Grzegorz Rempala - US grants

[unreadable] DESCRIPTION (provided by applicant): In studying trend data such as cancer mortality and incidence data one is frequently concerned with detecting a change in recent trend. The ability to identify such changes in a cohort is an important problem for both retrospective and prospective cohort studies when looking for disease patterns. The proposed research seeks to develop a method to broaden the applicability of the join point regression model in detecting changes in disease trends. Specifically, we shall consider the extension of the simple Gaussian joinpoint regression model to logistic regression with K responses and possibly non-homogenous dispersion parameters. We shall derive and implement with the software the method for estimation and testing of the model parameters on the basis of the conditional maximum likelihood. Since the location of the joinpoints (change points) in the model is unknown the method would employ the iterative conditional maximization algorithm in seeking the solutions of the likelihood equations. In order to test the validity of the final model as well as to assess the significance of the final set of detected change points we shall sequentially apply the parametric bootstrap method. The conditions for consistency and general appropriateness of all the resulting estimation and testing procedures in our setting shall be also derived. Additionally, we shall compare via simulation studies the performance of the joinpoint logistic regression model versus that of penalized splines (P-splines) and multivariate adaptive regression splines (MARS) models. Finally we shall also apply the developed model to the longitudinal dataset on cancer mortality among the members of the Louisville VC cohort of now retired chemical workers up until 1996. The dataset is available via the University of Louisville Health Surveillance Program. Using the joinpoint logistic regression model we shall determine the pattern of longitudinal changes (time change-points) in the cohort cancer occurrences as compared with the state reference population, adjusting for the temporal clustering of the disease in the different production areas. The use of the Louisville VC cohort data shall allow us to illustrate our approach in an innovative application to monitoring occupational diseases and to compare its effectiveness with that of the standard methodology in view of the multiplicity of different analysis of this dataset available in the literature. [unreadable] [unreadable]

With the completion of numerous genome projects for bacteria, yeast, and humans, there is an increasing interest in understanding how molecules encoded within the genomes interact to define various functional networks of the cell. Network of integrated molecular reactions tend to involve many different molecular species, thus posing complex analytical problems. For prediction and simulation purposes it is essential to reduce both the model and computational complexity of the problem, while still capturing all the essential characteristics and potential behavior of the network. This project will systematically develop stochastic models for chemical reaction networks, beginning with classical Markov chain models and developing new models that take into account the stepwise development of reactions involving RNA and DNA molecules. Specific issues to be addressed include scaling limits based on the wide range of time and other quantitative scales in the system, model reduction through scaling limit approximations and other approaches, the implications of the combinatorial restrictions the reaction structure places on the system, sensitivity analysis for the parameters of the stochastic models, and statistical methods for model validation based on data that is frequently obtained through indirect and/or aggregated measurements.

At the level of the cell, the chemical dynamics may well be dominated by the action of regulatory molecules that are present at levels of only a few copies per cell. Therefore, the molecular fluctuations of these components may determine the dynamics of the reaction network. These molecular fluctuations appear to have significant consequences; the observed large variation in rates of development, morphology and concentration of molecular species in a cell often lead to a randomization of phenotypic outcomes and non-genetic population heterogeneity. Since these fluctuations may have profound effects on the physiology of the cell, stochastic models for the intra-cellular reaction networks and careful statistical analysis appear to be essential if the system is to be well understood. The project will also provide a fertile training ground for graduate students and postdoctoral researchers. There is a high demand for well-trained mathematical scientists with the interest and expertise necessary to contribute to the solution of problems arising in cell and molecular biology.

