Mathematical and computational models of drug transport in tumours

The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a ‘tumour cord’ geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are ‘pharmacokinetically resistant’ to chemotherapeutic strategies

The failed liberalisation of Algeria and the international context: a legacy of stable authoritarianism

The paper attempts to challenge the somewhat marginal role of international factors in the study of transitions to democracy. Theoretical and practical difficulties in proving causal mechanisms between international variables and domestic outcomes can be overcome by defining the international dimension in terms of Western dominance of world politics and by identifying Western actions towards democratising countries. The paper focuses on the case of Algeria, where international factors are key in explaining the initial process of democratisation and its following demise. In particular, the paper argues that direct Western policies, the pressures of the international system and external shocks influence the internal distribution of power and resources, which underpins the different strategies of all domestic actors. The paper concludes that analysis based purely on domestic factors cannot explain the process of democratisation and that international variables must be taken into more serious account and much more detailed

Bifurcation of critical points for continuous families of C^2 functionals of Fredholm type

Given a continuous family of C^2 functionals of Fredholm type, we show that the non-vanishing of the spectral flow for the family of Hessians along a known (trivial) branch of critical points not only entails bifurcation of nontrivial critical points but also allows to estimate the number of bifurcation points along the branch. We use this result for several parameter bifurcation, estimating the number of connected components of the complement of the set of bifurcation points and apply our results to bifurcation of periodic orbits of Hamiltonian systems. By means of a comparison principle for the spectral flow, we obtain lower bounds for the number of bifurcation points of periodic orbits on a given interval in terms of the coefficients of the linearization

Dynamics of ions in the selectivity filter of the KcsA channel

The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion’s dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications

Challenges Associated With the Design and Deployment of Food Intake Urine Biomarker Technology for Assessment of Habitual Diet in Free-Living Individuals and Populations:A Perspective

Improvement of diet at the population level is a cornerstone of national and international strategies for reducing chronic disease burden. A critical challenge in generating robust data on habitual dietary intake is accurate exposure assessment. Self-reporting instruments (e.g., food frequency questionnaires, dietary recall) are subject to reporting bias and serving size perceptions, while weighed dietary assessments are unfeasible in large-scale studies. However, secondary metabolites derived from individual foods/food groups and present in urine provide an opportunity to develop potential biomarkers of food intake (BFIs). Habitual dietary intake assessment in population surveys using biomarkers presents several challenges, including the need to develop affordable biofluid collection methods, acceptable to participants that allow collection of informative samples. Monitoring diet comprehensively using biomarkers requires analytical methods to quantify the structurally diverse mixture of target biomarkers, at a range of concentrations within urine. The present article provides a perspective on the challenges associated with the development of urine biomarker technology for monitoring diet exposure in free-living individuals with a view to its future deployment in real world situations. An observational study (n = 95), as part of a national survey on eating habits, provided an opportunity to explore biomarker measurement in a free-living population. In a second food intervention study (n = 15), individuals consumed a wide range of foods as a series of menus designed specifically to achieve exposure reflecting a diversity of foods commonly consumed in the UK, emulating normal eating patterns. First Morning Void urines were shown to be suitable samples for biomarker measurement. Triple quadrupole mass spectrometry, coupled with liquid chromatography, was used to assess simultaneously the behavior of a panel of 54 potential BFIs. This panel of chemically diverse biomarkers, reporting intake of a wide range of commonly-consumed foods, can be extended successfully as new biomarker leads are discovered. Towards validation, we demonstrate excellent discrimination of eating patterns and quantitative relationships between biomarker concentrations in urine and the intake of several foods. In conclusion, we believe that the integration of information from BFI technology and dietary self-reporting tools will expedite research on the complex interactions between dietary choices and health. (c) Copyright (c) 2020 Beckmann, Wilson, Lloyd, Torres, Goios, Willis, Lyons, Phillips, Mathers and Draper

Rings and rigidity transitions in network glasses

Three elastic phases of covalent networks, (I) floppy, (II) isostatically rigid and (III) stressed-rigid have now been identified in glasses at specific degrees of cross-linking (or chemical composition) both in theory and experiments. Here we use size-increasing cluster combinatorics and constraint counting algorithms to study analytically possible consequences of self-organization. In the presence of small rings that can be locally I, II or III, we obtain two transitions instead of the previously reported single percolative transition at the mean coordination number $\bar r=2.4$, one from a floppy to an isostatic rigid phase, and a second one from an isostatic to a stressed rigid phase. The width of the intermediate phase $~ \bar r$ and the order of the phase transitions depend on the nature of medium range order (relative ring fractions). We compare the results to the Group IV chalcogenides, such as Ge-Se and Si-Se, for which evidence of an intermediate phase has been obtained, and for which estimates of ring fractions can be made from structures of high T crystalline phases.Comment: 29 pages, revtex, 7 eps figure

Development and characterization of a microfluidic model of the tumour microenvironment

The physical microenvironment of tumours is characterized by heterotypic cell interactions and physiological gradients of nutrients, waste products and oxygen. This tumour microenvironment has a major impact on the biology of cancer cells and their response to chemotherapeutic agents. Despite this, most in vitro cancer research still relies primarily on cells grown in 2D and in isolation in nutrient- and oxygen-rich conditions. Here, a microfluidic device is presented that is easy to use and enables modelling and study of the tumour microenvironment in real-time. The versatility of this microfluidic platform allows for different aspects of the microenvironment to be monitored and dissected. This is exemplified here by real-time profiling of oxygen and glucose concentrations inside the device as well as effects on cell proliferation and growth, ROS generation and apoptosis. Heterotypic cell interactions were also studied. The device provides a live ‘window’ into the microenvironment and could be used to study cancer cells for which it is difficult to generate tumour spheroids. Another major application of the device is the study of effects of the microenvironment on cellular drug responses. Some data is presented for this indicating the device’s potential to enable more physiological in vitro drug screening

Atom capture by nanotube and scaling anomaly

The existence of bound state of the polarizable neutral atom in the inverse square potential created by the electric field of single walled charged carbon nanotube (SWNT) is shown to be theoretically possible. The consideration of inequivalent boundary conditions due to self-adjoint extensions lead to this nontrivial bound state solution. It is also shown that the scaling anomaly is responsible for the existence of bound state. Binding of the polarizable atoms in the coupling constant interval \eta^2\in[0,1) may be responsible for the smearing of the edge of steps in quantized conductance, which has not been considered so far in literature.Comment: Accepted in Int.J.Theor.Phy