Modeling intrinsic noise and delays in chemical kinetics of coupled autoregulated oscillating cells

Delays are an important feature in temporal models of genetic regulation due to slow biochemical processes, such as transcription and translation. In this paper, we show how to model intrinsic noise effects in a delayed setting by either using a delay stochastic simulation algorithm (DSSA) or, for larger and more complex systems, a generalized Binomial τ-leap method (Bτ-DSSA). As a particular application, we apply these ideas to modeling somite segmentation in zebra fish across a number of cells in which two linked oscillatory genes (her1 and her7) are synchronized via Notch signaling between the cells.

A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

Clinical strategies for the alleviation of contractures from a predictive mathematical model of dermal repair

Hypertrophic scars arise when there is an overproduction of collagen during wound healing. These are often associated with poor regulation of the rate of programmed cell death(apoptosis) of the cells synthesizing the collagen or by an exuberant inflammatory response that prolongs collagen production and increases wound contraction. Severe contractures that occur, for example, after a deep burn can cause loss of function especially if the wound is over a joint such as the elbow or knee. Recently, we have developed a morphoelastic mathematical model for dermal repair that incorporates the chemical, cellular and mechanical aspects of dermal wound healing. Using this model, we examine pathological scarring in dermal repair by first assuming a smaller than usual apoptotic rate for myofibroblasts, and then considering a prolonged inflammatory response, in an attempt to determine a possible optimal intervention strategy to promote normal repair, or terminate the fibrotic scarring response. Our model predicts that in both cases it is best to apply the intervention strategy early in the wound healing response. Further, the earlier an intervention is made, the less aggressive the intervention required. Finally, if intervention is conducted at a late time during healing, a significant intervention is required; however, there is a threshold concentration of the drug or therapy applied, above which minimal further improvement to wound repair is obtained.

A continuum model of the growth of engineered epidermal skin substitutes

We present a porous medium model of the growth and deterioration of the viable sublayers of an epidermal skin substitute. It consists of five species: cells, intracellular and extracellular calcium, tight junctions, and a hypothesised signal chemical emanating from the stratum corneum. The model is solved numerically in Matlab using a finite difference scheme. Steady state calcium distributions are predicted that agree well with the experimental data. Our model also demonstrates epidermal skin substitute deterioration if the calcium diffusion coefficient is reduced compared to reported values in the literature.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Understanding QC and EQA : an authentic learning model for undergraduate students (Conference Abstract)

Introduction QC and EQA are integral to good pathology laboratory practice. Medical Laboratory Science students undertake a project exploring internal QC and EQA procedures used in chemical pathology laboratories. Each student represents an individual lab and the class group represents the peer group of labs performing the same assay using the same method. Methods Using a manual BCG assay for serum albumin, normal and abnormal controls are run with a patient sample over 7 weeks. The QC results are assessed each week using calculated z-scores and both 2S & 3S control rules to determine whether a run is ‘in control’. At the end of the 7 weeks a completed LJ chart is assessed using the Westgard Multirules. Students investigate causes of error and the implications for both lab practice and patient care if runs are not ‘in control’. Twice in the 7 weeks two EQA samples (with target values unknown) are assayed alongside the weekly QC and patient samples. Results from each student are collated and form the basis of an EQA program. ALP are provided and students complete a Youden Plot, which is used to analyse the performance of each ‘lab’ and the method to identify bias. Students explore the concept of possible clinical implications of a biased method and address the actions that should be taken if a lab is not in consensus with the peer group. Conclusion This project is a model of ‘real world’ practice in which student demonstrate an understanding of the importance of QC procedures in a pathology laboratory, apply and interpret statistics and QC rules and charts, apply critical thinking and analytical skills to quality performance data to make recommendations for further practice and improve their technical competence and confidence.

Synthesis of an erodible biomimetic hydrogel for drug delivery using native chemical ligation

Hydrogels are hydrophilic, three dimensional polymers that imbibe large quantities of water while remaining insoluble in aqueous solutions due to chemical or physical cross-linking. The polymers swell in water or biological fluids, immobilizing the bioactive agent, leading to drug release in a well-defined specific manner. Thus the hydrogels’ elastic properties, swellability and biocompatibility make them excellent formulations for drug delivery. Currently, many drug potencies and therapeutic effects are limited or otherwise reduced because of the partial degradation that occurs before the administered drug reaches the desired site of action. On the other hand, sustained release medications release drugs continually, rather than providing relief of symptoms and protection solely when necessary. In fact, it would be much better if drugs could be administered in a manner that precisely matches physiological needs at desired times and at the desired site (site specific targeting). There is therefore an unmet need to develop controlled drug delivery systems especially for delivery of peptide and protein bound drugs. The purpose of this project is to produce hydrogels for structural drug delivery and time-dependent sustained release of drugs (bioactive agents). We use an innovative polymerisation strategy based on native chemical ligation (NCL) to covalently cross-link polymers to form hydrogels. When mixed in aqueous solution, four armed (polyethylene glycol) amine (PEG-4A) end functionalised with thioester and four branched Nterminal cysteine peptide dendrimers spontaneously conjugated to produce biomimetic hydrogels. These hydrogels showed superior resistance to shear stress compared to an equivalent PEG macromonomer system and were shown to be proteolytically degradable with concomitant release of a model payload molecule. This is the first report of a peptide dendrimers/PEG macromonomer approach to hydrogel production and opens up the prospect of facile hydrogel synthesis together with tailored payload release.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

