Reaction-based Modeling Research Articles

Virtual Parts Repository 2: Model-Driven Design of Genetic Regulatory Circuits.

Engineering genetic regulatory circuits is key to the creation of biological applications that are responsive to environmental changes. Computational models can assist in understanding especially large and complex circuits for which manual analysis is infeasible, permitting a model-driven design process. However, there are still few tools that offer the ability to simulate the system under design. One of the reasons for this is the lack of accessible model repositories or libraries that cater to the modular composition of models of synthetic systems. Here, we present the second version of the Virtual Parts Repository, a framework to facilitate the model-driven design of genetic regulatory circuits, which provides reusable, modular, and composable models. The new framework is service-oriented, easier to use in computational workflows, and provides several new features and access methods. New features include supporting hierarchical designs via a graph-based repository or compatible remote repositories, enriching existing designs, and using designs provided in Synthetic Biology Open Language documents to derive system-scale and hierarchical Systems Biology Markup Language models. We also present a reaction-based modeling abstraction inspired by rule-based modeling techniques to facilitate scalable and modular modeling of complex and large designs. This modeling abstraction enhances the modeling capability of the framework, for example, to incorporate design patterns such as roadblocking, distributed deployment of genetic circuits using plasmids, and cellular resource dependency. The framework and the modeling abstraction presented in this paper allow computational design tools to take advantage of computational simulations and ultimately help facilitate more predictable applications.

Multi-zone reaction-based modeling of combustion for multiple-injection diesel engines

As the requirements for performance and restrictions on emissions become stringent, diesel engines are equipped with advanced air, fuel, exhaust gas recirculation techniques, and associated control strategies, making them incredibly complex systems. To enable model-based engine control, control-oriented combustion models, including Wiebe-based and single-zone reaction-based models, have been developed to predict engine burn rate or in-cylinder pressure. Despite model simplicity, they are not suitable for engines operating outside the normal range because of the large error beyond calibrated region with extremely high calibration effort. The purpose of this article is to obtain a parametric understanding of diesel combustion by developing a physics-based model which can predict the combustion metrics, such as in-cylinder pressure, burn rate, and indicated mean effective pressure accurately, over a wide range of operating conditions, especially with multiple injections. In the proposed model, it is assumed that engine cylinder is divided into three zones: a fuel zone, a reaction zone, and an unmixed zone. The formulation of reaction and unmixed zones is based on the reaction-based modeling methodology, where the interaction between them is governed by Fick’s law of diffusion. The fuel zone is formulated as a virtual zone, which only accounts for mass and heat transfer associated with fuel injection and evaporation. The model is validated using test data under different speed and load conditions, with multiple injections and exhaust gas recirculation rates. It is shown that the multi-zone model outperformed the single-zone model in in-cylinder pressure prediction and calibration effort with a mild penalty in computational time.

Kappa rule-based modeling in synthetic biology.

Rule-based modeling, an alternative to traditional reaction-based modeling, allows us to intuitively specify biological interactions while abstracting from the underlying combinatorial complexity. One such rule-based modeling formalism is Kappa, which we introduce to readers in this chapter. We discuss the application of Kappa to three modeling scenarios in synthetic biology: a unidirectional switch based on nitrosylase induction in Saccharomyces cerevisiae, the repressilator in Escherichia coli formed from BioBrick parts, and a light-mediated extension to said repressilator developed by the University of Edinburgh team during iGEM 2010. The second and third scenarios in particular form a case-based introduction to the Kappa BioBrick Framework, allowing us to systematically address the modeling of devices and circuits based on BioBrick parts in Kappa. Through the use of these examples, we highlight the ease with which Kappa can model biological interactions both at the genetic and the protein-protein interaction level, resulting in detailed stochastic models accounting naturally for transcriptional and translational resource usage. We also hope to impart the intuitively modular nature of the modeling processes involved, supported by the introduction of visual representations of Kappa models. Concluding, we explore future endeavors aimed at making modeling of synthetic biology more user-friendly and accessible, taking advantage of the strengths of rule-based modeling in Kappa.

Impact of phosphate on U(VI) immobilization in the presence of goethite

Past mining, processing, and waste disposal activities have left a legacy of uranium-contaminated soil and groundwater. Phosphate addition to subsurface environments can potentially immobilize U(VI) in-situ through interactions with uranium at mineral-water interfaces. Phosphate can induce the precipitation of low solubility U(VI)-phosphates, and it may enhance or inhibit U(VI) adsorption to iron(III) (oxy)hydroxide surfaces. Such surfaces may also facilitate the heterogeneous nucleation of U(VI)-phosphate precipitates. The interactions among phosphate, U(VI), and goethite (α-FeOOH) were investigated in a year-long series of experiments at pH 4. Reaction time, total U(VI), total phosphate, and the presence and absence of goethite were systematically varied to determine their effects on the extent of U(VI) uptake and the dominant uranium immobilization mechanism. Dissolved U(VI) and phosphate concentrations were interpreted within a reaction-based modeling framework that included dissolution-precipitation reactions and a surface complexation model to account for adsorption. The best available thermodynamic data and past surface complexation models were integrated to form an internally consistent framework. Additional evidence for the uptake mechanisms was obtained using scanning electron microscopy and X-ray diffraction. The formation and crystal growth of a U(VI)-phosphate phase, most likely chernikovite, UO 2HPO 4·4H 2O (s), occurred rapidly for initially supersaturated suspensions both with and without goethite. Nucleation appears to occur homogeneously for almost all conditions, even in the presence of goethite, but heterogeneous nucleation was likely at one condition. The U(VI)-phosphate solids exhibited metastability depending on the TOTU:TOTP ratio. At the highest phosphate concentration studied (130 μM), U(VI) uptake was enhanced due to the likely formation of a ternary surface complex for low (∼1 μM) to intermediate (∼10 μM) TOTU concentrations and to U(VI)-phosphate precipitation for high TOTU (∼100 μM) concentrations. For conditions favoring precipitation, the goethite surface acted as a sink for dissolved phosphate that resulted in higher dissolved U(VI) concentrations relative to goethite-free conditions. Based on the total uranium and available sorption sites, a critical phosphate concentration between 15 μM and 130 μM was required for preferential precipitation of uranium phosphate over U(VI) adsorption.

