Some solutions for a compressible isotropic elastic material

In this article we obtain closed-form solutions for the combined inflation and axial shear of an elastic tube in respect of the compressible Isotropic elastic material introduced by Levinson and Burgess. Several other boundary-value problems are also examined, including the bending of a rectangular block and straightening of a cylindrical sector, both coupled with stretching and shearing, and an axially varying twist deformation. Some of the solutions appear in closed form, others are expressible in terms of elliptic functions.

On helical shear of a compressible elastic circular cylindrical tube

In this paper we examine the combined azimuthal and axial shear of a compressible isotropic elastic circular cylindrical tube of finite extent, otherwise referred to as helical shear (which is an isochoric deformation). The equilibrium equations are formulated in terms of the principal stretches, and explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation are obtained and compared with those obtained previously for this problem. Several classes of strain-energy functions are derived and in some general cases complete solutions of the equilibrium equations are obtained. Existing results are recovered as special cases and some new results for the strain-energy functions derived are determined and discussed.

A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

On extension and torsion of a compressible elastic circular cylinder

In this paper we examine the combined extension and torsion of a compressible isotropic elastic cylinder of finite extent. The equilibrium equations are formulated in terms of the principal stretches and then applied to the special case of pure torsion superimposed on a uniform extension (an isochoric deformation). Explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation with vanishing traction on the lateral surfaces of the cylinder are obtained. Some strain-energy functions satisfying these conditions are considered, existing results are recovered as special cases and new results are obtained. We also point out how the strain-energy functions generated from the considered isochoric deformation considered (of a compressible material) can be used to generate energy functions and corresponding solutions for the incompressible theory.

Critical dependence of blood-borne biomarker concentrations on the half-lives of their carrier proteins

Until recently, the low-abundance (LA) range of the serum proteome was an unexplored reservoir of diagnostic information. Today it is increasingly appreciated that a diagnostic goldmine of LA biomarkers resides in the blood stream in complexed association with more abundant higher molecular weight carrier proteins such as albumin and immunoglobulins. As we now look to the possibility of harvesting these LA biomarkers more efficiently through engineered nano-scale particles, mathematical approaches are needed in order to reveal the mechanisms by which blood carrier proteins act as molecular 'mops' for LA diagnostic cargo, and the functional relationships between bound LA biomarker concentrations and other variables of interest such as biomarker intravasation and clearance rates and protein half-lives in the bloodstream. Here we show, by simple mathematical modeling, how the relative abundance of large carrier proteins and their longer half-lives in the bloodstream work together to amplify the total blood concentration of these tiny biomarkers. The analysis further suggests that alterations in the production of biomarkers lead to gradual rather than immediate changes in biomarker levels in the blood circulation. The model analysis also points to the characteristics of artificial nano-particles that would render them more efficient harvesters of tumor biomarkers in the circulation, opening up possibilities for the early detection of curable disease, rather than simply better detection of advanced disease.

Proteins, drug targets and the mechanisms they control : the simple truth about complex networks

Realizing the promise of molecularly targeted inhibitors for cancer therapy will require a new level of knowledge about how a drug target is wired into the control circuitry of a complex cellular network. Here we review general homeostatic principles of cellular networks that enable the cell to be resilient in the face of molecular perturbations, while at the same time being sensitive to subtle input signals. Insights into such mechanisms may facilitate the development of combination therapies that take advantage of the cellular control circuitry, with the aim of achieving higher efficacy at a lower drug dosage and with a reduced probability of drug-resistance development.

Analysis of albumin-associated peptides and proteins from ovarian cancer patients

Albumin binds low–molecular-weight molecules, including proteins and peptides, which then acquire its longer half-life, thereby protecting the bound species from kidney clearance. We developed an experimental method to isolate albumin in its native state and to then identify [mass spectrometry (MS) sequencing] the corresponding bound low–molecular-weight molecules. We used this method to analyze pooled sera from a human disease study set (high-risk persons without cancer, n= 40; stage I ovarian cancer, n = 30; stage III ovarian cancer, n = 40) to demonstrate the feasibility of this approach as a discovery method. Methods Albumin was isolated by solid-phase affinity capture under native binding and washing conditions. Captured albumin-associated proteins and peptides were separated by gel electrophoresis and subjected to iterative MS sequencing by microcapillary reversed-phase tandem MS. Selected albumin-bound protein fragments were confirmed in human sera by Western blotting and immunocompetition. Results In total, 1208 individual protein sequences were predicted from all 3 pools. The predicted sequences were largely fragments derived from proteins with diverse biological functions. More than one third of these fragments were identified by multiple peptide sequences, and more than one half of the identified species were in vivo cleavage products of parent proteins. An estimated 700 serum peptides or proteins were predicted that had not been reported in previous serum databases. Several proteolytic fragments of larger molecules that may be cancer-related were confirmed immunologically in blood by Western blotting and peptide immunocompetition. BRCA2, a 390-kDa low-abundance nuclear protein linked to cancer susceptibility, was represented in sera as a series of specific fragments bound to albumin. Conclusion Carrier-protein harvesting provides a rich source of candidate peptides and proteins with potential diverse tissue and cellular origins that may reflect important disease-related information.

