Replication stochastic process

Ultimately a plasmid is defined by its mode of DNA replication. DNA replication is initiated at a single, characteristic sequence, termed the origin. The origin sequence determines the copy number of the plasmid relative to the host chromosome and the host enzymes that are involved in plasmid replication. Two different plasmids that contain the same origin sequence are termed incompatible. This term does not refer to the active exclusion of one plasmid by another from the cell but rather to a stochastic process by which the two plasmids are partitioned differentially into progeny cells. A cell which contains two plasmids of the same incompatibility group segregates two clonal populations, each of which has one of the two plasmids in it. 

The first example is due to Rudd (1960) and concerns the optimal number of replications of the preparation of chemicals needed in a main process. If these preparations are subject to failure and if it is quite essential that they should be available without delay to the main process, it will be advisable to prepare more than one batch but this will become expensive if too many are prepared. The second example is a transliteration into manufacturing terms of Bellman s stochastic gold mining process (1957, Chapter 2). The third is a consideration of some of the simpler models of catalyst replacement policy that have been discussed by Roberts (1960a,b). 

Several attempts to describe replication-mutation networks by stochastic techniques were made in the past. We cannot discuss them in detail here, but we shall brieffy review some general ideas that are relevant for the quasispecies model. The approach that is related closest to our model has been mentioned already [51] the evolutionary process is viewed as a sequence of stepwise increases in the populations mean fitness. Fairly long, quasi-stationary phases are interrupted by short periods of active selection during which the mean fitness increases. The approach towards optimal adaptation to the environment is resolved in a manner that is hierarchical in time. Evolution taking place on the slow time scale represents optimization in the whole of the sequence space. It is broken up into short periods of time within which the quasi-species model applies only locally. During a single evolutionary step only a small part of sequence space is explored by the population. There, the actual distributions of sequences resemble local quasispecies confined to well-defined regions. Error thresholds can be defined locally as well. 

A problem with random profiles is their repeatability from sample to sample, since it depends on a number of process parameters and their very nature is stochastic. Some solutions that could be applied to overcome this is to use advanced replication technologies like, e.g., nanoimprint to replicate the optimized random profile. Another is to apply top-down planar fabrication to pattern quasiperiodic stmctures that behave as pseudorandom, although they are actually deterministic. 

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