Mathematical and Computational Neurosciences

The results of neuroscience research in the last decade have clearly shown that the knowledge of properties of molecules, genes, neurons and pathways is insufficient to adequately understand many neurological and psychiatric diseases (epilepsy, Parkinson's disease, sleep disorders, memory disorders, schizophrenia, etc.) as well as normal neural processes (motor control, cognitive integration etc.) (Llinas et al., Trends Neurosci, 2005; Schnitzler and Gross, Nature Rev Neurosci, 2005 Buzsaki and Draguhn, Science, 2004; Dostrovsky and Bergman, Brain, 2004). However, most modern methods in neuroscience research continue to focus on particular elements of neuronal, cellular, or molecular networks, lacking integration of these entities.

Information about the way in which these elements interact is essential to understanding brain physiology and, not insignificantly, in planning effective therapies when this physiology is disordered. To integrate the substantial amount of factual knowledge about the elements of the networks, mathematical and computational methods are indispensable. Even though the application of some mathematical methods to neuroscience is not new, for the most part they have been used as auxiliary tools for the description of relatively limited neuronal systems. The unifying role of mathematics in neuroscience has been only minimally explored so far and is the focus of the current proposal. The use of mathematical methods as the basis for the study of the dynamics of systems of neurons is a new and promising direction, which is the focus of our research collaboration.

The group's expertise in the mathematical methods of the analysis of dynamics of systems and in applications to neuroscience puts us in a very strong position to study several important issues in neuroscience. Faculty members in our group have experience, as documented by publications, in the following areas:

• Mathematical analysis of dynamics of generic networks Frankel, Kuznetsov, Rubchinsky)
• Mathematical analysis and simulation of dynamics of neurons in basal ganglia, part of the brain affected in Parkinson's disease
  Kuznetsov
• Mathematical analysis and simulations of neuronal networks affected in Parkinson's' disease (Rubchinsky) and epilepsy (Worth)
• Mathematical analysis of the clinical and experimental data obtained in patients with Parkinson's disease (Rubchinsky, Sen, Worth) and epilepsy (Sen, Worth) with implications for therapeutic brains stimulation.
• Mathematical analysis of signal transduction processes(Sen).

In addition, group members have

• Extensive clinical experience in the brain dynamics of patients with Parkinson's disease and epilepsy and with the therapeutic deep brain stimulation in these disorders and neuropsychiatric illness such as depression and obsessive-compulsive disorder (Friedman, Worth).
• As a Professor of Neurological Surgery at IUSOM, Dr. Worth has direct access to the collection of human brain electrical data including intraoperative microelectrode recordings in movement disorder patients and chronic depth electrode data in epilepsy patients. In fact, he and Dr. Rubchinsky already have an IRB-approved protocol for the recordings in movement disorder patients, needed to develop the adaptive brain stimulation.

Our expertise in these areas allows us to focus our collaborative research efforts on the interdisciplinary approach to the following problems:

• Dynamics of basal ganglia neurons and neuronal networks (basal ganglia is impacted in Parkinson's disease). This study may shed light on the pathophysiological origin of symptoms of this disease, which is still poorly understood, despite a larger number of studies that utilizing classical methods of neurobiology. This study also will have relevance to the basic mechanisms involved in reinforcement learning and other phenomena where basal ganglia play an important role.
• Dynamics of cortical and hippocampal networks during epilepsy. Two important issues, the network origin of seizures and the prediction of seizures, are full of controversies as different studies point to different possible answers. These controversies indicate that methods of simple data collection have been exhausted and we expect that mathematical analysis integrating different types of data may be very helpful in finding the solutions and directing future neurobiological experiments.
• Therapeutic brain stimulation. Although deep brain stimulation has become a standard surgical treatment in movement disorders and neurostimulation is in clinical trials for therapy of epilepsy, the stimulation parameters are empirically determined. This leads to energetically inefficient stimulation and an increased incidence of adverse effects. This is primarily because the neurophysiological dynamics in normal and pathological brain are not well understood. The mathematical analysis of the dynamics of neuronal networks has a high potential for providing such information, which will open the way for adaptive brain stimulation techniques.

Each of the mentioned directions of research has a clear potential for development of new treatment strategies and for building general mathematical approaches to the dynamics of biological networks. We believe this is the area where our collaborative studies can attract external research funding for both basic (NSF) and more clinically related studies (NIH). Also, smaller organizations, which fund research relevant to specific diseases, are interested in funding novice approaches.

