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DC-SIGN is a C-type lectin receptor of dendritic cells and is involved in the early stages of numerous infectious diseases. DC-SIGN is organized into a tetramer enabling multivalent interaction with pathogens. Once formed, the DC-SIGN-pathogen complex can be internalized into compartments of increasing acidity. We have studied the pH dependence of the oligomerization state and conformation of the entire extracellular domain and neck region. We present evidence for equilibrium between the monomeric and tetrameric states of the extracellular domain, which exhibits a marked dependence with respect to both pH and ionic strength. Using solution x-ray scattering we have obtained a molecular envelope of the extracellular domain in which a model has been built. Our results highlight the central role of the neck domain in the pH-sensitive control of the oligomerization state, in the extended conformation of the protein, and in carbohydrate recognition domain organization and presentation. This work opens new insight into the molecular mechanism of ligand release and points to new avenues to block the first step of this important infection pathway.Dendritic cells (DCs),2 which are found in peripheral tissues and act as sentinels against invading pathogens are considered to be the most efficient professional antigen presenting cells identified so far (1). A major subset of these DCs, dermal DCs, is characterized by the membrane expression of the DC-SIGN (dendritic cell-specific ICAM3 grabbing non-integrin) receptor (CD209). DC-SIGN is a calcium-dependent (C-type) lectin able to recognize highly glycosylated proteins. It is implicated in the early stages of many viral infections (2) and is spatially distributed in well defined membranous microdomains with an average diameter of 200 nm that act as docking platforms for pathogens and endogenous antigen attachment (3, 4). DC-SIGN binds to viral pathogens through their exposed glycoproteins such as HIV-1 envelope protein (gp120) (5), GP1 of Ebola (6), E1 and E2 of HCV (7, 8), and Dengue virus E glycoprotein (9). Apart from the viral world, DC-SIGN has also been implicated in infection processes involving fungi (10, 11), bacteria, such as Neisseria meningitidis (12) and Leishmania pifanoi (13), and parasites, such as Schistosoma mansoni (14). In addition, DC-SIGN mediates DC contacts with endothelial cells, naive T lymphocytes, and neutrophils by interacting with the endogenous adhesion molecules ICAM2 (15), ICAM3 (16), and the CD11b/CD18 integrin (17), respectively.DC-SIGN is a type II membrane protein comprising three main domains: a cytoplasmic region, a transmembrane segment, and an extracellular domain (ECD). The ECD can be divided into two structurally and functionally distinct regions: a neck region involved in the tetramerization of the receptor and a calcium-dependent carbohydrate-recognition domain (CRD), which is at the heart of the molecular recognition processes mediated by DC-SIGN.The cytoplasmic region contains recycling and internalization motifs important for targeting receptors, together with their associated ligands, to subcellular compartments as shown for DEC 205 and DC-SIGN itself (18, 19). Indeed, in some conditions, combined deletion of the triacidic cluster (EEE), the dileucine (LL), and the tyrosine-based (YXXL) internalization motifs induces the loss of DC capacity to enhance T-cell HIV-1 infection (19). The ability of DC-SIGN to promote T-cell infection by HIV-1 involves different pathways depending on the kinetics of the infection process. HIV transfers from DCs to T cells have been described to occur in two phases: a short-term phase (up to 24 h after viral exposure) and a long-term phase (from 24 to 72 h) (20, 21). The long-term phase is proposed to involve membrane fusion and subsequent DC infection and does not need to concern us further in this study. In contrast, short-term phase transfer involves virion internalization into DCs through vesicles. A pH dependence of HIV transfer has been suggested, based on the abrogation of the trans-enhancement of T-cell infection upon intracellular pH neutralization by concanamycin A (19). Indeed, internalization of HIV particles into low pH non-lysosomal compartments has been described in DC-SIGN-expressing cells (19). At the molecular level, a pH dependence of DC-SIGN binding to gp120 has been reported (22), as well as ligand release from DC-SIGN in pH conditions mimicking the acidic luminal environment of endosomes/lysosomes (23). However, no molecular explanation has yet been proposed for this phenomenon that might play a key role in the initiation