Fractal Methods to Analyze Ion Channel Kinetics

Liebovitch, Larry S.; Scheurle, Daniela; Rusek, Marian; Żochowski, Michał

doi:10.1006/meth.2001.1206

Cited by 48 publications

(34 citation statements)

References 24 publications

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“…To convert from millimeters on the printed map to geographic distance we used a scaling factor of 5/27 lengths). Therefore, to estimate the PDFs of the data sets we used the "multihistogram" or "fractal" method developed by Liebovitch et al (1987Liebovitch et al ( , 1999Liebovitch et al ( , 2001. We computed histograms of different bin sizes, evaluated the PDF from each histogram, and then combined those values to form the completed PDF (Liebovitch et al, 1999, pp.…”

Section: Methodsmentioning

confidence: 99%

Lévy Flights in Dobe Ju/’hoansi Foraging Patterns

Brown

Liebovitch

Glendon³

2006

Hum Ecol

Self Cite

383

198

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We analyzed data on Ju/'hoansi hunter-gatherer foraging patterns and found that their movements between residence camps can be modeled as a Lévy flight. The step lengths of their movements scale as a power law with an exponent μ=1.97. Their wait times (residence times) at the camps also scale as a power law (μ=1.45). A Lévy flight with step lengths μ=2 is an optimal search pattern for scarce, randomly located targets; thus, the Ju/'hoansi foraging pattern may approach an optimal search in this area of sparse plant and animal resources. These findings affect the application of optimal foraging theory to humans in anthropology and archaeology because they alter the way in which search and travel times should be quantified. These results may also carry implications for the study of other patterns of human movement, such as demic diffusion and migration.

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Section: Methodsmentioning

confidence: 99%

Lévy Flights in Dobe Ju/’hoansi Foraging Patterns

Brown

Liebovitch

Glendon³

2006

Hum Ecol

Self Cite

383

198

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“…This pattern served as clue to surmise an underlying fractal process with infinite variance. On this basis Liebovitch et al (1987, 2001) asked how the switching probabilities at one time scale of observation are related to those at another time scale. It turned out that these probabilities (defined as effective kinetic rate) at a given time scale are characterized by fractal scaling, and that effective kinetic rates for different time scales of observation display self-similarity: there are bursts within bursts of openings and closings.…”

Section: Power-law Scaling In Neuronal Structures and Processesmentioning

confidence: 99%

Fractals in the nervous system: conceptual implications for theoretical neuroscience

Werner¹

2010

Front. Physio.

165

177

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This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power-law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review.

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“…In order to fit the histograms with different bin sizes together, the counts in each bin were normalized by 1/(t i N total ), where N total is the total number of open times. The first bin must be excluded because it will contain all of the the times unresolved at time t i [11]. As soon as a bin is encountered that contains no counts the loop breaks to the next t i .…”

Section: Data and Analysismentioning

confidence: 99%

“…Reference [11] also shows how to calculate the transition rate k(t) from the open time histogram data. Kinetic rate constants were calculated at each bin size by fitting the 2 nd , 3…”

Section: Data and Analysismentioning

confidence: 99%

Ion-channel-like behavior in lipid bilayer membranes at the melting transition

et al. 2010

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It is well known that at the gel-liquid phase transition temperature a lipid bilayer membrane exhibits an increased ion permeability. We analyze the quantized currents in which the increased permeability presents itself. The open time histogram shows a "-3/2" power law which implies an open-closed transition rate that decreases like k(t) ∝ t −1 as time evolves. We propose a "pore freezing" model to explain the observations. We discuss how this model also leads to the 1/f α noise that is commonly observed in currents across biological and artificial membranes.

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Fractal Methods to Analyze Ion Channel Kinetics

Cited by 48 publications

References 24 publications

Lévy Flights in Dobe Ju/’hoansi Foraging Patterns

Lévy Flights in Dobe Ju/’hoansi Foraging Patterns

Fractals in the nervous system: conceptual implications for theoretical neuroscience

Ion-channel-like behavior in lipid bilayer membranes at the melting transition

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