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

Dating of divergences within the Rattus genus phylogeny using whole mitochondrial genomes

The timing and order of divergences within the genus Rattus have, to date, been quite speculative. In order to address these important issues we sequenced six new whole mitochondrial genomes from wild-caught specimens from four species, Rattus exulans, Rattus praetor, Rattus rattus and Rattus tanezumi. The only rat whole mitochondrial genomes available previously were all from Rattus norvegicus specimens. Our phylogenetic and dating analyses place the deepest divergence within Rattus at ∼3.5 million years ago (Mya). This divergence separates the New Guinean endemic R. praetor lineage from the Asian lineages. Within the Asian/Island Southeast Asian clade R. norvegicus diverged earliest at ∼2.9 Mya. R. exulans and the ancestor of the sister species R. rattus and R. tanezumi subsequently diverged at ∼2.2 Mya, with R. rattus and R. tanezumi separating as recently as ∼0.4 Mya. Our results give both a better resolved species divergence order and diversification dates within Rattus than previous studies.

The evolutionary history of the extinct ratite moa and New Zealand Neogene paleogeography

The ratite moa (Aves: Dinornithiformes) were a speciose group of massive graviportal avian herbivores that dominated the New Zealand (NZ) ecosystem until their extinction �600 years ago. The phylogeny and evolutionary history of this morphologically diverse order has remained controversial since their initial description in 1839. We synthesize mitochondrial phylogenetic information from 263 subfossil moa specimens from across NZ with morphological, ecological, and new geological data to create the first comprehensive phylogeny, taxonomy, and evolutionary timeframe for all of the species of an extinct order. We also present an important new geological/paleogeographical model of late Cenozoic NZ, which suggests that terrestrial biota on the North and South Island landmasses were isolated for most of the past 20–30 Ma. The data reveal that the patterns of genetic diversity within and between differentmoaclades reflect a complex history following a major marine transgression in the Oligocene, affected by marine barriers, tectonic activity, and glacial cycles. Surprisingly, the remarkable morphological radiation of moa appears to have occurred much more recently than previous early Miocene (ca. 15 Ma) estimates, and was coincident with the accelerated uplift of the Southern Alps just ca. 5–8.5 Ma. Together with recent fossil evidence, these data suggest that the recent evolutionary history of nearly all of the iconic NZ terrestrial biota occurred principally on just the South Island.

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.

Wing shape as a potential discriminator of morphologically similar pest taxa within the Bactrocera dorsalis species complex (Diptera: Tephritidae)

Four morphologically cryptic species of the Bactrocera dorsalis fruit fly complex (B. dorsalis s.s., B. papayae, B. carambolae and B. philippinensis) are serious agricultural pests. As they are difficult to diagnose using traditional taxonomic techniques, we examined the potential for geometric morphometric analysis of wing size and shape to discriminate between them. Fifteen wing landmarks generated size and shape data for 245 specimens for subsequent comparisons among three geographically distinct samples of each species. Intraspecific wing size was significantly different within samples of B. carambolae and B. dorsalis s.s. but not within samples of B. papayae or B. philippinensis. Although B. papayae had the smallest wings (average centroid size=6.002 mm±0.061 SE) and B. dorsalis s.s. the largest (6.349 mm±0.066 SE), interspecific wing size comparisons were generally non-informative and incapable of discriminating species. Contrary to the wing size data, canonical variate analysis based on wing shape data discriminated all species with a relatively high degree of accuracy; individuals were correctly reassigned to their respective species on average 93.27% of the time. A single sample group of B. carambolae from locality 'TN Malaysia' was the only sample to be considerably different from its conspecific groups with regards to both wing size and wing shape. This sample was subsequently deemed to have been originally misidentified and likely represents an undescribed species. We demonstrate that geometric morphometric techniques analysing wing shape represent a promising approach for discriminating between morphologically cryptic taxa of the B. dorsalis species complex.

Investigating the potential value of individual parameters of histological grading systems in a sheep model of cartilage damage : the modified Mankin method

A total histological grade does not necessarily distinguish between different manifestations of cartilage damage or degeneration. An accurate and reliable histological assessment method is required to separate normal and pathological tissue within a joint during treatment of degenerative joint conditions and to sub-classify the latter in meaningful ways. The Modified Mankin method may be adaptable for this purpose. We investigated how much detail may be lost by assigning one composite score/grade to represent different degenerative components of the osteoarthritic condition. We used four ovine injury models (sham surgery, anterior cruciate ligament/medial collateral ligament instability, simulated anatomic anterior cruciate ligament reconstruction and meniscal removal) to induce different degrees and potentially 'types' (mechanisms) of osteoarthritis. Articular cartilage was systematically harvested, prepared for histological examination and graded in a blinded fashion using a Modified Mankin grading method. Results showed that the possible permutations of cartilage damage were significant and far more varied than the current intended use that histological grading systems allow. Of 1352 cartilage specimens graded, 234 different manifestations of potential histological damage were observed across 23 potential individual grades of the Modified Mankin grading method. The results presented here show that current composite histological grading may contain additional information that could potentially discern different stages or mechanisms of cartilage damage and degeneration in a sheep model. This approach may be applicable to other grading systems.