Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the A phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. in this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Advanced computing for systems biology

Systems biology is based on computational modelling and simulation of large networks of interacting components. Models may be intended to capture processes, mechanisms, components and interactions at different levels of fidelity. Input data are often large and geographically disperse, and may require the computation to be moved to the data, not vice versa. In addition, complex system-level problems require collaboration across institutions and disciplines. Grid computing can offer robust, scaleable solutions for distributed data, compute and expertise. We illustrate some of the range of computational and data requirements in systems biology with three case studies: one requiring large computation but small data (orthologue mapping in comparative genomics), a second involving complex terabyte data (the Visible Cell project) and a third that is both computationally and data-intensive (simulations at multiple temporal and spatial scales). Authentication, authorisation and audit systems are currently not well scalable and may present bottlenecks for distributed collaboration particularly where outcomes may be commercialised. Challenges remain in providing lightweight standards to facilitate the penetration of robust, scalable grid-type computing into diverse user communities to meet the evolving demands of systems biology.

Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.

Modeling of Turbulent Natural Gas and Biogas Flames of the Delft Jet-in-Hot-Coflow Burner: Effects of Coflow Temperature, Fuel Temperature and Fuel Composition on the Flame Lift-Off Height

The structure of a turbulent non-premixed flame of a biogas fuel in a hot and diluted coflow mimicking moderate and intense low dilution (MILD) combustion is studied numerically. Biogas fuel is obtained by dilution of Dutch natural gas (DNG) with CO2. The results of biogas combustion are compared with those of DNG combustion in the Delft Jet-in-Hot-Coflow (DJHC) burner. New experimental measurements of lift-off height and of velocity and temperature statistics have been made to provide a database for evaluating the capability of numerical methods in predicting the flame structure. Compared to the lift-off height of the DNG flame, addition of 30 % carbon dioxide to the fuel increases the lift-off height by less than 15 %. Numerical simulations are conducted by solving the RANS equations using Reynolds stress model (RSM) as turbulence model in combination with EDC (Eddy Dissipation Concept) and transported probability density function (PDF) as turbulence-chemistry interaction models. The DRM19 reduced mechanism is used as chemical kinetics with the EDC model. A tabulated chemistry model based on the Flamelet Generated Manifold (FGM) is adopted in the PDF method. The table describes a non-adiabatic three stream mixing problem between fuel, coflow and ambient air based on igniting counterflow diffusion flamelets. The results show that the EDC/DRM19 and PDF/FGM models predict the experimentally observed decreasing trend of lift-off height with increase of the coflow temperature. Although more detailed chemistry is used with EDC, the temperature fluctuations at the coflow inlet (approximately 100K) cannot be included resulting in a significant overprediction of the flame temperature. Only the PDF modeling results with temperature fluctuations predict the correct mean temperature profiles of the biogas case and compare well with the experimental temperature distributions.

Behavior of Granular Materials Under Triaxial Compression with Pulsating Deviator Stress, HR-131, Special Report

Behavior of granular material subjected to repeated load triaxial compression tests is characterized by a model based on rate process theory. Starting with the Arrhenius equation from chemical kinetics, the relationship of temperature, shear stress, normal stress and volume change to deformation rate is developed. The proposed model equation includes these factors as a product of exponential terms. An empirical relationship between deformation and the cube root of the number of stress applications at constant temperature and normal stress is combined with the rate equation to yield an integrated relationship of temperature, deviator stress, confining pressure and number of deviator stress applications to axial strain. The experimental program consists of 64 repeated load triaxial compression tests, 52 on untreated crushed stone and 12 on the same crushed stone material treated with 4% asphalt cement. Results were analyzed with multiple linear regression techniques and show substantial agreement with the model equations. Experimental results fit the rate equation somewhat better than the integrated equation when all variable quantities are considered. The coefficient of shear temperature gives the activation enthalpy, which is about 4.7 kilocalories/mole for untreated material and 39.4 kilocalories/mole for asphalt-treated material. This indicates the activation enthalpy is about that of the pore fluid. The proportionality coefficient of deviator stress may be used to measure flow unit volume. The volumes thus determined for untreated and asphalt-treated material are not substantially different. This may be coincidental since comparison with flow unit volumes reported by others indicates flow unit volume is related to gradation of untreated material. The flow unit volume of asphalt-treated material may relate to asphalt cement content. The proposed model equations provide a more rational basis for further studies of factors affecting deformation of granular materials under stress similar to that in pavement subjected to transient traffic loads.

