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]     

Dbf4-Cdc7 Phosphorylation of Mcm2 Is Required for Cell Growth

The Dbf4-Cdc7 kinase (DDK) is required for the activation of the origins of replication, and DDK phosphorylates Mcm2 in vitro. We find that budding yeast Cdc7 alone exists in solution as a weakly active multimer. Dbf4 forms a likely heterodimer with Cdc7, and this species phosphorylates Mcm2 with substantially higher specific activity. Dbf4 alone binds tightly to Mcm2, whereas Cdc7 alone binds weakly to Mcm2, suggesting that Dbf4 recruits Cdc7 to phosphorylate Mcm2. DDK phosphorylates two serine residues of Mcm2 near the N terminus of the protein, Ser-164 and Ser-170. Expression of mcm2-S170A is lethal to yeast cells that lack endogenous MCM2 (mcm2Δ); however, this lethality is rescued in cells harboring the DDK bypass mutant mcm5-bob1. We conclude that DDK phosphorylation of Mcm2 is required for cell growth.The Cdc7 protein kinase is required throughout the yeast S phase to activate origins (1, 2). The S phase cyclin-dependent kinase also activates yeast origins of replication (3–5). It has been proposed that Dbf4 activates Cdc7 kinase in S phase, and that Dbf4 interaction with Cdc7 is essential for Cdc7 kinase activity (6). However, it is not known how Dbf4-Cdc7 (DDK)² acts during S phase to trigger the initiation of DNA replication. DDK has homologs in other eukaryotic species, and the role of Cdc7 in activation of replication origins during S phase may be conserved (7–10).The Mcm2-7 complex functions with Cdc45 and GINS to unwind DNA at a replication fork (11–15). A mutation of MCM5 (mcm5-bob1) bypasses the cellular requirements for DBF4 and CDC7 (16), suggesting a critical physiologic interaction between Dbf4-Cdc7 and Mcm proteins. DDK phosphorylates Mcm2 in vitro with proteins purified from budding yeast (17, 18) or human cells (19). Furthermore, there are mutants of MCM2 that show synthetic lethality with DBF4 mutants (6, 17), suggesting a biologically relevant interaction between DBF4 and MCM2. Nevertheless, the physiologic role of DDK phosphorylation of Mcm2 is a matter of dispute. In human cells, replacement of MCM2 DDK-phosphoacceptor residues with alanines inhibits DNA replication, suggesting that Dbf4-Cdc7 phosphorylation of Mcm2 in humans is important for DNA replication (20). In contrast, mutation of putative DDK phosphorylation sites at the N terminus of Schizosaccharomyces pombe Mcm2 results in viable cells, suggesting that phosphorylation of S. pombe Mcm2 by DDK is not critical for cell growth (10).In budding yeast, Cdc7 is present at high levels in G₁ and S phase, whereas Dbf4 levels peak in S phase (18, 21, 22). Furthermore, budding yeast DDK binds to chromatin during S phase (6), and it has been shown that Dbf4 is required for Cdc7 binding to chromatin in budding yeast (23, 24), fission yeast (25), and Xenopus (9). Human and fission yeast Cdc7 are inert on their own (7, 8), but Dbf4-Cdc7 is active in phosphorylating Mcm proteins in budding yeast (6, 26), fission yeast (7), and human (8, 10). Based on these data, it has been proposed that Dbf4 activates Cdc7 kinase in S phase and that Dbf4 interaction with Cdc7 is essential for Cdc7 kinase activity (6, 9, 18, 21–24). However, a mechanistic analysis of how Dbf4 activates Cdc7 has not yet been accomplished. For example, the multimeric state of the active Dbf4-Cdc7 complex is currently disputed. A heterodimer of fission yeast Cdc7 (Hsk1) in complex with fission yeast Dbf4 (Dfp1) can phosphorylate Mcm2 (7). However, in budding yeast, oligomers of Cdc7 exist in the cell (27), and Dbf4-Cdc7 exists as oligomers of 180 and 300 kDa (27).DDK phosphorylates the N termini of human Mcm2 (19, 20, 28), human Mcm4 (10), budding yeast Mcm4 (26), and fission yeast Mcm6 (10). Although the sequences of the Mcm N termini are poorly conserved, the DDK sites identified in each study have neighboring acidic residues. The residues of budding yeast Mcm2 that are phosphorylated by DDK have not yet been identified.In this study, we find that budding yeast Cdc7 is weakly active as a multimer in phosphorylating Mcm2. However, a low molecular weight form of Dbf4-Cdc7, likely a heterodimer, has a higher specific activity for phosphorylation of Mcm2. Dbf4 or DDK, but not Cdc7, binds tightly to Mcm2, suggesting that Dbf4 recruits Cdc7 to Mcm2. DDK phosphorylates two serine residues of Mcm2, Ser-164 and Ser-170, in an acidic region of the protein. Mutation of Ser-170 is lethal to yeast cells, but this phenotype is rescued by the DDK bypass mutant mcm5-bob1. We conclude that DDK phosphorylation of Ser-170 of Mcm2 is required for budding yeast growth.     

