Deterministic in contrast to stochastic modeling.

The first attempt to model a process is often a deterministic setup with differential equations. The existing stochastic influence is suppressed and hopefully negligible. However, sometimes the stochastic component is important. We demonstrate and clarify this for a growth process. The deterministic approach is given by Yn + 1 = Yn + g(Yn) or dYt = g(Yt)dt, Y0 = 1, g a positive function. The corresponding stochastic equation is Xn + 1 = Xn + g(Xn)(1 + xi n) or dXt = g(Xt)dt + f(Xt)dWt, xi some random variable, W the Brownian motion. We compare the asymptotic behavior of the deterministic solution versus the stochastic solution.     

Low-pass filtering, a new method of fractal analysis: application to PET images of pulmonary blood flow.

The pattern of a spatial structure that repeats itself independently of the scale of magnification or resolution is often characterized by a fractal dimension (D). Two-dimensional low-pass filtering, which may serve as a method to assess D, was applied to functional images of pulmonary perfusion measured by positron emission tomography. The corner frequency of a low-pass filter is inversely proportional to the resolution scale. The method was applied to three types of images: random noise images, synthetic fractal images, and positron emission tomographic images of pulmonary perfusion. Images were processed with two-dimensional low-pass filters of decreasing corner frequencies, and a spatial heterogeneity index, the coefficient of variation, was calculated for each low-pass-filtered image. The natural logarithm of the coefficient of variation scaled linearly with the natural logarithm of the resolution scale for the PET images studied (average R(2) = 0.99). D ranged from 1.25 to 1.36 for the residual distribution of pulmonary perfusion after vertical gradients were removed by linear regression. D of the same data without removal of vertical gradients ranged from 1.11 to 1.14, but the fractal plots had systematic deviations from linearity and a lower linear correlation coefficient (R(2) = 0. 96). The method includes all data in the lung field and is insensitive to the effects of misregistration. We conclude that low-pass filtering offers new insights into the interpretation of D of two-dimensional functional images as a measure of the frequency content of spatial heterogeneity.     

一种滤除医学影像噪声的混合滤波算法

目的：医学影像在获取、存储、传输过程中会不同程度地受到噪声污染,这极大影像了其在临床诊疗中的应用。为了有效地滤除医学影像噪声,提出了一种混合滤波算法。方法：该算法首先将含有高斯和椒盐噪声的图像进行形态学开运算,然后对开运算后的图像进行二维小波分解,得到高频和低频小波分解系数。保留低频系数不变,将高频系数经过维纳滤波器进行滤波,最后进行小波系数重构。结果：采用该混合滤波算法、小波阚值去噪、中值滤波、维纳滤波分别对含有混合噪声的医学影像分别进行滤除噪声处理,该滤波算法去噪后影像的PSNR值明显高于其他三种方法。结论：该混合滤波算法是一种较为有效的医学影像噪声滤除方法。     

Biochemical and immunological demonstration of prostaglandin D2, E2, and F2 alpha formation from prostaglandin H2 by various rat glutathione S-transferase isozymes