A combined temperature-programmed reaction spectroscopy and Fourier-transform infrared spectroscopy study of CO2/H2 and CO/CO2/H2 interactions with model ZnO/SiO2, Cu/SiO2 and Cu/ZnO/SiO2 methanol-synthesis catalysts

The reaction of CO2 and H2 with ZnO/SiO2 catalyst at 295 K gave predominantly hydrogencarbonate on zinc oxide and a small quantity of formate was evolved after heating at 393 K. Elevation of the reaction temperature to 503 K enhanced the rate of formation of zinc formate species. Significantly these formate species decomposed at 573 K almost entirely to CO2 and H2. Even after exposure of CO2-H2 or CO-CO2-H2 mixtures to highly defected ZnO/SiO2 catalyst, the formate species produced still decomposed to give CO2 and H2. It was concluded that carboxylate species which were formed at oxygen anion vacancies on polar Zn planes were not significantly hydrogenated to formate. Consequently it was proposed that the non-polar planes on zinc oxide contained sites which were specific for the synthesis of methanol. The interaction of CO2 and H2 with reduced Cu/ZnO/SiO2 catalyst at 393 K gave copper formate species in addition to substantial quantities of formate created at interfacial sites between copper and zinc oxide. It was deduced that interfacial formate species were produced from the hydrogenation of interfacial bidentate carbonate structures. The relevance of interfacial formate species in the methanol synthesis reaction is discussed. Experiments concerning the reaction of CO2-H2 with physical mixtures of Cu/SiO2 and ZnO/SiO2 gave results which were simply characteristic of the individual components. By careful consideration of previous data a detailed proposal regarding the role of spillover hydrogen is outlined. Admission of CO to a gaseous CO2-H2 feedstock resulted in a considerably diminished amount of formate species on copper. This was ascribed to a combination of over-reduction of the surface and site-blockage.

Effect of chemical conjugation of L-leucine to chitosan on the dispersibility and drug release of a dry powder inhaler nanoparticle formulation

Purpose: This study investigated the effect of chemical conjugation of the amino acid L-leucine to the polysaccharide chitosan on the dispersibility and drug release pattern of a polymeric nanoparticle (NP)-based controlled release dry powder inhaler (DPI) formulation. Methods: A chemical conjugate of L-leucine with chitosan was synthesized and characterized by Infrared (IR) Spectroscopy, Nuclear Magnetic Resonance (NMR) Spectroscopy, Elemental Analysis and X-ray Photoelectron Spectroscopy (XPS). Nanoparticles of both chitosan and its conjugate were prepared by a water-in-oil emulsification – glutaraldehyde cross-linking method using the antihypertensive agent, diltiazem (Dz) hydrochloride as the model drug. The surface morphology and particle size distribution of the nanoparticles were determined by Scanning Electron Microscopy (SEM) and Dynamic Light Scattering (DLS). The dispersibility of the nanoparticle formulation was analysed by a Twin Stage Impinger (TSI) with a Rotahaler as the DPI device. Deposition of the particles in the different stages was determined by gravimetry and the amount of drug released was analysed by UV spectrophotometry. The release profile of the drug was studied in phosphate buffered saline at 37 ⁰C and analyzed by UV spectrophotometry. Results: The TSI study revealed that the fine particle fractions (FPF), as determined gravimetrically, for empty and drug-loaded conjugate nanoparticles were significantly higher than for the corresponding chitosan nanoparticles (24±1.2% and 21±0.7% vs 19±1.2% and 15±1.5% respectively; n=3, p<0.05). The FPF of drug-loaded chitosan and conjugate nanoparticles, in terms of the amount of drug determined spectrophotometrically, had similar values (21±0.7% vs 16±1.6%). After an initial burst, both chitosan and conjugate nanoparticles showed controlled release that lasted about 8 to 10 days, but conjugate nanoparticles showed twice as much total drug release compared to chitosan nanoparticles (~50% vs ~25%). Conjugate nanoparticles also showed significantly higher dug loading and entrapment efficiency than chitosan nanoparticles (conjugate: 20±1% & 46±1%, chitosan: 16±1% & 38±1%, n=3, p<0.05). Conclusion: Although L-leucine conjugation to chitosan increased dispersibility of formulated nanoparticles, the FPF values are still far from optimum. The particles showed a high level of initial burst release (chitosan, 16% and conjugate, 31%) that also will need further optimization.

