Death processes

In apoptotic cell death, several factors such as growth factors, NO, the tumor suppressor gene p53, and the protein encoded by this gene contribute to the process that leads to cell death. One of the functions of p53 protein is the activation of apoptosis if a cell is transformed to a malignant cell. Apoptosis typically leads to the formation of smaller membrane-encapsulated particles within the cell. Apoptotic cell death begins in the nucleus and proceeds to other parts of the cell. The death process may be quite advanced before it can... 

Particle conservation in a vessel is governed by the particle-number continuity equation, essentially a population balance to identify particle numbers in each and every size range and account for any changes due to particle formation, growth and destruction, termed particle birth and death processes reflecting formation and loss of particulate entities, respectively. 

Apoptosis is known as programmed cell death and represents also a control mechanism within the cell that reacts to the changes in its environment. This active cellular death process is characterized by distinctive morphological changes... 

Then, since in any system accumulation is the net result of both evolution and birth/death processes, and since any latex particle can be characterized by a set of physical quantities which will fully specify a given particle or class of particles, one can obtain the following population balance equation (33) ... 

Once apoptosis is triggered, a stereotyped sequence of premitochondrial events occurs that executes the death process 609... 

Once apoptosis is triggered, a stereotyped sequence of premitochondrial events occurs that executes the cell death process. In many cases proteins and/or lipid mediators that induce changes in mitochondrial membrane permeability and calcium regulation are produced or activated. For example, the pro-apoptotic Bcl-2 family members Bax, Bad and Bid may associate with the mitochondrial membrane and modify its permeability. Membrane-derived lipid mediators such as ceramide and 4-hydroxynonenal can also induce mitochondrial membrane alterations that are critical for the execution of apoptosis. 

Antiapoptotic proteins. There are many different intracellular proteins that can prevent apoptosis by inhibiting specific steps in the cell death process. These include Bcl-2 family members such as Bcl-2 and Bcl-xL which can stabilize (mitochondrial, ER and plasma) membranes (Bcl-2 may also have intrinsic antioxidant activity). Other proteins, IAPs such as XIAP (X-linked) and NIAP (neuronal), which can directly inhibit caspases [31]. Additional examples of antiapoptotic proteins include protease inhibitors such as calpastatin, and protein chaperones such as GRP-78 and heat shock protein (HSP)-70. 

Examples include birth—death processes, die Poisson process, and die random telegraph process. 

Antonsson and Marinou 2000 Adams and Cory, 1998). Stress may also cause inaease, nitric oxide (NO), or reactive oxygen species (ROS) production which, in turn, triggers release of apoptotic proteins from the intermemhrane space (Kroemer and Reed, 2000 Vieira et at, 2000). Release of these proteins from mitochondria are required for stress induced killing hut are, with a few exceptions (Bergmann et al, 1994, Schulze- Osthoff et al, 1993), dispensible for CD95 and TNF-receptor transduced apoptosis. These other death processes require FADD and caspase-8 to be recruited into the death receptor complexes and cannot be blocked by Bcl-2 (Krammer, 2000 Scaffidi et al, 1998). 

According to the second law, (W) = Q) > 0, which implies that the average switching field is positive, (// ) > 0 (as expected due to the time lag between the reversal of the field and the reversal of the dipole). The work distribution is just given by the switching field distribution p H ). This is a quantity easy to compute. The probability that the dipole is in the down state at field H satisfies a master equation that only includes the death process,... 

Appearance of dying cells Shrink by 50% Swell during death process... 

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... 

Although not all cell death involves mitochondrial dysfunction, it often does. The various cellular changes and sequelae and effects on and changes in the mitochondria have been described above and the critical "decision points" between recovery, necrosis, and apoptosis have been outlined. What then occurs in the orderly cell death process of apoptosis ... 

In this section we shall present a few of the elementary type reactions that have been solved exactly. By elementary we mean unimolecular and bimolecular reactions, and simple extensions of them. In a more classical stochastic context, these reactions may be thought of as birth and death processes, unimolecular reactions being linear birth and death processes and bimolecular being quadratic. These reactions may be described by a finite or infinite set of states, (x), each member of which corresponds to a specified number of some given type of molecule in the system. One then describes a set of transition probabilities of going from state x to x — i, which in unimolecular reactions depend linearly upon x and in bimolecular reactions depend quadratically upon x. The simplest example is that of the unimolecular irreversible decay of A into B, which occurs particularly in radioactive decay processes. This process seems to have been first studied in a chemical context by Bartholomay.6... 

Just as in the unimolecular cases, the basis for the stochastic approach is to consider the reaction 2A-> B as being a pure death process with a continuous time parameter and transition probabilities for the elementary events that make up the reaction process. Letting the random variable X(t) be the number of A molecules in the system at time t, the stochastic model is then completely defined by the following assumptions ... 

Exercise. In a population of n bacteria, each individual has a probability a per unit time to die and / to give birth to a new individual. Construct the M-equation ( birth and death process , compare chapter VI). 

The one-step or birth-and-death processes are a special class of Markov processes, which occur in many applications and can be analyzed in some detail. 

Many stochastic processes are of a special type called birth-and-death processes or generation-recombination processes . We employ the less loaded name one-step processes . This type is defined as a continuous time Markov process whose range consists of integers n and whose transition matrix W permits only jumps between adjacent sites,... 

Observe that the steps only go in one direction, as in radioactive decay ( pure death process ). As a consequence it is, in principle, possible to obtain... 

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