods in order to address the measurement challenge posed by the state-dependent jump in the resetting process. We found the existence of two distinctive states, a chaotic state involving primarily turbulent movement and an intermittent chaotic state. In order to assess the signal responses of CR in these classified states, we introduced an extended Izhikevich neuron model by considering weak periodic signals, and defined the cycle histogram of neuron spikes as well as the corresponding mutual correlation and information. Through computer simulations, we confirmed that both chaotic states in CR can sensitively respond to weak signals. Moreover, we found that the intermittent chaotic state exhibited a prompter response than the chaotic state with primarily turbulent movement.

Fatigue Life from Sine-on-random Excitations

This presentation concentrates on calculating the high cycle fatigue life from sine-on-random excitations. A spectral domain approach offers advantages over the time domain approach when computation times are prohibitive.The proposed approach is to derive the statistical rainflow cycle histogram from a sine-on-random spectrum of stress data and then to use the appropriate material fatigue curve to obtain the estimated life.A case study illustrates the application of the method on a component attached to a helicopter. Comparisons with traditional time-domain approaches are presented and show excellent agreement.

Temporal Nature of Fatigue Damage in Highway Bridges

To develop a valid method of estimating fatigue life of a highway bridge, it is first necessary to have a reasonable understanding of the manner in which fatigue damage occurs over time. This paper presents the findings from an extensive highway bridge monitoring program focused on monitoring vehicle-induced strain cycles; the cause of fatigue damage. The purpose of the study was to identify the temporal character (if any) of fatigue damage accumulation. A sample of 24 bridges in the State of Ohio was monitored; each bridge in the sample for 1year. The data collected during the study captured hourly, daily, and monthly variation in fatigue damage accumulation. The raw data were resolved to a fatigue damage metric representation. The damage metric was analyzed with the intent of determining the temporal nature of fatigue damage accumulation. The analyses led to the development of postulates regarding fatigue damage in highway bridges. The postulates stated in this study should provide a sound basis for development of a fatigue-life estimation procedure using site-specific strain cycle histograms collected over an abbreviated time window.

C/EBPβ Promotes Transition from Proliferation to Hypertrophic Differentiation of Chondrocytes through Transactivation of p57Kip2

BackgroundAlthough transition from proliferation to hypertrophic differentiation of chondrocytes is a crucial step for endochondral ossification in physiological skeletal growth and pathological disorders like osteoarthritis, the underlying mechanism remains an enigma. This study investigated the role of the transcription factor CCAAT/enhancer-binding protein β (C/EBPβ) in chondrocytes during endochondral ossification.Methodology/Principal FindingsMouse embryos with homozygous deficiency in C/EBPβ (C/EBPβ−/−) exhibited dwarfism with elongated proliferative zone and delayed chondrocyte hypertrophy in the growth plate cartilage. In the cultures of primary C/EBPβ−/− chondrocytes, cell proliferation was enhanced while hypertrophic differentiation was suppressed. Contrarily, retroviral overexpression of C/EBPβ in chondrocytes suppressed the proliferation and enhanced the hypertrophy, suggesting the cell cycle arrest by C/EBPβ. In fact, a DNA cell cycle histogram revealed that the C/EBPβ overexpression caused accumulation of cells in the G0/G1 fraction. Among cell cycle factors, microarray and real-time RT-PCR analyses have identified the cyclin-dependent kinase inhibitor p57Kip2 as the transcriptional target of C/EBPβ. p57Kip2 was co-localized with C/EBPβ in late proliferative and pre-hypertrophic chondrocytes of the mouse growth plate, which was decreased by the C/EBPβ deficiency. Luciferase-reporter and electrophoretic mobility shift assays identified the core responsive element of C/EBPβ in the p57Kip2 promoter between −150 and −130 bp region containing a putative C/EBP motif. The knockdown of p57Kip2 by the siRNA inhibited the C/EBPβ-induced chondrocyte hypertrophy. Finally, when we created the experimental osteoarthritis model by inducing instability in the knee joints of adult mice of wild-type and C/EBPβ+/− littermates, the C/EBPβ insufficiency caused resistance to joint cartilage destruction.Conclusions/SignificanceC/EBPβ transactivates p57Kip2 to promote transition from proliferation to hypertrophic differentiation of chondrocytes during endochondral ossification, suggesting that the C/EBPβ-p57Kip2 signal would be a therapeutic target of skeletal disorders like growth retardation and osteoarthritis.

