scholarly journals On three dimensional fractal dynamics with fractional inputs and applications

2021 ◽  
Vol 7 (2) ◽  
pp. 1982-2000
Author(s):  
Emile Franc Doungmo Goufo ◽  
◽  
Abdon Atangana ◽  

<abstract><p>The environment around us naturally represents number of its components in fractal structures. Some fractal patterns are also artificially simulated using real life mathematical systems. In this paper, we use the fractal operator combined to the fractional operator with both exponential and Mittag-leffler laws to analyze and solve generalized three-dimensional systems related to real life phenomena. Numerical solutions are provided in each case and applications to some related systems are given. Numerical simulations show the existence of the models' initial three-dimensional structure followed by its self- replication in fractal structure mathematically produced. The whole dynamics are also impacted by the fractional part of the operator as the derivative order changes.</p></abstract>


1998 ◽  
Vol 11 (1) ◽  
pp. 19-27
Author(s):  
Joseph A. Tami

The quest to understand how genetic information is passed from one generation to the next reached a major milestone in the 1950s with the discovery of the complementary double-helix structure of DNA by Watson and Crick and the demonstration by Kornberg that DNA was capable of self-replication. These breakthroughs provided the stimulus for a flurry of research that culminated in a basic understanding of the genetic code and a statement of the central dogma of molecular biology: DNA goes to RNA goes to protein. In expressing a gene, RNA is formed from the DNA template in a process called transcription. The process of RNA forming protein is known as translation. During translation, amino acids are linked to form protein. The primary structure of proteins is thus determined by the sequence of amino acids. Using x-ray crystallography and computer imaging, it has been possible to determine the three-dimensional structure of many proteins and to design small molecule peptides which can either mimic or block the function of the protein and thus be useful therapeutic agents.



Author(s):  
John Maynard Smith ◽  
Eors Szathmary

The most fundamental distinction in biology is between nucleic acids, with their role as carriers of information, and proteins, which generate the phenotype. In existing organisms, nucleic acids and proteins mutually presume one another. The former, owing to their template activity, store the heritable information: the latter, by enzymatic activity, read and express this information. It seems that neither can function without the other. Which came first, nucleic acids or proteins? There are three possible answers: (1) nucleic acids; (2) proteins; (3) neither: they coevolved. In this chapter, we discuss various possible answers to this 'chicken or egg?' problem. In section 5.2, we discuss what seems to us the most likely answer, that at first RNA performed both functions, as replicator and enzyme. In section 5.3, we consider an alternative view, in which protein enzymes existed either before, or alongside, the first nucleic acids. In section 5.4, we ask whether, perhaps, the first replicators were not nucleic acids. Finally, in section 5.5, we ask why, given that the genetic message is carried by nucleic acids, there are only four nucleotides and two base pairs. So far, we have tacitly assumed nucleic acids preceeded proteins, without stating the main reason. Nucleic acids came first because they can perform both functions: they are replicable, and they can have enzymatic activity. For many years, a common opinion was that to be replicable almost amounted to self-replicative ability, but that it was far-fetched to assume enzymatic activity. Today, there is increasing evidence that RNA can act as an enzyme, but we are more aware of the difficulty of self-replication. It should have been expected on theoretical grounds that RNA could act as an enzyme: the possibility was discussed by Woese (1967), Crick (1968) and Orgel (1968). Consider first why proteins can act as enzymes. An enzyme has a well-determined three-dimensional structure of chemical groups that, in most cases, arises automatically from the primary structure. Substrates of the enzyme are bound by the chemical groups on the surface. This means that the reactants will be kept in close proximity, and hence experience a much higher local concentration of each other than in solution. This by itself increases the rate of the reaction.



Author(s):  
M. Boublik ◽  
W. Hellmann ◽  
F. Jenkins

The present knowledge of the three-dimensional structure of ribosomes is far too limited to enable a complete understanding of the various roles which ribosomes play in protein biosynthesis. The spatial arrangement of proteins and ribonuclec acids in ribosomes can be analysed in many ways. Determination of binding sites for individual proteins on ribonuclec acid and locations of the mutual positions of proteins on the ribosome using labeling with fluorescent dyes, cross-linking reagents, neutron-diffraction or antibodies against ribosomal proteins seem to be most successful approaches. Structure and function of ribosomes can be correlated be depleting the complete ribosomes of some proteins to the functionally inactive core and by subsequent partial reconstitution in order to regain active ribosomal particles.



Author(s):  
Robert Glaeser ◽  
Thomas Bauer ◽  
David Grano

In transmission electron microscopy, the 3-dimensional structure of an object is usually obtained in one of two ways. For objects which can be included in one specimen, as for example with elements included in freeze- dried whole mounts and examined with a high voltage microscope, stereo pairs can be obtained which exhibit the 3-D structure of the element. For objects which can not be included in one specimen, the 3-D shape is obtained by reconstruction from serial sections. However, without stereo imagery, only detail which remains constant within the thickness of the section can be used in the reconstruction; consequently, the choice is between a low resolution reconstruction using a few thick sections and a better resolution reconstruction using many thin sections, generally a tedious chore. This paper describes an approach to 3-D reconstruction which uses stereo images of serial thick sections to reconstruct an object including detail which changes within the depth of an individual thick section.



