Scholarly Works, Mathematics

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Browsing Scholarly Works, Mathematics by Department "Biological Sciences"

Now showing 1 - 7 of 7
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    JigCell Run Manager (JC-RM): a tool for managing large sets of biochemical model parametrizations
    Palmisano, Alida; Hoops, Stefan; Watson, Layne T.; Jones, Thomas C.; Tyson, John J.; Shaffer, Clifford A. (Biomed Central, 2015-12-24)
    Background Most biomolecular reaction modeling tools allow users to build models with a single list of parameter values. However, a common scenario involves different parameterizations of the model to account for the results of related experiments, for example, to define the phenotypes for a variety of mutations (gene knockout, over expression, etc.) of a specific biochemical network. This scenario is not well supported by existing model editors, forcing the user to manually generate, store, and maintain many variations of the same model. Results We developed an extension to our modeling editor called the JigCell Run Manager (JC-RM). JC-RM allows the modeler to define a hierarchy of parameter values, simulations, and plot settings, and to save them together with the initial model. JC-RM supports generation of simulation plots, as well as export to COPASI and SBML (L3V1) for further analysis. Conclusions Developing a model with its initial list of parameter values is just the first step in modeling a biological system. Models are often parameterized in many different ways to account for mutations of the organism and/or for sets of related experiments performed on the organism. JC-RM offers two critical features: it supports the everyday management of a large model, complete with its parameterizations, and it facilitates sharing this information before and after publication. JC-RM allows the modeler to define a hierarchy of parameter values, simulation, and plot settings, and to maintain a relationship between this hierarchy and the initial model. JC-RM is implemented in Java and uses the COPASI API. JC-RM runs on all major operating systems, with minimal system requirements. Installers, source code, user manual, and examples can be found at the COPASI website (http://www.copasi.org/Projects).
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    Linked within-host and between-host models and data for infectious diseases: a systematic review
    Childs, Lauren M.; El Moustaid, Fadoua; Gajewski, Zachary J.; Kadelka, Sarah; Nikin-Beers, Ryan; Smith, John W. Jr.; Walker, Melody; Johnson, Leah R. (PeerJ, 2019-06-19)
    The observed dynamics of infectious diseases are driven by processes across multiple scales. Here we focus on two: within-host, that is, how an infection progresses inside a single individual (for instance viral and immune dynamics), and between-host, that is, how the infection is transmitted between multiple individuals of a host population. The dynamics of each of these may be influenced by the other, particularly across evolutionary time. Thus understanding each of these scales, and the links between them, is necessary for a holistic understanding of the spread of infectious diseases. One approach to combining these scales is through mathematical modeling. We conducted a systematic review of the published literature on multi-scale mathematical models of disease transmission (as defined by combining within-host and between-host scales) to determine the extent to which mathematical models are being used to understand across-scale transmission, and the extent to which these models are being confronted with data. Following the PRISMA guidelines for systematic reviews, we identified 24 of 197 qualifying papers across 30 years that include both linked models at the within and between host scales and that used data to parameterize/calibrate models. We find that the approach that incorporates both modeling with data is under-utilized, if increasing. This highlights the need for better communication and collaboration between modelers and empiricists to build well-calibrated models that both improve understanding and may be used for prediction.
