Poster session and reception
Wednesday, May 30, 2018 - 4:30pm - 6:00pm
- Modeling acute myeloid leukemia from RNA sequencing data in a continuum of differentiation states
Heyrim Cho (University of Maryland)
We present a mathematical model of movement in a reduced dimensional space representing states of cellular differentiation. We motivate this work with recent examples that demonstrate a continuum of cellular differentiation using single-cell RNA sequencing (scRNA-Seq) data to characterize cellular states in a high-dimensional space, which is then mapped into lower dimensions with dimension reduction techniques. We represent trajectories in the differentiation space as a graph, and model directed and random movement on the graph with PDEs. We present a PDE model of hematopoiesis parameterized with publicly available scRNA-Seq data and use it to simulate the pathogenesis of acute myeloid leukemia (AML). The model predicts the emergence of cells in novel intermediate states of differentiation consistent with immunophenotypic characterizations of a mouse model of AML.
- Eco-evolutionary Dynamics of Cooperation
Rebecca Terry (The University of Utah)
An organism’s phenotype is defined as the expression of its genetic material. This expression may change under different environmental conditions. The ability to alter one’s phenotype by turning on or off specific genes in response to changes in one’s environment is known as phenotypic plasticity. Cooperation in certain microbial species is an example of phenotypic plasticity whereby some individuals express particular genetic machinery to produce a population while others fail to express that same machinery but benefit from consumption of the resource without the cost of its production. Depending on the availability of the resource in the environment, an organism may switch from an expressing to a non-expressing state or vice versa. We seek to develop mechanistic models to explore the dynamics of cooperation and phenotypic plasticity in social microbes under varying environmental conditions. Using an adaptive dynamics approach, we examine whether there exists an evolutionarily stable cooperating strategy.
- Patient-Specific Glioblastoma Implicit Nutrient Model
Lauren Johnson (Arizona State University)
Glioblastoma multiforme (GBM) is a highly aggressive, highly malignant form of brain cancer with a survival rate of 14-15 months following diagnosis. Part of the dismal prognosis lies in GBMs being both markedly invasive and migratory. Many mathematical GBM models focus on these aspects through migration and net growth terms. By disaggregating growth as an explicit birth and death, we seek to capture the necrotic component, a hallmark characteristic of GBM. In doing so, we endeavor to establish a relationship between growth and MRI appearance and thus propose an implicit nutrient model with necrotic cells behaving as a quasi-predator to the live tumor cells.
- A kinetic model for two monomer copolymerization with conversion
Anna Nelson (The University of Utah)
During the blood clotting process, fibrinogen is cleaved by thrombin to produce fibrin monomers, which polymerize into a fibrin gel that stabilizes the clot. Although fibrinogen cannot react with itself, fibrinogen can interact with fibrin and affect clot structure. Motivated by these fibrin-fibrinogen interactions, we introduce a kinetic gelation model of polymer growth with two types of monomers that have differing functionalities (reaction sites). The heterotypic aggregation of two monomer types is modeled using a Ziff-Stell approach by tracking the temporal evolution of the concentrations of both types of free reaction sites on oligomers. We also allow conversion of one monomer type to another. We propose three different models of polymerization with two distinct monomers and conversion to investigate conditions for which finite time blow-up occurs.
- A fluid-phase model of alternative pathway initiation of the complement system
Kathryn Link (The University of Utah)
The complement system is an important component of innate immunity made up of over 50 constituents such as pattern recognition molecules (PRM), protein fragments, proteases/convertases, regulators, and cell surface receptors whose interactions are responsible for cell lysis and phagocytosis in the blood. Initiation of the alternative pathway (AP), also known as tick-over, is an essential component of the complement system. It is one of three activation pathways that converges to a lytic pathway, which results in the formation of a transmembrane pore. In this modeling effort, we examine the dynamics of AP C3-convertase formation, the production of C3 and C5 fragments, and the regulation of these processes. As an initial step, we created a well-mixed ordinary differential equation (ODE) model that captures elements of the AP that take place in the fluid. The model was partially validated/calibrated using a weighted least-squares minimization procedure with a typical set of available experimental data resulting in estimated parameter values. Our model exhibits a basal level of activation without amplification when stimulated. We intend to extend the model to include membrane-associated interactions and eventually flow-mediated transport of proteins and inhibitors. Such a model will contribute to the identification and investigation of fluid and membrane conditions that support amplification.
- Parameter Estimation for Tear Film Dynamics
Rayanne Luke (University of Delaware)
The tear film forms after a blink and serves to protect the ocular surface as well as promote clear vision. Tear film breakup (TBU) occurs when a dry spot appears on the eye, and is often evaporation-driven. Many parameters effect the film height and fluorescein intensity distributions over time; exact values or ranges for some are not well known. Our dry lab simulation lays the groundwork for deducing certain parameters from wet lab data through optimization.
