Immunoglobulin G (IgG) Fab Glycosylation Analysis Using a New Mass Spectrometric High-throughput Profiling Method Reveals Pregnancy-associated Changes

The N-linked glycosylation of the constant fragment (Fc) of immunoglobulin G has been shown to change during pathological and physiological events and to strongly influence antibody inflammatory properties. In contrast, little is known about Fab-linked N-glycosylation, carried by ∼20% of IgG. Here we present a high-throughput workflow to analyze Fab and Fc glycosylation of polyclonal IgG purified from 5 μl of serum. We were able to detect and quantify 37 different N-glycans by means of MALDI-TOF-MS analysis in reflectron positive mode using a novel linkage-specific derivatization of sialic acid. This method was applied to 174 samples of a pregnancy cohort to reveal Fab glycosylation features and their change with pregnancy. Data analysis revealed marked differences between Fab and Fc glycosylation, especially in the levels of galactosylation and sialylation, incidence of bisecting GlcNAc, and presence of high mannose structures, which were all higher in the Fab portion than the Fc, whereas Fc showed higher levels of fucosylation. Additionally, we observed several changes during pregnancy and after delivery. Fab N-glycan sialylation was increased and bisection was decreased relative to postpartum time points, and nearly complete galactosylation of Fab glycans was observed throughout. Fc glycosylation changes were similar to results described before, with increased galactosylation and sialylation and decreased bisection during pregnancy. We expect that the parallel analysis of IgG Fab and Fc, as set up in this paper, will be important for unraveling roles of these glycans in (auto)immunity, which may be mediated via recognition by human lectins or modulation of antigen binding.Immunoglobulins are key players of the human immune system. Immunoglobulin G (IgG)¹ is the most abundant representative of this group, with serum concentrations of ∼10 mg/ml (1). It consists of two heavy chains (γ-chains) made up of three constant regions (C_H1, C_H2, and C_H3) and one variable region (V_H). Attached to each heavy chain is a light chain (λ or κ). Based on chemical and biological properties, different regions can be distinguished in the IgG molecule: two antigen binding fragments (obtained as F(ab′)₂ by IdeS treatment; herein referred to as Fab) and a crystallizable fragment (Fc). The structure of IgG is schematically presented in Fig. 1.Open in a separate windowFig. 1.Schematic representation of IgG with the heavy γ chains (dark blue), light chains (lighter blue), and N-glycans. In the top right-hand corner of the Fc and Fab areas, the percentages of galactosylation, sialylation, bisection, and fucosylation are depicted. The inset represents the stable heptasaccharide core with possible extensions.IgGs are glycoproteins, and N-glycans are present at Asn297 of the C_H2 domain. These glycans consist of a constant heptasaccharide core that is often modified by a core fucose and is in part decorated with bisecting N-acetylglucosamine (GlcNAc), galactose(s), and sialic acid(s) (Fig. 1) (1). The Fc glycans have been extensively studied, and glycosylation changes have been found to be associated with disease (e.g. rheumatoid arthritis) (2, 3) and aging (4–6). Several immune regulatory properties