Effect of synaptic plasticity on sensory coding and steady-state filtering properties in the electric sense

Our modeling study examines short-term plasticity at the synapse between afferents from electroreceptors and pyramidal cells in the electrosensory lateral lobe (ELL) of the weakly electric fish Apteronotus leptorhynchus. It focusses on steady-state filtering and coherence-based coding properties. While developed for electroreception, our study exposes general functional features for different mixtures of depression and facilitation. Our computational model, constrained by the available in vivo and in vitro data, consists of a synapse onto a deterministic leaky integrate-and-fire (LIF) neuron. The synapse is either depressing ( D), facilitating ( F) or both ( FD), and is driven by a sinusoidally or randomly modulated Poisson process. Due to nonlinearity, numerically computed input–output transfer functions are used to determine the filtering properties. The gain of the response at each sinusoidally modulated frequency is computed by dividing the fitted amplitudes of the input and output cycle histograms of the LIF models. While filtering is always low-pass for F alone, D alone exhibits a gain resonance (non-monotonicity) at a frequency that decreases with increasing recovery time constant of synaptic depression ( τ d ). This resonance is mitigated by the presence of F. For D, F and FD, coherence improves as the synaptic conductance time constant ( τ g ) increases, yet the mutual information per spike decreases. The information per spike for D and F follows opposite trends as their respective time constants increase. The broadband but non-monotonic gain and coherence functions seen in vivo suggest that D and perhaps FD dynamics are involved at this synapse. Our results further predict that the likely synaptic configuration is a slower τ g , e.g. via a mixture of AMPA and NMDA synapses, and a relatively smaller synaptic facilitation time constant ( τ f ) and larger τ d (with τ f smaller than τ d and τ g ). These results are compatible with known physiology.

Quantization effects on the equilibrium behavior of combined fuzzy cognitive maps

Fuzzy cognitive maps (FCMs) allow experts to express their knowledge by drawing weighted causal digraphs. Experts can pool or fuse their knowledge by adding the underlying FCM causal matrices. This naturally extends the ordered-weighted-averaging (OWA) technique to averaging dynamical systems and can create complex dynamical systems from several simpler ones. Edge quantization allows experts to state their knowledge in the simpler terms of causal increase (1), decrease (−1), or absence (0). We model the expert FCMs as a sequence of random fields to study the small-sample effects of quantizing both the causal edges and the fuzzy-set concept nodes. The averaged quantized random matrices exhibit large-sample convergence to the population means of the unquantized matrices in accordance with the Strong Law of Large Numbers. But the small-sample averages can show substantial diversity of equilibrium attractors (fixed points or limit cycles). We use statistical tests—chi-square tests, Spearman's rank coefficient, the Kolmogorov–Smirnov test, and the fuzzy equality of limit cycle histograms—to show that this small-sample equilibrium diversity increases as the node multivalence or fuzzy-set quantization increases. The appendix presents a new probabilistic convergence theorem that shows that edge quantization or thresholding does not affect FCM combination for large expert sample sizes: the sample mean of quantized expert causal edge values converges with probability one to the population mean causal edge values. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 181–202, 2007.

Acquirement of Rituximab Resistance Is Associated with the Development of Chemotherapy Resistance in B-Cell Lymphoma Cells: Evidence of Shared Pathways of Resistance between Chemotherapeutic Agents and Biological Therapies.

Pre-clinical studies have demonstrated that rituximab triggers apoptotic signals in B-cell lymphoma cells upon biding to CD20 antigen. Downstream signaling events observed in lymphoma cells following in vitro exposure of rituximab or chemotherapy include: 1) activation of the intrinsic apoptotic pathway and 2) increased mitogen activated protein kinase (MAPK) activity. In addition, pre-clinical and clinical studies strongly suggest that rituximab may sensitize lymphoma cells to apoptotic effects of various drugs used to treat NHL. Despite its anti-tumor activity, many patients relapse after initial response to rituximab-based therapy and demonstrate variable degrees of rituximab resistance. To further study the impact of rituximab resistance in cellular responses to chemotherapy we developed several rituximab resistant cell lines (RRCL) derived from Raji, SU-DHL-4 and RL cells by exposing cells to escalating doses of rituximab with (4RH cells) or without (2R cells) human serum. The rituximab resistance of each RRCL was confirmed by immunological assays. Subsequently, lymphoma cells (parental and RRCL) were exposed to various chemotherapeutic agents (cisplatin, doxorubicin, paclitaxel, or vincristine) for up to 48 hours. Detection of cell death was determined by trypan blue and/or propidium iodine staining. Caspase-3 activity was measured by PhiPhi Lux G1D2 enzymatic cleavage. Bcl-2 expression was determined by Western blotting. Chemotherapy resistance to all agents tested was observed in RRCL when compared to parental Raji, SU-DHL-4 and RL cell lines. In addition, caspase-3 activity was lower in RRCL following chemotherapy exposure than in parental cell lines. A significantly lower percent of RRCL cells within sub-G0/G1 peaks in cell cycle histograms confirmed that RRCL were less sensitive to chemotherapy-induced apoptosis. Additionally, an increase in Bcl-2 expression was observed in RRCL when compared parental cell lines. Our data strongly suggest that chemotherapy resistance emerges concomitantly with the acquirement of rituximab resistance in lymphoma cells. Chronic exposure to rituximab appears to cause overexpression of Bcl-2, which likely renders RRCL less susceptible to the apoptotic effects of chemotherapy agents. Ongoing studies are aimed at identifying and overcoming rituximab/chemotherapy shared cellular pathways of resistance.

