Removal of natural organic matter from water using a nano-structured photocatalyst coupled with filtration membrane.

A study of the characteristics of a novel photocatalyst indicated that it consisted of 17.3 nm nano size (average) TiO2 in the anatase phase and porous Fe2O3. SEM results revealed that nano size TiO2 was uniformly deposited onto the surface of Fe2O3 to form a bulk photocatalyst, as TiO2/Fe2O3. The porous TiO2/Fe2O3 catalyst had a BET surface area of 168 m2/g, which is three times higher than that of commercial TiO2. The experimental results indicated that the suspended TiO2/Fe2O3 photocatalyst in a photocatalytic oxidation (PCO) reactor was effective in removing TOC at 61.58% and color400 at 93.25% at 180 min illumination time, under 0.4 g/l catalyst loading and pH 7. Experimental results also revealed that pH at 7 and TiO2/Fe2O3 loading at 0.4 g/l was the optimum condition for removal of humic acids using a PCO reactor. Experimental results clearly indicated that the permeate flux rate of the ultrafiltration (UF) membrane was improved and the filtration membrane fouling phenomenon was reduced with the addition of TiO2/Fe2O3 photocatalysts to the UF membrane system. It was found that increasing the filtration time from 40 min to 185 min, the improvement to the permeate flux rate was from 57 to 83 L/hr x m2.

Statistical mechanics of secondary structures formed by random RNA sequences.

The formation of secondary structures by a random RNA sequence is studied as a model system for the sequence-structure problem omnipresent in biopolymers. Several toy energy models are introduced to allow detailed analytical and numerical studies. First, a two-replica calculation is performed. By mapping the two-replica problem to the denaturation of a single homogeneous RNA molecule in six-dimensional embedding space, we show that sequence disorder is perturbatively irrelevant, i.e., an RNA molecule with weak sequence disorder is in a molten phase where many secondary structures with comparable total energy coexist. A numerical study of various models at high temperature reproduces behaviors characteristic of the molten phase. On the other hand, a scaling argument based on the external statistics of rare regions can be constructed to show that the low-temperature phase is unstable to sequence disorder. We performed a detailed numerical study of the low-temperature phase using the droplet theory as a guide, and characterized the statistics of large-scale, low-energy excitations of the secondary structures from the ground state structure. We find the excitation energy to grow very slowly (i.e., logarithmically) with the length scale of the excitation, suggesting the existence of a marginal glass phase. The transition between the low-temperature glass phase and the high-temperature molten phase is also characterized numerically. It is revealed by a change in the coefficient of the logarithmic excitation energy, from being disorder dominated to being entropy dominated.

Extracting transcriptional events from temporal gene expression patterns during Dictyostelium development.

MOTIVATION: The DNA microarray technology can generate a large amount of data describing the time-course of gene expression. These data, when properly interpreted, can yield a great deal of information concerning differential gene expression during development. Much current effort in bioinformatics has been devoted to the analysis of gene expression data, usually via some 'clustering analysis' on the raw data in some abstract high dimensional space. Here, we describe a method where we first 'process' the raw time-course data using a simple biologically based kinetic model of gene expression. This allows us to reduce the vast data to a few vital attributes characterizing each expression profile, e.g. the times of the onset and cessation of the expression of the developmentally regulated genes. These vital attributes can then be trivially clustered by visual inspection to reveal biologically significant effects. RESULTS: We have applied this approach to microarray expression data from samples isolated every 2 h throughout the 24 h developmental program of Dictyostelium discoideum. mRNA accumulation patterns for 50 developmental genes were found to fit the kinetic model with a p-value of 0.05 or better. Transcription of these genes appears to be initiated in bursts at well-defined periods during development, in a manner suggestive of a dependent sequence. This approach can be applied to analyses of other temporal gene expression patterns, including those of the cell cycle.

Statistical significance of probabilistic sequence alignment and related local hidden Markov models.

The score statistics of probabilistic gapped local alignment of random sequences is investigated both analytically and numerically. The full probabilistic algorithm (e.g., the "local" version of maximum-likelihood or hidden Markov model method) is found to have anomalous statistics. A modified "semi-probabilistic" alignment consisting of a hybrid of Smith-Waterman and probabilistic alignment is then proposed and studied in detail. It is predicted that the score statistics of the hybrid algorithm is of the Gumbel universal form, with the key Gumbel parameter lambda taking on a fixed asymptotic value for a wide variety of scoring systems and parameters. A simple recipe for the computation of the "relative entropy," and from it the finite size correction to lambda, is also given. These predictions compare well with direct numerical simulations for sequences of lengths between 100 and 1,000 examined using various PAM substitution scores and affine gap functions. The sensitivity of the hybrid method in the detection of sequence homology is also studied using correlated sequences generated from toy mutation models. It is found to be comparable to that of the Smith-Waterman alignment and significantly better than the Viterbi version of the probabilistic alignment.

Expression patterns of cell-type-specific genes in Dictyostelium.