New Catalysts for the Renewable Production of Monomers for Bioplastics

Terephthalic acid (PTA) is one of the monomers used for the synthesis of the polyester, polyethylene terephthalate (PET), that is used for the large-scale manufacture of synthetic fibers and plastic bottles. PTA is largely produced from the liquid-phase oxidation of petroleum-derived p-xylene (PX). However, there are now ongoing worldwide efforts exploring alternative routes for producing PTA from renewable, biomass resources.

In this thesis, I present a new route to PTA starting from the biomass-derived platform chemical, 5-hydroxymethylfurfural (HMF). This route utilizes new, selective Diels-Alder-dehydration reactions involving ethylene and is advantageous over the previously proposed Diels-Alder-dehydration route to PTA from HMF via 2,5-dimethylfuran (DMF) since the H₂ reduction of HMF to DMF is avoided. Specifically, oxidized derivatives of HMF are reacted as is, or after etherification-esterification with methanol, with ethylene over solid Lewis acid catalysts that do not contain strong Brønsted acids in order to synthesize intermediates of PTA and its equally important diester, dimethyl terephthalate (DMT). The partially oxidized HMF, 5-(hydroxymethyl)furoic acid (HMFA) is reacted with high pressure ethylene over a pure-silica molecular sieve catalyst containing framework tin (Sn-Beta) to produce the Diels-Alder-dehydration product, 4-(hydroxymethyl)benzoic acid (HMBA), with ~30% selectivity at ~20% yield. If HMFA is protected with methanol to form methyl 5-(methoxymethyl)furan-2-carboxylate (MMFC), MMFC can react with ethylene in the presence of a pure-silica molecular sieve containing framework zirconium (Zr-Beta) to produce methyl 4-(methoxymethyl)benzenecarboxylate (MMBC) with >70% selectivity at >20% yield. HMBA and MMBC can then be oxidized to produce PTA and DMT, respectively. When Lewis acid containing mesoporous silica (MCM-41) and amorphous silica, or Brønsted acid containing zeolites (Al-Beta), are used as catalysts, a significant decrease in selectivity/yield of the Diels-Alder-dehydration product is observed.

An investigation to elucidate the reaction network and side products in the conversion of MMFC to MMBC was performed, and the main side products are found to be methyl 4-formylcyclohexa-1,3-diene-1-carboxylate and the ethylene Diels-Alder adduct of this cyclohexadiene. These products presumably form by a different dehydration pathway of the MMFC/ethylene Diels-Alder adduct and should be included when determining the overall selectivity to PTA or DMT since, like MMBC, these compounds are precursors to PTA or DMT.

Fundamental physical and chemical information on the ethylene Diels-Alder-dehydration reactions catalyzed by the Lewis acid-containing molecular sieves was obtained. Madon-Boudart experiments using Zr-Beta as catalyst show that the reaction rates are limited by chemical kinetics only (physical transport limitations are not present), all the Zr⁴⁺ centers are incorporated into the framework of the molecular sieve, and the whole molecular sieve crystal is accessible for catalysis. Apparent activation energies using Zr-Beta are low, suggesting that the overall activation energy of the system may be determined by a collection of terms and is not the true activation energy of a single chemical step.