have been demonstrated for IgG Fc glycans (7–13). For example, Fc-linked glycans influence the IgG effector function by altering the three-dimensional structure of the protein, and thereby the binding to Fcγ-receptors (12, 13). Additionally, glycan–glycan interactions occur between IgG and Fcγ-receptor-IIIa (8), with the presence of a core fucose decreasing this affinity by ∼2 orders of magnitude (7).The Fab portion consists of the heavy chain C_H1 and V_H regions combined with a light chain and exhibits the antigen binding sites formed by the variable and hypervariable regions of those two chains. N-glycans are known to occur on 15% to 25% of the IgG Fab portions (1, 14, 15). The Fab N-glycans can be involved in immunomodulation, because they influence the affinity and avidity of antibodies for antigens (16–19), as well as antibody half-life (17, 20). The glycans of the Fab have been described as biantennary complex-type structures that are, in contrast to Fc glycans, highly sialylated (21–23). Additionally, high-mannose-type structures have been said to be located on the Fab portion (23).Pregnancy is known to be associated with overall changes in IgG glycosylation. Indeed, a marked increase of galactosylation and sialylation has been observed in IgG Fc glycosylation during pregnancy (3, 24, 25). In addition, lectin binding studies suggest changes in Fab glycosylation of IgG during pregnancy (26), which may be caused by increased levels of progesterone (27). Changes in glycosylation during pregnancy could be one of the mechanisms that contribute to acceptance of the fetal allograft by the maternal immune system (26).Our knowledge on the Fab glycosylation of IgGs from peripheral blood is scarce, which is in part due to difficulty detecting the glycans in a Fab-region-specific manner. Because of the polyclonal nature of serum IgG, one may expect Fab glycans to be attached to a large variety of sequence motifs arising from somatic rearrangements and mutations (28), making the analysis of Fab glycopeptides from polyclonal serum IgG very demanding, if feasible at all. Therefore, study of the Fab glycosylation of polyclonal serum IgG has mainly been pursued at the level of released glycans (14, 23). Difficulties lie in the purification of IgG and the separation of Fc and Fab glycosylation, which is essential for the assignment of the glycans to either part of the IgG molecule.Here we present a high-throughput method for studying Fab glycosylation at the level of released glycans obtained from serum-derived polyclonal IgG. Using state-of-the-art affinity capturing beads and enzymes, we were able to obtain Fab and Fc separately, which, after glycan release, resulted in Fc- and Fab-specific glycan pools. The released glycans were subjected to a novel derivatization protocol resulting in linkage-specific modification of sialic acids, followed by HILIC sample purification and MALDI-TOF-MS. Finally, because marked changes in glycosylation during pregnancy have been described, the technique was applied to consecutive serum samples from a cohort of pregnant women. This approach was chosen to determine the usefulness of this technique in a clinical setting. The method proved to be able to demonstrate pregnancy-related changes in glycosylation of the Fab portion, in addition to the already known changes in Fc glycosylation (3, 24, 25).     

