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Adrianne Jenner
(ONCO)
University of Montreal
"Exploring the impact of intratumoral heterogeneity on oncolytic virotherapy using agent-based modelling"
Oncolytic viruses (OV) are an exciting immunotherapeutic modality currently being investigated for the treatment of glioblastoma multiforme (GBM), an aggressive brain cancer with a poor clinical prognosis. Unfortunately, promising pre-clinical investigations of immunotherapies have led to a number of disappointing trail results. It is clear that recapitulating the tumour microenvironment (TME) and finding useful pre-clinical models to elucidate the efficacy of OVs is crucial to improve OV treatments. CANscript is an ex vivo tumour spheroid model that has been used to improve pre-clinical evaluation as it recapitulates native, patient autologous TME. Leveraging pre-clinical GBM spheroids, we evaluated the infiltration of a herpes simplex OV in patient GBM samples, and constructed a computational representation of this system in PhysiCell, an open-source cell-based simulator, to determine OV characteristics that optimized therapeutic efficacy with respect to the impact of stromal density on OV infiltration. Additionally, we examined how intratumoural heterogeneity in the uptake rate of the OV influences efficacy. Overall, our results showed that the intracellular viral replication rate is the primary driver of OV infiltration patterns observed in the ex vivo samples. This work, therefore, has implications on the development of OVs for the treatment of GBM and in our understanding of the impact of spatial heterogeneity on new treatment approaches.
Angela Michelle Jarrett
(ONCO)
The University of Texas at Austin
"Modeling of the spatio-temporal evolution of tumor vasculature to improve predictions of breast cancer response to neoadjuvant chemotherapy regimens"
One of the great challenges for treating cancer is the inability to design optimal therapeutic regimens for individual patients. Without a reasonable mathematical framework, selecting treatment regimens for the individual patient is fundamentally limited to trial and error. We have previously established a mechanically coupled, reaction-diffusion model at the tissue scale for predicting breast tumor response to therapy. The patient-specific, 3D model is initialized with tumor cell number estimated from quantitative, diffusion-weighted magnetic resonance imaging (DW-MRI) data. Additionally, the model includes a tumor cell reduction term due to drug delivery as estimated from dynamic contrast-enhanced (DCE-) MRI data (per individual clinical patient treatment schedules). We have expanded this model to differentiate between the effects of different chemotherapies to generate personalized and, potentially, optimized regimens for individual patients. This original model’s predictions have been found to be highly correlated to actual tumor response, but one limitation is that it does not account for the spatio-temporal changes of the tumor vasculature. Therefore, we now seek to extend this work by explicitly including the dynamics of an evolving vasculature to better simulate delivery of chemotherapies and account for the effect of these drugs on the vasculature itself. Importantly, by adding a second governing equation to the mathematical model representing the vasculature, we are able to reduce the parameter space of the model by coupling proliferation to the vasculature component—instead of defining proliferation as a local parameter in space. For an initial cohort of nine breast cancer patients, we evaluate the performance of the extended model by comparing its predictive ability to that of the original model (without vasculature). We report preliminary findings that the extended model’s results have lower median errors for its predictions. Future work will focus on expanding the model to account for targeted therapies and the simulation of alternative treatment regimens. We propose that an integrated mathematical-experimental approach leveraging patient-specific imaging data can provide optimal strategies for delivering therapy for breast cancer.
Anuraag Bukkuri
(ONCO)
University of Minnesota
"GLUT1 Production in Cancer Cells: A Tragedy of the Commons"
The tragedy of the commons, a concept originally developed by economist William Lloyd to describe overgrazing by cattle, is a phenomenon in which individual selfishness in a group setting leads to depletion of a shared resource, to the detriment of the overall population. We hypothesize that such a situation occurs in cancer cells in which cells increase production of membrane GLUT transporters for glucose in the presence of competing cells, obtaining a modest personal gain at a great group cost. To formalize this notion, we create a game-theoretic model for capturing the effects of competition on cancer cell transporter production and nutrient uptake. We show that the production of transporters per cell increases with a logistic trend as the number of competing cells in a microenvironment increase, but nutrient uptake per cell decreases in a power law fashion. By simulating GLUT1 inhibitor and glucose deprivation treatments, we demonstrate a synergistic combination of standard-of-care therapies and clustering of cancer cells, while also displaying the existence of a trade-off between competition among cancer cells and depression of the gain function. Assuming cancer cell transporter production is heritable, we then show the potential for a sucker's gambit technique to be used to counteract this trade-off, thereby allowing one to take advantage of both cellular competition and gain function depression by strategically changing environmental conditions.
Artur César Fassoni
(ONCO)
Universidade Federal de Itajubá
"Mathematical modeling and methodology to identify patient-specific immunological landscapes in CML treatment using TKI cessation and dose reduction data"
Chronic myeloid leukemia (CML) is an example of how mathematical models can help on understanding and describing cancer treatment. In the last years, the paradigm in CML treatment with tyrosine kinase inhibitors (TKI) changed from a life-long treatment to a scenario where patients with good response can stop treatment and remain in treatment free remission (TFR). Although it is still not clear which are the mechanisms and markers that identify those patients, recent evidence suggests that the immune response is crucial for maintaining TFR. Here, we present an ODE model for CML treatment and the role of an anti-leukemic immune response. Keeping the model as simple as possible we show that it fits well to 21 individual time courses under standard treatment. However, the optimal fits are not unique, which leads to ambiguity in the predictions about the outcome of treatment cessation. To overcome it, we show that additional data after TKI stop allows to capture the information necessary to use the model for making predictions. Applying this methodology to those 21 patients and calculating the multiple basins of attraction of stable equilibria in the patient-specific calibrated model, we identify three qualitatively different 'immunological landscapes' among which the patients are distributed. One set corresponds to those patients that require complete CML eradication to achieve TFR, meaning in practice a lifelong therapy or a likely recurrence after TKI stop. A second class corresponds to those patients where the immune system controls residual CML cells after treatment cessation if a certain threshold is achieved. A third class corresponds to patients where the immunological control of CML is achieved only if intricated balance between TKI effects and immune activation is achieved. Mathematically, this corresponds to phase portraits where one basin of attraction presents a topological defect arising from a heteroclinic bifurcation, and model simulations suggest that such optimal balance leading to TFR can be achieved with protocols of dose reduction. Finally, we show that the information necessary to classify the patient’s immunological landscape can be obtained not only from TKI stop data, but also from measuring the effects of TKI dose reduction during a six-month period. This provides a general strategy consisting of three phases: standard treatment, then standard reduced treatment and accurate observation of response, then model-based patient-specific treatments based on the previous phase. Summed up, these results illustrate the potential of mathematical modeling to the era of personalized medicine, with CML as a concrete example, but potential to more complex cancers, and also illustrates the difficulties that mathematical oncologists may encounter on this way, such as parameter unidentifiability and possibilities to circumvent it.
Bin Zhang
(ONCO)
Georgia State University
"The Ecology of Collective Cancer Invasion: An Evolutionary Game Theory Model"
Cancer is an evolutionary disease which exhibits genomic and phenotypic heterogeneity. Together with the tumor microenvironments, the cell subclones within the a tumor form a complex multi-cellular ecosystem. Tumors compromise a variety of specialized phenotypical subclones adapted to various ecological conditions, which influence the response to treatments and prognosis of the diseases. Recent experiments revealed two distinct phenotypes, leaders and followers, in non-small cell lung cancer during collective invasion. We adopt an evolutionary game theory framework to model the cancer microenvironments and the interactions between leader and follower cells. Measuring the total tumor burden and the leader fraction that drive collective invasion, we show that the pairwise interactions between leader and follower cells could alter the collective dynamics. These findings suggest potential new treatment strategies, targeting leader-follower cells interactions. Combinations treatments could reduce tumor burden as well as lower the risk for invasion.
Chandler Gatenbee
(ONCO)
Moffitt Cancer Center
"Immune escape at the onset of human colorectal cancer"
The evolutionary dynamics of tumor initiation remain undetermined, and the interplay between neoplastic cells and the immune system is hypothesized to be critical in transformation. Colorectal cancer (CRC) presents a unique opportunity to study the transition to malignancy as pre-cancers (adenomas) and early stage cancers are frequently detected and surgically removed. Here, we examine the role of the immune response in tumor initiation by studying tumor-immune eco-evolutionary dynamics from pre-cancer to carcinoma. The integrated approach uses a computational model, ecological analysis of digital pathology, and multi-region neoantigen prediction. Model results indicate that there are several routes to malignancy, each of which uniquely shapes the tumor ecology and sculpts intra-tumor antigenic heterogeneity (aITH). These routes include combinations of evading detection via accumulating mutations with low antigenicity, the ability to block immune attack (e.g. PD-L1), and the ability to recruit immunosuppressive cells. Modeling predicts that, in general, the most common route from benign to malignant is the construction of an immunosuppressive niche. To determine which route is dominant in CRC initiation, we used a cohort of 21 colorectal adenomas, 15 carcinomas, and 26 adenomas with a focus of carcinoma (“ca-in-ad”) cases. The immune microenvironment was characterized using the spatial distribution of 17 markers across registered whole-slide images at 40x magnification, while patterns of intra-lesion aITH were described using multi-region neoantigen prediction. Observed changes in aITH, the tumor ecology, and spatial patterns of both cell associations and gene expression are consistent with simulations where immunogenic adenomas do not progress to CRC because they are under immune control. Conversely, adenomas that progress initially avoid detection through low immunogenicity, but gradually construct an immunosuppressive niche isolated from CD8+ cytotoxic T cells, thereby evading immune elimination and allowing for an increase in neoantigen burden. Both modeling and data indicate that immune blockade (e.g. PD-L1 expression) plays a secondary role to immune suppression in tumor initiation or progression. These results suggest that re-engineering the immunosuppressive niche may prove to be a most effective immunotherapy in CRC.
Chay Paterson
(ONCO)
InSync Technology
"Cancer incidence as a form of convergent evolution"
Cancers occur after a gradual accumulation of mutations in a tissue. Together, these mutations enable cells to grow and spread in an uncontrolled way. This process takes many years, with one problematic lineage incrementally gaining an advantage over surrounding, normal tissue. This process repeatedly involves mutations on a few key oncogenes and tumour suppressors. Starting only with the sequences of a critical set of such genes and probability theory, we show that lifetime cancer risk can be calculated with no statistical fitting. We also show that certain orders of these mutations are more likely than others, and that these orders form a structure similar to a phylogenetic tree.
