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1.  A Mathematical Model of Skeletal Muscle Disease and Immune Response in the mdx Mouse 
BioMed Research International  2014;2014:871810.
Duchenne muscular dystrophy (DMD) is a genetic disease that results in the death of affected boys by early adulthood. The genetic defect responsible for DMD has been known for over 25 years, yet at present there is neither cure nor effective treatment for DMD. During early disease onset, the mdx mouse has been validated as an animal model for DMD and use of this model has led to valuable but incomplete insights into the disease process. For example, immune cells are thought to be responsible for a significant portion of muscle cell death in the mdx mouse; however, the role and time course of the immune response in the dystrophic process have not been well described. In this paper we constructed a simple mathematical model to investigate the role of the immune response in muscle degeneration and subsequent regeneration in the mdx mouse model of Duchenne muscular dystrophy. Our model suggests that the immune response contributes substantially to the muscle degeneration and regeneration processes. Furthermore, the analysis of the model predicts that the immune system response oscillates throughout the life of the mice, and the damaged fibers are never completely cleared.
doi:10.1155/2014/871810
PMCID: PMC4071953  PMID: 25013809
2.  An algebra-based method for inferring gene regulatory networks 
BMC Systems Biology  2014;8:37.
Background
The inference of gene regulatory networks (GRNs) from experimental observations is at the heart of systems biology. This includes the inference of both the network topology and its dynamics. While there are many algorithms available to infer the network topology from experimental data, less emphasis has been placed on methods that infer network dynamics. Furthermore, since the network inference problem is typically underdetermined, it is essential to have the option of incorporating into the inference process, prior knowledge about the network, along with an effective description of the search space of dynamic models. Finally, it is also important to have an understanding of how a given inference method is affected by experimental and other noise in the data used.
Results
This paper contains a novel inference algorithm using the algebraic framework of Boolean polynomial dynamical systems (BPDS), meeting all these requirements. The algorithm takes as input time series data, including those from network perturbations, such as knock-out mutant strains and RNAi experiments. It allows for the incorporation of prior biological knowledge while being robust to significant levels of noise in the data used for inference. It uses an evolutionary algorithm for local optimization with an encoding of the mathematical models as BPDS. The BPDS framework allows an effective representation of the search space for algebraic dynamic models that improves computational performance. The algorithm is validated with both simulated and experimental microarray expression profile data. Robustness to noise is tested using a published mathematical model of the segment polarity gene network in Drosophila melanogaster. Benchmarking of the algorithm is done by comparison with a spectrum of state-of-the-art network inference methods on data from the synthetic IRMA network to demonstrate that our method has good precision and recall for the network reconstruction task, while also predicting several of the dynamic patterns present in the network.
Conclusions
Boolean polynomial dynamical systems provide a powerful modeling framework for the reverse engineering of gene regulatory networks, that enables a rich mathematical structure on the model search space. A C++ implementation of the method, distributed under LPGL license, is available, together with the source code, at http://www.paola-vera-licona.net/Software/EARevEng/REACT.html.
doi:10.1186/1752-0509-8-37
PMCID: PMC4022379  PMID: 24669835
Reverse-engineering; network inference; Boolean networks; molecular networks; gene regulatory networks; polynomial dynamical systems; algebraic dynamic models; evolutionary computation; DNA microarray data; time series data; data noise
3.  The Genome-Wide Early Temporal Response of Saccharomyces cerevisiae to Oxidative Stress Induced by Cumene Hydroperoxide 
PLoS ONE  2013;8(9):e74939.