Hinge-Region O-Glycosylation of Human Immunoglobulin G3 (IgG3)

Immunoglobulin G (IgG) is one of the most abundant proteins present in human serum and a fundamental component of the immune system. IgG3 represents ∼8% of the total amount of IgG in human serum and stands out from the other IgG subclasses because of its elongated hinge region and enhanced effector functions. This study reports partial O-glycosylation of the IgG3 hinge region, observed with nanoLC-ESI-IT-MS(/MS) analysis after proteolytic digestion. The repeat regions within the IgG3 hinge were found to be in part O-glycosylated at the threonine in the triple repeat motif. Non-, mono- and disialylated core 1-type O-glycans were detected in various IgG3 samples, both poly- and monoclonal. NanoLC-ESI-IT-MS/MS with electron transfer dissociation fragmentation and CE-MS/MS with CID fragmentation were used to determine the site of IgG3 O-glycosylation. The O-glycosylation site was further confirmed by the recombinant production of mutant IgG3 in which potential O-glycosylation sites had been knocked out.For IgG3 samples from six donors we found similar O-glycan structures and site occupancies, whereas for the same samples the conserved N-glycosylation of the Fc CH2 domain showed considerable interindividual variation. The occupancy of each of the three O-glycosylation sites was found to be ∼10% in six serum-derived IgG3 samples and ∼13% in two monoclonal IgG3 allotypes.Immunoglobulin G (IgG) is one of the most abundant proteins present in human serum and represents approximately three-quarters of the total serum immunoglobulin content (1). As the main mediator of humoral immunity and an important link between the adaptive and innate immune system, IgG is a fundamental component of the immune system. IgG consists of two heavy and light chains, linked by disulfide bonds. The protein can be subdivided into the antigen-binding (Fab) and the receptor-binding (Fc) region. There are four subclasses of IgG, all of which share an overall structure homology but differ slightly in their amino acid sequence; the quantity of the subclasses in human serum is as follows: IgG1 > 2 > 3 > 4 (2).IgG3 represents ∼8% of the total amount of IgG in human serum (2), and stands out from the other IgG subclasses for a number of reasons. First of all, IgG3 contains an elongated hinge region with up to a triple repeat sequence (the actual number ranging from one to three depending on the allotype (3)), which is responsible for the increased flexibility between the Fab and the Fc part, as well as the wider and more flexible angle between the two Fab arms (4, 5). This flexibility is likely the cause of the increased affinity of IgG3, compared with the other subclasses, for divalent binding to certain types of antigens (4, 6, 7). Second, IgG3 has a higher affinity for C1q, which initiates the classical complement pathway (5, 8). The interaction between IgG3 and C1q is not due to the elongated hinge region, as demonstrated by studies showing that recombinant IgG3 with an IgG1- or IgG4-like hinge sequence exhibited even greater binding affinity for C1q than wild-type IgG3 (8–10). Third, IgG3 has a higher overall affinity for the Fcγ receptors (FcγRs), through which it can influence effector cells of the innate immune system (11). The CH2 domain and hinge region of IgG3 were shown to be instrumental in binding to the high affinity FcγRI receptor (12). Finally, IgG3 generally has a shorter half-life compared with the other IgG subclasses (1 versus 3 weeks) (2). This difference was traced back to an H435R mutation that confers a positive charge at physiological pH, resulting in a decreased binding to the neonatal Fc receptor (FcRn), which is involved in recycling IgG targeted for lysosomal degradation (13). The low-efficiency FcRn-mediated transport also gives rise to decreased levels of IgG3 in mucosal tissue and impaired transport of IgG3 across the placenta (14). These properties do not hold true for all types of IgG3 since a large number of IgG3 allotypes have been described, some of which lack the H435R substitution and have a half-life and placental transport rates similar to IgG1 (13–16). IgG3 is more polymorphic than the other IgG subclasses, as evidenced by the high number of known allotypes (16). Most of the polymorphisms reside in the CH2 or CH3 domain, but the length of the hinge region can also display a high degree of variation. Depending on the number of sequence repeats, the hinge region can vary from 27 to 83 amino acid residues between different IgG3 allotypes (3, 16, 17).An N-linked complex type glycan is highly conserved and found in the CH2 domain of all IgG subclasses and allotypes. The type of glycan present at this site has been shown to influence the effector functions of IgG (18). N-glycans that lack a core fucose cause IgG to have an enhanced proinflammatory capacity through stronger binding to FcγRIIIa and FcγRIIIb (18–20). In contrast, IgG carrying sialylated N-glycans exhibits anti-inflammatory properties, likely due to increased binding affinity to C-type lectins and/or reduced binding to FcγR (18, 21, 22).O-linked glycosylation has been reported for various immunoglobulins. O-glycans are present on the hinge region of human IgA1 and IgD and mouse IgG2b (23–25). IgA1 contains nine potential sites for O-glycosylation (serine and threonine) in the hinge region, of which 3–5 are occupied, while IgD has been reported to carry between four and seven O-glycans (24–26). The O-glycosylation in the hinge of murine IgG2b was observed to protect against proteolytic digestion (23). Likewise, IgA1 was found to be more susceptible to degradation by Streptococci proteases after neuraminidase treatment (27).In this study, we report partial O-glycosylation of the human IgG3 hinge. We obtained both poly- and monoclonal IgG3 from various sources and performed proteolytic digestion with trypsin or proteinase K. NanoLC-reverse phase (RP)-ESI-ion trap (IT)-MS/MS was used to examine the resulting (glyco)peptides, revealing core 1-type O-glycans on multiple sites within the IgG3 hinge region.     

