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T F Nonnenmacher

Publications and source records attributed to T F Nonnenmacher.

11 recordsLinked to original sources
PubMed1999

Propagator representation of anomalous diffusion: the orientational structure factor formalism in NMR.

The radial Fourier transform for the isotropic space with a fractal dimension is discussed. The moments of diffusive displacements with non-Gaussian propagators arising as solutions of fractional diffusion equations are calculated. The Fourier propagator is applied to NMR correlation and spectral density functions in context with the orientational structure factor formalism. It is shown that the low-frequency molecular fluctuations of liquids in porous media with strong or forced adsorption at surfaces are due to reorientations mediated by translational displacements caused by surface diffusion of the adsorbate molecules. In terms of this formalism, field-cycling NMR experiments provide information on the static and dynamic fractal dimensions related to surface diffusion. The experimental results for liquids in porous silica glass can be explained by a surface fractal dimension df=2.5, where the mean squared displacement scales as proportional, variantt(2/dw) with dw=1 (ballistic transport), if the surface population can exchange with the bulklike phase in the pores, and with dw=2, if the bulklike phase is frozen. The former dynamics is interpreted in terms of bulk-mediated surface diffusion.

Journal Article↗
PubMed1999

Effects of steroid hormones on nuclear membrane and membrane-bound heterochromatin from breast cancer cells evaluated by fractal morphometry.

OBJECTIVE: To evaluate the effect of steroid hormones on the ultrastructure of nuclear heterochromatin and perinuclear membranes in human MCF-7 breast cancer cells. STUDY DESIGN: MCF-7 cells were cultured briefly (five minutes) in the presence of 10(-9) M estrogen 17 beta-estradiol, a stimulator of cell proliferation and/or 10(-9) M glucocorticoid dexamethasone. Changes in the morphologic complexity of nuclear membrane-bound heterochromatin (NMBHC) and nuclear membranes (ENM) were assessed by means of the fractal capacity dimension, D, a noneuclidean geometric descriptor of complex, irregular bodies. RESULTS: 17 beta-estradiol (10(-9) M) enhanced the ultrastructural irregularity of NMBHC, as documented by the increased value of D, whereas dexamethasone (10(-9) M) reduced it when compared to NMBHC from untreated MCF-7 control cells. In contrast, neither steroid modified ENM ultrastructure. Changes in the nuclear heterochromatin complexity induced by estrogen 17 beta-estradiol occurred concomitantly with functional changes at the cell periphery, such as activation of the phospholipase C, a cell membrane-associated enzyme involved in signal transduction. Dexamethasone reduced the ultrastructural complexity of NMBHC without affecting functional processes. CONCLUSION: Fractal morphometry proved its usefulness in quantifying early ultrastructural changes in nuclear components induced in MCF-7 cells by steroid hormones, 17 beta-estradiol and dexamethasone.

Breast Neoplasms↗
PubMed1998

Steroid hormones modify nuclear heterochromatin structure and plasma membrane enzyme of MCF-7 cells. A combined fractal, electron microscopical and enzymatic analysis.

Ultrastructural features of the nuclear membrane envelope (ENM) and the nuclear membrane-bound heterochromatin (NMBHC) were investigated in MCF-7 human breast cancer cells by fractal morphometry. The fractal dimension D established by the box counting method proved to be effective for quantifying nuclear changes in MCF-7 cells treated with steroid hormones, namely the estrogen 17 beta-estradiol, which stimulates cell proliferation, and the glucocorticoid dexamethasone. When MCF-7 cells were briefly (5 min) cultured in the presence of 17 beta-estradiol (10(-9) M), the irregularity of the NMBHC outline was increased as documented by the increased fractal dimension D. Changes in the ultrastructural complexity of the nuclear heterochromatin were observed in concomitance with functional changes at the cell periphery, namely the modulation of the estrogen-induced activity of phospholipase C, a cell membrane-associated enzyme involved in the signal transduction pathway via phosphoinositides metabolism. Dexamethasone did not affect the in vitro proliferation, the phospholipase C activity nor the shape of the ENM of MCF-7 cells, but reduced the structural complexity of the nuclear membrane-bound heterochromatin.

Cell Membrane↗
PubMed1996

Anomalous diffusion of water in biological tissues.

This article deals with the characterization of biological tissues and their pathological alterations. For this purpose, diffusion is measured by NMR in the fringe field of a large superconductor with a field gradient of 50 T/m, which is rather homogenous and stable. It is due to the unprecedented properties of the gradient that we are able not only to determine the usual diffusion coefficient, but also to observe the pronounced Non-Debye feature of the relaxation function due to cellular structure. The dynamics of the probability density follow a stretched exponential or Kohlrausch-Williams-Watts function. In the long time limit the Fourier transform of the probability density follows a long-tail Lévy function, whose asymptotic is related to the fractal dimension of the underlying cellular structure. Some of the properties of Lévy walk statistics are discussed and its potential importance in understanding certain biophysical phenomena like diffusion processes in biological tissues are pointed out. We present and discuss for the first time NMR data giving evidence for Lévy processes that capture the essential features of the observed power law (scaling) dynamics of water diffusion in fresh tissue specimens: carcinomas, fibrous mastopathies, adipose and liver tissues.

Adipose Tissue↗
PubMed1996

Self-similarity and fractal irregularity in pathologic tissues.

