Exponential death

The death of a single microbial cell is a biochemical process (or series of processes) the entrapment of individual microbial cells in or on filters is due to physical forces. These effects on individual cells are peculiar to individual sterilization processes. On the other hand, the effects of inactivating processes and filtering processes on populations of microbial cells are sufficiently similar to be described by one general form—exponential death. Exponential kinetics are typical of first-order chemical reactions. For inactivation this can be attributed to cell death arising from some reaction that causes irreparable damage to a molecule or molecules essential for continuing viability. 

The death rate coefficient is usually relatively small unless inhibitoiy substances accumulate, so Eq. (24-10) shows an exponential rise until S becomes depleted to reduce [L. This explains the usual growth curve (Fig. 24-21) with its lag phase, logarithmic phase, resting phase, and declining phase as the effect of takes over. 

During the stationary phase, the growth rate is zero as a result of the depletion of nutrients and essential metabolites. Several important fermentation produets (ineluding most antibioties) are produeed in the stationary phase. The stationary phase is followed by a phase where eells die or sporulate. During the death phase, there is a deerease in live eell eoneentration, whieh results from the toxie byproduets eoupled with the depletion of the nutrient. The number of viable eells usually follows an exponential deeay eurve during this period. 

Figure 2.5-2 depicts the force of mortality as a bathtub curve for the life-death history of a component without repair. The reasons for the near universal use of the constant X exponential distribution (which only applies to the mid-life region) are mathematical convenience, inherent truth (equation 2.5-19), the use of repair to keep components out of the wearout region, startup testing to eliminate infant mortality, and detailed data to support a time-dependent X. 

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... 

If the cells are in the exponential growth period and there is no cell death rate, a 0. The net cell concentration is ... 

For each run, calculate and plot the cell biomass concentration, glucose concentration, ethanol concentration, and pH as a function of time. Identify the major phases in batch fermentation lag, exponential, stationary and death. 

It was realized at the end of the nineteenth century that there was an exponential relationship between potency and concentration. Thus, if the log)o of a death time, that is the time to kill a standard inoculum, is plotted against the logio of the concentration, a straight line is usually obtained, the slope of which is the concentration exponent (77)... 

The fluorescence decay time is one of the most important characteristics of a fluorescent molecule because it defines the time window of observation of dynamic phenomena. As illustrated in Figure 3.2, no accurate information on the rate of phenomena occurring at time-scales shorter than about t/100 ( private life of the molecule) or longer than about 10t ( death of the molecule) can be obtained, whereas at intermediate times ( public life of the molecule) the time evolution of phenomena can be followed. It is interesting to note that a similar situation is found in the use of radioisotopes for dating the period (i.e. the time constant of the exponential radioactive decay) must be of the same order of magnitude as the age of the object to be dated (Figure 3.2). 

The solution to these kinetics is clearly unstable because it predicts unlimited exponential growth. Therefore, we need to assume that there is some sort of a death reaction. One form of this might be... 

The first implantable cardioverter-defibrillator (ICD) was placed in 1982. Since that time, their use has expanded exponentially. Several large clinical trials have demonstrated the superiority of ICDs compared with pharmacological therapy for the secondary prevention of arrhythmic death and possibly as primary therapy for patients at risk for ventricular arrhythmias. 

In a well mixed bioreactor a homogeneous suspension exists and typical growth kinetics an be observed as illustrated in Figure 5.17. Six phases can be distinguished the lag phase acceleration phase the exponential growth phase the deceleration phase the stationary phase and the phase at which death/decline occurs. 

The BEIR III risk estimates formulated under several dose-response models demonstrate that the choice of the model can affect the estimated excess more than can the choice of the data to which the model is applied. BEIR III estimates of lifetime excess cancer deaths among a million males exposed to 0.1 Gy (10 rad) of low-LET radiation, derived with the three dose-response functions employed in that report, vary by a factor of 15, as shown in Ikble 6.1 (NAS/NRC, 1980). In animal experiments with high-LET radiation, the most appropriate dose-response function for carcinogenesis is often found to be linear at least in the low to intermediate dose range (e.g., Ullrich and Storer, 1978), but the data on bone sarcomas among radium dial workers are not well fitted by either a linear or a quadratic form. A good fit for these data is obtained only with a quadratic to which a negative exponential term has been added (Rowland et al., 1978). 

These considerations have been extensively explored by producers of canned foods and some simplified kinetics have been derived to allow better control of sterilization procedures. For example, the overall death process in a mixed culture can be described by an exponential decay curve. The equation will follow the form... 

The D value is the determining factor if the death rate is, indeed, exponential, an assumption which is not necessarily always valid. Although only conditions which supply a single D value would be sufficient to completely sterilize a solution containing, say, one organism per unit volume, most heat sterilization processes are designed to administer 12D. This is an example of overkill and becomes more evident the fewer organisms there are in the untreated product in the first place. 

Biocompatibility of implanted devices is exponentially more complicated than biocompatibility of topical devices. Rejection of a topical device is not a major issue but it represents the primary difficulty for a device that enters the body. The device will come into contact with fluids and cells that are sensitive to contacts with foreign materials. The success of the biofilters discussed in the last chapters is an implication of a level of biocompatibility. Bacteria are somewhat forgiving because they are able to tolerate contacts that would cause instant death to mammalian cells. Bacteria have evolved to the point where they are able to attach themselves to almost anything. 

The stationary phase is usually followed by a death phase in which the organisms in the population die. Death occurs either because of the depletion of the cellular reserves of energy, or the accumulation of toxic products. Like growth, death is an exponential function. In some cases, the organisms not only die but also disintegrate, a process called lysis. 

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