Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

A model to estimate the durability performance of both normal and light-weight concrete

There has been an increasing focus on the development of test methods to evaluate the durability performance of concrete. This paper contributes to this focus by presenting a study that evaluates the effect of water accessible porosity and oven-dry unit weight on the resistance of both normal and light-weight concrete to chloride-ion penetration. Based on the experimental results and regression analyses, empirical models are established to correlate the total charge passed and the chloride migration coefficient with the basic properties of concrete such as water accessible porosity, oven dry unit weight, and compressive strength. These equations can be broadly applied to both normal and lightweight aggregate concretes. The model was also validated by an independent set of experimental results from two different concrete mixtures. The model provides a very good estimate on the concrete’s durability performance in respect to the resistance to chloride ion penetration.

A novel ambiguity acceptance test threshold determination method with controllable failure rate

Ambiguity validation as an important procedure of integer ambiguity resolution is to test the correctness of the fixed integer ambiguity of phase measurements before being used for positioning computation. Most existing investigations on ambiguity validation focus on test statistic. How to determine the threshold more reasonably is less understood, although it is one of the most important topics in ambiguity validation. Currently, there are two threshold determination methods in the ambiguity validation procedure: the empirical approach and the fixed failure rate (FF-) approach. The empirical approach is simple but lacks of theoretical basis. The fixed failure rate approach has a rigorous probability theory basis, but it employs a more complicated procedure. This paper focuses on how to determine the threshold easily and reasonably. Both FF-ratio test and FF-difference test are investigated in this research and the extensive simulation results show that the FF-difference test can achieve comparable or even better performance than the well-known FF-ratio test. Another benefit of adopting the FF-difference test is that its threshold can be expressed as a function of integer least-squares (ILS) success rate with specified failure rate tolerance. Thus, a new threshold determination method named threshold function for the FF-difference test is proposed. The threshold function method preserves the fixed failure rate characteristic and is also easy-to-apply. The performance of the threshold function is validated with simulated data. The validation results show that with the threshold function method, the impact of the modelling error on the failure rate is less than 0.08%. Overall, the threshold function for the FF-difference test is a very promising threshold validation method and it makes the FF-approach applicable for the real-time GNSS positioning applications.

Clinoenstatite coatings have high bonding strength, bioactive ion release, and osteoimmunomodulatory effects that enhance in vivo osseointegration

A number of coating materials have been developed over past two decades seeking to improve the osseointegration of orthopedic metal implants. Despite the many candidate materials trialed, their low rate of translation into clinical applications suggests there is room for improving the current strategies for their development. We therefore propose that the ideal coating material(s) should possess the following three properties: (i) high bonding strength, (ii) release of functional ions, and (iii) favourable osteoimmunomodulatory effects. To test this proposal, we developed clinoenstatite (CLT, MgSiO3), which as a coating material has high bonding strength, cytocompability and immunomodulatory effects that are favourable for in vivo osteogenesis. The bonding strength of CLT coatings was 50.1 ± 3.2 MPa, more than twice that of hydroxyapatite (HA) coatings, at 23.5 ± 3.5 MPa. CLT coatings released Mg and Si ions, and compared to HA coatings, induced an immunomodulation more conducive for osseointegration, demonstrated by downregurelation of pro-inflammatory cytokines, enhancement of osteogenesis, and inhibition of osteoclastogenesis. In vivo studies demonstrated that CLT coatings improved osseointegration with host bone, as shown by the enhanced biomechanical strength and increased de novo bone formation, when compared with HA coatings. These results support the notion that coating materials with the proposed properties can induce an in vivo environment better suited for osseointegration. These properties could, therefore, be fundamental when developing high-performance coating materials.

