A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy

Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.     

Nonlinear system identification for prostate cancer and optimality of intermittent androgen suppression therapy

These days prostate cancer is one of the most common types of malignant neoplasm in men. Androgen ablation therapy (hormone therapy) has been shown to be effective for advanced prostate cancer. However, continuous hormone therapy often causes recurrence. This results from the progression of androgen-dependent cancer cells to androgen-independent cancer cells during the continuous hormone therapy. One possible method to prevent the progression to the androgen-independent state is intermittent androgen suppression (IAS) therapy, which ceases dosing intermittently. In this paper, we propose two methods to estimate the dynamics of prostate cancer, and investigate the IAS therapy from the viewpoint of optimality. The two methods that we propose for dynamics estimation are a variational Bayesian method for a piecewise affine (PWA) system and a Gaussian process regression method. We apply the proposed methods to real clinical data and compare their predictive performances. Then, using the estimated dynamics of prostate cancer, we observe how prostate cancer behaves for various dosing schedules. It can be seen that the conventional IAS therapy is a way of imposing high cost for dosing while keeping the prostate cancer in a safe state. We would like to dedicate this paper to the memory of Professor Luigi M. Ricciardi.     

Quantum dots-based multiplexed immunohistochemistry of protein expression in human prostate cancer cells

Semiconductor quantum dots (QDs) are bright fluorescent nanoparticles that have been successfully used for the detection of biomarker expression in cells. The objective of the present study is to use this technology in a multiplexing manner to determine at a single cell level the expression of a cell-specific bio-marker, prostate-specific antigen (PSA) expressed by human prostate cancer LNCaP and ARCaP cell lines. Here we compared the sensitivity of immunohistochemistry (IHC) and QD-based detection of AR and PSA expression in these cell lines. Further, we conducted multiplexing QD-based detection of PSA and androgen receptor (AR) expression in LNCaP cells subjecting to androgen (R1881) stimulation. The involvement of AR in PSA regulation in LNCaP cells, at a single cell level, was confirmed by the co-incubation of LNCaP cells in the presence of both R1881 and its receptor antagonist, bicalutamide (Casodex). We showed here the superior quality of QDs, in comparison to IHC, for the detection of AR and PSA in cultured LNCaP and ARCaP cells. Multiplexing QDs technique can be used to detect simultaneously AR and PSA expression induced by R1881 which promoted AR translocation from its cytosolic to the nuclear compartment. We observed AR antagonist, bicalutamide, inhibited AR nuclear translocation and PSA, but not AR expression in LNCaP cells.     

Steroids inversely affect the biosynthesis and secretion of human prostatic acid phosphatase and prostate-specific antigen in the LNCaP cell line

In order to elucidate the mechanism of androgen-regulation of genes expressed only in the prostate gland, the effects of steroid hormones on the biosynthesis and secretion of human prostatic acid phosphatase (PAP) and prostate-specific antigen (PSA) were studied in the human prostatic carcinoma cell line, LNCaP. This cell line produces PAP and PSA, both of which were found to be similar to the proteins purified from and located in human prostatic tissue, as shown by Western blot analysis. The synthetic androgen, R1881, regulated the biosynthesis of these two important tumour marker proteins inversely: the amount of PSA released into the medium was increased to 506%±100 of the control levels, while that of PAP was decreased to 26%±3, in 7 days. These effects were dependent on the concentration of the steroid in the growth medium. The androgen-dependent changes observed in the amounts of the secreted proteins were correlated with alterations in their intra-cellular levels. LNCaP cells were found to have very different capacities for secreting PAP and PSA. Whereas the measurable, cellular amounts of PSA and PAP were of similar magnitudes, much larger amounts of PSA than PAP were secreted into the medium. PSA was also found to be more stable than PAP in the culture medium of the LNCaP cells. Other steroids could elicit effects on PAP and PSA biosynthesis similar to those induced by R1881, and the combined effects of effective concentrations of these steroids were undistinguishable from those caused by each one of them separately, suggesting that all these compounds compete for binding to the same modified androgen receptors of the LNCaP cells. Thus, our results confirm the observations of the altered nature of the LNCaP androgen receptors, and demonstrate the ability of these ligands to produce changes in the expression of androgen-dependent prostatic genes. The fact that the changes observed at the protein level were accompanied by increased levels of PSA mRNAs and by decreased levels of PAP mRNA in steroid-treated cells, suggests that one of the targets of androgen and steroid action in the regulation of these genes is at the mRNA level.     

