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.

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.

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.

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.

Energy Landscapes, Self-Assembly and Viruses

Phenomena such as protein folding, crystallisation, self-assembly, and the observation of magic number clusters in molecular beams are all the result of non-random searches. Analysis of the underlying potential energy surface may provide a unifying framework to explain how such events occur as the result of a guided exploration of the landscape. In particular, icosahedral shells composed of 12 pentagonal pyramids are found to be thermodynamically favourable and kinetically accessible when the pyramids are not too spiky and not too flat. Hence, viruses with icosahedral capsids not only minimise the genetic material required to encode the repeated subunits, but may also utilise the favourable properties of a potential energy surface that effectively directs self-assembly.

RNA Multimerisation in the DNA Packaging Motor of Bacteriophage φ29

The use of bacteriophages as experimental tools allows the investigation of interactions between components at the molecular level that are often not possible in more complex virus systems. The bacteriophage φ29 acts as a molecular machine to package its own genomic DNA during viral assembly. Self-associating RNA molecules, called pRNA, have an essential role in the function of this machine. This paper reports the characterization of this self-association (which leads to multimerisation of wild-type and truncated variant pRNAs) by analytical ultracentrifugation (including determination of the partial specific volume of the pRNA), together with an investigation into the domains of the molecule important for multimerisation by the use of complementary DNA probes.

The Solution of Inverse Non-Linear Elasticity Problems That Arise When Locating Breast Tumours

Non-linear elasticity theory may be used to calculate the coordinates of a deformed body when the coordinates of the undeformed, stress-free body are known. In some situations, such as one of the steps in the location of tumours in a breast, the coordinates of the deformed body are known and the coordinates of the undeformed body are to be calculated, i.e. we require the solution of the inverse problem. Other than for situations where classical linear elasticity theory may be applied, the simple approach for solving the inverse problem of reversing the direction of gravity and modelling the deformed body as an undeformed body does not give the correct solution. In this study, we derive equations that may be used to solve inverse problems. The solution of these equations may be used for a wide range of inverse problems in non-linear elasticity.