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.

Exploring the parameter space of a rabbit ventricular action potential model to investigate the effect of variation on action potential and calcium transients

Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.

Computational approaches for modelling intrinsic noise and delays in genetic regulatory networks

This chapter focuses on the interactions and roles between delays and intrinsic noise effects within cellular pathways and regulatory networks. We address these aspects by focusing on genetic regulatory networks that share a common network motif, namely the negative feedback loop, leading to oscillatory gene expression and protein levels. In this context, we discuss computational simulation algorithms for addressing the interplay of delays and noise within the signaling pathways based on biological data. We address implementational issues associated with efficiency and robustness. In a molecular biology setting we present two case studies of temporal models for the Hes1 gene (Monk, 2003; Hirata et al., 2002), known to act as a molecular clock, and the Her1/Her7 regulatory system controlling the periodic somite segmentation in vertebrate embryos (Giudicelli and Lewis, 2004; Horikawa et al., 2006).

Parameter estimation for a phenomenological model of the cardiac action potential

The action potential (ap) of a cardiac cell is made up of a complex balance of ionic currents which flow across the cell membrane in response to electrical excitation of the cell. Biophysically detailed mathematical models of the ap have grown larger in terms of the variables and parameters required to model new findings in subcellular ionic mechanisms. The fitting of parameters to such models has seen a large degree of parameter and module re-use from earlier models. An alternative method for modelling electrically exciteable cardiac tissue is a phenomenological model, which reconstructs tissue level ap wave behaviour without subcellular details. A new parameter estimation technique to fit the morphology of the ap in a four variable phenomenological model is presented. An approximation of a nonlinear ordinary differential equation model is established that corresponds to the given phenomenological model of the cardiac ap. The parameter estimation problem is converted into a minimisation problem for the unknown parameters. A modified hybrid Nelder–Mead simplex search and particle swarm optimization is then used to solve the minimisation problem for the unknown parameters. The successful fitting of data generated from a well known biophysically detailed model is demonstrated. A successful fit to an experimental ap recording that contains both noise and experimental artefacts is also produced. The parameter estimation method’s ability to fit a complex morphology to a model with substantially more parameters than previously used is established.

Evolving noisy oscillatory dynamics in genetic regulatory networks

We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation and post-translational modifications. The stochastic, reaction-based GP system is similar but not identical with algorithmic chemistries. We evolved genetic networks with noisy oscillatory dynamics. The results show the practicality of evolving particular dynamics in gene regulatory networks when modelled with intrinsic noise.

Population genetic structure and patterns of dispersal in the Giant Long-Armed Prawn, Macrobrachium lar (Fabricius, 1798) (Decapoda : Palaemonidae)

The Giant Long-Armed Prawn, Macrobrachium lar is a freshwater species native to the Indo-Pacific. M. lar has a long-lived, passive, pelagic marine larval stage where larvae need to colonise freshwater within three months to complete their development. Dispersal is likely to be influenced by the extensive distances larvae must transit between small oceanic islands to find suitable freshwater habitat, and by prevailing east to west wind and ocean currents in the southern Pacific Ocean. Thus, both intrinsic and extrinsic factors are likely to influence wild population structure in this species. The present study sought to define the contemporary broad and fine-scale population genetic structure of Macrobrachium lar in the south-western Pacific Ocean. Three polymorphic microsatellite loci were used to assess patterns of genetic variation within and among 19 wild adult sample sites. Statistical procedures that partition variation implied that at both spatial scales, essentially all variation was present within sample sites and differentiation among sites was low. Any differentiation observed also was not correlated with geographical distance. Statistical approaches that measure genetic distance, at the broad-scale, showed that all south-western Pacific Islands were essentially homogeneous, with the exception of a well supported divergent Cook Islands group. These findings are likely the result of some combination of factors that may include the potential for allelic homoplasy, through to the effects of sampling regime. Based on the findings, there is most likely a divergent M. lar Cook Islands clade in the south-western Pacific Ocean, resulting from prevailing ocean currents. Confirmation of this pattern will require a more detailed analysis of nDNA variation using a larger number of loci and, where possible, use of larger population sizes.

