Mathematical modeling of the cancer cell’s control circuitry : paving the way to individualized therapeutic strategies

Cancer is a disease of signal transduction in which the dysregulation of the network of intracellular and extracellular signaling cascades is sufficient to thwart the cells finely-tuned biochemical control mechanisms. A keen interest in the mathematical modeling of cell signaling networks and the regulation of signal transduction has emerged in recent years, and has produced a glimmer of insight into the sophisticated feedback control and network regulation operating within cells. In this review, we present an overview of published theoretical studies on the control aspects of signal transduction, emphasizing the role and importance of mechanisms such as ‘ultrasensitivity’ and feedback loops. We emphasize that these exquisite and often subtle control strategies represent the key to orchestrating ‘simple’ signaling behaviors within the complex intracellular network, while regulating the trade-off between sensitivity and robustness to internal and external perturbations. Through a consideration of these apparent paradoxes, we explore how the basic homeostasis of the intracellular signaling network, in the face of carcinogenesis, can lead to neoplastic progression rather than cell death. A simple mathematical model is presented, furnishing a vivid illustration of how ‘control-oriented’ models of the deranged signaling networks in cancer cells may enucleate improved treatment strategies, including patient-tailored combination therapies, with the potential for reduced toxicity and more robust and potent antitumor activity.

Gravity-induced coronal plane joint moments in the adolescent scoliotic spine

INTRODUCTION Calculating segmental (vertebral level-by-level) torso masses in Adolescent Idiopathic Scoliosis (AIS) patients allows the gravitational loading on the scoliotic spine during relaxed standing to be estimated. METHODS Existing low dose CT scans were used to calculate vertebral level-by-level torso masses and joint moments occurring in the spine for a group of female AIS patients with right-sided thoracic curves. Image processing software, ImageJ (v1.45 NIH USA) was used to reconstruct the torso segments and subsequently measure the torso volume and mass corresponding to each vertebral level. Body segment masses for the head, neck and arms were taken from published anthropometric data. Intervertebral joint moments at each vertebral level were found by summing each of the torso segment masses above the required joint and multiplying it by the perpendicular distance to the centre of the disc. RESULTS AND DISCUSSION Twenty patients were included in this study with a mean age of 15.0±2.7 years and a mean Cobb angle 52±5.9°. The mean total trunk mass, as a percentage of total body mass, was 27.8 (SD 0.5) %. Mean segmental torso mass increased inferiorly from 0.6kg at T1 to 1.5kg at L5. The coronal plane joint moments during relaxed standing were typically 5-7Nm at the apex of the curve (Figure 1), with the highest apex joint of 7Nm. CT scans were performed in the supine position and curve magnitudes are known to be 7-10° smaller than those measured in standing [1]. Therefore joint moments produced by gravity will be greater than those calculated here. CONCLUSIONS Coronal plane joint moments as high as 7Nm can occur during relaxed standing in scoliosis patients, which may help to explain the mechanics of AIS progression. The body mass distributions calculated in this study can be used to estimate joint moments derived using other imaging modalities such as MRI and subsequently determine if a relationship exists between joint moments and progressive vertebral deformity.

People’s perceptions about the importance of forests on Borneo

We ascertained villagers’ perceptions about the importance of forests for their livelihoods and health through 1,837 reliably answered interviews of mostly male respondents from 185 villages in Indonesian and Malaysian Borneo. Variation in these perceptions related to several environmental and social variables, as shown in classification and regression analyses. Overall patterns indicated that forest use and cultural values are highest among people on Borneo who live close to remaining forest, and especially among older Christian residents. Support for forest clearing depended strongly on the scale at which deforestation occurs. Deforestation for small-scale agriculture was generally considered to be positive because it directly benefits people’s welfare. Large-scale deforestation (e.g., for industrial oil palm or acacia plantations), on the other hand, appeared to be more context-dependent, with most respondents considering it to have overall negative impacts on them, but with people in some areas considering the benefits to outweigh the costs. The interviews indicated high awareness of negative environmental impacts of deforestation, with high levels of concern over higher temperatures, air pollution and loss of clean water sources. Our study is unique in its geographic and trans-national scale. Our findings enable the development of maps of forest use and perceptions that could inform land use planning at a range of scales. Incorporating perspectives such as these could significantly reduce conflict over forest resources and ultimately result in more equitable development processes.