Daniel Abler
(ONCO)
University of Bern
"Tumor Growth and Biomechanics – Challenges & Opportunities"
Physical forces are recognized to play a critical role in shaping the micro-environment of tumors. Compression of cancer and stromal cells, as well as blood and lymphatic vessels, are direct consequences of mechanical solid stress, the compressive and tensile mechanical forces exerted by the solid components of the tissue. By altering the mechanical micro-environment of tumors, elevated solid stress can affect their pathophysiology, driving tumors to more aggressive phenotypes and compromise therapeutic outcome [1]. Mechanical stress also affects healthy tissue: It causes neuronal loss in brain tissue, and is linked to neurological deficits and reduced survival in patients with glioblastoma (GBM), the most common malignant primary brain tumor in adults. Given their far-reaching micro- and macroscopic consequences, tumor-induced mechanical forces may provide mechanistic insights into inter and intra-tumor heterogeneities, differential response to treatment and other phenotypical characteristics.
In this contribution, we survey the literature of spatial tumor growth modeling from a perspective of macroscopic tissue mechanics to assess the current status of mechanically-coupled growth models and to identify opportunities for further research: We summarize the types of modeling approaches previously used for capturing tumor-induced mechanical effects and their biological or physiological consequences. Based on this review, we identify the scenarios in which accounting for tissue mechanics proved to improve calibration to and prediction of clinical data. Drawing from examples of our and others’ research on mechanically-coupled growth modeling for GBM, we discuss challenges involved in the implementation and calibration of such models. In this context, we identify areas of mechanically-coupled growth modeling where further research is needed and explore application opportunities that such models may open.
Daniel J Glazar
(ONCO)
Moffitt Cancer Center
"Tumor growth and inhibition model predicts progression in recurrent high-grade glioma"
Recurrent high-grade glioma (HGG) remains incurable with inevitable evolution of resistance and high inter-patient heterogeneity in time to progression (TTP). Here, we evaluate if early tumor volume response dynamics can calibrate a mathematical model to predict patient-specific resistance to develop opportunities for treatment adaptation for patients with a high risk of progression. A total of 95 T1-weighted contrast-enhanced (T1post) MRIs from 14 patients treated in a phase I clinical trial with hypo-fractionated stereotactic radiation (HFSRT; 6 Gy × 5) plus pembrolizumab (100 or 200 mg, every 3 weeks) and bevacizumab (10 mg/kg, every 2 weeks; NCT02313272) were delineated to derive longitudinal tumor volumes. We developed, calibrated, and validated a mathematical model that simulates and forecasts tumor volume dynamics with rate of resistance evolution as the single patient-specific parameter. Model prediction performance is evaluated based on how early progression is predicted and the number of false-negative predictions. The model with one patient-specific parameter describing the rate of evolution of resistance to therapy fits untrained data (R^2=0.70). In a leave-one-out study, for the nine patients that had T1post tumor volumes ≥1cm^3 , the model was able to predict progression on average two imaging cycles early, with a median of 9.3 (range: 3–39.3) weeks early (median progression-free survival was 27.4 weeks). Our results demonstrate that early tumor volume dynamics measured on T1post MRI has the potential to predict progression following the protocol therapy in select patients with recurrent HGG. Future work will include testing on an independent patient dataset and evaluation of the developed framework on T2/FLAIR-derived data.
David Cheek
(ONCO)
Harvard University
"Genetic composition of an exponentially growing cell population"
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values in bacteria and cancer cell populations, we take the mutation rate to zero and the final number of cells to infinity. We prove that almost every site (entry of the nucleotide sequence) is mutated in only a finite number of cells, and these numbers are independent across sites. However independence breaks down for the rare sites which are mutated in a positive fraction of the population. The model is free from the popular but disputed infinite sites assumption. Violations of the infinite sites assumption are widespread while their impact on mutation frequencies is negligible at the scale of population fractions. Some results are generalised to allow for cell death, selection, and site-specific mutation rates. For illustration we estimate mutation rates in a lung adenocarcinoma.
Denis Hünniger
(ONCO)
University of Applied Sciences Dresden
"Effects of tumor-originating niches on intra-tumor heterogeneity"
Intra-tumor heterogeneity plays a crucial role during tumor initiation and progression. In practice, information about the genetic diversity in tumors is needed for developing individual therapies. However, there are still open questions in which manner intra-tumor heterogeneity evolves throughout tumor progression. In particular, it is unclear to which extent the architecture of the originally healthy tissue determines spatial patterns of intra-tumor heterogeneity. In this context, recent studies on the competition between tumor cells and wild-type cells lead to the concept of tumor-originating niches: Niches consist of a few cells whose competition during tumor initiation may predetermine the heterogeneity of the macroscopic, detectable tumor [1]. We study effects of tumor-originating niches on intra-tumor heterogeneity of the observed tumor and contrast them with the classical approach, where a tumor grows from a single cell. We examine in which manner mutations are spatially distributed throughout a tumor under presence and absence of tumor-originating niches. More precisely, we analyze the corresponding time scales of tumor initiation and identify spatial patterns of intra-tumor heterogeneity. To accomplish this, we use stochastic cellular automata and Markov theory for modeling, simulation and analysis. Understanding the spatial distribution of intra-tumor heterogeneity which originate from niches will contribute to more reliable prognoses in cancer therapy.
Derek Park
(ONCO)
Moffitt Cancer Center
"Synergizing chemotherapy with immune and evolutionary tradeoffs: Searching for Goldilocks"
A mainstay treatment for many cancers is chemotherapy, for which the dosing strategy is primarily limited by patient toxicity. While this Maximum Tolerated Dose (MTD) approach builds upon the intuitively appealing principle that maximum therapeutic benefit is achieved by killing the largest possible number of cancer cells, there is increasing evidence that moderation may be better. The increasing use of immune therapies which seek to use the patient’s own immune system therapeutically, bring the effectiveness of MTD into question. In some cases, there may exist a ‘Goldilocks Window’ of sub-maximal chemotherapy that yields improved overall outcomes. This window reflects the complex interplay of cancer cell death, changes in immune function, emergence of chemoresistance, and the potential for metastatic dissemination. Importantly, the many changes induced by chemotherapy have tradeoffs that depend on the specific agents being used, as well as their dosing levels and scheduling. We present experimental and clinical observations across cancer types that support the idea that MTD may not always be the best approach. Our mathematical model driven results indicate which patient states would benefit most from a Goldilocks chemotherapy dosing schedule. Implementation of such a personalized treatment regime, that incorporates insights from eco-evolutionary dynamics, will require the integration of predictive mathematical models of tumor-immune responses to therapy with appropriate patient specific clinical data.
Dhananjay Bhaskar
(ONCO)
Center for Biomedical Engineering, Brown University
"Quantifying cellular (re)-organization in 3-D cancer models using persistent homology"
Automated analysis of high-throughput, time-lapse microscopy data is essential for the development of multi-scale, patient-specific models that accurately mimic the complex behavior of cells observed in vivo. Many state-of-the-art methods for processing 3-D microscopy datasets rely on supervised machine learning methods for image segmentation, cell tracking and cell shape classification. These methods are computationally expensive, requiring difficult-to-obtain training data and parameter tuning. We propose an alternative approach, based on topological data analysis, to quantify changes in tumor architecture by analyzing point clouds obtained from cell nuclei positions. Using persistent homology, a topological barcode is extracted from each point cloud, which corresponds to the presence of topological features (clusters, acini and lumens) at multiple spatial scales. The barcode provides a unique insight into the spatial organization of data, which is often missing from typical analyses based on machine learning and statistics. By linking topological barcodes across time, the temporal persistence of topological features can be measured. The proposed methodology is able to identify nuclei associated with distinct clusters, acini and lumens in an unsupervised manner. Using this information, we ascertain the movement of cells between topological features. Furthermore, we classify qualitatively distinct organizational structures by clustering based on pairwise Wasserstein distances between topological barcodes. In this talk, I will introduce our methodology and demonstrate its potential for investigating tissue reorganization during tumorigenesis and metastasis.
Divyoj Singh
(ONCO)
Indian Institute of Science
"Emergent Properties of the HNF4α-PPARγ Network May Drive Consequent Phenotypic Plasticity in NAFLD"
Non-alcoholic fatty liver disease (NAFLD) is the most common form of chronic liver disease in adults and children. It is characterized by excessive accumulation of lipids in the hepatocytes of patients without any excess alcohol intake. With a global presence of 24% and limited therapeutic options, the disease burden of NAFLD is increasing. Thus, it becomes imperative to attempt to understand the dynamics of disease progression at a systems-level. Here, we decoded the emergent dynamics of underlying gene regulatory networks that were identified to drive the initiation and the progression of NAFLD. We developed a mathematical model to elucidate the dynamics of the HNF4α-PPARγ gene regulatory network. Our simulations reveal that this network can enable multiple co-existing phenotypes under certain biological conditions: an adipocyte, a hepatocyte, and a “hybrid” adipocyte-like state of the hepatocyte. These phenotypes may also switch among each other, thus enabling phenotypic plasticity and consequently leading to simultaneous deregulation of the levels of molecules that maintain a hepatic identity and/or facilitate a partial or complete acquisition of adipocytic traits. These predicted trends are supported by the analysis of clinical data, further substantiating the putative role of phenotypic plasticity in driving NAFLD. Our results unravel how the emergent dynamics of underlying regulatory networks can promote phenotypic plasticity, thereby propelling the clinically observed changes in gene expression often associated with NAFLD. This abstract is taken from an already published research paper co-authored by me (https://www.mdpi.com/2077-0383/9/3/870).
Elizabeth A Fedak
(ONCO)
University of Utah
"Getting mixed messages: How p53 controls its dynamics to interpret variable upstream signals"
p53 is one of the most widely studied proteins in molecular biology for its central role in tumorigenesis. In a healthy, replicating cell, p53 makes cell fate decisions based on signals it receives from repair pathways. Not only must p53 consolidate information from multiple sources, the signals it receives do not correspond exactly to the total amount of damage in the cell; rather, comparably lethal amounts of damage can induce dissimilar signals. For example, gamma radiation induces DNA lesions that p53-activating kinases bind to within minutes, while the DNA lesions created by UV radiation are harder for the cell to detect and only communicate with p53-activating kinases during repair.