Numerical assessment of the water injection application to GDI engines

A possible future scenario for the water injection (WI) application has been explored as an advanced strategy for modern GDI engines. The aim is to verify whether the PWI (Port Water Injection) and DWI (Direct Water Injection) architectures can replace current fuel enrichment strategies to limit turbine inlet temperatures (TiT) and knock engine attitude. In this way, it might be possible to extend the stoichiometric mixture condition over the entire engine map, meeting possible future restrictions in the use of AES (Auxiliary Emission Strategies) and future emission limitations. The research was first addressed through a comprehensive assessment of the state-of-the-art of the technology and the main effects of the chemical-physical water properties. Then, detailed chemical kinetics simulations were performed in order to compute the effects of WI on combustion development and auto-ignition. The latter represents an important methodology step for accurate numerical combustion simulations. The water injection was then analysed in detail for a PWI system, through an experimental campaign for macroscopic and microscopic injector characterization inside a test chamber. The collected data were used to perform a numerical validation of the spray models, obtaining an excellent matching in terms of particle size and droplet velocity distributions. Finally, a wide range of three-dimensional CFD simulations of a virtual high-bmep engine were realized and compared, exploring also different engine designs and water/fuel injection strategies under non-reacting and reacting flow conditions. According to the latter, it was found that thanks to the introduction of water, for both PWI and DWI systems, it could be possible to obtain an increase of the target performance and an optimization of the bsfc (Break Specific Fuel Consumption), lowering the engine knock risk at the same time, while the TiT target has been achieved hardly only for one DWI configuration.

Correlation Between Testosterone And Psa Kinetics In Metastatic Prostate Cancer Patients Treated With Diverse Chemical Castrations.

To assess total testosterone and prostatic-specific antigen (PSA) kinetics among diverse chemical castrations, advanced-stage prostate cancer patients were randomized into three groups of 20: Group 1, Leuprolide 3.75 mg; Group 2, Leuprolide 7.5 mg; and Group 3, Goserelin 3.6 mg. All groups were treated with monthly application of the respective drugs. The patients' levels of serum total testosterone and PSA were evaluated at two time periods: before the treatment and 3 months after the treatment. Spearman's rank correlation coefficient was utilized to verify the hypothesis of linear correlation between total testosterone and PSA levels. At the beginning the patients' age, stage, grade, PSA, and total testosterone were similar within the three groups, with median age 72, 70, and 70 years in Groups 1, 2, and 3, respectively. Three months after the treatment, patients who received Leuprolide 7.5 mg presented significantly lower median total testosterone levels compared with Goserelin 3.6 mg and Leuprolide 3.75 mg (9.5 ng/dL vs. 20.0 ng/dL vs. 30.0 ng/dL, respectively; p = .0072), while those who received Goserelin 3.6 mg presented significantly lower PSA levels compared with Leuprolide 7.5 mg and Leuprolide 3.75 mg (0.67 vs. 1.86 vs. 2.57, respectively; p = .0067). There was no linear correlation between total testosterone and PSA levels. Overall, regarding castration levels of total testosterone, 28.77% of patients did not obtain levels ≤50 ng/dL and 47.80% did not obtain levels ≤20 ng/dL. There was no correlation between total testosterone and PSA kinetics and no equivalence among different pharmacological castrations.

Dinámica y cinética de los procesos físicos y químicos del radical OH con compuestos orgánicos volátiles (COVs) de relevancia atmosférica. Dynamics and kinetics of the physical and chemical processes of OH radicals with atmospheric relevant volatile organic compounds (VOCs)

