Robustness of mathematical models for biological systems

The robustness of mathematical models for biological systems is studied by sensitivity analysis and stochastic simulations. Using a neural network model with three genes as the test problem, we study robustness properties of synthesis and degradation processes. For single parameter robustness, sensitivity analysis techniques are applied for studying parameter variations and stochastic simulations are used for investigating the impact of external noise. Results of sensitivity analysis are consistent with those obtained by stochastic simulations. Stochastic models with external noise can be used for studying the robustness not only to external noise but also to parameter variations. For external noise we also use stochastic models to study the robustness of the function of each gene and that of the system.

A multi-scaled approach for simulating chemical reaction systems

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work.

Metagenomic analysis of two enhanced biological phosphorus removal (EBPR) sludge communities

Enhanced biological phosphorus removal (EBPR) is one of the best-studied microbially mediated industrial processes because of its ecological and economic relevance. Despite this, it is not well understood at the metabolic level. Here we present a metagenomic analysis of two lab-scale EBPR sludges dominated by the uncultured bacterium, Candidatus Accumulibacter phosphatis.'' The analysis sheds light on several controversies in EBPR metabolic models and provides hypotheses explaining the dominance of A. phosphatis in this habitat, its lifestyle outside EBPR and probable cultivation requirements. Comparison of the same species from different EBPR sludges highlights recent evolutionary dynamics in the A. phosphatis genome that could be linked to mechanisms for environmental adaptation. In spite of an apparent lack of phylogenetic overlap in the flanking communities of the two sludges studied, common functional themes were found, at least one of them complementary to the inferred metabolism of the dominant organism. The present study provides a much needed blueprint for a systems-level understanding of EBPR and illustrates that metagenomics enables detailed, often novel, insights into even well-studied biological systems.

Endothelial cell serine proteases expressed during vascular morphogenesis and angiogenesis

Many serine proteases play important regulatory roles in complex biological systems, but only a few have been linked directly with capillary morphogenesis and angiogenesis. Here we provide evidence that serine protease activities, independent of the plasminogen activation cascade, are required for microvascular endothelial cell reorganization and capillary morphogenesis in vitro. A homology cloning approach targeting conserved motifs present in all serine proteases, was used to identify candidate serine proteases involved in these processes, and revealed 5 genes (acrosin, testisin, neurosin, PSP and neurotrypsin), none of which had been associated previously with expression in endothelial cells. A subsequent gene-specific RT-PCR screen for 22 serine proteases confirmed expression of these 5 genes and identified 7 additional serine protease genes expressed by human endothelial cells, urokinase-type plasminogen activator, protein C,TMPRSS2, hepsin, matriptase/ MT-SPI, dipepticlylpepticlase IV, and seprase. Differences in serine protease gene expression between microvascular and human umbilical vein endothelial cells (HUVECs) were identified and several serine protease genes were found to be regulated by the nature of the substratum, ie. artificial basement membrane or fibrillar type I collagen. mRNA transcripts of several serine protease genes were associated with blood vessels in vivo by in situ hybridization of human tissue specimens. These data suggest a potential role for serine proteases, not previously associated with endothelium, in vascular function and angiogenesis.

Synthesis of gadolinium-labeled shell-crosslinked nanoparticles for magnetic resonance imaging applications

Shell-crosslinked knedel-like nanoparticles (SCKs; knedel is a Polish term for dumplings) were derivatized with gadolinium Shell chelates and studied as robust magnetic-resonance-imaging-active structures with hydrodynamic diameters of 40 +/- 3 nm. SCKs possessing an amphiphilic core-shell morphology were produced from the aqueous assembly of diblock copolymers of poly(acrylic acid) (PAA) and poly(methyl acrylate) (PMA), PAA(52)-b-PMA(128), and subsequent covalent crosslinking by amidation upon reaction with 2,2'-(ethylenedioxy)bis(ethylamine) throughout the shell layer. The properties of these materials, including non-toxicity towards mammalian cells, non-immunogenicity within mice, and capability for polyvalent targeting, make them ideal candidates for utilization within biological systems. The synthesis of SCKs derivatized with Gd-III and designed for potential use as a unique nanometer-scale contrast agent for MRI applications is described herein. Utilization of an amino-functionalized diethylenetriaminepentaacetic acid-Gd analogue allowed for direct covalent conjugation throughout the hydrophilic shell layer of the SCKs and served to increase the rotational correlation lifetime of the Gd. In addition, the highly hydrated nature of the shell layer in which the Gd was located allowed for rapid water exchange; thus, the resulting material demonstrated large ionic relaxivities (39 s(-1) mM(-1)) in an applied magnetic field of 0.47 T at 40 degrees C and, as a result of the large loading capacity of the material, also demonstrated high molecular relaxivities (20 000 s(-1) mM(-1)).

