Analysis of a local fitness landscape with a model of the rough Mt. Fuji-type landscape: application to prolyl endopeptidase and thermolysin

A method of analysis of a local fitness landscape for a current biopolymer is presented. Based on the assumption of additivity of mutational effects in the biopolymer, we assigned a site-fitness to each residue at each site. The assigned values of site-fitnesses were obtained by the least-squares method to minimize discrepancies between experimental fitnesses and theoretical ones. As test cases, we analyzed a section of a local landscape for the thermostability of prolyl endopeptidase and that for the enzymatic activity of thermolysin. These sections were proved to be of the rough Mt. Fuji-type with straight theta values of larger than 1.0, where straight theta is defined as the ratio of the "mean slope" to the "degree of roughness" on the fitness surface. Furthermore, we theoretically explained discrepancies between the fitnesses of multiple mutants and those predicted based on strict additivity of the component mutations by using a model of the rough Mt. Fuji-type landscape. According to this model, the discrepancies depend on the local landscape property (such as the straight theta value) and the location of the wild type on the landscape and the mean change in fitness by the component mutations. Our results suggest that this model may provide a good approximation of real sections of local landscapes for current biopolymers phenomenologically.     

The optimality of the standard genetic code assessed by an eight-objective evolutionary algorithm

Background

The standard genetic code (SGC) is a unique set of rules which assign amino acids to codons. Similar amino acids tend to have similar codons indicating that the code evolved to minimize the costs of amino acid replacements in proteins, caused by mutations or translational errors. However, if such optimization in fact occurred, many different properties of amino acids must have been taken into account during the code evolution. Therefore, this problem can be reformulated as a multi-objective optimization task, in which the selection constraints are represented by measures based on various amino acid properties.

Results

To study the optimality of the SGC we applied a multi-objective evolutionary algorithm and we used the representatives of eight clusters, which grouped over 500 indices describing various physicochemical properties of amino acids. Thanks to that we avoided an arbitrary choice of amino acid features as optimization criteria. As a consequence, we were able to conduct a more general study on the properties of the SGC than the ones presented so far in other papers on this topic. We considered two models of the genetic code, one preserving the characteristic codon blocks structure of the SGC and the other without this restriction. The results revealed that the SGC could be significantly improved in terms of error minimization, hereby it is not fully optimized. Its structure differs significantly from the structure of the codes optimized to minimize the costs of amino acid replacements. On the other hand, using newly defined quality measures that placed the SGC in the global space of theoretical genetic codes, we showed that the SGC is definitely closer to the codes that minimize the costs of amino acids replacements than those maximizing them.

Conclusions

The standard genetic code represents most likely only partially optimized systems, which emerged under the influence of many different factors. Our findings can be useful to researchers involved in modifying the genetic code of the living organisms and designing artificial ones.

     

Correlated Flexible Molecular Coding and Molecular Evolvability

Evolvability of biopolymers is based on molecular coding. The molecular coding is represented by biopolymer function vs monomeric sequence relationship, that is, a proper fitness landscape on the sequence space. On the other hand, molecular coding is mostly realized by monomeric sequence vs biopolymer structure relationship. We suggest the evolution of evolvability based on flexible or multiplex coding originating from flexible or polymorphic conformation of evolving biopolymers. We report a finding supporting that the amino acid landscape of the standard genetic code for an amino acid property which is more important to the protein function gives higher value of an evolvability measure. We developed a promising molecular construct which realized genotype-phenotype linking in order to study the in vitroprotein evolution to clarify above mentioned protein evolvability.     