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    Multistate Model Builder (MSMB): a flexible editor for compact biochemical models
    Palmisano, Alida; Hoops, Stefan; Watson, Layne T.; Jones, Thomas C, Jr.; Tyson, John J.; Shaffer, Clifford A. (Biomed Central, 2014-04-04)
    Background Building models of molecular regulatory networks is challenging not just because of the intrinsic difficulty of describing complex biological processes. Writing a model is a creative effort that calls for more flexibility and interactive support than offered by many of today’s biochemical model editors. Our model editor MSMB -- Multistate Model Builder -- supports multistate models created using different modeling styles. Results MSMB provides two separate advances on existing network model editors. (1) A simple but powerful syntax is used to describe multistate species. This reduces the number of reactions needed to represent certain molecular systems, thereby reducing the complexity of model creation. (2) Extensive feedback is given during all stages of the model creation process on the existing state of the model. Users may activate error notifications of varying stringency on the fly, and use these messages as a guide toward a consistent, syntactically correct model. MSMB default values and behavior during model manipulation (e.g., when renaming or deleting an element) can be adapted to suit the modeler, thus supporting creativity rather than interfering with it. MSMB’s internal model representation allows saving a model with errors and inconsistencies (e.g., an undefined function argument; a syntactically malformed reaction). A consistent model can be exported to SBML or COPASI formats. We show the effectiveness of MSMB’s multistate syntax through models of the cell cycle and mRNA transcription. Conclusions Using multistate reactions reduces the number of reactions need to encode many biochemical network models. This reduces the cognitive load for a given model, thereby making it easier for modelers to build more complex models. The many interactive editing support features provided by MSMB make it easier for modelers to create syntactically valid models, thus speeding model creation. Complete information and the installation package can be found at http://www.copasi.org/SoftwareProjects. MSMB is based on Java and the COPASI API.
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    Optimization and model reduction in the high dimensional parameter space of a budding yeast cell cycle model
    Oguz, Cihan; Laomettachit, Teeraphan; Chen, Katherine C.; Watson, Layne T.; Baumann, William T.; Tyson, John J. (Biomed Central, 2013-06-28)
    Background 'Parameter estimation from experimental data is critical for mathematical modeling of protein regulatory networks. For realistic networks with dozens of species and reactions, parameter estimation is an especially challenging task. In this study, we present an approach for parameter estimation that is effective in fitting a model of the budding yeast cell cycle (comprising 26 nonlinear ordinary differential equations containing 126 rate constants) to the experimentally observed phenotypes (viable or inviable) of 119 genetic strains carrying mutations of cell cycle genes. Results Starting from an initial guess of the parameter values, which correctly captures the phenotypes of only 72 genetic strains, our parameter estimation algorithm quickly improves the success rate of the model to 105-111 of the 119 strains. This success rate is comparable to the best values achieved by a skilled modeler manually choosing parameters over many weeks. The algorithm combines two search and optimization strategies. First, we use Latin hypercube sampling to explore a region surrounding the initial guess. From these samples, we choose ∼20 different sets of parameter values that correctly capture wild type viability. These sets form the starting generation of differential evolution that selects new parameter values that perform better in terms of their success rate in capturing phenotypes. In addition to producing highly successful combinations of parameter values, we analyze the results to determine the parameters that are most critical for matching experimental outcomes and the most competitive strains whose correct outcome with a given parameter vector forces numerous other strains to have incorrect outcomes. These “most critical parameters” and “most competitive strains” provide biological insights into the model. Conversely, the “least critical parameters” and “least competitive strains” suggest ways to reduce the computational complexity of the optimization. Conclusions Our approach proves to be a useful tool to help systems biologists fit complex dynamical models to large experimental datasets. In the process of fitting the model to the data, the tool identifies suggestive correlations among aspects of the model and the data.
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    Pathogenesis and shedding of Usutu virus in juvenile chickens
    Kuchinsky, Sarah C.; Frere, Francesca; Heitzman-Breen, Nora; Golden, Jacob; Vázquez, Ana; Honaker, Christa F.; Siegel, Paul B.; Ciupe, Stanca M.; LeRoith, Tanya; Duggal, Nisha K. (Taylor & Francis, 2021-01-01)
    Usutu virus (USUV; family: Flaviviridae, genus: Flavivirus), is an emerging zoonotic arbovirus that causes severe neuroinvasive disease in humans and has been implicated in the loss of breeding bird populations in Europe. USUV is maintained in an enzootic cycle between ornithophilic mosquitos and wild birds. As a member of the Japanese encephalitis serocomplex, USUV is closely related to West Nile virus (WNV) and St. Louis encephalitis virus (SLEV), both neuroinvasive arboviruses endemic in wild bird populations in the United States. An avian model for USUV is essential to understanding zoonotic transmission. Here we describe the first avian models of USUV infection with the development of viremia. Juvenile commercial ISA Brown chickens were susceptible to infection by multiple USUV strains with evidence of cardiac lesions. Juvenile chickens from two chicken lines selected for high (HAS) or low (LAS) antibody production against sheep red blood cells showed markedly different responses to USUV infection. Morbidity and mortality were observed in the LAS chickens, but not HAS chickens. LAS chickens had significantly higher viral titers in blood and other tissues, as well as oral secretions, and significantly lower development of neutralizing antibody responses compared to HAS chickens. Mathematical modelling of virus-host interactions showed that the viral clearance rate is a stronger mitigating factor for USUV viremia than neutralizing antibody response in this avian model. These chicken models provide a tool for further understanding USUV pathogenesis in birds and evaluating transmission dynamics between avian hosts and mosquito vectors.