Using a mechanistic model, we argue that this difference in response speed causes distinct dynamical profiles of p53 to arise. If p53 receives a strong signal with a short duration, as it would for a low dose of gamma radiation, the cell would be susceptible to premature apoptosis if p53 became overactive due to this signal. Instead, causing p53 to oscillate weakens its response and the signal only recovers if the damage persists after the initial round of suppression. For UV radiation, the delay between damage induction and communication to p53 creates a signal that starts low and increases over several hours. An under-regulated system may ignore a weak but long-lasting signal even if it represents extensive DNA damage. Instead, because this system can escape to a bistable region with higher levels of p53 at intermediate levels of activating signal, the cell can compensate for low kinase activation by raising the amount of available substrate. This allows active p53 to accumulate when exposed to a low but durable signal. Other models have focused on the mechanistic cause of p53 oscillations; this model provides a hypothesis as to why they exist.
Here, we focus on the surprising hypotheses that arise from reconciling p53's paradoxical behavior and discuss how this model extends our knowledge of tumor survival strategies.
Emilia Kozlowska
(ONCO)
Silesian University of Technology
"Mathematical modeling of palliative treatment in non-small cell lung cancer"
The most common subtype of lung cancer is non-small cell lung cancer (NSCLC) that constitutes 80% of all lung cancer cases. NSCLC is usually diagnosed at an advanced stage because of non-specific symptoms, leading to high mortality. The standard treatment for NSCLC patients is a combination of chemotherapy and radiotherapy and, as emerging mode of treatment, immunotherapy. We collected, from a retrospective cohort of patients, 47 patients treated with platinum-doublet chemotherapy with a palliative intent or with symptoms treatment only. Thus, the patients are treated under the assumption of failed cure. From the cohort of patients, clinical data were collected, which serve as input data for computational platform. We developed a computational platform including a machine learning algorithm and a mechanistic mathematical model to find the best protocol for administration of platinum-doublet chemotherapy in palliative setting. The core of the platform is the mathematical model, in the form of a system of ordinary differential equations, describing dynamics of platinum-sensitive and platinum-resistant cancer cells and interactions reflecting competition for space and resources. The model is simulated stochastically by sampling the parameter values from a joint probability distribution. Machine learning algorithm is applied to calibrate the mathematical model and to fit it to overall survival curve. The model simulations faithfully reproduce the clinical cohort at three levels, long-term response (OS), initial response, and the relationship between number of chemotherapy cycles and time between two consecutive chemotherapy cycles. In addition, we investigated the relationship between initial and long-term response. We showed that these two variables do not correlate, which means that we cannot predict patient survival based solely on initial response. We also tested several chemotherapy schedules to find the best one for patients treated with a palliative intent. We found that optimal treatment schedule depends, among other, on the strength of competition among sensitive and resistant subclones in a tumor.
Giulia Laura Celora
(ONCO)
University of Oxford
"Analysis of the dynamics of tumour cells along a stemness axis under different oxygen conditions"
The concept of cancer stem cells (CSCs) was first introduced to explain intra-tumour heterogeneity. According to the so called ‘CSC’ hypothesis, tumours are organised according to a rigid hierarchical structure where CSCs have the capacity to self-renew. Through asymmetric cell division, CSCs can initiate and maintain tumours that also contain differentiated cells with limited clonogenic potential. Recent studies have challenged this framework and led to the development of the so-called ‘CSC plasticity’ hypothesis. Here, stemness is viewed as a continuous rather than a discrete trait, and it may change in response to micro-environmental signals. In line with this conceptual model, we develop a mathematical model to describe the dynamics of a population of tumour cells structured by their stemness. Cells continuously transition between cancer stem cells (CSC) and terminally differentiated cancer cells. Evolution along the stemness axis is driven by extrinsic (micro-environment) and intrinsic (random epimutation) ``forces'', which are represented by advective and diffusion fluxes respectively. We account for natural selection and competition by introducing a fitness landscape, i.e. phenotypic dependent net growth of the cells. We consider a well-mixed environment in which cells are exposed to a prescribed oxygen environment, and their time-evolution determined by a non-local reaction-advection-diffusion equation, where the non-locality rises from the competition between different phenotypes. We analyse two scenarios, normoxia and hypoxia, in order to capture the different niches present in vivo. In our model, oxygen levels affect not only cell fitness but also act as an extrinsic force, favouring cell maturation (under normoxia) or de-differentiation into CSC (under hypoxia). We show how the qualitative behaviour of the system dynamics and its equilibrium distribution changes as model parameters vary, with tumour extinction predicted for certain regimes. The numerical results are validated by using spectral theory which allow us to characterise the stability property of the trivial steady-state, i.e. extinction. In addition to reproducing a variety of tumour cell distributions characterised by different mean clonogenic capacity, proportion of CSCs and population size, our analysis also gives insight into the role that extrinsic and intrinsic forces play in shaping the organisation of cells in phenotypic space. Finally, we discuss how the model can be extended to incorporate treatment, specifically radiotherapy, accounting for stem-ness dependent radio-resistance.
Harsimran Kaur
(ONCO)
Indian Institute of Technology Bombay
"Computational modeling of mechano-metabolic adaptation to a stiff microenvironment in Cancer cells"
Extracellular matrix (ECM) is a highly dynamic cohort of macromolecules present in the cellular microenvironment that regulates cellular behavior chemically and mechanically. Numerous studies have demonstrated the effect of mechanical cues on cellular differentiation and morphology. These studies also highlight the imperative role of ECM in the activation of specific signaling pathways through which ECM influences cellular behavior. Continuous remodeling of the Tumor microenvironment, which also includes ECM stiffening, has emerged as a prominent hallmark of poor disease prognosis and cancer metastasis. In addition to that, cancer cells are also known for their highly reprogrammed metabolism. The objective of this study was to establish a relationship between increased stiffness of tumor microenvironment and metabolism in cancer cells. A deterministic analytical model has been constructed to demonstrate the mechanoadaptation of metabolism in cancer cells. This mathematical model shows that increased stiffness has a positive effect on HIF1α accumulation under hypoxia. As HIF1α promotes the Warburg effect, this result highlights the potential link between Tumor mechanics and metabolism.
Heber Rocha
(ONCO)
Indiana University
"Qualitative study of cell migration associated with hypoxia in the dynamics of tumor growth"
Recent results point to the importance of hypoxia in the development of cancer. In particular, hypoxia is generated by an intratumoral oxygen gradient, driving tumor cells towards a migratory phenotype, which in turn promotes invasion and metastatic risk. Recently, experimentalists developed a novel bioengineered reporter system where normoxic cells fluoresce red (DsRed) until exposure to hypoxic conditions, at which point increases in hypoxia-inducible factors (HIFs) induce a permanent genetic change to express green fluorescent protein (GFP). Observations of this system in a mouse model allow us to formulate and evaluate new hypotheses on the frequency and duration of phenotypic changes in cancer cells under the influence of hypoxic conditions. In this work, we present a qualitative study of the response of the GFP+ cells to the migratory stimulus from hypoxia, with a focus on understanding the role of phenotypic transience or permanence on cancer invasion. We use a hybrid continuum-discrete model on two scales that describes the behavior of normoxic and hypoxic cells in the dynamics of tumor growth and invasion. On the cellular scale, the cells are individually represented as discrete agents according to their physical and phenotypic attributions, while on the tissue scale, the dispersion of the oxygen pressure in the microenvironment is represented using continuum diffusion-reaction equations. As in the in vivo experiments, we model changes in red/green fluorescence based on hypoxic exposure. We calibrate changes in cell motility following hypoxic exposure to ex vivo measurements of DsRed+ and GFP+ in cells, using an Approximate Bayesian Computation (ABC) method. The initial results of the in silico model present a plausible representation of the biological experiments and suggest new research themes.
Jairo G Silva
(ONCO)
Instituto Federal de Mato Grosso
"Mathematical Models About Radioactive Iodine-Refractory Differentiated Thyroid Cancer"
Clinical and pathological evidence suggests that the progression of Differentiated Thyroid Carcinomas to a poorly differentiated stage, or even an anaplasic cancer, is a natural process in the development of malignancy. The immune regulatory molecule PD-L1, Programmed Death-Ligand 1, blocks the immune response of activated T cells by binding to the PD-1 receptor, an immune checkpoint expressed in T cells and others, to modulate their activation or inhibition. In addition to the traditional 131-I radioiodine treatment, other therapeutic options for DTC are needed when cells lose their ability to capture and concentrate iodine. Two examples of drugs used due to the evolution of DTC to a progressive state in the loss of sensitivity to RAI correspond to Lenvatinib, which is a target therapy with the function of inhibiting multiple tyrosine kinases, and thus reducing tumor cell proliferation; and Pembrolizumab, a monoclonal antibody of human immunoglobulin G4 that aims to prevent the binding of PD-1 to PD-L1, and thus restore the anti-tumor immune response of anti-tumor T cells.
We propose two mathematical models of ordinary differential equations in order to evaluate two modes of treatment for patients with DTC refractory to RAI. In the first model, considering the variables concentration of Lenvatinib, number of malignant cells and NK cells, we evaluated the effectiveness of the target therapy in the treatment. The second model includes the addition of the variable concentration of Pembrolizumab, and T cells in the group of NK immune cells, and for this reason, we simulate in this case the effectiveness of the therapeutic combination with patients. As a result, we obtained that both drugs were able to generate responses such as stable disease or partial response, however, greater control of the tumor was observed from the combination of the proposed therapies.