We feel that our group is in a unique position because mathematicians have strong neurobiology backgrounds (during postdoctoral years Dr. Kuznetsov collaborated with neurobiologists and Dr. Rubchinsky did his postdoctoral studies at a neuroscience center) and neuroscientists have mathematical backgrounds (in particular, Dr. Worth is an adjunct faculty member at the Department of Mathematical Sciences) and thus can efficiently communicate with each other. The Mathematical Neuroscience seminar, which started as an informal activity between Dr. Frankel and Dr. Worth several years ago and is now a weekly meeting in the Department of Mathematical Sciences with frequent external speakers and a journal club. It provides a convenient way for cross-fertilization of ideas as well as visibility for the group within and outside IUPUI, and means to attract and educate students.

Performed in a setting optimized for the analysis of clinical samples, these comprehensive quantitative measurements enable clinical researchers to visualize global changes in protein expression, and when appropriate, to mine these protein expressions for relevant protein marker(s) while accounting for biological pathways that are derived from genomics analysis. However, most clinical researchers lack the computational infrastructure and expertise necessary for the successful integration of such proteomic technologies into clinical trials. On the other hand, proteomics experts require access to human tissue and focus on clinically relevant problems to maximize the value of the state of the art high throughput methods. Therefore for progress in this area it is absolutely necessary to engage an interdisciplinary team of clinicians, protein-chemists, biomedical informaticians, and mathematicians. The focus group is currently working within such a team that combines researchers from Riley Children's Cancer Center, Regenstrief Institute, and Department of Mathematical Sciences. Several projects have been launched in the pursuit to reduce the barriers for the application of proteomics technology to clinical research. Fundamental to understanding the biological pathways responsible for each biological process is an understanding of the mechanism of how each molecule interacts with other molecules in such a pathway. Elucidation of such mechanisms can be obtained by a combination of coarse-grained and detailed computational simulations of the biomolecules involved. As a result, much effort in this area is directed at first determining such structures either through ab initio or homology-based folding methods of proteins and nucleic acids or computationally-aided refinement of experimental data. Once structural models are determined, simulations are employed to understand molecular stability, dynamics and hence functions. Finally, coupling such simulations together into a multi-scale hierarchical modeling framework, the mechanisms of inter-molecular interaction and hence biological pathways are investigated.

Computational Proteomics

Protein analytical technologies have rapidly matured over the past few years to yield relative quantitative measurements of hundreds to thousands of proteins simultaneously. Performed in a setting optimized for the analysis of clinical samples, these comprehensive quantitative measurements enable clinical researchers to visualize global changes in protein expression, and when appropriate, to mine these protein expressions for relevant protein marker(s). However, most clinical researchers lack the computational infrastructure and expertise necessary for the successful integration of proteomic technologies into clinical trials. On the other hand, proteomics experts require access to human tissue and focus on clinically relevant problems to maximize the value of the state of the art high throughput methods. Therefore for progress in this area it is absolutely necessary to engage an interdisciplinary team of clinicians, protein-chemists, biomedical informaticians, and mathematicians in the pursuit to reduce the barriers for the meaningful application of proteomics technology for clinical research.

Despite major advances in high-throughput analytical technologies, the medical field has been slow to integrate these technologies into clinical research trials and to turn them into benefits for patient care. The major impediments include the low availability of high quality blood samples from healthy control subjects, the required expertise in mass spectroscopy, the lack of expertise at most clinical institutions in analyzing high dimensional proteomic data, the lack of available biostatistics support for designing the experiments, and most importantly the lack of medical informatics support providing workflows and computing capacity to deal with the timely analysis of these large and complex data sets.

