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At least 37 records · Page 2

Comparative study of two Saccharomyces cerevisiae strains with kinetic models at genome-scale

The parameterization of kinetic models requires measurement of fluxes and/or metabolite levels for a base strain and a few genetic perturbations thereof. Unlike stoichiometric models that are mostly invariant to the specific strain, it remains unclear whether kinetic models constructed for different strains of the same species have similar or significantly different kinetic parameters. This important question underpins the applicability range and prediction limits of kinetic reconstructions. To this end, herein we parameterize two separate large-scale kinetic models using K-FIT with genome-wide coverage corresponding to two distinct strains of Saccharomyces cerevisiae: CEN.PK 113-7D strain (model k-sacce306-CENPK), and growth-deficient BY4741 (isogenic to S288c; model k-sacce306-BY4741). The metabolic network for each model contains 306 reactions, 230 metabolites, and 119 substrate-level regulatory interactions. The two models (for CEN.PK and BY4741) recapitulate, within one standard deviation, 77% and 75% of the fitted dataset fluxes, respectively, determined by 13 C metabolic flux analysis for wild-type and eight single-gene knockout mutants of each strain. Strain-specific kinetic parameterization results indicate that key enzymes in the TCA cycle, glycolysis, and arginine and proline metabolism drive the metabolic differences between these two strains of S. cerevisiae. Our results suggest that although kinetic models cannot be readily used across strains as stoichiometric models, they can capture species-specific information through the kinetic parameterization process.

59 BASIC BIOLOGICAL SCIENCES↗

A novel semi-structured kinetic model of methanotroph-photoautotroph cocultures for biogas conversion

Through metabolic coupling of methane oxidation and oxygenic photosynthesis, methanotroph-photoautotroph (M-P) cocultures offer a highly promising technology platform for biogas conversion. However, there has not been any quantitative modeling of the coculture growth kinetics. This is mainly due to the inherent difficulty associated with real time characterization of the M-P cocultures and the complex interactions such as the cross-feeding mechanism within the coculture. To address this challenge, we recently developed a novel experimental-computational (E-C) protocol to accurately characterize the M-P coculture in real-time, and validated its accuracy through cell counting. Enabled by the E-C protocol, this work presents the very first kinetic model for M-P cocultures. By explicitly modeling the exchange of in situ produced O 2 /CO 2 within the M-P coculture and coupling the individual biomass growth with mass transfer between the gas and liquid phases, the semi-structured kinetic model accurately predicts the growth dynamics of the M-P coculture under a wide range of growth conditions. The proposed model is validated by a series of wet-lab experiments using Methylomicrobium buryatense 5GB1 - Arthrospira platensis as the model coculture. Although it has been speculated that there may exist other emergent metabolic interactions within the M-P coculture, in addition to the exchange of in situ produced O 2 /CO 2 , there has not been any experimental validation prior to this study. By integrating designed experiments with the semi-structured kinetic model, this study is the first to confirm the existence of the additional emergent metabolic exchanges within the coculture. Furthermore, this study further quantifies the effect of these unknown metabolic interactions on the growth of both species in the model coculture, supporting further research to identify these exchanged metabolites for metabolic engineering.

42 ENGINEERING↗

Autoignition of cyclohexane at low-to-intermediate temperatures: Rapid compression machine experiments and improved comprehensive chemical kinetic model

