A MARKOV-MODULATED GROWTH COLLAPSE MODEL

We consider a growth collapse model in a random environment for which the input rates might depend on the state of an underlying irreducible Markov chain and at state change epochs there is a possible downward jump to a level that is a random fraction of the level just before the jump. The distributions of these jumps are allowed to depend on both the originating and target states. Under a very weak assumption we develop an explicit formula for the conditional moments (of all orders) of the time stationary distribution. We then consider special cases and show how to use this result to study a growth collapse process in which the times between collapses have a phase-type distribution.

Optimal harvest of a forest in the presence of uncertainty

A method is described for finding logging levels to maximize harvest in a finite horizon type II model. Uncertainty is considered in the form of the risk of forest fires and other environmental hazards, which may destroy a random fraction of the existing forest. Numerical results include upper and lower bound approximations to the original problem.

Saccharomyces cerevisiae cdc2 mutants fail to replicate approximately one-third of their nuclear genome.

Chromosomal DNA replication was examined in temperature-sensitive mutants of Saccharomyces cerevisiae defective in a gene required for the completion of S phase at the nonpermissive temperature, 37 degrees C. Based on incorporation of radioactive precursors and density transfer experiments, strains carrying three different alleles of cdc2 failed to replicate approximately one-third of their nuclear genome at 37 degrees C. Whole-cell autoradiography experiments demonstrated that 93 to 96% of the cells synthesized DNA at 37 degrees C. Therefore, all cells failed to replicate part of their genome. DNA isolated from terminally arrested cells was of normal size as measured on neutral and alkaline sucrose gradients, suggesting that partially replicated DNA molecules do not accumulate and that DNA strands are ligated properly in cdc2 mutants. In addition, electron microscopic examination of the equivalent of more than one genome's DNA from arrested cells failed to reveal any partially replicated molecules. The sequences which failed to replicate at 37 degrees C were not highly specific; eight different cloned sequences replicated to the same extent as total DNA. The 2-microns plasmid DNA and rDNA replicated significantly less well than total DNA, but approximately one-half of these sequences replicated at 37 degrees C. These observations suggest that cdc2 mutants are defective in an aspect of initiation of DNA replication common to all chromosomes such that a random fraction of the chromosomes fail to initiate replication at 37 degrees C, but that once initiated, replication proceeds normally.

Saccharomyces cerevisiae cdc2 mutants fail to replicate approximately one-third of their nuclear genome

Chromosomal DNA replication was examined in temperature-sensitive mutants of Saccharomyces cerevisiae defective in a gene required for the completion of S phase at the nonpermissive temperature, 37 degrees C. Based on incorporation of radioactive precursors and density transfer experiments, strains carrying three different alleles of cdc2 failed to replicate approximately one-third of their nuclear genome at 37 degrees C. Whole-cell autoradiography experiments demonstrated that 93 to 96% of the cells synthesized DNA at 37 degrees C. Therefore, all cells failed to replicate part of their genome. DNA isolated from terminally arrested cells was of normal size as measured on neutral and alkaline sucrose gradients, suggesting that partially replicated DNA molecules do not accumulate and that DNA strands are ligated properly in cdc2 mutants. In addition, electron microscopic examination of the equivalent of more than one genome's DNA from arrested cells failed to reveal any partially replicated molecules. The sequences which failed to replicate at 37 degrees C were not highly specific; eight different cloned sequences replicated to the same extent as total DNA. The 2-microns plasmid DNA and rDNA replicated significantly less well than total DNA, but approximately one-half of these sequences replicated at 37 degrees C. These observations suggest that cdc2 mutants are defective in an aspect of initiation of DNA replication common to all chromosomes such that a random fraction of the chromosomes fail to initiate replication at 37 degrees C, but that once initiated, replication proceeds normally.