El objetivo del presente proyecto es estudiar los procesos físicos y químicos del radical OH con compuestos orgánicos volátiles (COVs), con los cuales sea factible la formación de agregados de van der Waals (vdW) responsables de la curvatura en los gráficos de Arrhenius, empleando técnicas modernas, complementarias entre si y novedosas en el país. El problema será abordado desde tres perspectivas complementarias: 1) estudios cinéticos, 2) estudios mecanísticos y de distribución de productos y 3) estudios de la dinámica de los procesos físicos y químicos. La finalidad es alcanzar una mejor comprensión de los mecanismos que intervienen en el comportamiento químico de especies presentes en la atmósfera y obtener datos cinéticos de alta calidad que puedan alimentar modelos computacionales capaces de describir la composición de la atmósfera, presente y futura. Los objetivos son estudiar: 1) mediante fotólisis láser pulsada con detección por fluorescencia inducida por láser (PLP-LIF), en reactores de flujo, la cinética de reacción del radical OH(v”=0) con COVs que presentan gráficos de Arrhenius curvos con energías de activación negativas, tales como alcoholes insaturados, alquenos halogenados, éteres halogenados, ésteres alifáticos; 2) en una cámara de simulación de condiciones atmosféricas de gran volumen (4500 L), la identidad y el rendimiento de productos de las reacciones mencionadas, a fines de evaluar su impacto atmosférico y dilucidar los mecanismos de reacción; 3) mediante haces moleculares y espectroscopía láser, la estructura y reactividad de complejos de vdW entre alcoholes insaturados o aromáticos (cresoles) y el radical OH, como modelo de los aductos propuestos como responsables de la desviación al comportamiento de Arrhenius de las reacciones mencionadas; 4) mediante PLP-LIF y expansiones supersónicas, las constantes específicas estado a estado (ksts) de relajación/reacción del radical OH(v”=1-4) vibracionalmente excitado con los COVs mencionados. Los resultados experimentales obtenidos serán contrastados con cálculos ab-initio de estructura electrónica, los cuales apoyarán las interpretaciones, permitirán proponer estructuras de estados de transición y aductos colisionales, como así también calcular las frecuencias de vibración de los complejos de vdW para su posterior asignación en los espectros LIF y REMPI. Asimismo, los mecanismos de reacción propuestos y los parámetros cinéticos medidos experimentalmente serán comparados con aquellos obtenidos por cálculos teóricos. The aim of this project is to study the physical and chemical processes of OH radicals with volatile organic compounds (VOCs) with which the formation of van der Waals (vdW) clusters, responsible for the observed curvature in the Arrhenius plots, might be feasible. The problem will be addressed as follow : 1) kinetic studies; 2) products distribution and mechanistic studies and 3) dynamical studies of the physical and chemical processes. The purpose is to obtain a better understanding of the mechanisms that govern the chemical behavior of species present in the atmosphere and to obtain high quality kinetic data to be used as input to computational models. We will study: 1) the reaction kinetics of OH (v”=0) radicals with VOCs such as unsaturated alcohols, halogenated alkenes, halogenated ethers, aliphatic esters, which show curved Arrhenius plots and negative activation energies, by PLP-LIF, in flow systems; 2) in a large volume (4500 L) atmospheric simulation chamber, reaction products yields in order to evaluate their atmospheric impact and reaction mechanisms; 3) using molecular beams and laser spectroscopy, the structure and reactivity of the vdW complexes formed between the unsaturated or aromatic alcohols and the OH radicals as a model of the adducts proposed as responsible for the non-Arrhenius behavior; 4) the specific state-to-state relaxation/reaction rate constants (ksts) of the vibrationally excited OH (v”=1-4) radical with the VOCs by PLP-LIF and supersonic expansions. Ab-initio calculations will be carried out to support the interpretation of the experimental results, to obtain the transition state and collisional adducts structures, as well as to calculate the vibrational frequencies of the vdW complexes to assign to the LIF and REMPI spectra. Also, the proposed reaction mechanisms and the experimentally measured kinetic parameters will be compared with those obtained from theoretical calculations.

Animal manure phosphorus characterization by sequential chemical fractionation, release kinetics and 31P-NMR analysis

Phosphate release kinetics from manures are of global interest because sustainable plant nutrition with phosphate will be a major concern in the future. Although information on the bioavailability and chemical composition of P present in manure used as fertilizer are important to understand its dynamics in the soil, such studies are still scarce. Therefore, P extraction was evaluated in this study by sequential chemical fractionation, desorption with anion-cation exchange resin and 31P nuclear magnetic resonance (31P-NMR) spectroscopy to assess the P forms in three different dry manure types (i.e. poultry, cattle and swine manure). All three methods showed that the P forms in poultry, cattle and swine dry manures are mostly inorganic and highly bioavailable. The estimated P pools showed that organic and recalcitrant P forms were negligible and highly dependent on the Ca:P ratio in manures. The results obtained here showed that the extraction of P with these three different methods allows a better understanding and complete characterization of the P pools present in the manures.