Oxidative stress is a well-known biological process that occurs in all respiring cells and is involved in pathophysiological processes such as aging and apoptosis. Oxidative stress agents include peroxides such as hydrogen peroxide, cumene hydroperoxide, and linoleic acid hydroperoxide, the thiol oxidant diamide, and menadione, a generator of superoxide, amongst others. The present study analyzed the early temporal genome-wide transcriptional response of Saccharomyces cerevisiae to oxidative stress induced by the aromatic peroxide cumene hydroperoxide. The accurate dataset obtained, supported by the use of temporal controls, biological replicates and well controlled growth conditions, provided a detailed picture of the early dynamics of the process. We identified a set of genes previously not implicated in the oxidative stress response, including several transcriptional regulators showing a fast transient response, suggesting a coordinated process in the transcriptional reprogramming. We discuss the role of the glutathione, thioredoxin and reactive oxygen species-removing systems, the proteasome and the pentose phosphate pathway. A data-driven clustering of the expression patterns identified one specific cluster that mostly consisted of genes known to be regulated by the Yap1p and Skn7p transcription factors, emphasizing their mediator role in the transcriptional response to oxidants. Comparison of our results with data reported for hydrogen peroxide identified 664 genes that specifically respond to cumene hydroperoxide, suggesting distinct transcriptional responses to these two peroxides. Genes up-regulated only by cumene hydroperoxide are mainly related to the cell membrane and cell wall, and proteolysis process, while those down-regulated only by this aromatic peroxide are involved in mitochondrial function.
doi:10.1371/journal.pone.0074939
PMCID: PMC3779239  PMID: 24073228
4.  Modeling stochasticity and variability in gene regulatory networks 
Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This article contributes an approach as an alternative to these classical settings. Within the discrete paradigm, where genes, proteins, and other molecular components of gene regulatory networks are modeled as discrete variables and are assigned as logical rules describing their regulation through interactions with other components. Stochasticity is modeled at the biological function level under the assumption that even if the expression levels of the input nodes of an update rule guarantee activation or degradation there is a probability that the process will not occur due to stochastic effects. This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations to study cell-to-cell variability. We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.
doi:10.1186/1687-4153-2012-5
PMCID: PMC3419641  PMID: 22673395
5.  Differential gene expression in normal and transformed human mammary epithelial cells in response to oxidative stress 
Free radical biology & medicine  2011;50(11):1565-1574.
Oxidative stress plays a key role in breast carcinogenesis. To investigate whether normal and malignant breast epithelial cells differ in their responses to oxidative stress, we examined the global gene expression profiles of three cell types, representing cancer progression from a normal to a malignant stage, under oxidative stress. Normal human mammary epithelial cells (HMEC), an immortalized cell line (HMLER-1), and a tumorigenic cell line (HMLER-5), were exposed to increased levels of reactive oxygen species (ROS) by treatment with glucose oxidase. Functional analysis of the metabolic pathways enriched with differentially expressed genes demonstrates that normal and malignant breast epithelial cells diverge substantially in their response to oxidative stress. While normal cells exhibit the up-regulation of antioxidant mechanisms, cancer cells are unresponsive to the ROS insult. However, the gene expression response of normal HMEC cells under oxidative stress is comparable to that of the malignant cells under normal conditions, indicating that altered redox status is persistent in breast cancer cells, which makes them resistant to increased generation of ROS. This study discusses some of the possible adaptation mechanisms of breast cancer cells under persistent oxidative stress that differentiate them from the response to acute oxidative stress in normal mammary epithelial cells.
doi:10.1016/j.freeradbiomed.2011.03.002
PMCID: PMC3119600  PMID: 21397008
Oxidative stress; breast cancer; human mammary epithelial cells; microarrays; glucose oxidase; GluOx
6.  ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra 
BMC Bioinformatics  2011;12:295.
Background
Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed.
Results
We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second.
Conclusions
Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.
doi:10.1186/1471-2105-12-295
PMCID: PMC3154873  PMID: 21774817
7.  Discretization of Time Series Data 
Journal of Computational Biology  2010;17(6):853-868.
