Chemical Kinetic Simulations Research Articles

Chemical kinetics simulation of semi-dry dechlorination in coal-fired flue gas

HCl in coal-fired flue gas has adverse impact on the environment, equipment, and the flue gas desulfurization (FGD) system. The existence of HCl also increases the difficulty of the treatment of desulfurization waste water. Semi-dry dechlorination technology is put forward to attach chlorine to fly ash by spraying in alkaline solution. Simultaneously, desulphurization waste water is used as the solvent of alkali, and this could help realize the target of near-zero emission of desulfurization waste water. CHEMKIN is used to build a chemical kinetics model, which is based on the measured components of flue gas in a coal-fired power plant. NaOH is set as the alkali absorbent in the model. Both the competitive relationship of SO2 and HCl and the effects of different factors on HCl reaction efficiency are analyzed. SO2 with high concentration would compete for more NaOH, but when Na/Cl (ratio in mole) is 1, the reaction efficiency of HCl achieves 22.28%, and it is positively correlated with Na/Cl. When Na/Cl surpasses 5, the reaction efficiency of HCl increases to beyond 70%. As Na/Cl continues to increase, there is a slower growth of HCl reaction efficiency and it finally achieves 100% when Na/Cl reaches 12. With a fixed value of Na/Cl, a change of 1000 mg/m3 in SO2 concentration would change the reaction efficiency of HCl about 13%. The effect of flue temperature on HCl reaction efficiency is not significant. Acid gases in flue gas react with NaOH completely in 0.1 s and come to equilibrium after about 1 s.

Study on the Optimization Design of TWC Based on Chemical Reaction Kinetics Simulation

Based on the simulation of exhaust gas after-treatment established by GT-Power, the washcoat partition approach has been studied both experimentally and by numerical modeling. It shows that, as the mass of noble metal keeping constant, the washcoat partition approach, in which the substrate is equally separated into two partitions and the concentration ratio of precious metal between the two partitions is 4:1, presents the content of CH, 0.037g/km, in exhaust has been decreased in 26.7% comparing to the non-partition approach.

Chemical kinetics in an atmospheric pressure helium plasma containing humidity.

Atmospheric pressure plasmas are sources of biologically active oxygen and nitrogen species, which makes them potentially suitable for the use as biomedical devices. Here, experiments and simulations are combined to investigate the formation of the key reactive oxygen species, atomic oxygen (O) and hydroxyl radicals (OH), in a radio-frequency driven atmospheric pressure plasma jet operated in humidified helium. Vacuum ultra-violet high-resolution Fourier-transform absorption spectroscopy and ultra-violet broad-band absorption spectroscopy are used to measure absolute densities of O and OH. These densities increase with increasing H2O content in the feed gas, and approach saturation values at higher admixtures on the order of 3 × 1014 cm-3 for OH and 3 × 1013 cm-3 for O. Experimental results are used to benchmark densities obtained from zero-dimensional plasma chemical kinetics simulations, which reveal the dominant formation pathways. At low humidity content, O is formed from OH+ by proton transfer to H2O, which also initiates the formation of large cluster ions. At higher humidity content, O is created by reactions between OH radicals, and lost by recombination with OH. OH is produced mainly from H2O+ by proton transfer to H2O and by electron impact dissociation of H2O. It is lost by reactions with other OH molecules to form either H2O + O or H2O2. Formation pathways change as a function of humidity content and position in the plasma channel. The understanding of the chemical kinetics of O and OH gained in this work will help in the development of plasma tailoring strategies to optimise their densities in applications.

Unraveling the structure and chemical mechanisms of highly oxygenated intermediates in oxidation of organic compounds

Decades of research on the autooxidation of organic compounds have provided fundamental and practical insights into these processes; however, the structure of many key autooxidation intermediates and the reactions leading to their formation still remain unclear. This work provides additional experimental evidence that highly oxygenated intermediates with one or more hydroperoxy groups are prevalent in the autooxidation of various oxygenated (e.g., alcohol, aldehyde, keto compounds, ether, and ester) and nonoxygenated (e.g., normal alkane, branched alkane, and cycloalkane) organic compounds. These findings improve our understanding of autooxidation reaction mechanisms that are routinely used to predict fuel ignition and oxidative stability of liquid hydrocarbons, while also providing insights relevant to the formation mechanisms of tropospheric aerosol building blocks. The direct observation of highly oxygenated intermediates for the autooxidation of alkanes at 500-600 K builds upon prior observations made in atmospheric conditions for the autooxidation of terpenes and other unsaturated hydrocarbons; it shows that highly oxygenated intermediates are stable at conditions above room temperature. These results further reveal that highly oxygenated intermediates are not only accessible by chemical activation but also by thermal activation. Theoretical calculations on H-atom migration reactions are presented to rationalize the relationship between the organic compound's molecular structure (n-alkane, branched alkane, and cycloalkane) and its propensity to produce highly oxygenated intermediates via extensive autooxidation of hydroperoxyalkylperoxy radicals. Finally, detailed chemical kinetic simulations demonstrate the influence of these additional reaction pathways on the ignition of practical fuels.

