Algorithms for Finding Small Attractors in Boolean Networks

A Boolean network is a model used to study the interactions between different genes in genetic regulatory networks. In this paper, we present several algorithms using gene ordering and feedback vertex sets to identify singleton attractors and small attractors in Boolean networks. We analyze the average case time complexities of some of the proposed algorithms. For instance, it is shown that the outdegree-based ordering algorithm for finding singleton attractors works in time for , which is much faster than the naive time algorithm, where is the number of genes and is the maximum indegree. We performed extensive computational experiments on these algorithms, which resulted in good agreement with theoretical results. In contrast, we give a simple and complete proof for showing that finding an attractor with the shortest period is NP-hard.[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]     

Proinsulin and the Genetics of Diabetes Mellitus

Insulin plays a central role in the regulation of vertebrate metabolism. The hormone, the post-translational product of a single-chain precursor, is a globular protein containing two chains, A (21 residues) and B (30 residues). Recent advances in human genetics have identified dominant mutations in the insulin gene causing permanent neonatal-onset DM² (1–4). The mutations are predicted to block folding of the precursor in the ER of pancreatic β-cells. Although expression of the wild-type allele would in other circumstances be sufficient to maintain homeostasis, studies of a corresponding mouse model (5–7) suggest that the misfolded variant perturbs wild-type biosynthesis (8, 9). Impaired β-cell secretion is associated with ER stress, distorted organelle architecture, and cell death (10). These findings have renewed interest in insulin biosynthesis (11–13) and the structural basis of disulfide pairing (14–19). Protein evolution is constrained not only by structure and function but also by susceptibility to toxic misfolding.Insulin plays a central role in the regulation of vertebrate metabolism. The hormone, the post-translational product of a single-chain precursor, is a globular protein containing two chains, A (21 residues) and B (30 residues). Recent advances in human genetics have identified dominant mutations in the insulin gene causing permanent neonatal-onset DM² (1–4). The mutations are predicted to block folding of the precursor in the ER of pancreatic β-cells. Although expression of the wild-type allele would in other circumstances be sufficient to maintain homeostasis, studies of a corresponding mouse model (5–7) suggest that the misfolded variant perturbs wild-type biosynthesis (8, 9). Impaired β-cell secretion is associated with ER stress, distorted organelle architecture, and cell death (10). These findings have renewed interest in insulin biosynthesis (11–13) and the structural basis of disulfide pairing (14–19). Protein evolution is constrained not only by structure and function but also by susceptibility to toxic misfolding.     

Fatty Acids Modulate Toll-like Receptor 4 Activation through Regulation of Receptor Dimerization and Recruitment into Lipid Rafts in a Reactive Oxygen Species-dependent Manner