A Monomeric Chicken IgY Receptor Binds IgY with 2:1 Stoichiometry

IgY is the principal serum antibody in birds and reptiles, and an IgY-like molecule was the evolutionary precursor of both mammalian IgG and IgE. A receptor for IgY on chicken monocytes, chicken leukocyte receptor AB1 (CHIR-AB1), lies in the avian leukocyte receptor cluster rather than the classical Fc receptor cluster where the genes for mammalian IgE and IgG receptors are found. IgG and IgE receptors bind to the lower hinge region of their respective antibodies with 1:1 stoichiometry, whereas the myeloid receptor for IgA, FcαRI, and the IgG homeostasis receptor, FcRn, which are found in the mammalian leukocyte receptor cluster, bind with 2:1 stoichiometry between the heavy chain constant domains 2 and 3 of each heavy chain. In this paper, the extracellular domain of CHIR-AB1 was expressed in a soluble form and shown to be a monomer that binds to IgY-Fc with 2:1 stoichiometry. The two binding sites have similar affinities: K_a1 = 7.22 ± 0.22 × 10⁵ m⁻¹ and K_a2 = 3.63 ± 1.03 × 10⁶ m⁻¹ (comparable with the values reported for IgA binding to its receptor). The affinity constants for IgY and IgY-Fc binding to immobilized CHIR-AB1 are 9.07 ± 0.07 × 10⁷ and 6.11 ± 0.02 × 10⁸ m⁻¹, respectively, in agreement with values obtained for IgY binding to chicken monocyte cells and comparable with reported values for human IgA binding to neutrophils. Although the binding site for CHIR-AB1 on IgY is not known, the data reported here with a monomeric receptor binding to IgY at two sites with low affinity suggest an IgA-like interaction.Fc receptors link the specificity of the adaptive immune system with the effector mechanisms of innate immune cells. In birds and reptiles, IgY is the principal serum antibody, and both mammalian IgG and IgE have evolved from an IgY-like ancestor, so studies of IgY offer insights into their origins (1). The historical contribution of chicken immunology to a wider understanding of the subject has been considerable (2), and recently several chicken IgY-Fc receptors have been identified. In this paper, the chicken antibody, IgY, is shown to bind to a chicken leukocyte receptor, CHIR-AB1,⁴ in a different manner from that of its mammalian orthologues, IgG and IgE, to their respective Fc receptors.Phagocytosis, mediated in mammals by IgG, and passive cutaneous anaphylaxis, mediated by both IgG and IgE in mammals, have been observed in chickens (3, 4), presumably both effected by IgY. In vitro, IgY binds to monocyte cell lines (5, 6), and an IgY receptor (CHIR-AB1) has been identified that is able to mediate the influx of calcium into cells (5).The genes for the mammalian high affinity IgE receptor, and several IgG receptors, are located in the classical Fc receptor cluster, whereas in chickens, this cluster is represented by a single gene, the product of which has been expressed and found not to bind IgY (7). Intriguingly, the first IgY leukocyte receptor, CHIR-AB1, was found to be a member of the chicken leukocyte receptor cluster (LRC) (5), adjacent to over 100 genes with high intersequence homology (8). This finding, together with phylogenetic analysis of the orthologous Fc receptor gene clusters (7, 9), implies that during the evolution of the IgY-like ancestor of both IgG and IgE, antibody-Fc binding function migrated from proteins expressed in the LRC to those in the classical Fc receptor cluster. The human LRC is the site of FcαRI, the leukocyte receptor for IgA (an antibody involved in mucosal immunity), the fetal IgG receptor (FcRn, involved in adult IgG homeostasis), and also a number of natural killer cell receptors including the HLA-G ligand, KIR2DL4 (10). A further leukocyte receptor for chicken IgY, also related to LRC receptors, was identified recently, on chromosome 20 (11), and remains to be characterized.Typically, the stoichiometry of the receptor-antibody complex differs for receptors located in the classical Fc receptor cluster and the LRC. Crystal structures of IgG complexes with FcγRIII and of IgE with FcϵRI show 1:1 receptor:antibody stoichiometry, with the receptor binding across both heavy chains in the lower hinge (12). In contrast, the crystal structure of FcαRI complexed with IgA shows 2:1 stoichiometry (13) as does that of FcRn with IgG (14), with the two receptors binding between the heavy chain constant domains 2 and 3 on each heavy chain. The IgY/receptor interaction could have either stoichiometry; on the one hand, IgY is an orthologue of IgG and IgE, which can both show 1:1 stoichiometry, but on the other hand, the location of the IgY receptor, CHIR-AB1, in the same gene cluster as the IgA and FcRn receptors suggests the possibility of a 2:1 stoichiometry. Consistent with either of these binding modes, the crystal structure of IgY-Fc reveals that many of the residues located in the receptor-binding sites in human IgE, IgG, and IgA are present and accessible in IgY (15).The single extracellular domain of the chicken leukocyte IgY receptor, CHIR-AB1, has been expressed in insect cells by Arnon et al. (16), who showed that this preparation consists of a mixture of soluble monomer and dimer. Because of the heterogeneity of the protein, it was not possible to ascertain whether the observed 2:1 stoichiometry of receptor binding to antibody involved two monomers or a single dimer binding to IgY. Thus, it was not possible to answer the question of whether the antibody-receptor complex most resembles that of human IgA or of IgG and IgE. We have expressed the extracellular domain of CHIR-AB1 in human HEK cells. It is a monomer, and we report here that it binds to IgY and IgY-Fc with 2:1 stoichiometry.     