Cycloalkanes are an important class of hydrocarbons found in conventional and alternative transportation fuels. Being one of the simplest practical cycloalkanes, cyclohexane is often used as a surrogate in studies to understand the oxidation, ignition, and sooting characteristics of cycloalkanes more broadly. Although cyclohexane has been extensively studied, very limited datasets for cyclohexane oxidation at low-to-intermediate temperatures are available in the literature. Moreover, the literature autoignition data from rapid compression machines (RCMs) did not provide information on volume histories or experimental heat transfer characteristics which can significantly impact model predictions, thereby hindering the detailed validation of chemical kinetic models. It has also been observed that the cyclohexane kinetic models developed so far are not able to predict the literature data across a wide range of operating and mixture conditions. Hence, further studies are recommended to understand and improve model predictions for cyclohexane oxidation. In this study, RCM experiments were conducted using cyclohexane/air mixtures at varying compressed pressures (P C =15, 20, and 30 bar), equivalence ratios (ϕ=0.5, 1.0, and 2.0), and compressed temperatures (T C =670–960 K). The current RCM results of cyclohexane were found to complement well with the literature data, with the first-stage IDTs at high pressures and volume histories at all test conditions being first reported for better development and validation of chemical kinetic models. Additionally, a detailed chemical kinetic model for the cyclohexane oxidation has been developed and validated using both newly acquired experimental IDTs in this study and literature experimental studies (IDTs in RCMs and STs, species profiles in jet-stirred reactors, and laminar burning velocities). Unlike literature models, the proposed model was observed to provide an overall better prediction for experimental results over a wide range of conditions. Chemical kinetic analysis of the developed model was further conducted to identify the reaction pathways controlling the autoignition of cyclohexane.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Distinguishing Electron and Hole Dynamics in Functionalized CdSe/CdS Core/Shell Quantum Dots Using Complementary Ultrafast Spectroscopies and Kinetic Modeling

The evolution of excitation energy and photogenerated charges in semiconductor quantum dots (QDs) functionalized with molecular acceptors can be probed on ultrafast time scales using techniques such as transient absorption (TA) spectroscopy. However, historical interpretations that the 1S(e)-1S 3/2 (h) transition in Cd-chalcogenide QDs is fully attributable to electrons may be misleading, and multiexponential models used to fit TA kinetics do not correspond directly to specific photophysical processes. Here, we present visible-wavelength and mid-IR TA and time-resolved photoluminescence measurements to inform a comprehensive kinetic model of the photoexcited CdSe/CdS core/shell QDs functionalized with passivating oleic acid (OA), hole-accepting ferrocene, or electron-accepting naphthalene bisimide (NBI). We show that ~30% of the 1S signal and 72% of the IR signal can originate from holes in well-passivated core/shell QDs. We also demonstrate evidence of electron trapping in OA-capped core/shell QDs, with additional electron transfer and hole trapping in the QDs functionalized with NBI. Electron (hole) trapping and detrapping occur in 450 ± 100 ps (430 ± 70 ps) and 340 ± 100 ps (1.1 ± 0.4 ns) respectively, while the time constant for electron transfer to NBI is ~1.8 ns. The comprehensive picture of photophysical processes provided by the complementary ultrafast techniques and kinetic modeling can accelerate both the fundamental science and application development of nanostructured and molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

KETCHUP: Parameterizing of large-scale kinetic models using multiple datasets with different reference states

Large-scale kinetic models provide the computational means to dynamically link metabolic reaction fluxes to metabolite concentrations and enzyme levels while also conforming to substrate level regulation. However, the development of broadly applicable frameworks for efficiently and robustly parameterizing models remains a challenge. Challenges arise due to both the heterogeneity, paucity, and difficulty in obtaining flux and/or concentration data but also due to the computational difficulties of the underlying parameter identification problem. Both the computational demands for parameterization, degeneracy of obtained parameter solutions and interpretability of results has so far limited widespread adoption of large-scale kinetic models despite their potential. Herein, we introduce the Kinetic Estimation Tool Capturing Heterogeneous Datasets Using Pyomo (KETCHUP), a flexible parameter estimation tool that leverages a primal-dual interior-point algorithm to solve a nonlinear programming (NLP) problem that identifies a set of parameters capable of recapitulating the (non)steady-state fluxes and concentrations in wild-type and perturbed metabolic networks. KETCHUP is benchmarked against previously parameterized large-scale kinetic models demonstrating an at least an order of magnitude faster convergence than the tool K-FIT while at the same time attaining better data fits. Finally, this versatile toolbox accepts different kinetic descriptions, metabolic fluxes, enzyme levels and metabolite concentrations, under either steady-state or instationary conditions to enable robust kinetic model construction and parameterization. KETCHUP supports the SBML format and can be accessed at https://github.com/maranasgroup/KETCHUP.