The saturated fatty acids acylated on Lipid A of lipopolysaccharide (LPS) or bacterial lipoproteins play critical roles in ligand recognition and receptor activation for Toll-like Receptor 4 (TLR4) and TLR2. The results from our previous studies demonstrated that saturated and polyunsaturated fatty acids reciprocally modulate the activation of TLR4. However, the underlying mechanism has not been understood. Here, we report for the first time that the saturated fatty acid lauric acid induced dimerization and recruitment of TLR4 into lipid rafts, however, dimerization was not observed in non-lipid raft fractions. Similarly, LPS and lauric acid enhanced the association of TLR4 with MD-2 and downstream adaptor molecules, TRIF and MyD88, into lipid rafts leading to the activation of downstream signaling pathways and target gene expression. However, docosahexaenoic acid (DHA), an n-3 polyunsaturated fatty acid, inhibited LPS- or lauric acid-induced dimerization and recruitment of TLR4 into lipid raft fractions. Together, these results demonstrate that lauric acid and DHA reciprocally modulate TLR4 activation by regulation of the dimerization and recruitment of TLR4 into lipid rafts. In addition, we showed that TLR4 recruitment to lipid rafts and dimerization were coupled events mediated at least in part by NADPH oxidase-dependent reactive oxygen species generation. These results provide a new insight in understanding the mechanism by which fatty acids differentially modulate TLR4-mediated signaling pathway and consequent inflammatory responses which are implicated in the development and progression of many chronic diseases.Toll-like receptors (TLRs)³ are one of the key pattern recognition receptor families that play a critical role in inducing innate and adaptive immune responses in mammals by recognizing conserved pathogen-associated molecular pattern of invading microbes. So far, at least thirteen TLRs have been identified in mammalian species (1, 2).Lipopolysaccharide (LPS) from Gram-negative bacteria is the ligand for the TLR4 complex (3), whereas, TLR2 can recognize lipoproteins/lipopeptides of Gram-positive bacteria and mycoplasma (1, 2). LPS forms a complex with LPS-binding protein in serum leading to the conversion of oligomeric micelles of LPS to monomers, which are delivered to CD14. Monomeric LPS is known to bind TLR4/MD-2/CD14 complex (4). Lipid A, which possesses most of the biological activities of LPS, is acylated with hydroxy saturated fatty acids. The 3-hydroxyl groups of these saturated fatty acids are further 3-Ο-acylated by saturated fatty acids. Removal of these Ο-acylated saturated fatty acids from Lipid A not only results in complete loss of endotoxic activity, but also makes Lipid A act as an antagonist against the native Lipid A (5, 6). One or more Lipid As containing unsaturated fatty acids are known to be non-toxic and act as an antagonist against endotoxin (7, 8). In addition, deacylated lipoproteins are unable to activate TLR2 and to induce cytokine expression in monocytes (9). Together, these results suggest that saturated fatty acids acylated on Lipid A or bacterial lipoproteins play critical roles in ligand recognition and receptor activation for TLR4 and TLR2. Indeed, it is suggested that the rapid interaction of bacterial lipopeptides with plasma membrane of macrophages occurs via insertion of their acylated saturated fatty acids as determined by electron energy loss spectroscopy and freeze-fracture techniques (10, 11). TLR2 can form a heterodimer with TLR1 or TLR6, which can discriminate the molecular structure of triacyl or diacyl lipopeptides (12–14). So far there is no evidence that microbial ligands for other TLRs are acylated by saturated fatty acids.Results from our previous studies demonstrated that saturated fatty acids activate TLR4 and polyunsaturated fatty acids (PUFA) inhibit both saturated fatty acid- and LPS-induced activation of TLR4 (15, 16). In addition, the saturated fatty acid lauric acid potentiates, but the n-3 PUFA docosahexaenoic acid (DHA) inhibits lipopeptide (TLR2 agonist)-induced TLR2 activation (17). Together, these results suggest that both TLR2 and TLR4 signaling pathways and target gene expression are reciprocally modulated by saturated and polyunsaturated fatty acids. However, the mechanism for this modulation by fatty acids is not understood.TLR4 is recruited to lipid raft factions after cells are treated with LPS and subsequently induces tumor necrosis factor-α expression in RAW264.7 cells (18). This process occurs in an ROS-dependent manner because inhibition of NADPH oxidase suppresses TLR4 recruitment to lipid rafts (19). Methyl-β-dextrin, a lipid raft inhibitor, significantly inhibits the LPS-induced expression of cytokine (19), suggesting that lipid rafts are essential for TLR4-mediated signal transduction and target gene expression. Lipid rafts are a collection of lipid membrane microdomains characterized by insolubility in non-ionic detergents. Lipid rafts serve as a platform where receptor-mediated signal transduction is initiated (20). Lipid rafts have a special lipid composition that is rich in cholesterol, sphingomyelin, and glycolipids (21). The polar lipids in detergent-resistant membrane contain predominantly saturated fatty acyl residues with underrepresented PUFAs (22–24), suggesting that saturated fatty acyl chains favor lipid raft association. On the other hand, n-3 PUFAs displace signaling proteins from lipid rafts by altering lipid composition, and the displacement leads to the suppression of T-cell receptor-mediated signaling (25). It is now well documented that TLRs form homo- or hetero-oligomers (1, 2). TLR4 homodimerization is the initial step of the receptor activation. Results from our previous studies suggest that the molecular target by which saturated fatty acids and n-3 PUFAs reciprocally modulate TLR4 activation is the receptor complex itself or the event leading to the receptor activation instead of the downstream signaling components (15, 16). Therefore, we determined whether the reciprocal modulation of TLR4 activation is mediated by regulation of the dimerization and recruitment of TLR4 into lipid rafts, and if these processes occur in an ROS-dependent manner.     

