Hill's Equation with Random Forcing Parameters: Determination of Growth Rates through Random Matrices

This paper derives expressions for the growth rates for the random 2 x 2 matrices that result from solutions to the random Hill's equation. The parameters that appear in Hill's equation include the forcing strength and oscillation frequency. The development of the solutions to this periodic differential equation can be described by a discrete map, where the matrix elements are given by the principal solutions for each cycle. Variations in the forcing strength and oscillation frequency lead to matrix elements that vary from cycle to cycle. This paper presents an analysis of the growth rates including cases where all of the cycles are highly unstable, where some cycles are near the stability border, and where the map would be stable in the absence of fluctuations. For all of these regimes, we provide expressions for the growth rates of the matrices that describe the solutions.Comment: 22 pages, 3 figure

Peptides designed from molecular modeling studies of the ras-p21 protein induce phenotypic reversion of a pancreatic carcinoma cell line but have no effect on normal pancreatic acinar cell growth

Summarization: From molecular modeling studies we found that two ras-p21 peptides, corresponding to p21 residues 35-47 (PNC-7) and 96-110 (PNC-2), selectively block oncogenic (Val 12-p21), but not insulin-activated wild-type, p21-induced oocyte maturation. Our purpose was to determine if these peptides block the growth of mammalian cancer cells but not their normal counterpart cells. Since oncogenic ras has been implicated as a causative factor in over 90% of human pancreatic cancers, we have established a normal pancreatic acinar cell line (BMRPA1) and the corresponding ras-transformed pancreatic cancer cell line (TUC-3). We treated both cell lines with PNC-7 and PNC-2 and the unrelated negative control peptide, X13, attached to the penetratin sequence that allows membrane penetration and also transfected these cell lines with plasmids encoding all three peptides. Treatment of TUC-3 cells with each peptide resulted in their complete phenotypic reversion to the untransformed phenotype as revealed by the lack of tumor formation of these revertant cells implanted in the peritoneal cavities of nude mice. In contrast, treatment with X13-leader resulted in no inhibition of cell growth. Identical results were obtained when TUC-3 cells were transfected with plasmids expressing PNC-2, PNC-7 and X13. None of these peptides affected the normal growth of BMRPA1 cells. PNC-2 and PNC-7 peptides induce phenotypic reversion of ras-induced pancreatic cancer cells and have no effect on normal pancreatic cell growth. Since the plasmid encoding PNC-2 without penetratin also had the same effect on the TUC-3 cell line, we conclude that the penetratin sequence has no effect on the activity of this peptide. Since X13 attached to penetratin had no effect on TUC-3 cells, the effect is specific for PNC-2 and PNC-7 and further confirms that the effect is not caused by the penetratin sequence. PNC-2- and PNC-7-penetratin may therefore be useful in the treatment of ras-induced pancreatic carcinomas. Peptides designed from molecular modeling studies of the ras-p21 protein induce phenotypic reversion of a pancreatic carcinoma cell line but have no effect on normal pancreatic acinar cell growth.Presented on: Cancer Chemotherapy and Pharmacolog