A control theoretic paradigm for cell signaling networks : a simple complexity for a sensitive robustness

The fields of molecular biology and cell biology are being flooded with complex genomic and proteomic datasets of large dimensions. We now recognize that each molecule in the cell and tissue can no longer be viewed as an isolated entity. Instead, each molecule must be considered as one member of an interacting network. Consequently, there is an urgent need for mathematical models to understand the behavior of cell signaling networks in health and in disease.

The amplified peptidome : the new treasure chest of candidate biomarkers

Mass spectrometric analysis of the low-molecular weight (LMW) range of the serum/plasma proteome is revealing the existence of large numbers of previously unknown peptides and protein fragments predicted to be derived from low- abundance proteins. This raises the question of why such low abundance molecules would be retained at detectable levels in the circulation, instead of being rapidly cleared and excreted. Theoretical models of biomarker production and association with serum carrier proteins have been developed to elucidate the mechanisms governing biomarker half-life in the bloodstream. These models predict that the vast majority of LMW biomarkers exist in association with circulating high molecular mass carrier proteins. Moreover, the total serum/ plasma concentration of the biomarker is largely determined by the clearance rate of the carrier protein, not the free-phase biomarker clearance itself. These predictions have been verified experimentally using molecular mass fractionation of human serum before mass spectrometry sequence analysis. These principles have profound implications for biomarker discovery and measurement.

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.

Serosorting may increase the risk of HIV acquisition among men who have sex with men

Background: Serosorting, the practice of seeking to engage in unprotected anal intercourse with partners of the same HIV status as oneself, has been increasing among men who have sex with men. However, the effectiveness of serosorting as a strategy to reduce HIV risk is unclear, especially since it depends on the frequency of HIV testing. Methods: We estimated the relative risk of HIV acquisition associated with serosorting compared with not serosorting by using a mathematical model, informed by detailed behavioral data from a highly studied cohort of gay men. Results: We demonstrate that serosorting is unlikely to be highly beneficial in many populations of men who have sex with men, especially where the prevalence of undiagnosed HIV infections is relatively high. We find that serosorting is only beneficial in reducing the relative risk of HIV transmission if the prevalence of undiagnosed HIV infections is less than ∼20% and ∼40%, in populations of high (70%) and low (20%) treatment rates, respectively, even though treatment reduces the absolute risk of HIV transmission. Serosorting can be expected to lead to increased risk of HIV acquisition in many settings. In settings with low HIV testing rates serosorting can more than double the risk of HIV acquisition. Conclusions: Therefore caution should be taken before endorsing the practice of serosorting. It is very important to continue promotion of frequent HIV testing and condom use, particularly among people at high risk.

Mathematical modelling of intramembranous bone formation during fracture healing

During fracture healing, many complex and cryptic interactions occur between cells and bio-chemical molecules to bring about repair of damaged bone. In this thesis two mathematical models were developed, concerning the cellular differentiation of osteoblasts (bone forming cells) and the mineralisation of new bone tissue, allowing new insights into these processes. These models were mathematically analysed and simulated numerically, yielding results consistent with experimental data and highlighting the underlying pattern formation structure in these aspects of fracture healing.

Multiphase porous media model for heat and mass transfer during drying of agricultural products

Modelling of food processing is complex because it involves sophisticated material and transport phenomena. Most of the agricultural products such fruits and vegetables are hygroscopic porous media containing free water, bound water, gas and solid matrix. Considering all phase in modelling is still not developed. In this article, a comprehensive porous media model for drying has been developed considering bound water, free water separately, as well as water vapour and air. Free water transport was considered as diffusion, pressure driven and evaporation. Bound water assumed to be converted to free water due to concentration difference and also can diffuse. Binary diffusion between water vapour and air was considered. Since, the model is fundamental physics based it can be applied to any drying applications and other food processing where heat and mass transfer takes place in porous media with significant evaporation and other phase change.

Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

A framework for model integration and holistic modelling of socio-technical systems

This paper presents a layered framework for the purposes of integrating different Socio-Technical Systems (STS) models and perspectives into a whole-of-systems model. Holistic modelling plays a critical role in the engineering of STS due to the interplay between social and technical elements within these systems and resulting emergent behaviour. The framework decomposes STS models into components, where each component is either a static object, dynamic object or behavioural object. Based on existing literature, a classification of the different elements that make up STS, whether it be a social, technical or a natural environment element, is developed; each object can in turn be classified according to the STS elements it represents. Using the proposed framework, it is possible to systematically decompose models to an extent such that points of interface can be identified and the contextual factors required in transforming the component of one model to interface into another is obtained. Using an airport inbound passenger facilitation process as a case study socio-technical system, three different models are analysed: a Business Process Modelling Notation (BPMN) model, Hybrid Queue-based Bayesian Network (HQBN) model and an Agent Based Model (ABM). It is found that the framework enables the modeller to identify non-trivial interface points such as between the spatial interactions of an ABM and the causal reasoning of a HQBN, and between the process activity representation of a BPMN and simulated behavioural performance in a HQBN. Such a framework is a necessary enabler in order to integrate different modelling approaches in understanding and managing STS.

Correcting flaws in Mitchell’s analysis of EPBC

Efficient error-Propagating Block Chaining (EPBC) is a block cipher mode intended to simultaneously provide both confidentiality and integrity protection for messages. Mitchell’s analysis pointed out a weakness in the EPBC integrity mechanism that can be used in a forgery attack. This paper identifies and corrects a flaw in Mitchell’s analysis of EPBC, and presents other attacks on the EPBC integrity mechanism.

Mathematical models of calcium and tight junctions in normal and reconstructed epidermis

This project investigated the calcium distributions of the skin, and the growth patterns of skin substitutes grown in the laboratory, using mathematical models. The research found that the calcium distribution in the upper layer of the skin is controlled by three different mechanisms, not one as previously thought. The research also suggests that tight junctions, which are adhesions between neighbouring skin cells, cannot be solely responsible for the differences in the growth patterns of skin substitutes and normal skin.