Connecting the Elementary Reaction Pathways of Criegee Intermediates to the Chemical Erosion of Squalene Interfaces during Ozonolysis.

Criegee intermediates (CI), formed in alkene ozonolysis, are central for controlling the multiphase chemistry of organic molecules in both indoor and outdoor environments. Here, we examine the heterogeneous ozonolysis of squalene, a key species in indoor air chemistry. Aerosol mass spectrometry is used to investigate how the ozone (O3) concentration, relative humidity (RH), and particle size control reaction rates and mechanisms. Although the reaction rate is found to be independent of RH, the reaction products and particle size depend upon H2O. Under dry conditions (RH = 3%) the reaction produces high-molecular-weight secondary ozonides (SOZ), which are known skin irritants, and a modest change in particle size. Increasing the RH reduces the aerosol size by 30%, while producing mainly volatile aldehyde products, increases potential respiratory exposure. Chemical kinetics simulations link the elementary reactions steps of CI to the observed kinetics, product distributions, and changes in particle size. The simulations reveal that ozonolysis occurs near the surface and is O3-transport limited. The observed secondary ozonides are consistent with the formation of mainly secondary CI, in contrast to gas-phase ozonolysis mechanisms.

Effect of Fuel Reactivity on Ignitability and Combustion Phasing in a Heavy-Duty Engine Simulation for Mixing-Controlled and Partially Premixed Combustion

Light-end fuels have recently garnered interest as potential fuel for advanced compression ignition (CI) engines. This next generation of engines, which aim to combine the high efficiency of diesel engines with the relative simplicity of gasoline engines, may allow engine manufacturers to continue improving efficiency and reducing emissions without a large increase in engine and aftertreatment system complexity. In this work, a 1D heavy-duty engine model was validated with measured data and then used to generate boundary conditions for the detailed chemical kinetic simulation corresponding to various combustion modes and operating points. Using these boundary conditions, homogeneous simulations were conducted for 242 fuels with research octane number (RON) from 40 to 100 and sensitivity (S) from 0 to 12. Combustion phasing (CA50) was most dependent on RON and less dependent on S under all conditions. Both RON and S had a greater effect on combustion phasing under partially premixed compression ignition (PPCI) conditions (19.3 deg) than under mixing-controlled combustion (MCC) conditions (5.8 deg). The effect of RON and S were also greatest for the lowest reactivity (RON > 90) fuels and under low-load conditions. The results for CA50 reflect the relative ignition delay for the various fuels at the start-of-injection (SOI) temperature. At higher SOI temperatures (>950K), CA50 was found to be less dependent on fuel sensitivity due to the convergence of ignition delay behavior of different fuels in the high-temperature region. Combustion of light-end fuels in CI engines can be an important opportunity for regulators, consumers, and engine-makers alike. However, selection of the right fuel specifications will be critical in development of the combustion strategy. This work, therefore, provides a first look at quantifying the effect of light-end fuel chemistry on advanced CI engine combustion across the entire light-end fuel reactivity space and provides a comparison of the trends for different combustion modes.

Improvement of combustion performance and emissions in diesel engines by fueling n-butanol/diesel/PODE3–4 mixtures