Glutathione S-transferase isozymes purified from normal rat liver (1-1, 1-2, 2-2, 3-3, 3-4, and 4-4), liver with hyperplastic nodules (7-7), brain (Yn1Yn1), and testis (Yn1Yn2) all had prostaglandin H2-converting activity. The prostaglandin H2 E-isomerase activity was high in 1-1 (1400 nmol/min/mg protein), 1-2 (1170), and 2-2 (420), moderate in 3-3, 3-4, 4-4, Yn1Yn1, and Yn1Yn2 (52-100), and weak but significant in 7-7 (33). The prostaglandin H2 D-isomerase activity was relatively high in 1-1 (170) and 1-2 (200), moderate in 2-2 (60) and Yn1Yn2 (43), and weak but marked in 3-3 (16), 4-4 (16), and 7-7 (14). The prostaglandin H2 F-reductase activity was remarkable in 1-1 (1250), 1-2 (920), and 2-2 (390), and weakly detected in 3-3 (24), 4-4 (28), and 7-7 (14). Glutathione was absolutely required for these prostaglandin H2-converting reactions, and its stoichiometric consumption was associated with F-reductase activity but not E- and D-isomerase activities. The Km values for glutathione and prostaglandin H2 were about 200 and 10-40 microM, respectively. By immunoabsorption analyses with various antibodies specific for each isozyme, we examined its contribution to the formation of prostaglandins D2, E2, and F2 alpha from prostaglandin H2 in 100,000g supernatants of rat liver, kidney, and testis. In the liver, about 90% of the F-reductase activity (9.8 nmol/min/mg protein) was shown to be catalyzed by the 1-2 group of isozymes. The E-isomerase activity (16.5) was catalyzed about 60 and 40% by the 1-2 and 3-4 groups, respectively; and the D-isomerase activity (3.7) was catalyzed by the 1-2 group (50%) and the 3-4 group and Yn1Yn2 (15-25%). In the kidney, the E-isomerase activity (9.4) was catalyzed by 1-1, 1-2 (40%), 2-2, 3-4 group, and 7-7 (10-20%). The F-reductase activity (3.3) was mostly catalyzed by the 1-2 group (75%). In the testis, the E-isomerase activity (3.9) was catalyzed by the 1-2 group (20-30%), the 3-4 group, and Yn1Yn2 (30-60%).     

长江源区高寒草原和高寒草甸土壤粒径分布特征

为探究长江源区主要下垫面土壤空间异质性与粒径分布(PSD)非均匀性,运用分形理论描述高寒草原和高寒草甸2种下垫面土壤粒径分布特征,分析了 2种下垫面土壤的分形维数特征差异及其与土壤颗粒组成的关系.结果表明:研究区土壤颗粒粒径主要分布于100-800 μm,高寒草原土壤单重分形维数(Dv)为2.429～2.508,高寒草...     

The subunit structure of a major glutathione S-transferase form, MT, in rat testis. Evidence for a heterodimer consisting of subunits with different isoelectric points

A major glutathione S-transferase form (pI 5.7) in rat testis (MT) purified by S-hexyl-glutathione affinity chromatography, followed by chromatofocusing, showed two polypeptide of pI 6.7 (Yn1) and 6.0 (Yn2), having apparently the same molecular mass of 26 kDa on two-dimensional gel electrophoresis. Rechromatofocusing of the MT preparation after 4 M guanidine hydrochloride treatment revealed two additional protein peaks (pI 6.2 and 5.4). These were identified as the two homodimers consisting of the subunits of MT, Yn1Yn1 and Yn2Yn2, respectively. Furthermore, MT could be reconstituted from Yn1Yn1 and Yn2Yn2. These results indicate that MT is a heterodimer, Yn1Yn2, consisting of subunits with very similar molecular masses but different isoelectric points. The Yn1Yn1 form had glutathione S-transferase activities towards 1-chloro-2,4-dinitrobenzene and 1,2-dichloro-4-nitrobenzene. However, the Yn2Yn2 form had no activity towards any of the substrates examined. N-terminal amino acid sequences of subunits Yn1 and Yn2 revealed differences at two positions in the first 20 residues; the amino acid compositions of these subunits were also similar but not identical, indicating that these two subunits are different in the primary structure. Subunits Yn1 and Yn2 are immunologically related to each other and also to subunits 3 (Yb1) and 4 (Yb2) but they are not identical. These four subunits also showed a high degree of similarity in N-terminal amino acid sequences. Subunits Yn1 and Yn2 seem to belong to the rat GST 3-4 family or class mu. Subunits Yn1 and 4 can make a heterodimer, which is detectable not only in rat testis, but also in the heart, kidney and lung. The Yn1Yn1 form was not detected in the testis, but is present in rat brain [Tsuchida et al. (1987) Eur. J. Biochem. 170, 159-164]. The Yn2Yn2 form seemed to differ from GST 5-5 and may be a new form of rat glutathione S-transferase.     