Effect of ion nitriding on the microstructure and properties of Maraging steel (250 Grade)

In the present investigation, ion nitriding of Maraging steel (250 grade) has been carried out at three different temperatures i.e., at 435 degrees C, 450 degrees C and 465 degrees C for 10 h duration in order to achieve good wear resistance along with high strength required for the slat track component of aircraft. The microstructure of the base material and the nitrided layer was examined by optical and scanning electron microscope, and various phases present were determined by X-ray diffraction. Various properties, such as, hardness, case depth, tensile, impact, fatigue properties and corrosion resistance were investigated for both un-nitrided and ion-nitrided materials. It is observed that the microstructure of the core material remains unaltered and Fe4N is formed in the hardened surface layer after ion nitriding at all the three temperatures employed. Surface hardness increases substantially after ion nitriding. Surface hardness remains almost the same but case depth increases with the increase in ion nitriding temperature due to greater diffusivity at higher temperatures. Tensile strength, fatigue strength and corrosion resistance are improved but ductility and energy absorbed in impact test decrease on ion nitriding. These results are explained on the basis of microstructural observations. The properties obtained after ion nitriding at 450 degrees C for 10 h are found to be optimum when compared to the other two ion nitriding temperatures.

A high-density association screen of 155 ion transport genes for involvement with common migraine

The clinical overlap between monogenic Familial Hemiplegic Migraine (FHM) and common migraine subtypes, and the fact that all three FHM genes are involved in the transport of ions, suggest that ion transport genes may underlie susceptibility to common forms of migraine. To test this leading hypothesis, we examined common variation in 155 ion transport genes using 5257 single nucleotide polymorphisms (SNPs) in a Finnish sample of 841 unrelated migraine with aura cases and 884 unrelated non-migraine controls. The top signals were then tested for replication in four independent migraine case-control samples from the Netherlands, Germany and Australia, totalling 2835 unrelated migraine cases and 2740 unrelated controls. SNPs within 12 genes (KCNB2, KCNQ3, CLIC5, ATP2C2, CACNA1E, CACNB2, KCNE2, KCNK12, KCNK2, KCNS3, SCN5A and SCN9A) with promising nominal association (0.00041 < P < 0.005) in the Finnish sample were selected for replication. Although no variant remained significant after adjusting for multiple testing nor produced consistent evidence for association across all cohorts, a significant epistatic interaction between KCNB2 SNP rs1431656 (chromosome 8q13.3) and CACNB2 SNP rs7076100 (chromosome 10p12.33) (pointwise P = 0.00002; global P = 0.02) was observed in the Finnish case-control sample. We conclude that common variants of moderate effect size in ion transport genes do not play a major role in susceptibility to common migraine within these European populations, although there is some evidence for epistatic interaction between potassium and calcium channel genes, KCNB2 and CACNB2. Multiple rare variants or trans-regulatory elements of these genes are not ruled out.

Factors influencing kinetic and equilibrium behaviour of sodium ion exchange with strong acid cation resin

This study reports an investigation of the ion exchange treatment of sodium chloride solutions in relation to use of resin technology for applications such as desalination of brackish water. In particular, a strong acid cation (SAC) resin (DOW Marathon C) was studied to determine its capacity for sodium uptake and to evaluate the fundamentals of the ion exchange process involved. Key questions to answer included: impact of resin identity; best models to simulate the kinetics and equilibrium exchange behaviour of sodium ions; difference between using linear least squares (LLS) and non-linear least squares (NLLS) methods for data interpretation; and, effect of changing the type of anion in solution which accompanied the sodium species. Kinetic studies suggested that the exchange process was best described by a pseudo first order rate expression based upon non-linear least squares analysis of the test data. Application of the Langmuir Vageler isotherm model was recommended as it allowed confirmation that experimental conditions were sufficient for maximum loading of sodium ions to occur. The Freundlich expression best fitted the equilibrium data when analysing the information by a NLLS approach. In contrast, LLS methods suggested that the Langmuir model was optimal for describing the equilibrium process. The Competitive Langmuir model which considered the stoichiometric nature of ion exchange process, estimated the maximum loading of sodium ions to be 64.7 g Na/kg resin. This latter value was comparable to sodium ion capacities for SAC resin published previously. Inherent discrepancies involved when using linearized versions of kinetic and isotherm equations were illustrated, and despite their widespread use, the value of this latter approach was questionable. The equilibrium behaviour of sodium ions form sodium fluoride solution revealed that the sodium ions were now more preferred by the resin compared to the situation with sodium chloride. The solution chemistry of hydrofluoric acid was suggested as promoting the affinity of the sodium ions to the resin.