The irregularity and self-similarity under scale changes are the main attributes of the morphologic complexity of cells and tissues, either normal or pathologic. In other words, the shape of a self-similar object does not change when scales of measure change because any part of it might be similar to the original object. Size and geometric parameters of an irregular object, however, differ when inspected at increasing resolution, which reveals more details. Significant progress has been made over the past three decades in understanding how to analyze irregular shapes and structures in the physical and biologic sciences. Dominant influences have been the discovery by B.B. Mandelbrot of a new, practical geometry of nature, now called fractal geometry, and the continuous improvements in computational capabilities. The application of the principles of fractal geometry, unlike the conventional Euclidean geometry developed for describing regular and ideal geometric shapes practically unknown in nature, enables one to measure the fractal dimension, contour length, surface area, and other dimensional parameters of almost all irregular and complex biologic tissues. During the past decade, a large amount of experimental evidence has accumulated showing that even in biomedical sciences fractal patterns could be observed. Through several examples borrowed from the recent literature, we focus on the application of the fractal approach to measuring irregular and complex features of pathologic cells and tissues and also on its potential role in the understanding of tumor biology.

Fractals↗
PubMed1995

A fractional calculus approach to self-similar protein dynamics.

Relaxation processes and reaction kinetics of proteins deviate from exponential behavior because of their large amount of conformational substrates. The dynamics are governed by many time scales and, therefore, the decay of the relaxation function or reactant concentration is slower than exponential. Applying the idea of self-similar dynamics, we derive a fractal scaling model that results in an equation in which the time derivative is replaced by a differentiation (d/dt)beta of non-integer order beta. The fractional order differential equation is solved by a Mittag-Leffler function. It depends on two parameters, a fundamental time scale tau 0 and a fractional order beta that can be interpreted as a self-similarity dimension of the dynamics. Application of the fractal model to ligand rebinding and pressure release measurements of myoglobin is demonstrated, and the connection of the model to considerations of energy barrier height distributions is shown.

Animals↗
PubMed1994

Digital image analysis of self-similar cell profiles.

Many biological objects appear to have self-similar structures which can be characterized by their fractal dimension D. However, applications of the concept of fractal geometry are rather scarce in cell and tissue biology. Here we adapt and analyse critically 3 methods of digital image analysis to measure D of cellular profiles. As prototype examples we investigate in detail 2 samples of cells: (i) human T-lymphocytes from normal donors, and (ii) hairy leukemic cells. It is shown that D correlates to the structural complexity of the individual cell contour. The calculated D values for cells out of the same cell line scatter around a mean value D = 1.15 for T-lymphocytes (S.D. = 0.03) and D = 1.34 for hairy leukemic cells (S.D. = 0.04). Consequently, we interprete D as a statistical measure for the sample's fractal dimension.

Flow Cytometry↗
PubMed1992

Fractal dimension of pericellular membranes in human lymphocytes and lymphoblastic leukemia cells.

When blood cells are projected into an image plane their contours appear as borderlines of irregular shape with the property of the statistical self-similarity. The dimension D of these cell perimeters may be fractal rather than an integer as in the Euclidean space. The fractal dimension D for different q'order moments was evaluated by means of a probabilistic method after recording EM image profiles of normal peripheral blood mononuclear cells (PBMN) and mature lymphocytes and also of lymphoblasts isolated from humans with acute leukemia or obtained by lectin stimulation in vitro. PBMN cells, CD 4 and CD 8 T-lymphocytes showed a fractal dimension D quite similar among five moments, ranging from 1.23-1.17. Cells of hairy-cell leukemia with highly convoluted morphology displayed D comprised between 1.32-1.36, whereas blasts of T or B acute lymphoblastic leukemia were characterized by a smaller D of 1.11 and 1.13-1.16 respectively. When normal T-lymphocytes were transformed into blasts by lectin PHA stimulation in vitro, the fractal dimension D was significantly reduced and found close to the value recorded on pericellular contour of blasts from acute T-lymphoblastic leukemia.

Cell Membrane↗
PubMed1990

Non-random spatial distribution of intermembraneous particles in red blood cell membrane.

A combined analysis using digital image processing and quantitative evaluation of computed radial distribution of freeze fracture P face particles irradiated and nonirradiated has been carried out. Important quantitative features of the arrangement of particles can be described by computing a statistical measure, the radial distribution function g(r), commonly used to study the structure of liquids. The coordinates for calculating g(r) for each sample were measured automatically by a digital image processing system. The results for the radial distribution function were found to closely resemble g(r) for fluids, indicating the presence of shortrange order. This measure distinguishes three different patterns: i) random distribution, ii) dilute gas like and iii) a liquid like model. The mean number of first nearest neighbours surrounding each particle (coordination number) was found to be of the order of three. The RBC intramembraneous particles are heterogeneous in their behavioural pattern: two thirds random; one fifth, dilute gas; and one tenth, liquid.

Animals↗
PubMed1989

Fractal scaling mechanisms in biomembranes. Oscillations in the lateral diffusion coefficient.

A modified model of the Cohen-Turnbull free volume theory for lateral transport processes in biomembranes is presented. The model which is based on renormalization group theoretical concepts incorporates fractal rather than Markovian diffusion kinetics. It predicts harmonic oscillations in the lateral diffusion coefficient around a dominant power-law trend and clarifies, in addition, recently observed deviations from the Cohen-Turnbull exponential law.

Cell Membrane↗