The evolutionary impact of androgen levels on prostate cancer in a multi-scale mathematical model

Abstract

Background: Androgens bind to the androgen receptor (AR) in prostate cells and are essential survival factors for healthy prostate epithelium. Most untreated prostate cancers retain some dependence upon the AR and respond, at least transiently, to androgen ablation therapy. However, the relationship between endogenous androgen levels and cancer etiology is unclear. High levels of androgens have traditionally been viewed as driving abnormal proliferation leading to cancer, but it has also been suggested that low levels of androgen could induce selective pressure for abnormal cells. We formulate a mathematical model of androgen regulated prostate growth to study the effects of abnormal androgen levels on selection for pre-malignant phenotypes in early prostate cancer development.

Results: We find that cell turnover rate increases with decreasing androgen levels, which may increase the rate of mutation and malignant evolution. We model the evolution of a heterogeneous prostate cell population using a continuous state-transition model. Using this model we study selection for AR expression under different androgen levels and find that low androgen environments, caused either by low serum testosterone or by reduced 5alpha-reductase activity, select more strongly for elevated AR expression than do normal environments. High androgen actually slightly reduces selective pressure for AR upregulation. Moreover, our results suggest that an aberrant androgen environment may delay progression to a malignant phenotype, but result in a more dangerous cancer should one arise.

Conclusions: The model represents a useful initial framework for understanding the role of androgens in prostate cancer etiology, and it suggests that low androgen levels can increase selection for phenotypes resistant to hormonal therapy that may also be more aggressive. Moreover, clinical treatment with 5alpha-reductase inhibitors such as finasteride may increase the incidence of therapy resistant cancers.

Figure 1

Intraprostatic concentrations of T and DHT when 5α-reductase is and is not blocked (i.e. finasteride treatment) in the rat. Data is from Wright et al. [60].

Figure 2

Influx of free testosterone, U, as function of serum testosterone, as determined using the data of Wright et al. [60] The algebraic fit for U(T_S) with R_t = 45 nM is also indicated.

Figure 3

T and DHT concentrations predicted by the AR kinetics model versus the actual concentrations in Wright et al. [60]as a function of serum testosterone. R_t is fixed at 45 nM, all other parameters are fixed at the baseline values. (a) 5α-reductase allowed, α = 5 mg L^-1. (b) 5α-reductase blocked, α = 0 mg L^-1.

Figure 4

Oxidative stress, S, as a function of C_t.

Figure 5

Curves for the different growth signals. Because the ROS level S is a function of C_t, the proliferation and death signals mediated by S can be given as a function of either S (as in (a)) or of C_t (as in (b)). Attenuation of proliferation by crowding (the -σP) is disregarded here because it affects the proliferation signal in a way that depends on the instantaneous prostate mass. (a) Prostate cell growth and death signals due to ROS as a function of S. (b) Prostate cell growth and death signals due to ROS given as a function of C_t, as S is itself a function of C_t. (c) Proliferation and death signal due to the effective AR:ligand concentration, C_t. (d) Overall proliferation and death signals mediated by both ROS and AR:ligand concentration. Because ROS level is a function of the AR:ligand concentration, C_t, the overall signal can be given as a function of only C_t.

Figure 6

Time-series for the AR kinetics model. Free AR is set to 45 nM as an initial condition; all other variables are initially zero and baseline parameter values are used. Serum T is prescribed at 5 nM, inducing an influx of testosterone, and the model runs to a steady state. (a) Time-series for all model variables - free T, free DHT, T:AR complex, DHT:AR complex, and free AR. (b) Time-series for total T, DHT, and AR concentrations. (a) Time-series for all model variables - free T, free DHT, T:AR complex, DHT:AR complex, and free AR. (b) Time-series for total T, DHT, and AR concentrations.

Figure 7

Concentrations of free T, free DHT, T:AR complex, and DHT:AR complex at steady state as a function of serum testosterone. R_t is fixed at 45 nM.

Figure 8

Steady state prostate mass as a function of serum testosterone for different levels of R_t. Note that below R_t = 25 nM mass quickly decreases for all serum T, while there is a reasonable stable region between 25 and 45 nM, after which mass increases roughly linearly with R_t before leveling off. For higher values of R_t than those displayed, increases in serum T can cause a reduction in prostate mass (see Figure 9).

Figure 9

Steady state prostate mass as a function of R_t for different serum testosterone concentrations. Note that for sufficiently high AR concentrations, increases in serum T actually reduce prostate mass.

Figure 10

Turnover as a function of serum T for different ηs. Higher η indicates greater 5α-reductase inhibition, and turnover increases with increasing η. Cell turnover decreases as serum T increases.

Figure 11

Evolution of average R_t in the state-transition model under different serum T. AR expression is presumably a marker for the malignant potential of a strain. Low serum T selects for higher R_t than the normal environment (serum T = 5 nM), but takes longer to do so. High serum T selects for a slightly lower R_t.

Figure 12

Evolution of average R_t in the state-transition model under different levels of 5α-reductase inhibition by finasteride.

Figure 13

Evolution of average R_t in the state transition model under high and low serum testosterone concentrations for 2 different values of the θ₁ parameter. For θ₁ = 20, the more typical pattern is observed with the appearance of AR overexpression occurring later in time but to a greater magnitude under the low androgen environment. A more unique pattern is seen for θ₁ = 60. (a) Evolution of average R_t for θ₁ = 20. (b) Evolution of average R_t for θ₁ = 60.