Control of cell state transitions.

Understanding cell state transitions and purposefully controlling them is a longstanding challenge in biology. Here we present cell state transition assessment and regulation (cSTAR), an approach for mapping cell states, modelling transitions between them and predicting targeted interventions to convert cell fate decisions. cSTAR uses omics data as input, classifies cell states, and develops a workflow that transforms the input data into mechanistic models that identify a core signalling network, which controls cell fate transitions by influencing whole-cell networks. By integrating signalling and phenotypic data, cSTAR models how cells manoeuvre in Waddington's landscape1 and make decisions about which cell fate to adopt. Notably, cSTAR devises interventions to control the movement of cells in Waddington's landscape. Testing cSTAR in a cellular model of differentiation and proliferation shows a high correlation between quantitative predictions and experimental data. Applying cSTAR to different types of perturbation and omics datasets, including single-cell data, demonstrates its flexibility and scalability and provides new biological insights. The ability of cSTAR to identify targeted perturbations that interconvert cell fates will enable designer approaches for manipulating cellular development pathways and mechanistically underpinned therapeutic interventions.

Estimating the conditional probability of developing human papilloma virus related oropharyngeal cancer by combining machine learning and inverse Bayesian modelling.

The epidemic increase in the incidence of Human Papilloma Virus (HPV) related Oropharyngeal Squamous Cell Carcinomas (OPSCCs) in several countries worldwide represents a significant public health concern. Although gender neutral HPV vaccination programmes are expected to cause a reduction in the incidence rates of OPSCCs, these effects will not be evident in the foreseeable future. Secondary prevention strategies are currently not feasible due to an incomplete understanding of the natural history of oral HPV infections in OPSCCs. The key parameters that govern natural history models remain largely ill-defined for HPV related OPSCCs and cannot be easily inferred from experimental data. Mathematical models have been used to estimate some of these ill-defined parameters in cervical cancer, another HPV related cancer leading to successful implementation of cancer prevention strategies. We outline a "double-Bayesian" mathematical modelling approach, whereby, a Bayesian machine learning model first estimates the probability of an individual having an oral HPV infection, given OPSCC and other covariate information. The model is then inverted using Bayes' theorem to reverse the probability relationship. We use data from the Surveillance, Epidemiology, and End Results (SEER) cancer registry, SEER Head and Neck with HPV Database and the National Health and Nutrition Examination Surveys (NHANES), representing the adult population in the United States to derive our model. The model contains 8,106 OPSCC patients of which 73.0% had an oral HPV infection. When stratified by age, sex, marital status and race/ethnicity, the model estimated a higher conditional probability for developing OPSCCs given an oral HPV infection in non-Hispanic White males and females compared to other races/ethnicities. The proposed Bayesian model represents a proof-of-concept of a natural history model of HPV driven OPSCCs and outlines a strategy for estimating the conditional probability of an individual's risk of developing OPSCC following an oral HPV infection.

Mapping connections in signaling networks with ambiguous modularity.

Modular Response Analysis (MRA) is a suite of methods that under certain assumptions permits the precise reconstruction of both the directions and strengths of connections between network modules from network responses to perturbations. Standard MRA assumes that modules are insulated, thereby neglecting the existence of inter-modular protein complexes. Such complexes sequester proteins from different modules and propagate perturbations to the protein abundance of a downstream module retroactively to an upstream module. MRA-based network reconstruction detects retroactive, sequestration-induced connections when an enzyme from one module is substantially sequestered by its substrate that belongs to a different module. Moreover, inferred networks may surprisingly depend on the choice of protein abundances that are experimentally perturbed, and also some inferred connections might be false. Here, we extend MRA by introducing a combined computational and experimental approach, which allows for a computational restoration of modular insulation, unmistakable network reconstruction and discrimination between solely regulatory and sequestration-induced connections for a range of signaling pathways. Although not universal, our approach extends MRA methods to signaling networks with retroactive interactions between modules arising from enzyme sequestration effects.

Repeatability analysis of airborne electromagnetic surveys.

PURPOSE: We provide methods for determining the repeatability of airborne electromagnetic surveys when conducted at different altitudes over a number of repeated flights. Our data arise from the TELLUS project carried out by the Geological Surveys of Ireland and Northern Ireland and we examine the repeatability of the apparent resistivity at different frequencies. METHODS: After considering a number of issues with the data, we propose two different models from the functional data analysis literature; a Weiner process with random effects, and a penalised spline smoother. RESULTS: Both methods arrive at the same conclusion regarding repeatability of the data; results obtained are more repeatable for flights at lower altitudes. CONCLUSIONS: The target altitude for aircraft carrying out airborne electromagnetic surveys should be as low as possible.

Mathematical methods in systems biology.

The editors of this Special Issue of Mathematical Biosciences and Engineering were the organizers for the Third International Workshop "Mathematical Methods in System Biology" that took place on June 15-18, 2015 at the University College Dublin in Ireland. As stated in the workshop goals, we managed to attract a good mix of mathematicians and statisticians working on biological and medical applications with biologists and clinicians interested in presenting their challenging problems and looking to find mathematical and statistical tools for their solutions.

A model of thermotherapy treatment for bladder cancer.