The oxygen migration in the apatite-type lanthanum silicate with the cation substitution

A theoretical model is proposed to determine the effects of Si substitution with Al on the oxygen diffusion in apatite-type lanthanum silicates based on density-functional theory (DFT) calculations for La10(SiO 4)4(AlO4)2O2. Substitution changes the stable configuration for excess oxygen from the split interstitial to a new cluster form with the original cluster. Al doping completely changes the migration mechanism from the interstitialcy one, which was proposed for the La9.33(SiO4)6O2 starting material, to a mechanism which contains an interstitial process. Nevertheless, the migration barrier is calculated to be 0.81 eV, which indicates small changes in oxygen conduction and is consistent with the observations. The present study indicates that the cation substitution on silicon site alone does not promise the improvement of the oxide ion conduction in the lanthanum silicate.

Position preference and diffusion path of an oxygen ion in apatite-type lanthanum silicate La9.33Si6O26: A density functional study

Using density functional theory, we investigated the position preference and diffusion mechanisms of interstitial oxygen ions in lanthanum silicate La9.33Si6O26, which is an apatite-structured oxide and a promising candidate electrolyte material for solid oxide fuel cells. The reported lanthanum vacancies were explicitly taken into account by theoretically determining their arrangement with a supercell model. The most stable structures and the formation energies of oxygen interstitials were determined for each charged state. It was found that the double-negatively charged state is stable over a wide range of the Fermi level, and that the excess oxygen ions form split interstitials with the original oxygen ions, while the neutral and the single-negatively charged states preferably form molecular oxygen. These species were found near the lanthanum vacancy site. The theoretically determined migration pathway along the c-axis essentially follows an interstitialcy mechanism. The obtained migration barrier is sensitive to the charge state, and is also affected by the lanthanum vacancy. The barrier height of the double-negatively charged state was calculated to be 0.58 eV for the model structure, which is consistent with the measured activation energy.

BDST modelling of sodium ion exchange column behaviour with strong acid cation resin in relation to coal seam water treatment

Reverse osmosis is the dominant technology utilized for desalination of saline water produced during the extraction of coal seam gas. Alternatively, ion exchange is of interest due to potential cost advantages. However, there is limited information regarding the column performance of strong acid cation resin for removal of sodium ions from both model and actual coal seam water samples. In particular, the impact of bed depth, flow rate, and regeneration was not clear. Consequently, this study applied Bed Depth Service Time (BDST) models to reveal that increasing sodium ion concentration and flow rates diminished the time required for breakthrough to occur. The loading of sodium ions on fresh resin was calculated to be ca. 71.1 g Na/kg resin. Difficulties in regeneration of the resin using hydrochloric acid solutions were discovered, with 86% recovery of exchange sites observed. The maximum concentration of sodium ions in the regenerant brine was found to be 47,400 mg/L under the conditions employed. The volume of regenerant waste formed was 6.2% of the total volume of water treated. A coal seam water sample was found to load the resin with only 53.5 g Na/kg resin, which was consistent with not only the co-presence of more favoured ions such as calcium, magnesium, barium and strontium, but also inefficient regeneration of the resin prior to the coal seam water test.

Influence of carbide particles on the dynamic recrystallization of as-cast 304 stainless steel: a study using secondary ion mass spectrometric (SIMS) analysis

The domain of dynamic recrystallization (DRX) in as-cast 304 stainless steel material occurs at higher temperatures (1250 degrees C) and lower strain rates (0.001 s(-1)) than in wrought 304 stainless steel (1100 degrees C and 0.01 s(-1)). The above result has been explained earlier on the basis of a simple theoretical DRX model involving the rate of nucleation versus rate of grain boundary migration. The present investigation is aimed at examining experimentally the influence of carbide particles on the DRX of ascast 304 using secondary ion mass spectrometric (SIMS) analysis. Isothermal compression tests at a constant true strain rate have been performed on wrought 304 and as-cast 304 materials in the temperature and strain rate ranges of 1000 to 1250 degrees C and 0.001 to 1 s(-1) respectively. The SIMS analysis carried out on the deformed samples revealed that the large carbides present in the as-cast 304 material strongly influence the DRX process. In as-cast 304 material, the presence of large carbide particles in the microstructure shifts the DRX domain to higher temperature and lower strain rate in comparison with wrought 304 material.

