Functional Data Analysis of Copy Number Alterations in Bladder Cancer Tumors
David Burton* – East Tennessee State University, Sarah Robinson* – University of Georgia, Miranda L. Lynch, Ph.D. – Uconn Health, Center for Quantitative Medicine
Genomic structural changes known as copy number alterations (CNAs) have a role in tumor progression. CNAs are changes in the chromosome where regions are either amplified or deleted. They can range in length from 100 kb to the entire chromosome. We’re interested in the effects of CN in bladder cancer, because 75,000 new diagnoses of bladder cancer are expected this year in the US alone. CNAs are known to affect gene function in bladder cancer. Array comparative genomic hybridization (aCGH) is a DNA hybridization based technology for measuring CNAs using a mixture of tumor DNA and reference sample DNA, returning a log2-ratio of tumor CN count to healthy CN count. Our data consist of CN measurements from bladder cancer tumor tissue from 93 patients whose profiles are in muscle invasive and non-muscle invasive subgroups. It is thought that bladder cancer subgroups have varying CN profiles that are similar within groups but differ across groups. We are treating these CN profiles as functions across the entire chromosome, and using functional data analysis tools for inference. Using wavelet methods, we fit both aCGH CN profiles as well as simulated aCGH profiles created using our own method where the underlying functions are known. We then use functional response regression to characterize the CN profiles of muscle invasive and non-muscle invasive patients. Preliminary work indicates functional data regression methods may provide a useful inferential framework to delineate CN profile differences between muscle invasive and non-muscle invasive bladder cancer.
Reverse Engineering Functional Brain Networks from fMRI Data Using Probabilistic Boolean Networks
Erin Boggess* – Simpson College, Tiffany Jann* – University of California, Berkeley, Michael Stevens – Olin Neuropsychiatry Research Center, Institute of Living, Reinhard Laubenbacher – Uconn Health, Center for Quantitative Medicine, Paola Vera-Licona – UConn Health, Center for Quantitative Medicine
Background: The brain functions by communicating information across multiple regions, and neurological diseases can alter the way these brain regions communicate. To characterize brain disorders and eventually propose systematic approaches to diagnosis, we should study the brain as a whole and consider both its structure and dynamics. Method: The objective of this project is to develop and validate a pipeline to infer the static and dynamic mathematical models of the brain from fMRI data. Using probabilistic Boolean networks (PBNs) as our mathematical framework, the pipeline we propose consists of iteratively applying the following steps: (1) Inference of static functional brain network from fMRI data, (2) Binary discretization of fMRI data and, (3) Inference of deterministic Boolean network using as input the outcome of steps (1) and (2). To infer a PBN, we segment both our original and discretized time series into overlapping windows and generate a Boolean network from each window. We then combine these networks to generate a PBN.
Results: We studied the different steps of our proposed pipeline using in silico networks to generate in silico fMRI data. Each step had non-trivial aspects to resolve and we successfully validated steps (1) and (2) of the pipeline. For step (1), the inference of static networks, we used 44 different reverse engineering methods and identified the top-performing methods for which we proposed a way to combine them such that the result, a consensus network, outperformed any method individually. In step (2) we used 11 different discretization methods and proposed a novel method to benchmark and rank them. Finally, we were able to do some preliminary studies to construct deterministic Boolean network and PBNs.
Conclusions: We found that creating consensus networks from combining the top performing network inference methods proved effective. Our proposed benchmarking discretization metric was helpful in identifying appropriate discretization methods for our fMRI data. The fMRI data discretized using our identified top performing discretization method, BiK-means, yielded the most promising results when inferring the dynamic deterministic and probabilistic Boolean models.
For the last step of our pipeline, the inference of the dynamic models, we only had the opportunity for preliminary studies and future work should be focused on the validation of inferred dynamic models.
