Some novel techniques of parameter estimation for the dynamical models in biological systems

Inverse problems based on using experimental data to estimate unknown parameters of a system often arise in biological and chaotic systems. In this paper, we consider parameter estimation in systems biology involving linear and non-linear complex dynamical models, including the Michaelis–Menten enzyme kinetic system, a dynamical model of competence induction in Bacillus subtilis bacteria and a model of feedback bypass in B. subtilis bacteria. We propose some novel techniques for inverse problems. Firstly, we establish an approximation of a non-linear differential algebraic equation that corresponds to the given biological systems. Secondly, we use the Picard contraction mapping, collage methods and numerical integration techniques to convert the parameter estimation into a minimization problem of the parameters. We propose two optimization techniques: a grid approximation method and a modified hybrid Nelder–Mead simplex search and particle swarm optimization (MH-NMSS-PSO) for non-linear parameter estimation. The two techniques are used for parameter estimation in a model of competence induction in B. subtilis bacteria with noisy data. The MH-NMSS-PSO scheme is applied to a dynamical model of competence induction in B. subtilis bacteria based on experimental data and the model for feedback bypass. Numerical results demonstrate the effectiveness of our approach.

A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

A software tool for simulating spatial separation and kinetics in biological membranes

Self-segregation and compartimentalisation are observed experimentally to occur spontaneously on live membranes as well as reconstructed model membranes. It is believed that many of these processes are caused or supported by anomalous diffusive behaviours of biomolecules on membranes due to the complex and heterogeneous nature of these environments. These phenomena are on the one hand of great interest in biology, since they may be an important way for biological systems to selectively localize receptors, regulate signaling or modulate kinetics; and on the other, they provide an inspiration for engineering designs that mimick natural systems. We present an interactive software package we are developing for the purpose of simulating such processes numerically using a fundamental Monte Carlo approach. This program includes the ability to simulate kinetics and mass transport in the presence of either mobile or immobile obstacles and other relevant structures such as liquid-ordered lipid microdomains. We also present preliminary simulation results regarding the selective spatial localization and chemical kinetics modulating power of immobile obstacles on the membrane, obtained using the program.

Biological and environmental determinants

- describe the complex web of determinants as part of broad causal pathways that affect health - identify and discuss the range of physical, biological and environmental determinants that impact on health - suggest why it is important to the practice of public health that you understand how determinants contribute to health - understand the complexity of health and illness and the multifaceted role of health determinants - relate determinants of health to public health activity and realise the need for multisectoral action and multiple approaches when working to improve health

Biological responses of human bone marrow mesenchymal stem cells to Sr-M-Si (M = Zn, Mg) silicate bioceramics

Strontium (Sr), Zinc (Zn), magnesium (Mg), and silicon (Si) are reported to be essential trace elements for the growth and mineralization of bone. We speculated that the combination of these bioactive elements in bioceramics may be effective to regulate the osteogenic property of boneforming cells. In this study, two Sr-containing silicate bioceramics, Sr2ZnSi2O7 (SZS) and Sr2MgSi2O7 (SMS), were prepared. The biological response of human bone marrow mesenchymal stem cells (BMSCs) to the two bioceramics (in the forms of powders and dense ceramic bulks) was systematically studied. In powder form, the effect of powder extracts on the viability and alkaline phosphatase (ALP) activity of BMSCs was investigated. In ceramic disc form, both direct and indirect coculture of BMSCs with ceramic discs were used to investigate their biological response, including attachment, proliferation, ALP activity, and bone-related genes expression. Beta-tricalcium phosphate (b-TCP) and akermanite (Ca2MgSi2O7, CMS) were used as control materials. The results showed that the Sr, Zn, and Si (or Sr, Mg, and Si)-containing ionic products from SZS and SMS powders enhanced ALP activity of BMSCs, compared to those from b-TCP. Both SZS and SMS ceramic discs supported the growth of BMSCs, and most importantly, significantly enhanced the ALP activity and bone-related genes expression of BMSCs as compared to b-TCP. The results suggest that the specific combination of bioactive ions (Sr, Zn, Si, e.g.) in bioceramics is a viable way to improve the biological performance of biomaterials, and the form of materials and surface properties were nonnegligible factors to influence cell response.