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]     

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]     

Reconstitution of Rad53 Activation by Mec1 through Adaptor Protein Mrc1

Upon DNA replication stress, stalled DNA replication forks serve as a platform to recruit many signaling proteins, leading to the activation of the DNA replication checkpoint. Activation of Rad53, a key effector kinase in the budding yeast Saccharomyces cerevisiae, is essential for stabilizing DNA replication forks during replication stress. Using an activity-based assay for Rad53, we found that Mrc1, a replication fork-associated protein, cooperates with Mec1 to activate Rad53 directly. Reconstitution of Rad53 activation using purified Mec1 and Mrc1 showed that the addition of Mrc1 stimulated a more than 70-fold increase in the ability of Mec1 to activate Rad53. Instead of increasing the catalytic activity of Mec1, Mrc1 was found to facilitate the phosphorylation of Rad53 by Mec1 via promotion of a stronger enzyme-substrate interaction between them. Further, the conserved C-terminal domain of Mrc1 was found to be required for Rad53 activation. These results thus provide insights into the role of the adaptor protein Mrc1 in activating Rad53 in the DNA replication checkpoint.Faithful replication of the genome is important for the survival of all organisms. During DNA replication, replication stress can arise from a variety of situations, including intrinsic errors made by DNA polymerases, difficulties in replicating repeated DNA sequences, and failures to repair damaged DNA caused by either endogenous oxidative agents or exogenous mutagens such as UV light and DNA-damaging chemicals (1–3). In eukaryotes, there is an evolutionarily conserved DNA replication checkpoint that becomes activated in response to DNA replication stress. It helps to stabilize DNA replication forks, block late replication origin firing, and delay mitosis and ultimately helps recovery from stalled replication forks after DNA repair (4–7). Defects in the DNA replication checkpoint could result in elevated genomic instabilities, cancer development, or cell death (8, 9).Aside from replicating the genome, the DNA replication forks also provide a platform to assemble many signaling proteins that function in the DNA replication checkpoint. In the budding yeast Saccharomyces cerevisiae, Mec1, an ortholog of human ATR,² is a phosphoinositide 3-kinase-like kinase (PIKK) involved in sensing stalled DNA replication forks. Mec1 forms a protein complex with Ddc2 (ortholog of human ATRIP). The Mec1-Ddc2 complex is recruited to stalled replication forks through replication protein A (RPA)-coated single-stranded DNA (10, 11). The Mec3-Rad17-Ddc1 complex, a proliferating cell nuclear antigen (PCNA)-like checkpoint clamp and ortholog of the human 9-1-1 complex, was shown to be loaded onto the single- and double-stranded DNA junction of the stalled replication forks by the clamp loader Rad24-RFC complex (12). Once loaded, the Mec3-Rad17-Ddc1 complex stimulates Mec1 kinase activity (13). Dbp11 and its homolog TopBP1 in vertebrates are known components of the replication machinery (14). In addition to regulating the initiation of DNA replication, they were found to play a role in the DNA replication checkpoint (15–17). They interact with the 9-1-1 complex and directly stimulate Mec1/ATR activity in vitro (18–20). Thus, the assembly of multiple protein complexes at stalled DNA replication forks appears to facilitate activation of the DNA replication checkpoint (13, 18).Mrc1 (for mediator of replication checkpoint) was originally identified to be important