A linear-elastic model of anisotropic tumour growth

This paper examines the effect of anisotropic growth on the evolution of mechanical stresses in a linear-elastic model of a growing, avascular tumour. This represents an important improvement on previous linear-elastic models of tissue growth since it has been shown recently that spatially-varying isotropic growth of linear-elastic tissues does not afford the necessary stress-relaxation for a steady-state stress distribution upon reaching a nutrient-regulated equilibrium size. Time-dependent numerical solutions are developed using a Lax-Wendroff scheme, which show the evolution of the tissue stress distributions over a period of growth until a steady-state is reached. These results are compared with the steady-state solutions predicted by the model equations, and key parameters influencing these steady-state distributions are identified. Recommendations for further extensions and applications of this model are proposed.

Senataxin plays an essential role with DNA damage response proteins in meiotic recombination and gene silencing

Senataxin, mutated in the human genetic disorder ataxia with oculomotor apraxia type 2 (AOA2), plays an important role in maintaining genome integrity by coordination of transcription, DNA replication, and the DNA damage response. We demonstrate that senataxin is essential for spermatogenesis and that it functions at two stages in meiosis during crossing-over in homologous recombination and in meiotic sex chromosome inactivation (MSCI). Disruption of the Setx gene caused persistence of DNA double-strand breaks, a defect in disassembly of Rad51 filaments, accumulation of DNA:RNA hybrids (R-loops), and ultimately a failure of crossing-over. Senataxin localised to the XY body in a Brca1-dependent manner, and in its absence there was incomplete localisation of DNA damage response proteins to the XY chromosomes and ATR was retained on the axial elements of these chromosomes, failing to diffuse out into chromatin. Furthermore persistence of RNA polymerase II activity, altered ubH2A distribution, and abnormal XY-linked gene expression in Setx⁻/⁻ revealed an essential role for senataxin in MSCI. These data support key roles for senataxin in coordinating meiotic crossing-over with transcription and in gene silencing to protect the integrity of the genome.

Computational model of membrane fission catalyzed by ESCRT-III

ESCRT-III proteins catalyze membrane fission during multi vesicular body biogenesis, budding of some enveloped viruses and cell division. We suggest and analyze a novel mechanism of membrane fission by the mammalian ESCRT-III subunits CHMP2 and CHMP3. We propose that the CHMP2-CHMP3 complexes self-assemble into hemi-spherical dome-like structures within the necks of the initial membrane buds generated by CHMP4 filaments. The dome formation is accompanied by the membrane attachment to the dome surface, which drives narrowing of the membrane neck and accumulation of the elastic stresses leading, ultimately, to the neck fission. Based on the bending elastic model of lipid bilayers, we determine the degree of the membrane attachment to the dome enabling the neck fission and compute the required values of the protein-membrane binding energy. We estimate the feasible values of this energy and predict a high efficiency for the CHMP2-CHMP3 complexes in mediating membrane fission. We support the computational model by electron tomography imaging of CHMP2-CHMP3 assemblies in vitro. We predict a high efficiency for the CHMP2-CHMP3 complexes in mediating membrane fission.

Differential subcellular and extracellular localisations of proteins required for insulin-like growth factor- and extracellular matrix-induced signalling events in breast cancer progression

Background: Cancer metastasis is the main contributor to breast cancer fatalities as women with the metastatic disease have poorer survival outcomes than women with localised breast cancers. There is an urgent need to develop appropriate prognostic methods to stratify patients based on the propensities of their cancers to metastasise. The insulin-like growth factor (IGF)-I:IGF binding protein (IGFBP):vitronectin complexes have been shown to stimulate changes in gene expression favouring increased breast cancer cell survival and a migratory phenotype. We therefore investigated the prognostic potential of these IGF- and extracellular matrix (ECM) interaction-induced proteins in the early identification of breast cancers with a propensity to metastasise using patient-derived tissue microarrays. Methods: Semiquantitative immunohistochemistry analyses were performed to compare the extracellular and subcellular distribution of IGF- and ECM-induced signalling proteins among matched normal, primary cancer and metastatic cancer formalin-fixed paraffin-embedded breast tissue samples. Results: The IGF- and ECM-induced signalling proteins were differentially expressed between subcellular and extracellular localisations. Vitronectin and IGFBP-5 immunoreactivity was lower while β1 integrin immunoreactivity was higher in the stroma surrounding metastatic cancer tissues, as compared to normal breast and primary cancer stromal tissues. Similarly, immunoreactive stratifin was found to be increased in the stroma of primary as well as metastatic breast tissues. Immunoreactive fibronectin and β1 integrin was found to be highly expressed at the leading edge of tumours. Based on the immunoreactivity it was apparent that the cell signalling proteins AKT1 and ERK1/2 shuffled from the nucleus to the cytoplasm with tumour progression. Conclusion: This is the first in-depth, compartmentalised analysis of the distribution of IGF- and ECM-induced signalling proteins in metastatic breast cancers. This study has provided insights into the changing pattern of cellular localisation and expression of IGF- and ECM-induced signalling proteins in different stages of breast cancer. The differential distribution of these biomarkers could provide important prognostic and predictive indicators that may assist the clinical management of breast disease, namely in the early identification of cancers with a propensity to metastasise, and/or recur following adjuvant therapy.