A single-cell model to study changes in neuronal fractal dimension

Many methods have been developed to quantify neuronal morphology: measurement of neurite length, neurite number, etc. However, none of these approaches provides a comprehensive view of the complexity of neuronal morphology. In this work we have analyzed the evaluation of fractal dimension (D) as a tool to represent and quantify changes in complexity of the dendritic arbor, in in vitro cultures grown under low-density conditions. Neurons grown in isolation developed a bipolar morphology corresponding to a fractal dimension close to the unit. The analysis showed that neuronal complexity increased when cells were incubated with a depolarizing potassium concentration and there was a correlation with an increase in fractal dimension (D5 mM KCl = 1.08 +/- 0.01, D25 mM KCl =1.25 +/- 0.01). We conclude that fractal dimension is a suitable parameter to quantify changes in neuronal morphological complexity.     

Anomalous electrophoretic behaviour of the glutathione S-transferase Ya and Yk subunits isolated from man and rodents. A potential pitfall for nomenclature.

GSH S-transferases are dimeric enzymes. The subunits in the rat are resolved into six types, designated Yf, Yk, Ya, Yn, Yb and Yc, by discontinuous SDS/polyacrylamide-gel electrophoresis [Hayes (1986) Biochem. J. 233, 789-798]. The relative electrophoretic mobility of the Ya and Yk subunits is dependent on the amount of cross-linker (NN'-methylenebisacrylamide) in the resolving gel. At low degrees of cross-linking, CBis 0.6% (w/w), the Yk and Ya subunits possess a faster anodal mobility than do the Yf, Yn, Yb and Yc subunits (i.e. order of mobility Yk greater than Ya greater than Yf greater than Yn greater than Yb greater than Yc), whereas at higher degrees of cross-linking, CBis 5.0% (w/w), Yf subunits possess the fastest mobility (i.e. order of mobility Yf greater than Yk greater than or equal to Yn greater than Yb greater than or equal to Ya greater than Yc). Resolving gels that contain low concentrations of cross-linker [CBis 0.6% (w/w)] allow the resolution of a hitherto unrecognized polypeptide that is isolated by S-hexyl-GSH-Sepharose affinity chromatography. This new polypeptide, which we have designated Yb, is normally obscured by the main Yb band in resolving gels that comprise concentrations of cross-linker of at least CBis 1.6% (w/w). The Ya- and Yb-type subunits in guinea pig, mouse, hamster and man were identified by immuno-blotting and their apparent Mr values in different electrophoresis systems were determined. The Ya subunits in all species studied possess a variable cross-linker-dependent mobility during electrophoresis. Since the transferase subunits are currently classified according to their mobilities during SDS/polyacrylamide-gel electrophoresis, it is apparent that the variable electrophoretic behaviour of the Ya and Yk subunits may lead to the mis-identification of enzymes.     

Identifying kinetic gating mechanisms for ion channels by using two-dimensional distributions of simulated dwell times.

Ion channels are integral membrane proteins that regulate ionic flux through cell membranes by opening and closing (or gating) their pores. The gating can be monitored by observing step changes in the current flowing through single channels. Analysis of the durations of the open and closed intervals and of the correlations among the interval durations can give insight into the gating mechanism. Although it is well known that the correlation information can be essential to distinguish among possible gating mechanisms, it has been difficult to use this information because it has not been possible to correct the predicted correlations for the distortion of the single-channel data because of filtering and noise. To overcome this limitation we present a method based on a comparison of simulated and experimental two-dimensional dwell-time distributions constructed by analysing simulated and experimental single-channel currents in an identical manner. The simulated currents incorporate the true effects of filtering and noise, the two-dimensional distributions retain the correlation information, and the identical analysis allows direct maximum-likelihood comparison of the simulated and experimental two-dimensional distributions. We show that the two-dimensional simulation method has a greatly increased ability to distinguish among models, compared with methods that use one-dimensional distributions.     