Gas-phase kinetics of chlorosilylene reactions II. ClSiH + C2H4: absolute rate measurements and quantum chemical and RRKM calculations for the prototype pi addition reaction

Time-resolved studies of chlorosilylene, ClSiH, generated by the 193 nm laser flash photolysis of 1-chloro-1-silacyclopent-3-ene, are carried out to obtain rate constants for its bimolecular reaction with ethene, C2H4, in the gas-phase. The reaction is studied over the pressure range 0.13-13.3 kPa (with added SF6) at five temperatures in the range 296-562 K. The second order rate constants, obtained by extrapolation to the high pressure limits at each temperature, fitted the Arrhenius equation: log(k(infinity)/cm(3) molecule(-1) s(-1))=(-10.55 +/- 0.10) + (3.86 +/- 0.70) kJ mol(-1)/RT ln10. The Arrhenius parameters correspond to a loose transition state and the rate constant at room temperature is 43% of that for SiH2 + C2H4, showing that the deactivating effect of Cl-for-H substitution in the silylene is not large. Quantum chemical calculations of the potential energy surface for this reaction at the G3MP2//B3LYP level show that, as well as 1-chlorosilirane, ethylchlorosilylene is a viable product. The calculations reveal how the added effect of the Cl atom on the divalent state stabilisation of ClSiH influences the course of this reaction. RRKM calculations of the reaction pressure dependence suggest that ethylchlorosilylene should be the main product. The results are compared and contrasted with those of SiH2 and SiCl2 with C2H4.

The gas-phase reaction between silylene and 2-butyne: kinetics, isotope studies, pressure dependence studies and quantum chemical calculations

Time-resolved kinetic studies of the reactions of silylene, SiH2, and dideutero-silylene, SiD2, generated by laser. ash photolysis of phenylsilane and phenylsilane-d(3), respectively, have been carried out to obtain rate coefficients for their bimolecular reactions with 2-butyne, CH3C CCH3. The reactions were studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas at five temperatures in the range 294-612 K. The second-order rate coefficients, obtained by extrapolation to the high pressure limits at each temperature, fitted the Arrhenius equations where the error limits are single standard deviations: log(k(H)(infinity)/cm(3) molecule(-1) s(-1)) = (-9.67 +/- 0.04) + (1.71 +/- 0.33) kJ mol(-1)/RTln10 log(k(D)(infinity)/cm(3) molecule(-1) s(-1)) = (-9.65 +/- 0.01) + (1.92 +/- 0.13) kJ mol(-1)/RTln10 Additionally, pressure-dependent rate coefficients for the reaction of SiH2 with 2-butyne in the presence of He (1-100 Torr) were obtained at 301, 429 and 613 K. Quantum chemical (ab initio) calculations of the SiC4H8 reaction system at the G3 level support the formation of 2,3-dimethylsilirene [cyclo-SiH2C(CH3)=C(CH3)-] as the sole end product. However, reversible formation of 2,3-dimethylvinylsilylene [CH3CH=C(CH3)SiH] is also an important process. The calculations also indicate the probable involvement of several other intermediates, and possible products. RRKM calculations are in reasonable agreement with the pressure dependences at an enthalpy value for 2,3-dimethylsilirene fairly close to that suggested by the ab initio calculations. The experimental isotope effects deviate significantly from those predicted by RRKM theory. The differences can be explained by an isotopic scrambling mechanism, involving H - D exchange between the hydrogens of the methyl groups and the D-atoms in the ring in 2,3-dimethylsilirene-1,1-d(2). A detailed mechanism involving several intermediate species, which is consistent with the G3 energy surface, is proposed to account for this.