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]     

Aldo-keto Reductase Family 1 Member B10 Promotes Cell Survival by Regulating Lipid Synthesis and Eliminating Carbonyls

Aldo-keto reductase family 1 member B10 (AKR1B10) is primarily expressed in the normal human colon and small intestine but overexpressed in liver and lung cancer. Our previous studies have shown that AKR1B10 mediates the ubiquitin-dependent degradation of acetyl-CoA carboxylase-α. In this study, we demonstrate that AKR1B10 is critical to cell survival. In human colon carcinoma cells (HCT-8) and lung carcinoma cells (NCI-H460), small-interfering RNA-induced AKR1B10 silencing resulted in caspase-3-mediated apoptosis. In these cells, the total and subspecies of cellular lipids, particularly of phospholipids, were decreased by more than 50%, concomitant with 2–3-fold increase in reactive oxygen species, mitochondrial cytochrome c efflux, and caspase-3 cleavage. AKR1B10 silencing also increased the levels of α,β-unsaturated carbonyls, leading to the 2–3-fold increase of cellular lipid peroxides. Supplementing the HCT-8 cells with palmitic acid (80 μm), the end product of fatty acid synthesis, partially rescued the apoptosis induced by AKR1B10 silencing, whereas exposing the HCT-8 cells to epalrestat, an AKR1B10 inhibitor, led to more than 2-fold elevation of the intracellular lipid peroxides, resulting in apoptosis. These data suggest that AKR1B10 affects cell survival through modulating lipid synthesis, mitochondrial function, and oxidative status, as well as carbonyl levels, being an important cell survival protein.Aldo-keto reductase family 1 member B10 (AKR1B10,² also designated aldose reductase-like-1, ARL-1) is primarily expressed in the human colon, small intestine, and adrenal gland, with a low level in the liver (1–3). However, this protein is overexpressed in hepatocellular carcinoma, cervical cancer, lung squamous cell carcinoma, and lung adenocarcinoma in smokers, being a potential diagnostic and/or prognostic marker (1, 2, 4–6).The biological function of AKR1B10 in the intestine and adrenal gland, as well as its role in tumor development and progression, remains unclear. AKR1B10 is a monomeric enzyme that efficiently catalyzes the reduction to corresponding alcohols of a range of aromatic and aliphatic aldehydes and ketones, including highly electrophilic α,β-unsaturated carbonyls and antitumor drugs containing carbonyl groups, with NADPH as a co-enzyme (1, 7–12). The electrophilic carbonyls are constantly produced by lipid peroxidation, particularly in oxidative conditions, and are highly cytotoxic; through interaction with proteins, peptides, and DNA, the carbonyls cause protein dysfunction and DNA damage (breaks and mutations), resulting in mutagenesis, carcinogenesis, or apoptosis (10, 13–19). AKR1B10 also shows strong enzymatic activity toward all-trans-retinal, 9-cis-retinal, and 13-cis-retinal, reducing them to the corresponding retinols, which may regulate the intracellular retinoic acid, a signaling molecule modulating cell proliferation and differentiation (6, 20–23). In lung cancer, AKR1B10 expression is correlated with the patient smoking history and activates procarcinogens in cigarette smoke, such as polycyclic aromatic hydrocarbons, thus involved in lung tumorigenesis (24–26).Recent studies have shown that in breast cancer cells, AKR1B10 associates with acetyl-CoA carboxylase-α (ACCA) and blocks its ubiquitination and proteasome degradation (27). ACCA is a rate-limiting enzyme of de novo synthesis of long chain fatty acids, catalyzing the ATP-dependent carboxylation of acetyl-CoA to form malonyl-CoA (28). Long chain fatty acids are the building blocks of biomembranes and the precursor of lipid second messengers, playing a critical role in cell growth and proliferation (29, 30). Therefore, ACCA activity is tightly regulated by both metabolite-mediated allosteric mechanisms and phosphorylation-dependent mechanisms; the latter are controlled by multiple hormones, such as insulin, glucagon, and growth factors (31–33). ACCA activity is also regulated through physical protein-protein interaction. For instance, breast cancer 1 (BRCA1) protein associates with the ACCA and blocks its Ser⁷⁹ residue from dephosphorylation (34, 35). The AKR1B10-mediated regulation on ACCA stability represents a novel regulatory mechanism, and this current study elucidated the biological significance of this regulation. The results show that AKR1B10 promotes cell survival via modulating lipid synthesis, mitochondrial function and oxidative stress, and carbonyl levels.     

