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 5α-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 5α-reductase inhibitors such as finasteride may increase the incidence of therapy resistant cancers.

The objective of the Indianapolis Flux Experiment (INFLUX) is to develop, evaluate and improve methods for measuring greenhouse gas (GHG) emissions from cities. INFLUX’s scientific objectives are to quantify CO₂ and CH₄ emission rates at 1 km₂ resolution with a 10% or better accuracy and precision, to determine whole-city emissions with similar skill, and to achieve high (weekly or finer) temporal resolution at both spatial resolutions. The experiment employs atmospheric GHG measurements from both towers and aircraft, atmospheric transport observations and models, and activity-based inventory products to quantify urban GHG emissions. Multiple, independent methods for estimating urban emissions are a central facet of our experimental design. INFLUX was initiated in 2010 and measurements and analyses are ongoing. To date we have quantified urban atmospheric GHG enhancements using aircraft and towers with measurements collected over multiple years, and have estimated whole-city CO₂ and CH₄ emissions using aircraft and tower GHG measurements, and inventory methods. Significant differences exist across methods; these differences have not yet been resolved; research to reduce uncertainties and reconcile these differences is underway. Sectorally- and spatially-resolved flux estimates, and detection of changes of fluxes over time, are also active research topics. Major challenges include developing methods for distinguishing anthropogenic from biogenic CO₂ fluxes, improving our ability to interpret atmospheric GHG measurements close to urban GHG sources and across a broader range of atmospheric stability conditions, and quantifying uncertainties in inventory data products. INFLUX data and tools are intended to serve as an open resource and test bed for future investigations. Well-documented, public archival of data and methods is under development in support of this objective.

Predicting the timing of a castrate resistant prostate cancer is critical to lowering medical costs and improving the quality of life of advanced prostate cancer patients. We formulate, compare and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). We accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). While these models are simplifications of a previously published model, they fit data with similar accuracy and improve forecasting results. Both models describe the progression of androgen resistance. Although Model 1 is simpler than the more realistic Model 2, it can fit clinical data to a greater precision. However, we found that Model 2 can forecast future PSA levels more accurately. These findings suggest that including more realistic mechanisms of androgen dynamics in a two population model may help androgen resistance timing prediction.

Background:
Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.

Results:
We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.

Conclusions:
The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.