Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence

The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs) from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation is that the characteristics of a single Boolean network without perturbation may be determined by its pairwise transitions. Because the network function is fixed and there are no perturbations, a given state will always be followed by a unique state at the succeeding time point. Thus, a transition counting matrix compiled over a data sequence will be sparse and contain only one entry per line. If the network also has perturbations, with small perturbation probability, then the transition counting matrix would have some insignificant nonzero entries replacing some (or all) of the zeros. If a data sequence is sufficiently long to adequately populate the matrix, then determination of the functions and inputs underlying the model is straightforward. The difficulty comes when the transition counting matrix consists of data derived from more than one Boolean network. We address the PBN inference procedure in several steps: (1) separate the data sequence into "pure" subsequences corresponding to constituent Boolean networks; (2) given a subsequence, infer a Boolean network; and (3) infer the probabilities of perturbation, the probability of there being a switch between constituent Boolean networks, and the selection probabilities governing which network is to be selected given a switch. Capturing the full dynamic behavior of probabilistic Boolean networks, be they binary or multivalued, will require the use of temporal data, and a great deal of it. This should not be surprising given the complexity of the model and the number of parameters, both transitional and static, that must be estimated. In addition to providing an inference algorithm, this paper demonstrates that the data requirement is much smaller if one does not wish to infer the switching, perturbation, and selection probabilities, and that constituent-network connectivity can be discovered with decent accuracy for relatively small time-course sequences.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]     

Analysis of Free Energy Signals Arising from Nucleotide Hybridization Between rRNA and mRNA Sequences during Translation in Eubacteria

A decoding algorithm is tested that mechanistically models the progressive alignments that arise as the mRNA moves past the rRNA tail during translation elongation. Each of these alignments provides an opportunity for hybridization between the single-stranded, -terminal nucleotides of the 16S rRNA and the spatially accessible window of mRNA sequence, from which a free energy value can be calculated. Using this algorithm we show that a periodic, energetic pattern of frequency 1/3 is revealed. This periodic signal exists in the majority of coding regions of eubacterial genes, but not in the non-coding regions encoding the 16S and 23S rRNAs. Signal analysis reveals that the population of coding regions of each bacterial species has a mean phase that is correlated in a statistically significant way with species () content. These results suggest that the periodic signal could function as a synchronization signal for the maintenance of reading frame and that codon usage provides a mechanism for manipulation of signal phase.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]     

The Wavelet-Based Cluster Analysis for Temporal Gene Expression Data

A variety of high-throughput methods have made it possible to generate detailed temporal expression data for a single gene or large numbers of genes. Common methods for analysis of these large data sets can be problematic. One challenge is the comparison of temporal expression data obtained from different growth conditions where the patterns of expression may be shifted in time. We propose the use of wavelet analysis to transform the data obtained under different growth conditions to permit comparison of expression patterns from experiments that have time shifts or delays. We demonstrate this approach using detailed temporal data for a single bacterial gene obtained under 72 different growth conditions. This general strategy can be applied in the analysis of data sets of thousands of genes under different conditions.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]     

Splitting the BLOSUM Score into Numbers of Biological Significance

Mathematical tools developed in the context of Shannon information theory were used to analyze the meaning of the BLOSUM score, which was split into three components termed as the BLOSUM spectrum (or BLOSpectrum). These relate respectively to the sequence convergence (the stochastic similarity of the two protein sequences), to the background frequency divergence (typicality of the amino acid probability distribution in each sequence), and to the target frequency divergence (compliance of the amino acid variations between the two sequences to the protein model implicit in the BLOCKS database). This treatment sharpens the protein sequence comparison, providing a rationale for the biological significance of the obtained score, and helps to identify weakly related sequences. Moreover, the BLOSpectrum can guide the choice of the most appropriate scoring matrix, tailoring it to the evolutionary divergence associated with the two sequences, or indicate if a compositionally adjusted matrix could perform better.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]     

Multipattern Consensus Regions in Multiple Aligned Protein Sequences and Their Segmentation