Abstract
An increasing number of algorithms for biochemical network inference from experimental data require discrete data as input. For example, dynamic Bayesian network methods and methods that use the framework of finite dynamical systems, such as Boolean networks, all take discrete input. Experimental data, however, are typically continuous and represented by computer floating point numbers. The translation from continuous to discrete data is crucial in preserving the variable dependencies and thus has a significant impact on the performance of the network inference algorithms. We compare the performance of two such algorithms that use discrete data using several different discretization algorithms. One of the inference methods uses a dynamic Bayesian network framework, the other—a time-and state-discrete dynamical system framework. The discretization algorithms are quantile, interval discretization, and a new algorithm introduced in this article, SSD. SSD is especially designed for short time series data and is capable of determining the optimal number of discretization states. The experiments show that both inference methods perform better with SSD than with the other methods. In addition, SSD is demonstrated to preserve the dynamic features of the time series, as well as to be robust to noise in the experimental data. A C++ implementation of SSD is available from the authors at http://polymath.vbi.vt.edu/discretization.
doi:10.1089/cmb.2008.0023
PMCID: PMC3203514  PMID: 20583929
gene networks; genetic algorithms; linear algebra; reverse engineering; time discrete dynamical systems
8.  Bioinformatics tools for cancer metabolomics 
Metabolomics  2011;7(3):329-343.
It is well known that significant metabolic change take place as cells are transformed from normal to malignant. This review focuses on the use of different bioinformatics tools in cancer metabolomics studies. The article begins by describing different metabolomics technologies and data generation techniques. Overview of the data pre-processing techniques is provided and multivariate data analysis techniques are discussed and illustrated with case studies, including principal component analysis, clustering techniques, self-organizing maps, partial least squares, and discriminant function analysis. Also included is a discussion of available software packages.
doi:10.1007/s11306-010-0270-3
PMCID: PMC3155682  PMID: 21949492
Metabolomics; Cancer; Metabolite profiling; NMR; Mass spectrometry; Bioinformatics
9.  A Systems Biology View of Cancer 
Biochimica et biophysica acta  2009;1796(2):129-139.
SUMMARY
In order to understand how a cancer cell is functionally different from a normal cell it is necessary to assess the complex network of pathways involving gene regulation, signaling, and cell metabolism, and the alterations in its dynamics caused by the several different types of mutations leading to malignancy. Since the network is typically complex, with multiple connections between pathways and important feedback loops, it is crucial to represent it in the form of a computational model that can be used for a rigorous analysis. This is the approach of systems biology, made possible by new –omics data generation technologies. The goal of this review is to illustrate this approach and its utility for our understanding of cancer. After a discussion of recent progress using a network-centric approach, three case studies related to diagnostics, therapy, and drug development are presented in detail. They focus on breast cancer, B cell lymphomas, and colorectal cancer. The discussion is centered on key mathematical and computational tools common to a systems biology approach.
doi:10.1016/j.bbcan.2009.06.001
PMCID: PMC2782452  PMID: 19505535
systems biology; cancer; mathematical modeling
10.  A General Map of Iron Metabolism and Tissue-specific Subnetworks 
Molecular bioSystems  2009;5(5):422-443.
Iron is required for survival of mammalian cells. Recently, understanding of iron metabolism and trafficking has increased dramatically, revealing a complex, interacting network largely unknown just a few years ago. This provides an excellent model for systems biology development and analysis. The first step in such an analysis is the construction of a structural network of iron metabolism, which we present here. This network was created using CellDesigner version 3.5.2 and includes reactions occurring in mammalian cells of numerous tissue types. The iron metabolic network contains 151 chemical species and 107 reactions and transport steps. Starting from this general model, we construct iron networks for specific tissues and cells that are fundamental to maintaining body iron homeostasis. We include subnetworks for cells of the intestine and liver, tissues important in iron uptake and storage, respectively; as well as the reticulocyte and macrophage, key cells in iron utilization and recycling. The addition of kinetic information to our structural network will permit the simulation of iron metabolism in different tissues as well as in health and disease.
doi:10.1039/b816714c
PMCID: PMC2680238  PMID: 19381358
iron; liver; macrophage; reactive oxygen species; red blood cells
11.  Nested Canalyzing, Unate Cascade, and Polynomial Functions 1 
Physica D. Nonlinear phenomena  2007;233(2):167-174.