A mathematical model for genetic regulation of the lactose operon

In this paper we construct a mathematical model for the genetic regulatory network of the lactose operon. This mathematical model contains transcription and translation of the lactose permease (LacY) and a reporter gene GFP. The probability of transcription of LacY is determined by 14 binding states out of all 50 possible binding states of the lactose operon based on the quasi-steady-state assumption for the binding reactions, while we calculate the probability of transcription for the reporter gene GFP based on 5 binding states out of 19 possible binding states because the binding site O2 is missing for this reporter gene. We have tested different mechanisms for the transport of thio-methylgalactoside (TMG) and the effect of different Hill coefficients on the simulated LacY expression levels. Using this mathematical model we have realized one of the experimental results with different LacY concentrations, which are induced by different concentrations of TMG.

Evolving genetic regulatory networks performing as stochastic switches

Recent studies have shown that small genetic regulatory networks (GRNs) can be evolved in silico displaying certain dynamics in the underlying mathematical model. It is expected that evolutionary approaches can help to gain a better understanding of biological design principles and assist in the engineering of genetic networks. To take the stochastic nature of GRNs into account, our evolutionary approach models GRNs as biochemical reaction networks based on simple enzyme kinetics and simulates them by using Gillespie’s stochastic simulation algorithm (SSA). We have already demonstrated the relevance of considering intrinsic stochasticity by evolving GRNs that show oscillatory dynamics in the SSA but not in the ODE regime. Here, we present and discuss first results in the evolution of GRNs performing as stochastic switches.

QoS-aware web service composition using genetic algorithms

Web service technology is increasingly being used to build various e-Applications, in domains such as e-Business and e-Science. Characteristic benefits of web service technology are its inter-operability, decoupling and just-in-time integration. Using web service technology, an e-Application can be implemented by web service composition — by composing existing individual web services in accordance with the business process of the application. This means the application is provided to customers in the form of a value-added composite web service. An important and challenging issue of web service composition, is how to meet Quality-of-Service (QoS) requirements. This includes customer focused elements such as response time, price, throughput and reliability as well as how to best provide QoS results for the composites. This in turn best fulfils customers’ expectations and achieves their satisfaction. Fulfilling these QoS requirements or addressing the QoS-aware web service composition problem is the focus of this project. From a computational point of view, QoS-aware web service composition can be transformed into diverse optimisation problems. These problems are characterised as complex, large-scale, highly constrained and multi-objective problems. We therefore use genetic algorithms (GAs) to address QoS-based service composition problems. More precisely, this study addresses three important subproblems of QoS-aware web service composition; QoS-based web service selection for a composite web service accommodating constraints on inter-service dependence and conflict, QoS-based resource allocation and scheduling for multiple composite services on hybrid clouds, and performance-driven composite service partitioning for decentralised execution. Based on operations research theory, we model the three problems as a constrained optimisation problem, a resource allocation and scheduling problem, and a graph partitioning problem, respectively. Then, we present novel GAs to address these problems. We also conduct experiments to evaluate the performance of the new GAs. Finally, verification experiments are performed to show the correctness of the GAs. The major outcomes from the first problem are three novel GAs: a penaltybased GA, a min-conflict hill-climbing repairing GA, and a hybrid GA. These GAs adopt different constraint handling strategies to handle constraints on interservice dependence and conflict. This is an important factor that has been largely ignored by existing algorithms that might lead to the generation of infeasible composite services. Experimental results demonstrate the effectiveness of our GAs for handling the QoS-based web service selection problem with constraints on inter-service dependence and conflict, as well as their better scalability than the existing integer programming-based method for large scale web service selection problems. The major outcomes from the second problem has resulted in two GAs; a random-key GA and a cooperative coevolutionary GA (CCGA). Experiments demonstrate the good scalability of the two algorithms. In particular, the CCGA scales well as the number of composite services involved in a problem increases, while no other algorithms demonstrate this ability. The findings from the third problem result in a novel GA for composite service partitioning for decentralised execution. Compared with existing heuristic algorithms, the new GA is more suitable for a large-scale composite web service program partitioning problems. In addition, the GA outperforms existing heuristic algorithms, generating a better deployment topology for a composite web service for decentralised execution. These effective and scalable GAs can be integrated into QoS-based management tools to facilitate the delivery of feasible, reliable and high quality composite web services.

