Bacterial fractal

Serra, T. and Logan, B. E. (1999). Collision frequencies of fractal bacterial aggregates with small particles in a sheared fluid. Environ. Set Technol., 33, 2247-2251. 

The fractal nature of bacterial aggregates (floes) has implications for transport processes, including movement of dissolved respiratory gases to and from the outside of the aggregate, and for movement of dissolved nutrient sources and metabolic products. Several methods have been employed to estimate fractal dimensions of floes in three dimensions. One approach is to measure light scattering of suspended floes [17,18]. The two-slopes method calculates fractal dimensions A from the slope of the cumulative size distribution for maximum length / and the slope of the cumulative solid volume F [17] ... 

Confocal optical microscopy can be used to take a sequence of randomly chosen images through a bacterial floe. Methodologies for calculation of three-dimensional fractal dimensions have been described for this approach [18-20]. One method determines the fractal dimension of each section 7)f using a two-point correlation function C(r) [20] ... 

The majority of studies of fractal geometry of bacteria and unicellular fungi (yeasts) have been performed in agar culture, in which the solidity of the medium, nutrient concentration, inhibitory chemicals and incubation conditions (temperature) have been varied. With regard to bacterial pathogens, Escherichia coli, Citrobacter freundii, Klebsiella pneumoniae, Proteus mirabilis. Salmonella anatum. Salmonella typhimurium and Serratia marcescens produced colonies with Dbm values between 1.7 and 1.8 [22, 23], whereas Klebsiella ozaenae had more open colonies, Dbm = 1.6 [24]. Colony morphology is dramatically affected by nutrient supply [19, 20] and nonlethal concentrations of antibiotics [5]. For example, the fractal dimension of... 

Ben-Jacob, E., Shochet, O., Cohen, L, Tenenbaum, A., Czirok, A. and Vicsek, T. (1995). Cooperative strategies in formation of complex bacterial patterns. Fractals - Interdiscipl. J. Complex GeorrL Nature, 3, 849-868. 

In the earlier chapter we have discussed the formation of colour bands in moving wave fronts, stationary structures which are governed by coupling of reaction and diffusion. In this chapter we will be concerned with pattern formation governed by the process of mass flow and diffusion related to precipitation as crystals, electro-deposits, bacterial colonies and diffusion. Just as in the former case, in the present case also we come across very complex patterns, depending on the experimental conditions. However in the present case it is possible to rationalize the complex structure with use of new mathematical concepts of fractal geometry. 

Fractal dimensions of some non-living and living systems including crystallization patterns, electro-deposited aggregates, polymers, chemical dissolution patterns, dielectric breakdown, sputter deposited film of NbGcj, retinal vessel and bacterial growth are given in Table 13.3. 

Recently, considerable efforts have been made to understand the formation of biological patterns using fractal ideas and models. Of particular interest has been the study of simple biological forms such as bacterial colonies similar to diffusion-limited aggregates obtained during non-equilibrium growth process in non-living systems. 

Blood vessels of the heart exhibit fractal-like branching. The large vessels branch into smaller vessels, which in turn branch into smaller and smaller capillaries. Ultimately, they become so narrow that blood cells are forced to flow through a single file. The fractal character of bacterial growth has already been pointed out in Chapter 12 on fractals. 

The aggregates comprised of bacterial cells can be treated using a fractal dimension [144]. Thus, the radius Ta,k of a size class (c-aggregate can be expressed as [147]... 

In the laboratories of professor Eshel Ben-Jacob of Tel-Aviv University, in collaboration with professor Herbert Levine of University of California, San Diego s Center for Theoretical Biological Physics, bacterial forms grown in petri dishes display remarkable fractal oi anization, demonstrating principles of intelligent cooperation in response to a variety of environmental stressors. 

Because most of thermodynamic computations are carried out in the thermodynamic limit (i.e., for V +oo, N oo, N/V = constant), the effect of periodic boxmdary conditions disappears in this limit. There are, however, several systems of practical and conceptual interest, the shape of which is not regular among them, we mention queer systems, with areas inereasing in proportion to V (examples being zeolites or bacterial strains) [14], or fractal systems, with unmeasurable areas (examples being certain porous solids) [15]. In these systems, the boxmdary conditions affect the thermodynamic properties even in the thermodynamie limit and eaimot, therefore, be assumed on the basis of easier computability. 

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