59 BASIC BIOLOGICAL SCIENCES↗

Progress in Accurate Chemical Kinetic Modeling, Simulations, and Parameter Estimation for Heterogeneous Catalysis

Chemical kinetic modeling in heterogeneous catalysis is gaining ground in its ability to provide qualitatively or even quantitatively accurate prediction of real-world behavior because of new advances in the physical and chemical representations of catalytic systems, estimation of relevant kinetic parameters, and capabilities in kinetic modeling. This Perspective chronicles current trends and future areas of advancement in chemical kinetic modeling, simulation, and parameter estimation: ranging from elementary step calculations to multiscale modeling to the role of advanced statistical methods for incorporating uncertainties in predictions. Multiple new or growing methodologies are covered, examples are provided, and forward-looking topics for advancement are noted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ensemble cell-wide kinetic modeling of anaerobic organisms to support fuels and chemicals production

The goal of this project is to understand the metabolism and underlying regulatory networks of two anaerobic microorganisms, Moorella thermoacetica and Clostridium thermocellum by making use of Ensemble Modeling (EM) paradigm through integration of multiple omic information (transcriptomic, proteomic, metabolomic & fluxomic). Kinetic models have the potential to provide a mechanistic description of cellular metabolism by combining several layers of regulatory events into an integrated framework. The foundation of the kinetic model is a stoichiometric network description. To this end, we have developed and curated genome-scale metabolic (GSM) models of the organisms that will serve as scaffold for building the kinetic models. For M. thermoacetica, the GSM model was constructed and tested by the Stephanopoulos group with experimental growth rate. The GSM elucidated the energy conservation mechanism under autotrophic growth conditions. For C. thermocellum, the Maranas group has developed the second-generation GSM model through integration of experimental data. The Maranas group has also constructed a core metabolic kinetic model of the organism which includes the central metabolism and all relevant pathways for biofuels production. The stoichiometric and kinetic model predictions were tested extensively using experimental data for wild-type and 20 mutant strains. We have outlined below in detail the progress related to specific individual aims. Below are listed publications of research carried out based on this research grant support.

09 BIOMASS FUELS↗

Spall kinetics model description

Under high-rate loading in tension, metals can sustain much larger tensile stresses for sub-microsecond time periods than would be possible under quasi-static conditions. This type of failure, known as spall, is not adequately reproduced by hydrocodes with commonly used failure models. The Spall Kinetics Model treats spall by incorporating a time scale into the process of failure. Under sufficiently strong tensile states of stress, damage accumulates over this time scale, which can be thought of as an incubation time. The time scale depends on the previous loading history of the material, reflecting possible damage by a shock wave. The model acts by modifying the hydrostatic pressure that is predicted by any equation of state and is therefore simple to implement. Examples illustrate the ability of the model to reproduce the spall stress and resulting release waves in plate impact experiments on stainless steel.

36 MATERIALS SCIENCE↗

Nitromethane Decomposition via Automated Reaction Discovery and an Ab Initio Corrected Kinetic Model

In the explore the systematic construction of kinetic models from in silico reaction data for the decomposition of nitromethane. Our models are constructed in a computationally affordable manner by using reactions discovered through accelerated molecular dynamics simulations using the ReaxFF reactive force field. The reaction paths are then optimized to determine reaction rate parameters. We introduce a reaction barrier correction scheme that combines accurate thermochemical data from density functional theory with ReaxFF minimal energy paths. We validate our models across different thermodynamic regimes, showing predictions of gas phase CO and NO concentrations and high-pressure induction times that are similar to experimental data. The kinetic models are analyzed to find fundamental decomposition reactions in different thermodynamic regimes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A detailed chemical kinetic modeling and experimental investigation of the low- and high-temperature chemistry of n-butylcyclohexane