Author(s):  
T.D. Pollard ◽  
P. Maupin

In this paper we review some of the contributions that electron microscopy has made to the analysis of actin and myosin from nonmuscle cells. We place particular emphasis upon the limitations of the ultrastructural techniques used to study these cytoplasmic contractile proteins, because it is not widely recognized how difficult it is to preserve these elements of the cytoplasmic matrix for electron microscopy. The structure of actin filaments is well preserved for electron microscope observation by negative staining with uranyl acetate (Figure 1). In fact, to a resolution of about 3nm the three-dimensional structure of actin filaments determined by computer image processing of electron micrographs of negatively stained specimens (Moore et al., 1970) is indistinguishable from the structure revealed by X-ray diffraction of living muscle.



Author(s):  
J.L. Williams ◽  
K. Heathcote ◽  
E.J. Greer

High Voltage Electron Microscope already offers exciting experimental possibilities to Biologists and Materials Scientists because the increased specimen thickness allows direct observation of three dimensional structure and dynamic experiments on effectively bulk specimens. This microscope is designed to give maximum accessibility and space in the specimen region for the special stages which are required. At the same time it provides an ease of operation similar to a conventional instrument.



Author(s):  
G. E. Tyson ◽  
M. J. Song

Natural populations of the brine shrimp, Artemia, may possess spirochete- infected animals in low numbers. The ultrastructure of Artemia's spirochete has been described by conventional transmission electron microscopy. In infected shrimp, spirochetal cells were abundant in the blood and also occurred intra- and extracellularly in the three organs examined, i.e. the maxillary gland (segmental excretory organ), the integument, and certain muscles The efferent-tubule region of the maxillary gland possessed a distinctive lesion comprised of a group of spirochetes, together with numerous small vesicles, situated in a cave-like indentation of the base of the tubule epithelium. in some instances the basal lamina at a lesion site was clearly discontinuous. High-voltage electron microscopy has now been used to study lesions of the efferent tubule, with the aim of understanding better their three-dimensional structure.Tissue from one maxillary gland of an infected, adult, female brine shrimp was used for HVEM study.



Author(s):  
Jerome J. Paulin

Within the past decade it has become apparent that HVEM offers the biologist a means to explore the three-dimensional structure of cells and/or organelles. Stereo-imaging of thick sections (e.g. 0.25-10 μm) not only reveals anatomical features of cellular components, but also reduces errors of interpretation associated with overlap of structures seen in thick sections. Concomitant with stereo-imaging techniques conventional serial Sectioning methods developed with thin sections have been adopted to serial thick sections (≥ 0.25 μm). Three-dimensional reconstructions of the chondriome of several species of trypanosomatid flagellates have been made from tracings of mitochondrial profiles on cellulose acetate sheets. The sheets are flooded with acetone, gluing them together, and the model sawed from the composite and redrawn.The extensive mitochondrial reticulum can be seen in consecutive thick sections of (0.25 μm thick) Crithidia fasciculata (Figs. 1-2). Profiles of the mitochondrion are distinguishable from the anterior apex of the cell (small arrow, Fig. 1) to the posterior pole (small arrow, Fig. 2).



Author(s):  
Kenneth H. Downing ◽  
Hu Meisheng ◽  
Hans-Rudolf Went ◽  
Michael A. O'Keefe

With current advances in electron microscope design, high resolution electron microscopy has become routine, and point resolutions of better than 2Å have been obtained in images of many inorganic crystals. Although this resolution is sufficient to resolve interatomic spacings, interpretation generally requires comparison of experimental images with calculations. Since the images are two-dimensional representations of projections of the full three-dimensional structure, information is invariably lost in the overlapping images of atoms at various heights. The technique of electron crystallography, in which information from several views of a crystal is combined, has been developed to obtain three-dimensional information on proteins. The resolution in images of proteins is severely limited by effects of radiation damage. In principle, atomic-resolution, 3D reconstructions should be obtainable from specimens that are resistant to damage. The most serious problem would appear to be in obtaining high-resolution images from areas that are thin enough that dynamical scattering effects can be ignored.



Author(s):  
J.S. Wall ◽  
V. Maridiyan ◽  
S. Tumminia ◽  
J. Hairifeld ◽  
M. Boublik

The high contrast in the dark-field mode of dedicated STEM, specimen deposition by the wet film technique and low radiation dose (1 e/Å2) at -160°C make it possible to obtain high resolution images of unstained freeze-dried macromolecules with minimal structural distortion. Since the image intensity is directly related to the local projected mass of the specimen it became feasible to determine the molecular mass and mass distribution within individual macromolecules and from these data to calculate the linear density (M/L) and the radii of gyration.2 This parameter (RQ), reflecting the three-dimensional structure of the macromolecular particles in solution, has been applied to monitor the conformational transitions in E. coli 16S and 23S ribosomal RNAs in solutions of various ionic strength.In spite of the differences in mass (550 kD and 1050 kD, respectively), both 16S and 23S RNA appear equally sensitive to changes in buffer conditions. In deionized water or conditions of extremely low ionic strength both appear as filamentous structures (Fig. la and 2a, respectively) possessing a major backbone with protruding branches which are more frequent and more complex in 23S RNA (Fig. 2a).



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