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.

Scaling digital radiographs for templating in total hip arthroplasty using conventional acetate templates independent of calibration markers

We describe a scaling method for templating digital radiographs using conventional acetate templates independent of template magnification without the need for a calibration marker. The mean magnification factor for the radiology department was determined (119.8%, range117%-123.4%). This fixed magnification factor was used to scale the radiographs by the method described. 32 femoral heads on postoperative THR radiographs were then measured and compared to the actual size. The mean absolute accuracy was within 0.5% of actual head size (range 0 to 3%) with a mean absolute difference of 0.16mm (range 0-1mm, SD 0.26mm). Intraclass Correlation Coefficient (ICC) showed excellent reliability for both inter and intraobserver measurements with ICC scores of 0.993 (95% CI 0.988-0.996) for interobserver measurements and intraobserver measurements ranging between 0.990-0.993 (95% CI 0.980-0.997).

Corneal markers of diabetic neuropathy

Diabetic neuropathy is a significant clinical problem that currently has no effective therapy, and in advanced cases, leads to foot ulceration and lower limb amputation. The accurate detection, characterization and quantification of this condition are important in order to define at-risk patients, anticipate deterioration, monitor progression, and assess new therapies This review evaluates novel corneal methods of assessing diabetic neuropathy. Two new non-invasive corneal markers have emerged, and in cross-sectional studies have demonstrated their ability to stratify the severity of this disease. Corneal confocal microscopy allows quantification of corneal nerve parameters and non-contact corneal esthesiometry, the functional correlate of corneal structure, assesses the sensitivity of the cornea. Both these techniques are quick to perform, produce little or no discomfort for the patient, and are suitable for clinical settings. Each has advantages and disadvantages over traditional techniques for assessing diabetic neuropathy. Application of these new corneal markers for longitudinal evaluation of diabetic neuropathy has the potential to reduce dependence on more invasive, costly, and time-consuming assessments, such as skin biopsy.

Neuropsychological development in children with early and continuously treated phenylketonuria : association with biochemical markers

PKU is a genetically inherited inborn error of metabolism caused by a deficiency of the enzyme phenylalanine hydroxylase. The failure of this enzyme causes incomplete metabolism of protein ingested in the diet, specifically the conversion of one amino acid, phenylalanine, to tyrosine, which is a precursor to the neurotransmitter dopamine. Rising levels of phenylalanine is toxic to the developing brain, disrupting the formation of white matter tracts. The impact of tyrosine deficiency is not as well understood, but is hypothesized to lead to a low dopamine environment for the developing brain. Detection in the newborn period and continuous treatment (a low protein phe-restricted diet supplemented with phenylalanine-free protein formulas) has resulted in children with early and continuously treated PKU now developing normal I.Q. However, deficits in executive function (EF) are common, leading to a rate of Attention Deficit Hyperactivity Disorder (ADHD) up to five times the norm. EF worsens with exposure to higher phenylalanine levels, however recent research has demonstrated that a high phenylalanine to tyrosine ratio (phenylalanine:tyrosine ratio), which is hypothesised to lead to poorer dopamine function, has a more negative impact on EF than phenylalanine levels alone. Research and treatment of PKU is currently phenylalanine-focused, with little investigation of the impact of tyrosine on neuropsychological development. There is no current consensus as to the veracity of tyrosine monitoring or treatment in this population. Further, the research agenda in this population has demonstrated a primary focus on EF impairment alone, even though there may be additional neuropsychological skills compromised (e.g., mood, visuospatial deficits). The aim of this PhD research was to identify residual neuropsychological deficits in a cohort of children with early and continuously treated phenylketonuria, at two time points in development (early childhood and early adolescence), separated by eight years. In addition, this research sought to determine which biochemical markers were associated with neuropsychological impairments. A clinical practice survey was also undertaken to ascertain the current level of monitoring/treatment of tyrosine in this population. Thirteen children with early and continuously treated PKU were tested at mean age 5.9 years and again at mean age 13.95 years on several neuropsychological measures. Four children with hyperphenylalaninemia (a milder version of PKU) were also tested at both time points and provide a comparison group in analyses. Associations between neuropsychological function and biochemical markers were analysed. A between groups analysis in adolescence was also conducted (children with PKU compared to their siblings) on parent report measures of EF and mood. Minor EF impairments were evident in the PKU group by age 6 years and these persisted into adolescence. Life-long exposure to high phenylalanine:tyrosine ratio and/or low tyrosine independent of phenylalanine were significantly associated with EF impairments at both time points. Over half the children with PKU showed severe impairment on a visuospatial task, and this was associated only with concurrent levels of tyrosine in adolescence. Children with PKU also showed a statistically significant decline in a language comprehension task from 6 years to adolescence (going from normal to subnormal), this deficit was associated with lifetime levels of phenylalanine. In comparison, the four children with hyperphenylalaninemia demonstrated normal function at both time points, across all measures. No statistically significant differences were detected between children with PKU and their siblings on the parent report of EF and mood. However, depressive symptoms were significantly correlated with: EF; long term high phe:tyr exposure; and low tyrosine levels independent of phenylalanine. The practice survey of metabolic clinics from 12 countries indicated a high level of variability in terms of monitoring/treatment of tyrosine in this population. Whilst over 80% of clinics surveyed routinely monitored tyrosine levels in their child patients, 25% reported treatment strategies to increase tyrosine (and thereby lower the phenylalanine:tyrosine ratio) under a variety of patient presentation conditions. Overall, these studies have shown that EF impairments associated with PKU provide support for the dopamine-deficiency model. A language comprehension task showed a different trajectory, serving a timely reminder that non-EF functions also remain vulnerable in this population; and that normal function in childhood does not guarantee normal function by adolescence. Mood impairments were associated with EF impairments as well as long term measures of phenylalanine:tyrosine and/or tyrosine. The implications of this research for enhanced clinical guidelines are discussed given varied current practice.