Polyoxymethylene dimethyl ethers (PODEn) are an excellent biofuel with no CC bond and substantial soot-reduction potential. The effects of BMEPs on the characteristics of combustion performance and emissions in a four-cylinder direct injection diesel engine with n-butanol/diesel/PODE3–4 blends were investigated. Mechanism of the PODE blends on soot reduction is discussed. The experimental results indicate that upon adding PODE3–4 to the blend of n-butanol with diesel can improve the thermal efficiency and combustion efficiency with an increment in the brake specific fuel consumption (BSFC). As the BMEP increased, a decreasing trend was observed in the emissions of soot, CO, and THC, while increasing NOx formation. Under a BMEP of 1.2MPa, the soot emissions from the combustion of BD20, BDP10, and BDP20 reduced by 61.5%, 80.7, and 91.1%, respectively, compared to that from pure diesel. Under equal BMEP value, adding PODE3–4 to n-butanol/diesel blend reduced the soot, CO and THC emissions, and the lowest soot and THC emissions were found for BDP20, followed by BDP10, BD20, and D100. The number concentration of the accumulated particulate matter as well as the mass concentration of total particulate matters can be decreased by adding PODE3–4. The chemical kinetics simulation results reveal that CO bonds break and CH2O is first produced in the pyrolysis of PODEn; as the value of n increases, more CH2O is produced and further oxidized to form HCO, which is finally transformed into CO and CO2, avoiding the production of soot precursors.

Combustion and Heat Release Characteristics of Biogas under Hydrogen- and Oxygen-Enriched Condition

Combustion and heat release characteristics of biogas non-premixed flames under various hydrogen-enriched and oxygen-enriched conditions were investigated through chemical kinetics simulation using detailed chemical mechanisms. The heat release rates, chemical reaction rates, and molar fraction of all species of biogas at various methane contents (35.3–58.7%, mass fraction), hydrogen addition ratios (10–50%), and oxygen enrichment levels (21–35%) were calculated considering the GRI 3.0 mechanism and P1 radiation model. Results showed that the net reaction rate of biogas increases with increasing hydrogen addition ratio and oxygen levels, leading to a higher net heat release rate of biogas flame. Meanwhile, flame length was shortened with the increase in hydrogen addition ratio and oxygen levels. The formation of free radicals, such as H, O, and OH, are enhanced with increase in hydrogen addition ratio and oxygen levels. Higher reaction rates of exothermic elementary reactions, especially those with OH free radical are increased, are beneficial to the improvement in combustion and heat release characteristics of biogas in practical applications.

Investigation of ignition characteristics and performance of a neat n-butanol direct injection compression ignition engine at low load

Neat (100%) n-butanol was implemented in a direct injection (DI) compression ignition (CI) engine. The ignition, combustion, and emission characteristics at low engine load (below 6.5bar IMEP), including near idling, were investigated. The engine experiments were performed using a modern common rail type single cylinder DI CI engine with a compression ratio of 18.2:1. Chemical kinetic simulations were also conducted to analyze the ignition characteristics of the experiments. The research results showed that neat n-butanol could not be auto-ignited at normal intake temperature and pressure conditions due to its low reactivity. However, the use of a high intake pressure of 0.75bar gauge, and an injection timing of −26° ATDC at 5.0bar IMEP, enabled auto-ignition even without the use of intake heating. One possible reason for this was attributed to the enhancement of the low temperature reaction regime. The ignition timing advancement sensitivity to intake pressure was approximately 1.0°CA/0.1bar at 5.0bar IMEP, and a higher intake pressure allowed a wider injection timing range. A neat n-butanol fueled DI CI engine had a five times longer ignition delay and a 85% longer combustion duration than the same engine fueled with diesel at 2.0bar IMEP. However, the combustion duration tended to shorten rapidly with increasing engine load, which was the opposite tendency to diesel. At low load, the nitrogen oxides (NOx) and soot emissions were very low compared to those of diesel, whereas the total hydrocarbons (THC), formaldehyde (HCHO), and carbon monoxide (CO) were higher than those of diesel. Carbon dioxide (CO2) emission was lower than that of diesel. This could be due to the reduced CO oxidation and the lower carbon content in n-butanol. Finally, by combining the previously published results with these results in this research, fuel injection strategies and intake oxygen conditions required to achieve low NOx (≤0.60g/kWh) and soot (≤0.02g/kWh) emissions and moderated maximum cylinder pressure rise rate (≤10bar/°CA) were summarized over a wide load range of 2.0–11.5bar IMEP.