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the A phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. in this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

On parameter estimation in population models

We describe methods for estimating the parameters of Markovian population processes in continuous time, thus increasing their utility in modelling real biological systems. A general approach, applicable to any finite-state continuous-time Markovian model, is presented, and this is specialised to a computationally more efficient method applicable to a class of models called density-dependent Markov population processes. We illustrate the versatility of both approaches by estimating the parameters of the stochastic SIS logistic model from simulated data. This model is also fitted to data from a population of Bay checkerspot butterfly (Euphydryas editha bayensis), allowing us to assess the viability of this population. (c) 2006 Elsevier Inc. All rights reserved.

Reduced variability of postural strategy prevents normalization of motor changes induced by back pain: A risk factor for chronic trouble?

Variability is fundamental to biological systems and is important in posturomotor learning and control. Pain induces a protective postural strategy, although variability is normally preserved. If variability is lost, does the normal postural strategy return when pain stops? Sixteen subjects performed arm movements during control trials, when the movement evoked back pain and then when it did not. Variability in the postural strategy of the abdominal muscles and pain-related cognitions were evaluated. Only those subjects for whom pain induced a reduction in variability of the postural strategy failed to return to a normal strategy when pain stopped. They were also characterized by their pain-related cognitions. Ongoing perception of threat to the back may exert tighter evaluative control over variability of the postural strategy.

Parallel implementation of stochastic simulation for large scale cellular processes

Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes

Multilevel modelling for inference of genetic regulatory networks

Time-course experiments with microarrays are often used to study dynamic biological systems and genetic regulatory networks (GRNs) that model how genes influence each other in cell-level development of organisms. The inference for GRNs provides important insights into the fundamental biological processes such as growth and is useful in disease diagnosis and genomic drug design. Due to the experimental design, multilevel data hierarchies are often present in time-course gene expression data. Most existing methods, however, ignore the dependency of the expression measurements over time and the correlation among gene expression profiles. Such independence assumptions violate regulatory interactions and can result in overlooking certain important subject effects and lead to spurious inference for regulatory networks or mechanisms. In this paper, a multilevel mixed-effects model is adopted to incorporate data hierarchies in the analysis of time-course data, where temporal and subject effects are both assumed to be random. The method starts with the clustering of genes by fitting the mixture model within the multilevel random-effects model framework using the expectation-maximization (EM) algorithm. The network of regulatory interactions is then determined by searching for regulatory control elements (activators and inhibitors) shared by the clusters of co-expressed genes, based on a time-lagged correlation coefficients measurement. The method is applied to two real time-course datasets from the budding yeast (Saccharomyces cerevisiae) genome. It is shown that the proposed method provides clusters of cell-cycle regulated genes that are supported by existing gene function annotations, and hence enables inference on regulatory interactions for the genetic network.

Anaerobic metabolism of propionate by polyphosphate-accumulating organisms in enhanced biological phosphorus removal systems