Chemical kinetic models of gasoline, jet, and diesel fuels and their mixtures with bioderived fuels are needed to assess fuel property effects on efficiency, emissions, and other performance metrics in internal combustion and gas turbine engines. As these real fuels have too many fuel components to be included in a chemical kinetic model, surrogate fuels containing fewer components are used to represent them. These surrogate fuels mimic the chemical classes or molecular structures contained in the real fuel. One of the important chemical classes in gasoline, jet, and diesel fuels comprises cyclohexanes. Cyclohexanes comprise about 30% or more by weight in diesel fuel. Also, Mueller et al proposed n-butylcyclohexane (nBCH) as a component in a nine-component surrogate palette to represent the ignition properties, distillation curve, density, and molecular structures of a diesel certification fuel. Herein, experimental measurements of the ignition delay times (IDTs) of nBCH in a shock tube and in a rapid compression machine are reported over a wide range of temperature, pressure, and equivalence ratio important for enabling the validation of a chemical kinetic model for nBCH for combustion in diesel engines. The range of conditions are temperatures of 630–1420 K, pressures of 10, 30, and 50 bar, and equivalence ratios of 0.3, 0.5, 1.0, and 2.0 in ‘air’. A detailed chemical model is developed for nBCH to simulate its ignition at both low and high-temperature conditions and at relevant elevated pressures. The experimentally measured IDTs are used to improve and validate the chemical kinetic model.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Review of Molten Salt Reactor Kinetics Models

Interest in circulating fuel reactors (CFRs), particularly molten salt reactors (MSRs) of the fluid fuel type, has been growing in the last two decades. Starting with a resurgence of interest in Europe, there have been a growing number of methods proposed and codes developed to model the kinetics of CFRs, which is a capability essential to the design and evaluation of such reactors. This work first reviews the physical phenomena unique to CFRs in light of current research and how CFR kinetics are impacted by these considerations. In general, it is found that the movement of delayed neutron precursors (DNPs) through the primary loop has significant impacts on transients at low reactor powers or those with significant spatial components such as a change in the primary loop mass flow rate. Effects on the neutron flux are exceedingly minimal and entirely negligible. An extensive review of published models and methods for simulating CFR kinetics is presented, along with transient simulations in fast and thermal neutron flux systems using representative codes from each of the main modeling categories. Comparisons among methods are presented as are recommendations for their use or nonuse in various transient and work-flow scenarios. In general, it is recommended that time-resolved, multigroup neutron diffusion approaches be used to establish ranges of applicability for point reactor kinetics (PRK)–based approaches that themselves may not be applicable for all modeling situations. In such cases, it is suggested that quasi-static approaches be used where PRK-based approaches cannot be used. Finally, a review of common assumptions used in these models is presented, along with an evaluation of their impact on model performance. It is found that neglecting turbulent diffusion in open core–type CFRs is a poor assumption that leads to an underestimation of the reduction of the delayed neutron fraction. Furthermore, it is seen that exclusion of secondary heat transfer loops in models leads to underestimation of transient peaks and troughs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Toward a Unified Kinetic Model of Nitrogenase Catalysis

The microbial enzyme nitrogenase catalyzes the MgATP-dependent reduction of N 2 to 2NH 3 , a transformation central to the global nitrogen cycle. While the canonical Thorneley−Lowe (TL) kinetic model has long served as a mechanistic framework, it does not incorporate several recent insights. Here, we present an updated kinetic model for Monitrogenase that incorporates these new findings. A significant insight is that electron transfer (ET) from the reduced Fe protein to the FeMo-cofactor is gated by MgATP-dependent conformational transitions and can be described as a probabilistic event that is dependent on the ligand bound to the active-site metallocofactor. The updated kinetic model quantitatively reproduces steady-state product formation rates across a broad range of experimental conditions, yielding revised estimates for key rate constants. It is demonstrated that under N 2 turnover, the probability of productive ET to the active site decreases by ∼60%, resulting in a significant fraction of Fe protein cycles that are unproductive for electron delivery. This mechanistic feature explains the observed rate limitation in N 2 reduction and implies a revised minimum energetic cost of approximately 25 MgATP per N 2 reduced. Integrating these new features into the revised kinetic model provides a more complete and usable foundation for understanding nitrogenase catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Kinetic modeling of microbial growth, enzyme activity, and gene deletions: An integrated model of β-glucosidase function in Cellvibrio japonicus