Our research team addresses the barriers to proteomics for clinical research by creating an analysis workflow platform, which will be inspired and validated through analyzing the specimens in pursuit of biomarkers. We create high quality reproducible mass-spectrometric data sets, and analyze these data sets using state of the art methodology and tools. We develop the statistical framework necessary for validating the tools and analysis strategies. We develop methodology and tools to better exploit the results of current reliable proteomics technology. We also track much needed improvements in proteomics technology and utilize them as their reliability matures. All methodologies, tools, analysis workflows, and the proteomics data sets are made openly available to other researchers. This effort is performed by a multidisciplinary group of investigators with a track record of innovation and consciousness of practicability. Their experience spans all the essential competencies needed, including Clinical Care and Research, Molecular Biology, and Pathology (Ragg, Czader, Lee, and Davis), Proteomics (Wang, Higgs, Hale), Mathematics and Biostatistics (Podgorski, Fokin, Qun, Lang, Shen), and Biomedical Informatics (Schadow). The clinical team is led by Susanne Ragg, MD, Ph.D., who is an Assistant Professor of Pediatrics at Indiana University School of Medicine, a board-certified pediatric oncologist, a member of the Children's Oncology Group, the director of the Center for Computational Diagnostics and the director of the Osteosarcoma Clinical Care & Research Program at Indiana University. She also is a member of the IU Cancer Center and its breast cancer research group and the proteomics project officer on the NSABP B-40 protocol. She has completed fellowship training in Bioinformatics and Medical Informatics and is an affiliate member of the Regenstrief Institute, and has a Ph.D. in human genetics. Dr Ragg is one of the very few physicians in the United States who are uniquely qualified to integrate efforts from all the involved disciplines into clinical medicine. She is the Principal Investigator on NIH- and foundation-supported studies that involve protein profiling. Other Clinical research collaborators that are contributing their expertise are: N. Deannie Lee MD, Ph.D., Mary Davis, MD and Magdalena Czader, MD, from the IUSOM.

Dimension Reduction for High Dimensional Data

The term "high dimensional" become almost ubiquitous with the subject bioinformatics. Traditional statistical techniques have a long history of contributing in different dimension reduction methods such as Principal Component Analysis (PCA) and Independent Component Analysis (ICA), to name a few. However dimension reduction through non linear projection by some kernel function proves much more useful for "modern data." Hence Kernel PCA, support vector machine (SVM) and other reproducing kernel Hilbert space (RKHS) methodologies are receiving much more attention for their robustness as well as regularizing capabilities in handling high dimensional data. We are focusing on different RKHS based methodologies from both classical as well as Bayesian point of view for new model development targeted towards different domains of bioinformatics such as Metabonomics and Proteomic.

High Dimensional Clustering

Clustering is a general data analytic problem, with many possible application domains. For example, in a medical system often we get subjects with unknown disease status. A statistical system to quickly identify them properly is an unsupervised learning task. However in high dimensional data it is possible to discover clusters in lower dimension simply because of spurious correlation. We need to focus on two additional issues namely robustness and regularization. We have already developed a regularized clustering algorithm for high dimensional data having some of these characteristics. Some of the key future issues that remain open are,

• Domain specific "bias, " "variance" tradeoff and the choice of similarity measure;
• Clustering in any convex shape such as inside a helix structure; and
• Subspace clustering in high dimension.

Biomolecular Theory, Structure and Simulations

The scope is on the determination of biomolecular structure, stability, and dynamics, including protein and RNA folding and biomolecular multi-scale modeling. At a higher level, it involves the analytical and numerical study of biomolecular function, biomolecular interactions, and the networks of those interactions. Marcos Betancourt's research involves the theoretical and computational studies of the physical properties of bio-molecules. The general goal is to develop physical models and theoretical techniques for the simulation, statistical analysis, and design of the structure and dynamics of biological macromolecules and their complexes. The current effort is focused around proteins. A current project involves the development of more accurate and efficient coarse grain models of proteins. In order to carry out long time simulations of complex systems, the resolution of the protein models is simplified to capture the relevant features. This requires the re-derivation of effective potentials and the design of efficient simulation techniques. These models can then be used to study the physical properties of proteins, including the determination of their native structure. Another project involves the design of protein sequences to yield a desired 3-D structure ( de novo protein sequence design). The objective is to find a sequence of amino acids that self assemble into a target structure, with optimal stability, kinetic, and functional properties, under given solvent or physical conditions such as temperature. This problem has important applications in the development of novel nano-machines and drug design.

Andrew Rader's research involves the applications of graph theoretic methods to analyze network models of protein and nucleic acid structures and their complexes. The resulting computational analysis indicates potential dynamics of these biomolecular structures and hence insight into their biologically relevant, functional motions. Simulations of these motions further indicate potential mechanistic explanations for protein-protein interactions as well as protein-ligand interactions. Application of rigidity theory to such models readily identifies their structurally flexible and rigid regions which have been shown to have biological importance. Such techniques have allowed him to identify functionally and/or structurally relevant components in individual enzymes such as adenylate kinase, in families of related structures, in the G-protein coupled receptor, rhodopsin, in the ribosome and virus capsids.

