BioLogic: A mathematical modeling framework for immunologists.

The immune response to pathogens is a result of complex interactions among many cell types and a large number of molecular processes. As such it poses numerous challenges for modeling, simulation, and analysis. In this work we aim at addressing major issues regarding modeling of large biological systems with a special focus on the immune system. We address (1) the hierarchy in the system, from genes to organelles to cells to organs to organism, (2) the high variability due to experimentation, (3) the high variability among organisms, and (4) the need to bridge between immunologists/experimentalists and mathematicians/modelers. We provide an intuitive syntax to describe biological knowledge in terms of interactions (reactions) and objects (cells, organs, etc.) and illustrate how to use it in describing very complex systems. We describe the main elements of a simulation program that use that syntax to define models and to automatically simulate them. We restrict our discussion to modeling using logical network, although other modeling techniques, for example, differential equations and probabilistic/stochastic modeling, are also possible. Examples demonstrating the different features of the framework are given throughout the chapter.

Multiplex assessment of serum biomarker concentrations in well-appearing children with inflicted traumatic brain injury.

Proper diagnosis of mild inflicted traumatic brain injury (ITBI) is difficult; children often present without a history of trauma and with nonspecific symptoms, such as vomiting. Previous studies suggest that biomarkers may be able to screen for brain injury in this population, but these studies focused on only a few biomarkers. We hypothesized that using multiplex bead technology we would be able to identify multiple differences in the serum biomarker profile between in children with ITBI and those without brain injury. We compared the concentrations of 44 serum biomarkers in 16 infants with mild ITBI and 20 infants without brain injury. There were significant group differences in the concentrations of nine of the 44 markers. Vascular cellular adhesion molecule (VCAM) (p < 0.00) and IL-6 (IL-6) (p < 0.00) had the most significant group differences; IL-6 was higher after ITBI, whereas VCAM was lower. Using VCAM and IL-6 in classification algorithms, we could discriminate the groups with a sensitivity and specificity of 87% and 90%, respectively. The results suggest significant changes in the serum biomarker profile after mild ITBI. Future research is needed to determine whether these biomarkers can screen for brain injury in infants with nonspecific symptoms.

Development of multimarker panel for early detection of endometrial cancer. High diagnostic power of prolactin.

OBJECTIVE: Endometrial carcinoma is the most common gynecologic cancer. Although the prognosis for endometrial cancer is generally good, cancers identified at late stages are associated with high levels of morbidity and mortality. Therefore, prevention and early detection may further reduce the burden of this challenging disease. METHODS: A panel of 64 serum biomarkers was analyzed in sera of patients with stages I-III endometrial cancer and age-matched healthy women, utilizing a multiplex xMAP bead-based immunoassay. For multivariate analysis, four different statistical classification methods were used: logistic regression (LR), separating hyperplane (SHP), k nearest neighbors (KNN), and classification tree (CART). For each of these classifiers, a diagnostic model was created based on the cross-validation set consisting of sera from 115 patients with endometrial cancer and 135 healthy women. RESULTS: Our data have demonstrated that patients with endometrial cancer have significantly different expression patterns of several serum biomarkers as compared to healthy controls. Prolactin was the strongest discriminative biomarker for endometrial cancer providing 98.3% sensitivity and 98.0% specificity alone. Our results have revealed that serum concentration of cancer antigens, including CA 125, CA 15-3, and CEA are higher in patients with Stage III endometrial cancer as compared to those with Stage I. In addition, we have shown that the expression of CA 125, AFP, and ACTH is elevated in women with tumor grade 3 vs. grade 1. Furthermore, five-biomarker panel (prolactin, GH, Eotaxin, E-selectin, and TSH) identified in this study was able to discriminate endometrial cancer from ovarian and breast cancers with high sensitivity and specificity. CONCLUSIONS: The ability of prolactin to accurately discriminate between cancer and control groups indicates that this biomarker could potentially be used for development of blood-based test for the early detection of endometrial cancer in high-risk populations. Combining the information on multiple serum markers using flexible statistical methods allows for achieving high cancer selectivity.