A Mathematical Model for Copper Homeostasis in Pseudomonas aeruginosa
Brianna Kozemzak* – Saint Mary’s College, Joseph Roth* – University of Dallas, Jigneshkumar Parmar – UConn Health, Center for Quantitative Medicine, Pedro Mendes – UConn Health, Center for Quantitative Medicine
Copper is an ideal biological redox cofactor because it accepts and donates electrons with relative ease. However, free copper can interfere with other important cellular redox reactions. Therefore, bacteria maintain tight control of cellular copper levels. In collaboration with the Argüello group at Worcester Polytechnic Institute, we obtained data measuring copper levels across the periplasmic and cytoplasmic compartments of P. aeruginosa. Using this data, we modeled copper homeostasis in P. aeruginosa as a system of chemical reactions transferring copper between protein pools according to mass action kinetics. Mathematically, this is a series of ordinary differential equations describing the fluxes between different copper pools. We used the biochemical modeling software COPASI to simulate and estimate parameters for the model. During the modeling process we determined that knowledge of the protein levels is required to accurately estimate the model parameters. Additionally, it seems necessary to invoke regulation of periplasmic cuproproteins to fit a model to the data. These results will help our collaborators design experiments that produce the most crucial information for developing a more detailed model of the copper homeostasis system in P. aeruginosa.
Minimal Models of Actin-based Cell Motility
Jamie Brandon* – Adrian College, Aaron Rumack* – Cornell University, Boris M. Slepchenko – UConn Health, Richard D. Berlin Center for Cell Analysis and Modeling, Masoud Nickaeen – UConn Health, Richard D. Berlin Center for Cell Analysis and Modeling
Motile cells can be in a stationary or moving state. In a stationary mode, forces acting on the cell are symmetric. In order to achieve movement, a cell must break its symmetry. When symmetry is broken, the forces exerted on the cell cause it to move. We aim to model how symmetry is broken in motile cells. Our minimal mathematical model, based on ideas first proposed by A. Mogilner, considers three factors that influence cell movement: actin flow, contractile forces due to myosin bound to actin, and cell protrusion due to actin polymerization. We make use of two versions of the model differing by the role of cell adhesion to a substrate. The "Zero-Velocity" model assumes very strong adhesion at the cell periphery, while the "Zero-Stress" model assumes cell adhesion is finite and uniform throughout. We show that the mechanisms modeled are sufficient to break symmetry in the cell and initiate movement. By simulating cells with various parameters, we discover which characteristics must change to break symmetry. Higher levels of myosin, faster polymerization of actin, and weaker actin viscosity lead to symmetry breaking and movement. Among moving cells, higher myosin concentrations and slower actin polymerization rates stabilize unidirectional linear motion as opposed to rotation. Regulation of levels of myosin, as well as membrane protrusion and factors affecting actin viscosity, are sufficient to prevent, initiate, or change the type of cell movements
Comparative Analysis of Linear and Nonlinear Dimension Techniques on Mass Cytometry Data
Emily Vidal* – Angelo State University, Nathan Jekel* – Penn State Harrisburg, Anna Konstorum – UConn Health, Center for Quantitative Medicine, Reinhard Laubenbacher – UConn Health, Center for Quantitative Medicine.
Mass cytometry is a newly developed technology for quantification and classification of immune cells that can analyze up to 100 markers per cell. High dimensional data resulting from these experiments require innovative methods for analysis and visualization. We conducted a comparative analysis of four mathematical dimension reduction techniques – principal component analysis (PCA), isometric feature mapping (Isomap), t-distributed stochastic neighbor embedding (t-SNE), and diffusion maps – implementing them on a mass cytometry data set with manually gated cell populations. We compare the results of these reductions using three metrics: computation time, residual variance, and neighborhood proportion error (NPE). In addition to quantitative metrics, we compare qualitatively based upon two and three-dimensional visualizations. We find that t-SNE and diffusion maps are the two most effective methods for preserving local distance relationships among cells and providing informative visualizations. In low dimensional embeddings, t-SNE exhibits well-defined phenotypic clustering. Additionally, diffusion maps appears to represent cell differentiation pathways with long projections along each diffusion component. We use diffusion maps to dimension reduce a novel dataset from mouse-derived T cells representing acute inflammation and observe that a rare population of T cells, TCRγδ, maps to the extreme range of a top diffusion component. This indicates that the phenotype of these cells is distinct from the assayed cell population with respect to the majority of markers.