Investigation of Methane Oxy-Fuel Combustion in a Swirl-Stabilised Gas Turbine Model Combustor

CO2 has a strong impact on both operability and emission behaviours in gas turbine combustors. In the present study, an atmospheric, preheated, swirl-stabilised optical gas turbine model combustor rig was employed. The primary objectives were to analyse the influence of CO2 on the fundamental characteristics of combustion, lean blowout (LBO) limits, CO emission and flame structures. CO2 dilution effects were examined with three preheating temperatures (396.15, 431.15, and 466.15 K). The fundamental combustion characteristics were studied utilising chemical kinetic simulations. To study the influence of CO2 on the operational range of the combustor, equivalence ratio (Ф) was varied from stoichiometric conditions to the LBO limits. CO emissions were measured at the exit of the combustor using a water-cooled probe over the entire operational range. The flame structures and locations were characterised by performing CH chemiluminescence imaging. The inverse Abel transformation was used to analyse the CH distribution on the axisymmetric plane of the combustor. Chemical kinetic modelling indicated that the CO2 resulted in a lower reaction rate compared with the CH4/air flame. Fundamental combustion properties such as laminar flame speed, ignition delay time and blowout residence time were found to be affected by CO2. The experimental results revealed that CO2 dilution resulted in a narrower operational range for the equivalence ratio. It was also found that CO2 had a strong inhibiting effect on CO burnout, which led to a higher concentration of CO in the combustion exhaust. CH chemiluminescence showed that the CO2 dilution did not have a significant impact on the flame structure.

Sensitivity analysis and validation of a predictive procedure for high and low-temperature ignition delays under engine conditions for n-dodecane using a Rapid Compression-Expansion Machine

A predictive procedure for cool flames and high-temperature ignition delays based on the accumulation and consumption of chain carriers has been validated for n-dodecane under engine conditions. To do so, an experimental parametric study has been carried out in a Rapid Compression-Expansion Machine, measuring the ignition times for different compression ratios (14 and 19), initial temperatures (from 403K to 463K), O2 molar fractions (from 0.21 to 0.16) and equivalence ratios (from 0.4 to 0.7). The measured ignition delays have been compared to results from chemical kinetic simulations performed in CHEMKIN using a 0-D reactor that replicates the experimental conditions by solving five different chemical kinetic mechanisms, as a way to evaluate the mechanisms accuracy and variability. In general, all chemical kinetic mechanisms are able to accurately replicate the experimental ignition delays, being the mean relative deviation lower than 1.9% and 1.6% for both ignition stages, cool flames and the high-temperature ignition respectively. Furthermore, small differences have been appreciated between mechanisms in terms of ignition delay. Then, the predictive method has been applied using different databases obtained from each mechanism and a sensitivity analysis has been performed in order to evaluate the effects of the selected database on the predicted ignition delay. It has been found that while cool flames seems to be independent on the selected mechanism, the predicted high-temperature ignition delay is very sensitive to the species selected as chain carrier. Thus, if formaldehyde is assumed as ignition tracer, the predicted ignition time can vary up to 3%, while this percent decreases up to 1.3% when hydrogen peroxide takes the role of chain carrier.

Experimental validation and analysis of seven different chemical kinetic mechanisms for n-dodecane using a Rapid Compression-Expansion Machine

Seven different chemical kinetic mechanisms for n-dodecane, two detailed and five reduced, have been evaluated under Engine Combustion Network (ECN) thermodynamic conditions by comparison to experimental measurements in a Rapid Compression-Expansion Machine (RCEM). The target ECN conditions are imposed at Top Dead Center (TDC), which cover a wide range of temperatures (from 850 K to 1000 K), oxygen molar fractions (0.21 and 0.15) and equivalence ratios (0.8, 0.9 and 1), while the pressure is fixed to keep a constant density at TDC equal to 22.8 kg/m3. The results obtained have been used to validate the chemical kinetic simulations, which have been performed with CHEMKIN, by comparing both cool flames and high temperature ignition delays, as well as the heat released in each stage of the combustion process in case of having a two-stage ignition pattern. The experimental results show good agreement with the chemical kinetic simulations. In fact, the mean relative deviation in ignition delay between experiments and simulations among all the chemical mechanisms is equal to 18.0% (3 CAD) for both cool flames and high temperature ignition. In general, closer correspondence has been obtained for the ignition delay referred to the high-temperature stage of the process, being the cool flames phenomenon more difficult to reproduce. Moreover, the differences between the reduced mechanisms and the most detailed one have been analyzed, concluding that the enhanced specific reaction rates of the most reduced mechanisms cause differences not only on the ignition delays, but also on the Negative Temperature Coefficient (NTC) behavior and on the heat released during cool flames.

