Growth dynamics

This section gives models for the rates of birth, growth, and death of cell populations. We seek models for (1) the rate at which biomass is created, (2) the rates at which substrates are consumed, (3) the rates at which products are generated, (4) the maintenance requirements for a static population, and (5) the death rate of cells. The emphasis is on unstructured models. 

Biomass Production. Biomass is usually measured by dry weight of viable cells per unit volume X. We bypass the sometimes tricky problems associated with this measurement except to say that it is the province of the microbiologist and usually involves plate cultures and filtration followed by drying. Suppose there is one limiting nutrient S, and that all other nutrients are available in excess. Then the Monod model for growth is 

It is possible for two or more substrates to become simultaneously limiting. Define a growth limitation factor, G, 1, for substrate i such that 

Any substance present in great excess can inhibit growth or even cause death. Metabolic products are often toxic to the organism that produces them. Thus, a batch fermentation can be limited by accumulation of products as well as by depletion of the substrate. A simple model for growth in the presence of an inhibitor is 

Cell cultures can be inhibited by an excessive concentration of the substrate. One way to model substrate inhibition is to include an term in the denominator of the rate equation. See Equation (12.4). 

The factor Giis determined by growth experiments that manipulate the single variable 5i. Dual limitations can be modeled using a multiplicative form 

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A. Hopkinson, J. M. Bradley, X.-C. Guo, D. A. King, Nonlinear island growth dynamics in adsorbate-induced restructuring of quasihexagonal reconstructed Pt(lOO) by CO. Phys Rev Lett 77 1597-1600, 1993. 

Note that it is important for final drive-train alignment to compensate for actual operating conditions because machines often move after start up. Such movement is generally the result of wear, thermal growth, dynamic loads, and support or stmctural shifts. These factors must be considered and compensated for during the alignment process. 

Once we know the chemical nature of the allelopathic agents and their effects on plant growth dynamics, as well as on health and environment, we can apply genetic manipulation and biotechnology to develop toxin-resistant plants and to reduce the toxin levels frcm the donor plants. These approaches serve a dual purpose because they contribute to increased agricultural productivity and help to minimize the potential risks on health and environment. 

As stated earlier, mycorrhizae enhance nutrient absorption. Greater soil exploitation by mycorrhizal roots as a means of increasing phosphate uptake is well established. The normal phosphate depletion zone around non-mycorrhizal roots is 1-2 mm, but an endomycorrhizal root symbiont increased this zone to 7 cm (140). This ability to increase the nutritional level (particularly with regard to phosphorus), and subsequently the overall better growth dynamics of the mycorrhizal plant has been suggested as the reason for the salt (43) and drought (44-46) tolerance and increased nodulation (47) observed in mycorrhizal associations. Another interesting aspect of this enhanced nutrient uptake is the possible effect of mycorrhizae on competitive ability between two plant species. Under some conditions, mycorrhizal... 

Beyrouty CA, Wells BR, Norman RJ, Marvel JN, Pillow JA. Root growth dynamics of a rice cultivar grown at two locations. Agron. J. 1988 80 1001-1004. 

Most treatments of bubble growth dynamics assume that, as the bubble expands, Eq. (7) is still valid although the pressure may drop due to the expansion from both temperature variations in the bubble and the increase in radius—to lessen the surface forces, i.e., at any time in the growth. 

Thurman GB, Mays CW, Taylor GN, et al. 1971. Growth dynamics of beagle osteosarcomas. Growth 35 119-125. 

Meyer zu Heringdorf F-J, Reuter MC, Tromp RM (2001) Growth dynamics of pentacene thin films. Nature 412 517-520... 

Billig (98) realized this point and used a one-dimensional heat-transfer analysis for the crystal with assumptions about the temperature field in the melt to derive the the following relationship that has been used heavily in qualitative discussions of crystal growth dynamics ... 

Williams, F. M., "A Model of Cell Growth Dynamics," /, Theoret. Biol. 15(1967) 190-207. 

Several studies have recently appeared which combine UPD and SHG on single crystal Ag, Cu (Section 5.2.3) and Au (Section 5.3.3). Ideally, one would like to be able to characterize the physical structure, the electronic properties and the growth dynamics of the interfacial region by SHG as deposition occurs. On the more fundamental side, one would like to gain further insight into the nonlinear polarizability at metal surfaces by taking advantage of the unique alterations in the surface properties that can be done easily by UPD. All of these issues have been addressed in the studies described below. 

Pirc, H. (1985) Growth dynamics in Posidonia oceanica (L.) Delile. I. Seasonal changes of soluble carbohydrates, starch, free amino acids, nitrogen and organic anions in different parts of the plant. Publ. Staz. Zool. Napoli I Mar. Ecol. 6, 141-165. 

Hence, the location of bacteria in cheese at the fat-casein interface may be important in relation to the growth dynamics of starter and non-starter bacteria in cheese and their effects on cheese maturation (cf. Sections 11.5, 11.7-11.8). 

Smith WO, Carlson CA, Ducklow HW, Hansell DA (1998) Growth dynamics of Phaeocystis antarctica-Aomm ttA... 

Smith WO, Carlson CA, Ducklow HW, Hansell DA (1998) Growth dynamics of Phaeocystis antarctica-dominated plankton assemblages from the Ross Sea. Mar Ecol Prog Ser 168 229-244 Solomon CM, Lessard EJ, Keil RG, Foy MS (2003) Characterization of extracellular polymers of Phaeocystis globosa and P. antarctica. Mar Ecol Prog Ser 250 81-89... 

Solar furnace Solar rays focused on a metal doped graphite target. Growth dynamics similar to PLV 1.4 Good quality CNTs, little amorphous carbon. Spreading not expected in the near furture... 

Deactivation of growing carbenium ions by reaction with sulfides is evidently very fast. Sulfonium ion formation is exothermic (AH = -40 kJ/mol) and exoentropic (AS = -74 J/mol-K) [271]. High equilibrium constants (Keq = 104 moI-1L) for sulfonium ion formation were calculated from the apparent rate constants of propagation and the rate constants of carbocationic growth. Dynamic NMR experiments of model systems with tetrahydrothiophene indicate that the bimolecular deactivation rate constant is kdeacl 106 mol-1-Lsec-1 at 0° C (AH = 20 kJ/mol, AS = -37 J-mol-K), and that activation is faster than bimolecular exchange (k act foe) [67]. 

Rod growth dynamics also depend upon the identity of the phosphonic acid. The effectiveness of the phosphonic acid in promoting rod growth depends critically on its steric bulk, or the length of its alkyl chain. Shorter-chain phosphonic acids, such as HPA, more effectively promote rod growth compared to longer-chain phosphonic acids, such as tetradecylphosphonic acid (TOPA). Combinations of longer-and shorter-chain phosphonic acids can be used to readily tune rod aspect ratios and control shape evolution dynamics. 

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