Offsetting greenhouse gas emissions through biological carbon sequestration in North Eastern Australia

The Kyoto Protocol recognises trees as a sink of carbon and a valid means to offset greenhouse gas emissions and meet internationally agreed emissions targets. This study details biological carbon sequestration rates for common plantation species Araucaria cunninghamii (hoop pine), Eucalyptus cloeziana, Eucalyptus argophloia, Pinus elliottii and Pinus caribaea var hondurensis and individual land areas required in north-eastern Australia to offset greenhouse gas emissions of 1000tCO 2e. The 3PG simulation model was used to predict above and below-ground estimates of biomass carbon for a range of soil productivity conditions for six representative locations in agricultural regions of north-eastern Australia. The total area required to offset 1000tCO 2e ranges from 1ha of E. cloeziana under high productivity conditions in coastal North Queensland to 45ha of hoop pine in low productivity conditions of inland Central Queensland. These areas must remain planted for a minimum of 30years to meet the offset of 1000tCO 2e.

Viable chimaeric viruses confirm the biological importance of sequence specific maize streak virus movement protein and coat protein interactions

Background. A variety of interactions between up to three different movement proteins (MPs), the coat protein (CP) and genomic DNA mediate the inter- and intra-cellular movement of geminiviruses in the genus Begomovirus. Although movement of viruses in the genus Mastrevirus is less well characterized, direct interactions between a single MP and the CP of these viruses is also clearly involved in both intra- and intercellular trafficking of virus genomic DNA. However, it is currently unknown how specific these MP-CP interactions are, nor how disruption of these interactions might impact on virus viability. Results. Using chimaeric genomes of two strains of Maize streak virus (MSV) we adopted a genetic approach to investigate the gross biological effects of interfering with interactions between virus MP and CP homologues derived from genetically distinct MSV isolates. MP and CP genes were reciprocally exchanged, individually and in pairs, between maize (MSV-Kom)- and Setaria sp. (MSV-Set)-adapted isolates sharing 78% genome-wide sequence identity. All chimaeras were infectious in Zea mays c.v. Jubilee and were characterized in terms of symptomatology and infection efficiency. Compared with their parental viruses, all the chimaeras were attenuated in symptom severity, infection efficiency, and the rate at which symptoms appeared. The exchange of individual MP and CP genes resulted in lower infection efficiency and reduced symptom severity in comparison with exchanges of matched MP-CP pairs. Conclusion. Specific interactions between the mastrevirus MP and CP genes themselves and/or their expression products are important determinants of infection efficiency, rate of symptom development and symptom severity. © 2008 van der Walt et al; licensee BioMed Central Ltd.

Automatic particle picking of biological molecules imaged by electron microscopy

One of the next great challenges of cell biology is the determination of the enormous number of protein structures encoded in genomes. In recent years, advances in electron cryo-microscopy and high-resolution single particle analysis have developed to the point where they now provide a methodology for high resolution structure determination. Using this approach, images of randomly oriented single particles are aligned computationally to reconstruct 3-D structures of proteins and even whole viruses. One of the limiting factors in obtaining high-resolution reconstructions is obtaining a large enough representative dataset ($>100,000$ particles). Traditionally particles have been manually picked which is an extremely labour intensive process. The problem is made especially difficult by the low signal-to-noise ratio of the images. This paper describes the development of automatic particle picking software, which has been tested with both negatively stained and cryo-electron micrographs. This algorithm has been shown to be capable of selecting most of the particles, with few false positives. Further work will involve extending the software to detect differently shaped and oriented particles.

Protein monoubiquitination and polyubiquitination generate structural diversity to control distinct biological processes

Ubiquitination involves the attachment of ubiquitin (Ub) to lysine residues on substrate proteins or itself, which can result in protein monoubiquitination or polyubiquitination. Polyubiquitination through different lysines (seven) or the N-terminus of Ub can generate different protein-Ub structures. These include monoubiquitinated proteins, polyubiqutinated proteins with homotypic chains through a particular lysine on Ub or mixed polyubiquitin chains generated by polymerization through different Ub lysines. The ability of the ubiquitination pathway to generate different protein-Ub structures provides versatility of this pathway to target proteins to different fates. Protein ubiquitination is catalyzed by Ub-conjugating and Ub-ligase enzymes, with different combinations of these enzymes specifying the type of Ub modification on protein substrates. How Ub-conjugating and Ub-ligase enzymes generate this structural diversity is not clearly understood. In the current review, we discuss mechanisms utilized by the Ub-conjugating and Ub-ligase enzymes to generate structural diversity during protein ubiquitination, with a focus on recent mechanistic insights into protein monoubiquitination and polyubiquitination.

