Mathematical models for collective cell spreading

Collective cell spreading is frequently observed in development, tissue repair and disease progression. Mathematical modelling used in conjunction with experimental investigation can provide key insights into the mechanisms driving the spread of cell populations. In this study, we investigated how experimental and modelling frameworks can be used to identify several key features underlying collective cell spreading. In particular, we were able to independently quantify the roles of cell motility and cell proliferation in a spreading cell population, and investigate how these roles are influenced by factors such as the initial cell density, type of cell population and the assay geometry.

Bayesian parametric bootstrap for models with intractable likelihoods

In this paper it is demonstrated how the Bayesian parametric bootstrap can be adapted to models with intractable likelihoods. The approach is most appealing when the semi-automatic approximate Bayesian computation (ABC) summary statistics are selected. After a pilot run of ABC, the likelihood-free parametric bootstrap approach requires very few model simulations to produce an approximate posterior, which can be a useful approximation in its own right. An alternative is to use this approximation as a proposal distribution in ABC algorithms to make them more efficient. In this paper, the parametric bootstrap approximation is used to form the initial importance distribution for the sequential Monte Carlo and the ABC importance and rejection sampling algorithms. The new approach is illustrated through a simulation study of the univariate g-and- k quantile distribution, and is used to infer parameter values of a stochastic model describing expanding melanoma cell colonies.

Assessing testamentary and decision-making capacity: Approaches and models

The need for better and more accurate assessments of testamentary and decision-making capacity grows as Australian society ages and incidences of mentally disabling conditions increase. Capacity is a legal determination, but one on which medical opinion is increasingly being sought. The difficulties inherent within capacity assessments are exacerbated by the ad hoc approaches adopted by legal and medical professionals based on individual knowledge and skill, as well as the numerous assessment paradigms that exist. This can negatively affect the quality of assessments, and results in confusion as to the best way to assess capacity. This article begins by assessing the nature of capacity. The most common general assessment models used in Australia are then discussed, as are the practical challenges associated with capacity assessment. The article concludes by suggesting a way forward to satisfactorily assess legal capacity given the significant ramifications of getting it wrong.

Modelling interregional links in electricity price spikes

Abnormally high price spikes in spot electricity markets represent a significant risk to market participants. As such, a literature has developed that focuses on forecasting the probability of such spike events, moving beyond simply forecasting the level of price. Many univariate time series models have been proposed to dealwith spikes within an individual market region. This paper is the first to develop a multivariate self-exciting point process model for dealing with price spikes across connected regions in the Australian National Electricity Market. The importance of the physical infrastructure connecting the regions on the transmission of spikes is examined. It is found that spikes are transmitted between the regions, and the size of spikes is influenced by the available transmission capacity. It is also found that improved risk estimates are obtained when inter-regional linkages are taken into account.

Cultural adaptation and resilience: Controversies, issues and emerging models

What enables people to bounce back from stressful experiences? How do certain individuals maintain a sense of purpose and direction over the long term, even in the face of adversity? This is the first book to move beyond childhood and adolescence to explore resilience across the lifespan. Coverage ranges from genetic and physiological factors through personal, family, organizational, and community processes. Contributors examine how resilience contributes to health and well-being across the adult life cycle; why—and what happens when—resilience processes fail; ethnic and cultural dimensions of resilience; and ways to enhance adult resilience, including reviews of exemplary programs.

N-ethyl-N-nitrosourea (ENU) induced mutations within the Klotho gene lead to ectopic calcification and reduced lifespan in mouse models

Ectopic calcification (EC), which is the pathological deposition of calcium and phosphate in extra-skeletal tissues, may be associated with hypercalcaemic and hyperphosphataemic disorders, or it may occur in the absence of metabolic abnormalities. In addition, EC may be inherited as part of several monogenic disorders and studies of these have provided valuable insights into the metabolic pathways regulating mineral metabolism. For example, studies of tumoural calcinosis, a disorder characterised by hyperphosphataemia and progressive EC, have revealed mutations of fibroblast growth factor 23 (FGF23), polypeptide N-acetyl galactosaminyltransferase 3 (GALNT3) and klotho (KL), which are all part of a phosphate-regulating pathway. However, such studies in humans are limited by the lack of available large families with EC, and to facilitate such studies we assessed the progeny of mice treated with the chemical mutagen N-ethyl-N-nitrosourea (ENU) for EC. This identified two mutants with autosomal recessive forms of EC, and reduced lifespan, designated Ecalc1 and Ecalc2. Genetic mapping localized the Ecalc1 and Ecalc2 loci to a 11.0 Mb region on chromosome 5 that contained the klotho gene (Kl), and DNA sequence analysis identified nonsense (Gln203Stop) and missense (Ile604Asn) Kl mutations in Ecalc1 and Ecalc2 mice, respectively. The Gln203Stop mutation, located in KL1 domain, was severely hypomorphic and led to a 17-fold reduction of renal Kl expression. The Ile604Asn mutation, located in KL2 domain, was predicted to impair klotho protein stability and in vitro expression studies in COS-7 cells revealed endoplasmic reticulum retention of the Ile604Asn mutant. Further phenotype studies undertaken in Ecalc1 (kl203X/203X) mice demonstrated elevations in plasma concentrations of phosphate, FGF23 and 1,25-dihydroxyvitamin D. Thus, two allelic variants of Kl that develop EC and represent mouse models for tumoural calcinosis have been established. © 2015 Esapa et al.

Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.

Revisiting the Task-Capability interface model for incorporating human factors into car-following models

Human factors such as distraction, fatigue, alcohol and drug use are generally ignored in car-following (CF) models. Such ignorance overestimates driver capability and leads to most CF models’ inability in realistically explaining human driving behaviors. This paper proposes a novel car-following modeling framework by introducing the difficulty of driving task measured as the dynamic interaction between driving task demand and driver capability. Task difficulty is formulated based on the famous Task Capability Interface (TCI) model, which explains the motivations behind driver’s decision making. The proposed method is applied to enhance two popular CF models: Gipps’ model and IDM, and named as TDGipps and TDIDM respectively. The behavioral soundness of TDGipps and TDIDM are discussed and their stabilities are analyzed. Moreover, the enhanced models are calibrated with the vehicle trajectory data, and validated to explain both regular and human factor influenced CF behavior (which is distraction caused by hand-held mobile phone conversation in this paper). Both the models show better performance than their predecessors, especially in presence of human factors.

Predicting surgical outcomes for paediatric spinal deformity patients using subject specific finite element models

INTRODUCTION Adolescent idiopathic scoliosis (AIS) is a spinal deformity, which may require surgical correction by attaching rods to the patient’s spine using screws inserted into the vertebrae. Complication rates for deformity correction surgery are unacceptably high. Determining an achievable correction without overloading the adjacent spinal tissues or implants requires an understanding of the mechanical interaction between these components. Our novel patient specific modelling software creates individualized finite element models (FEM) representing the thoracolumbar spine and ribcage of scoliosis patients. We have recently applied the model to investigate the influence of increasing magnitudes of surgically applied corrective force on predicted deformity correction...

Analysis of complex molecular systems: The impact of multivariate analysis for resolving the interactions of small molecules with biopolymers - a review

This review is focused on the impact of chemometrics for resolving data sets collected from investigations of the interactions of small molecules with biopolymers. These samples have been analyzed with various instrumental techniques, such as fluorescence, ultraviolet–visible spectroscopy, and voltammetry. The impact of two powerful and demonstrably useful multivariate methods for resolution of complex data—multivariate curve resolution–alternating least squares (MCR–ALS) and parallel factor analysis (PARAFAC)—is highlighted through analysis of applications involving the interactions of small molecules with the biopolymers, serum albumin, and deoxyribonucleic acid. The outcomes illustrated that significant information extracted by the chemometric methods was unattainable by simple, univariate data analysis. In addition, although the techniques used to collect data were confined to ultraviolet–visible spectroscopy, fluorescence spectroscopy, circular dichroism, and voltammetry, data profiles produced by other techniques may also be processed. Topics considered including binding sites and modes, cooperative and competitive small molecule binding, kinetics, and thermodynamics of ligand binding, and the folding and unfolding of biopolymers. Applications of the MCR–ALS and PARAFAC methods reviewed were primarily published between 2008 and 2013.

Adjustable stiffness, external fixator for the rat femur osteotomy and segmental bone defect models

The mechanical environment around the healing of broken bone is very important as it determines the way the fracture will heal. Over the past decade there has been great clinical interest in improving bone healing by altering the mechanical environment through the fixation stability around the lesion. One constraint of preclinical animal research in this area is the lack of experimental control over the local mechanical environment within a large segmental defect as well as osteotomies as they heal. In this paper we report on the design and use of an external fixator to study the healing of large segmental bone defects or osteotomies. This device not only allows for controlled axial stiffness on the bone lesion as it heals, but it also enables the change of stiffness during the healing process in vivo. The conducted experiments have shown that the fixators were able to maintain a 5 mm femoral defect gap in rats in vivo during unrestricted cage activity for at least 8 weeks. Likewise, we observed no distortion or infections, including pin infections during the entire healing period. These results demonstrate that our newly developed external fixator was able to achieve reproducible and standardized stabilization, and the alteration of the mechanical environment of in vivo rat large bone defects and various size osteotomies. This confirms that the external fixation device is well suited for preclinical research investigations using a rat model in the field of bone regeneration and repair.

Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

Mimicking breast cancer-induced bone metastasis in vivo: Current transplantation models and advanced humanized strategies

Bone metastasis is a complication that occurs in 80 % of women with advanced breast cancer. Despite the prevalence of bone metastatic disease, the avenues for its clinical management are still restricted to palliative treatment options. In fact, the underlying mechanisms of breast cancer osteotropism have not yet been fully elucidated due to a lack of suitable in vivo models that are able to recapitulate the human disease. In this work, we review the current transplantation-based models to investigate breast cancer-induced bone metastasis and delineate the strengths and limitations of the use of different grafting techniques, tissue sources, and hosts. We further show that humanized xenograft models incorporating human cells or tissue grafts at the primary tumor site or the metastatic site mimic more closely the human disease. Tissue-engineered constructs are emerging as a reproducible alternative to recapitulate functional humanized tissues in these murine models. The development of advanced humanized animal models may provide better platforms to investigate the mutual interactions between human cancer cells and their microenvironment and ultimately improve the translation of preclinical drug trials to the clinic.

Population of computational rabbit-specific ventricular action potential models for investigating sources of variability in cellular repolarisation

Variability is observed at all levels of cardiac electrophysiology. Yet, the underlying causes and importance of this variability are generally unknown, and difficult to investigate with current experimental techniques. The aim of the present study was to generate populations of computational ventricular action potential models that reproduce experimentally observed intercellular variability of repolarisation (represented by action potential duration) and to identify its potential causes. A systematic exploration of the effects of simultaneously varying the magnitude of six transmembrane current conductances (transient outward, rapid and slow delayed rectifier K(+), inward rectifying K(+), L-type Ca(2+), and Na(+)/K(+) pump currents) in two rabbit-specific ventricular action potential models (Shannon et al. and Mahajan et al.) at multiple cycle lengths (400, 600, 1,000 ms) was performed. This was accomplished with distributed computing software specialised for multi-dimensional parameter sweeps and grid execution. An initial population of 15,625 parameter sets was generated for both models at each cycle length. Action potential durations of these populations were compared to experimentally derived ranges for rabbit ventricular myocytes. 1,352 parameter sets for the Shannon model and 779 parameter sets for the Mahajan model yielded action potential duration within the experimental range, demonstrating that a wide array of ionic conductance values can be used to simulate a physiological rabbit ventricular action potential. Furthermore, by using clutter-based dimension reordering, a technique that allows visualisation of multi-dimensional spaces in two dimensions, the interaction of current conductances and their relative importance to the ventricular action potential at different cycle lengths were revealed. Overall, this work represents an important step towards a better understanding of the role that variability in current conductances may play in experimentally observed intercellular variability of rabbit ventricular action potential repolarisation.

Mixture models of nucleotide sequence evolution that account for heterogeneity in the substitution process across sites and across lineages

Molecular phylogenetic studies of homologous sequences of nucleotides often assume that the underlying evolutionary process was globally stationary, reversible, and homogeneous (SRH), and that a model of evolution with one or more site-specific and time-reversible rate matrices (e.g., the GTR rate matrix) is enough to accurately model the evolution of data over the whole tree. However, an increasing body of data suggests that evolution under these conditions is an exception, rather than the norm. To address this issue, several non-SRH models of molecular evolution have been proposed, but they either ignore heterogeneity in the substitution process across sites (HAS) or assume it can be modeled accurately using the distribution. As an alternative to these models of evolution, we introduce a family of mixture models that approximate HAS without the assumption of an underlying predefined statistical distribution. This family of mixture models is combined with non-SRH models of evolution that account for heterogeneity in the substitution process across lineages (HAL). We also present two algorithms for searching model space and identifying an optimal model of evolution that is less likely to over- or underparameterize the data. The performance of the two new algorithms was evaluated using alignments of nucleotides with 10 000 sites simulated under complex non-SRH conditions on a 25-tipped tree. The algorithms were found to be very successful, identifying the correct HAL model with a 75% success rate (the average success rate for assigning rate matrices to the tree's 48 edges was 99.25%) and, for the correct HAL model, identifying the correct HAS model with a 98% success rate. Finally, parameter estimates obtained under the correct HAL-HAS model were found to be accurate and precise. The merits of our new algorithms were illustrated with an analysis of 42 337 second codon sites extracted from a concatenation of 106 alignments of orthologous genes encoded by the nuclear genomes of Saccharomyces cerevisiae, S. paradoxus, S. mikatae, S. kudriavzevii, S. castellii, S. kluyveri, S. bayanus, and Candida albicans. Our results show that second codon sites in the ancestral genome of these species contained 49.1% invariable sites, 39.6% variable sites belonging to one rate category (V1), and 11.3% variable sites belonging to a second rate category (V2). The ancestral nucleotide content was found to differ markedly across these three sets of sites, and the evolutionary processes operating at the variable sites were found to be non-SRH and best modeled by a combination of eight edge-specific rate matrices (four for V1 and four for V2). The number of substitutions per site at the variable sites also differed markedly, with sites belonging to V1 evolving slower than those belonging to V2 along the lineages separating the seven species of Saccharomyces. Finally, sites belonging to V1 appeared to have ceased evolving along the lineages separating S. cerevisiae, S. paradoxus, S. mikatae, S. kudriavzevii, and S. bayanus, implying that they might have become so selectively constrained that they could be considered invariable sites in these species.