Evidence-based modeling of critical illness: an initial consensus from the Society for Complexity in Acute Illness.

INTRODUCTION: Given the complexity of biological systems, understanding their dynamic behaviors, such as the Acute Inflammatory Response (AIR), requires a formal synthetic process. Dynamic Mathematical Modeling (DMM) represents a suite of methods intended for inclusion within the required synthetic framework. The DMM, however, is a relatively novel approach in the practice of biomedical research. The Society for Complexity in Acute Illness (SCAI) was formed in 2004 from the leading research groups using DMM in the study of acute inflammation. This society believes that it is important to offer guidelines for the design, development, and use of DMM in the setting of AIR research to avoid the "garbage in, garbage out" problem. Accordingly, SCAI identified a need for and carried out a critical appraisal of DMM as currently used in the setting of acute illness. METHODS: The SCAI annual meeting in 2005, the Fourth International Conference on Complexity in Acute Illness (Cologne, Germany), was structured with the intent of developing a consensus statement on the methods and execution of DMM in AIR research. The conference was organized to include a series of interactive breakout sessions that included thought leaders from both the DMM and acute illness fields, the results of which were then presented in summary form to the entire group for discussion and consensus. The information in this article represents the concatenation of those presentations. RESULTS: The output from the Fourth International Conference on Complexity in Acute Illness involved consensus statements for the following topics: (1) the need for DMM; (2) a suggested approach for the process of establishing a modeling project; (3) the type of "wet" laboratory experiments and data needed to establish a modeling project; (4) general quality measures for data to be input to a modeling project; and (5) a descriptive list of several types of DMM to provide guidance in selection of a method for a project. CONCLUSION: We believe that the complexity of biological systems requires that DMM needs to be among the methods used to improve understanding and make progress with attempts to characterize and manipulate the AIR. We believe that this consensus statement will help guide the integration, rational implementation, and standardization of DMM into general biomedical research.

Evaluating spatial constraints in cellular assembly processes using a monte carlo approach.

Biomolecular behavior commonly involves complex sets of interacting components that are challenging to understand through solution-based chemical theories. Molecular assembly is especially intriguing in the cellular environment because of its links to cell structure in processes such as chemotaxis. We use a coarse-grained Monte Carlo simulation to elucidate the importance of spatial constraints in molecular assembly. We have performed a study of actin filament polymerization through this space-aware probabilistic lattice-based model. Quantitative results are compared with nonspatial models and show convergence over a wide parameter space, but marked divergence over realistic levels corresponding to macromolecular crowding inside cells and localized actin concentrations found at the leading edge during cell motility. These conclusions have direct implications for cell shape and structure, as well as tumor cell migration.

New insights into mathematical modeling of the immune system.

In order to understand the integrated behavior of the immune system, there is no alternative to mathematical modeling. In addition, the advent of experimental tools such as gene arrays and proteomics poses new challenges to immunologists who are now faced with more information than can be readily incorporated into existing paradigms of immunity. We review here our ongoing efforts to develop mathematical models of immune responses to infectious disease, highlight a new modeling approach that is more accessible to immunologists, and describe new ways to analyze microarray data. These are collaborative studies between experimental immunologists, mathematicians, and computer scientists.

Understanding actin organization in cell structure through lattice based Monte Carlo simulations.

Understanding the connection between mechanics and cell structure requires the exploration of the key molecular constituents responsible for cell shape and motility. One of these molecular bridges is the cytoskeleton, which is involved with intracellular organization and mechanotransduction. In order to examine the structure in cells, we have developed a computational technique that is able to probe the self-assembly of actin filaments through a lattice based Monte Carlo method. We have modeled the polymerization of these filaments based upon the interactions of globular actin through a probabilistic model encompassing both inert and active proteins. The results show similar response to classic ordinary differential equations at low molecular concentrations, but a bi-phasic divergence at realistic concentrations for living mammalian cells. Further, by introducing localized mobility parameters, we are able to simulate molecular gradients that are observed in nonhomogeneous protein distributions in vivo. The method and results have potential applications in cell and molecular biology as well as self-assembly for organic and inorganic systems.