Abstract. The long term goal of the proposed project is to define the development of signaling networks that induce differentiation of cells into mature salivary serous acinar cells to allow gene therapy approaches to regenerating or replacing salivary tissue in patients. Millions of patients suffer loss of salivary gland function due to Sjogren's syndrome or radiation therapy. Understanding the differentiation of salivary cells is a necessary step to enable the restoration of diseased or destroyed parotid salivary tissue. Previous work has described terminal differentiation of acinar cells histologically, and by characterizing the expression of markers of differentiation, but has not used genomics-level approaches, or mathematical models, to define regulatory pathways. The primary goal of the current application is to develop formal mathematical and statistical models that will identify networks which cause terminal differentiation of parotid acinar cells. The dynamical mathematical models will serve to generate hypotheses which will be tested, and the model will be repeatedly refined by the incorporation of new data. This proposal is responsive to the RFA A Systems Approach to Salivary Gland Biology. Our overall hypothesis for these studies is that a mathematical model can identify key regulatory pathways that control parotid acinar cell differentiation. Specific Aim #1 will use Laser Capture Microdissection (LCM) to obtain RNA from embryonic and newborn rat parotid acinar cells for microarray analysis of the patterns of gene expression across the period of differentiation. A coupled Ordinary Differential Equation (ODE) model will be created to describe the hypothetical interactions that direct the process of differentiation. The hypotheses will be tested, and the ODE model refined, by a combination of RT-PCR, IHC, and western blots. Since microRNAs are important regulators of development, Specific Aim #2 will define the expression of microRNAs in acinar cells, and the pattern of changes during differentiation. There are currently no publications describing microRNAs in the parotid. The results will be used to revise the mathematical model of differentiation. Specific Aim #3 will create a statistical algorithm to validate and revise the ODE model by defining the sources of bias and variation as well as by assessing the model's predictive power overall, and in its various sub-modules. This will allow confidence intervals to be associated with different pathways within the ODE model. Specific Aim #4 will use the ODE model to make hypotheses about specific pathways regulating gene expression in the parotid acinar cells. These hypotheses will be tested by transfection and transduction experiments, and the results shall be used to refine and validate the mathematical model. This systems biology approach should identify molecular pathways that drive cytodifferentiation of parotid acinar cells. Project Narrative. The overall goal of this research is to define the molecular mechanisms which control differentiation of cells into secretory salivary acinar cells. This addresses the needs of millions of Americans who suffer from salivary gland dysfunction due to Sj¿gren's Syndrome, radiation therapy, or xerostomia due to essential medications. This research is a necessary foundation for developing new technologies such as gene transfer therapy and biologics for treating or alleviating the oral symptoms of xerostomia.

The proposed research aims at developing new mathematical and statistical results needed to efficiently analyze biochemical network models based on data arriving from the new molecular technology of "deep" DNA sequencing. The project will focus on developing likelihood-based estimates of the biochemical network parameters and structure from the data consisting of longitudinal species counts. With respect to parameter estimation, we shall (i) derive conditions on the data process which guarantee identifiability and estimators consistency as well as (ii) consider ways of approximating the likelihood of a partially observed biochemical network with certain other likelihoods (e.g., Gaussian) for which inference problem is simplified. With respect to network structure discovery, we shall develop methods of analyzing algebraic varieties associated with the geometry of chemical reaction networks in order to find stoichometry structure most consistent with given data. The theoretical results obtained will be used to develop a flexible framework for statistical analysis of deep sequencing data. The resulting algorithms will be implemented with software and their performance tested in real DNA sequencing experiments.

The deep (or next-gen) sequencing technology is a revolutionary, up-and-coming tool of modern molecular biology, allowing for very precise high-throughput measuring of DNA and RNA molecular counts in cellular systems. The next-gen technology will make it possible for biologists to formulate and test very specific hypothesis about biochemical interactions of various molecular species, provided that the proper mathematical modeling and statistical analysis tools (and their software implementations) will be broadly available. Due to his scientific background and an interdisciplinary nature of his work, the proposer is in a unique position to develop and then test such tools on data of biological relevance, ensuring that the mathematical results of this research are broadly disseminated to the scientific community of experimental biologists. By transforming the methodology for data analysis in DNA-sequencing, the proposed mathematical research will have broad influence on experimental high-throughput methodology in many different areas of modern genetics, ecology, and population studies. The project will also result in further promotion, both statewide and nationally, of the fields of mathematics and statistics in the context of biological research and the interdisciplinary training of young researchers.

Modern biology is in the midst of profound change, owing in part to the convergence of ideas from the mathematical sciences with those in the biological and life sciences. It is a national goal to accelerate this convergence and it is the role of the Mathematical Biosciences Institute (MBI) to help with this acceleration. Common principles in mathematics, statistics, and computational science are helping scientific understanding in fields as diverse as neuroscience, epidemiology, ecology, genomics, physiology, and cancer, among many others. MBI supports these interactions through robust postdoctoral fellow and early career research and training programs and through a workshop program that brings together interdisciplinary researchers in the mathematical and life sciences.

MBI has four principal goals. (1) To foster innovation in the application of mathematical, statistical, and computational methods in the resolution of significant problems in the biosciences. (2) To foster the development of new areas in the mathematical sciences motivated by important questions in the biosciences. (3) To engage mathematical and biological scientists in these pursuits. (4) To expand the community of scholars in mathematical biosciences through education, training, and support of students, postdoctoral fellows, and researchers. MBI will achieve these goals through its extensive and distributed postdoctoral fellow program based on co-mentoring by researchers in both the mathematical and biological sciences; through its early career training program that enables tenure-track but untenured researchers to participate in MBI programming for an extended period; through its robust interdisciplinary workshop programs; and through its long-term visitor program.

As the world faces a large outbreak of Ebola epidemic, several vaccines are currently in clinical trials with a reasonable chance of being available in the field in early 2015. Since the initial amount of vaccine will be limited, the understanding of Ebola epidemic dynamics is essential for maximizing the effectiveness of public health intervention through a combination of targeted vaccination, monitoring and quarantine.