Effect of Long-Lived Species Generated by Non-Thermal Plasmas on the Auto-Ignition Delay of Liquid Hydrocarbon Fuel-Air Pre-Mixtures

ABSTRACTThe effect of long-lived species induced by irradiation of air/fuel mixtures with non-thermal plasmas was studied to understand the mechanism of plasma-assisted ignition. The dependence of auto-ignition delay on temperature was measured using a rapid compression and expansion machine. Mixtures of air with i-octane, primary reference fuel, or methylcyclohexane as fuels were passed through the non-thermal plasma at the intake generated by surface dielectric barrier discharge before compression. The ignition delay was observed to be shortened owing to the effect of long-lived intermediate species such as NOx in the pre-mixture. This shortening behavior was found to be similar to those in compression experiments with NOx externally added. However, the presence of NOx only partly explained the results. Other species in the plasma-irradiated gas were identified by a chemical detecting tube and mass spectrometry with ion attachment ionization. The role of other species in inducing ignition-delay shortening was discussed with chemical kinetic simulations.

Kinetics of Thermal Unimolecular Decomposition of Acetic Anhydride: An Integrated Deterministic and Stochastic Model.

An integrated deterministic and stochastic model within the master equation/Rice-Ramsperger-Kassel-Marcus (ME/RRKM) framework was first used to characterize temperature- and pressure-dependent behaviors of thermal decomposition of acetic anhydride in a wide range of conditions (i.e., 300-1500 K and 0.001-100 atm). Particularly, using potential energy surface and molecular properties obtained from high-level electronic structure calculations at CCSD(T)/CBS, macroscopic thermodynamic properties and rate coefficients of the title reaction were derived with corrections for hindered internal rotation and tunneling treatments. Being in excellent agreement with the scattered experimental data, the results from deterministic and stochastic frameworks confirmed and complemented each other to reveal that the main decomposition pathway proceeds via a 6-membered-ring transition state with the 0 K barrier of 35.2 kcal·mol-1. This observation was further understood and confirmed by the sensitivity analysis on the time-resolved species profiles and the derived rate coefficients with respect to the ab initio barriers. Such an agreement suggests the integrated model can be confidently used for a wide range of conditions as a powerful postfacto and predictive tool in detailed chemical kinetic modeling and simulation for the title reaction and thus can be extended to complex chemical reactions.

Ignition characterization of F-76 and algae-derived HRD-76 at elevated temperatures and pressures

This study investigates the impact of fuel structure and chemistry on the combustion dynamics of a high-pressure fuel spray under realistic diesel engine conditions. The focus of the research was to better understand the combustion characteristics of a bio-derived hydroreformed Navy diesel, HRD-76, which is populated with a higher percentage of paraffins and expected to exhibit more rapid ignition behavior in comparison to the conventional Navy diesel, F-76. Specific attention was paid to intermediate temperature ignition conditions, which are of particular interest due to unique ignition behavior and the potential for reducing common oxide pollutants in this region. Experiments were conducted in a constant pressure flow chamber using dry air at ambient temperatures of 800K≤T≤975K, under various compressed pressures within the standard engine operating envelope (20–95bar), and under a moderate to high fuel loading condition when compared to realistic engine applications. The ignition delays, combustion duration, and ignition dwell of the fuels at various temperatures and pressures were measured utilizing a photodiode to capture the OH* emission signature. In addition, high-speed broadband chemiluminescence imaging and intensified high-speed OH* chemiluminescence imaging were utilized to understand the fuel's ignition behavior at frame-rates of 60kHz. The optical diagnostics employed showed that the HRD-76 has a higher propensity to ignite in comparison to F-76 under the same ambient conditions. The results were correlated with shock tube data and chemical kinetic simulations to determine the impact of the fuels’ physical delay time on the overall ignition delay. These results will supply fundamental combustion information for the use of alternative fuels in current and future engine technologies.

Investigation of late-cycle soot oxidation using laser extinction and in-cylinder gas sampling at varying inlet oxygen concentrations in diesel engines

This study focuses on the relative importance of O2 and OH as oxidizers of soot during the late cycle in diesel engines, where the soot oxidation is characterized in an optically accessible engine using laser extinction measurements. These are combined with in-cylinder gas sampling data from a single-cylinder engine fitted with a fast gas-sampling valve. Both measurements confirm that the in-cylinder soot oxidation slows down when the inlet concentration of O2 is reduced. A 38% decrease in intake O2 concentration reduces the soot oxidation rate by 83%, a non-linearity suggesting that O2 in itself is not the main soot oxidizing species. Chemical kinetics simulations of OH concentrations in the oxidation zone and estimates of the OH-soot oxidation rates point towards OH being the dominant oxidizer.