Javier C Urcuyo
(ONCO)
Mayo Clinic
"Understanding glioblastoma-macrophage interactions through radiomics, transcriptome sequencing, and mathematical modeling"
Glioblastoma (GBM) is the most common primary brain tumor and has a poor median overall survival of just under 15 months. To combat this heterogeneous disease, the immune system initiates an inflammatory response, where both brain-resident microglia and blood-derived macrophages work to fight the tumor. However, some immune cells are co-opted by the tumor to express immune-suppressive signals, allowing for continued tumor growth and are thereby termed ‘glioma-associated macrophages’. To better understand the spatiotemporal dynamics of the interactions between tumor cells and these two macrophage phenotypes, we proposed the Proliferation-Invasion-Macrophage (PIM) model, which is a partial differential equation model that incorporates the proliferative and invasive behavior of GBM cells, as well as populations for both ‘healthy’ and ‘glioma-associated’ macrophages. Through exploring the parameter space, we classified the various dynamics of tumor progression. To apply the model to patient data, spatially-distributed image-localized biopsies were collected from a cohort of patients and RNA sequencing was performed. Correlations between normalized RNA counts of key genetic markers (i.e. CD68, CD163, SOX2, KI67) were analyzed. Patient imaging and RNA sequencing data were then utilized to train and validate a predictive machine learning model that outputs transcriptome expression maps for the aforementioned key genetic markers. This was then used to parameterize the PIM model for each patient. In doing so, this provided us with a detailed characterization of the interactions between the GBM and macrophage populations on a patient-by-patient basis. Through gaining an understanding of the interactions between glioma cells and the macrophage phenotypes, we can work towards developing personalized immunotherapies and other immune-targeted therapeutic strategies that combat this phenomenon.
John Metzcar
(ONCO)
SICE, Indiana University
"Mathematical modeling of leader-follower cell invasion of tumor-associated stroma using a novel extracellular matrix model"
Collective cell migration and invasion are challenging topics to study as diverse biological processes may drive these behaviors. Mathematical modeling informed by biological experiments can lead to new insights. Here, we focus on a particular form of collective migration: collective invasion of tumor-associated stroma via a cell-based leader-follower mechanism. For the stroma, we implement a novel, simple extracellular matrix (ECM) model using three variables to represent a unit of ECM: a fiber density, anisotropy, and orientation. Furthermore, we implement bi-directional interactions between cells, represented as discrete agents, and the ECM. Cells remodel the ECM within their vicinity based on their motion and the ECM alters cellular motility. With this representation, we attempt to recapitulate experimental results of an organoid model of invasive breast cancer through a series of models that build additively on one another to introduce new biological hypotheses as additional agent model rules. Despite the increasing complexity of individual cells and short-range interactions, we find that our results do not significantly vary from one model to the next in overall qualitative behavior. This suggests that long range ECM remodeling and asymmetric cell-cell attachment/detachment processes might be necessary to recapitulate experimental results. By proxy, it also suggests that these phenomena may possibly be necessary to enable collective invasion of ECM in organoid systems.
Joshua A Bull
(ONCO)
University of Oxford
"Description of immune cell infiltration in solid tumours using spatial statistics and topological data analysis"
The increasing digitization of immunohistochemistry slides provides opportunities for pathologists to automate routine tasks and improve current workflows. Techniques for identifying immune cells in biopsies or surgically resected tumours are now widespread, with several open-source or commercial image analysis platforms providing cell identification tools. While these tools can be used to calculate statistics such as the density of immune cells in a given tumour region, a property which correlates with patient prognosis, consideration of spatial statistics and topological analyses which can provide more detailed spatial descriptions of localisation is not widespread.
We introduce several spatial statistical descriptors which can be used to describe localisation of immune cells within a tumour, and apply them to macrophage distributions in human IHC images and in simulated datasets. We show that key features of the spherical contact distribution, the pair correlation function, and the J-function vary predictably as the degree of immune cell infiltration from stromal to tumour regions increases in simulated data. Using these statistics, we introduce a new method based on maximum likelihood estimation which combines the strengths of different spatial descriptors to automatically classify macrophage infiltration into tumour nests. We validate our approach by applying it to macrophage distributions from clinical datasets, obtaining infiltration indices which match the qualitative assessments of experienced pathologists. Finally, we demonstrate how topological data analysis can be applied to macrophage distributions in human IHC images and in simulated datasets to enhance these descriptions.
Junho Lee
(ONCO)
Konkuk University
"Synergistic Effects of Bortezomib-OV Therapy and Anti-Invasive Strategies in Glioblastoma: A Mathematical Model"
Recent experimental studies have demonstrated the great potential of combination therapies, using oncolytic viruses (OVs) in conjunction with proteasome inhibitor, bortezomib (BTZ), for the treatment of glioblastoma. So, we have developed a mathematical model of combination (bortezomib+OV) therapy, including intracellular signaling network (proteasome-NKkB-Bcl2-Bax) which mediate anti-apoptosis, apoptosis, and necroptosis of tumor cells. In addition, a challenging tumor microenvironment (TME) such as gray matter and dense ECM structure in brain, has been shown to regulate tumor invasion. But the critical role of TME in such therapies has not been studied in the context of combination therapies. We show (i) how the intracellular signaling regulates tumor cell killing in the combination therapy, (ii) that the TME plays a significant role in controlling the anti-tumor efficacy in Bortezomib-OV combination therapies and generating various spatial patterns of tumor growth. The simulation results show the possibility of development of new tumor treatment options within TME and new anti-invasion strategy.
Karina Vilches
(ONCO)
Catholic University of Maule
"A mathematical approach for visualizing cell migration during tumor progression"
The present research project consists of a mathematical approach that captures and explores a wide range of mechanisms and biological variability to simulate the collective cell migration during the tumor progression. This orchestrates multiple phenomena in cancer dynamics is represented by a chemotaxis two-species system, which is supported by an extensive literature. In this respect, we promote the realization of modeling platforms that facilitate the integration of interdisciplinary perspectives in tumor progression. Furthermore, the theoretical migration scenario of tumor cells extends the previous results of the chemotaxis and chemotaxis-haptotaxis systems adding more complexity to the mathematical model for representing these cell-cell dynamics including micro-environmental influence. The seeking of regimes in which tumor invasion occurs with a low total mass of tumor cells could be an interesting initial point for an interdisciplinary discussion about theoretical results obtained, and how such analytical results could be transferred to the laboratory. This last consideration is that the density of tumor-associated macrophages in tumor site results in an important characteristic to identify the cancer state, and some researchers suggest that targeting processes required for collective migration may be effective in combating certain types of tumors.
Lan K Nguyen
(ONCO)
Monash University
"Integrative mathematical modelling unveils hidden mechanism of resistance to PI3K inhibition and identifies new effective combination therapies for breast cancer"
The phosphatidylinositol 3-kinase (PI3K)-AKT-mTOR signalling pathway is a master regulator of cell growth and its activation is frequently associated with cell transformation and cancer. This is particularly common in breast cancer, where alterations in members of this pathway occur in over 50% of patients, irrespective of tumour subtype. Over the last decade, targeted drugs directed at the PI3K pathway, particularly inhibitors directed at PI3K, have been under intense clinical development. However, the emergence of acquired and/or adaptive resistance to these agents, the latter involving dynamic rewiring of signalling networks and crosstalk, has presented major challenges for the delivery of impactful treatments. This highlights the critical need to identify the molecular mechanisms through which tumour cells rewire their signalling outputs and bypass the inhibitory effect of targeted therapies, and to develop more effective combination therapies. To address these challenges, we constructed a multi-pathway mechanistic model based on differential equations that integrates the PI3K-AKT signalling axis with key cancer-relevant pathways, incorporating known feedback and cross-talk mechanisms. We calibrated this model using time-course kinetic data in response to inhibition of PI3K by a selective and clinically-relevant inhibitor BYL719 (BYL), obtained from the T47D breast cancer cell lines. Integrative simulations/experimental analyses reveal an unexpected role for the cyclin-dependent kinase inhibitor p21, which in contrary to its known growth-inhibitory function, appears to promote resistance to PI3K inhibition. Consistent with this, model simulations further predict a dynamic and adaptive reactivation of p21 following acute BYL treatment, which we validated experimentally using immunoblotting and phosphoproteomic profiling in both parental T47D cells and cells that have become resistant to BYL. Next, following a similar approach we recently published, we simulated the effect of various potential drug combinations targeting pair-wise nodes within the PI3K integrative network to identify potential co-targets that can be effectively combined with PI3K inhibition for more anti-tumour benefit. Among these, we predict dual inhibition of PI3K and the kinase PDK1 displays the most potent synergistic effect in suppressing pro-growth signalling and cancer cell growth. Model predictions were subsequently validated using immunoblotting and cell viability assays. In addition, analysis of breast cancer patient data from TCGA demonstrates concomitant overexpression of the genes encoding PIK3 and PDK1 is associated with worse patient survival, further supporting their validity as co-targets. Collectively, our integrative analyses uncovered novel resistance mechanisms against PI3K inhibition, and identified effective combination therapeutic strategies that overcome such resistance, leading to better treatment for PI3K-driven breast cancer.
Lee Curtin
(ONCO)
Mayo Clinic
"Lacunarity and fractal dimension as prognostic biomarkers in glioblastoma"
Glioblastoma (GBM) is the most aggressive primary brain tumor with a median survival of only 15 months with standard of care treatment. Typically, these tumors present with regions of necrosis, contrast enhancement and edema, visible on standard clinical magnetic resonance imaging (MRI). The prognostic impact of the shape of these regions has not been fully explored. Lacunarity and fractal dimension are two quantitative morphological measures that describe how shapes fill space and their complexity at varying spatial scales. Both of these measures have been shown to distinguish overall survival (OS) and progression free survival (PFS) when applied to regions of necrosis. In our cohort of patients with first-diagnosis GBM (n=400), we sought to validate these previously published results and extend this work to other tumor-induced imaging abnormalities. We calculated median lacunarity and fractal dimension values of necrosis (n=390), necrosis with contrast enhancement (n=400), and edema (n=257) on a per patient basis and searched for cutoffs that significantly distinguished survival. In our cohort, we found that lacunarity can significantly distinguish PFS when applied to necrosis and can significantly distinguish OS when applied to necrosis with contrast enhancement, or edema. We find that fractal dimension can also significantly distinguish OS when applied to edema. We believe that morphological measures such as lacunarity and fractal dimension may play an important prognosticating role in GBM presentation. This link between morphological and survival metrics could be driven by underlying biological phenomena, tumor location, or microenvironmental factors that should be further explored.
