ASU Scholarship Showcase

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.

The ongoing Zika virus (ZIKV) epidemic in the Americas poses a major global public health emergency. While ZIKV is transmitted from human to human by bites of Aedes mosquitoes, recent evidence indicates that ZIKV can also be transmitted via sexual contact with cases of sexually transmitted ZIKV reported in Argentina, Canada, Chile, France, Italy, New Zealand, Peru, Portugal, and the USA. Yet, the role of sexual transmission on the spread and control of ZIKV infection is not well-understood. We introduce a mathematical model to investigate the impact of mosquito-borne and sexual transmission on the spread and control of ZIKV and calibrate the model to ZIKV epidemic data from Brazil, Colombia, and El Salvador. Parameter estimates yielded a basic reproduction number R_0 = 2.055 (95% CI: 0.523–6.300), in which the percentage contribution of sexual transmission is 3.044% (95% CI: 0.123–45.73). Our sensitivity analyses indicate that R_0 is most sensitive to the biting rate and mortality rate of mosquitoes while sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. Prevention and control efforts against ZIKV should target both the mosquito-borne and sexual transmission routes.

Cells routinely compartmentalize enzymes for enhanced efficiency of their metabolic pathways. Here we report a general approach to construct DNA nanocaged enzymes for enhancing catalytic activity and stability. Nanocaged enzymes are realized by self-assembly into DNA nanocages with well-controlled stoichiometry and architecture that enabled a systematic study of the impact of both encapsulation and proximal polyanionic surfaces on a set of common metabolic enzymes. Activity assays at both bulk and single-molecule levels demonstrate increased substrate turnover numbers for DNA nanocage-encapsulated enzymes. Unexpectedly, we observe a significant inverse correlation between the size of a protein and its activity enhancement. This effect is consistent with a model wherein distal polyanionic surfaces of the nanocage enhance the stability of active enzyme conformations through the action of a strongly bound hydration layer. We further show that DNA nanocages protect encapsulated enzymes against proteases, demonstrating their practical utility in functional biomaterials and biotechnology.

Gompertz’s empirical equation remains the most popular one in describing cancer cell population growth in a wide spectrum of bio-medical situations due to its good fit to data and simplicity. Many efforts were documented in the literature aimed at understanding the mechanisms that may support Gompertz’s elegant model equation. One of the most convincing efforts was carried out by Gyllenberg and Webb. They divide the cancer cell population into the proliferative cells and the quiescent cells. In their two dimensional model, the dead cells are assumed to be removed from the tumor instantly. In this paper, we modify their model by keeping track of the dead cells remaining in the tumor. We perform mathematical and computational studies on this three dimensional model and compare the model dynamics to that of the model of Gyllenberg and Webb. Our mathematical findings suggest that if an avascular tumor grows according to our three-compartment model, then as the death rate of quiescent cells decreases to zero, the percentage of proliferative cells also approaches to zero. Moreover, a slow dying quiescent population will increase the size of the tumor. On the other hand, while the tumor size does not depend on the dead cell removal rate, its early and intermediate growth stages are very sensitive to it.

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 relationship between sequence and binding properties of an aptamer for immunoglobulin E (IgE) was investigated using custom DNA microarrays. Single, double and some triple mutations of the aptamer sequence were created to evaluate the importance of specific base composition on aptamer binding. The majority of the positions in the aptamer sequence were found to be immutable, with changes at these positions resulting in more than a 100-fold decrease in binding affinity. Improvements in binding were observed by altering the stem region of the aptamer, suggesting that it plays a significant role in binding. Results obtained for the various mutations were used to estimate the information content and the probability of finding a functional aptamer sequence by selection from a random library. For the IgE-binding aptamer, this probability is on the order of 10^-10 to 10^-9. Results obtained for the double and triple mutations also show that there are no compensatory mutations within the space defined by those mutations. Apparently, at least for this particular aptamer, the functional sequence space can be represented as a rugged landscape with sharp peaks defined by highly constrained base compositions. This makes the rational optimization of aptamer sequences using step-wise mutagenesis approaches very challenging.

There is an increasing awareness that health care must move from post-symptomatic treatment to presymptomatic intervention. An ideal system would allow regular inexpensive monitoring of health status using circulating antibodies to report on health fluctuations. Recently, we demonstrated that peptide microarrays can do this through antibody signatures (immunosignatures). Unfortunately, printed microarrays are not scalable. Here we demonstrate a platform based on fabricating microarrays (~10 M peptides per slide, 330,000 peptides per assay) on silicon wafers using equipment common to semiconductor manufacturing. The potential of these microarrays for comprehensive health monitoring is verified through the simultaneous detection and classification of six different infectious diseases and six different cancers. Besides diagnostics, these high-density peptide chips have numerous other applications both in health care and elsewhere.

Swinging arms are a key functional component of multistep catalytic transformations in many naturally occurring multi-enzyme complexes. This arm is typically a prosthetic chemical group that is covalently attached to the enzyme complex via a flexible linker, allowing the direct transfer of substrate molecules between multiple active sites within the complex. Mimicking this method of substrate channelling outside the cellular environment requires precise control over the spatial parameters of the individual components within the assembled complex. DNA nanostructures can be used to organize functional molecules with nanoscale precision and can also provide nanomechanical control. Until now, protein–DNA assemblies have been used to organize cascades of enzymatic reactions by controlling the relative distance and orientation of enzymatic components or by facilitating the interface between enzymes/cofactors and electrode surfaces. Here, we show that a DNA nanostructure can be used to create a multi-enzyme complex in which an artificial swinging arm facilitates hydride transfer between two coupled dehydrogenases. By exploiting the programmability of DNA nanostructures, key parameters including position, stoichiometry and inter-enzyme distance can be manipulated for optimal activity.