mechanisms of DC-SIGN-mediated infectious processes. An effect of pH on the CRD binding properties has been reported (22) but no detailed molecular study of the pH dependence of the oligomerization properties of the neck domain, essential for the integrity of ECD, has yet been reported.The neck region comprises seven complete and one incomplete 23-amino acid long repeat. These repeats exhibit a distinct pattern of hydrophobic residues, positioned at regular intervals along an α-helical stretch that could favor coiled-coil interaction between helices from the four chains within a tetramer (24, 25). Comparison of circular dichroism spectra from the entire ECD and the CRD fragment led to a similar suggestion (26). The neck domain, which is responsible for tetramer formation and stability of the whole ECD, is thereby at the onset of the avidity mechanism that endows the DC-SIGN receptor with a very high affinity toward its target as compared with the weak affinity of isolated CRD. Indeed, the dissociation constant of the complex with the HIV gp120 envelope protein is in the nanomolar range with the whole ECD, whereas it is in the millimolar range when using monomeric CRD (22). Moreover, DC-SIGN neck region variants, resulting from alternative splicing and genomic polymorphism, exhibit altered sugar binding (27). DC-SIGN neck polymorphism has recently been correlated with differential susceptibility to HIV-1 and other pathogens as a result of modified DC-SIGN multimerization on the cell surface (27). Beyond the avidity mechanism already mentioned, the association of the four chains within the neck largely constraints the CRD spatial arrangement that must bear on the ligand interaction and recognition properties. However, despite the importance of the DC-SIGN tetrameric state in molecular recognitions, structural information is scarce and mostly restricted to the CRD moiety. High-resolution structures of the CRD in complex with various carbohydrate ligands are available (2831). The partial structure of a repeat has been obtained using a truncated dimeric form of the related homolog, DC-SIGNR (29, 32). However, structural information on the tetramer is still lacking although it is a prerequisite to a precise understanding of CRD presentation, pathogen recognition, and to rationalize emerging strategies for the design of DC-SIGN multivalent inhibitors (3336).Our study of the ECD, and more particularly of the neck domain, addresses two issues. First of all, we investigate the role of the neck domain in the structural organization of DC-SIGN ECD. We analyze its stability and dynamic as a function of pH conditions encountered in the various cell compartments. Our studies involve various constructs (CRD, ECD, and neck region) using several techniques: analytical ultracentrifugation, size exclusion chromatography (SEC), and circular dichroism (CD). We show that physiologically encountered pH variations significantly affect the protein oligomerization and structure. Slightly acidic pH destabilizes the tetramer as well as the CRD structure with possible consequences on the strength of ligand binding, which is strongly dependent on the multiplicity of interactions. In parallel, a molecular envelope of DC-SIGN ECD derived from small angle x-ray scattering (SAXS) measurements in solution highlights the extended organization of DC-SIGN and suggests a tighter arrangement of the four CRDs than hereto proposed.  相似文献   

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Heterogeneous ribonucleoprotein K (hnRNP K) binds to the 5′ untranslated region of the hepatitis C virus (HCV) and is required for HCV RNA replication. The hnRNP K binding site on HCV RNA overlaps with the sequence recognized by the liver-specific microRNA, miR-122. A proteome chip containing ∼17,000 unique human proteins probed with miR-122 identified hnRNP K as one of the strong binding proteins. In vitro kinetic study showed hnRNP K binds miR-122 with a nanomolar dissociation constant, in which the short pyrimidine-rich residues in the central and 3′ portion of the miR-122 were required for hnRNP K binding. In liver hepatocytes, miR-122 formed a coprecipitable complex with hnRNP K. High throughput Illumina DNA sequencing of the RNAs precipitated with hnRNP K was enriched for mature miR-122. SiRNA knockdown of hnRNP K in human hepatocytes reduced the levels of miR-122. These results show that hnRNP K is a cellular protein that binds and affects the accumulation of miR-122. Its ability to also bind HCV RNA near the miR-122 binding site suggests a role for miR-122 recognition of HCV RNA.MicroRNAs (miRNAs) are a class of noncoding RNA of ∼22-nucleotides in length