Spike detection, characterization, and discrimination using feature analysis software written in LabVIEW

Rapid and accurate discrimination of single units from extracellular recordings is a fundamental process for the analysis and interpretation of electrophysiological recordings. We present an algorithm that performs detection, characterization, discrimination, and analysis of action potentials from extracellular recording sessions. The program was entirely written in LabVIEW (National Instruments), and requires no external hardware devices or a priori information about action potential shapes. Waveform events are detected by scanning the digital record for voltages that exceed a user-adjustable trigger. Detected events are characterized to determine nine different time and voltage levels for each event. Various algebraic combinations of these waveform features are used as axis choices for 2-D Cartesian plots of events. The user selects axis choices that generate distinct clusters. Multiple clusters may be defined as action potentials by manually generating boundaries of arbitrary shape. Events defined as action potentials are validated by visual inspection of overlain waveforms. Stimulus-response relationships may be identified by selecting any recorded channel for comparison to continuous and average cycle histograms of binned unit data. The algorithm includes novel aspects of feature analysis and acquisition, including higher acquisition rates for electrophysiological data compared to other channels. The program confirms that electrophysiological data may be discriminated with high-speed and efficiency using algebraic combinations of waveform features derived from high-speed digital records.

In vitro studies on the toxicity of isoniazid in different cell lines.

The aim of the present study was to investigate in vitro the mechanism of toxicity of isoniazid (= INH), the drug most widely used for treatment of tuberculosis. The human hepatoma line HepG2, the human lymphoblastoid line AHH-1 and the murine lymphoma cells YAC-1 were used as test systems. Active cell death (= apoptosis) and necrosis were detected by different flow cytometric methods: the binding of annexin V to the cell membrane and staining with propidium iodide (PI), the TUNEL assay for detection of DNA fragmentation and the occurrence of a sub G1 peak in cell cycle histograms. Mitochondrial membrane potential was analysed with the fluorescent probe JC-1. In addition to cytotoxicity, effects of INH on cell cycle were studied in HepG2 cells. The data of the present investigations indicate that INH induces cytotoxicity via apoptosis both in hepatoma and lymphoma cells. Twenty-four hours of application of INH in concentrations > 26 mM led to a remarkable number of apoptotic cells positive for Annexin V. The induction of apoptosis was accompanied by a break down of the mitochondrial membrane potential and the occurrence of DNA strand breaks. At incubation times from 36 to 48 hours, a sub-G1 peak of late apoptotic cells was detected in cell cycle analysis. Furthermore, cell cycle studies showed a disruption of the cycle at low concentrations of INH which are only mildly cytotoxic. Thus the present study unequivocally demonstrated that INH induces cytotoxicity via apoptosis and can lead to a significant disturbance of the cell cycle in mammalian cells.

Independent representations of limb axis length and orientation in spinocerebellar response components.

Dorsal spinocerebellar tract (DSCT) neurons transmit sensory signals to the cerebellum that encode global hindlimb parameters, such as the hindlimb end-point position and its direction of movement. Here we use a population analysis approach to examine further the characteristics of DSCT neuronal responses during continuous movements of the hind foot. We used a robot to move the hind paw of anesthetized cats through the trajectories of a step or a figure-8 footpath in a parasagittal plane. Extracellular recordings from 82 cells converted to cycle histograms provided the basis for a principal-component analysis to determine the common features of the DSCT movement responses. Five principal components (PCs) accounted for about 80% of the total variance in the waveforms across units. The first two PCs accounted for about 60% of the variance and they were highly robust across samples. We examined the relationship between the responses and limb kinematic parameters by correlating the PC waveforms with waveforms of the joint angle and limb axis trajectories using multivariate linear regression models. Each PC waveform could be at least partly explained by a linear relationship to joint-angle trajectories, but except for the first PC, they required multiple angles. However, the limb axis parameters more closely related to both the first and second PC waveforms. In fact, linear regression models with limb axis length and orientation trajectories as predictors explained 94% of the variance in both PCs, and each was related to a particular linear combination of position and velocity. The first PC correlated with the limb axis orientation and orientation velocity trajectories, whereas second PC with the length and length velocity trajectories. These combinations were found to correspond to the dynamics of muscle spindle responses. The first two PCs were also most representative of the data set since about half the DSCT responses could be at least 85% accounted for by weighted linear combinations of these two PCs. Higher-order PCs were unrelated to limb axis trajectories and accounted instead for different dynamic components of the responses. The findings imply that an explicit and independent representation of the limb axis length and orientation may be present at the lowest levels of sensory processing in the spinal cord.