On the Origin of Frameshift-Robustness of the Standard Genetic Code

The standard genetic code (SGC) has been extensively analyzed for the biological ramifications of its nonrandom structure. For instance, mismatch errors due to point mutation or mistranslation have an overall smaller effect on the amino acid polar requirement under the SGC than under random genetic codes (RGCs). A similar observation was recently made for frameshift errors, prompting the assertion that the SGC has been shaped by natural selection for frameshift-robustness—conservation of certain amino acid properties upon a frameshift mutation or translational frameshift. However, frameshift-robustness confers no benefit because frameshifts usually create premature stop codons that cause nonsense-mediated mRNA decay or production of nonfunctional truncated proteins. We here propose that the frameshift-robustness of the SGC is a byproduct of its mismatch-robustness. Of 564 amino acid properties considered, the SGC exhibits mismatch-robustness in 93–133 properties and frameshift-robustness in 55 properties, respectively, and that the latter is largely a subset of the former. For each of the 564 real and 564 randomly constructed fake properties of amino acids, there is a positive correlation between mismatch-robustness and frameshift-robustness across one million RGCs; this correlation arises because most amino acid changes resulting from a frameshift are also achievable by a mismatch error. Importantly, the SGC does not show significantly higher frameshift-robustness in any of the 55 properties than RGCs of comparable mismatch-robustness. These findings support that the frameshift-robustness of the SGC need not originate through direct selection and can instead be a site effect of its mismatch-robustness.     

Searching of Code Space for an Error-Minimized Genetic Code Via Codon Capture Leads to Failure, or Requires At Least 20 Improving Codon Reassignments Via the Ambiguous Intermediate Mechanism

The standard genetic code (SGC) has a fundamental error-minimizing property which has been widely attributed to the action of selection. However, a clear mechanism for how selection can give rise to error minimization (EM) is lacking. A search through a space of alternate codes (code space) via codon reassignments would be required, to select a code optimized for EM. There are two commonly discussed mechanisms of codon reassignment; the Codon Capture mechanism, which proposes a loss of the codon during reassignment, and the Ambiguous Intermediate mechanism, which proposes that the codon underwent an ambiguous phase during reassignment. When searching of code space via the Codon Capture mechanism is simulated, an optimized genetic code can rarely be achieved (0–3.2% of the time) with most searches ending in failure. When code space is searched via the Ambiguous Intermediate mechanism, under constraints derived from empirical observations of codon reassignments from extant genomes, the searches also often end in failure. When a local minimum is avoided and optimization is achieved, 20–41 sequential improving codon reassignments are required. Furthermore, the structures of the optimized codes produced by these simulations differ from the structure of the SGC. These data are challenges for the Adaptive Code hypothesis to address, which proposes that the EM property was directly selected for, and suggests that EM is simply a byproduct of the addition of amino acids to the expanding code, as described by the alternative ‘Emergence’ hypothesis.     

The Level and Landscape of Optimization in the Origin of the Genetic Code

We consider a model of the origin of genetic code organization incorporating the biosynthetic relationships between amino acids and their physicochemical properties. We study the behavior of the genetic code in the set of codes subject both to biosynthetic constraints and to the constraint that the biosynthetic classes of amino acids must occupy only their own codon domain, as observed in the genetic code. Therefore, this set contains the smallest number of elements ever analyzed in similar studies. Under these conditions and if, as predicted by physicochemical postulates, the amino acid properties played a fundamental role in genetic code organization, it can be expected that the code must display an extremely high level of optimization. This prediction is not supported by our analysis, which indicates, for instance, a minimization percentage of only 80%. These observations can therefore be more easily explained by the coevolution theory of genetic code origin, which postulates a role that is important but not fundamental for the amino acid properties in the structuring of the code. We have also investigated the shape of the optimization landscape that might have arisen during genetic code origin. Here, too, the results seem to favor the coevolution theory because, for instance, the fact that only a few amino acid exchanges would have been sufficient to transform the genetic code (which is not a local minimum) into a much better optimized code, and that such exchanges did not actually take place, seems to suggest that, for instance, the reduction of translation errors was not the main adaptive theme structuring the genetic code.     