This paper focuses on the study of certain classes of Boolean functions that have appeared in several different contexts. Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory networks. In the same context, polynomial functions over finite fields have been used to develop network inference methods for gene regulatory networks. Finally, unate cascade functions have been studied in the design of logic circuits and binary decision diagrams. This paper shows that the class of nested canalyzing functions is equal to that of unate cascade functions. Furthermore, it provides a description of nested canalyzing functions as a certain type of Boolean polynomial function. Using the polynomial framework one can show that the class of nested canalyzing functions, or, equivalently, the class of unate cascade functions, forms an algebraic variety which makes their analysis amenable to the use of techniques from algebraic geometry and computational algebra. As a corollary of the functional equivalence derived here, a formula in the literature for the number of unate cascade functions provides such a formula for the number of nested canalyzing functions.
doi:10.1016/j.physd.2007.06.022
PMCID: PMC2330334  PMID: 18437250
nested canalyzing function; unate cascade function; parametrization; polynomial function; Boolean function; algebraic variety
12.  A Virtual Look at Epstein–Barr Virus Infection: Biological Interpretations 
PLoS Pathogens  2007;3(10):e137.
The possibility of using computer simulation and mathematical modeling to gain insight into biological and other complex systems is receiving increased attention. However, it is as yet unclear to what extent these techniques will provide useful biological insights or even what the best approach is. Epstein–Barr virus (EBV) provides a good candidate to address these issues. It persistently infects most humans and is associated with several important diseases. In addition, a detailed biological model has been developed that provides an intricate understanding of EBV infection in the naturally infected human host and accounts for most of the virus' diverse and peculiar properties. We have developed an agent-based computer model/simulation (PathSim, Pathogen Simulation) of this biological model. The simulation is performed on a virtual grid that represents the anatomy of the tonsils of the nasopharyngeal cavity (Waldeyer ring) and the peripheral circulation—the sites of EBV infection and persistence. The simulation is presented via a user friendly visual interface and reproduces quantitative and qualitative aspects of acute and persistent EBV infection. The simulation also had predictive power in validation experiments involving certain aspects of viral infection dynamics. Moreover, it allows us to identify switch points in the infection process that direct the disease course towards the end points of persistence, clearance, or death. Lastly, we were able to identify parameter sets that reproduced aspects of EBV-associated diseases. These investigations indicate that such simulations, combined with laboratory and clinical studies and animal models, will provide a powerful approach to investigating and controlling EBV infection, including the design of targeted anti-viral therapies.
Author Summary
The possibility of using computer simulation and mathematical modeling to gain insight into biological systems is receiving increased attention. However, it is as yet unclear to what extent these techniques will provide useful biological insights or even what the best approach is. Epstein–Barr virus (EBV) provides a good candidate to address these issues. It persistently infects most humans and is associated with several important diseases, including cancer. We have developed an agent-based computer model/simulation (PathSim, Pathogen Simulation) of EBV infection. The simulation is performed on a virtual grid that represents the anatomy where EBV infects and persists. The simulation is presented on a computer screen in a form that resembles a computer game. This makes it readily accessible to investigators who are not well versed in computer technology. The simulation allows us to identify switch points in the infection process that direct the disease course towards the end points of persistence, clearance, or death, and identify conditions that reproduce aspects of EBV-associated diseases. Such simulations, combined with laboratory and clinical studies and animal models, provide a powerful approach to investigating and controlling EBV infection, including the design of targeted anti-viral therapies.
doi:10.1371/journal.ppat.0030137
PMCID: PMC2034398  PMID: 17953479

Results 1-12 (12)