that can regulate gene expression by either targeting RNA for degradation or suppressing their translation through base pairing to the RNAs (1). Since their discovery in 1993 in Caenorhabditis elegans, miRNAs have been found in many species and are involved in the regulation of proliferation, differentiation, apoptosis, and development (1, 2). Moreover, miRNAs are also critical factors in the development of cancers, neurodegenerative diseases, and infectious diseases (3).MiR-122 is a highly abundant RNA in hepatocytes that regulates lipid metabolism, regeneration, and neoplastic transformation (46). In addition, miR-122 is required for the replication of the hepatitis C virus (HCV), a positive-strand RNA virus that infects over 170 million people worldwide (79). MiR-122 binds to a conserved sequence in the 5′ untranslated region (UTR) of the HCV RNA to increase the stability of the HCV RNA (10). Silencing of miR-122 can abolish HCV RNA accumulation in non-human primates (11). The expression of human miR-122 in non-hepatic cells can confer the ability to replicate HCV RNA (12). MiR-122 is one of the most critical host factors for HCV replication.We previously reported that the HCV RNA sequence that anneals to miR-122 is recognized by the heterogeneous ribonucleoprotein K (hnRNP K), a multifunctional RNA-binding protein known to be involved in RNA processing, translation, and the replication of several RNA viruses (1315). In an unbiased screen for proteins from human proteome chips containing over 17,000 proteins, we identified 40 proteins that bind mature miR-122, including hnRNP K. Recombinant hnRNP K recognizes short pyrimidine sequences in miR-122 in vitro and a similar sequence in the HCV 5′ UTR. In hepatocytes endogenous hnRNP K can form a coprecipitable complex with miR-122, whether or not the cells contain replicating HCV. HnRNP K is thus a protein that binds a mature microRNA.  相似文献   

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Many biological processes involve the mechanistic/mammalian target of rapamycin complex 1 (mTORC1). Thus, the challenge of deciphering mTORC1-mediated functions during normal and pathological states in the central nervous system is challenging. Because mTORC1 is at the core of translation, we have investigated mTORC1 function in global and regional protein expression. Activation of mTORC1 has been generally regarded to promote translation. Few but recent works have shown that suppression of mTORC1 can also promote local protein synthesis. Moreover, excessive mTORC1 activation during diseased states represses basal and activity-induced protein synthesis. To determine the role of mTORC1 activation in protein expression, we have used an unbiased, large-scale proteomic approach. We provide evidence that a brief repression of mTORC1 activity in vivo by rapamycin has little effect globally, yet leads to a significant remodeling of synaptic proteins, in particular those proteins that reside in the postsynaptic density. We have also found that curtailing the activity of mTORC1 bidirectionally alters the expression of proteins associated with epilepsy, Alzheimer''s disease, and autism spectrum disorder—neurological disorders that exhibit elevated mTORC1 activity. Through a protein–protein interaction network analysis, we have identified common proteins shared among these mTORC1-related diseases. One such protein is Parkinson protein 7, which has been implicated in Parkinson''s disease, yet not associated with epilepsy, Alzheimers disease, or autism spectrum disorder. To verify our finding, we provide evidence that the protein expression of Parkinson protein 7, including new protein synthesis, is sensitive to mTORC1 inhibition. Using a mouse model of tuberous sclerosis complex, a disease that displays both epilepsy and autism spectrum disorder phenotypes and has overactive mTORC1 signaling, we show that Parkinson protein 7 protein is elevated in the dendrites and colocalizes with the postsynaptic marker postsynaptic density-95. Our work offers a comprehensive view of mTORC1 and its role in regulating regional protein expression in normal and diseased states.The mechanistic/mammalian target of rapamycin complex 1 (mTORC1)1 is a serine/threonine protein kinase that is highly expressed in many cell types (1). In the brain, mTORC1 tightly coordinates different synaptic plasticities — long-term potentiation (LTP) and long-term depression (LTD) — the molecular correlates of learning and memory (25). Because mTORC1 is at the core of many synaptic signaling pathways downstream of glutamate and neurotrophin receptors, many hypothesize that dysregulated mTORC1 signaling underlies cognitive