Leili Shahriyari
(ONCO)
University of Massechusetts Amherst
"A path toward personalized cancer treatments"
A major clinical challenge for cancer therapies is to obtain an effective treatment strategy for each patient or at least identify a subset of patients who could benefit from a particular treatment. Since each cancer has its own unique features, it is very important to obtain personalized cancer treatments and find a way to tailor treatment strategies for each patient. Recently, mathematical models have been commonly used to discover, validate, and test drugs. Since these models are a complex system of nonlinear equations with many unknown parameters, estimating the values of the model's parameters is extremely difficult. Existing parameter estimation methods for these models often use assembled data from various sources rather than a single curated dataset. These datasets are usually obtained through various biological experiments, in vitro and in vivo animal studies. To arrive at personalized treatments, we need to obtain values of parameters of the model for each patient separately. Since the set of variables of the model includes relative amount of each cell type and cytokines in the tumor, we developed a tumor deconvolution software, which is a combination of recently developed methods, to predict the relative amount of these variables from the gene expression profile of the tumor. The output of the tumor deconvolution software can be used to predict the values of the parameters for each patient. In other words, we propose to use patients’ gene expression data of primary tumor to estimate the values of parameters of the mathematical model for each patient separately, instead of the common approach of assuming these parameters have the same values across all patients and using animal studies to estimate them. This new approach provides us with a unique opportunity to suggest the optimal treatment strategy for each patient and predict the efficacy of each treatment for each patient.
Lucas Barberis
(ONCO)
IFEG-CONICET
"Modeling Helps Understand the Influence of Substrate on Tumorsphere Growth"
Tumorspheres, cellular spheroids formed by clonal proliferation from established cell lines or tumor tissue, are experimental systems used to investigate diverse features of cancer. They may be especially useful to ascertain the effects of cancer stem cells on neoplastic development. Here we use a recently developed model that considers the interactions between cell subpopulations [L. Benitez et al, Physica A 533, 121906 (2019)] to interpret the results of experiments probing the influence of substrate hardness on tumorsphere growth [Wang et al, Oncol. Lett. 12, 1355 (2016)]. These authors cultured breast cancer stem cells on soft and hard matrix surfaces using stem cell growth factors, observing that the number of cancer stem cells increased continuously, albeit in different ways. They also cultured the cancer stem cells on hard agar in the absence of growth factors (the “control” experiment). In this case the spheroids grew faster, even if the stem cell number remained stationary. Fitting our model results to the data corresponding to the use of growth factors, we found that interspecific interactions between cells in different populations always promoted growth via a positive feedback loop. These interactions enhanced the stem cell doubling rate in what appears to be a frustrated attempt to reach the equilibrium fractions corresponding to the cancer stem cell niche. Moreover, if growth proceeded on soft agar, intraspecific interactions were always inhibitory, as we should expect from their competition for nutrients, but on hard agar the interactions between differentiated cells were strongly inhibitory while those between stem cells were collaborative. Experimental evidence also suggests that the hard substrate induces a large fraction of asymmetric stem cell divisions and the likelihood of plasticity processes, two features that appear to be absent in the case of the soft substrate. In the absence of stem cell growth factors, the barrier to differentiation is broken: although the stem cell number was conserved, overall growth was faster than in the other two cases. The interactions accelerate the effective growth rate of the differentiated cell fraction. Our interpretation of the results points to the centrality of the concept of stem cell niche and helps us to understand the relation between substrate stiffness and the dynamics of stem-cell fueled tumor growth.
Mark Robertson-Tessi
(ONCO)
Moffitt Cancer Center
"Immune predation promotes aggressive metabolic phenotypes in a context-dependent manner"
Metabolism plays a complex but key role in the evolution of cancerous tumors. Localized hypoxia due to vascular dysfunction within the tumor microenvironment facilitates the metabolic response of the tissue (the Pasteur effect), causing acidification that leads to the evolutionary selection of acid-resistant tumor cell phenotypes. The subsequent emergence of a glycolytic phenotype in poor nutrient conditions leads to subsequent aggressive invasion. This evolutionary trajectory from normal to acid-resistant to glycolytic, is highly nonlinear and is modulated by vascular dynamics as well as the immune response. We present a multiscale hybrid-discrete-continuum cellular automata model that captures the phenotypic, vascular, microenvironmental, and spatial heterogeneity that shape acid-mediated invasion over biologically-realistic temporal scales. Specifically, we explore two major components in the interplay between tumor metabolism and immune function. First, T cells are subject to inactivation in acidic microenvironments. Second, competition for glucose inactivates the immune response through glucose starvation. These two processes are viewed as immune escape mechanisms that tumors may differentially employ in response to immune predation. A third mechanism considered is the expression of inhibitory immune checkpoint receptor (PD-L1). Model predictions indicate that fomenting a stronger immune response in a tumor leads to initial benefits with respect to additional cytotoxicity; however, this advantage is offset by the increased turnover of cells that leads to accelerated evolution and emergence of aggressive phenotypes. This creates a bimodal therapy landscape: either the immune system should be maximized for complete cure, or kept in check to avoid rapid evolution of invasive cells. The second option is akin to a natural adaptive therapy. These constraints are context-dependent and critically depend on the stability of intratumoral vascular dynamics and microenvironmental acidification.
Michelle Przedborski
(ONCO)
University of Waterloo
"A combined systems biology and machine learning approach to study patient response to anti-PD1 immunotherapy"
Anti-PD-1 immunotherapy has produced the highest response rate of any single-agent immunotherapy and has recently shown promise for the treatment of several aggressive cancers including melanoma, non-small-cell lung cancer, bladder, and head and neck cancers. However, there is high variability and unpredictability in the treatment outcome. While it remains an intensive area of research, this variability is thought to be driven by patient-specific biology, particularly, the interactions of the patient’s immune system with the tumor. Here I will introduce an integrative experimental and theoretical approach which was developed to study the patient-specific interactions between immune cells and tumor cells, to capture the variability in patient response to anti-PD-1 immunotherapy. This integrative approach utilizes clinical data from an ex vivo human tumor system that incorporates fragments from tumor biopsies in co-culture with patient-matched peripheral immune cells and plasma. The patient-derived cytokine expression levels and immune cell populations under control and Nivolumab treatment conditions were used to develop and calibrate a multi-scale systems biology model of the immune system which includes interactions of immune cells with the tumor cells and cytokine signaling. I will illustrate how the patient data was integrated into the model to capture the variability in patient response to treatment. Then I will show how the application of machine learning approaches to a simulated patient data set obtained from the calibrated model can be used to stratify features of response from non-response to anti-PD-1 immunotherapy. Next, I will discuss how transfer learning can be implemented using simulated clinical data with a subset of identified response features to significantly improve the response prediction accuracy on the ex vivo patient data. This approach has the potential to identify targeted experiments for patient screening as well as novel therapeutic targets that may sensitize otherwise non-responsive patients to anti-PD-1 immunotherapy. To illustrate this point further, I determine the optimal timing of triple combination therapy using IL-6 inhibition and recombinant IL-12 along with anti-PD1 immunotherapy to significantly improve patient response to treatment. Finally, I identify additional features of response beyond those encompassed in the systems biology model, which, while seemingly counter-intuitive, agree with recent clinical findings that may reshape our approach to cancer immunotherapy.
Min Song
(ONCO)
University of Southern California
"Model Predicts Distinct Mechanisms of Endothelial Cell Growth Upon the Stimulation of FGF and VEGF"
Angiogenesis is the formation of new blood capillaries from pre-existing ones. The essential role of blood vessels in delivering nutrients makes angiogenesis important in the survival of tissues, such as wound healing process and tumor growth. Thus, targeting angiogenesis is a prominent strategy in both tissue engineering and cancer treatment. However, not all approaches to target angiogenesis lead to successful outcomes. Current therapies primarily target pro-angiogenic factors such as vascular endothelial growth factor (VEGF) and fibroblast growth factor (FGF) in isolation. However, there is a limited understanding of how these promoters combine together to stimulate angiogenesis. We aim to quantitatively characterize the crosstalk between VEGF- and FGF-mediated angiogenic signaling in endothelial cells and the effects of the interactions on a cellular level, specifically endothelial cell growth, in order to identify novel therapeutic strategies. We constructed a hybrid agent-based mathematical model that characterizes endothelial cell growth driven by FGF and VEGF-mediated signaling. The molecular interactions were implemented with our published ordinary differential equation model that focuses on FGF- and VEGF-induced mitogen-activated protein kinase (MAPK) signaling and the phosphatidylinositol 3-kinase/protein kinase B (PI3K/Akt) pathway which promote cell survival and proliferation. To link the molecular signals with the cellular responses, we assumed that the endothelial cell growth is dependent on the maximum pAkt and pERK levels upon the stimulation of FGF and VEGF within two hours, following Hill functions. We used the total number of endothelial cells as an indicator of cell growth. Cell heterogeneity within a cell population is also considered in the model. The parameters that significantly influence cell growth rate were identified using a global sensitivity analysis and estimated by fitting the model to experimental data using particle swarm optimization. The model was validated against independent experimental data. The trained and validated model predicts the optimal concentrations for mono- and co-stimulation of FGF and VEGF needed to maximize endothelial cell growth. Also, FGF and VEGF show different mechanisms in promoting the overall cell growth rate. Additionally, combinations of FGF and VEGF do not exhibit an obvious greater effect in promoting cell growth compared to FGF stimulation alone. Moreover, our model identifies the influential species and kinetic parameters that specifically modulate the cell growth, which represent potential targets for modulating angiogenesis signaling. The model provides mechanistic insight into VEGF and FGF interactions in angiogenesis and predicts the combination effects of FGF and VEGF co-stimulation. More broadly, this model can be utilized to identify targets that influence angiogenic signaling leading to cell growth and to study the effects of pro- and anti-angiogenic therapies.