Toxic state–corporate crimes, Neo-liberalism and green criminology : the hazards and legacies of the oil, chemical and mineral industries

This paper uses examples from the history and practices of multi-national and large companies in the oil, chemical and asbestos industries to examine their legal and illegal despoiling and destruction of the environment and impact on human and non-human life. The discussion draws on the literature on green criminology and state-corporate crime and considers measures and arrangements that might mitigate or prevent such damaging acts. This paper is part of ongoing work on green criminology and crimes of the economy. It places these actions and crimes in the context of a global neo-liberal economic system and considers and critiques the distorting impact of the GDP model of ‘economic health’ and its consequences for the environment.

Estimation of biodiesel properties from chemical composition – An artificial neural network (ANN) approach

Biodiesel, produced from renewable feedstock represents a more sustainable source of energy and will therefore play a significant role in providing the energy requirements for transportation in the near future. Chemically, all biodiesels are fatty acid methyl esters (FAME), produced from raw vegetable oil and animal fat. However, clear differences in chemical structure are apparent from one feedstock to the next in terms of chain length, degree of unsaturation, number of double bonds and double bond configuration-which all determine the fuel properties of biodiesel. In this study, prediction models were developed to estimate kinematic viscosity of biodiesel using an Artificial Neural Network (ANN) modelling technique. While developing the model, 27 parameters based on chemical composition commonly found in biodiesel were used as the input variables and kinematic viscosity of biodiesel was used as output variable. Necessary data to develop and simulate the network were collected from more than 120 published peer reviewed papers. The Neural Networks Toolbox of MatLab R2012a software was used to train, validate and simulate the ANN model on a personal computer. The network architecture and learning algorithm were optimised following a trial and error method to obtain the best prediction of the kinematic viscosity. The predictive performance of the model was determined by calculating the coefficient of determination (R2), root mean squared (RMS) and maximum average error percentage (MAEP) between predicted and experimental results. This study found high predictive accuracy of the ANN in predicting fuel properties of biodiesel and has demonstrated the ability of the ANN model to find a meaningful relationship between biodiesel chemical composition and fuel properties. Therefore the model developed in this study can be a useful tool to accurately predict biodiesel fuel properties instead of undertaking costly and time consuming experimental tests.

Multiscale coupling and multiphysics approaches in earth sciences : theory

Measuring Earth material behaviour on time scales of millions of years transcends our current capability in the laboratory. We review an alternative path considering multiscale and multiphysics approaches with quantitative structure-property relationships. This approach allows a sound basis to incorporate physical principles such as chemistry, thermodynamics, diffusion and geometry-energy relations into simulations and data assimilation on the vast range of length and time scales encountered in the Earth. We identify key length scales for Earth systems processes and find a substantial scale separation between chemical, hydrous and thermal diffusion. We propose that this allows a simplified two-scale analysis where the outputs from the micro-scale model can be used as inputs for meso-scale simulations, which then in turn becomes the micro-model for the next scale up. We present two fundamental theoretical approaches to link the scales through asymptotic homogenisation from a macroscopic thermodynamic view and percolation renormalisation from a microscopic, statistical mechanics view.

Capital cost model for Robert evaporators

ROBERT EVAPORATORS in Australian sugar factories are traditionally constructed with 44.45 mm outside diameter stainless steel tubes of ~2 m length for all stages of evaporation. There are a few vessels with longer tubes (up to 2.8 m) and smaller and larger diameters (38.1 and 50.8 mm). Queensland University of Technology is undertaking a study to investigate the heat transfer performance of tubes of different lengths and diameters for the whole range of process conditions typically encountered in the evaporator set. Incorporation of these results into practical evaporator designs requires an understanding of the cost implications for constructing evaporator vessels with calandrias having tubes of different dimensions. Cost savings are expected for tubes of smaller diameter and longer length in terms of material, labour and installation costs in the factory. However these savings must be considered in terms of the heat transfer area requirements for the evaporation duty, which will likely be a function of the tube dimensions. In this paper a capital cost model is described which provides a relative cost of constructing and installing Robert evaporators of the same heating surface area but with different tube dimensions. Evaporators of 2000, 3000, 4000 and 5000 m2 are investigated. This model will be used in conjunction with the heat transfer efficiency data (when available) to determine the optimum tube dimensions for a new evaporator at a specified evaporation duty. Consideration is also given to other factors such as juice residence time (and implications for sucrose degradation and control) and droplet de-entrainment in evaporators of different tube dimensions.