deficits observed in several neurodegenerative diseases (3, 617). For example, mTORC1 and its downstream targets are hyperactive in human brains diagnosed with Alzheimer''s disease (AD) (1820). Additionally in animal models of autism spectrum disorder (ASD), altered mTORC1 signaling contributes to the observed synaptic dysfunction and aberrant network connectivity (13, 15, 2127). Furthermore, epilepsy, which is common in AD and ASD, has enhanced mTORC1 activity (2832).Phosphorylation of mTORC1, considered the active form, is generally regarded to promote protein synthesis (33). Thus, many theorize that diseases with overactive mTORC1 arise from excessive protein synthesis (14). Emerging data, however, show that suppressing mTORC1 activation can trigger local translation in neurons (34, 35). Pharmacological antagonism of N-methyl-d-aspartate (NMDA) receptors, a subtype of glutamate receptors that lies upstream of mTOR activation, promotes the synthesis of the voltage-gated potassium channel, Kv1.1, in dendrites (34, 35). Consistent with these results, in models of temporal lobe epilepsy there is a reduction in the expression of voltage-gated ion channels including Kv1.1 (30, 31, 36). Interestingly in a model of focal neocortical epilepsy, overexpression of Kv1.1 blocked seizure activity (37). Because both active and inactive mTORC1 permit protein synthesis, we sought to determine the proteins whose expression is altered when mTORC1 phosphorylation is reduced in vivo.Rapamycin is an FDA-approved, immunosuppressive drug that inhibits mTORC1 activity (38). We capitalized on the ability of rapamycin to reduce mTORC1 activity in vivo and the unbiased approach of mass spectrometry to identify changes in protein expression. Herein, we provide evidence that mTORC1 activation bidirectionally regulates protein expression, especially in the PSD where roughly an equal distribution of proteins dynamically appear and disappear. Remarkably, using protein–protein interaction networks facilitated the novel discovery that PARK7, a protein thus far only implicated in Parkinson''s disease, (1) is up-regulated by increased mTORC1 activity, (2) resides in the PSD only when mTORC1 is active, and (3) is aberrantly expressed in a rodent model of TSC, an mTORC1-related disease that has symptoms of epilepsy and autism. Collectively, these data provide the first comprehensive list of proteins whose abundance or subcellular distributions are altered with acute changes in mTORC1 activity in vivo.  相似文献   

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A complete understanding of the biological functions of large signaling peptides (>4 kDa) requires comprehensive characterization of their amino acid sequences and post-translational modifications, which presents significant analytical challenges. In the past decade, there has been great success with mass spectrometry-based de novo sequencing of small neuropeptides. However, these approaches are less applicable to larger neuropeptides because of the inefficient fragmentation of peptides larger than 4 kDa and their lower endogenous abundance. The conventional proteomics approach focuses on large-scale determination of protein identities via database searching, lacking the ability for in-depth elucidation of individual amino acid residues. Here, we present a multifaceted MS approach for identification and characterization of large crustacean hyperglycemic hormone (CHH)-family neuropeptides, a class of peptide hormones that play central roles in the regulation of many important physiological processes of crustaceans. Six crustacean CHH-family neuropeptides (8–9.5 kDa), including two novel peptides with extensive disulfide linkages and PTMs, were fully sequenced without reference to genomic databases. High-definition de novo sequencing was achieved by a combination of bottom-up, off-line top-down, and on-line top-down tandem MS methods. Statistical evaluation indicated that these methods provided complementary information for sequence interpretation and increased the local identification confidence of each amino acid. Further investigations by MALDI imaging MS mapped the spatial distribution and colocalization patterns of various CHH-family neuropeptides in the neuroendocrine organs, revealing that two CHH-subfamilies are involved in distinct signaling pathways.Neuropeptides and hormones comprise a diverse class of signaling molecules involved in numerous essential physiological processes, including analgesia, reward, food intake, learning and memory (1). Disorders of the neurosecretory and neuroendocrine systems influence many pathological processes. For example, obesity results from