Mohammad U Zahid
(ONCO)
Moffitt Cancer Center
"Forecasting Individual Patient Response to Radiotherapy with a Dynamic Carrying Capacity Model in Head and Neck Cancer"
Nearly 66% of all cancer patients receive radiotherapy (RT). Currently, RT scheduling does not take into consideration tumor volume dynamics. If response to an RT schedule can be predicted accurately, then there is a potential for treatment adjustment. The objectives of this study are to model tumor volume dynamics in response to RT and to evaluate the patient-specific predictive power of the model for patient outcomes. Tumor volume data were collected for 2 independent cohorts of head and neck cancer patients from Moffitt Cancer Center (MCC) and M.D. Anderson Cancer Center (MDACC) that received 66-70 Gy RT in 2 Gy daily fractions. Tumor volume measurements were derived from CT scans: 2 before RT and weekly scans during RT. Tumor growth was described with a logistic growth model with intrinsic growth rate, λ, and tumor carrying capacity, K. The effect of RT was modeled as an instantaneous reduction in carrying capacity with fraction δ. To predict response to RT for individual patients, we combined the distribution of MCC-learned δ values and weekly measurements of volume reduction in the untrained MDACC cohort to estimate δ to predict volume reduction and patient outcomes. The model fit data from MCC with patient-specific values for λ and δ with high accuracy (R2 = 0.95). Model analysis revealed that growth rate λ is not patient specific. A uniform λ reduces R2 to 0.92 while reducing the number of free parameters in the model (K and δ being patient specific). This MCC-trained model was then cross-validated on the independent cohort from MDACC (R2 = 0.98), demonstrating transferability of λ. The trained model predicts patient-specific RT responses with >70% accuracy for loco-regional control and disease-free survival without considering any patient-specific observations, and inclusion of on-treatment observations further increases prediction accuracy.
Mohsin Saleet Jafri
(ONCO)
George Mason University
"Predicting Drug Resistance by Applying Machine Learning to Molecular Simulation"
Distinct missense mutations in a specific gene have been associated with different diseases as well as differing severity of a disease. Current computational methods predict potential pathogenicity of a missense variant but fail to differentiate between separate disease or severity phenotypes. We have developed a method to overcome this limitation by applying machine learning to features extracted from molecular dynamics simulations, creating a way to predict the effect of novel genetic variants in causing a disease, drug resistance, or another specific trait. As an example, we have applied this novel approach to variants in calmodulin associated with two distinct arrhythmias, as well as two different neurodegenerative diseases caused by variants in amyloid beta peptide. The new method successfully predicts the specific disease caused by a gene variant and ranks its severity with more accuracy than existing methods. We have applied this methods to predicting cancer drug resistance for specific variants.
Nara Yoon
(ONCO)
Adelphi University
"Modeling collaterally sensitive drug cycles: shaping heterogeneity to allow adaptive therapy"
Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. Particularly, there is utility in a drug sequence which completes a cycle of such relationships. With such cycles, one could, in theory, generate infinitely long drug sequences which can be used in long term therapy to mitigate the evolution of resistance in a tumor. In this work, we explored the optimal therapeutic strategy using the drugs involved in such a cycle with an arbitrary length, N (>=2). We developed a mathematical model for this research, in which tumor cells are classified as one of N subpopulations represented as { R_i|i =1,2,...,N}. Each subpopulation, R_i , is resistant to Drug i and each subpopulation, R _{ i -1} (or R_N , if i =1), is sensitive to it, so that R_i increases under Drug i as it is resistant to it, and after drug-switching, decreases under Drug i+1 as it is sensitive to that drug(s). Based on the model, we found that there is an initial period of time in which the tumor is `shaped' into a specific makeup of each subpopulation, at which time all the drugs are equally effective ( R* ). After this shaping period, all the drugs are quickly switched with duration relative to their efficacy in order to maintain each subpopulation, consistent with the ideas underlying adaptive therapy. Additionally, we have developed methodologies to administer the optimal regimen under clinical or experimental situations in which no drug parameters and limited information of trackable populations data (all the subpopulations or only total population) are known. The therapy simulation based on these methodologies showed consistency with the theoretical effect of optimal therapy.
Nikolaos Dimitriou
(ONCO)
Department of Bioengineering, McGill University
"Modelling geometric patterns of cancer progression"
Throughout the years the morphological characteristics of malignant tumours have played a major role to perform cancer staging, which in turn determines the selection of therapy [1]. Studies that quantify the geometry of tumours have shown that tumours progress towards less smooth boundaries with strands of cells invading in surrounding tissues [2,3,4], thus, resulting in poor therapeutic outcomes [5,6]. Mathematical models can provide useful insights towards the understanding the morphological progression of cancer as well as improve their therapeutic outcomes. In this context, a computational framework that focuses on the modelling of complex geometric patterns is presented. The framework utilizes hybrid spatiotemporal models that describe cancer growth in terms of both tumour and cellular levels. Model validation is performed with 3D cell culture experiments of triple negative breast cancer cells (MDA-MB-231) grown in Matrigel. The model is calibrated to the experimental data with the use of combined approximate bayesian computation and monte carlo techniques (ABC-MCMC). Spatial statistical analysis methods are then utilized towards the identification of geometric patterns across tumour volumes, formed in both experiments and simulations. Results so far indicate cell organization into clusters that progressively tend to accumulate in the boundaries of the examined space. The resulted collective migration pattern suggests cell-cell cooperativity and combined with increased mobility leads to the escape from the examined space.
Noemi Andor
(ONCO)
Moffitt Cancer Center
"Invasion of homogeneous and polyploid populations in nutrient-limiting environments"
Breast cancer progresses in a multistep process from primary tumor growth and stroma invasion to metastasis. Progression is accompanied by a switch to an invasive cell phenotype. Nutrient-limiting environments promote chemotaxis with aggressive morphologies characteristic of invasion. It is unknown how co-existing cells differ in their response to nutrient limitations and how this impacts invasion of the metapopulation as a whole. We integrate mathematical modeling with microenvironmental perturbation-data to investigate invasion in nutrient-limiting environments inhabited by one or two cancer cell subpopulations. Hereby, subpopulations are defined by their energy efficiency and chemotactic ability. We estimate the invasion-distance traveled by a homogeneous population. For heterogeneous populations, our results suggest that an imbalance between nutrient efficacy and chemotactic superiority accelerates invasion. Such imbalance will spatially segregate the two populations and only one type will dominate at the invasion front. Only if these two phenotypes are balanced do the two subpopulations compete for the same space, which decelerates invasion. We investigate ploidy as a candidate biomarker of this phenotypic heterogeneity to discern circumstances when inhibiting chemotaxis amplifies internal competition and decelerates tumor progression, from circumstances that render clinical consequences of chemotactic inhibition unfavorable.
Oke I Segun
(ONCO)
University of Pretoria, South Africa
"Mathematical model for the estrogen paradox in breast cancer treatment"
Background: Breast cancer is one of the major causes of mortality in women world- wide. Estrogens are known to stimulate the growth of breast cancer but are also effective in treating the disease. This is referred to as the “estrogen paradox”. Several studies have been dedicated to describe the possible mechanisms behind this paradox. Other studies highlighted the correlations between the tumor suppressor protein p53 and the estrogen receptor alpha (ERα). Aim: We investigate possible trade-offs between the tumor suppressor protein p53 and the estrogen receptor alpha (ERα) that can lead to breast cancer elimination. Methods: We propose a novel ODE-based mathematical model describing the interac- tions between both dormant and active cancer cells, estrogen hormone, a tumor suppressor protein (p53), and a treatment combination with high-dose of estrogens (HDEs) and p53. We calculate the model’s equilibrium points and determine their global stability behavior by means of a comparison theorem. Findings: We find a range for the ratio of estrogen to p53 outside with active cancer cells can be eliminated without any treatment. Inside this range, we show that active cancer cells will grow to their maximum size, and that treatment with high-dose of estrogens can achieve cancer elimination. We carry out numerical simulation to confirm our mathemat- ical finding and investigate the scenario of low, moderate, and high ratio of estrogen to p53.
Praneeth Reddy Sudalagunta
(ONCO)
H. Lee Moffitt Cancer Center & Research Institute
"A pharmacodynamic model of clinical synergy in multiple myeloma"
Most anti-cancer therapies involve combinations of three or more agents, with the rationale that combining drugs with different mechanisms of action could maximize efficacy by targeting several subpopulations of a heterogeneous tumor. Synergy cannot be investigated in a clinical trial setting as the same patient cannot simultaneously receive single agents and their combination to quantify synergistic effect, while pre-clinical studies successfully quantify this effect, they do so in homogeneous cell lines. For this reason, clinical synergy remains difficult to investigate and translate into clinical utility. We focus our study on Multiple Myeloma (MM), an incurable hematological malignancy, due to its widespread use of combination therapy and the importance of timely therapeutic decisions in extending patient survival. We developed a mathematical framework that employs a second-order drug response model to fit patient-specific ex vivo responses of 203 MM patients to inform a novel pharmacodynamic model that accounts for two-way combination effects for 130 two-drug combinations. We have demonstrated that this model is sufficiently parameterized by single-agent and fixed-ratio combination responses, by validating model estimates with ex vivo combination responses for different concentration ratios, using a checkerboard assay. This novel model reconciles ex vivo observations from both Loewe and BLISS synergy models, by accounting for the dimension of time, as opposed to focusing on arbitrary time-points or drug effect. Clinical outcomes of patients were simulated by coupling patient-specific drug combination models with pharmacokinetic data from phase I clinical trials. Combination screening showed 1 in 5 combinations (21.43% by LD50, 18.42% by AUC) were synergistic ex vivo with statistical significance (P<0.05), but clinical synergy was predicted for only 1 in 10 combinations (8.69%), which was attributed to the role of pharmacokinetics and dosing schedules. Pre-clinical model predictions were used to accurately classify patients’ responses with statistically significant (P<0.05) accuracy as per International Myeloma Working Group response stratification criteria. This high-throughput combination screening framework identified drug combinations that are putatively clinically synergistic, and thus could potentially be used to screen for combinations that are likely candidates for a phase-III clinical trial. This could greatly benefit patients enrolling in these trials by improving the response on the experimental arm. The combinations shown to be most synergistic could be investigated to identify molecular pathways that govern their synergistic interaction.