Identification of optimal epitopes for Plasmodium falciparum rapid diagnostic tests that target histidine-rich proteins 2 and 3

Rapid diagnostic tests (RDTs) represent important tools to diagnose malaria infection. To improve understanding of the variable performance of RDTs that detect the major target in Plasmodium falciparum, namely, histidine-rich protein 2 (HRP2), and to inform the design of better tests, we undertook detailed mapping of the epitopes recognized by eight HRP-specific monoclonal antibodies (MAbs). To investigate the geographic skewing of this polymorphic protein, we analyzed the distribution of these epitopes in parasites from geographically diverse areas. To identify an ideal amino acid motif for a MAb to target in HRP2 and in the related protein HRP3, we used a purpose-designed script to perform bioinformatic analysis of 448 distinct gene sequences from pfhrp2 and from 99 sequences from the closely related gene pfhrp3. The frequency and distribution of these motifs were also compared to the MAb epitopes. Heat stability testing of MAbs immobilized on nitrocellulose membranes was also performed. Results of these experiments enabled the identification of MAbs with the most desirable characteristics for inclusion in RDTs, including copy number and coverage of target epitopes, geographic skewing, heat stability, and match with the most abundant amino acid motifs identified. This study therefore informs the selection of MAbs to include in malaria RDTs as well as in the generation of improved MAbs that should improve the performance of HRP-detecting malaria RDTs.

Global sequence variation in the histidine-rich proteins 2 and 3 of Plasmodium falciparum: implications for the performance of malaria rapid diagnostic tests

Background Accurate diagnosis is essential for prompt and appropriate treatment of malaria. While rapid diagnostic tests (RDTs) offer great potential to improve malaria diagnosis, the sensitivity of RDTs has been reported to be highly variable. One possible factor contributing to variable test performance is the diversity of parasite antigens. This is of particular concern for Plasmodium falciparum histidine-rich protein 2 (PfHRP2)-detecting RDTs since PfHRP2 has been reported to be highly variable in isolates of the Asia-Pacific region. Methods The pfhrp2 exon 2 fragment from 458 isolates of P. falciparum collected from 38 countries was amplified and sequenced. For a subset of 80 isolates, the exon 2 fragment of histidine-rich protein 3 (pfhrp3) was also amplified and sequenced. DNA sequence and statistical analysis of the variation observed in these genes was conducted. The potential impact of the pfhrp2 variation on RDT detection rates was examined by analysing the relationship between sequence characteristics of this gene and the results of the WHO product testing of malaria RDTs: Round 1 (2008), for 34 PfHRP2-detecting RDTs. Results Sequence analysis revealed extensive variations in the number and arrangement of various repeats encoded by the genes in parasite populations world-wide. However, no statistically robust correlation between gene structure and RDT detection rate for P. falciparum parasites at 200 parasites per microlitre was identified. Conclusions The results suggest that despite extreme sequence variation, diversity of PfHRP2 does not appear to be a major cause of RDT sensitivity variation.

KRAB zinc-finger proteins localise to novel KAP1-containing foci that are adjacent to PML nuclear bodies

The KRAB-zinc finger proteins (KRAB-ZFPs) represent a very large, but poorly understood, family of transcriptional regulators in mammals. They are thought to repress transcription via their interaction with KRAB-associated protein 1 (KAP1), which then assembles a complex of chromatin modifiers to lay down histone marks that are associated with inactive chromatin. Studies of KRAB-ZFP/KAP1-mediated gene silencing, using reporter constructs and ectopically expressed proteins, have shown colocalisation of both KAP1 and repressed reporter target genes to domains of constitutive heterochromatin in the nucleus. However, we show here that although KAP1 does indeed become recruited to pericentric heterochromatin during differentiation of mouse embryonic stem (ES) cells, endogenous KRAB-ZFPs do not. Rather, KRAB-ZFPs and KAP1 relocalise to novel nucleoplasmic foci that we have termed KRAB- and KAP1-associated (KAKA) foci. HP1s can also concentrate in these foci and there is a close spatial relationship between KAKA nuclear foci and PML nuclear bodies. Finally, we reveal differential requirements for the recruitment of KAP1 to pericentric heterochromatin and KAKA foci, and suggest that KAKA foci may contain sumoylated KAP1 - the form of the protein that is active in transcriptional repression.