Decomposing a biological sequence into its functional regions is an important prerequisite to understand the molecule. Using the multiple alignments of the sequences, we evaluate a segmentation based on the type of statistical variation pattern from each of the aligned sites. To describe such a more general pattern, we introduce multipattern consensus regions as segmented regions based on conserved as well as interdependent patterns. Thus the proposed consensus region considers patterns that are statistically significant and extends a local neighborhood. To show its relevance in protein sequence analysis, a cancer suppressor gene called p53 is examined. The results show significant associations between the detected regions and tendency of mutations, location on the 3D structure, and cancer hereditable factors that can be inferred from human twin studies.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]     

Coomassie Blue as a Near-infrared Fluorescent Stain: A Systematic Comparison With Sypro Ruby for In-gel Protein Detection

Quantitative proteome analyses suggest that the well-established stain colloidal Coomassie Blue, when used as an infrared dye, may provide sensitive, post-electrophoretic in-gel protein detection that can rival even Sypro Ruby. Considering the central role of two-dimensional gel electrophoresis in top-down proteomic analyses, a more cost effective alternative such as Coomassie Blue could prove an important tool in ongoing refinements of this important analytical technique. To date, no systematic characterization of Coomassie Blue infrared fluorescence detection relative to detection with SR has been reported. Here, seven commercial Coomassie stain reagents and seven stain formulations described in the literature were systematically compared. The selectivity, threshold sensitivity, inter-protein variability, and linear-dynamic range of Coomassie Blue infrared fluorescence detection were assessed in parallel with Sypro Ruby. Notably, several of the Coomassie stain formulations provided infrared fluorescence detection sensitivity to <1 ng of protein in-gel, slightly exceeding the performance of Sypro Ruby. The linear dynamic range of Coomassie Blue infrared fluorescence detection was found to significantly exceed that of Sypro Ruby. However, in two-dimensional gel analyses, because of a blunted fluorescence response, Sypro Ruby was able to detect a few additional protein spots, amounting to 0.6% of the detected proteome. Thus, although both detection methods have their advantages and disadvantages, differences between the two appear to be small. Coomassie Blue infrared fluorescence detection is thus a viable alternative for gel-based proteomics, offering detection comparable to Sypro Ruby, and more reliable quantitative assessments, but at a fraction of the cost.Gel electrophoresis is an accessible, widely applicable and mature protein resolving technology. As the original top-down approach to proteomic analyses, among its many attributes the high resolution achievable by two dimensional gel-electrophoresis (2DE)¹ ensures that it remains an effective analytical technology despite the appearance of alternatives. However, in-gel detection remains a limiting factor for gel-based analyses; available technology generally permits the detection and quantification of only relatively abundant proteins (35). Many critical components in normal physiology and also disease may be several orders of magnitude less abundant and thus below the detection threshold of in-gel stains, or indeed most techniques. Pre- and post-fractionation technologies have been developed to address this central issue in proteomics but these are not without limitations (1–5). Thus improved detection methods for gel-based proteomics continue to be a high priority, and the literature is rich with different in-gel detection methods and innovative improvements (6–34). This history of iterative refinement presents a wealth of choices when selecting a detection strategy for a gel-based proteomic analysis (35).Perhaps the best known in-gel detection method is the ubiquitous Coomassie Blue (CB) stain; CB has served as a gel stain and protein quantification reagent for over 40 years. Though affordable, robust, easy to use, and compatible with mass spectrometry (MS), CB staining is relatively insensitive. In traditional organic solvent formulations, CB detects ∼ 10 ng of protein in-gel, and some reports suggest poorer sensitivity (27, 29, 36, 37). Sensitivity is hampered by relatively high background staining because of nonspecific retention of dye within the gel matrix (32, 36, 38, 39). The development of colloidal CB (CCB) formulations largely addressed these limitations (12); the concentration of soluble CB was carefully controlled by sequestering the majority of the dye into colloidal particles, mediated by pH, solvent, and the ionic strength of the solution. Minimizing soluble dye concentration and penetration