Logarithmic growth

The above rate law has been observed for many metals and alloys either anodically oxidized or exposed to oxidizing atmospheres at low to moderate temperatures—see e.g. [60]. It should be noted that a variety of different mechanisms of growth have been proposed (see e.g. [61, 62]) but they have in common that they result in either the inverse logaritlnnic or the direct logarithmic growth law. For many systems, the experimental data obtained up to now fit both growth laws equally well, and, hence, it is difficult to distinguish between them. 

A logarithmic growth curve when cavities acted as diffusion barriers. 

Batch fermentation is the most widely used method of amino add production. Here the fermentation is a dosed culture system which contains an initial, limited amount of nutrient. After the seed inoculum has been introduced the cells start to grow at the expense of the nutrients that are available. A short adaptation time is usually necessary (lag phase) before cells enter the logarithmic growth phase (exponential phase). Nutrients soon become limited and they enter the stationary phase in which growth has (almost) ceased. In amino add fermentations, production of the amino add normally starts in the early logarithmic phase and continues through the stationary phase. 

Conway BE, Barnett B, Angerstein-Kozlowska H, Tilak BV. 1990. A surface-electrochemical basis for the direct logarithmic growth law for initial stages of extension of anodic oxide films formed at noble metals. J Chem Phys 93 8361-8373. 

An exponential (or logarithmic) growth phase follows the lag phase, and during this period the cell mass increases exponentially. The growth rate is at a maximum during this phase, and the population of cells are fairly uniform with respect to chemical composition and metabolic composition. 

Where i is determined from the logarithmic growth rate. 

Figure 5. Production of subtilisin. A culture of B.subtilis was grown in supplemented nutrient broth (75) and subtilisin production was followed. T-0 indicates the time of first departure from logarithmic growth. Subtilisin levels are indicated as arbitrary units/ml.

The temperature of incubators must be uniform throughout and should not vary more than 0.2 C. The vegetative assay organism must be sensitive to the analyte, be stable (resistant to spontaneous change), be in the logarithmic growth phase (for uniformity of response), and be easily cultured, maintained and standardized. Spores suspension have similar criteria except that the spores must be capable of germinating with reasonable synchrony. 

A striking accumulation of Mn2+ often occurs within bacterial spores (Chapter 32). Bacillus subtilus absolutely requires Mn2+ for initiation of sporulation. During logarithmic growth the bacteria can concentrate Mn2+ from 1 pM in the external medium to 0.2 mM internally during sporulation the concentrations become much higher.593... 

Equation (6) predicts a logarithmic growth of the concentration of defects without any saturation. To obtain the saturation effect, which has been experimentally observed by the authors themselves [17], a hypothetical secondary reaction was introduced. The defects of this model were discussed earlier, while we note only that in the initial stage the relationship (6) qualitatively resemble the previous ones. This also has been used in interpreting... 

A mathematical model of the fermentation of the bacterium Pseudomonas ovalis, which produces gluconic acid, has been developed (Rai Constantinides, AIChE Symposium Series 69 No 132, 114, 1973). This model which describes the dynamics of the logarithmic growth phase is summarized as follows. 

Maintain Raji cells in RPMI-1640/10% fetal calf syndrom (FCS) in a humidified 37°C, 5% C02 incubator. Before the day of electroporation, dilute the culture 3X to ensure that the cells are in logarithmic growth phase. 

Suspension cells should be transfected when they are in the logarithmic growth phase which is generally, 106-107 cells per mL. It is important to avoid extra pipetting or unnecessary washing steps. Do not vortex cells. 

For this purpose, an 18-hour-old nutrient broth culture of a bacterium sensitive to a particular phenothiazine was used. 2 ml of this 18-hour-old broth culture was added to 4 ml of a fresh broth. This was incubated at 37 °C for 2 h, so that the bacterial culture could attain the logarithmic growth phase. At this point, the number of viable cells in the culture was determined by the colony forming unit (CFU) count, as described by Miles and Misra [65]. The drug was added at a concentration higher than the respective MIC value at the logarithmic growth phase of the culture. The CFU counts were determined at intervals of 2 h, 6 h and then after 18 h. 

The MIC of thioridazine with respect to Staphylococcus aureus ML 322 was 200 pg/ml. At the logarithmic growth phase of the culture, when CFU count was 7.6 x 108, 400 xg/ml of the drug was added. After 2 h there were no five cells in the culture, proving severe bactericidal action of thioridazine on Staphylococcus aureus (Fig. 3). Similar action was observed when the drug... 

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