褐飞虱(Nilaparvata lugens)发生的分形性质研究

运用分形理论以安徽省庐江县植保站和江苏省吴县值保站1979～1990年及太湖地区农科所1986～1998年间褐飞虱发生的田间系统调查资料为例,对褐飞虱发生的性质进行了探讨。结果表明：(1)庐江站、吴县站和太湖地区农科所褐飞虱发生在一定标度域内具有分形性质。其分维值分别为0．7158、0．52l2和0．2816;(2)褐飞虱发生的分维值是表征一定标度区间的发生程度差异的一个新的参数,分维值大,则发生程度轻,反之则重(3)分维数D值与褐飞虱发生的聚集程度是密切相关的,D值小聚集程度大,反之聚集程度小,D值可以作为褐E虱聚集分布程度的一个指标;(4)褐飞虱发生具有多重分形结构,其广义维数谱Dq曲线可以用于褐飞虱发生的预测预报。     

Fractal dimension analysis of factor X activation in the presence of tissue factor-factor viia complex in a continuous flow reactor

Summary The characteristics of a phospholipid surface are of major importance in the activation of factor X in the presence of tissue factor-factor VIIa (TF-VIIa) complex. A possible tool which provides a measure of the surface corrugation and roughness is the fractal dimension analysis. This paper uses the fractal characterization of a phospholipid surface to develop a model for analyzing surface based enzymatic reaction data. The modeling indicates that the fractal dimension (D) of a phospholipid surface is a function of the wall shear rate. The results also indicate that the fractal dimension of the phospholipid surface decreases from approximately 2.9 to 1.4 as the wall shear rate increases from 50 to 1600 sec^–1. At the same time the factor Xa production increases from 1.9 to 5.8 pmoles/ (min. cm^–2).The results of the fractal dimension analysis clearly indicates that the surface roughness of a phospholipid surface may have a significant effect on factor X activation.     

Use of the fractal dimension for the analysis of electroencephalographic time series

 Electroencephalogram (EEG) traces corresponding to different physiopathological conditions can be characterized by their fractal dimension, which is a measure of the signal complexity. Generally this dimension is evaluated in the phase space by means of the attractor dimension or other correlated parameters. Nevertheless, to obtain reliable values, long duration intervals are needed and consequently only long-term events can be analysed; also much calculation time is required. To analyse events of brief duration in real-time mode and to apply the results obtained directly in the time domain, thus providing an easier interpretation of fractal dimension behaviour, in this work we optimize and propose a new method for evaluating the fractal dimension. Moreover, we study the robustness of this evaluation in the presence of white or line noises and compare the results with those obtained with conventional spectral methods. The non-linear analysis carried out allows us to investigate relevant EEG events shorter than those detectable by means of other linear and non-linear techniques, thus achieving a better temporal resolution. An interesting link between the spectral distribution and the fractal dimension value is also pointed out. Received: 21 November 1996 / Accepted in revised form: 1 July 1997     

Purification and characterization of glutathione S-transferases P, S and N. Isolation from rat liver of Yb1 Yn protein, the existence of which was predicted by subunit hybridization in vitro.