of the gel matrix mitigated background staining, and the introduction of phosphoric acid into the staining reagent enhanced dye-protein interactions (8, 12, 40), contributing to an in-gel staining sensitivity of 5–10 ng protein, with some formulations reportedly yielding sensitivities of 0.1–1 ng (8, 12, 22, 39, 41, 42). Thus CCB achieved higher sensitivity than traditional CB staining, yet maintained all the advantages of the latter, including low cost and compatibility with existing densitometric detection instruments and MS. Although surpassed by newer methods, the practical advantages of CCB ensure that it remains one of the most common gel stains in use.Fluorescent stains have become the routine and sensitive alternative to visible dyes. Among these, the ruthenium-organometallic family of dyes have been widely applied and the most commercially well-known is Sypro Ruby (SR), which is purported to interact noncovalently with primary amines in proteins (15, 18, 19, 43). Chief among the attributes of these dyes is their high sensitivity. In-gel detection limits of < 1 ng for some proteins have been reported for SR (6, 9, 14, 44, 45). Moreover, SR staining has been reported to yield a greater linear dynamic range (LDR), and reduced interprotein variability (IPV) compared with CCB and silver stains (15, 19, 46–49). SR is easy to use, fully MS compatible, and relatively forgiving of variations in initial conditions (6, 15). The chief consequence of these advances remains high cost; SR and related stains are notoriously expensive, and beyond the budget of many laboratories. Furthermore, despite some small cost advantage relative to SR, none of the available alternatives has been consistently and quantitatively demonstrated to substantially improve on the performance of SR under practical conditions (9, 50).Notably, there is evidence to suggest that CCB staining is not fundamentally insensitive, but rather that its sensitivity has been limited by traditional densitometric detection (50, 51). When excited in the near IR at ∼650 nm, protein-bound CB in-gel emits light in the range of 700–800 nm. Until recently, the lack of low-cost, widely available and sufficiently sensitive infrared (IR)-capable imaging instruments prevented mainstream adoption of in-gel CB infrared fluorescence detection (IRFD); advances in imaging technology are now making such instruments far more accessible. Initial reports suggested that IRFD of CB-stained gels provided greater sensitivity than traditional densitometric detection (50, 51). Using CB R250, in-gel IRFD was reported to detect as little as 2 ng of protein in-gel, with a LDR of about an order of magnitude (2 to 20 ng, or 10 to 100 ng in separate gels), beyond which the fluorescent response saturated into the μg range (51). Using the G250 dye variant, it was determined that CB-IRFD of 2D gels detected ∼3 times as many proteins as densitometric imaging, and a comparable number of proteins as seen by SR (50). This study also concluded that CB-IRFD yielded a significantly higher signal to background ratio (S/BG) than SR, providing initial evidence that CB-IRFD may be superior to SR in some aspects of stain performance (50).Despite this initial evidence of the viability of CB-IRF as an in-gel protein detection method, a detailed characterization of this technology has not yet been reported. Here a more thorough, quantitative characterization of CB-IRFD is described, establishing its lowest limit of detection (LLD), IPV, and LDR in comparison to SR. Finally a wealth of modifications and enhancements of CCB formulations have been reported (8, 12, 21, 24, 26, 29, 40, 41, 52–54), and likewise there are many commercially available CCB stain formulations. To date, none of these formulations have been compared quantitatively in terms of their relative performance when detected using IRF. As a general detection method for gel-based proteomics, CB-IRFD was found to provide comparable or even slightly superior performance to SR according to most criteria, including sensitivity and selectivity (50). Furthermore, in terms of LDR, CB-IRFD showed distinct advantages over SR. However, assessing proteomes resolved by 2DE revealed critical distinctions between CB-IRFD and SR in terms of protein quantification versus threshold detection: neither stain could be considered unequivocally superior to the other by all criteria. Nonetheless, IRFD proved the most sensitive method of detecting CB-stained protein in-gel, enabling high sensitivity detection without the need for expensive reagents or even commercial formulations. Overall, CB-IRFD is a viable alternative to SR and other mainstream fluorescent stains, mitigating the high cost of large-scale gel-based proteomic analyses, making high sensitivity gel-based proteomics accessible to all labs. With improvements to CB formulations and/or image acquisition instruments, the performance of this detection technology may be further enhanced.