failure of energy homeostasis in association with endocrine alterations (2, 3). Previous work from our lab used crustaceans as model organisms found that multiple neuropeptides were implicated in control of food intake, including RFamides, tachykinin related peptides, RYamides, and pyrokinins (46).Crustacean hyperglycemic hormone (CHH)1 family neuropeptides play a central role in energy homeostasis of crustaceans (717). Hyperglycemic response of the CHHs was first reported after injection of crude eyestalk extract in crustaceans. Based on their preprohormone organization, the CHH family can be grouped into two sub-families: subfamily-I containing CHH, and subfamily-II containing molt-inhibiting hormone (MIH) and mandibular organ-inhibiting hormone (MOIH). The preprohormones of the subfamily-I have a CHH precursor related peptide (CPRP) that is cleaved off during processing; and preprohormones of the subfamily-II lack the CPRP (9). Uncovering their physiological functions will provide new insights into neuroendocrine regulation of energy homeostasis.Characterization of CHH-family neuropeptides is challenging. They are comprised of more than 70 amino acids and often contain multiple post-translational modifications (PTMs) and complex disulfide bridge connections (7). In addition, physiological concentrations of these peptide hormones are typically below picomolar level, and most crustacean species do not have available genome and proteome databases to assist MS-based sequencing.MS-based neuropeptidomics provides a powerful tool for rapid discovery and analysis of a large number of endogenous peptides from the brain and the central nervous system. Our group and others have greatly expanded the peptidomes of many model organisms (3, 1833). For example, we have discovered more than 200 neuropeptides with several neuropeptide families consisting of as many as 20–40 members in a simple crustacean model system (5, 6, 2531, 34). However, a majority of these neuropeptides are small peptides with 5–15 amino acid residues long, leaving a gap of identifying larger signaling peptides from organisms without sequenced genome. The observed lack of larger size peptide hormones can be attributed to the lack of effective de novo sequencing strategies for neuropeptides larger than 4 kDa, which are inherently more difficult to fragment using conventional techniques (3437). Although classical proteomics studies examine larger proteins, these tools are limited to identification based on database searching with one or more peptides matching without complete amino acid sequence coverage (36, 38).Large populations of neuropeptides from 4–10 kDa exist in the nervous systems of both vertebrates and invertebrates (9, 39, 40). Understanding their functional roles requires sufficient molecular knowledge and a unique analytical approach. Therefore, developing effective and reliable methods for de novo sequencing of large neuropeptides at the individual amino acid residue level is an urgent gap to fill in neurobiology. In this study, we present a multifaceted MS strategy aimed at high-definition de novo sequencing and comprehensive characterization of the CHH-family neuropeptides in crustacean central nervous system. The high-definition de novo sequencing was achieved by a combination of three methods: (1) enzymatic digestion and LC-tandem mass spectrometry (MS/MS) bottom-up analysis to generate detailed sequences of proteolytic peptides; (2) off-line LC fractionation and subsequent top-down MS/MS to obtain high-quality fragmentation maps of intact peptides; and (3) on-line LC coupled to top-down MS/MS to allow rapid sequence analysis of low abundance peptides. Combining the three methods overcomes the limitations of each, and thus offers complementary and high-confidence determination of amino acid residues. We report the complete sequence analysis of six CHH-family neuropeptides including the discovery of two novel peptides. With the accurate molecular information, MALDI imaging and ion mobility MS were conducted for the first time to explore their anatomical distribution and biochemical properties.  相似文献   

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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]  相似文献   