Cellular model systems to study the tumor biological role of kallikrein-related peptidases in ovarian and prostate cancer

Since the identification of the gene family of kallikrein related peptidases (KLKs), their function has been robustly studied at the biochemical level. In vitro biochemical studies have shown that KLK proteases are involved in a number of extracellular processes that initiate intracellular signaling pathways by hydrolysis, as reviewed in Chapters 8, 9, and 15, Volume 1. These events have been associated with more invasive phenotypes of ovarian, prostate, and other cancers. Concomitantly, aberrant expression of KLKs has been associated with poor prognosis of patients with ovarian and prostate cancer (Borgoño and Diamandis, 2004; Clements et al., 2004; Yousef and Diamandis, 2009), with prostate-specific antigen (PSA, KLK3) being a long standing, clinically employed biomarker for prostate cancer (Lilja et al., 2008). Data generated from patient samples in clinical studies, alongwith biochemical activity, suggests that KLKs function in the development and progression of these diseases. To bridge the gap between their function at the molecular level and the clinical need for efficacious treatment and prognostic biomarkers, functional assessment at the in vitro cellular level, using various culture models, is increasing, particularly in a three-dimensional (3D) context (Abbott, 2003; Bissell and Radisky, 2001; Pampaloni et al., 2007; Yamada and Cukierman, 2007).

A description of the Mei2-like protein family; structure, phylogenetic distribution and biological context

The Schizosaccharomyces pombe Mei2 gene encodes an RNA recognition motif (RRM) protein that stimulates meiosis upon binding a specific non-coding RNA and subsequent accumulation in a “mei2-dot” in the nucleus. We present here the first systematic characterization of the family of proteins with characteristic Mei2-like amino acid sequences. Mei2-like proteins are an ancient eukaryotic protein family with three identifiable RRMs. The C-terminal RRM (RRM3) is unique to Mei2-like proteins and is the most highly conserved of the three RRMs. RRM3 also contains conserved sequence elements at its C-terminus not found in other RRM domains. Single copy Mei2-like genes are present in some fungi, in alveolates such as Paramecium and in the early branching eukaryote Entamoeba histolytica, while plants contain small families of Mei2-like genes. While the C-terminal RRM is highly conserved between plants and fungi, indicating conservation of molecular mechanisms, plant Mei2-like genes have changed biological context to regulate various aspects of developmental pattern formation.

Biological performance of a polycaprolactone-based scaffold plus recombinant human morphogenetic protein-2 (rhBMP-2) in an ovine thoracic interbody fusion model

Introduction. We develop a sheep thoracic spine interbody fusion model to study the suitability of polycaprolactone-based scaffold and recombinant human bone morphogenetic protein-2 (rhBMP-2) as a bone graft substitute within the thoracic spine. The surgical approach is a mini- open thoracotomy with relevance to minimally invasive deformity correction surgery for adolescent idiopathic scoliosis. To date there are no studies examining the use of this biodegradable implant in combination with biologics in a sheep thoracic spine model. Methods. In the present study, six sheep underwent a 3-level (T6/7, T8/9 and T10/11) discectomy with randomly allocated implantation of a different graft substitute at each of the three levels; (i) calcium phosphate (CaP) coated polycaprolactone based scaffold plus 0.54µg rhBMP-2, (ii) CaP coated PCL- based scaffold alone or (iii) autograft (mulched rib head). Fusion was assessed at six months post-surgery. Results. Computed Tomographic scanning demonstrated higher fusion grades in the rhBMP-2 plus PCL- based scaffold group in comparison to either PCL-based scaffold alone or autograft. These results were supported by histological evaluations of the respective groups. Biomechanical testing revealed significantly higher stiffness for the rhBMP-2 plus PCL- based scaffold group in all loading directions in comparison to the other two groups. Conclusions. The results of this study demonstrate that rhBMP-2 plus PCL-based scaffold is a viable bone graft substitute, providing an optimal environment for thoracic interbody spinal fusion in a large animal model.

Fractional models for the migration of biological cells in complex spatial domains

Travelling wave phenomena are observed in many biological applications. Mathematical theory of standard reaction-diffusion problems shows that simple partial differential equations exhibit travelling wave solutions with constant wavespeed and such models are used to describe, for example, waves of chemical concentrations, electrical signals, cell migration, waves of epidemics and population dynamics. However, as in the study of cell motion in complex spatial geometries, experimental data are often not consistent with constant wavespeed. Non-local spatial models have successfully been used to model anomalous diffusion and spatial heterogeneity in different physical contexts. In this paper, we develop a fractional model based on the Fisher-Kolmogoroff equation and analyse it for its wavespeed properties, attempting to relate the numerical results obtained from our simulations to experimental data describing enteric neural crest-derived cells migrating along the intact gut of mouse embryos. The model proposed essentially combines fractional and standard diffusion in different regions of the spatial domain and qualitatively reproduces the behaviour of neural crest-derived cells observed in the caecum and the hindgut of mouse embryos during in vivo experiments.