Exponential growth constant

Thus, the exponential growth constant of the pressure oscillation is directly related to the acoustic admittance of the propellant. Hence, the acoustic admittance can be evaluated directly from the growth rate of the pressure amplitude. Ryan (R5) has also desired this espression on the basis of acoustic-energy considerations. 

Since the right-hand side of (6.4.3) is the unconditional cell division rate, the exponential growth constant also inherits this interpretation. Alternatively, pdt represents the probability that there is a division between t and t + dt regardless of the size of the dividing cell. In what follows, we first address the determination of the growth rate L(/). 

The specific growth constant for exponential growth, )J., is defined a.s x dt = dM/M where M is the yeast mass and / is time. Growth is also... 

A function is said to be piecewise continuous on an intei val if it has only a finite number of finite (or jump) discontinuities. A function/on 0 < f < oo is said to be of exponential growth at infinity if there exist constants M and Ot such that l/(t)l < for sufficiently large t. 

Xanthan is synthesised during exponential growth of the culture, whereas sucdnoglycan is synthesised after growth has ceased (biomass constant). 

Once there is an appreciable amount of cells and they are growing very rapidly, the cell number exponentially increases. The optical cell density of a culture can then be easily detected that phase is known as the exponential growth phase. The rate of cell synthesis sharply increases the linear increase is shown in the semi-log graph with a constant slope representing a constant rate of cell population. At this stage carbon sources are utilised and products are formed. Finally, rapid utilisation of substrate and accumulation of products may lead to stationary phase where the cell density remains constant. In this phase, cell may start to die as the cell growth rate balances the death rate. It is well known that the biocatalytic activities of the cell may gradually decrease as they age, and finally autolysis may take place. The dead cells and cell metabolites in the fermentation broth may create... 

The cultures grew at 18-20°C under a constant illumination (150 pmol photons m 2-s 1) provided by cool-white fluorescence lamps. For the anaerobic induction, cells were harvested by centrifugation (5 min, 3000xg) in the exponential growth phase at an approximate culture concentration of2><106 cells ml 1 and afterwards resuspended in fresh TAP medium. 

Chinese hamster ovary cells in which there has been an extensive rearrangement of chromosome material and the chromosome number may not be constant from cell to cell, are frequently used. Polyploidy, endoreduplication and high spontaneous chromosome aberration frequencies can sometimes be found in these established cell lines, but careful cell culture techniques should minimize such effects. Cells should be treated in exponential growth when cells are in all stages of the cell cycle. 

In general the stoichiometry can be messy with fractional yields changing with composition. Treatment of that case can be difficult. We d like therefore to make the simplification that all

mixed flow, or for the exponential growth period of batch reactors, otherwise it is questionable. 

To describe the long-term trend we use an exponential growth or decay curve and characterize it by the rate constant a [T1] ... 

The exponential growth rate constant k is equal to the number of doublings per unit time. Thus, k is the reciprocal of the doubling time. It is easy to show that the number of bacteria present at time t will be given by the following equation. 

When bacteria are inoculated into growth medium, there is a delay (lag phase) before division and exponential growth ensue. The rate of exponential growth is a characteristic of the bacterial strain, the temperature, and the nutritional environment. The amount of DNA per nuclear body remains constant at various growth rates, although cell mass and average number of nuclei per cell are functions of the growth rate. 

KNIGHTS163 devised a procedure for determining the kinetic constants of a batch fermentation system which involves monitoring both the biomass and substrate concentrations, but without assuming a constant yield coefficient. Exponential growth in a batch fermenter is represented by equation 5.55 written as ... 

Figure 4. Preparative isoelectric focusing in a granulated gel of a desalted lyophilized culture filtrate (50 mg protein) from the late exponential growth phase of Thermoactinomyces sp. Separation carried out for 48 hr at a constant power of 8 W (29). (C>) CM-cellulase activity (A) Avicelase activity (6).

Therefore, the growth rate defined as the change of cell number with time is the slope of the CN versus t curve, while the division rate is the slope of the log2CN versus t curve. As explained later, the division rate is constant during the exponential growth period, while the growth rate is not. Therefore, these two terms should not be confused with each other. 

Exponential growth phase The cell number increases exponentially as the cells start to divide. The growth rate is increasing during this phase, but the division rate which is proportional to dlnCNl/dt, is constant at its maximum value, as illustrated in Figure 6.1. 

If jl is constant with time during the exponential growth period, Eq. (6.5) can be integrated from time t1 to t as... 

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