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STIM1 and ORAI1, the two limiting components in the Ca2+ release-activated Ca2+ (CRAC) signaling cascade, have been reported to interact upon store depletion, culminating in CRAC current activation. We have recently identified a modulatory domain between amino acids 474 and 485 in the cytosolic part of STIM1 that comprises 7 negatively charged residues. A STIM1 C-terminal fragment lacking this domain exhibits enhanced interaction with ORAI1 and 2–3-fold higher ORAI1/CRAC current densities. Here we focused on the role of this CRAC modulatory domain (CMD) in the fast inactivation of ORAI1/CRAC channels, utilizing the whole-cell patch clamp technique. STIM1 mutants either with C-terminal deletions including CMD or with 7 alanines replacing the negative amino acids within CMD gave rise to ORAI1 currents that displayed significantly reduced or even abolished inactivation when compared with STIM1 mutants with preserved CMD. Consistent results were obtained with cytosolic C-terminal fragments of STIM1, both in ORAI1-expressing HEK 293 cells and in RBL-2H3 mast cells containing endogenous CRAC channels. Inactivation of the latter, however, was much more pronounced than that of ORAI1. The extent of inactivation of ORAI3 channels, which is also considerably more prominent than that of ORAI1, was also substantially reduced by co-expression of STIM1 constructs missing CMD. Regarding the dependence of inactivation on Ca2+, a decrease in intracellular Ca2+ chelator concentrations promoted ORAI1 current fast inactivation, whereas Ba2+ substitution for extracellular Ca2+ completely abrogated it. In summary, CMD within the STIM1 cytosolic part provides a negative feedback signal to Ca2+ entry by triggering fast Ca2+-dependent inactivation of ORAI/CRAC channels.The Ca2+ release-activated Ca2+ (CRAC)5 channel is one of the best characterized store-operated entry pathways (17). Substantial efforts have led to identification of two key components of the CRAC channel machinery: the stromal interaction molecule 1 (STIM1), which is located in the endoplasmic reticulum and acts as a Ca2+ sensor (810), and ORAI1/CRACM1, the pore-forming subunit of the CRAC channel (1113). Besides ORAI1, two further homologues named ORAI2 and ORAI3 belong to the ORAI channel family (12, 14).STIM1 senses endoplasmic reticulum store depletion primarily by its luminal EF-hand in its N terminus (8, 15), redistributes close to the plasma membrane, where it forms puncta-like structures, and co-clusters with ORAI1, leading to inward Ca2+ currents (12, 1619). The STIM1 C terminus, located in the cytosol, contains two coiled-coil regions overlapping with an ezrin-radixin-moesin (ERM)-like domain followed by a serine/proline- and a lysine-rich region (2, 8, 2022). Three recent studies have described the essential ORAI-activating region within the ERM domain, termed SOAR (Stim ORAI-activating region) (23), OASF (ORAI-activating small fragment) (24), and CAD (CRAC-activating domain) (25), including the second coiled coil domain and the following ∼55 amino acids. We and others have provided evidence that store depletion leads to a dynamic coupling of STIM1 to ORAI1 (2628) that is mediated by a direct interaction of the STIM1 C terminus with ORAI1 C terminus probably involving the putative coiled-coil domain in the latter (27).Furthermore, different groups have proven that the C terminus of STIM1 is sufficient to activate CRAC as well as ORAI1 channels independent of store depletion (2225, 27, 29). We have identified that OASF-(233–474) or shorter fragments exhibit further enhanced coupling to ORAI1 resulting in 3-fold increased constitutive Ca2+ currents. A STIM1 fragment containing an additional cluster of anionic amino acids C-terminal to position 474 displays weaker interaction with ORAI1 as well as reduced Ca2+ current comparable with that mediated by wild-type STIM1 C terminus. Hence, we have suggested that these 11 amino acids (474–485) act in a modulatory manner onto ORAI1; however, their detailed mechanistic impact within the STIM1/ORAI1 signaling machinery has remained so far unclear.In this study, we focused on the impact of this negative cluster on fast inactivation of STIM1-mediated ORAI Ca2+ currents. Lis et al. (30) have shown that all three ORAI homologues display distinct inactivation profiles, where ORAI2 and ORAI3 show a much more pronounced fast inactivation than ORAI1. Moreover, it has been reported (31) that different expression levels of STIM1 to ORAI1 affect the properties of CRAC current inactivation. Yamashita et al. (32) have demonstrated a linkage between the selectivity filter of ORAI1 and its Ca2+-dependent fast inactivation. Here we provide evidence that a cluster of acidic residues within the C terminus of STIM1 is involved in the fast inactivation of ORAI1 and further promotes that of ORAI3 and native CRAC currents.  相似文献   

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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]  相似文献   

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