The analysis of oligonucleotide preparations by fractal measures

In this paper we put forward improved mathematical methods for detecting synthesis parameters in connection with analyzing crude products of chemically synthesized oligonucleotides. The crude products experimentally sampled are separated by high-performance capillary electrophoresis and ion-exchange high-performance liquid chromatography. The measured separation profiles of experimental syntheses can be expressed as target and nontarget yields; they are characterized by a few parameters. These parameters account for nonlinear synthesis equations that are solvable by employing iteration procedures. We provide here a theoretical as well as computational analysis based upon specific models for stepwise chain growth. Under nonconstant (nonuniform) conditions we use here an exponential form of growth, with different expressions for calculating the fractal dimension of the biochemical process under study. Step lengths of parameter variations in an interval of finite length have to be adjusted properly to find convergent solutions in a mathematical, regularly four-dimensional parameter space. It is conceivable to have most, if not all, of the calculating and plotting carefully done by a computer. This analysis represents the experimental situation up to 65-mer target oligonucleotides analyzed so far. We thus obtain the dynamics of the polymerization process limited in number by fractal models. The advantage, calculating these new methods as compared to qualitatively judged experimental methods, lies in the satisfactory evaluation of crude products, also of large amounts, of syntheses of these biopolymers. © 1998 John Wiley & Sons, Inc. Biopoly 45: 361–379, 1998     

The fine structure of growing and non-growing whole glia cell preparations.

Human glia cells become blocked in G1 if starved of serum. The characteristics of the GI blocked state are flattening on the substrate, and absence of cell translocation, ruffling and macropinocytosis. Re-entry into the cell cycle, as a result of growth factor stimulation, is accompained and even preceded by the return of this cellular locomotion. We have studied the fine structure of intact human glia cells and ultrathin sections of these cells when proliferating normally in vitro, when starved of serum and during their return to the cell cycle following stimulation with mEGF (mouse epidermal growth factor). Particular attention was paid to morphologically definable components of the cellular musculoskeletal system. Proliferating interphase glia generally had a leading lamella containing few organelles and oriented bundles of 7 nm microfilaments with structureless lamellipodia at their tips, which often formed ruffles. The perinuclear area was thick and contained many cell organelles, including mitochondria and secondary lysosomes. Glia starved of serum were thinly spread; their peripheral cytoplasm was filled with a diffuse mat of microfilaments, they had no structureless lamellipodia and their perinuclear areas, although thinner, contained cell organelles in equal amounts and of similar type of those found in proliferating cells. On EGF stimulation, after approximately 2 hours the perinuclear area of the cells thickened, and structureless lamellipodia subsequently appeared at the tips of the leading lamellae, forming ruffles. The cells finally began to translocate, the process being accompained by the reorientation and packing of the microfilaments into bundles. As the kinetics of EGF binding and break down by glia cells are similar to those described for fibroblasts, the findings do not support the concept of EGF receptor interactions inducing ultrastructurally demonstrable microfilament or other musculoskeletal structural changes in the cell. They do, however, define the differing cellular morphologies of motile and immobile structures.     

Modeling fractal structure of city-size distributions using correlation functions

Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences.     

The fractal structure of glycogen: A clever solution to optimize cell metabolism.

Fractal objects are complex structures built with a simple procedure involving very little information. This has an obvious interest for living beings, because they are splendid examples of optimization to achieve the most efficient structure for a number of goals by means of the most economic way. The lung alveolar structure, the capillary network, and the structure of several parts of higher plant organization, such as ears, spikes, umbels, etc., are supposed to be fractals, and, in fact, mathematical functions based on fractal geometry algorithms can be developed to simulate them. However, the statement that a given biological structure is fractal should imply that the iterative process of its construction has a real biological meaning, i.e., that its construction in nature is achieved by means of a single genetic, enzymatic, or biophysical mechanism successively repeated; thus, such an iterative process should not be just an abstract mathematical tool to reproduce that object. This property has not been proven at present for any biological structure, because the mechanisms that build the objects mentioned above are unknown in detail. In this work, we present results that show that the glycogen molecule could be the first known real biological fractal structure.     

Protozoan community structure in a fractal soil environment.