The glutathione S-transferases are dimeric proteins and comprise subunits of Mr 25 500 (Ya), 26 500 (Yn), 27 000 (Yb1 and Yb2) and 28 500 (Yc). Enzymes containing Ya and/or Yc subunits have been isolated as have forms containing binary combinations of Yn, Yb1 and Yb2 subunits. To date only one enzyme, transferase S, has been described that is a YbYn heterodimer [Hayes & Chalmers (1983) Biochem. J. 215, 581-588]; the identity of the Yb monomer found in transferase S has not been reported previously. The identification and isolation of a YnYn dimer (transferase N) from rat testis is now described. This has enabled structural and functional comparisons to be made between Yb1, Yb2 and Yn monomers. Reversible dissociation experiments between the YnYn and Yb1Yb1 homodimers and between the YnYn and Yb2Yb2 homodimers demonstrated that Yn monomers can hybridize with both Yb1 and Yb2 monomers. Reversible dissociation of transferases N and C (Yb1Yb2) showed that both Yb1 and Yb2 monomers can hybridize with Yn monomers under competitive conditions. The hydridization data suggest that transferase S represents the Yb2Yn subunit combination. A knowledge of the elution position from chromatofocusing columns of the Yb1Yn hybrid that was formed in vitro enabled a purification scheme to be devised for an enzyme from rat liver (transferase P) believed to consist of Yb1Yn subunits. A comparison of the chromatographic behaviour of the YnYn, Yb1Yb1 and Yb2Yb2 dimers on chromatofocusing and hydroxyapatite columns with the behaviour of transferases P and S on the same matrices suggests these two enzymes may be identified as the Yb1Yn and Yb2Yn dimers respectively. The catalytic activities and the inhibitory effects of non-substrate ligands on transferases P and S are significantly different and again suggest they comprise Yb1 and Yn subunits and Yb2 and Yn subunits respectively; transferase P exhibits a 6-fold higher specific activity for 1,2-dichloro-4-nitrobenzene than does transferase S, whereas, conversely, transferase S possesses a 9-fold higher specific activity for trans-4-phenylbut-3-en-2-one than does transferase P. The quaternary structure of transferases P and S was verified by using peptide mapping and 'Western blotting' techniques.     

Developing a denoising filter for electron microscopy and tomography data in the cloud

The low radiation conditions and the predominantly phase-object image formation of cryo-electron microscopy (cryo-EM) result in extremely high noise levels and low contrast in the recorded micrographs. The process of single particle or tomographic 3D reconstruction does not completely eliminate this noise and is even capable of introducing new sources of noise during alignment or when correcting for instrument parameters. The recently developed Digital Paths Supervised Variance (DPSV) denoising filter uses local variance information to control regional noise in a robust and adaptive manner. The performance of the DPSV filter was evaluated in this review qualitatively and quantitatively using simulated and experimental data from cryo-EM and tomography in two and three dimensions. We also assessed the benefit of filtering experimental reconstructions for visualization purposes and for enhancing the accuracy of feature detection. The DPSV filter eliminates high-frequency noise artifacts (density gaps), which would normally preclude the accurate segmentation of tomography reconstructions or the detection of alpha-helices in single-particle reconstructions. This collaborative software development project was carried out entirely by virtual interactions among the authors using publicly available development and file sharing tools.     

Fractal dimension in human cerebellum measured by magnetic resonance imaging

Fractal dimension has been used to quantify the structures of a wide range of objects in biology and medicine. We measured fractal dimension of human cerebellum (CB) in magnetic resonance images of 24 healthy young subjects (12 men and 12 women). CB images were resampled to a series of image sets with different 3D resolutions. At each resolution, the skeleton of the CB white matter was obtained and the number of pixels belonging to the skeleton was determined. Fractal dimension of the CB skeleton was calculated using the box-counting method. The results indicated that the CB skeleton is a highly fractal structure, with a fractal dimension of 2.57 +/- 0.01. No significant difference in the CB fractal dimension was observed between men and women.     

Dopamine receptor regulation of Ca2+ levels in individual isolated nerve terminals from rat striatum: comparison of presynaptic D1-like and D2-like receptors