Compatibility of stormwater treatment performance data between different geographical areas

Using a case study approach, this paper presents a robust methodology for assessing the compatibility of stormwater treatment performance data between two geographical regions in relation to a treatment system. The desktop analysis compared data derived from a field study undertaken in Florida, USA, with South East Queensland (SEQ) rainfall and pollutant characteristics. The analysis was based on the hypothesis that when transposing treatment performance information from one geographical region to another, detailed assessment of specific rainfall and stormwater quality parameters is required. Accordingly, characteristics of measured rainfall events and stormwater quality in the Florida study were compared with typical characteristics for SEQ. Rainfall events monitored in the Florida study were found to be similar to events that occur in SEQ in terms of their primary characteristics of depth, duration and intensity. Similarities in total suspended solids (TSS) and total nitrogen (TN) concentration ranges for Florida and SEQ suggest that TSS and TN removal performances would not be very different if the treatment system is installed in SEQ. However, further investigations are needed to evaluate the treatment performance of total phosphorus (TP). The methodology presented also allows comparison of other water quality parameters.

A review of modern computational algorithms for Bayesian optimal design

Bayesian experimental design is a fast growing area of research with many real-world applications. As computational power has increased over the years, so has the development of simulation-based design methods, which involve a number of algorithms, such as Markov chain Monte Carlo, sequential Monte Carlo and approximate Bayes methods, facilitating more complex design problems to be solved. The Bayesian framework provides a unified approach for incorporating prior information and/or uncertainties regarding the statistical model with a utility function which describes the experimental aims. In this paper, we provide a general overview on the concepts involved in Bayesian experimental design, and focus on describing some of the more commonly used Bayesian utility functions and methods for their estimation, as well as a number of algorithms that are used to search over the design space to find the Bayesian optimal design. We also discuss other computational strategies for further research in Bayesian optimal design.

Mathematical Models of Tumor-Immune System Dynamics

"This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction between the immune system and a growing tumor. The multidimensional nature of these complex interactions requires a cross-disciplinary approach to capture more realistic dynamics of the essential biology. The papers presented in this volume explore these issues and the results will be of interest to graduate students and researchers in a variety of fields within mathematical and biological sciences."--Publisher website

Mathematical modelling of fumigant transport in stored grain

Computational fluid dynamics, analytical solutions, and mathematical modelling approaches are used to gain insights into the distribution of fumigant gas within farm-scale, grain storage silos. Both fan-forced and tablet fumigation are considered in this work, which develops new models for use by researchers, primary producers and silo manufacturers to assist in the eradication grain storage pests.

The choice of spatial scales and spatial smoothness priors for various spatial patterns

Given the drawbacks for using geo-political areas in mapping outcomes unrelated to geo-politics, a compromise is to aggregate and analyse data at the grid level. This has the advantage of allowing spatial smoothing and modelling at a biologically or physically relevant scale. This article addresses two consequent issues: the choice of the spatial smoothness prior and the scale of the grid. Firstly, we describe several spatial smoothness priors applicable for grid data and discuss the contexts in which these priors can be employed based on different aims. Two such aims are considered, i.e., to identify regions with clustering and to model spatial dependence in the data. Secondly, the choice of the grid size is shown to depend largely on the spatial patterns. We present a guide on the selection of spatial scales and smoothness priors for various point patterns based on the two aims for spatial smoothing.

What is the apparent angle of a Kelvin ship wave pattern?

