Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics. (C) 2011 Elsevier B.V. All rights reserved.

Gene Expression Profile in Response to Doxorubicin-Rapamycin Combined Treatment of HER-2-Overexpressing Human Mammary Epithelial Cell Lines

HER-2-positive breast cancers frequently sustain elevated AKT/mTOR signaling, which has been associated with resistance to doxorubicin treatment. Here, we investigated whether rapamycin, an mTOR inhibitor, increased the sensitivity to doxorubicin therapy in two HER-2-overexpressing cell lines: C5.2, which was derived from the parental HB4a by transfection with HER-2 and SKBR3, which exhibits HER-2 amplification. The epithelial mammary cell line HB4a was also analyzed. The combined treatment using 20 nmol/L of rapamycin and 30 nmol/L of doxorubicin arrested HB4a and C5.2 cells in S to G(2)-M, whereas SKBR3 cells showed an increase in the G(0)-G(1) phase. Rapamycin increased the sensitivity to doxorubicin in HER-2-overexpressing cells by approximately 2-fold, suggesting that the combination displayed a more effective antiproliferative action. Gene expression profiling showed that these results might reflect alterations in genes involved in canonical pathways related to purine metabolism, oxidative phosphorylation, protein ubiquitination, and mitochondrial dysfunction. A set of 122 genes modulated by the combined treatment and specifically related to HER-2 overexpression was determined by finding genes commonly regulated in both C5.2 and SKBR3 that were not affected in HB4a cells. Network analysis of this particular set showed a smaller subgroup of genes in which coexpression pattern in HB4a cells was disrupted in C5.2 and SKBR3. Altogether, our data showed a subset of genes that might be more robust than individual markers in predicting the response of HER-2-overexpressing breast cancers to doxorubicin and rapamycin combination. Mol Cancer Ther; 11(2); 464-74. (C) 2011 AACR.