Rafael Ramon Bravo
(ONCO)
Moffitt Cancer Center
"Cancer Crusade: Crowdsourcing Adaptive Therapy"
Cancer Crusade is a citizen science game in which players design treatment strategies to influence a virtual tumor growth model. The treatment regimens that the players construct are collected and sent to an online database for analysis, which may give insights into clinically effective adaptive strategies. In parallel, a machine learning-based approach was applied to the game, and the optimized therapy generated is compared to those generated by the human players. For the core game engine in Cancer Crusade, we started with a previously published hybrid cellular automata model of tumor metabolism and growth. The original model was used to study how tumor cells evolve acid-mediated invasion and the impact of treatment on these metabolic processes. We expanded the model by adding more drugs and cell phenotypes, including drug-resistant cells. The game was released on mobile platforms and has been generating data from plays for several years. The treatment strategies were analyzed using dendrogram clustering to find key decision differences and profile their relative performance. We also performed network analysis to observe treatment transitions. These analyses indicated several effective strategies, which tended to oscillate between chemotherapy and a pro-angiogenic drug, or chemotherapy and a hypoxia-activated prodrug, or combinations of all three of these drugs. These results parallel a machine learning (Q-learning) approach to the problem, which yielded a preferred strategy based on chemotherapy combined with a pro-angiogenic drug. The existence of several human-discovered alternative strategies suggests that in general human players may offer greater variety of successful strategies via citizen science games than Q-learning.
Ranjini Bhattacharya
(ONCO)
Moffitt Cancer Center
"Interpreting the Evolutionary Games Played in the NSCLC Microenvironment"
Lung cancer is the second most common type of cancer and non- small cell lung cancer (NSCLC) accounts for 84% of lung cancer diagnoses. Like other cancers, NSCLC is driven by somatic selection of fitter cells that can cheat the host. While there are treatments available to these patients, tumor heterogeneity enables selection of resistant cells. The tumor microenvironment can promote drug resistance and relapse by aiding tumor growth, angiogenesis, metastasis etc. Evolutionary Game Theory (EGT) can be used as a framework to map out the dynamics of different cellular strategies in a given tumor context to study cancer evolution. In our work we employ EGT to study the evolution of resistance to EML4- ALK positive NSCLC, with a focus on three cellular strategies- producers of hepatocyte growth factor (HGF), resistant cells, and sensitive cells. Tyrosine kinase inhibitors have been developed to block the oncogenic tyrosine kinase activity of ALK and inhibit cancer progression. progression. Resistance to TKIs has been attributed to expression of HGF which activates the alternative MET pathway, enabling cancer progression. We set up in vitro game assays to study the pairwise interactions between the three phenotypic strategies in control and drug (Alectinib) exposed environments. We find that HGF producers are the fittest and that they extend a protective effect on sensitive cells thus, enhancing their fitness. Curiously, this protection depends on the frequency of producers and undergoes saturation after a frequency of 0.4. Resistant cells do not show any significant interactions with the other two types. We then try to extrapolate the predictions from the pairwise games to predict outcomes of the three-player game involving all three phenotypes. Our study can give novel insights into possible therapeutic interventions targeting NSCLC and provides a framework for studying evolution of other cancers.
Rebecca Bekker
(ONCO)
Moffitt Cancer Center
"Immunological Consequences of Uniform vs Spatially Fractionated Radiotherapy"
Radiotherapy (RT) is the single most frequently used cancer treatment, with approximately 60% of patients undergoing either monotherapy or combination with other therapeutics. The immunogenicity of the tumor micro-environment (TME) affects how well a tumor responds to treatment. TMEs can be hot or cold, with tumors in immunologically cold micro-environments generally showing less of a radiation response than those in immunologically hot micro-environments. Radiation can be immunosuppressive or immuno-stimulatory, but these contradictory effects are poorly understood. It is thought that the immune response initiated by radiotherapy is curtailed by subsequent application of RT. Spatially fractionated radiotherapy shields areas of the tumor, thereby potentially protecting the immune environment. An ABM model was developed to evaluate the effects that different radiation doses, scheduling and SFRT architectures have on the immunological consequences of RT. We identify which types of TME respond better to spatially uniform or spatially fractionated radiotherapy, in the pursuit of advancing radiotherapy personalization.
Rifaldy Fajar
(ONCO)
Yogyakarta State University
"Analysis of Mathematical Model on the Development of Tumor Cells after Drug Therapy"
Mathematical modeling way to explain the reality to the mathematic equations. One of the phenomena that can be modeling is the development of tumor cells after drug therapy. Tumor cells defend mutations with a process of cell reproduction and cells will be a move to all of the body. Cells occupy one of the other organs. Splitting about this case used drug therapy or chemotherapy. This research has the purpose of identifying and analysis mathematical models on the development of tumor cells after drug therapy. Identification of mathematical modeling includes the fixed point, the stability around the fixed point, and computer simulations. System of equations in this research using system differential equations non-linear of the first order and it is using four variables. They are immune cells I(t), tumor cells T(t), normal cells N(t), and drug therapy u(t). This system of equations obtained two fixed points is a fixed point of disease-free tumor and influence tumor. Stability around the fixed point will be stable when the fixed points of tumor cells T(t) = 0 and T(t) not equal to 0, with the fixed point tumor cells T(t) = 0,6900203854 cells/㎣, immune cells I(t) = 0,3671110057 cells/㎣, normal cells N(t) = 0,1835555029 cells/㎣, and drug therapy u(t) = 1 pg/ml. From the numerical simulation results can be the comparison between the graph model populations of tumor cells before and after administration drug therapy. Before the population of tumor cell given drug therapy will be increased and decline after being given drug therapy, whereas immune cells and a normal cell is increasing. This suggests drug therapy can impede the growth of tumor cells and increase the population of immune cells and normal cells.
Ryan Murphy
(ONCO)
Queensland University of Technology
"Mechanical cell competition in heterogeneous epithelial tissues"
Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimensional mechanical model of heterogeneous epithelial tissue dynamics that includes cell-length-dependent proliferation and death mechanisms. Proliferation and death are incorporated into the discrete model stochastically and arise as source/sink terms in the corresponding continuum model that we derive. Using the new discrete model and continuum description, we explore several applications including the evolution of homogeneous tissues experiencing proliferation and death, and competition in a heterogeneous setting with a cancerous tissue competing for space with an adjacent normal tissue. This framework allows us to postulate new mechanisms that explain the ability of cancer cells to outcompete healthy cells through mechanical differences rather than by having some intrinsic proliferative advantage. We advise when the continuum model is beneficial and demonstrate why naively adding source/sink terms to a continuum model without considering the underlying discrete model may lead to incorrect results.
Ryan Schenck
(ONCO)
Moffitt Cancer Center
"The Tick-Tock of the Molecular Clock: Random methylation state changes inform homeostasis in the intestinal crypt"
The small intestinal and colon crypts are hierarchical, dynamic systems. Small numbers of stem cells give rise to daughter cells which proliferate within the transient amplifying zone, giving rise to a differentiated cell population. Stem cell numbers are constant, but survival is stochastic because divisions may result in renewal, expansion, or extinction. This hierarchy is largely maintained even in the face of disease and early dysplasias, where the microenvironment strives to re-establish homeostasis. Surprisingly, little is known about the stem cell numbers within these crypts. We use a distribution of CpG sites taken from four individual crypts across 60 patients to integrate with a statistical fitting approach and an agent based mechanistic model of the homeostatic crypt. Using this integrative approach we are better able to understand the dynamics of the stem cell pool. Most notably, using this method we can determine the number of stem cells and estimation of the error rates associated with DNA methyltransferase during cell division. The model splits the crypt into two compartments, the base and body of the crypt, and incorporates base pair resolution genomes and CpG sites. We calibrate our exclamatory bowel model with normal human small intestinal and colon crypt data using Approximate Bayesian Computation. This approach provides numerous insights into the dynamics of aging and underlying diseases within human crypts. The model can also be used to investigate why small intestinal crypts rarely develop cancers while colon cancer is frequently seen.
Sara Sommariva
(ONCO)
University of Geneva
"Mathematical model of loss and gain of function mutations in a chemical reaction network for colorectal cancer cells."
All cellular functions are regulated by a complex network of chemical reactions that translates extracellular signals into cellular responses. Most cancer diseases are induced by alterations of this signalling network due to loss or gain of function mutations that respectively reduce or enhance the activity of specific proteins. Here we present a computational tool for simulating chemical reaction networks and their alteration due to loss and gain of function mutations. By applying mass action kinetics, we first describe the concentration dynamics of the species involved in the reaction network through a system of ordinary differential equations (ODEs), whose stationary stable state describes the species concentrations in the physiological cell. We then show that loss of function mutations can be implemented in the model via modification of the initial conditions of the system while gain of function mutations can be implemented by eliminating specific reactions. Eventually our model is extended to account for the concatenation of multiple mutations. As example we consider the chemical reaction network devised by Tortolina and colleagues for the G1-S transition point in colorectal cancer cells. We validate our approach by simulating the most frequent mutations in this type of cancer and comparing the results predicted by our model with those in the literature.
Shaon C Chakrabarti
(ONCO)
National Centre for Biological Sciences
"Why cousins are more similar than mother daughters: implications for cell cycle control"
The origin of lineage correlations among single cells and heterogeneity in their intermitotic and apoptosis times (IMT and AT) may reflect underlying principles of cell cycle control. We developed lineage-tracking experiments and computational algorithms to uncover correlations and heterogeneity in the IMT and AT of a colon cancer cell line before and during cisplatin treatment. These correlations could not be explained using simple protein production/degradation models. Sister cell fates were similar regardless of whether they divided before or after cisplatin administration and did not arise from proximity-related factors, suggesting fate determination early in a cell’s lifetime. Based on these findings, we developed a theoretical model explaining how the observed correlation structure can arise from oscillatory mechanisms underlying cell fate control. Our model recapitulated the data only with very specific oscillation periods that fit measured circadian rhythms, thereby suggesting an important role of the circadian clock in controlling cell cycle progression.
