Inherent size constraints on prokaryote gene networks due to "accelerating" growth

Networks exhibiting accelerating growth have total link numbers growing faster than linearly with network size and either reach a limit or exhibit graduated transitions from nonstationary-to-stationary statistics and from random to scale-free to regular statistics as the network size grows. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single-celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale-free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value. (c) 2005 Elsevier GmbH. All rights reserved.

Spin exchange and superconductivity in a t-J(')-V model for two-dimensional quarter-filled systems

The effect of antiferromagnetic spin fluctuations on two-dimensional quarter-filled systems is studied theoretically. An effective t-J(')-V model on a square lattice which accounts for checkerboard charge fluctuations and next-nearest-neighbor antiferromagnetic spin fluctuations is considered. From calculations based on large-N theory on this model it is found that the exchange interaction J(') increases the attraction between electrons in the d(xy) channel only, so that both charge and spin fluctuations work cooperatively to produce d(xy) pairing.

The prion protein gene: Identifying regulatory signals using marsupial sequence

The function of the prion protein gene (PRNP) and its normal product PrPC is elusive. We used comparative genomics as a strategy to understand the normal function of PRNP. As the reliability of comparisons increases with the number of species and increased evolutionary distance, we isolated and sequenced a 66.5 kb BAC containing the PRNP gene from a distantly related mammal, the model Australian marsupial Macropus eugenii (tammar wallaby). Marsupials are separated from eutherians such as human and mouse by roughly 180 million years of independent evolution. We found that tammar PRNP, like human PRNP, has two exons. Prion proteins encoded by the tammar wallaby and a distantly related marsupial, Monodelphis domestica (Brazilian opossum) PRNP contain proximal PrP repeats with a distinct, marsupial-specific composition and a variable number. Comparisons of tammar wallaby PRNP with PRNPs from human, mouse, bovine and ovine allowed us to identify non-coding gene regions conserved across the marsupial-eutherian evolutionary distance, which are candidates for regulatory regions. In the PRNP 3' UTR we found a conserved signal for nuclear-specific polyadenylation and the putative cytoplasmic polyadenylation element (CPE), indicating that post-transcriptional control of PRNP mRNA activity is important. Phylogenetic footprinting revealed conserved potential binding sites for the MZF-1 transcription factor in both upstream promoter and intron/intron 1, and for the MEF2, MyTI, Oct-1 and NFAT transcription factors in the intron(s). The presence of a conserved NFAT-binding site and CPE indicates involvement of PrPC in signal transduction and synaptic plasticity. (c) 2004 Elsevier B.V. All rights reserved.

Quantum dynamics of a model for two Josephson-coupled Bose-Einstein condensates

In this work, we investigate the quantum dynamics of a model for two singlemode Bose-Einstein condensates which are coupled via Josephson tunnelling. Using direct numerical diagonalization of the Hamiltonian, we compute the time evolution of the expectation value for the relative particle number across a wide range of couplings. Our analysis shows that the system exhibits rich and complex behaviours varying between harmonic and non-harmonic oscillations, particularly around the threshold coupling between the delocalized and selftrapping phases. We show that these behaviours are dependent on both the initial state of the system and regime of the coupling. In addition, a study of the dynamics for the variance of the relative particle number expectation and the entanglement for different initial states is presented in detail.

Modelling of two-stage anaerobic digestion using the IWA Anaerobic Digestion Model No. 1 (ADM1)

The aim of the study presented was to implement a process model to simulate the dynamic behaviour of a pilot-scale process for anaerobic two-stage digestion of sewage sludge. The model implemented was initiated to support experimental investigations of the anaerobic two-stage digestion process. The model concept implemented in the simulation software package MATLAB(TM)/Simulink(R) is a derivative of the IWA Anaerobic Digestion Model No.1 (ADM1) that has been developed by the IWA task group for mathematical modelling of anaerobic processes. In the present study the original model concept has been adapted and applied to replicate a two-stage digestion process. Testing procedures, including balance checks and 'benchmarking' tests were carried out to verify the accuracy of the implementation. These combined measures ensured a faultless model implementation without numerical inconsistencies. Parameters for both, the thermophilic and the mesophilic process stage, have been estimated successfully using data from lab-scale experiments described in literature. Due to the high number of parameters in the structured model, it was necessary to develop a customised procedure that limited the range of parameters to be estimated. The accuracy of the optimised parameter sets has been assessed against experimental data from pilot-scale experiments. Under these conditions, the model predicted reasonably well the dynamic behaviour of a two-stage digestion process in pilot scale. (C) 2004 Elsevier Ltd. All rights reserved.