A second area involves the study of the biological and mechanical aspects of bone using animal models and cell cultures, as well as the study of molecular and cellular mechanisms of mechanotransduction, and the mathematical modeling of the distribution of forces in bone and shear stress on bone cells and their relationship with bone formation and molecular response. Problems from these areas are notoriously difficult due to their inherent wide-range of scales of interaction. A combination of methods is required in studying such problems, making use of numerical simulation, visualization, and local asymptotic analysis. The existing group consists of three applied mathematicians and one MD/PhD biologist, with expertise in modeling of fluid and solid mechanics problems.

Microcirculation and Mechanotransductioni

Microcirculation is common to every organ and nurtures the various tissues by providing oxygen and nutrients, and by removing waste products. Hence, the physiology of the microcirculation has profound impact on the transport phenomena and nutrient exchange, and, consequently on human health and disease. From a biomedical viewpoint, microcirculation is an immensely complex problem of the intrinsic blood flow that carries oxygen and nutrients and its interaction with the containing vasculature. From a biomechanical viewpoint, this is a structure-fluid interaction problem in which the blood vessel undergoes large deformation and, in turn, gives rises to formation of recirculation regions in the flow that induces large variation in the flow shear stress. Shear stress changes induce changes in gene expression and function in endothelial cell linings the blood vessel. This may explain why certain areas of the vasculature are prone to develop atherosclerotic plaques while others are protected. Pathologists have known for decades that plaques are selective in their location as they tend to form in regions of backflow where the shear stress is reduced. The endothelial cells lining these regions will be greatly affected. In modeling this interesting and yet complex flow problem, it is necessary to include the interaction of a compliant vessel wall with the flowing blood as well as the transport and reaction of constituents in the blood.

In our Department, we have the necessary modeling and computational capability and expertise to tackle such a complex fluid- structure problem to include mass transport and chemical reaction. An effective method for simulating structure-fluid interaction with large deformation is the immersed-boundary method which Zhu has employed to study the interaction of elastic filaments with a two-dimensional viscous pulsatile flow. Chin, while at Lawrence Livermore National Laboratory, was engaged in developing effective numerical methods for chemically reacting flow problem with mass transport. We will be working collaboratively with Dr. Kassab, recently appointed Guidant Professor of Biomedical Engineering, to develop experimental techniques for validating the model and its computations. We will also work with Fang at Computer Science to develop an interrogative visualization method to not only display the results of the computation but to give an on-demand analysis of the local interactions that gives rise to the computed solution. It is important that a deeper understanding of the local physical interaction can lead to approximations that, in turn, can feedback into the solution method to gain accuracy and efficiency.

Sleep Apnea

Structure-fluid interaction with large deformation forms the basis of a genioglossal muscle contraction model that comes from the study of obstructive sleep apnea. Sleep apnea is a disorder characterized by repetitive collapse of the pharyngeal airway during sleep. The consequence of sleep apnea is sleep disruption, hypersomnolence, and decreased quality of life in addition to potential adverse cardiovascular outcome. Zhu and Chin have been working with Dr. B. Foresman, Director of IU Sleep Laboratory to formulate an upper airway collapse model that can predict the effects of the muscle contraction on upper airway collapsibility. This will involve a realistic model of the tongue muscle and its interaction with the air flow. To validate the modeling, a set of experiments will be designed to compare the shape of the tongue and uvula with measurements using image processing.

Drug-Drug Interaction Prediction

Pharmacokinetic (PK) interactions among multiple drugs have received a great deal of attention since it makes a significant contribution to detailing adverse drug reaction of new drugs. In drug-drug interaction (DDI) research, a central question is whether two individual drugs' PK model together with their in-vitro DDI parameters can predict their in-vivo interaction. Since all the prior PK models and their parameters are summarized from multiple data sources and formats, the synthesis of an effective parameter set from these sources is a challenging problem. A heirarchical Bayesian meta-analysis approach is developed by L. Li of the IUSOM to perform the parameter estimation problem necessary for the prediction of drug-drug interaction. Unfortunately, it is computationally extensive and requires many hours of high performance computation. A fast and accurate computational method is desired. Chin and a Ph.D. student are collaborating with Li to develop a fast and accurate method that requires rethinking of traditional numerical integration routines. Results of our collaboration were presented in a recent national meeting of the Society for Industrial and Applied Mathematics.