An improved genetic algorithm and graph theory based method for optimal sectionalizer switch placement in distribution networks with DG

In this paper a new graph-theory and improved genetic algorithm based practical method is employed to solve the optimal sectionalizer switch placement problem. The proposed method determines the best locations of sectionalizer switching devices in distribution networks considering the effects of presence of distributed generation (DG) in fitness functions and other optimization constraints, providing the maximum number of costumers to be supplied by distributed generation sources in islanded distribution systems after possible faults. The proposed method is simulated and tested on several distribution test systems in both cases of with DG and non DG situations. The results of the simulations validate the proposed method for switch placement of the distribution network in the presence of distributed generation.

Impacts of traditional husbandry practices on exploitable levels of genetic diversity in cultured 'Tra' catfish (Pangasianodon hypophthalmus) in the Mekong Delta, Vietnam

Sutchi catfish (Pangasianodon hypophthalmus) – known more universally by the Vietnamese name ‘Tra’ is an economically important freshwater fish in the Mekong Delta in Vietnam that constitutes an important food resource. Artificial propagation technology for Tra catfish has only recently been developed along the main branches of the Mekong River where more than 60% of the local human population participate in fishing or aquaculture. Extensive support for catfish culture in general, and that of Tra (P. hypophthalmus) in particular, has been provided by the Vietnamese government to increase both the scale of production and to develop international export markets. In 2006, total Vietnamese catfish exports reached approximately 286,602 metric tons (MT) and were valued at 736.87 $M with a number of large new export destinations being developed. Total value of production from catfish culture has been predicted to increase to approximately USD 1 billion by 2020. While freshwater catfish culture in Vietnam has a promising future, concerns have been raised about long-term quality of fry and the effectiveness of current brood stock management practices, issues that have been largely neglected to date. In this study, four DNA markers (microsatellite loci: CB4, CB7, CB12 and CB13) that were developed specifically for Tra (P. hypophthalmus) in an earlier study were applied to examine the genetic quality of artificially propagated Tra fry in the Mekong Delta in Vietnam. The goals of the study were to assess: (i) how well available levels of genetic variation in Tra brood stock used for artificial propagation in the Mekong Delta of Vietnam (breeders from three private hatcheries and Research Institute of Aquaculture No2 (RIA2) founders) has been conserved; and (ii) whether or not genetic diversity had declined significantly over time in a stock improvement program for Tra catfish at RIA2. A secondary issue addressed was how genetic markers could best be used to assist industry development. DNA was extracted from fins of catfish collected from the two main branches of the Mekong River inf Vietnam, three private hatcheries and samples from the Tra improvement program at RIA2. Study outcomes: i) Genetic diversity estimates for Tra brood stock samples were similar to, and slightly higher than, wild reference samples. In addition, the relative contribution by breeders to fry in commercial private hatcheries strongly suggest that the true Ne is likely to be significantly less than the breeder numbers used; ii) in a stock improvement program for Tra catfish at RIA2, no significant differences were detected in gene frequencies among generations (FST=0.021, P=0.036>0.002 after Bonferroni correction); and only small differences were observed in alleles frequencies among sample populations. To date, genetic markers have not been applied in the Tra catfish industry, but in the current project they were used to evaluate the levels of genetic variation in the Tra catfish selective breeding program at RIA2 and to undertake genetic correlations between genetic marker and trait variation. While no associations were detected using only four loci, they analysis provided training in the practical applications of the use of molecular markers in aquaculture in general, and in Tra culture, in particular.