The role of androgen in determining differentiation and regulation of androgen receptor expression in the human prostatic epithelium transient amplifying population

Abnormal differentiation in epithelial stem cells or their immediate proliferative progeny, the transiently amplifying population (TAP), may explain malignant pathogenesis in the human prostate. These models are of particular importance as differing sensitivities to androgen among epithelial cell subpopulations during differentiation are recognised and may account for progression to androgen independent prostate cancer. Androgens are crucial in driving terminal differentiation and their indirect effects via growth factors from adjacent androgen responsive stroma are becoming better characterised. However, direct effects of androgen on immature cells in the context of a prostate stem cell model have not been investigated in detail and are studied in this work. In alpha2beta1hi stem cell enriched basal cells, androgen analogue R1881 directly promoted differentiation by the induction of differentiation-specific markers CK18, androgen receptor (AR), PSA and PAP. Furthermore, treatment with androgen down-regulated alpha2beta1 integrin expression, which is implicated in the maintenance of the immature basal cell phenotype. The alpha2beta1hi cells were previously demonstrated to lack AR expression and the direct effects of androgen were confirmed by inhibition using the anti-androgen bicalutamide. AR protein expression in alpha2beta1hi cells became detectable when its degradation was repressed by the proteosomal inhibitor MG132. Stratifying the alpha2beta1hi cells into stem (CD133(+)) and transient amplifying population (TAP) (CD133(-)) subpopulations, AR mRNA expression was found to be restricted to the CD133(-) (TAP) cells. The presence of a functional AR in the TAP, an androgen independent subpopulation for survival, may have particular clinical significance in hormone resistant prostate cancer, where both the selection of immature cells and functioning AR regulated pathways are involved.     

Androgen inhibits the growth of carcinoma cell lines established from prostate cancer xenografts that escape androgen treatment

Most prostate cancers escape endocrine therapy by diverse mechanisms. One of them might be growth repression by androgen. We reported that androgen represses the growth in culture of MOP cells (a sub-line of LNCaP cells) and that of MOP cell xenografts, although tumor growth becomes androgen-independent (AI). Here we explore whether AI tumors contain androgen-responsive cells. ME carcinoma cells were established from AI tumors. The responses to androgen were examined by cell counting, DAPI labeling, flow cytometry, PSA immunoassay and tumor size follow-up. Androgen receptors (AR) were analyzed by western blotting and DNA sequencing. The pattern of responses of these cells to androgen was compared to that of MOP cells and that of JAC cells established from LNCaP-like MOP cells. R1881, a synthetic androgen: (1) repressed the growth of all the six ME cell lines obtained, MOP and JAC cells, (2) augmented the secretion of PSA, (3) induced spectacular cell bubbling/fragmentation and (4) blocked the cell cycle and induced a modest increase of apoptosis. All the androgen-repressed cells expressed the same level of mutated AR as LNCaP cells. In nude mice, the growth of ME-2 cell xenografts displayed transient androgen repression similar to that of MOP cells. In culture neither fibroblasts nor extra-cellular matrix altered the effects of R1881 on cell proliferation. These results demonstrate that androgen-independent tumors contain androgen-responsive cells. The apparent discrepancy between the responses to androgen of tumors and those of carcinoma cells in culture suggests that microenvironmental factors contribute to the androgen responsiveness of tumor cells in vivo. These modifications, albeit unspecified, could be suitable targets for restoring the androgen responsiveness of AI tumors.     

