Four strand recombination models

A main point of this paper is to develop the idea that synapsis of DNA duplexes might take place by Watson-Crick base pairing between essentially intact duplex structure to form a four stranded intermediate. This intermediate is the same regular and compact four strand structure already discussed (e.g., McGavin, 1971a, J. molec. Biol., 55, 293-298; 1979, J. theor. Biol., 77, 83-99) and which has been used in several related recombination models (see, for example, McGavin, 1977, Heredity, 39, 15-25; 1984, J. theor. Biol., 107, 37-56; Wilson, 1979, Proc. natn. Acad. Sci. U.S.A., 76, 3641-3645; Nash et al., 1980, Cold Spring Harbor Symposium of Quantitative Biology, 45, 417-428; Nash, 1981, A. Rev. Genetics, 15, 143-167). These models can also be related to one recently suggested by Hopkins (1986, J. theor. Biol. 120, 215-222). An immediate stimulus to the development of the idea was the recent work of Griffith & Nash (1985, Proc. natn. Acad. Sci. U.S.A., 82, 3124-3128), on the site specific recombination system of the lambda bacteriophage. They observed trefoil knots with exclusively positive nodes among the products of the interaction of two relatively inverted attachment sites within circular molecules. The model discussed here may though be of interest in itself. The paper also compares several closely related models for recombination which involve formation of either identical or closely related four strand secondary structures.     

An application of membrane theory to tip morphogenesis in Acetabularia

Focusing our attention on the cell wall and the plasmalemma (i.e. the cell membrane), we seek to show that the initiation of the regenerative, growing tip in the unicellular marine alga Acetabularia mediterranea, can be predicted using the techniques of thin-shell and elasticity theory. We build upon and extend the work of Goodwin & Trainor (1985, J. theor. Biol. 117, 79-106), Trainor & Goodwin (1986, Physica D. 21D, 137-145) and Brière & Goodwin (1988, J. theor. Biol. 131, 461-475) where the attention was focused on the calcium-regulated strain and stress fields of the cortical cytoplasm. Finally, we attempt to model the subsequent tip growth using a moving-boundary formulation, with cytosolic free calcium concentration and turgor pressure being the two variables responsible for the growth.     

Circular codes revisited: a statistical approach

In 1996 Arquès and Michel [1996. A complementary circular code in the protein coding genes. J. Theor. Biol. 182, 45-58] discovered the existence of a common circular code in eukaryote and prokaryote genomes. Since then, circular code theory has provoked great interest and underwent a rapid development. In this paper we discuss some theoretical issues related to the synchronization properties of coding sequences and circular codes with particular emphasis on the problem of retrieval and maintenance of the reading frame. Motivated by the theoretical discussion, we adopt a rigorous statistical approach in order to try to answer different questions. First, we investigate the covering capability of the whole class of 216 self-complementary, C³ maximal codes with respect to a large set of coding sequences. The results indicate that, on average, the code proposed by Arquès and Michel has the best covering capability but, still, there exists a great variability among sequences. Second, we focus on such code and explore the role played by the proportion of the bases by means of a hierarchy of permutation tests. The results show the existence of a sort of optimization mechanism such that coding sequences are tailored as to maximize or minimize the coverage of circular codes on specific reading frames. Such optimization clearly relates the function of circular codes with reading frame synchronization.     

Design of large metabolic responses. Constraints and sensitivity analysis

Metabolic control analysis (Kacser & Burns (1973). Symp. Soc. Exp. Biol.27, 65-104; Heinrich & Rapoport (1974). Eur. J. Biochem.42, 89-95) has been extensively used to describe the response of metabolic concentrations and fluxes to small (infinitesimal) changes in enzyme concentrations and effectors. Similarly, metabolic control design (Acerenza (1993). J. theor. Biol.165, 63-85) has been proposed to design small metabolic responses. These approaches have the limitation that they were not devised to deal with large (non-infinitesimal) responses. Here we develop a strategy to design large changes in the metabolic variables. The only assumption made is that, for all the parameter values under consideration, the system has a unique stable steady state. The procedure renders the kinetic parameters of the rate equations that when embedded in the metabolic network produce the pattern of large changes in the steady-state variables that we aim to design. Structural and kinetic constraints impose restrictions on the type of responses that could be designed. We show that these conditions can be transformed into the language of mean-sensitivity coefficients and, as a consequence, a sensitivity analysis of large metabolic responses can be performed after the system has been designed. The mean-sensitivity coefficients fulfil conservation and summation relationships that in the limit reduce to the well-known theorems for infinitesimal changes. Finally, it is shown that the same procedure that was used to design metabolic responses and analyse their sensitivity properties can also be used to determine the values of kinetic parameters of the rate laws operating "in situ".     

Mitochondrial assembly in respiration-deficient mutants of Saccharomyces cerevisiae. IV. Effects of nuclear amber suppressors on the accumulation of a mitochondrially made subunit of cytochrome c oxidase.