Enhanced Virus Clearance by Early Inducible Lymphocytic Choriomeningitis Virus-Neutralizing Antibodies in Immunoglobulin-Transgenic Mice

Following infection of mice with lymphocytic choriomeningitis virus (LCMV), virus-neutralizing antibodies appear late, after 30 to 60 days. Such neutralizing antibodies play an important role in protection against reinfection. To analyze whether a neutralizing antibody response which developed earlier could contribute to LCMV clearance during the acute phase of infection, we generated transgenic mice expressing LCMV-neutralizing antibodies. Transgenic mice expressing the immunoglobulin μ heavy chain of the LCMV-neutralizing monoclonal antibody KL25 (H25 transgenic mice) mounted LCMV-neutralizing immunoglobulin M (IgM) serum titers within 8 days after infection. This early inducible LCMV-neutralizing antibody response significantly improved the host’s capacity to clear the infection and did not cause an enhancement of disease after intracerebral (i.c.) LCMV infection. In contrast, mice which had been passively administered LCMV-neutralizing antibodies and transgenic mice exhibiting spontaneous LCMV-neutralizing IgM serum titers (HL25 transgenic mice expressing the immunoglobulin μ heavy and the κ light chain) showed an enhancement of disease after i.c. LCMV infection. Thus, early-inducible LCMV-neutralizing antibodies can contribute to viral clearance in the acute phase of the infection and do not cause antibody-dependent enhancement of disease.Against many cytopathic viruses such as poliovirus, influenza virus, rabies virus, and vesicular stomatitis virus, protective virus-neutralizing antibodies are generated early, within 1 week after infection (3, 31, 36, 44, 49). In contrast, several noncytopathic viruses (e.g., human immunodeficiency virus and hepatitis viruses B and C in humans or lymphocytic choriomeningitis virus [LCMV] in mice) elicit poor and delayed virus-neutralizing antibody responses (1, 7, 20, 24, 27, 35, 45, 48).In the mouse, the natural host of LCMV, the acute LCMV infection is predominantly controlled by cytotoxic T lymphocytes (CTLs) in an obligatory perforin-dependent manner (13, 18, 28, 50). In addition to the CTL response, LCMV-specific antibodies are generated. Early after infection (by day 8), a strong antibody response specific for the internal viral nucleoprotein (NP) is mounted (7, 19, 23, 28). These early LCMV NP-specific antibodies exhibit no virus-neutralizing capacity (7, 10). Results from studies of B-cell-depleted mice and B-cell-deficient mice implied that the early LCMV NP-specific antibodies are not involved in the clearance of LCMV (8, 11, 12, 40). Late after infection (between days 30 and day 60), LCMV-neutralizing antibodies develop (7, 19, 22, 28, 33); these antibodies are directed against the surface glycoprotein (GP) of LCMV (9, 10). LCMV-neutralizing antibodies have an important function in protection against reinfection (4, 6, 38, 41, 47).In some viral infections, subprotective virus-neutralizing antibody titers can enhance disease rather than promote host recovery (i.e., exhibit antibody-dependent enhancement of disease [ADE] [14, 15, 21, 46]). For example, neutralizing antibodies are involved in the resolution of a primary dengue virus infection and in the protection against reinfection. However, if subprotective neutralizing antibody titers are present at the time of reinfection, a severe form of the disease (dengue hemorrhagic fever/dengue shock syndrome [15, 21]), which might be caused by Fc receptor-mediated uptake of virus-antibody complexes leading to an enhanced infection of monocytes (15, 16, 25, 39), can develop. Similarly, an enhancement of disease after intracerebral (i.c.) LCMV infection was observed in mice which had been treated with virus-neutralizing antibodies before the virus challenge (6). ADE in LCMV-infected mice was either due to an enhanced infection of monocytes by Fc receptor-mediated uptake of antibody-virus complexes or due to CTL-mediated immunopathology caused by an imbalanced virus spread and CTL response.To analyze whether LCMV-neutralizing antibodies generated early after infection improve the host’s capacity to clear the virus or enhance immunopathological disease, immunoglobulin (Ig)-transgenic mice expressing LCMV-neutralizing IgM antibodies were generated. After LCMV infection of transgenic mice expressing the Ig heavy chain (H25 transgenic mice), LCMV-neutralizing serum antibodies were mounted within 8 days, which significantly improved the host’s capacity to eliminate LCMV. H25 transgenic mice did not show any signs of ADE after i.c. LCMV infection.Transgenic mice expressing the Ig heavy and light chains (HL25 transgenic mice) exhibited spontaneous LCMV-neutralizing serum antibodies and confirmed the protective role of preexisting LCMV-neutralizing antibodies, even though the neutralizing serum antibodies were of the IgM isotype. Similar to mice which had been treated with LCMV-neutralizing antibodies, HL25 transgenic mice developed an enhanced disease after i.c. LCMV infection, which indicated that ADE was due to an imbalance between virus spread and CTL response. Thus, the early-inducible LCMV-neutralizing antibody response significantly enhanced clearance of the acute infection without any risk of causing ADE.     

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]     

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.     

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]     

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]