Propionate, a carbon substrate abundant in many prefermenters, has been shown in several previous studies to be a more favorable substrate than acetate for enhanced biological phosphorus removal (EBPR). The anaerobic metabolism of propionate by polyphosphate accumulating organisms (PAOs) is studied in this paper. A metabolic model is proposed to characterize the anaerobic biochemical transformations of propionate uptake by PAOs. The model is demonstrated to predict very well the experimental data from a PAO culture enriched in a laboratory-scale reactor with propionate as the sole carbon source. Quantitative fluorescence in-situ hybridization (FISH) analysis shows that Candidatus Accumulibacter phosphatis, the only identified PAO to date, constitute 63% of the bacterial population in this culture. Unlike the anaerobic metabolism of acetate by PAOs, which induces mainly poly-beta-hydroxybutyrate (PHB) production, the major fractions of poly-beta-hydroxyalkanoate (PHA) produced with propionate as the carbon source are poly-beta-hydroxyvalerate (PHV) and poly-beta-hydroxy-2-methylvalerate (PH2MV). PHA formation correlates very well with a selective (or nonrandom) condensation of acetyl-CoA and propionyl-CoA molecules. The maximum specific propionate uptake rate by PAOs found in this study is 0.18 C-mol/C-mol-biomass h, which is very similar to the maximum specific acetate uptake rate reported in literature. The energy required for transporting 1 carbon-mole of propionate across the PAO cell membrane is also determined to be similar to the transportation of 1 carbon-mole of acetate. Furthermore, the experimental results suggest that PAOs possess a similar preference toward acetate and propionate uptake on a carbon-mole basis. (c) 2005 Wiley Periodicals, Inc.

Optimisation of poly-b-hydroxyalkanoate analysis using gas chromatography for enhanced biological phosphorus removal systems

Poly-beta-hydroxyalkanoate (PHA) is a polymer commonly used in carbon and energy storage for many different bacterial cells. Polyphosphate accumulating organisms (PAOs) and glycogen accumulating organisms (GAOs), store PHA anaerobically through metabolism of carbon substrates such as acetate and propionate. Although poly-beta-hydroxybutyrate (PHB)and poly-beta-hydroxyvalerate (PHV) are commonly quantified using a previously developed gas chromatography (GC) method, poly-beta-hydroxy-2-methyl valerate (PH2MV) is seldom quantified despite the fact that it has been shown to be a key PHA fraction produced when PAOs or GAOs metabolise propionate. This paper presents two GC-based methods modified for extraction and quantification of PHB, PHV and PH2MV from enhanced biological phosphorus removal (EBPR) systems. For the extraction Of PHB and PHV from acetate fed PAO and GAO cultures, a 3% sulfuric acid concentration and a 2-20 h digestion time is recommended, while a 10% sulfuric acid solution digested for 20 h is recommended for PHV and PH2MV analysis from propionate fed EBPR systems. (c) 2005 Elsevier B.V. All rights reserved.

Competition between polyphosphate and glycogen accumulating organisms in enhanced biological phosphorus removal systems with acetate and propionate as carbon sources

Enhanced biological phosphorus removal (EBPR) is a widely used process for achieving phosphorus removal from wastewater. A potential reason for EBPR failure is the undesirable growth of glycogen accumulating organisms (GAOs), which can compete for carbon sources with the bacterial group responsible for phosphorus removal from wastewater: the polyphosphate accumulating organisms (PAOs). This study investigates the impact of carbon source on EBPR performance and the competition between PAOs and GAOs. Two sequencing batch reactors (SBRs) were operated during a 4-6 month period and fed with a media containing acetate or propionate, respectively, as the sole carbon source. It was found that the acetate fed SBR rarely achieved a high level of phosphorus removal, and that a large portion of the microbial community was comprised of Candidatus Competibacter phosphatis, a known GAO. The propionate fed SBR, however, achieved stable phosphorus removal throughout the study, apart from one brief disturbance. The bacterial community of the propionate fed SBR was dominated by Candidatus Accumulibacter phosphatis, a known PAO, and did not contain Competibacter In a separate experiment, another SBR was seeded with a mixture of PAOs and a group of alphaproteobacterial GAOs, both enriched with propionate as the sole carbon source. Stable EBPR was achieved and the PAO population increased while the GAOs appeared to be out-competed. The results of this paper suggest that propionate may provide PAOs with a selective advantage over GAOs in the PAO-GAO competition, particularly through the minimisation of Competibacter Propionate may be a more suitable substrate than acetate for enhancing phosphorus removal in EBPR systems. (c) 2005 Elsevier B.V. All rights reserved.