Fitness conferred by replaced amino acids declines with time

The fitness landscape of a locus, the array of fitnesses conferred by its alleles, can be affected by allele replacements at other loci, in the presence of epistatic interactions between loci. In a pair of diverging homologous proteins, the initially high probability that an amino acid replacement in one of them will make it more similar to the other declines with time, implying that the fitness landscapes of homologous sites diverge. Here, we use data on within-population non-synonymous polymorphisms and on amino acid replacements between species to study the dynamics, after an amino acid replacement, of the fitness of the ancestral amino acid, and show that selection against its restoration increases with time. This effect can be owing to increase of fitness conferred by the new amino acid occupying the site, and/or to decline of fitness conferred by the replaced amino acid. We show that the fitness conferred by the replaced amino acid rapidly declines, reaching a new lower steady-state level after approximately 20 per cent of amino acids in the protein get replaced. Therefore, amino acid replacements in evolving proteins are routinely involved in negative epistatic interactions with currently absent amino acids, and chisel off the unused parts of the fitness landscape.     

The NK model of rugged fitness landscapes and its application to maturation of the immune response

Adaptive evolution is, to a large extent, a complex combinatorial optimization process. Such processes can be characterized as "uphill walks on rugged fitness landscapes". Concrete examples of fitness landscapes include the distribution of any specific functional property such as the capacity to catalyze a specific reaction, or bind a specific ligand, in "protein space". In particular, the property might be the affinity of all possible antibody molecules for a specific antigenic determinant. That affinity landscape presumably plays a critical role in maturation of the immune response. In this process, hypermutation and clonal selection act to select antibody V region mutant variants with successively higher affinity for the immunizing antigen. The actual statistical structure of affinity landscapes, although knowable, is currently unknown. Here, we analyze a class of mathematical models we call NK models. We show that these models capture significant features of the maturation of the immune response, which is currently thought to share features with general protein evolution. The NK models have the important property that, as the parameter K increases, the "ruggedness" of the NK landscape varies from a single peaked "Fujiyama" landscape to a multi-peaked "badlands" landscape. Walks to local optima on such landscapes become shorter as K increases. This fact allows us to choose a value of K that corresponds to the experimentally observed number of mutational "steps", 6-8, taken as an antibody sequence matures. If the mature antibody is taken to correspond to a local optimum in the model, tuning the model requires that K be about 40, implying that the functional contribution of each amino acid in the V region is affected by about 40 others. Given this value of K, the model then predicts several features of "antibody space" that are in qualitative agreement with experiment: (1) The fraction of fitter variants of an initial "roughed in" germ line antibody amplified by clonal selection is about 1-2%. (2) Mutations at some sites of the mature antibody hardly affect antibody function at all, but mutations at other sites dramatically decrease function. (3) The same "roughed in" antibody sequence can "walk" to many mature antibody sequences. (4) Many adaptive walks can end on the same local optimum. (5) Comparison of different mature sequences derived from the same initial V region shows evolutionary hot spots and parallel mutations. All these predictions are open to detailed testing by obtaining monoclonal antibodies early in the immune response and carrying out in vitro mutagenesis and adaptive hill climbing with respect to affinity for the immunizing antigen.     

Target recognition of apocalmodulin by nitric oxide synthase I peptides

An increasing number of proteins are found that are regulated by the Ca(2+)-free state of calmodulin, apocalmodulin. Many of these targets harbor a so-called IQ motif within their primary sequence, but several target proteins of apocalmodulin lack this motif. We investigated whether the Ca(2+)-dependent calmodulin-binding site of nitric oxide synthase I could be transformed into a target site of apocalmodulin. Synthetic peptides representing the wild-type amino acid sequence and several peptides carrying mutations were studied by isothermal titration calorimetry and fluorescence spectroscopy. A single amino acid substitution of a negative charge to a positive charge can convert a classical Ca(2+)-dependent binding site of calmodulin into a target site for apocalmodulin. In addition, the introduction of hydrophobic amino acids increases the apparent binding affinity from the micromolar to the nanomolar range. Binding of wild-type and mutant peptides to Ca(2+)-calmodulin was enthalpically driven, and binding to apocalmodulin was entropically driven. Our data indicate that only a few selected amino acid positions in a calmodulin-binding site determine its Ca(2+) dependency.     

