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Vidakovic, Brani

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    Constructing stochastic models from deterministic process equations by propensity adjustment
    (Georgia Institute of Technology, 2011-11) Wu, Jialiang ; Vidakovic, Brani ; Voit, Eberhard O.
    BACKGROUND: Gillespie's stochastic simulation algorithm (SSA) for chemical reactions admits three kinds of elementary processes, namely, mass action reactions of 0th, 1st or 2nd order. All other types of reaction processes, for instance those containing non-integer kinetic orders or following other types of kinetic laws, are assumed to be convertible to one of the three elementary kinds, so that SSA can validly be applied. However, the conversion to elementary reactions is often difficult, if not impossible. Within deterministic contexts, a strategy of model reduction is often used. Such a reduction simplifies the actual system of reactions by merging or approximating intermediate steps and omitting reactants such as transient complexes. It would be valuable to adopt a similar reduction strategy to stochastic modelling. Indeed, efforts have been devoted to manipulating the chemical master equation (CME) in order to achieve a proper propensity function for a reduced stochastic system. However, manipulations of CME are almost always complicated, and successes have been limited to relative simple cases. RESULTS: We propose a rather general strategy for converting a deterministic process model into a corresponding stochastic model and characterize the mathematical connections between the two. The deterministic framework is assumed to be a generalized mass action system and the stochastic analogue is in the format of the chemical master equation. The analysis identifies situations: where a direct conversion is valid; where internal noise affecting the system needs to be taken into account; and where the propensity function must be mathematically adjusted. The conversion from deterministic to stochastic models is illustrated with several representative examples, including reversible reactions with feedback controls, Michaelis-Menten enzyme kinetics, a genetic regulatory motif, and stochastic focusing. CONCLUSIONS: The construction of a stochastic model for a biochemical network requires the utilization of information associated with an equation-based model. The conversion strategy proposed here guides a model design process that ensures a valid transition between deterministic and stochastic models.
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    Self-similarity in NMR Spectra: An Application in Assessing the Level of Cysteine,
    (Georgia Institute of Technology, 2010-01) Jung, Yoon Young ; Park, Youngja ; Jones, Dean P. ; Ziegler, Thomas R. ; Vidakovic, Brani
    High resolution of NMR spectroscopic data of biosamples are a rich source of information on the metabolic response to physiological variation or pathological events. There are many advantages of NMR techniques such as the sample preparation is fast, simple and non-invasive. Statistical analysis of NMR spectra usually focuses on differential expression of large resonance intensity corresponding to abundant metabolites and involves several data preprocessing steps. In this paper we estimate functional components of spectra and test their significance using multiscale techniques. We also explore scaling in NMR spectra and use the systematic variability of scaling descriptors to predict the level of cysteine, an important precursor of glutathione, a control antioxidant in human body. This is motivated by high cost (in time and resources) of traditional methods for assessing cysteine level by high performance liquid chromatograph (HPLC).
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    Potential and Challenges for Mid-Infrared Sensors in Breath Diagnostics
    (Georgia Institute of Technology, 2010-01) Kim, Seong-Soo ; Young, Christina ; Vidakovic, Brani ; Gabram-Mendola, Sheryl G. A. ; Bayer, Charlene W. ; Mizaikoff, Boris
    Exhaled breath contains more than 1000 constituents at trace level concentrations, with a wide variety of these compounds potentially serving as biomarkers for specific diseases, physiologic status, or therapeutic progress. Some of the compounds in exhaled breath (EB) are well studied, and their relationship with disease pathologies is well established. However, molecularly specific analysis of such biomarkers in EB at clinically relevant levels remains an analytical and practical challenge due to the low levels of such biomarkers frequently below the ppb (v/v) range in EB. In this contribution, mid-infrared (MIR) spectroscopic sensing techniques are reviewed for potential application in breath diagnostics. While the spectral regime from 3-20 ¿m has already been utilized for fundamental studies on breath analysis, significant further improvements are in demand for substantiating MIR spectroscopy and sensing techniques as a suitable candidate for clinically deployable breath analyzers. Several advantageous features including inherent molecular selectivity, real-time monitoring capability, comparable ease of operation, potentially low costs, and a compact device footprint promise reliable optical diagnostics in the MIR. Hence, while the application of MIR spectroscopy and sensing systems to breath analysis yet appear in their infancy, recent progress on advanced MIR light sources, waveguides, and device concepts forecasts next-generation optical sensing platforms suitable for addressing the challenges of in situ breath diagnostics.