A branching bivariate weibull distribution model for evaluating exosomes in androgen-deprived agency in the presence of prostate cancer

Abstract

Castration-resistant prostate cancer (CRPC) poses a significant challenge in the medical field. The study developed a novel model, the branching bivariate Weibull distribution (BBWD), tailored to address CRPC and stems from the maximum likelihood estimation (MLE) function. It considers a medicinal biosystem aimed at transitioning androgen-dependent prostate cancer into an androgen-independent state. The BBWD model is designed to optimize the solution for bio variables pertinent to CRPC and evaluate various treatment techniques for androgen-dependent and androgen-independent behaviour. Through rigorous analysis, the kinetics of LINC01213 in androgen-deprived mediums are highlighted as promising, showing superior efficacy in castration compared to other techniques. The model utilizes the joint effect on the log-likelihood function (JELF) as a crucial analytical tool to assess the impact of LINC01213 in both normal and androgen-deprived medium. The results affirm the veracity of statements made within the medical field and support the notion that LINC01213 may serve as a novel therapeutic target for CRPC patients. The analysis underscores the pivotal role of exosomal LINC01213 in androgen-dependent prostate cancer, demonstrating its significance in treatment efficacy. The BBWD model highlighting the efficacy of LINC01213 in androgen-deprived mediums provides compelling evidence for its potential as a therapeutic target. This study corroborates existing medical hypotheses and offers detailed clarification and reports on treatment techniques for prostate cancer patients. Ultimately, it emphasizes the critical role of exosomal LINC01213 in addressing the challenges posed by androgen-dependent prostate cancer, offering a pathway toward more effective treatments.

Keywords: Androgen deprived medium; Branching bivariate Weibull distribution (BBWD); Exosomes; Log-likelihood function; Maximum likelihood estimation function (MLE); Prostate cancer.

Fig. 1

BBWD modelling of LNCaP cell responses under various treatments and culture conditions: (a) In normal medium, LNCaP co-cultured with PC-3 shows faster recovery than LNCaP alone. (b) In androgen-deprived medium, co-cultured LNCaP exhibits more stable performance, indicating improved androgen-independent behaviour. (c) In normal medium, LNCaP cells treated with PC-3 exosomes maintain near-stable, while PBS-treated controls show progressive improvement over five days. (d) In androgen-deprived medium, exosome-treated LNCaP cells exhibit fluctuation, whereas PBS-treated cells show gradual but steady effects, suggesting distinct stress adaptation profiles. (e) In normal medium, both siRNA treatments show similar trends with slight differences in peak response and decline. (f) In androgen-deprived medium, Si-LINC01213-2 shows a more variable response compared to the steady profile of Si-LINC01213-1, suggesting differing roles in androgen-independent adaptation.

Fig. 2

BBWD analysis of LNCaP cells under different co-culture conditions with PC-3 cells over five days. (A) LNCaP cells were treated with PC-3-derived exosomes compared to PBS-treated controls. The results show a progressive reduction in BBWD values in the exosome-treated group, indicating a decrease in affected cell populations. (B) LNCaP cells before and after direct co-culture with PC-3 cells. A notable decrease in post co-culture suggests reduced cell complexity and enhanced viability in androgen-deficient conditions due to interaction with PC-3 cells.

Fig. 3

Variation in resistance of LNCaP cells in co-culture with PC-3 cells: Depicting the proliferation of LNCaP and PC-3 cells in both normal and androgen-deprived medium.

Fig. 4

Role of PC-3-derived exosomes in the development of castration resistance in LNCaP cells: Proliferation of LNCaP and PC-3 cells treated with exosomes, assessed in both normal and androgen-deprived medium.

Fig. 5

LINC01213 promotes androgen-independent behaviour through Wnt/β-catenin signalling: Cell proliferation of si-LINC01213-1 and si-LINC01213-2 transfected LNCaP cells in both normal and androgen-deprived medium.