for cells to respond to hydroxyurea in S. cerevisiae and Schizosaccharomyces pombe (21, 22). Mrc1 is a component of the DNA replisome and travels with the replication forks along chromosome during DNA synthesis (23–25). Deletion of MRC1 causes defects in DNA replication, indicating its role in the normal progression of DNA replication (23). Interestingly, when DNA replication is blocked by hydroxyurea, Mrc1 undergoes Mec1- and Rad3 (S. pombe ortholog of Mec1)-dependent phosphorylation (21, 22). In S. cerevisiae, mutations of Mrc1 at the (S/T)Q sites, which are consensus phosphorylation sites of the Mec1/ATR family kinases, abolishes hydroxyurea-induced Mrc1 phosphorylation in vivo, suggesting a direct phosphorylation of Mrc1 by Mec1 (21, 22).Rad53 and Cds1, homologs of human Chk2, are the major effector kinases in the DNA replication checkpoints in S. cerevisiae and S. pombe, respectively. Activation of Rad53 is a hallmark of DNA replication checkpoint activation and is important for the maintenance of DNA replication forks in response to DNA replication stress (5, 6). Thus, it is important to understand how Rad53 activity is controlled. Interestingly, mutation of all the (S/T)Q sites of Mrc1 not only abolishes the phosphorylation of Mrc1 by Mec1 but also compromises hydroxyurea-induced Rad53 activation in S. cerevisiae (21). Similarly, mutation of the TQ sites of Mrc1 in S. pombe was shown to abolish the binding between Cds1 and Mrc1 as well as Cds1 activation (22). Further, mutation of specific TQ sites of Mrc1 in S. pombe abolishes its binding to Cds1 in vitro and the activation of Cds1 in vivo (26). Thus, Mec1/Rad3-dependent phosphorylation of Mrc1 is responsible for Mrc1 binding to Rad53/Cds1, which is essential for Rad53/Cds1 activation.An intriguing property of the Chk2 family kinases is their ability to undergo autophosphorylation and activation in the absence of other proteins in vitro (27, 28). First, autophosphorylation of a conserved threonine residue in the activation loop of Chk2 family kinase was found to be an essential part of their activation processes (26, 29–31). Second, a direct and trans-phosphorylation of the N-terminal TQ sites of the Chk2 family kinases by the Mec1/ATR family kinases is also important for their activation in vivo. Analogous to the requirement of N-terminal TQ site phosphorylation of Chk2 by ATR in human (32), the activation of Rad53/Cds1 in vivo requires phosphorylation of TQ sites in their N termini by Mec1/Rad3 (33, 34).Considering that Mec1, Mrc1, and many other proteins are recruited at stalled DNA replication forks and have been shown to be involved in DNA replication checkpoint activation, a key question remains unresolved: what is the minimal system that is capable of activating Rad53 directly? Given the direct physical interaction between Mrc1 and Rad53 and the requirement of Mrc1 and Mec1 in vivo, it is likely that they both play a role in Rad53 activation. Furthermore, what is the molecular mechanism of Rad53 activation by its upstream activators? To address these questions, a faithful reconstitution of the activation of Rad53 using purified proteins is necessary. In this study, we developed an activity-based assay consisting of the Dun1 kinase, a downstream substrate of Rad53, and Sml1, as a substrate of Dun1, to quantitatively measure the activity of Rad53. Using this coupled kinase assay from Rad53 to Dun1 and then to Sml1, we screened for Mrc1 and its associated factors to see whether they could directly activate Rad53 in vitro. Our results showed that Mec1 and Mrc1 collaborate to constitute a minimal system in direct activation of Rad53.