Effects of varied ionic calcium and phosphate on the proliferation, osteogenic differentiation and mineralization of human periodontal ligament cells in vitro

Background and Objective: A number of bone filling materials containing calcium (Ca++) and phosphate (P) ions have been used in the repair of periodontal bone defects; however, the effect that local release of Ca++ and P ions have on biological reactions is not fully understood. In this study, we investigated the effects of various levels of Ca++ and P ions on the proliferation, osteogenic differentiation, and mineralization of human periodontal ligament cells (hPDLCs). Materials and Methods: hPDLCs were obtained using an explant culture method. Defined concentrations and ratios of ionic Ca++ to inorganic P were added to standard culture and osteogenic induction media. The ability of hPDLCs to proliferate in these growth media was assayed using the Cell Counting Kit-8 (CCK-8). Cell apoptosis was evaluated by FITC-Annexin V/PI double staining method. Osteogenic differentiation and mineralization were investigated by morphological observations, alkaline phosphatase (ALP) activity, and Alizarin red S/von Kossa staining. The mRNA expression of osteogenic related markers was analyzed using a reverse transcriptase polymerase chain reaction (RT-PCR). Results: Within the ranges of Ca++ and P ions concentrations tested, we observed that increased concentrations of Ca++ and P ions enhanced cell proliferation and formation of mineralized matrix nodules; whereas ALP activity was reduced. The RT-PCR results showed that elevated concentrations of Ca++ and P ions led to a general increase of Runx2 mRNA expression and decreased ALP mRNA expression, but gave no clear trend on OCN mRNA levels. Conclusion: The concentrations and ratios of Ca++ and P ions could significantly influence proliferation, differentiation, and mineralization of hPDLCs. Within the range of concentrations tested, we found that the combination of 9.0 mM Ca++ ions and 4.5 mM P ions were the optimum concentrations for proliferation, differentiation, and mineralization in hPDLCs.

Psycho-markers of weight loss. The roles of TFEQ Disinhibition and Restraint in exercise-induced weight management

Eating behaviour traits, namely Disinhibition and Restraint, have the potential to exert an effect on food intake and energy balance. The effectiveness of exercise as a method of weight management could be influenced by these traits. Fifty eight overweight and obese participants completed 12-weeks of supervised exercise. Each participant was prescribed supervised exercise based on an expenditure of 500 kcal/session, 5 d/week for 12-weeks. Following 12-weeks of exercise there was a significant reduction in mean body weight (-3.26 ± 3.63 kg), fat mass (FM: -3.26 ± 2.64 kg), BMI (-1.16 ± 1.17 kg/m2)and waist circumference (WC: -5.0 ± 3.23 cm). Regression analyses revealed a higher baseline Disinhibition score was associated with a greater reduction in BMI and WC, while Internal Disinhibition was associated with a larger decrease in weight, %FM and WC. Neither baseline Restraint or Hunger were associated with any of the anthropometric markers at baseline or after 12-weeks. Furthermore, after 12-weeks of exercise, a decrease in Disinhibition and increase in Restraint were associated with a greater reduction in WC, whereas only Restraint was associated with a decrease in weight. Post-hoc analysis of the sub-factors revealed a decrease in External Disinhibition and increase in Flexible Restraint were associated with weight loss. However, an increase in Rigid Restraint was associated with a reduction in %FM and WC. These findings suggest that exercise-induced weight loss is more marked in individuals with a high level of Disinhibition. These data demonstrate the important roles that Disinhibition and Restraint play in the relationship between exercise and energy balance.

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