Structure and silver ion transport in AgI-Ag2MoO4 glasses: A molecular dynamics study

The structure and dynamics of silver ion conducting AgI-Ag2MoO4 glasses have been simulated by molecular dynamics simulation over a wide range of compositions. Formation of silver iodide like aggregates have been identified only in the AgI rich glasses. Increase in silver ion conductivity with an increase in AgI content in the glass is seen as in experiments. The dynamics of ion transport suggests that Ag+ ion transport occurs largely through paths connected by silver ion sites of mixed iodide-oxide coordination. The Van Hove correlation functions indicate that Ag+ ions prefer migration along the pathways formed with connected sites of similar coordination.

One step synthesis of monoclinic VO2 (B) bundles of nanorods: Cathode for Li ion battery

One of the metastable phases of vanadium dioxide, VO2(B) bundles of nanorods and microspheres have been synthesized through a simple hydrothermal method by dispersing V2O5 in aqueous quinol. The obtained products were characterized by X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy (SEM) and electrochemical discharge-charge test for lithium battery. It was found that the morphologies of the obtained VO2(B) can be tuned by manipulating the relative amount of quinol. The electrochemical test found that the bundles of nanorods exhibit an initial discharge capacity of 171 mAh g(-1) and its almost stabilized capacity was reached to 108 mAh g(-1) after 47 cycles at a current density of 0.1 mA g(-1). The formation mechanism of the VO2(B) bundles of nanorods and microspheres was also discussed. (C) 2012 Elsevier Inc. All rights reserved.

Stereoselective geminal difunctionalization of vinyl arenes mediated by the bromonium ion

An anti-Markovnikov geminal oxyamination of styrenyl alkenes in an intermolecular fashion using the umpolung strategy mediated by the bromonium ion is reported. Isotope labeling studies confirm the migration of the phenyl group in the semipinacol rearrangement.

Mining Unit Tests for Discovery and Migration of Math APIs

Today's programming languages are supported by powerful third-party APIs. For a given application domain, it is common to have many competing APIs that provide similar functionality. Programmer productivity therefore depends heavily on the programmer's ability to discover suitable APIs both during an initial coding phase, as well as during software maintenance. The aim of this work is to support the discovery and migration of math APIs. Math APIs are at the heart of many application domains ranging from machine learning to scientific computations. Our approach, called MATHFINDER, combines executable specifications of mathematical computations with unit tests (operational specifications) of API methods. Given a math expression, MATHFINDER synthesizes pseudo-code comprised of API methods to compute the expression by mining unit tests of the API methods. We present a sequential version of our unit test mining algorithm and also design a more scalable data-parallel version. We perform extensive evaluation of MATHFINDER (1) for API discovery, where math algorithms are to be implemented from scratch and (2) for API migration, where client programs utilizing a math API are to be migrated to another API. We evaluated the precision and recall of MATHFINDER on a diverse collection of math expressions, culled from algorithms used in a wide range of application areas such as control systems and structural dynamics. In a user study to evaluate the productivity gains obtained by using MATHFINDER for API discovery, the programmers who used MATHFINDER finished their programming tasks twice as fast as their counterparts who used the usual techniques like web and code search, IDE code completion, and manual inspection of library documentation. For the problem of API migration, as a case study, we used MATHFINDER to migrate Weka, a popular machine learning library. Overall, our evaluation shows that MATHFINDER is easy to use, provides highly precise results across several math APIs and application domains even with a small number of unit tests per method, and scales to large collections of unit tests.