Secretion of endogenous kallikreins 2 and 3 by androgen receptor-transfected PC-3 prostate cancer cells

Androgen independent PC-3 cells lack androgen receptor (AR) expression and do not produce kallikrein 2 (hK2) or 3 (prostate-specific antigen, PSA). In this paper, we examined the ability of androgens to stimulate PSA and hK2 production in AR transfected PC-3 cells (PC-3(AR)) and compared this to LNCaP cells. PSA and hK2 were measured in the culture medium and cell lysates using an ELISA-based immunofluorometric assay. Only androgens were able to induce PSA and hK2 secretion in PC-3(AR) cells in a dose- and time-dependent manner depending on the level of AR present. The level of androgen-induced PSA and hK2 secretion in PC-3(AR) cells was approximately 1.5 and 0.9% that induced in LNCaP cells, respectively. Insulin-like growth factor-I (IGF-I), which has been shown to activate AR in the absence of ligand, did not activate PSA secretion in the absence of androgen, but further increased the dihydrotestosterone-induced PSA secretion in PC-3(AR) cells. The lack of PSA and hK2 production in parental PC-3 cells is thus a result of their lack of AR expression. PSA and/or hK2 production in PC-3(AR) cells can thus serve as an endogenous reporter system to investigate AR action or to screen putative endocrine disrupters.     

Butyrate analogue,isobutyramide, inhibits tumor growth and time to androgen-independent progression in the human prostate LNCaP tumor model

Progression to androgen independence remains the main obstacle to improving survival and quality of life in patients with advanced prostate cancer. Induction of differentiation may serve as a rational basis for prevention of progression to androgen independence by modulating gene expression activated by castration or upregulated during androgen-independent progression. The objectives of this study were to characterize the in vitro effects of sodium butyrate on human prostate cancer cell growth, PSA gene expression, and differentiation in the LNCaP tumor model and to determine whether tumor progression in vivo is delayed by isobutyramide, an orally bioavailable butyrate analogue with a longer half-life. The effects of isobutyramide on LNCaP tumor growth and serum PSA levels in both intact and castrate male mice were compared to controls. At concentrations > 1 mM, butyrate induced dose-dependent changes towards a more differentiated phenotype, G1 cell cycle arrest, and an 80% decrease in LNCaP cell growth rates. PSA gene expression was increased threefold by butyrate, indicative of differentiation-enhanced gene expression. The half-life of isobutyramide in athymic mice was determined by gas chromatography to be 4 h. During a 4 week period in intact-placebo mice, tumor volume and serum PSA increased 4.1- and 6.6-fold, respectively, compared to twofold and 2.7-fold increases in tumor volume and serum PSA in intact-treated mice. During a 7 week period in castrate-placebo mice, tumor volume and serum PSA levels increased 2.4-fold and fourfold, respectively, compared to a 50% reduction in tumor volume and a twofold increase in serum PSA above nadir levels in castrate mice treated with adjuvant isobutyramide. Isobutyramide treatment induced pronouced morphological changes in LNCaP tumor cells, with loss of defined nucleoli and dispersion of chromatin distribution. LNCaP tumor PSA mRNA levels actually increased threefold, indicative of differentiation-enhanced gene expression. This study demonstrates that butyrate causes LNCaP cell cycle arrest and increased PSA gene expression, both indicative of differentiation. The combination of castration and adjuvant isobutyramide was synergistic in delaying tumor progression. Decreased tumor cell proliferation and increased PSA gene expression induced by isobutyramide results in disconcordant changes in serum PSA and tumor volume and reduces the utility of serum PSA as a marker of response to therapy. J. Cell. Biochem. 69:271–281, 1998. © 1998 Wiley-Liss, Inc.     