Structure of Bones

Dr. Jiliang Li studies the mechanisms by which exercise builds bone with the goal of identifying novel drug targets linked to increased bone strength. His research activities include the study of the biological and mechanical aspects of bone using animal models and cell cultures, as well as the study of molecular and cellular mechanisms of mechanotransduction, the process of conversion of mechanical signals into biological signals in bone cells. The mechanisms by which bone adaptation works are poorly understood. When loads are applied on bone, the tissue deforms causing local strains. It is hypothesized that osteocytes, which are embedded in bone tissue, might serve as sensors of the local bone strains. Osteocytes are stretched to the same amount as the bone tissue. In addition, the pressure gradients in bone tissue caused by bending forces create extracellular fluid flow across the osteocytes. The study of the mechanotransduction is performed using both animal and cell models. Analysis of the strain distribution in bones and its relationship with bone formation rate are studied. The strain and bone formation rate induced by loading in different genetic modified animals are also compared in order to find molecular pathways involved in mechanotransduciton in vivo. In addition, fluid shear stress is applied on bone cells in culture and the cell's response to the shear stress, at both cellular and molecular levels, are also studied. The development and the application of appropriate mathematical modeling is critical to the understanding of the distribution of forces in bone and shear stress on bone cells and their relationship with bone formation and molecular response. The research projects have direct medical relevance to a variety of diseases such as osteoporosis, bone fracture, paraplegia and bone loss in space flight due to weightlessness.

Between the two groups there is a wide spectrum of applied and methodological research areas covered, including, survival analysis, longitudinal data analysis, categorical data analysis, and the like. Their collaborative work in research and training of graduate students will create a synergy that will not only benefit the two groups themselves, but also provide all researchers in Biosciences, both within IUPUI and among the Indiana BioCrossroads partnership, direct access to the statistical talent pool at the Center.

IUPUI has a number of research groups working in statistics and biostatistics. Notable among them are the Department of Mathematical Sciences, the Division of Biostatistics, the Regenstrief Institute, the School of Nursing, the Department of Medical and Molecular Genetics, and the INGEN funded facilities for bioinformatics, genomics and proteomics. The Department, which has five statisticians (Boukai, Ghosh, F. Li, Podgorski and Sarkar), offers a highly successful and visible Master's degree in Applied Statistics with a strong affinity to biostatistics. During the last 15 years since its inception, this program has trained over 100 applied statisticians, many of whom are employed as Master's-level biostatisticians in various life sciences organizations in Indiana.

Many of the past graduates are interested in a Ph.D. degree in statistics/biostatistics, especially in the wake of the Indiana BioCrossroads partnership, which created a need for training and retaining a highly skilled workforce that would help bring national and international recognition to the Indiana's health and life sciences. Realizing the pressing needs for highly trained professionals in biostatistics, the Division of Biostatistics of the IU School of Medicine and of the Department of Mathematical Sciences have jointly prepared a proposal for the creation of a Ph.D. program in Biostatistics at IUPUI. This program would utilize existing campus resources in statistical and biostatistical sciences, both in the Department and the Division, and would maximize the potential benefits to the profession and directly impact the health and medical sciences research on our campus. Among the expertise of these two groups of biostatisticians and statisticians are the following areas: Linear and Non-linear Regression, Statistical Methods, Design of Experiments, Design and Analysis of Clinical Trials, Probability, Mathematical Statistics, Statistical Inference, Longitudinal Data Analysis, Statistical Computing, Analysis of Failure-Time Data, Survival Analysis, Statistical Quality Control, Time Series Analysis, Sampling and Survey Techniques, Categorical Data Analysis, Multivariate Analysis, Bayesian Statistics and Decision Theory, Nonparametric Statistics, Stochastic Processes, Modeling in Biomedical and Health Sciences-all of which serve as fruitful grounds for research collaborations and for advanced training of graduate students.

As, such, the proposed Doctorate degree program in Biostatistics is designed for individuals with strong quantitative and analytical skills and strong interests in biological, medical and/or health sciences. It provides rigorous training in statistical theory and methodologies that are suitable for applications in research, collaboration and consulting on a broad spectrum of health-related problems. The program stresses the theory and concepts underlying statistical methods, the interpretation of results from experimental as well as observational studies, and the practical realities of health-related studies and their analysis. The primary goal is to prepare the students for independent careers as biostatisticians in any professional health-related or biomedical environment, such as in medical research institutes, universities, government agencies and private health-industries or organizations. Along with the planned implementation of the proposed Ph.D. program in Biostatistics, the proposed Center for Mathematical Biosciences at IUPUI, will be synergistic in fostering further research and programmatic collaborations amongst all the biostatistics constituencies at IUPUI. Furthermore, through the proposed CMB, any Indiana BioCrossroads partners will have a ready access to a highly visible entity to respond to their emerging needs collaborative projects in this area.