While the half-angle which encloses a Kelvin ship wave pattern is commonly accepted to be 19.47 degrees, recent observations and calculations for sufficiently fast-moving ships suggest that the apparent wake angle decreases with ship speed. One explanation for this decrease in angle relies on the assumption that a ship cannot generate wavelengths much greater than its hull length. An alternative interpretation is that the wave pattern that is observed in practice is defined by the location of the highest peaks; for wakes created by sufficiently fast-moving objects, these highest peaks no longer lie on the outermost divergent waves, resulting in a smaller apparent angle. In this paper, we focus on the problems of free surface flow past a single submerged point source and past a submerged source doublet. In the linear version of these problems, we measure the apparent wake angle formed by the highest peaks, and observe the following three regimes: a small Froude number pattern, in which the divergent waves are not visible; standard wave patterns for which the maximum peaks occur on the outermost divergent waves; and a third regime in which the highest peaks form a V-shape with an angle much less than the Kelvin angle. For nonlinear flows, we demonstrate that nonlinearity has the effect of increasing the apparent wake angle so that some highly nonlinear solutions have apparent wake angles that are greater than Kelvin's angle. For large Froude numbers, the effect on apparent wake angle can be more dramatic, with the possibility of strong nonlinearity shifting the wave pattern from the third regime to the second. We expect our nonlinear results will translate to other more complicated flow configurations, such as flow due to a steadily moving closed body such as a submarine.

A computational model for BMP movement in sea urchin embryos

Bone morphogen proteins (BMPs) are distributed along a dorsal-ventral (DV) gradient in many developing embryos. The spatial distribution of this signaling ligand is critical for correct DV axis specification. In various species, BMP expression is spatially localized, and BMP gradient formation relies on BMP transport, which in turn requires interactions with the extracellular proteins Short gastrulation/Chordin (Chd) and Twisted gastrulation (Tsg). These binding interactions promote BMP movement and concomitantly inhibit BMP signaling. The protease Tolloid (Tld) cleaves Chd, which releases BMP from the complex and permits it to bind the BMP receptor and signal. In sea urchin embryos, BMP is produced in the ventral ectoderm, but signals in the dorsal ectoderm. The transport of BMP from the ventral ectoderm to the dorsal ectoderm in sea urchin embryos is not understood. Therefore, using information from a series of experiments, we adapt the mathematical model of Mizutani et al. (2005) and embed it as the reaction part of a one-dimensional reaction–diffusion model. We use it to study aspects of this transport process in sea urchin embryos. We demonstrate that the receptor-bound BMP concentration exhibits dorsally centered peaks of the same type as those observed experimentally when the ternary transport complex (Chd-Tsg-BMP) forms relatively quickly and BMP receptor binding is relatively slow. Similarly, dorsally centered peaks are created when the diffusivities of BMP, Chd, and Chd-Tsg are relatively low and that of Chd-Tsg-BMP is relatively high, and the model dynamics also suggest that Tld is a principal regulator of the system. At the end of this paper, we briefly compare the observed dynamics in the sea urchin model to a version that applies to the fly embryo, and we find that the same conditions can account for BMP transport in the two types of embryos only if Tld levels are reduced in sea urchin compared to fly.

Including nonequilibrium interface kinetics in a continuum model for melting nanoscaled particles

The melting temperature of a nanoscaled particle is known to decrease as the curvature of the solid-melt interface increases. This relationship is most often modelled by a Gibbs--Thomson law, with the decrease in melting temperature proposed to be a product of the curvature of the solid-melt interface and the surface tension. Such a law must break down for sufficiently small particles, since the curvature becomes singular in the limit that the particle radius vanishes. Furthermore, the use of this law as a boundary condition for a Stefan-type continuum model is problematic because it leads to a physically unrealistic form of mathematical blow-up at a finite particle radius. By numerical simulation, we show that the inclusion of nonequilibrium interface kinetics in the Gibbs--Thomson law regularises the continuum model, so that the mathematical blow up is suppressed. As a result, the solution continues until complete melting, and the corresponding melting temperature remains finite for all time. The results of the adjusted model are consistent with experimental findings of abrupt melting of nanoscaled particles. This small-particle regime appears to be closely related to the problem of melting a superheated particle.