In this work, we investigate chemo- thermotherapy, a recently clinically-approved post-surgery treatment of non muscle invasive urothelial bladder carcinoma. We developed a mathematical model and numerically simulated the physical processes related to this treatment. The model is based on the conductive Maxwell's equations used to simulate the therapy administration and Convection-Diffusion equation for incompressible fluid to study heat propagation through the bladder tissue. The model parameters correspond to the data provided by the thermotherapy device manufacturer. We base our computational domain on a CT image of a human bladder. Our numerical simulations can be applied to further research on the effects of chemo- thermotherapy on bladder and surrounding tissues and for treatment personalization in order to maximize the effect of the therapy while avoiding burning of the bladder.

Modeling and simulation of a low-grade urinary bladder carcinoma.

In this work, we present a mathematical model of the initiation and progression of a low-grade urinary bladder carcinoma. We simulate the crucial processes affecting tumor growth, such as oxygen diffusion, carcinogen penetration, and angiogenesis, within the framework of the urothelial cell dynamics. The cell dynamics are modeled using the discrete technique of cellular automata, while the continuous processes of carcinogen penetration and oxygen diffusion are described by nonlinear diffusion-absorption equations. As the availability of oxygen is necessary for tumor progression, processes of oxygen transport to the tumor growth site seem most important. Our model yields a theoretical insight into the main stages of development and growth of urinary bladder carcinoma with emphasis on the two most common types: bladder polyps and carcinoma in situ. Analysis of histological structure of bladder tumor is important to avoid misdiagnosis and wrong treatment. We expect our model to be a valuable tool in the study of bladder cancer progression due to the exposure to carcinogens and the oxygen dependent expression of genes promoting tumor growth. Our numerical simulations have good qualitative agreement with in vivo results reported in the corresponding medical literature.

Application of ecological and mathematical theory to cancer: New challenges.

According to the World Health Organization, cancer is among the leading causes of morbidity and mortality worldwide. Despite enormous efforts of cancer researchers all around the world, the mechanisms underlying its origin, formation, progression, therapeutic cure or control are still not fully understood. Cancer is a complex, multi-scale process, in which genetic mutations occurring at a sub-cellular level manifest themselves as functional changes at the cellular and tissue scale.

Image formation of thick three-dimensional objects in differential-interference-contrast microscopy.

The differential-interference-contrast (DIC) microscope is of widespread use in life sciences as it enables noninvasive visualization of transparent objects. The goal of this work is to model the image formation process of thick three-dimensional objects in DIC microscopy. The model is based on the principles of electromagnetic wave propagation and scattering. It simulates light propagation through the components of the DIC microscope to the image plane using a combined geometrical and physical optics approach and replicates the DIC image of the illuminated object. The model is evaluated by comparing simulated images of three-dimensional spherical objects with the recorded images of polystyrene microspheres. Our computer simulations confirm that the model captures the major DIC image characteristics of the simulated object, and it is sensitive to the defocusing effects.

Hybrid discrete-continuous model of invasive bladder cancer.

Bladder cancer is the seventh most common cancer worldwide. Epidemiological studies and experiments implicated chemical penetration into urothelium (epithelial tissue surrounding bladder) in the etiology of bladder cancer. In this work we model invasive bladder cancer. This type of cancer starts in the urothelium and progresses towards surrounding muscles and tissues, causing metastatic disease. Our mathematical model of invasive BC consists of two coupled sub-models: (i) living cycle of the urothelial cells (normal and mutated) simulated using discrete technique of Cellular Automata and (ii) mechanism of tumor invasion described by the system of reaction-diffusion equations. Numerical simulations presented here are in good qualitative agreement with the experimental results and reproduce in vitro observations described in medical literature.

Mean field mutation dynamics and the continuous Luria-Delbrück distribution.

The Luria-Delbrück mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear statistical physics. Starting from the classical formulations we derive the corresponding differential models and show that under a suitable mean field scaling they correspond to generalized Fokker-Planck equations for the mutants distribution whose solutions are given by the corresponding Luria-Delbrück distribution. Numerical results confirming the theoretical analysis are also presented.

Emergence of compact structures in a Klein-Gordon model.

The Klein-Gordon model (KG) phi=P{'}(|phi|)phi/|phi| is Lorenz invariant and has a finite wave speed, yet its localized modes, whether Q balls or vortices, suffer from the same fundamental flaw as all other solitons-they extend indefinitely. Using the KG model as a case study, we demonstrate that appending the site potential, P{a}(phi|), with a subquadratic part P(|phi|)=b{2}|phi|{1+delta}+P{a}(|phi|), 0

Compactification of nonlinear patterns and waves.

We present a nonlinear mechanism(s) which may be an alternative to a missing wave speed: it induces patterns with a compact support and sharp fronts which propagate with a finite speed. Though such mechanism may emerge in a variety of physical contexts, its mathematical characterization is universal, very simple, and given via a sublinear substrate (site) force. Its utility is shown studying a Klein-Gordon -u(tt) + [phi/(u(x)]x = P'(u) equation, where phi'(sigma) = sigma + beta sigma3 and endowed with a subquadratic site potential P(u) approximately /1-u2/(alpha+1), 0 < or = alpha < 1, and the Schrödinger iZt + inverted delta2 Z = G(/Z/)Z equation in a plane with G(A) = gammaA(-delta) - sigmaA2, 0 < delta < or = 1.