Earlier studies from this laboratory have shown that cytochrome c oxidase from bakers' yeast contains seven subunits, three of which are made in the mitochondrion (Mason, T. L., and Schatz, G. (1973) J. Biol. Chem. 248, 1355). Moreover, a cytochrome c oxidase-less yeast mutant (pet 494-1) was isolated which lacked one of the mitochondrially made subunits (Ebner, E., Mason, T. L., and Schatz, G. (1973) J. Biol. Chem. 248, 5369). Surprisingly, the mutated gene was localized in the nucleus. The results presented here demonstrate that this mutant phenotype can be suppressed by nuclear amber suppressors which affect translation on cytoplasmic ribosomes. This fact was established by two methods, (a) By constructing pet 494-1 strains possessing various amber and ochre markers, isolating respiring revertants from these strains, and demonstrating co-reversion of the amber (but not of the ochre) markers. (b) By coupling the pet 494-1 allele with the well characterized amber suppressor gene SUP 4-3. These data show that suppressor genes located on nuclear chromosomes may control the accumulation of a mitochondrially synthesized polypeptide. The present results also allow some tentative conclusions about the mechanism of the pet 494 mutation. Because it is highly unlikely that the cytoplasmic and the mitochondrial translation system share a common suppressor, the pet 494 locus probably does not code for the missing mitochondrially made subunit, but for a cytoplasmically made protein. This as yet unidentified protein seems to control the synthesis or the integration of the mitochondrially made subunit. Nuclear suppressor genes may thus be useful tools for studying the role of cytoplasmic protein synthesis in mitochondrial formation.     

Self-complementary circular codes in coding theory

Self-complementary circular codes are involved in pairing genetic processes. A maximal \(C^3\) self-complementary circular code X of trinucleotides was identified in genes of bacteria, archaea, eukaryotes, plasmids and viruses (Michel in Life 7(20):1–16 2017, J Theor Biol 380:156–177, 2015; Arquès and Michel in J Theor Biol 182:45–58 1996). In this paper, self-complementary circular codes are investigated using the graph theory approach recently formulated in Fimmel et al. (Philos Trans R Soc A 374:20150058, 2016). A directed graph \(\mathcal {G}(X)\) associated with any code X mirrors the properties of the code. In the present paper, we demonstrate a necessary condition for the self-complementarity of an arbitrary code X in terms of the graph theory. The same condition has been proven to be sufficient for codes which are circular and of large size \(\mid X \mid \ge 18\) trinucleotides, in particular for maximal circular codes (\(\mid X \mid = 20\) trinucleotides). For codes of small-size \(\mid X \mid \le 16\) trinucleotides, some very rare counterexamples have been constructed. Furthermore, the length and the structure of the longest paths in the graphs associated with the self-complementary circular codes are investigated. It has been proven that the longest paths in such graphs determine the reading frame for the self-complementary circular codes. By applying this result, the reading frame in any arbitrary sequence of trinucleotides is retrieved after at most 15 nucleotides, i.e., 5 consecutive trinucleotides, from the circular code X identified in genes. Thus, an X motif of a length of at least 15 nucleotides in an arbitrary sequence of trinucleotides (not necessarily all of them belonging to X) uniquely defines the reading (correct) frame, an important criterion for analyzing the X motifs in genes in the future.     

Schematic methods for probabilistic enzyme kinetics.

The theory of steady-state enzyme processes which avoids using the mass action law of chemical kinetics and consistently describes catalytic mechanisms by probabilistic concepts has recently been proposed (Mazur, 1991, J. theor. Biol. 148, 229-242). To facilitate the analysis of complex reaction graphs by this theory the possibility of constructing schematic rules similar to those used in classical kinetics is studied. It is found that due to the similarity of algebraic procedures the popular method of King & Altman can be applied in probabilistic kinetics in addition to the earlier proposed rule based on enumeration of cycles of the reaction graph. This similarity also allows one to adapt many other shortcut methods of classical kinetics for probabilistic reaction graphs. The paper considers separately the possibility of transforming reaction mechanisms so that the initial graph is replaced by a simpler but equivalent one. It is shown that there are few cases when a group of states can be replaced by one united state, with earlier known rules such as the rule of Cha for equilibrium stages being particular cases of a more general procedure. In addition a novel method is proposed which performs step-by-step reduction of any reaction graph. All the new methods can be adapted for traditional kinetics as well. The results obtained demonstrate that many schematic rules of classical kinetics are of probabilistic origin.     