Understanding the complex growth and metabolic dynamics in microorganisms requires advanced kinetic models containing both metabolic reactions and enzymatic regulation to predict phenotypic behaviors under different conditions and perturbations. Most current kinetic models lack gene expression dynamics and are separately calibrated to distinct media, which consequently makes them unable to account for genetic perturbations or multiple substrates. This challenge limits our ability to gain a comprehensive understanding of microbial processes towards advanced metabolic optimizations that are desired for many biotechnology applications. Here, we present an integrated computational and experimental approach for the development and optimization of mechanistic kinetic models for microbial growth and metabolic and enzymatic dynamics. Our approach integrates growth dynamics, gene expression, protein secretion, and gene-deletion phenotypes. We applied this methodology to build a dynamic model of the growth kinetics in batch culture of the bacterium Cellvibrio japonicus grown using either cellobiose or glucose media. The model parameters were inferred from an experimental data set using an evolutionary computation method. The resulting model was able to explain the growth dynamics of C. japonicus using either cellobiose or glucose media and was also able to accurately predict the metabolite concentrations in the wild-type strain as well as in β-glucosidase gene deletion mutant strains. We validated the model by correctly predicting the non-diauxic growth and metabolite consumptions of the wild-type strain in a mixed medium containing both cellobiose and glucose, made further predictions of mutant strains growth phenotypes when using cellobiose and glucose media, and demonstrated the utility of the model for designing industrially-useful strains. Importantly, the model is able to explain the role of the different β-glucosidases and their behavior under genetic perturbations. Here, this integrated approach can be extended to other metabolic pathways to produce mechanistic models for the comprehensive understanding of enzymatic functions in multiple substrates.

59 BASIC BIOLOGICAL SCIENCES↗

A pseudo-kinetic model to simulate phase changes in gas hydrate bearing sediments

Herein, modeling of the phase transitions anticipated in gas hydrate bearing sediments (GHBS) is critical for a proper understanding of time-dependent changes in states and volumes (e.g. the production of methane from this type of soils). We propose a new pseudo-kinetic approach to simulate the typical phase changes anticipated in GHBS, using published experimental results involving gas hydrate dissociation that are the basis of a widely used kinetic model. The proposed pseudo-kinetic model is formulated in the pressure-temperature (P-T) plane and assumes a rate of gas hydrate dissociation (or formation) proportional to the distance between the current state and the phase boundary. The model consists of only one parameter and is simple to implement in numerical simulators. A similar concept is used to model ice formation/thawing phenomena, but based on the ice/liquid-water phase boundary. We implemented the pseudo-kinetic model in a fully coupled thermo-hydro-chemo-mechanical (THCM) finite element code and validated it against experimental results performed on the dissociation of synthetic gas hydrate. We also evaluated the pseudo-kinetic model using synthetic cases covering several scenarios associated with gas hydrate formation/dissociation and ice formation/thawing. The model successfully reproduced the gas production test from a natural GHBS core from Korea (scaled gas venting experiment over 14 h), and also the formation of gas hydrate and ice in permafrost in Alaska (over 2 × 10 6 years). -The analyses show the versatility of the proposed pseudo-kinetic approach by applying it to model the different types of phase transitions typically encounter in GHBS. The simple formulation, easy implementation in numerical simulator, and reduced number of parameters (only one per phase change) make this model an attractive option for simulating phase transformations in problems involving GHBS.

58 GEOSCIENCES↗

An experimental and kinetic modeling study of the oxidation of hexane isomers: Developing consistent reaction rate rules for alkanes