PolyUbiquitin Chain Linkage Topology Selects the Functions from the Underlying Binding Landscape

Ubiquitin (Ub) can generate versatile molecular signals and lead to different celluar fates. The functional poly-valence of Ub is believed to be resulted from its ability to form distinct polymerized chains with eight linkage types. To provide a full picture of ubiquitin code, we explore the binding landscape of two free Ub monomers and also the functional landscapes of of all eight linkage types by theoretical modeling. Remarkably, we found that most of the compact structures of covalently connected dimeric Ub chains (diUbs) pre-exist on the binding landscape. These compact functional states were subsequently validated by corresponding linkage models. This leads to the proposal that the folding architecture of Ub monomer has encoded all functional states into its binding landscape, which is further selected by different topologies of polymeric Ub chains. Moreover, our results revealed that covalent linkage leads to symmetry breaking of interfacial interactions. We further propose that topological constraint not only limits the conformational space for effective switching between functional states, but also selects the local interactions for realizing the corresponding biological function. Therefore, the topological constraint provides a way for breaking the binding symmetry and reaching the functional specificity. The simulation results also provide several predictions that qualitatively and quantitatively consistent with experiments. Importantly, the K48 linkage model successfully predicted intermediate states. The resulting multi-state energy landscape was further employed to reconcile the seemingly contradictory experimental data on the conformational equilibrium of K48-diUb. Our results further suggest that hydrophobic interactions are dominant in the functional landscapes of K6-, K11-, K33- and K48 diUbs, while electrostatic interactions play a more important role in the functional landscapes of K27, K29, K63 and linear linkages.     

Amino Acid Sequences of Neuropeptides in the Sinus Gland of the Land Crab Cardisoma carnifex: A Novel Neuropeptide Proteolysis Site

The sinus gland is a major neurosecretory structure in Crustacea. Five peptides, labeled C, D, E, F, and I, isolated from the sinus gland of the land crab have been hypothesized to arise from the incomplete proteolysis at two internal sites on a single biosynthetic intermediate peptide "H", based on amino acid composition additivities and pulse-chase radiolabeling studies. The presence of only a single major precursor for the sinus gland peptides implies that peptide H may be synthesized on a common precursor with crustacean hyperglycemic hormone forms, "J" and "L," and a peptide, "K," similar to peptides with molt inhibiting activity. Here I report amino acid sequences of these peptides. The amino terminal sequence of the parent peptide, H, (and the homologous fragments) proved refractory to Edman degradation. Data from amino acid analysis and carboxypeptidase digestion of the naturally occurring fragments and of fragments produced by endopeptidase digestion were used together with Edman degradation to obtain the sequences. Amino acid analysis of fragments of the naturally occurring "overlap" peptides (those produced by internal cleavage at one site on H) was used to obtain the sequences across the cleavage sites. The amino acid sequence of the land crab peptide H is Arg-Ser-Ala-Asp-Gly-Phe-Gly-Arg-Met-Glu-Ser-Leu-Leu-Thr-Ser-Leu-Arg-Gly- Ser-Ala-Glu- Ser-Pro-Ala-Ala-Leu-Gly-Glu-Ala-Ser-Ala-Ala-His-Pro-Leu-Glu. In vivo cleavage at one site involves excision of arginine from the sequence Leu-Arg-Gly, whereas cleavage at the other site involves excision of serine from the sequence Glu-Ser-Leu. Proteolysis at the latter sequence has not been previously reported in intact secretory granules. The aspartate at position 4 is possibly covalently modified.     

Effects of length and position of an extended linker on sequence-selective DNA recognition of zinc finger peptides

Engineered zinc finger proteins revealed that a linker sequence connecting zinc finger units has a significant effect on the DNA binding property of the protein. The recognition for a noncontiguous DNA target beyond the current recognition code of zinc finger proteins has never been determined because of the limitation of a zinc finger framework. DNA recognition of zinc finger proteins is limited only to a contiguous subset of three base pairs. We propose the recognition for a noncontiguous DNA target by inserting amino acids into the canonical linker between zinc finger units. The sequence selectivity of the new zinc finger peptides was evaluated by gel mobility shift assays. DNase I footprinting analyses clearly showed different DNA binding of various linker-extended zinc finger peptides. The application of a SPR measurement also revealed a DNA sequence selectivity of peptides. Insertion of three amino acids is enough for recognition of a noncontiguous DNA target with sequence selectivity. An extended linker will be useful for expansion of the recognition code of zinc finger proteins and for development of a new role for linker sequences in DNA binding of zinc finger proteins.     

