Bone Formation: Biological Aspects and Modelling Problems

In this work we succintly review the main features of bone formation in vertebrates. Out of the many aspects of this exceedingly complex process, some particular stages are selected for which mathematical modelling appears as both feasible and desirable. In this way, a number of open questions are formulated whose study seems to require interaction among mathematical analysis and biological experimentation.

Cancer Cell Invasion of Brain Tissue: Guided by a Prepattern?

The malignant brain tumourGlioblastoma multiforme(GBM) displays a highly invasive behaviour. Spreading of the malignant cells appears to be guided by the white matter fibre tracts within the brain. In order to understand the global growth process we introduce a lattice-gas cellular automaton model which describes the local interaction between individual malignant cells and their neighbourhood. We consider interactions between cells (brain cells and tumour cells) and between malignant cells and the fibre tracts in the brain, which are considered as a prepattern. The prepattern implies persistent individual cell motion along the fibre structure. Simulations with the model show that only the inclusion of the prepattern results in invading tumour and growing tumour islets in front of the expanding tumour bulk (i.e. the growth pattern observed in clinical practice). Our results imply that the infiltrative growth of GBMs is, in part, determined by the physical structure of the surrounding brain rather than by intrinsic properties of the tumour cells.

Dissecting the Fine Details of Assembly of aT = 3 Phage Capsid

The RNA bacteriophages represent ideal model systems in which to probe the detailed assembly pathway for the formation of aT = 3 quasi-equivalent capsid. For MS2, the assembly reaction can be probedin vitrousing acid disassembled coat protein subunits and a short (19 nt) RNA stem-loop that acts as the translational operator of the replicase gene and leads to sequence-specific sequestration and packaging of the cognate phage RNAin vivo. Reassembly reactions can be initiated by mixing these components at neutral pH. The molecular basis of the sequence-specific RNA–protein interaction is now well understood. Recent NMR studies on the protein demonstrate extensive mobility in the loops of the polypeptide that alter their conformations to form the quasi-equivalent conformers of the final capsid. It seems reasonable to assume that RNA binding results in reduction of this flexibility. However, mass spectrometry suggests that these RNA–protein complexes may only provide one type of quasi-equivalent capsid building block competent to form five-fold axes but not the full shell. Work with longer RNAs suggests that the RNA may actively template the assembly pathway providing a partial explanation of how conformers are selected in the growing shell.

A Coarse Grained Model for DNA and Polymer Packaging: Statics and Dynamics

We present a numerical characterization of the statics and dynamics of the packaging of a semi-flexible polymer inside a sphere. The study is motivated by recent experiments on the packaging of DNA inside viral capsids. It is found that the force required to confine the coarse-grained polymer is in fair agreement with that found in experiments for the packaging of the phi29 bacteriophage genome. Despite its schematic nature, the model is capable of reproducing the most salient dynamical features of packaging experiments such as the presence of pauses during individual packaging processes and the trend of the resisting force as a function of chain packed fraction.

Scheduling Medical Procedures: How One Single Delay Begets Multiple Subsequent Delays

Background: Delay is a common feature of medical disease management. Delays occur because schedules are filled, patients forget their appointment, equipment is unavailable, or because medical and non-medical complications interfere with the planned procedure. The aim of the present analysis is to model how one single delay can lead to multiple subsequent delays.Methods: The consecutive stream of delays is analyzed in terms of a stochastic process comprising of a random sum of random time periods. Any untoward event causes a procedural delay, which provides a time window of opportunity for yet another delaying event to occur.Results: The stochastic model explains why even a single initial delay can easily lead to a multitude of subsequent delays. The expected overall delay is always longer than the initial delay caused by the deferment of the initial procedure. The analysis demonstrates how in individual patients an initially short delay may subsequently expand into days or weeks.Conclusion: Because a single delay can easily burgeon into a lengthy series of multiple delays, the primary goal should be to avoid the precipitating delay at the onset.

Quantifying Vasculature: New Measures Applied to Arterial Trees in the Quail Chorioallantoic Membrane

A wide variety of measures is currently in use in the morphometry of vascular systems. We introduce two additional classes of measures based on erosions and dilations of the image. Each measure has a clear biological interpretation in terms of the measured structures and their function. The measures are illustrated on images of the arterial tree of the quail chorioallantoic membrane (CAM). The new measures are correlated with widely-used measures, such as fractal dimension, but allow a clearer biological interpretation. To distinguish one CAM arterial tree from another, we propose reporting just three independent, uncorrelated numbers: (i) the fraction of tissue which is vascular (VF0, a pure ratio), (ii) a measure of the typical distance of the vascularized tissue to its vessels (CL, a length), and (iii) the flow capacity of the tissue (P, an area). An unusually largeCLwould indicate the presence of large avascular areas, a characteristic feature of tumor tissue.CLis inversely highly correlated with fractal dimension of the skeletonized image, but has a more direct biological interpretation.

Development of a Species-Specific Model of Cerebral Hemodynamics

In this paper, a mathematical model for the description of cerebral hemodynamics is developed. This model is able to simulate the regulation mechanisms working on the small cerebral arteries and arterioles, and thus to adapt dynamically the blood flow in brain. Special interest is laid on the release of catecholamines and their effect on heart frequency, cardiac output and blood pressure. Therefore, this model is able to describe situations of severe head injuries in a very realistic way.

Abstract Action Potential Models for Toxin Recognition

In this paper, we present a robust methodology using mathematical pattern recognition schemes to detect and classify events in action potentials for recognizing toxins in biological cells. We focus on event detection in action potential via abstraction of information content into a low dimensional feature vector within the constrained computational environment of a biosensor. We use generated families of action potentials from a classic Hodgkin–Huxley model to verify our methodology and build toxin recognition engines. We demonstrate that good recognition rates are achievable with our methodology.