- In Good Company: Plant Neighbor Effects On Foragers
Samantha Hill (The University of Utah)
Plants survive by, among other things, not being eaten. Plant neighborhoods with high chemical or phylogenetic diversity have been shown to suffer less damage from herbivores, a trait known as associational resistance. To begin studying this phenomenon, we derive two models for optimal insect behavior in a patchy environment that we can extend to support more dimensions of diversity in the future. In the first model we show that in a fixed-density case with one plant type, plants suffer less damage in environments with higher neighbor frequencies, despite a lack of diversity. In the second model, we show that when patches are allowed to be empty, the forager's optimal giving-up time to leave a patch increases with distance between patches and the probability that the patch is non-empty, but is independent of its average time spent eating each plant.
- Tumour-immune dynamics with an immune checkpoint inhibitor
Elpiniki Nikolopoulou (Arizona State University)
The use of immune checkpoint inhibitors is becoming more commonplace in clinical trials across the nation. Two important factors in the tumour-immune response are the checkpoint protein programmed death-1 (PD-1) and its ligand PD-L1. We propose a mathematical tumour-immune model using a system of ordinary differential equations to study dynamics with and without the use of anti-PD-1. A sensitivity analysis is conducted, and series of simulations are performed to investigate the effects of intermittent and continuous treatments on the tumour-immune dynamics. We consider the system without the anti-PD-1 drug to conduct a mathematical analysis to determine the stability of the tumourfree and tumorous equilibria. Through simulations, we found that a normally functioning immune system may control tumour. We observe treatment with anti-PD-1 alone may not be sufficient to eradicate tumour cells. Therefore, it may be beneficial to combine single agent treatments with additional therapies to obtain a better antitumour response.
- Control Strategies for measles in countries with seasonal birth rates using supplementary immunization activities
Dominika Dec (University of Montana)
Infectious diseases such as polio, diptheria, and measles have not disappeared completely with the advent of vaccination strategies directed at eradication. Countries that do not have scheduled vaccination methods, do not have easy access to medical facilities, or face political turmoil experience the resurgence of these highly infectious diseases. The measles vaccine has been present for over 50 years but the difference in administration of the vaccine between nations leads to the need for developing control strategies to diminish and control measles related infections through supplemental immunization activities. This research concentrates on several Sub-Saharan countries with seasonal birth rates. Using an SIR model parameterized with a seasonal birth rate and measles data, we are able to find the ideal timing and proportion of vaccinated individuals that would effectively eradicate or at least minimize the infected ratio.
- Optimal control in HIV chemotherapy with termination viral load and latent reservoir
Damilola Olabode (Washington State University)
Although a number of cost-effective strategies have been proposed for the chemotherapy of HIV infection, the termination level of viral load and latent reservoir is barely considered. However, the viral load at the termination time is an important biomarker because suppressing viral load to below the detection limit is a major objective of current antiretroviral therapy. The pool size of latently infected cells at the termination time may also play a critical role in predicting a rapid viral rebound to the pre-treatment level or post-treatment control. In this work, we formulate an optimal control problem by incorporating the termination level in terms of viral load, latently and productively infected T cells into an existing HIV model. The necessary condition for this optimal system is derived using the Pontryagin's maximum principle. Numerical analysis is carried out using Runge-Kutta 4 method for the forward-backward sweep. Our results suggest that introducing the termination viral load into the control provides a better strategy in HIV chemotherapy.
- Biomathematical model of proneural tumors suggests PDGF-inhibitors should be given earlier in disease course
Susan Massey (Mayo Clinic)
Platelet Derived Growth Factor (PDGF) is often over-expressed in gliomas, where it can drive tumor growth via autocrine stimulation of PDGF receptor (PDGFR) expressing glioma cells and via paracrine stimulation of non-neoplastic oligodendrocyte progenitor cells (OPCs), which also express PDGFRa. To date, the use of PDGF inhibitors has remained largely unsuccessful at improving patient outcomes in glioblastoma; however, this may be due to inadequate targeting of these agents to the best candidates. In particular, these therapies have been given in the recurrent setting, when tumors that had been predominantly comprised by OPCs and OPC-like glioma cells (e.g., proneural subtype) have transformed to a mesenchymal phenotype with fewer OPC-like cells, thereby precluding the opportunity to target OPC-like cells with these agents. Using a mathematical model of PDGF-driven glioma, we explore which patients might receive the greatest benefit from PDGF-targeted therapies. The results of our mathematical model show that tumors with higher levels of PDGF signaling recruit more OPCs and grow faster, resulting in larger, but less infiltrating tumors. By incorporating different treatment simulations in our model, we show that PDGF inhibition results in decreased OPC recruitment, which leads to slower growing, but more diffusely infiltrating tumors. This suggests that PDGF inhibitors may be most effective at treating patients with more rapidly proliferating, less infiltrative tumors which show a predominance of OPCs on immunohistochemistry. Further, the model suggests that they should be given earlier in the disease course, i.e., prior to recurrence, but following resection.
- The combinatorics of shape and motion
Brigitte Servatius (Worcester Polytechnic Institute)
Molecules are often modeled as bar-and-joint frameworks in 3-space. While bar-and-joint frameworks are well understood combinatorially as well as goemetrically in the plane, there are many open problems in 3-space. Some nice toy research problems accessible even to (high school) students are based on Dill's HP-model. Zeolites provide yet another interesting set of examples illustrating the gap between their combinatorial and geometric properties.