Glycotyping of prostate specific antigen

Measurement of serum levels of the prostate specific antigen (PSA) is now widely used for the diagnosis of prostate cancer and benign prostate hyperplasia. This serum marker is of value since it is derived only from the tissue of interest, but increased levels of PSA in serum do not allow a completely clear cut diagnosis of benign versus malignant changes. Since PSA is a glycoprotein with one asparagine linked oligosaccharide, and since malignant transformation often leads to an increased branching of such oligosaccharides, we initially studied the asparagine linked structures on PSA made by a cell line derived from malignant metastatic prostate tissue. We observed that unlike normal PSA, which bears only biantennary oligosaccharides, PSA from the metastatic cell line has a mixture of biantennary and triantennary oligosaccharides. Further experiments will reveal carbohydrate differences derived from the PSA from sera or, prostate tissue of normal versus prostate cancer patients, and of the utility of such carbo-hydrate differences as a possible diagnostic marker for prostate cancer.     

The PSA(-/lo) prostate cancer cell population harbors self-renewing long-term tumor-propagating cells that resist castration

Prostate cancer (PCa) is heterogeneous and contains both differentiated and undifferentiated tumor cells, but the relative functional contribution of these two cell populations remains unclear. Here we report distinct molecular, cellular, and tumor-propagating properties of PCa cells that express high (PSA(+)) and low (PSA(-/lo)) levels of the differentiation marker PSA. PSA(-/lo) PCa cells are quiescent and refractory to stresses including androgen deprivation, exhibit high clonogenic potential, and possess long-term tumor-propagating capacity. They preferentially express stem cell genes and can undergo asymmetric cell division to generate PSA(+) cells. Importantly, PSA(-/lo) PCa cells can initiate robust tumor development and resist androgen ablation in castrated hosts, and they harbor highly tumorigenic castration-resistant PCa cells that can be prospectively enriched using ALDH(+)CD44(+)α2β1(+) phenotype. In contrast, PSA(+) PCa cells possess more limited tumor-propagating capacity, undergo symmetric division, and are sensitive to castration. Altogether, our study suggests that PSA(-/lo) cells may represent a critical source of castration-resistant PCa cells.     

Reversible and noisy progression towards a commitment point enables adaptable and reliable cellular decision-making

Cells must make reliable decisions under fluctuating extracellular conditions, but also be flexible enough to adapt to such changes. How cells reconcile these seemingly contradictory requirements through the dynamics of cellular decision-making is poorly understood. To study this issue we quantitatively measured gene expression and protein localization in single cells of the model organism Bacillus subtilis during the progression to spore formation. We found that sporulation proceeded through noisy and reversible steps towards an irreversible, all-or-none commitment point. Specifically, we observed cell-autonomous and spontaneous bursts of gene expression and transient protein localization events during sporulation. Based on these measurements we developed mathematical population models to investigate how the degree of reversibility affects cellular decision-making. In particular, we evaluated the effect of reversibility on the 1) reliability in the progression to sporulation, and 2) adaptability under changing extracellular stress conditions. Results show that reversible progression allows cells to remain responsive to long-term environmental fluctuations. In contrast, the irreversible commitment point supports reliable execution of cell fate choice that is robust against short-term reductions in stress. This combination of opposite dynamic behaviors (reversible and irreversible) thus maximizes both adaptable and reliable decision-making over a broad range of changes in environmental conditions. These results suggest that decision-making systems might employ a general hybrid strategy to cope with unpredictably fluctuating environmental conditions.     