Protozoan abundance was quantified, and 365 protozoan species were recorded, in 150 soil samples from an upland grassland in Scotland. Across the entire size range (2-200 pm) protozoan species richness varied by a factor of two, whereas abundance increased by a factor of 20 with decreasing body size. As the soil had fractal structure, the relatively flat species curve can be explained if spatial heterogeneity determines species number--for in a fractal environment, heterogeneity will be the same at all spatial scales. Community structure appeared to approach a temporary steady-state about six days after re-hydration of dried soil. A simple model based on combining the fractal character of increasing habitat area at smaller spatial scales, with the weight-specific energy requirements of protozoa, provided theoretical curves of abundance and biovolume on body size which provide a reasonable fit to real data. We suggest two possibilities--that the apparent competence of the theoretical model is fortuitous and the product of poorly understood dynamic elements of the trophic structure in the community; or that key elements of protozoan community structure in a fractal soil environment may be largely explained in terms of habitat space and energy requirements.     

Power-law species richness accumulation as manifestation of the fractal community structure

Applications of the fractal to describing the species structure of communities are discussed. Fundamental notions of fractal geometry are explained in the first part. The problem of applying the concept of fractal to describe the spatial allocation of particular species and of community as a whole is reviewed in the second part. In the final part, the usage of the selfsimirity principle for analyzing community organization is substantiated, and evidence of the fractal structure of biocenoses is presented according to Whittaker's concept of alpha diversity. It is shown that community is characterized, as a fractal object, by scale invariance, by power function relationship between the number of structural elements of the community (individuals, populations, species) and the scale (sampling effort), and, finally, by fractional value of the power (fractal dimension). Power function is the formula the takes into account the share of rare species, or species represented by a single individual. providing for no saturation of the function f(x). This formula also does not contradict the A.P. Levich's "rule of ecological non-additivity" and, lastly, allows the application of fractal formalism to characterize the species structure of a community. It is concluded that the mathematical image of species richness is a monofractal, i.e., a set characterised by only one parameter, fractal dimension. Thus, the species structure of a community (as well as the pattern of its spatial allocation) displays self-similarity and is a fractal.     

复杂生态系统分形层次结构的统计动力学分析

生态系统具有异质性、非线性、多层次性等复杂特性.针对生态系统的复杂性,从统计动力学的视角出发,从生态组元相互作用的微观动力学角度,对生态系统分形层次结构的起源及其形成过程的动力学机理进行了初步探讨,并分析了生态系统分形维数的影响因素及机理.对理论结果与实际例子进行了比较,并讨论了在实践中的可能应用.     

The preservation of nasal preparations

The intranasal route of administration provides an effective and convenient means of delivering a number of compounds to the systemic circulation when the more usual oral or parenteral routes are inappropriate. The preservation of multi-dose nasal drops and sprays is essential. However, preservatives should not impair any of the normal functions of the nasal cavity, such as mucociliary clearance, since patients with compromised clearance can suffer extensively from respiratory tract infections. This paper reviews the results of a number of investigations into the effects of a range of commonly used preservatives on the mucociliary clearance apparatus.     

Analysis of gypsogenin saponins in homeopathic tinctures

A relatively simple and short procedure for the quantitative determination of gypsogenin saponins was performed to evaluate homeopathic tinctures in which those compounds can be regarded as one of the active constituents. This method comprises partial hydrolysis of saponins, subsequent extraction of liberated prosaponin (gypsogenin 3-O-glucuronide) and its analysis by high performance liquid chromatography. Glycyrrhizic acid was used as an internal standard. This method was successfully applied to the analysis of mother tinctures obtained from Saponaria officinalis. Thus, the determination of triterpenoid saponins can be used as a convenient and sufficient method of standardization of selected homeopathic tinctures.     

An improved stochastic fractal search algorithm for 3D protein structure prediction

Protein structure prediction (PSP) is a significant area for biological information research, disease treatment, and drug development and so on. In this paper, three-dimensional structures of proteins are predicted based on the known amino acid sequences, and the structure prediction problem is transformed into a typical NP problem by an AB off-lattice model. This work applies a novel improved Stochastic Fractal Search algorithm (ISFS) to solve the problem. The Stochastic Fractal Search algorithm (SFS) is an effective evolutionary algorithm that performs well in exploring the search space but falls into local minimums sometimes. In order to avoid the weakness, Lvy flight and internal feedback information are introduced in ISFS. In the experimental process, simulations are conducted by ISFS algorithm on Fibonacci sequences and real peptide sequences. Experimental results prove that the ISFS performs more efficiently and robust in terms of finding the global minimum and avoiding getting stuck in local minimums.