Exponential cell growth

When microbial cells are incubated into a batch culture containing fresh culture media, their increase in concentration can be monitored. It is common to use the cell dry weight as a measurement of cell concentration. The simplest relationships describing exponential cell growth are unstructured models. Unstructured models view the cell as an entity in solution, which interacts with the environment. One of the simplest models is that of Malthus 19... 

The average time required for a cell to perform an entire cell cycle successively is defined as the cell cycle time (Tc), that in asynchronous cells and without quiescent fraction can be approximate to doubling time, calculated from exponential cell growth. 

Normal animal cell growth curve pattern, in which p is the specific cell growth rate. Lag phase (A) represents the culture adaptation period, followed by an exponential cell growth phase (B) until the attainment of a stationary or plateau phase (C), in which there is no increase in cell number. The culture reaches the senescence phase (D) when the percentage of cells in division becomes lower than the percentage of cells dying. 

However,this solution is not stable and small deviations from the steady state lead to either washout or exponential cell growth and limited growth.All solutions for tower loop reactors yield the corresponding solutions for tower reactors if y is set to zero. 

Exponential growth The phase of cell growth in which the number of cells or the cell mass increases exponentially. 

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... 

A limiting case of Monod kinetics has Ks = 0 so that cell growth is zero order with respect to substrate concentration. Rework Example 12.7 for this situation, but do remember to stop cell growth when S = 0. Compare your results for X and p with those of Example 12.7. Make the comparison at the end of the exponential phase. 

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. 

The exponential and limiting regions of cell growth can be described by a single relation, in which /x is a function of substrate concentration, i.e., the Monod equation... 

In case the Monod equation holds for the rates of cell growth in the exponential growth, with decelerating and stationary phases in a uniformly mixed fermentor operated batchwise, a combination of Equations 4.2 and 4.6 gives... 

Here are some other statistics on cell growth. Bacteria growing exponentially expand their linear dimensions by 1.5 nm and synthesize 1.6 x 107 Da of new cell material in one second. This is equivalent to -1000 small proteins and includes 23 ribosomes and 3000 base pairs of DNA at each growing point. The much larger HeLa human tumor cell grows by 0.13 nm / s but makes 4.6 x 108 Da/ s of materials... 

Table 6.1 shows the ACSL program and Figure 6.6 shows the results. Comparison of Figure 6.6 with Figure 6.1 shows that Monod kinetics can predict the cell growth from the start of the exponential growth phase to the stationary phase. 

Here /rmax is the nomenclature for the maximum cell growth rate [typically in h-1 (reciprocal hours)] and Cx is the mass concentration of cells (g/L). Hence the cell growth rate initially is exponential with time (called the exponential growth phase). 

The maximum biosurfactant production was verified at pH 7.0 and 8.0. The addition of EDTA and microsalts favored microbial synthesis of surface-active compounds. On the other hand, the addition of yeast extract stimulated cell growth to the detriment of biosurfactant production. The most suitable concentration of commercial sucrose for biosurfactant synthesis was 10 g/L. Biosurfactant production occurred in the late-exponential phase, achieving its maximum value at the early stationary phase of growth. The values of surface tension that we obtained compare favorably with those obtained with commercial synthetic surfactants. 

Cell growth phases comprise lag phase, exponential or log growth phase, stationary or plateau phase, and senescence or death phase, as shown in Figure 2.5. Cell growth can be mathematically represented by the following general equation ... 

The other typical situation is that shown in Figure 8.2E, in which the px is maximum from the beginning of culture. During the exponential growth phase, the specific growth rate remains at the maximum value (px,max) until any nutritional limitation or inhibition by toxic products alters cell growth. Thus, a specific growth rate reduction can be observed. 

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