Identification of Protein Domains That Control Proton and Calcium Sensitivity of ASIC1a

The acid-sensing ion channels (ASICs) open in response to extracellular acidic pH, and individual subunits display differential sensitivity to protons and calcium. ASIC1a acts as a high affinity proton sensor, whereas ASIC2a requires substantially greater proton concentrations to activate. Using chimeras composed of ASIC1a and ASIC2a, we determined that two regions of the extracellular domain (residues 87–197 and 323–431) specify the high affinity proton response of ASIC1a. These two regions appear to undergo intersubunit interactions within the multimeric channel to specify proton sensitivity. Single amino acid mutations revealed that amino acids around Asp³⁵⁷ play a prominent role in determining the pH dose response of ASIC1a. Within the same region, mutation F352L abolished PcTx1 modulation of ASIC1a. Surprisingly, we determined that another area of the extracellular domain was required for calcium-dependent regulation of ASIC1a activation, and this region functioned independently of high affinity proton sensing. These results indicate that specific regions play overlapping roles in pH-dependent gating and PcTx1-dependent modulation of ASIC1a activity, whereas a distinct region determines the calcium dependence of ASIC1a activation.The acid-sensing ion channels (ASICs)³ are proton-gated ion channels expressed in neurons throughout the central and peripheral nervous system (1–3). ASICs are activated by extracellular acidosis, and protons act as ligands triggering channel opening (4). Disruption of the accn2 gene (which encodes ASIC1) dramatically reduces proton-gated currents in central neurons and alters a variety of behaviors, including fear, learning, and memory (5, 6). ASIC1 also contributes to neuronal damage and death during the prolonged acidosis accompanying cerebral ischemia (7). Specifically, mice with disruptions in the accn2 gene display 60% smaller lesion size compared with normal mice in models of stroke (8). Application of PcTx1, a venom peptide that prevents ASIC1a activation, is similarly neuroprotective, even when administered hours after injury (8, 9). Thus, ASIC1a represents a novel pharmacological target for the prevention of neuronal death following stroke.Mammals have four genes encoding ASICs (accn1 to -4) that encode at least six different ASIC subunits (1–3, 10). Like all members of the DEG/ENaC family, individual ASIC subunits have two transmembrane regions separated by a large cysteine-rich extracellular region. Three ASIC subunits associate to form homomeric or heteromeric channels with distinct biophysical characteristics (11–14). Specifically, ASIC1a homomeric channels activate at pH values much closer to neutral pH compared with ASIC2a homomeric channels. The high affinity proton sensitivity of ASIC1a plays a prominent role in acidosis-induced neuronal death, and modulators that alter the pH dose response of ASIC1a affect neuronal sensitivity to prolonged acidosis (8, 9, 15). For example, the neuroprotective venom peptide PcTx1 increases the proton sensitivity of the ASIC1a channel, allowing the channel to desensitize at neutral pH and become unresponsive to subsequent acidic shifts in pH (16, 17). The large extracellular region of ASIC1a is thought to be the site of proton/modulator interaction and governs the characteristics of channel gating (10, 11, 18). However, the exact molecular mechanisms defining ASIC1a activation and the protein domains that are responsible for the apparent proton sensitivity of ASIC1a remain unclear. Here, we used chimeras containing specific regions from both ASIC1a and ASIC2a to identify the specific protein regions that confer high affinity proton sensing, PcTx1 sensitivity, and calcium modulation to ASIC1a.