Treatment for prevention of HIV transmission in a localised epidemic : the case for South Australia

Background: Discussion is currently taking place among international HIV/AIDS groups around increasing HIV testing and initiating earlier use of antiretroviral therapy (ART) among people diagnosed with HIV as a method to reduce the spread of HIV. In this study, we explore the expected epidemiological impact of this strategy in a small population in which HIV transmission is predominantly confined to men who have sex with men (MSM). Methods: A deterministic mathematical transmission model was constructed to investigate the impacts of strategies that increase testing and treatment rates, and their likely potential to mitigate HIV epidemics among MSM. Our novel model distinguishes men in the population who are more easily accessible to prevention campaigns through engagement with the gay community from men who are not. This model is applied to the population of MSM in South Australia. Results: Our model-based findings suggest that increasing testing rates alone will have minimal impact on reducing the expected number of infections compared to current conditions. However, in combination with increases in treatment coverage, this strategy could lead to a 59–68% reduction in the number of HIV infections over the next 5 years. Targeting men who are socially engaged with the gay community would result in the majority of potential reductions in incidence, with only minor improvements possible by reaching all other MSM. Conclusions: Investing in strategies that will achieve higher coverage and earlier initiation of treatment to reduce infectiousness of HIV-infected individuals could be an effective strategy for reducing incidence in a population of MSM.

Conceptual and statistical framework for a water quality component of the integrated report card for the Great Barrier Reef catchments

This report presents the final deliverable from the project titled Conceptual and statistical framework for a water quality component of an integrated report card’ funded by the Marine and Tropical Sciences Research Facility (MTSRF; Project 3.7.7). The key management driver of this, and a number of other MTSRF projects concerned with indicator development, is the requirement for state and federal government authorities and other stakeholders to provide robust assessments of the present ‘state’ or ‘health’ of regional ecosystems in the Great Barrier Reef (GBR) catchments and adjacent marine waters. An integrated report card format, that encompasses both biophysical and socioeconomic factors, is an appropriate framework through which to deliver these assessments and meet a variety of reporting requirements. It is now well recognised that a ‘report card’ format for environmental reporting is very effective for community and stakeholder communication and engagement, and can be a key driver in galvanising community and political commitment and action. Although a report card it needs to be understandable by all levels of the community, it also needs to be underpinned by sound, quality-assured science. In this regard this project was to develop approaches to address the statistical issues that arise from amalgamation or integration of sets of discrete indicators into a final score or assessment of the state of the system. In brief, the two main issues are (1) selecting, measuring and interpreting specific indicators that vary both in space and time, and (2) integrating a range of indicators in such a way as to provide a succinct but robust overview of the state of the system. Although there is considerable research and knowledge of the use of indicators to inform the management of ecological, social and economic systems, methods on how to best to integrate multiple disparate indicators remain poorly developed. Therefore the objective of this project was to (i) focus on statistical approaches aimed at ensuring that estimates of individual indicators are as robust as possible, and (ii) present methods that can be used to report on the overall state of the system by integrating estimates of individual indicators. It was agreed at the outset, that this project was to focus on developing methods for a water quality report card. This was driven largely by the requirements of Reef Water Quality Protection Plan (RWQPP) and led to strong partner engagement with the Reef Water Quality Partnership.

Predicting reduced driver alertness on monotonous highways : a driving simulator study

Impaired driver alertness increases the likelihood of drivers’ making mistakes and reacting too late to unexpected events while driving. This is particularly a concern on monotonous roads, where a driver’s attention can decrease rapidly. While effective countermeasures do not currently exist, the development of in-vehicle sensors opens avenues for monitoring driving behavior in real-time. The aim of this study is to predict drivers’ level of alertness through surrogate measures collected from in-vehicle sensors. Electroencephalographic activity is used as a reference to evaluate alertness. Based on a sample of 25 drivers, data was collected in a driving simulator instrumented with an eye tracking system, a heart rate monitor and an electrodermal activity device. Various classification models were tested from linear regressions to Bayesians and data mining techniques. Results indicated that Neural Networks were the most efficient model in detecting lapses in alertness. Findings also show that reduced alertness can be predicted up to 5 minutes in advance with 90% accuracy, using surrogate measures such as time to line crossing, blink frequency and skin conductance level. Such a method could be used to warn drivers of their alertness level through the development of an in-vehicle device monitoring, in real-time, drivers' behavior on highways.