Alkanes are key components in gasoline, jet and diesel fuels and considerably influence the combustion behavior of these fuels because of their wide range of reactivity. An improved understanding of their combustion behavior and the development of chemical kinetic models that can accurately simulate their combustion behavior are important for the development of next-generation internal-combustion and gas-turbine engines. The current work provides here improved insight into oxidation mechanisms of a representative family of hydrocarbon fuels, specifically the hexane isomers: n-hexane, 2-methylpentane, 3-methylpentane, 2,2-dimethylbutane and 2,3-dimethylbutane. These isomers provide carbon “skeletons” ranging from straight-chained to highly-branched and provide a framework for the subsequent development of kinetic mechanisms for larger alkanes. New ignition delay times for the four branched hexane isomers were measured in a high-pressure shock tube and in a rapid compression machine, both at stoichiometric conditions (φ = 1), p = 15 bar and X O2 = 21% over temperatures from 600 to1300 K. These data were combined with previously published measurements under the same conditions for the remaining n-hexane isomer to provide a complete body of experimental data for kinetic modeling analysis. In addition, very recent experimental measurements of individual intermediate chemical species concentrations from all five hexane isomers in a jet-stirred reactor are also included and provide another family of data for further assessment of hexane isomer reactivity. Different reactivities were observed for each hexane isomer in each experimental facility, resulting from differences in their molecular structures. Consistent reaction rate rules have been applied to develop a combined detailed chemical kinetic model for all five hexane isomers. Kinetic model validation studies are reported to show that the current model reproduces well the ignition delay times of all five alkane isomers, as well as their variations in reactivity over a wide range of temperatures and other operating conditions. Equally important, these results show that it is not necessary to have a separate, different kinetic model for each isomer of a family of alkane fuels and that a single, coherent, integrated set of reaction rate classes and rules is sufficient to accurately describe combustion rates of combustion of straight-chain n-alkanes and branched-chain alkane fuels. This suggests strongly that a single set of reaction classes and rate rules should be sufficient to describe combustion kinetics of alkane fuels of any size and degree of branching.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

TChem v2.0 - A Software Toolkit for the Analysis of Complex Kinetic Models

TChem is an open source software library for solving complex computational chemistry problems and analyzing detailed chemical kinetic models. The software provides support for: complex kinetic models for gas-phase and surface chemistry; thermodynamic properties based on NASA polynomials; species production/consumption rates; stable time integrator for solving stiff time ordinary differential equations; and, reactor models such as homogenous gas-phase ignition (with analytical Jacobian matrices), continuously stirred tank reactor, plug-flow reactor. This toolkit builds upon earlier versions that were written in C and featured tools for gas-phase chemistry only. The current version of the software was completely refactored in C++, uses an object-oriented programming model, and adopts Kokkos as its portability layer to make it ready for the next generation computing architectures i.e., multi/many core computing platforms with GPU accelerators. We have expanded the range of kinetic models to include surface chemistry and have added examples pertaining to Continuously Stirred Tank Reactors (CSTR) and Plug Flow Reactor (PFR) models to complement the homogenous ignition examples present in the earlier versions. To exploit the massive parallelism available from modern computing platforms, the current software interface is designed to evaluate samples in parallel, which enables large scale parametric studies, e.g. for sensitivity analysis and model calibration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Sensitivity of Chemical Kinetic Models on Flame Transfer Functions in High Frequency Acoustic Fluctuation Environments

This paper investigates how different chemical kinetics models are able to capture the dynamics of laminar premixed methane/air flames. In particular, this paper computes flame transfer functions and compares the performance of different global kinetic models as well as detailed kinetic models. This is accomplished using a sequence of one-dimensional incompressible simulations implemented in OpenFOAM. The detailed GRI Mech 3.0 is used as a baseline for comparison. Detailed kinetic analysis will be conducted to understand the underlying kinetics-dynamics coupling.

Girdhar, Anant↗

A dynamic kinetic model captures cell-free metabolism for improved butanol production

Cell-free systems are useful tools for prototyping metabolic pathways and optimizing the production of various bioproducts. Mechanistically-based kinetic models are uniquely suited to analyze dynamic experimental data collected from cell-free systems and provide vital qualitative insight. However, to date, dynamic kinetic models have not been applied with rigorous biological constraints or trained on adequate experimental data to the degree that they would give high confidence in predictions and broadly demonstrate the potential for widespread use of such kinetic models. In this work, we construct a large-scale dynamic model of cell-free metabolism with the goal of understanding and optimizing butanol production in a cell-free system. Using a combination of parameterization methods, the resultant model captures experimental metabolite measurements across two experimental conditions for nine metabolites at timepoints between 0 and 24 hours. Here, we present analysis of the model predictions, provide recommendations for butanol optimization, and identify the aldehyde/alcohol dehydrogenase as the primary bottleneck in butanol production. Sensitivity analysis further reveals the extent to which various parameters are constrained, and our approach for probing valid parameter ranges can be applied to other modeling efforts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