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    Predicting network modules of cell cycle regulators using relative protein abundance statistics
    Oguz, Cihan; Watson, Layne T.; Baumann, William T.; Tyson, John J. (2017-02-28)
    Background Parameter estimation in systems biology is typically done by enforcing experimental observations through an objective function as the parameter space of a model is explored by numerical simulations. Past studies have shown that one usually finds a set of “feasible” parameter vectors that fit the available experimental data equally well, and that these alternative vectors can make different predictions under novel experimental conditions. In this study, we characterize the feasible region of a complex model of the budding yeast cell cycle under a large set of discrete experimental constraints in order to test whether the statistical features of relative protein abundance predictions are influenced by the topology of the cell cycle regulatory network. Results Using differential evolution, we generate an ensemble of feasible parameter vectors that reproduce the phenotypes (viable or inviable) of wild-type yeast cells and 110 mutant strains. We use this ensemble to predict the phenotypes of 129 mutant strains for which experimental data is not available. We identify 86 novel mutants that are predicted to be viable and then rank the cell cycle proteins in terms of their contributions to cumulative variability of relative protein abundance predictions. Proteins involved in “regulation of cell size” and “regulation of G1/S transition” contribute most to predictive variability, whereas proteins involved in “positive regulation of transcription involved in exit from mitosis,” “mitotic spindle assembly checkpoint” and “negative regulation of cyclin-dependent protein kinase by cyclin degradation” contribute the least. These results suggest that the statistics of these predictions may be generating patterns specific to individual network modules (START, S/G2/M, and EXIT). To test this hypothesis, we develop random forest models for predicting the network modules of cell cycle regulators using relative abundance statistics as model inputs. Predictive performance is assessed by the areas under receiver operating characteristics curves (AUC). Our models generate an AUC range of 0.83-0.87 as opposed to randomized models with AUC values around 0.50. Conclusions By using differential evolution and random forest modeling, we show that the model prediction statistics generate distinct network module-specific patterns within the cell cycle network.
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    A Stochastic Model Correctly Predicts Changes in Budding Yeast Cell Cycle Dynamics upon Periodic Expression of CLN2
    Oguz, Cihan; Palmisano, Alida; Laomettachit, Teeraphan; Watson, Layne T.; Baumann, William T.; Tyson, John J. (PLOS, 2014-05-09)
    In this study, we focus on a recent stochastic budding yeast cell cycle model. First, we estimate the model parameters using extensive data sets: phenotypes of 110 genetic strains, single cell statistics of wild type and cln3 strains. Optimization of stochastic model parameters is achieved by an automated algorithm we recently used for a deterministic cell cycle model. Next, in order to test the predictive ability of the stochastic model, we focus on a recent experimental study in which forced periodic expression of CLN2 cyclin (driven by MET3 promoter in cln3 background) has been used to synchronize budding yeast cell colonies. We demonstrate that the model correctly predicts the experimentally observed synchronization levels and cell cycle statistics of mother and daughter cells under various experimental conditions (numerical data that is not enforced in parameter optimization), in addition to correctly predicting the qualitative changes in size control due to forced CLN2 expression. Our model also generates a novel prediction: under frequent CLN2 expression pulses, G1 phase duration is bimodal among small-born cells. These cells originate from daughters with extended budded periods due to size control during the budded period. This novel prediction and the experimental trends captured by the model illustrate the interplay between cell cycle dynamics, synchronization of cell colonies, and size control in budding yeast.