Fractals as Transpersonal Metaphor

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Correlation studies of open and closed states fluctuations in an ion channel: Analysis of ion current through a large conductance locust potassium channel

Ion current fluctuations occurring within open and closed states of large conductance locust potassium channel (BK channel) were investigated for the existence of correlation. Both time series, extracted from the ion current signal, were studied by the autocorrelation function (AFA) and the detrended fluctuation analysis (DFA) methods. The persistent character of the short- and middle-range correlations of time series is shown by the slow decay of the autocorrelation function. The DFA exponent $\alpha$ is significantly larger than 0.5. The existence of strongly-persistent long-range correlations was detected only for closed-states fluctuations, with $\alpha=0.98\pm0.02$. The long-range correlation of the BK channel action is therefore determined by the character of closed states. The main outcome of this study is that the memory effect is present not only between successive conducting states of the channel but also independently within the open and closed states themselves. As the ion current fluctuations give information about the dynamics of the channel protein, our results point to the correlated character of the protein movement regardless whether the channel is in its open or closed state.Comment: 12 pages, 5 figures; to be published in Phys. Rev.

Why Nonlinear Biomedical Physics?

The two goals of Nonlinear Biomedical Physics are: firstly to show how nonlinear methods can shed new light on biological phenomena and medical applications and secondly to bridge the technical, mathematical, and cultural divides between the physical disciplines where these methods are being developed and the audience for their use in the biological and medical sciences

Comparing ion conductance recordings of synthetic lipid bilayers with cell membranes containing TRP channels

In this article we compare electrical conductance events from single channel recordings of three TRP channel proteins (TRPA1, TRPM2 and TRPM8) expressed in human embryonic kidney cells with channel events recorded on synthetic lipid membranes close to melting transitions. Ion channels from the TRP family are involved in a variety of sensory processes including thermo- and mechano-reception. Synthetic lipid membranes close to phase transitions display channel-like events that respond to stimuli related to changes in intensive thermodynamic variables such as pressure and temperature. TRP channel activity is characterized by typical patterns of current events dependent on the type of protein expressed. Synthetic lipid bilayers show a wide spectrum of electrical phenomena that are considered typical for the activity of protein ion channels. We find unitary currents, burst behavior, flickering, multistep-conductances, and spikes behavior in both preparations. Moreover, we report conductances and lifetimes for lipid channels as described for protein channels. Non-linear and asymmetric current-voltage relationships are seen in both systems. Without further knowledge of the recording conditions, no easy decision can be made whether short current traces originate from a channel protein or from a pure lipid membraneComment: 13 pages, 9 Figure

Regular and stochastic behavior of Parkinsonian pathological tremor signals

Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.Comment: 39 pages, 10 figures, 1 table Physica A, in pres

Migration induced epidemics: Dynamics of flux-based multipatch models

Classical disease models use a mass action term as the interaction between infected and susceptible people in separate patches. We derive the equations when this interaction is a migration of people between patches. The results model what happens when a new population is moved into a region with endemic disease.Comment: 25 page

Behavioral and Emotional Dynamics of Two People Struggling to Reach Consensus about a Topic on Which They Disagree

We studied the behavioral and emotional dynamics displayed by two people trying to resolve a conflict. 59 groups of two people were asked to talk for 20 minutes to try to reach a consensus about a topic on which they disagreed. The topics were abortion, affirmative action, death penalty, and euthanasia. Behavior data were determined from audio recordings where each second of the conversation was assessed as proself, neutral, or prosocial. We determined the probability density function of the durations of time spent in each behavioral state. These durations were well fit by a stretched exponential distribution, with an exponent, , of approximately 0.3. This indicates that the switching between behavioral states is not a random Markov process, but one where the probability to switch behavioral states decreases with the time already spent in that behavioral state. The degree of this “memory” was stronger in those groups who did not reach a consensus and where the conflict grew more destructive than in those that did. Emotion data were measured by having each person listen to the audio recording and moving a computer mouse to recall their negative or positive emotional valence at each moment in the conversation. We used the Hurst rescaled range analysis and power spectrum to determine the correlations in the fluctuations of the emotional valence. The emotional valence was well described by a random walk whose increments were uncorrelated. Thus, the behavior data demonstrated a “memory” of the duration already spent in a behavioral state while the emotion data fluctuated as a random walk whose steps did not have a “memory” of previous steps. This work demonstrates that statistical analysis, more commonly used to analyze physical phenomena, can also shed interesting light on the dynamics of processes in social psychology and conflict management

Non-Markovian Stochastic Resonance

The phenomenological linear response theory of non-Markovian Stochastic Resonance (SR) is put forward for stationary two-state renewal processes. In terms of a derivation of a non-Markov regression theorem we evaluate the characteristic SR-quantifiers; i.e. the spectral power amplification (SPA) and the signal-to-noise ratio (SNR), respectively. In clear contrast to Markovian SR, a characteristic benchmark of genuine non-Markovian SR is its distinctive dependence of the SPA and SNR on small (adiabatic) driving frequencies; particularly, the adiabatic SNR becomes strongly suppressed over its Markovian counterpart. This non-Markovian SR theory is elucidated for a fractal gating dynamics of a potassium ion channel possessing an infinite variance of closed sojourn times.Comment: 4 pages, 1 figur

The role of conformational diffusion in ion channel gating

We consider an exactly tractable model of the Kramers type for the voltage-dependent gating dynamics of single ion channels. It is assumed that the gating dynamics is caused by the thermally activated transitions in a bistable potential. Moreover, the closed state of the channel is highly degenerate and embraces the whole manifold of closed substates. Opening of the ion channel is energetically prohibited from most of the closed substates and requires a special conformation where the voltage sensor can move along an activation pathway and trigger the transition into the open conformation. When the corresponding activation barrier towards the channel's opening is removed by the applied voltage, the statistics of non-conducting time intervals become strongly influenced by the conformational diffusion. For the corresponding supra-threshold voltages, our model explains the origin of the power law distribution of the closed time intervals. The exponential-linear dependence of the opening rate on voltage, often used as an experimental fit, is also reproduced by our model

Searching for self-similarity in switching time and turbulent cascades in ion transport through a biochannel. A time delay asymmetry

The process of ion transport through a locust potassium channel is described by means of the Fokker-Planck equation (FPE). The deterministic and stochastic components of the process of switching between various conducting states of the channel are expressed by two coefficients, $D^{(1)}$ and $D^{(2)}$, a drift and a diffusion coefficient, respectively. The FPE leads to a Langevin equation. This analysis reveals beside the well known deterministic aspects a turbulent, cascade type of action. The (noisy-like) switching between different conducting states prevents the channel from staying in one, closed or open state. The similarity between the hydrodynamic flow in the turbulent regime and hierarchical switching between conducting states of this biochannel is discussed. A non-trivial character of $D^{(1)}$ and $D^{(2)}$ coefficients is shown, which points to different processes governing the channel's action, asymetrically depending on the history of the previously conducting states. Moreover, the Fokker-Planck and Langevin equations provide information on whether and how the statistics of the channel action change over various time scales.Comment: submitted to physica A text : 12 pages + 8 figure