Reaction-based modeling of quinone-mediated bacterial iron(III) reduction

This paper presents and validates a new paradigm for modeling complex biogeochemical systems using a diagonalized reaction-based approach. The bioreduction kinetics of hematite (α-Fe 2O 3) by the dissimilatory metal-reducing bacterium (DMRB) Shewanella putrefaciens strain CN32 in the presence of the soluble electron shuttling compound anthraquinone-2,6-disulfonate (AQDS) is used for presentation/validation purposes. Experiments were conducted under nongrowth conditions with H 2 as the electron donor. In the presence of AQDS, both direct biological reduction and indirect chemical reduction of hematite by bioreduced anthrahydroquinone-2,6-disulfonate (AH 2DS) can produce Fe(II). Separate experiments were performed to describe the bioreduction of hematite, bioreduction of AQDS, chemical reduction of hematite by AH 2DS, Fe(II) sorption to hematite, and Fe(II) biosorption to DMRB. The independently determined rate parameters and equilibrium constants were then used to simulate the parallel kinetic reactions of Fe(II) production in the hematite-with-AQDS experiments. Previously determined rate formulations/parameters for the bioreduction of hematite and Fe(II) sorption to hematite were systematically tested by conducting experiments with different initial conditions. As a result, the rate formulation/parameter for hematite bioreduction was not modified, but the rate parameters for Fe(II) sorption to hematite were modified slightly. The hematite bioreduction rate formulation was first-order with respect to hematite ”free“ surface sites and zero-order with respect to DMRB based on experiments conducted with variable concentrations of hematite and DMRB. The AQDS bioreduction rate formulation was first-order with respect to AQDS and first-order with respect to DMRB based on experiments conducted with variable concentrations of AQDS and DMRB. The chemical reduction of hematite by AH 2DS was fast and considered to be an equilibrium reaction. The simulations of hematite-with-AQDS experiments were very sensitive to the equilibrium constant for the hematite-AH 2DS reaction. The model simulated the hematite-with-AQDS experiments well if it was assumed that the ferric oxide “surface” phase was more disordered than pure hematite. This is the first reported study where a diagonalized reaction-based model was used to simulate parallel kinetic reactions based on rate formulations/parameters independently obtained from segregated experiments.

Theoretical and Experimental Considerations Related to Reaction-Based Modeling: A Case Study Using Iron(III) Oxide Bioreduction

The kinetics of reductive dissolution of hematite ( f -Fe 2 O 3 ) by the dissimilatory iron-reducing bacterium Shewanella putrefaciens strain CN32 under nongrowth conditions with H 2 as the electron donor was measured and then modeled using a reaction-based biogeochemical model. Minimum data needs and a reaction matrix decomposition procedure are presented from a reaction-based modeling perspective and used to design subsequent experiments. Detailed step-by-step modeling methodology is presented. Independent experiments were performed to determine if Fe 2+ sorption to S. putrefaciens CN32 or hematite could be described as either kinetic or equilibrium reactions (i.e., slow or fast, respectively, relative to the time-scale of the bioreduction experiments). Fe 2+ sorption to S. putrefaciens CN32 was an equilibrium reaction and a linear adsorption isotherm was used to determine the associated equilibrium constant. Fe 2+ sorption to hematite was a kinetic reaction and an elementary rate formulation was independently determined from abiotic experiments. The ratio of the forward rate divided by the backward rate [log(k f /k b )] for the sorption of Fe 2+ to hematite was 6.33 - 0.14 (n = 2) and the corresponding log(k f ) was 6.66 - 0.28 (n = 2, M -1 h -1 ). Three different kinetic reaction rate formulations were used to model hematite bioreduction, an elementary rate law for the overall reaction, an empirical rate law physically based on hematite "free" surface sites, and an empirical rate law physically based on hematite free surface sites and bacterial inhibition caused by Fe(II) biosorption. All rate formulations modeled the measured results reasonably well (R 2 values ranged from 0.83 to 0.99). For the elementary rate formulation, log(k f /k b ) was 24.37 - 0.15 (n = 4) and the corresponding forward rate [log(k f )] was 26.46 - 0.27 (n = 4, M -4 h -1 ). These results demonstrate that independently determined reaction-based rate formulations were applicable in another experimental system, as theoretically expected. Therefore, the simulation and prediction of complex biogeochemical systems may eventually be able to be performed using reaction-based models.