A first-passage-time analysis of the periodically forced noisy leaky integrate-and-fire model.

We present a general method for the analysis of the discharge trains of periodically forced noisy leaky integrate-and-fire neuron models. This approach relies on the iterations of a stochastic phase transition operator that generalizes the phase transition function used for the study of periodically forced deterministic oscillators to noisy systems. The kernel of this operator is defined in terms of the the first passage time probability density function of the Ornstein Uhlenbeck process through a suitable threshold. Numerically, it is computed as the solution of a singular integral equation. It is shown that, for the noisy system, quantities such as the phase distribution (cycle histogram), the interspike interval distribution, the autocorrelation function of the intervals, the autocorrelogram and the power spectrum density of the spike train, as well as the input-output cross-correlation and cross-spectral density can all be computed using the stochastic phase transition operator. A detailed description of the numerical implementation of the method, together with examples, is provided.

The leaky integrate-and-fire with noise: a useful tool to investigate SR

The behaviour of a relaxation-like neural model, driven by noise and underthreshold sinusoidal signal, is analysed by computer simulation. The histograms of interspike intervals and the cycle histograms (CHs) are computed as well as the power spectral densities (PSDs) of the point process generated. The system is shown to exhibit bona fide stochastic resonance (SR).

Stochastic resonance and spike-timing precision in an ensemble of leaky integrate and fire neuron models

We analyze the transmission of sinelike periodic signals by an ensemble of leaky integrate-and-fire neuron models in the presence of additive noise. We observe that when the number of units in the ensemble is large enough, the point process formed by pooling the spike trains of all units is an inhomogeneous Poisson process. We obtain the intensity of this process, i.e., the instantaneous discharge rate of the ensemble, from the cycle histogram of the discharge of a single unit. This enables us to link measures of the regularity of the output discharge rate and the transmission of the periodic input, such as the signal to noise ratio and the input-output power norm and normalized power norm directly to the shape of the cycle histogram. Furthermore, we also show that firing precision in response to subthreshold stimulation is maximized at some intermediate noise value, and argue that in this regime the ensemble can reliably transmit fast periodic signals below the resolution of the individual units. Our analysis clarifies the conditions whereby noise enhances signal transmission and detection in ensembles.

Signalling of static and dynamic features of muscle spindle input by cuneate neurones in the cat.

1. The capacity of cuneate neurones to signal information derived from muscle spindle afferent fibres about static stretch or vibration of forearm extensor muscles was examined electrophysiologically in anaesthetized cats. 2. Static stretch (>= 2 mm in amplitude) and sinusoidal vibration (at frequencies of 50-800 Hz) were applied longitudinally to individual muscle tendons by means of a feedback controlled mechanical stimulator, and responses were recorded from individual cuneate neurones and from individual spindle afferent fibres. 3. Cuneate neurones sampled were located caudal to the obex and displayed a sensitivity to both vibration and static stretch of forearm muscles that was consistent with their input arising from primary spindle endings. In response to static muscle stretch, they displayed graded and approximately linear stimulus-response relations, and a stability of response level at fixed lengths that was consistent with these neurones contributing discriminative information about static muscle stretch. 4. In response to sinusoidal muscle vibration the cuneate neurones also showed graded stimulus-response relations (in contrast to spindle afferents which at low vibration amplitudes attain a plateau response level corresponding to a discharge of 1 impulse on each vibration cycle). Lowest thresholds were at 100-300 Hz and bandwidths of vibration sensitivity extended up to approximately 800 Hz. 5. Temporal precision in cuneate responses to muscle vibration was assessed by constructing phase scatter and cycle histograms from which measures of vector strength could be calculated. Cuneate responses displayed somewhat poorer phase locking (and lower vector strengths) than spindle afferent responses to vibration (a reflection of uncertainties associated with synaptic transmission). Nevertheless, the remarkable feature of cuneate responses to muscle vibration is the preservation of tight phase locking at frequencies up to 400-500 Hz, which presumably enables these central neurones to contribute accurate temporal information for the kinaesthetic sense in a variety of circumstances involving dynamic perturbations to skeletal muscle.

Periodic forcing of a single ion channel: dynamic aspects of the open-closed switching

An unconventional approach to studying ion channel kinetics is exploited. Here we describe the effects of a periodically varying membrane potential on the open-closed transitions of single K+ channels. The use of cycle histograms allows one to measure the transition probabilities as functions of the stimulus phase. The results show that such probabilities vary with the stimulation frequency and with the stimulus history, thus highlighting a dynamic aspect in the switching of this ion channel.