Cell-type specific genes were recognized by interrogating microarrays carrying Dictyostelium gene fragments with probes prepared from fractions enriched in prestalk and prespore cells. Cell-type specific accumulation of mRNA from 17 newly identified genes was confirmed by Northern analyses. DNA microarrays carrying 690 targets were used to determine expression profiles during development. The profiles were fit to a biologically based kinetic equation to extract the times of transcription onset and cessation. Although the majority of the genes that were cell-type enriched at the slug stage were first expressed as the prespore and prestalk cells sorted out in aggregates, some were found to be expressed earlier before the cells had even aggregated. These early genes may have been initially expressed in all cells and then preferentially turned over in one or the other cell type. Alternatively, cell type divergence may start soon after the initiation of development.

Force-induced denaturation of RNA.

We quantitatively describe an RNA molecule under the influence of an external force exerted at its two ends as in a typical single-molecule experiment. Our calculation incorporates the interactions between nucleotides by using the experimentally determined free energy rules for RNA secondary structure and models the polymeric properties of the exterior single-stranded regions explicitly as elastic freely jointed chains. We find that despite complicated secondary structures, force-extension curves are typically smooth in quasi-equilibrium. We identify and characterize two sequence/structure-dependent mechanisms that, in addition to the sequence-independent entropic elasticity of the exterior single-stranded regions, are responsible for the smoothness. These involve compensation between different structural elements on which the external force acts simultaneously and contribution of suboptimal structures, respectively. We estimate how many features a force-extension curve recorded in nonequilibrium, where the pulling proceeds faster than rearrangements in the secondary structure of the molecule, could show in principle. Our software is available to the public through an "RNA-pulling server."

Percolation clustering: a novel approach to the clustering of gene expression patterns in Dictyostelium development.

We present a novel approach to the clustering of gene expression patterns based on the mutual connectivity of the patterns. Unlike certain widely used methods (e.g., self-organizing maps and K-means) which essentially force gene expression data into a fixed number of predetermined clustering structures, our approach aims to reveal the natural tendency of the data to cluster, in analogy to the physical phenomenon of percolation. The approach is probabilistic in nature, and as such accommodates the possibility that one gene participates in multiple clusters. The result is cast in terms of the connectivity of each gene to a certain number of (significant) clusters. A computationally efficient algorithm is developed to implement our approach. Performance of the method is illustrated by clustering both constructed data and gene expression data obtained from Dictyostelium development.

The estimation of statistical parameters for local alignment score distributions.

The distribution of optimal local alignment scores of random sequences plays a vital role in evaluating the statistical significance of sequence alignments. These scores can be well described by an extreme-value distribution. The distribution's parameters depend upon the scoring system employed and the random letter frequencies; in general they cannot be derived analytically, but must be estimated by curve fitting. For obtaining accurate parameter estimates, a form of the recently described 'island' method has several advantages. We describe this method in detail, and use it to investigate the functional dependence of these parameters on finite-length edge effects.

Scaling laws and similarity detection in sequence alignment with gaps.

We study the problem of similarity detection by sequence alignment with gaps, using a recently established theoretical framework based on the morphology of alignment paths. Alignments of sequences without mutual correlations are found to have scale-invariant statistics. This is the basis for a scaling theory of alignments of correlated sequences. Using a simple Markov model of evolution, we generate sequences with well-defined mutual correlations and quantify the fidelity of an alignment in an unambiguous way. The scaling theory predicts the dependence of the fidelity on the alignment parameters and on the statistical evolution parameters characterizing the sequence correlations. Specific criteria for the optimal choice of alignment parameters emerge from this theory. The results are verified by extensive numerical simulations.

Optimizing Smith-Waterman alignments.

Mutual correlation between segments of DNA or protein sequences can be detected by Smith-Waterman local alignments. We present a statistical analysis of alignment of such sequences, based on a recent scaling theory. A new fidelity measure is introduced and shown to capture the significance of the local alignment, i.e., the extent to which the correlated subsequences are correctly identified. It is demonstrated how the fidelity may be optimized in the space of penalty parameters using only the alignment score data of a single sequence pair.

Rapid assessment of extremal statistics for gapped local alignment.

The statistical significance of gapped local alignments is characterized by analyzing the extremal statistics of the scores obtained from the alignment of random amino acid sequences. By identifying a complete set of linked clusters, "islands," we devise a method which accurately predicts the extremal score statistics by using only one to a few pairwise alignments. The success of our method relies crucially on the link between the statistics of island scores and extremal score statistics. This link is motivated by heuristic arguments, and firmly established by extensive numerical simulations for a variety of scoring parameter settings and sequence lengths. Our approach is several orders of magnitude faster than the widely used shuffling method, since island counting is trivially incorporated into the basic Smith-Waterman alignment algorithm with minimal computational cost, and all islands are counted in a single alignment. The availability of a rapid and accurate significance estimation method gives one the flexibility to fine tune scoring parameters to detect weakly homologous sequences and obtain optimal alignment fidelity.

A statistical theory of sequence alignment with gaps.

A statistical theory of local alignment algorithms with gaps is presented. Both the linear and logarithmic phases, as well as the phase transition separating the two phases, are described in a quantitative way. Markov sequences without mutual correlations are shown to have scale-invariant alignment statistics. Deviations from scale invariance indicate the presence of mutual correlations detectable by alignment algorithms. Conditions are obtained for the optimal detection of a class of mutual sequence correlations.