Reduced variance in monozygous twins for multiple MR parameters : implications for disease studies and the genetic basis of brain structure

Twin studies offer the opportunity to determine the relative contribution of genes versus environment in traits of interest. Here, we investigate the extent to which variance in brain structure is reduced in monozygous twins with identical genetic make-up. We investigate whether using twins as compared to a control population reduces variability in a number of common magnetic resonance (MR) structural measures, and we investigate the location of areas under major genetic influences. This is fundamental to understanding the benefit of using twins in studies where structure is the phenotype of interest. Twenty-three pairs of healthy MZ twins were compared to matched control pairs. Volume, T2 and diffusion MR imaging were performed as well as spectroscopy (MRS). Images were compared using (i) global measures of standard deviation and effect size, (ii) voxel-based analysis of similarity and (iii) intra-pair correlation. Global measures indicated a consistent increase in structural similarity in twins. The voxel-based and correlation analyses indicated a widespread pattern of increased similarity in twin pairs, particularly in frontal and temporal regions. The areas of increased similarity were most widespread for the diffusion trace and least widespread for T2. MRS showed consistent reduction in metabolite variation that was significant in the temporal lobe N-acetylaspartate (NAA). This study has shown the distribution and magnitude of reduced variability in brain volume, diffusion, T2 and metabolites in twins. The data suggest that evaluation of twins discordant for disease is indeed a valid way to attribute genetic or environmental influences to observed abnormalities in patients since evidence is provided for the underlying assumption of decreased variability in twins.

Possible genetic predisposition to lymphedema after breast cancer

Background: Known risk factors for secondary lymphedema only partially explain who develops lymphedema following cancer, suggesting that inherited genetic susceptibility may influence risk. Moreover, identification of molecular signatures could facilitate lymphedema risk prediction prior to surgery or lead to effective drug therapies for prevention or treatment. Recent advances in the molecular biology underlying development of the lymphatic system and related congenital disorders implicate a number of potential candidate genes to explore in relation to secondary lymphedema. Methods and Results: We undertook a nested case-control study, with participants who had developed lymphedema after surgical intervention within the first 18 months of their breast cancer diagnosis serving as cases (n=22) and those without lymphedema serving as controls (n=98), identified from a prospective, population-based, cohort study in Queensland, Australia. TagSNPs that covered all known genetic variation in the genes SOX18, VEGFC, VEGFD, VEGFR2, VEGFR3, RORC, FOXC2, LYVE1, ADM and PROX1 were selected for genotyping. Multiple SNPs within three receptor genes, VEGFR2, VEGFR3 and RORC, were associated with lymphedema defined by statistical significance (p<0.05) or extreme risk estimates (OR<0.5 or >2.0). Conclusions: These provocative, albeit preliminary, findings regarding possible genetic predisposition to secondary lymphedema following breast cancer treatment warrant further attention for potential replication using larger datasets.

Effect of soil parameter uncertainty on seismic response of buried segmented pipeline

Pipelines are important lifeline facilities spread over a large area and they generally encounter a range of seismic hazards and different soil conditions. The seismic response of a buried segmented pipe depends on various parameters such as the type of buried pipe material and joints, end restraint conditions, soil characteristics, burial depths, and earthquake ground motion, etc. This study highlights the effect of the variation of geotechnical properties of the surrounding soil on seismic response of a buried pipeline. The variations of the properties of the surrounding soil along the pipe are described by sampling them from predefined probability distribution. The soil-pipe interaction model is developed in OpenSEES. Nonlinear earthquake time-history analysis is performed to study the effect of soil parameters variability on the response of pipeline. Based on the results, it is found that uncertainty in soil parameters may result in significant response variability of the pipeline.