Characterization of two polymorphisms in the leukotriene C4 synthase gene in an Australian population of subjects with mild, moderate, and severe asthma

Background: The cysteinyl-leukotrienes (cys-LTs) are proinflammatory mediators that are important in the pathophysiology of asthma. LTC4 synthase is a key enzyme in the cys-LT biosynthetic pathway, and studies in small populations have suggested that a promoter polymorphism (A(-444)C) in the gene might be associated with asthma severity and aspirin intolerance. Objective: We sought to screen the LTC4 synthase gene for polymorphisms and to determine whether there is an association between these polymorphisms and asthma severity or aspirin sensitivity in a large, well-phenotyped population and to determine whether this polymorphism is functionally relevant. Methods: The coding regions of the LTC4 synthase gene were screened for polymorphisms and the A(-444)C polymorphism was analyzed in a large Australian white adult population of mild (n = 282), moderate (n = 236), and severe asthmatic subjects (n = 86) and nonasthmatic subjects (n = 458), as well as in aspirin-intolerant asthmatic subjects (n = 67). The functional activity of the promoter polymorphism was investigated by transient transfection of HL-60 cells with a promoter construct. Results: A new polymorphism was identified in intron 1 of the gene (IVS1-10c>a) but was not associated with asthma. Association studies showed that the A(-444)C polymorphism was weakly associated with asthma per se, but there was no association between the C-444 allele and chronic asthma severity or aspirin intolerance. A meta-analysis of all the genetic studies conducted to date found significant between-study heterogeneity in C-444 allele frequencies within different clinical subgroups. In vitro functional studies showed no significant differences in transcription efficiency between constructs containing the A(-444) allele or the C-444 allele. Conclusions: Our data confirm that, independent of transcriptional activity, the C-444 allele in the LTC4 synthase gene is weakly associated with the asthma phenotype, but it is not related to disease severity or aspirin intolerance.

A simple implementation of a normal mixture approach to differential gene expression in multiclass microarrays

Motivation: An important problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null. The problem can be expressed in a two-component mixture framework, using an empirical Bayes approach. Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with more specific assumptions are computationally intensive. Results: By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The usefulness of our approach is demonstrated on three real datasets.

A Mixture model with random-effects components for clustering correlated gene-expression profiles

Motivation: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. Results: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation) and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too.

Comparison of virulence gene profiles of Escherichia coli strains isolated from healthy and diarrheic swine

A combination of uni- and multiplex PCR assays targeting 58 virulence genes (VGs) associated with Escherichia coli strains causing intestinal and extraintestinal disease in humans and other mammals was used to analyze the VG repertoire of 23 commensal E. coli isolates from healthy pigs and 52 clinical isolates associated with porcine neonatal diarrhea (ND) and postweaning diarrhea (PWD). The relationship between the presence and absence of VGs was interrogated using three statistical methods. According to the generalized linear model, 17 of 58 VGs were found to be significant (P < 0.05) in distinguishing between commensal and clinical isolates. Nine of the 17 genes represented by iha, hlyA, aidA, east1, aah, fimH, iroN(E).(coli), traT, and saa have not been previously identified as important VGs in clinical porcine isolates in Australia. The remaining eight VGs code for fimbriae (F4, F5, F18, and F41) and toxins (STa, STh, LT, and Stx2), normally associated with porcine enterotoxigenic E. coli. Agglomerative hierarchical algorithm analysis grouped E. coli strains into subclusters based primarily on their serogroup. Multivariate analyses of clonal relationships based on the 17 VGs were collapsed into two-dimensional space by principal coordinate analysis. PWD clones were distributed in two quadrants, separated from ND and commensal clones, which tended to cluster within one quadrant. Clonal subclusters within quadrants were highly correlated with serogroups. These methods of analysis provide different perspectives in our attempts to understand how commensal and clinical porcine enterotoxigenic E. coli strains have evolved and are engaged in the dynamic process of losing or acquiring VGs within the pig population.

Leading coordinate analysis of reaction pathways in proton chain transfer: Application to a two-proton transfer model for the green fluorescent protein

The ‘leading coordinate’ approach to computing an approximate reaction pathway, with subsequent determination of the true minimum energy profile, is applied to a two-proton chain transfer model based on the chromophore and its surrounding moieties within the green fluorescent protein (GFP). Using an ab initio quantum chemical method, a number of different relaxed energy profiles are found for several plausible guesses at leading coordinates. The results obtained for different trial leading coordinates are rationalized through the calculation of a two-dimensional relaxed potential energy surface (PES) for the system. Analysis of the 2-D relaxed PES reveals that two of the trial pathways are entirely spurious, while two others contain useful information and can be used to furnish starting points for successful saddle-point searches. Implications for selection of trial leading coordinates in this class of proton chain transfer reactions are discussed, and a simple diagnostic function is proposed for revealing whether or not a relaxed pathway based on a trial leading coordinate is likely to furnish useful information.

Quantum entanglement in the two-impurity Kondo model

In order to quantify quantum entanglement in two-impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, namely the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, I. Due to the spin-rotational invariance of the ground state, the concurrence and negativity are uniquely determined by the spin-spin correlation between the impurities. It is found that there exists a critical minimum value of the antiferromagnetic correlation between the impurity spins which is necessary for entanglement of the two impurity spins. The critical value is discussed in relation with the unstable fixed point in the two-impurity Kondo problem. Specifically, at the fixed point there is no entanglement between the impurity spins. Entanglement will only be created [and quantum information processing (QIP) will only be possible] if the RKKY interaction exchange energy, I, is at least several times larger than the Kondo temperature, T-K. Quantitative criteria for QIP are given in terms of the impurity spin-spin correlation.