Effects of N2, CO2 and H2O dilutions on temperature and concentration fields of OH in methane Bunsen flames by using PLIF thermometry and bi-directional PLIF

The effects of N2, CO2 and H2O dilutions on the two-dimensional (2D) temperature and concentration fields of OH in methane Bunsen flames were investigated by employing two-line planar laser-induced fluorescence (PLIF) thermometry and bi-directional PLIF technique, respectively. The spatial resolution of the measured temperature and concentration fields of OH radical was 41.7μm. It was found that the measured temperature fields in methane Bunsen flames with different diluents exhibited a non-uniform and a symmetrical structure. In terms of decreasing the flame temperature, the CO2 diluent achieved a good result compared with N2 and H2O diluents. The total uncertainties in PLIF thermometry measurements were estimated to be ±8.44%, ±8.17% and ±8.27% for each diluent, respectively. The OH peak absorption cross sections at different heights were obtained in methane Bunsen flames with different diluents. Finally, the 2D absolute OH concentration filed in methane Bunsen flames diluted with three different diluents were obtained by using bi-directional PLIF technique. The peak absolute OH number densities in the flames with H2O, N2 and CO2 diluents were 9.84×1017cm−3, 8.57×1017cm−3 and 7.84×1017cm−3, with the overall uncertainties of ±20.56%, ±19.04% and ±23.43%, respectively. The numerical simulations of chemical kinetics were performed by using a physical model of one-dimensional laminar premixed flame and a detail methane reaction mechanism of GRI-Mech 3.0 so as to investigate the difference between the simulation results and experimental values. The comparison results for the temperature and OH concentration indicated that the reaction mechanism of GRI-Mech 3.0 might underestimate the chemical effects of CO2 and H2O diluents on the production of OH radical in premixed methane flames.

Experimental validation of an alternative method to predict high and low-temperature ignition delays under transient thermodynamic conditions for PRF mixtures using a Rapid Compression-Expansion Machine

An alternative procedure to predict both high-temperature stage and cool flames ignition delays under transient thermodynamic conditions is intended to be validated in this paper. An experimental study has been carried out in a Rapid Compression-Expansion Machine (RCEM), using different iso-octane/n-heptane blends in order to cover a wide range of octane numbers (from 25 to 75) under a wide range of initial temperatures (from 363K to 423K), compression ratios (14 and 19), O2 molar rates (from 21% to 16%) and equivalence ratios (from 0.4 to 0.8). The results obtained have been used to validate direct chemical kinetic simulations, as well as to evaluate the alternative predictive method and the Livengood & Wu integral method. Simulations have been performed solving a detailed chemical kinetic mechanism in CHEMKIN. The experimental results show good agreement with the chemical kinetic simulations and with the alternative predictive method. In fact, the mean relative deviation between experiments and simulations is equal to 1.7%, 2.2% and 3.1% for PRF25, PRF50 and PRF75, respectively. Besides, the alternative method has shown good predictive capability not only for the high-temperature stage of the process, but also for cool flames, being the mean relative deviation versus the experimental data lower than 3.3% for all fuels. Better predictions of the ignition delay have been obtained with the alternative procedure than the ones obtained with the classic Livengood & Wu expression, especially in those cases showing a two-stage ignition pattern, in which the Livengood & Wu integral method is not able to predict the high-temperature stage of the process.

Simulation of the M13 life cycle I: Assembly of a genetically-structured deterministic chemical kinetic simulation

To expand the quantitative, systems level understanding and foster the expansion of the biotechnological applications of the filamentous bacteriophage M13, we have unified the accumulated quantitative information on M13 biology into a genetically-structured, experimentally-based computational simulation of the entire phage life cycle. The deterministic chemical kinetic simulation explicitly includes the molecular details of DNA replication, mRNA transcription, protein translation and particle assembly, as well as the competing protein-protein and protein-nucleic acid interactions that control the timing and extent of phage production. The simulation reproduces the holistic behavior of M13, closely matching experimentally reported values of the intracellular levels of phage species and the timing of events in the M13 life cycle. The computational model provides a quantitative description of phage biology, highlights gaps in the present understanding of M13, and offers a framework for exploring alternative mechanisms of regulation in the context of the complete M13 life cycle.

Hybrid framework for the simulation of stochastic chemical kinetics

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.