The RFA regulatory sequence-binding protein in the promoter of

The prostate-specific antigen (PSA), which plays an important role during the liquefaction process of semen, is a differentiation marker for human prostate. It has become the most sensitive marker for monitoring and detecting prostate cancer. PSA as a serine protease can activate some growth factors that might be related to the advancement of prostate cancer by hydrolyzing growth factor-binding protein. The PSA gene is expressed specifically in prostate epithelial cells. The ex-pression of…     

Construction of enzalutamide-resistant cell model of prostate cancer and preliminary screening of potential drug-resistant genes

Among many factors of causing castration-resistant prostate cancer (CRPC) progression, a growing number of evidences have shown androgen receptors play a critical role. Therefore, blocking androgen receptor remains a therapeutic goal of CRPC. However, resistance to androgen receptor inhibitors, for example, enzalutamide, limits therapeutic efficacy for many patients. In this study, to develop an enzalutamide-resistant cell model for molecular mechanism investigation of enzalutamide-resistance, we continuously treated C4-2B cells with multiplied concentrations of enzalutamide. The IC50 of resistant cells was identified as 14.7705 µM, and the resistance index was calculated as 12.4. In addition, we verified the resistance of resistant cells through experiments in vivo and found the genes in androgen receptor signaling pathway (androgen receptor, Jagged1, Notch1) and those in androgen receptor alternative signaling pathways behaved the opposite. For some of the former, their mRNA and protein expression reduced markedly while for the latter, for example, CXCR7, AKT, STAT3, FOXP3, they rose dramatically in the expression level of protein and mRNA. More importantly, the tumor volume, tumor wet weight, PSA and VEGF secretion level, positive staining rate of Ki67 nuclei in resistant strain heterogeneous tumor treated with enzalutamide were significantly higher than those of maternal cell heterogeneous tumor treated with enzalutamide, whereas no obvious difference was detected between resistant strain heterogeneous tumor treated with enzalutamide and those of the resistant strain treated with reference drug. Finally, we identified 654 differentially expression genes and 2 compounds (atracurium besilate, methotrexates) associated with the amelioration of enzalutamide-resistance. Overall, we successfully established an enzalutamide-resistance cell model and screened out some resistance genes and candidate small molecule drugs.     

Irreversibility in unbranched pathways: preferred positions based on regulatory considerations

It has been observed experimentally that most unbranched biosynthetic pathways have irreversible reactions near their beginning, many times at the first step. If there were no functional reasons for this fact, then one would expect irreversible reactions to be equally distributed among all positions in such pathways. Since this is not the case, we have attempted to identify functional consequences of having an irreversible reaction early in the pathway. We systematically varied the position of the irreversible reaction in model pathways and compared the resulting systemic behavior according to several criteria for functional effectiveness, using the method of mathematically controlled comparisons. This technique minimizes extraneous differences in systemic behavior and identifies those that are fundamental. Our results show that a pathway with an irreversible reaction located at the first step, and with all other reactions reversible, is on average better than an otherwise equivalent pathway with all reactions reversible, which in turn is on average better than an otherwise equivalent pathway with an irreversible reaction located at any step other than the first. Pathways with an irreversible first reaction and low concentrations of intermediates (one of the primary criteria for functional effectiveness) exhibit the following profile when compared to fully reversible pathways: changes in the concentration of intermediates in response to changes in the level of initial substrate are equally low, the robustness of the intermediate concentrations and of the flux is similar, the margins of stability are similar, flux is more responsive to changes in demand for end product, intermediate concentrations are less responsive to changes in demand for end product, and transient times are shorter. These results provide a functional rationale for the positioning of irreversible reactions at the beginning of unbranched biosynthetic pathways.     

CELL DIFFERENTIATION AND CARCINOGENESIS: A CRITICAL REVIEW*

Many resemblances exist between cell differentiation and neoplastic change: the importance of cytoplasmic factors is particularly evident, as the genotype appears to remain unmodified in the nuclei of differentiated as in malignant cells. There is no opposition between malignancy and differentiation, highly malignant cells retaining in many cases a differentiation very close to normal. Loss of differentiation in malignancy is only an epiphenomenon. While differentiation appears to be partially reversible, and in some models totally reversible, neoplastic changes are, with a very small number of exceptions, irreversible. Differentiation involves the gradual change of a group or a population of cells, malignancy of a single cell. Further work on the molecular basis of differentiation would help to understand the nature of neoplasia, and vice versa.