We have directly observed the effects of activating presynaptic D1-like and D2-like dopamine receptors on Ca2+ levels in isolated nerve terminals (synaptosomes) from rat striatum. R-(+)-SKF81297, a selective D1-like receptor agonist, and (-)-quinpirole, a selective D2-like receptor agonist, induced increases in Ca2+ levels in different subsets of individual striatal synaptosomes. The SKF81297- and quinpirole-induced effects were blocked by R-(+)-SCH23390, a D1-like receptor antagonist, and (-)-sulpiride, a D2-like receptor antagonist, respectively. SKF81297- or quinpirole-induced Ca2+ increases were inhibited following blockade of voltage-gated calcium channels or sodium channels. In a larger subset of synaptosomes, quinpirole decreased baseline Ca2+. Quinpirole also inhibited veratridine-induced increases in intrasynaptosomal Ca2+ level. Immunostaining confirmed the presynaptic expression of D1, D5, D2 and D3 receptors, but not D4 receptors. The array of neurotransmitter phenotypes of the striatal nerve endings expressing D1, D5, D2 or D3 varied for each receptor subtype. These results suggest that presynaptic D1-like and D2-like receptors induce increases in Ca2+ levels in different subsets of nerve terminals via Na+ channel-mediated membrane depolarization, which, in turn, induces the opening of voltage-gated calcium channels. D2-like receptors also reduce nerve terminal Ca2+ in a different but larger subset of synaptosomes, consistent with the predominant presynaptic action of dopamine in the striatum being inhibitory.     

Spectral processing methods for the removal of t1 noise and solvent artifacts from NMR spectra

Summary A data processing method is described which reduces the effects of t₁ noise artifacts and improves the presentation of 2D NMR spectral data. A t₁ noise profile is produced by measuring the average noise in each column. This profile is then used to determine weighting coefficients for a sliding weighted smoothing filter that is applied to each row, such that the amount of smoothing each point receives is proportional to both its estimated t₁ noise level and the level of t₁ noise of neighbouring points. Thus, points in the worst t₁ noise bands receive the greatest smoothing, whereas points in low-noise regions remain relatively unaffected. In addition, weighted smoothing allows points in low-noise regions to influence neighbouring points in noisy regions. This method is also effective in reducing the noise artifacts associated with the solvent resonance in spectra of biopolymers in aqueous solution. Although developed primarily to improve the quality of 2D NMR spectra of biopolymers prior to automated analysis, this approach should enhance processing of spectra of a wide range of compounds and can be used whenever noise occurs in discrete bands in one dimension of a multi-dimensional spectrum.     

Acetylcholine-induced ionic channels in rat skeletal muscle.

This paper briefly reviews the evidence for ionic channels mediating the conductance increase caused by acetylcholine application to the end-plate of skeletal muscle fibers. "Membrane noise" observed during application of constant low concentrations of acetylcholine to an end-plate is thought to arise from the random superposition of many elementary events corresponding to the opening and closing of discrete ion channels. Statistical analysis of acetylcholine-induced noise reveals an elementary conductance event of of 34 pS (1 S = 1 omega-1) amplitude and 1 msec duration at room temperature in rat muscle fibers. Both size and duration of the elementary event are temperature dependent. Analysis of currents induced by application of acetylcholine to the extrasynaptic membrane of chronically denervated fibers shows that the elementary conductance has a similar size but is of much longer duration. Direct recording of square pulse-like currents by a patch clamp method confirms some of the conclusions drawn from fluctuation analysis.     

Fractal dimensions of pacing and grip force in drawing and handwriting production

We performed a repeated measures experiment to show that the pacing of a cyclic, ballistic drawing task has a fractal dimension. We also estimated the dimensionality of the force used to grip the drawing implement. Finally, we present an analysis of pediatric data to show that grip force has a fractal dimension in an actual handwriting task. In our experiment, subjects drew circles of varying sizes and at varying rates on a digitizing tablet, using a pen instrumented to measure radial force applied to its barrel. Subjects also drew circles in synchrony with a metronome. We found strong evidence for fractal scaling of both drawing period and grip force in the circle-drawing study. The dimensionality ranged from fractal Gaussian noise (fGn) to fractal Brownian motion, with Hurst coefficients clustering around the value for 1/f noise. When the subjects were required to synchronize their drawing with a metronome, the Hurst coefficient for the drawing period decreased, while the coefficient for grip force did not. This result indicates that independent processes control the variations in pacing and grip force. Grip force in the handwriting study also displayed fractal properties, with Hurst coefficients in the range of correlated fGn. We draw parallels between our handwriting measurements and studies of human gait.