Glutamate plays a pivotal role in drug addiction, and the N-methyl-D-aspartate (NMDA) glutamate receptor subtype serves as a molecular target for several drugs of abuse. In this review, we will provide an overview of NMDA receptor structure and function, followed by a review of the mechanism of action, clinical efficacy, and side effect profile of NMDA receptor ligands that are currently in use or being explored for the treatment of drug addiction. These ligands include the NMDA receptor modulators memantine and acamprosate, as well as the partial NMDA agonist D-cycloserine. Data collected to date suggest that direct NMDA receptor modulators have relatively limited efficacy in the treatment of drug addiction, and that partial agonism of NMDA receptors may have some efficacy with regards to extinction learning during cue exposure therapy. However, the lack of consistency in results to date clearly indicates that additional studies are needed, as are studies examining novel ligands with indirect mechanisms for altering NMDA receptor function.

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.