- A mathematical and computational model of the calcium dynamics in Caenorhabditis elegans ASH sensory neuron
Eleni Gourgou (University of Michigan)
We propose a mathematical and computational model that captures the stimulus-generated Ca2+ transients in a C. elegans key sensory neuron. We aim to develop a tool that will enable a cross-talk between modeling and experiments, using modeling results to guide targeted experimental efforts. C. elegans is a broadly used model organism in neuroscience, with fully mapped and excellently characterized nervous system. The proposed model is built based on biophysical events and molecular cascades known to unfold as part of ASH neurons' Ca2+ homeostasis mechanism, as well as on Ca2+ signaling events. The state of ion channels is described by their probability of being activated or inactivated, and the remaining molecular states are based on biochemically defined kinetic equations or known biochemical motifs. We estimate the parameters of the model using experimental data of hyperosmotic stimulus-evoked Ca2+ transients detected with a fluorescent Ca2+ sensor in young and aged worms, unstressed and exposed to oxidative stress. We use a hybrid optimization method composed of a multi-objective genetic algorithm and nonlinear least-squares to estimate the model parameters. We first obtain the model parameters for young unstressed worms. Next, we use these values of the parameters as a starting point to identify the model parameters for stressed and aged worms. We show that the model, in combination with experimental data, corroborates literature results, and can be used to predict ASH response to complex combinations of stimulation pulses. This mathematical and computational effort is the first to propose a dynamic model of the Ca2+ transients' mechanism in C. elegans neurons, based on biochemical pathways of the cell's Ca2+ homeostasis machinery. We believe that the proposed model can be used to further elucidate the Ca2+ dynamics of a key C. elegans neuron, to guide future experiments on C. elegans neurobiology, and to pave the way for the development of more mathematical models for neuronal Ca2+ dynamics.
- Spatial structure and occupancy dynamics in metapopulations
Zoi Rapti (University of Illinois at Urbana-Champaign)
We will present results on a stochastic and spatially explicit metapopulation model of zooplankton occupancy patterns in a small pond network. We assume that there are two main stochastic processes governing the dynamics, namely extinction and colonization and use a Markov model to capture main trends in the field data. We then investigate the role of spatial structure and initial conditions on the quasi-stationary distribution. Finally, we show results from a mean-field approximation and demonstrate that it accurately reproduces the stochastic simulations.
- Up-close and personal with drug delivery: from in silico organoids toward personalized chemotherapy
Katarzyna Rejniak (Moffitt Cancer Center)
Tumor heterogeneity—either genetic, phenotypic, metabolic or mechanical–is considered to constitute the barrier to effective chemotherapeutic treatments that allows for the development of drug resistance. However, typical pharmacological studies relay on compartmental well-mixed models and neglect temporal and spatial variability in properties of both the tumor and its microenvironment. We will present a collection of computational models developed in my group that were employed in testing drug delivery on a microscopic cell-to-tissue scale and in monitoring drug efficacy within the tissue on the level of individual cells. Our goal is to build a predictor of tumor chemoresistance based on clinical biopsies routinely collected for cancer diagnosis. The use of data from individual patients’ tumors will allow for designing of personalized treatments that hold promise to improve patient outcome.
- Modeling the Effects of the Macrophages on Bone Fracture Healing
Imelda Trejo-Lorenzo (The University of Texas at Arlington)
A new mathematical model is presented to study the effects of macrophages in the bone fracture healing process. The model consists of a system of nonlinear ordinary differential equations that represents the interactions among classical and alternative macrophages, mesenchymal stem cells, and osteoblasts. A qualitative analysis of the model is performed to determine the equilibria and their corresponding stability properties. A set of numerical simulations is presented to support the theoretical results. The model is also used to numerically monitor the evolution of a broken bone for different types of fractures and to explore possible treatments to accelerate bone healing by administrating anti-inflammatory drugs.l
- Glioblastoma Recurrence and the Role of MGMT Promoter Methylation
Katie Storey (University of Minnesota, Twin Cities)
Glioblastoma, also known as glioblastoma multiforme (GBM), is an extremely fast-growing and lethal form of brain cancer. Typically GBM is treated with temozolomide (TMZ), a cytotoxic drug that damages DNA and triggers cell death. Promoter methylation of the DNA repair gene MGMT has been associated with sensitivity to TMZ, while increased expression of MGMT has been associated with TMZ resistance. However, the evolutionary processes driving the emergence and outgrowth of TMZ-resistant tumor subpopulations are still poorly understood. We have developed a stochastic model, parameterized using clinical and experimental data, to investigate the role of MGMT methylation in TMZ resistance during the standard treatment regimen for GBM (surgery, chemotherapy and radiation). We utilize the model to study the impact of TMZ treatment on mechanisms of MGMT methylation and demethylation within GBM cells. In addition, we investigate the optimal number of doses administered during adjuvant chemotherapy and its connection to methylation status at diagnosis.