This project is concerned with developing a realistic but at the same time mathematically tractable and statistically predictive dynamic model of the current world-wide Ebola epidemics. The modeling approach that divides the population into three groups (susceptibles, infected, and removed--the so-called SIR model) and its various generalizations has been used historically as an important tool in deciding whether epidemics grow or dissipate. The investigators expand the traditional model of an SIR stochastic epidemic on a graph with a given degree distribution, in order to account for the Ebola-specific features. These include, among others, incorporating a class of individuals at high risk of infection (e.g., health workers), and incorporating a dynamic network structure that reflects how contacts with different segments of the population change over the course of infection within host.

The new mathematical model describing the way in which Ebola spreads through a network of human contacts, both in rural and urban areas as well as across countries and continents, will be informed by the actual field data from various parts of the world including Africa and the United States. It is expected that the model will allow public health and government officials to quickly analyze a host of different intervention scenarios in order to speed up the current epidemic's dissipation and to select the most effective way of preventing, or at least minimizing, the future outbreaks.

The goal of this project is to establish a multi-institution research experience for undergraduate students (REU) in the mathematical biosciences, facilitated by the Mathematical Biosciences Institute (MBI) at The Ohio State University. The objectives of the program are: (1) to introduce undergraduate students at all levels to the field of mathematical biology; (2) to encourage students to pursue graduate study in the mathematical biosciences; and (3) to increase the number of students who enter the workforce with training in this field. Students will work on applying mathematics and statistics to research in areas such as molecular evolution, neuronal patterns, cancer modeling, epidemic models and vaccination strategies, and models of sensory systems, such as vision and smell. The infrastructure provided by the MBI gives the necessary resources to accomplish these goals by providing both an authentic research experience as well as exposure to the field of mathematical biology broadly.

The program consists of three components. The first is a week-long Overview of Mathematical Biosciences, which consists of lectures by experts in the field, laboratory tours and field trips, and computer exercises using the Matlab software. This is held at the MBI in Columbus, OH annually in the second week of June. Following completion of the one-week overview session, the students will travel to one of MBI's Institute Partners to participate in an 8-week mentored research experience at the host institution. Finally, the participants will join other students doing research in the mathematical biosciences and present their results at a Capstone Conference hosted by the MBI. Throughout the program, a cohort will be maintained by weekly virtual seminars and discussions among participating institutions. They will work in pairs under the guidance of one or more mentors to make genuine research contributions in these areas, often leading to publications in peer-reviewed journals and presentations at conferences. The student participants will develop skills needed to continue work in these areas and to pursue graduate study. Their involvement in this research will expand the group of students trained to work in the field of mathematical biology.

The outbreak of COVID-19 has created a tremendous need for predicting both the dynamics and the size of regional COVID-19 outbreaks. Equally important is the need to determine the potential effects of early interventions such as school closures and mandatory or self-imposed quarantines. To answer these questions, this project will develop a general mathematical framework for analyzing the ongoing outbreak trends using data solely from partially observed new daily infection counts (also known as the epidemic curve). The PI?s new framework will not assume any specific infectious or recovery periods (which are often unknown) or observable prevalence of the disease. The tools developed as part of this project will both help predict the rate of growth of new infections and estimate the effect of social distancing and other preventative measures on flattening the epidemic curve. The PI will use a new dynamical survival analysis approach to predict the trajectory of the COVID-19 epidemic for a mid-western region of the United States. Data from elsewhere in the world, like the city of Wuhan in China, will be used to calibrate the predictions. The project will also provide a practical interdisciplinary training for a PhD student and a post-doctoral fellow.

The modeling and predictive framework to be developed is fundamentally different from the traditional approach based on the incidence or prevalence counts in a compartmental SIR model. Specifically, the PI will apply the dynamical survival analysis (DSA) approach that considers aggregated mean field equations for the underlying large stochastic network and regards them as the approximate survival law of the infection times. The PI will use these DSA-based equations to model both the epidemic and recovery curves and compare them with the ones observed during the COVID-19 outbreak. The statistical analysis of epidemic data performed with the help of the new framework will allow the quick elucidation of the dynamics of an epidemic (for example, the basic reproduction number, R0) and the potential impact of interventions (such as quarantine or social distancing). The new framework will help provide a better understanding of how preventive behaviors affect COVID-19 dynamics via changes in the network structure and changes in disease transmission across edges in the network. This project will develop a user-friendly software package for computer simulations under different parameter and intervention scenarios (for example, vaccination schemes) that will lead to a better understanding of how to control COVID-19 transmission.

This grant is being awarded using funds made available by the Coronavirus Aid, Relief, and Economic Security (CARES) Act supplemental funds allocated to MPS.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.