Mathematical modeling has a long history in the field of cancer therapeutics, and there is increasing recognition that it can help uncover the mechanisms that underlie tumor response to treatment. However, making quantitative predictions with such models often requires parameter estimation from data, raising questions of parameter identifiability and estimability. Even in the case of structural (theoretical) identifiability, imperfect data and the resulting practical unidentifiability of model parameters can make it difficult to infer the desired information, and in some cases, to yield biologically correct inferences and predictions. Here, we examine parameter identifiability and estimability using a case study of two compartmental, ordinary differential equation models of cancer treatment with drugs that are cell cycle-specific (taxol) as well as non-specific (oxaliplatin). We proceed through model building, structural identifiability analysis, parameter estimation, practical identifiability analysis and its biological implications, as well as alternative data collection protocols and experimental designs that render the model identifiable. We use the differential algebra/input-output relationship approach for structural identifiability, and primarily the profile likelihood approach for practical identifiability. Despite the models being structurally identifiable, we show that without consideration of practical identifiability, incorrect cell cycle distributions can be inferred, that would result in suboptimal therapeutic choices. We illustrate the usefulness of estimating practically identifiable combinations (in addition to the more typically considered structurally identifiable combinations) in generating biologically meaningful insights. We also use simulated data to evaluate how the practical identifiability of the model would change under alternative experimental designs. These results highlight the importance of understanding the underlying mechanisms rather than purely using parsimony or information criteria/goodness-of-fit to decide model selection questions. The overall roadmap for identifiability testing laid out here can be used to help provide mechanistic insight into complex biological phenomena, reduce experimental costs, and optimize model-driven experimentation.

Prostate cancer progression depends in part on the complex interactions between testosterone, its active metabolite DHT, and androgen receptors. In a metastatic setting, the first line of treatment is the elimination of testosterone. However, such interventions are not curative because cancer cells evolve via multiple mechanisms to a castrate-resistant state, allowing progression to a lethal outcome. It is hypothesized that administration of antiandrogen therapy in an intermittent, as opposed to continuous, manner may bestow improved disease control with fewer treatmentrelated toxicities. The present study develops a biochemically motivated mathematical model of antiandrogen therapy that can be tested prospectively as a predictive tool. The model includes "personalized" parameters, which address the heterogeneity in the predicted course of the disease under various androgen-deprivation schedules. Model simulations are able to capture a variety of clinically observed outcomes for "average" patient data under different intermittent schedules. The model predicts that in the absence of a competitive advantage of androgen-dependent cancer cells over castration-resistant cancer cells, intermittent scheduling can lead to more rapid treatment failure as compared to continuous treatment. However, increasing a competitive advantage for hormone-sensitive cells swings the balance in favor of intermittent scheduling, delaying the acquisition of genetic or epigenetic alterations empowering androgen resistance. Given the near universal prevalence of antiandrogen treatment failure in the absence of competing mortality, such modeling has the potential of developing into a useful tool for incorporation into clinical research trials and ultimately as a prognostic tool for individual patients.castration resistance | continuous androgen ablation | intermittent androgen ablation | rapid antiandrogen cycling

Graph generative models have been extensively studied in the data mining literature. While traditional techniques are based on generating structures that adhere to a pre-decided distribution, recent techniques have shifted towards learning this distribution directly from the data. While learning-based approaches have imparted significant improvement in quality, some limitations remain to be addressed. First, learning graph distributions introduces additional computational overhead, which limits their scalability to large graph databases. Second, many techniques only learn the structure and do not address the need to also learn node and edge labels, which encode important semantic information and influence the structure itself. Third, existing techniques often incorporate domainspecific rules and lack generalizability. Fourth, the experimentation of existing techniques is not comprehensive enough due to either using weak evaluation metrics or focusing primarily on synthetic or small datasets. In this work, we develop a domain-agnostic technique called GraphGen to overcome all of these limitations. Graph-Gen converts graphs to sequences using minimum DFS codes. Minimum DFS codes are canonical labels and capture the graph structure precisely along with the label information. The complex joint distributions between structure and semantic labels are learned through a novel LSTM architecture. Extensive experiments on million-sized, real graph datasets show GraphGen to be 4 times faster on average than state-of-the-art techniques while being significantly better in quality across a comprehensive set of 11 different metrics. Our code is released at: https://github.com/idea-iitd/graphgen.

Recent experiments show that vascular endothelial growth factor (VEGF) is the crucial mediator of downstream events that ultimately lead to enhanced endothelial cell survival and increased vascular density within many tumors. The newly discovered pathway involves up-regulation of the anti-apoptotic protein Bcl-2, which in turn leads to increased production of interleukin-8 (CXCL8). The VEGF-Bcl-2-CXCL8 pathway suggests new targets for the development of anti-angiogenic strategies including short interfering RNA (siRNA) that silence the CXCL8 gene and small molecule inhibitors of Bcl-2. In this paper, we present and validate a mathematical model designed to predict the effect of the therapeutic blockage of VEGF, CXCL8, and Bcl-2 at different stages of tumor progression. In agreement with experimental observations, the model predicts that curtailing the production of CXCL8 early in development can result in a delay in tumor growth and vascular development; however, it has little effect when applied at late stages of tumor progression. Numerical simulations also show that blocking Bcl-2 up-regulation, either at early stages or after the tumor has fully developed, ensures that both microvascular and tumor cell density stabilize at low values representing growth control. These results provide insight into those aspects of the VEGF-Bcl-2-CXCL8 pathway, which independently and in combination, are crucial mediators of tumor growth and vascular development. Continued quantitative modeling in this direction may have profound implications for the development of novel therapies directed against specific proteins and chemokines to alter tumor progression.

Tumor growth and progression are critically dependent on the establishment of a vascular support system. This is often accomplished via the expression of pro-angiogenic growth factors, including members of the vascular endothelial growth factor (VEGF) family of ligands. VEGF ligands are overexpressed in a wide variety of solid tumors and therefore have inspired optimism that inhibition of the different axes of the VEGF pathway-alone or in combination-would represent powerful anti-angiogenic therapies for most cancer types. When considering treatments that target VEGF and its receptors, it is difficult to tease out the differential anti-angiogenic and anti-tumor effects of all combinations experimentally because tumor cells and vascular endothelial cells are engaged in a dynamic cross-talk that impacts key aspects of tumorigenesis, independent of angiogenesis. Here we develop a mathematical model that connects intracellular signaling responsible for both endothelial and tumor cell proliferation and death to population-level cancer growth and angiogenesis. We use this model to investigate the effect of bidirectional communication between endothelial cells and tumor cells on treatments targeting VEGF and its receptors both in vitro and in vivo. Our results underscore the fact that in vitro therapeutic outcomes do not always translate to the in vivo situation. For example, our model predicts that certain therapeutic combinations result in antagonism in vivo that is not observed in vitro. Mathematical modeling in this direction can shed light on the mechanisms behind experimental observations that manipulating VEGF and its receptors is successful in some cases but disappointing in others.