Simon Mitchell
(ONCO)
University of Sussex
"A Systems Biology Approach Predicts Distinct Roles for NFkB Subunits cRel and RelA in DLBCL"
Heterogeneity in therapeutic response presents a challenge to the successful treatment of Diffuse Large B-Cell Lymphoma (DLBCL). Despite the recognition that DLBCL cases have diverse genetic and transcriptional characteristics, standard first-line therapy has remained unchanged for more than a decade. Canonical Nuclear Factor KappaB (NFκB) is a dimeric transcription factor usually consisting of either cRel or RelA bound to p50. While aberrant NFκB activation is frequently observed in DLBCL, subunit composition in individual DLBCL cases is not routinely characterized but has the potential to improve stratification and identify novel molecular targets for treatment. Computational simulations of NFκB control over B-cell proliferation and apoptosis accurately predict experimental results with accuracy at both single-cell and cell-population scale. However, the key regulatory networks controlling B-cell differentiation were not factored into these predictive models. Simulations based on known regulatory interactions were insufficient to recapitulate healthy B-cell differentiation. Using a systems biology approach we found that although cRel drives B-cell proliferation, it also blocks terminal differentiation to antibody-secreting plasma cells; dynamic downregulation of cRel by Blimp1 was a pre-requisite for differentiation. Inclusion of this interaction into multiscale computational models enabled simulations to accurately predict B-cell population dynamics in wild-type (WT) and cRel knockout cells. Simulations of aberrantly increased NFκB activity, recapitulated the increased proliferation and cell survival seen in both ABC- and GC-DLBCL. In order to interrogate the subunit-specific roles of cRel and RelA in DLBCL we performed simulations in which each subunit was individually upregulated. Both of these models predicted hyperproliferation and apoptosis avoidance, but only upregulation of cRel resulted in an inability to exit the germinal centre as seen in GC-DLBCL. In contrast, RelA- specific upregulation resulted in population expansion without a block on differentiation, with cells predicted to take on a more differentiated state consistent with cell-of-origin classification of ABC- DLBCL. This subunit-specific control over DLBCL sub-type aligns with experimental observations of the less differentiated state of GC- compared to ABC-DLBCL. Other commonly occurring mutations in DLBCL affecting BCL2, IRF4, and MYC were simulated to recapitulate dysregulated apoptosis, differentiation and cell-cycle respectively, along with “double-hit” mutations. These mutation-specific simulations of DLBCL represent in silico laboratories where biomarkers can be identified to stratify and target lymphoma.
Simona Catozzi
(ONCO)
Systems Biology Ireland
"Predicted ‘wiring landscape’ of Ras network in 29 human tissues"
Ras is an important hub protein at the head of numerous signaling pathways and plays a starring role in various types of cancers, notably in pancreas, colon and lung adenomas. The usual suspects are three oncogenic isoforms - i.e. HRAS, KRAS and NRAS - that are highly mutated and drive tumorigenesis. Our study is based on the paradigm of network medicine that sees disease as a perturbation of a network of interconnected proteins finely orchestrating cell's physiology and phenotype through the onset of downstream signal transduction. As such, we built a mechanistic model of the interactions of the three Ras oncoproteins with their direct interactors (known as 'effectors'), with protein abundances and binding affinities being the system's parameters, in order to study elementary pathological and physiological conditions of Ras network. Using high-quality proteomic data from 29 (healthy) human tissues, we quantified the amount of individual Ras-effector complexes, and characterized the (stationary, reference) Ras “wiring landscape” specific to each tissue. We simulated mutant- and stimulus-induced network re-configurations, miming respectively cancerous and physiological state, and compared them to the reference network. Moreover, we investigated the contribution of the input parameters (binding affinities and effector concentrations) in determining the complex formations underlying the specific wiring landscape, by 3D data interpolation onto (tissue-specific) surfaces. This revealed that high affinity - more than high concentration, - is critical for complex formation. As a consequence, we analyzed local and global binding affinity fluctuations and assessed their impact on the system's robustness. Further research will aim at the calibration of the binding affinity parameters, based on the Ras-effector complexes and the activation of the associated downstream pathway.
Stefano Pasetto
(ONCO)
Moffitt Cancer Center
"Bayesian framework for tumor board decision making"
Traditionally, the specific treatment for a cancer patient is decided by a multidisciplinary tumor board, which integrates prior clinical experience, published data, and patient-specific factors to develop a consensus on an optimal therapeutic strategy. However, tumor boards often encounter patients who incompletely match extant data and for whom several treatment options must be evaluated based on imprecise criteria. We propose optimizing treatment outcomes will require a flexible but rigorous mathematical tool that can define the probability of success of given therapies. Here, we propose a Bayesian approach to tumor forecasting using a multi-model framework that can predict response to different targeted therapies within individual patients. By exploiting the integrative power of the Bayesian decision theory, we demonstrate multiple therapeutic options can be simultaneously examined so that the resulting clinical course can be forecasted. From this, we detail a general decisional methodology built upon a robust and well-established mathematical framework that can support the clinical decision process for individual patients within a clinical tumor board.
Subbalakshmi A R
(ONCO)
Indian Institute of Science
"NFATc acts as a non-canonical phenotypic stability factor for a hybrid epithelial/mesenchymal phenotype"
More than 90% of cancer-related deaths can be attributed to metastasis. Cells adapt to their changing environmental conditions and avoid therapy and immune response during metastasis by employing the phenotypic plasticity. Reversible transitions between epithelial and mesenchymal phenotypes - Epithelial-Mesenchymal Transition (EMT) and its reverse Mesenchymal-Epithelial Transition (MET) - form a key axis of phenotypic plasticity during metastasis and therapy resistance. Recent studies have shown that the cells undergoing EMT/MET can attain one or more hybrid epithelial/mesenchymal (E/M) phenotypes, the process of which is termed as partial EMT/MET. Cells in hybrid E/M phenotype(s) can be more aggressive than those in either epithelial or mesenchymal state. Thus, it is crucial to identify the factors and regulatory networks enabling such hybrid E/M phenotypes. Here, employing an integrated computational-experimental approach, we show that the transcription factor NFATc can inhibit the process of complete EMT, thus stabilizing the hybrid E/M phenotype. It increases the range of parameters enabling the existence of a hybrid E/M phenotype, thus behaving as a phenotypic stability factor (PSF). However, unlike previously identified PSFs, it does not increase the mean residence time of the cells in hybrid E/M phenotypes, as shown by stochastic simulations; rather it enables the co-existence of epithelial, mesenchymal and hybrid E/M phenotypes and transitions among them. Clinical data suggests the effect of NFATc on patient survival in a tissue-specific or context-dependent manner. Together, our results indicate that NFATc behaves as a non-canonical phenotypic stability factor for a hybrid E/M phenotype.
William D Martinson
(ONCO)
University of Oxford
"Comparative analysis of continuum angiogenesis models"
While discrete approaches are increasingly used to model biological phenomena, it remains unclear in such frameworks how complex population-level behaviours emerge from the rules used to describe interactions between individuals. Insight may be gained by deriving coarse-grained continuum models, which describe the mean-field dynamics of a discrete model. Differential equations derived from such discrete-to-continuum approaches, however, often contain nonlinearities that depend on microscopic rules in the discrete model, and there has been little work done to analytically compare these coarse-grained equations with those constructed from simpler phenomenological frameworks. We address this problem in the context of angiogenesis (the creation of new blood vessels from existing vasculature). We compare asymptotic solutions of a classical, phenomenological 'snail-trail' partial differential equation (PDE) model for angiogenesis with those of a more complicated, fully nonlinear PDE system derived via a systematic coarse-graining procedure. For distinguished parameter regimes corresponding to chemotaxis-dominated cell movement and low branching rates, both continuum models reduce at leading order to an identical system of PDEs. Numerical and analytical results confirm that solutions to the two continuum models are in good agreement if these conditions hold, which allows us to determine when we can use the simpler model to capture the results of a more complicated coarse-grained system that describes the same biological process.
Yafei Wang
(ONCO)
Indiana University Bloomington
"Multicellular simulation in cancer treatment with nanoparticles"
Cancer is a complex systems problem that involves tumor cells and their microenvironment. Recently, research shows that engineered nanomedicine is playing an important role in cancer treatment. The traditional experimental methods involve intensive cost and time investments, as well as many operational challenges. With the increasing power of high throughput computing, it has become feasible to explore a vast variety of therapeutic designs in multicellular systems with computational modelling. In this talk, we propose an agent-based model (with PhysiCell) to investigate the therapeutic designs of cancer treatment with nanoparticles (NPs), where NPs uptaken or internalization, drug release and drug effects on tumor cells are explored. Our simulation studies show that drug-loaded nanoparticles have some allow promising new options for cancer therapy, and the point to the power of using large-scale model exploration to tune and improve therapy. In particular, we introduce a novel tracking of nanoparticle populations in each individual cells, allowing better modeling of drug release by internalized nanoparticles and long-term therapeutic implications. In this talk, I will cover the following parts:(1) how cells uptake NPs; (2) how NPs release drug inside of cells; (3) how daughter cells inherit NPs and drug from their parents; (4) how released drug treats tumor cells.
Zviiteyi Chazuka
(ONCO)
University of South Africa
"A mathematical model for in host dynamics of an immune evading virus"
High risk human papillomaviruses HPV types 16,18,31,45 are one of the major causative agents of cervical cancer in women globally and it is estimated that about 80% of women are infected by HPV mainly due to sexual activities within their life time. Out of these infections and re-infections some develop into persistent infections that lead to cancer lesions while some can be cleared provided they are detected by the immune system. Immune response within the body plays a pivotal role in clearing most infections that constantly affect us. Interestingly viruses such as HPV are seemingly very 'clever' in concealing their presence within cells as they devise many ways of avoiding detection by the immune system and therefore manage to create an anti-inflammatory micro environment. This leads us to interesting mathematical modelling research of a little 'clever immune evading virus'. We create a mathematical model for the dynamics of HPV in the presence of immune response and rigorous mathematical calculations show that there exist three equilibrium points whose stability both local and global is shown. An investigation into the probable possibility of a bifurcation is done using the centre manifold theory. Results show that a forward bifurcation exists and hence the endemic equilibrium is locally asymptotically stable provided that the reproduction number (R0) is less than unity and unstable otherwise. Numerical simulations prove and support the theoretical work presented. We also establish that HPV can be eliminated from the body when R0<1 and persistence occurs either when there is immune response evasion R0>1, Rk<1 where (Rk) is the immune response reproduction number or when there is immune response R0 >1, Rk>1. It is envisaged that the results of the study will be used further on to analyse the epidemiological link within the complex dynamics of HIV/HPV in the presence of stochastic perturbations, which is the core of the PhD work.
Hosted by eSMB2020 Follow
Virtual conference of the Society for Mathematical Biology, 2020.