On Nature’s Strategy for Assigning Genetic Code Multiplicity

Genetic code redundancy would yield, on the average, the assignment of three codons for each of the natural amino acids. The fact that this number is observed only for incorporating Ile and to stop RNA translation still waits for an overall explanation. Through a Structural Bioinformatics approach, the wealth of information stored in the Protein Data Bank has been used here to look for unambiguous clues to decipher the rationale of standard genetic code (SGC) in assigning from one to six different codons for amino acid translation. Leu and Arg, both protected from translational errors by six codons, offer the clearest clue by appearing as the most abundant amino acids in protein-protein and protein-nucleic acid interfaces. Other SGC hidden messages have been sought by analyzing, in a protein structure framework, the roles of over- and under-protected amino acids.     

Arsenite binding to synthetic peptides: the effect of increasing length between two cysteines

We utilized radioactive 73As-labeled arsenite and vacuum filtration methodology to determine the binding affinity of arsenite to eight synthetic peptides ranging from 13 to 24 amino acids long and containing one or two cysteines separated by 0-17 intervening amino acids. Six of the eight peptides were highly similar in amino acid sequence and were based on cysteine containing regions of the hormone-binding site of the human estrogen receptor-alpha (e.g., the sequence of peptide 28 is LEGAWCGKGVEGTEHLYSMKCKNV). The peptides with 0-14 intervening amino acids between two cysteines bound arsenite with Kd values of 2.7-20.1 uM and with Bmax values from 36 to 103 nmol/mg protein (from 0.083 to 0.19 nmol/nmol of protein). Thus, increasing the number of intervening amino acids from 0 to 14 made very little difference in the observed Kd values for arsenite, a surprising finding. Therefore, these peptides are flexible in solution and effectively contain a dithiol high affinity binding site for arsenite. Peptide 17 with two C separated by 19 amino acids bound arsenite with a Kd of 123 uM and a Bmax of 41.8 nmol/mg. The monothiol peptide 19 bound arsenite with a Kd of 124 uM and a Bmax of 26 nmol/mg protein. All experimental binding curves fit well to a one site binding model.     

The complete nucleotide sequence of the Pseudomonas gene coding for carboxypeptidase G2

The complete nucleotide sequence of the Pseudomonas chromosomal gene coding for the enzyme carboxypeptidase G2 (CPG2) has been determined. The nucleotide sequence obtained has been confirmed by comparing the predicted amino acid sequence with that of randomly derived peptide fragments and by N-terminal sequencing of the purified protein. The gene has been shown to code for a 22 amino acid signal peptide at its N-terminus which closely resembles the signal peptides of other secreted proteins. An alternative 36 amino acid signal peptide which may function in Pseudomonas has also been identified. The codon utilisation of the gene is influenced by the high G + C (67.2%) content of the DNA and exhibits a 92.8% preference for codons ending in G or C. This unusual codon preference may contribute to the generally observed weak expression of Pseudomonas genes in Escherichia coli. A region of DNA upstream of the structural gene has also been sequenced and a ribosome binding site and two putative promoter sequences identified.     

Complete amino acid sequence of the ubiquinone binding protein (QP-C), a protein similar to the 14,000-dalton subunit of the yeast ubiquinol-cytochrome c reductase complex

The amino acid sequence of the ubiquinone binding protein (QP-C) in the cytochrome bc1 region of the mitochondrial electron transfer chain was determined by analysis of peptides obtained by cyanogen bromide cleavage and staphylococcal protease digestion of succinylated derivatives. It was found to consist of 110 amino acid residues and its amino terminus to be blocked by an acetyl group, as determined by mass spectrometry of the amino-terminal peptide and a comparison with peptides chemically synthesized on high-performance liquid chromatography. The molecular weight of this ubiquinone binding protein including the acetyl group was calculated to be 13,389. The predicted secondary structure of QP-C has alpha-helical content of about 50% and QP-C was classified as an "all-alpha" or "alpha + beta" protein. This is the first report describing the amino acid sequence of the ubiquinone binding protein. A comparison of this sequence with that of the 14-kDa subunit of the yeast ubiquinol-cytochrome c reductase complex from the nucleotide sequence showed these two sequences to be quite similar.     

Editing by a tRNA synthetase: DNA aptamer-induced translocation and hydrolysis of a misactivated amino acid

Aminoacyl-tRNA synthetases establish the rules of the genetic code by aminoacylation reactions. Occasional activation of the wrong amino acid can lead to errors of protein synthesis. For isoleucyl-tRNA synthetase, these errors are reduced by tRNA-dependent hydrolytic editing reactions that occur at a site 25 A from the active site. These reactions require that the misactivated amino acid be translocated from the active site to the center for editing. One mechanism describes translocation as requiring the mischarging of tRNA followed by a conformational change in the tRNA that moves the amino acid from one site to the other. Here a specific DNA aptamer is investigated. The aptamer can stimulate amino acid-specific editing but cannot be aminoacylated. Although the aptamer could in principle stimulate hydrolysis of a misactivated amino acid by an idiosyncratic mechanism, the aptamer is shown here to induce translocation and hydrolysis of misactivated aminoacyl adenylate at the same site as that seen with the tRNA cofactor. Thus, translocation to the site for editing does not require joining of the amino acid to the nucleic acid. Further experiments demonstrated that aptamer-induced editing is sensitive to aptamer sequence and that the aptamer is directed to a site other than the active site or tRNA binding site of the enzyme.     

Amino acid sequences of substrate-binding sites in chicken liver fatty acid synthase

The amino acid sequences of three essential regions of chicken liver fatty acid synthase have been determined: that around 4'-phosphopantetheine ("carrier" site), the substrate "loading" site containing serine, and a "waiting" site for the growing fatty acid containing cysteine. The amino acid sequence of the 4'-phosphopantetheine region was determined for the acetyl-, malonyl-, hydroxybutyryl-, and butyryl-enzyme with peptides obtained by hydrolysis of the enzyme with trypsin and Staphylococcus aureus (V8) protease. The sequence region around the essential serine was obtained for the acetyl- and malonyl-enzyme. The N-terminus of the tryptic peptide was blocked. However, the same sequence is obtained for the acetyl- and malonyl-peptide after S. aureus protease digestion, suggesting that the enzyme contains a single acyl transferase rather than two separate transacylases. The sequence around the cysteine was obtained by use of a radioactive iodoacetamide label. An unusual sequence of three serines adjacent to the cysteine was found. The strong similarities between peptides from different species for all three of the regions suggest that the multifunctional polypeptides from yeast and animals have evolved from the monofunctional enzymes of lower species.     

cDNA cloning and immunological characterization of the rye grass allergen Lol p I.

The complete amino acid sequence of two "isoallergenic" forms of Lol p I, the major rye grass (Lolium perenne) pollen allergen, was deduced from cDNA sequence analysis. cDNA clones isolated from a Lolium perenne pollen library contained an open reading frame coding for a 240-amino acid protein. Comparison of the nucleotide and deduced amino acid sequence of two of these clones revealed four changes at the amino acid level and numerous nucleotide differences. Both clones contained one possible asparagine-linked glycosylation site. Northern blot analysis shows one RNA species of 1.2 kilobases. Based on the complete amino acid sequence of Lol p I, overlapping peptides covering the entire molecule were synthesized. Utilizing these peptides we have identified a determinant within the Lol p I molecule that is recognized by human leukocyte antigen class II-restricted T cells obtained from persons allergic to rye grass pollen.