An evolutionary analytical model of a complementary circular code

The subset X0=[AAC,AAT,ACC,ATC,ATT,CAG,CTC,CTG, GAA,GAC,GAG,GAT,GCC,GGC,GGT,GTA,GTC,GTT,TAC,TTC] of 20 trinucleotides has a preferential occurrence in the frame 0 (reading frame established by the ATG start trinucleotide) of protein (coding) genes of both prokaryotes and eukaryotes. This subset X0 is a complementary maximal circular code with two permutated maximal circular codes X1 and X2 in the frames 1 and 2 respectively (frame 0 shifted by one and two nucleotides respectively in the 5'-3' direction). X0 is called a C3 code (Arquès and Michel, 1997, J. Biosyst 44, 107-134). A quantitative study of these three subsets X0, X1 and X2 in the three frames 0, 1 and 2 of eukaryotic protein genes shows that their occurrence frequencies are constant functions of the trinucleotide positions in the sequences. The frequencies of X0, X1 and X2 in the frame 0 of eukaryotic protein genes are 48.5%, 29% and 22.5% respectively. These properties are not observed in the 5' and 3' regions of eukaryotes where X0, X1 and X2 occur with variable frequencies around the random value (1/3). Several frequency asymmetries unexpectedly observed, e.g. the frequency difference between X1 and X2 in the frame 0, are related to a new property of the C3 code X0 involving substitutions. An evolutionary analytical model at three parameters (p, q, t) based on an independent mixing of the 20 codons (trinucleotides in the frame 0) of X0 with equiprobability (1/20) followed by t approximately 4 substitutions per codon according to the proportions p approximately 0.1, q approximately 0.1 and r = 1 - p - q approximately 0.8 in the three codon sites respectively, retrieves the frequencies of X0, X1 and X2 observed in the three frames of protein genes and explains these asymmetries. The complex behaviour of these analytical curves is totally unexpected and a priori difficult to imagine. Finally, the evolutionary analytical method developed could be applied to the phylogenetic tree reconstruction and the DNA sequence alignment.     

Cloning and Sequencing of the cDNA Encoding the Rubber Elongation Factor of Hevea brasiliensis

In Hevea brasiliensis, the rubber particle in the laticiferous vessel is the site of rubber (cis-1-4-polyisoprene) biosynthesis. A 14 kilodalton protein, rubber elongation factor (REF), is associated with the rubber particle in a ratio of one REF to one rubber molecule (Dennis M, Henzel W, Bell J, Kohr W, Light D [1989] J Biol Chem 264: 18618-18628; Dennis M, Light D [1989] J Biol Chem 264: 18608-18617). To obtain more information concerning the function of REF and its synthesis and assembly in the rubber particle, we isolated cDNA clones encoding REF. We used antibodies to REF to screen a Hevea leaf γgt11 cDNA expression library and obtained several positive clones. Sequence analysis of the REF cDNA clones showed that the REF mRNA contains 121 nucleotides of 5′-nontranslated sequences and a 205 nucleotide 3′-nontranslated region. The open reading frame encodes the entire 14 kilodalton REF protein without any extra amino acids (Dennis M, Henzel W, Bell J, Kohr W, Light D [1989] J Biol Chem 264: 18618-18628). The REF cDNA was subcloned in pGEM-3Z/-4Z and expressed in vitro. The translation product is a 14 kilodalton protein that can be immunoprecipitated with antibodies to REF. Addition of microsomal membranes to the in vitro translation product did not alter the mobility of the REF protein. This, and the sequence data, indicate that REF is not made as a preprotein. Our results suggest that REF is synthesized on free polysomes in the laticifer cytoplasm and that assembly of the rubber particles is likely to occur in the cytosol.     

Mannitol-specific enzyme II of the phosphoenolpyruvate-dependent phosphotransferase system of Staphylococcus carnosus. Sequence and expression in Escherichia coli and structural comparison with the enzyme IImannitol of Escherichia coli.

The enzyme IImannitol (EIImtl) of the phosphoenolpyruvate-dependent phosphotransferase system (PTS) catalyses the uptake and concomitant phosphorylation of mannitol by bacteria; it is specified by the gene mtlA. MtlA is located near the genes mtlF and mtlD in the staphylococcal genome, encoding the enzyme IIImtl and the mannitol-1-phosphate dehydrogenase, respectively. We present the cloning of the whole operon by a novel complementation system which is generally suitable for cloning Gram-positive PTS genes. The nucleotide sequence of a 2.5-kbp subclone spanning mtlA has been determined. From the deduced amino acid sequence, it is predicted that the membrane-protein EIImtl consists of 505 amino acid residues (54112 Da). The protein has the expected hydropathy profile of an integral-membrane protein. The NH2-terminal part of the enzyme resides within the membrane, whereas the COOH-terminus of the enzyme has the properties of a soluble protein. Comparison with the known amino acid sequence of EIImtl of Escherichia coli [Lee, C. A. & Saier, M. H. (1983) J. Biol. Chem. 258, 10761-10767] showed significant similarity. The motif containing the cysteine, which is the putative second phosphorylation site in EIImtl of E. coli [Pas, H. H. & Robillard, G. T. (1988) Biochemistry 27, 5835-5839], is well conserved in EIImtl of Staphylococcus carnosus. Chemical modification of the single active site cysteine residue by Ellman's reagent leads to total inactivation, which can be reversed by treatment with 2-mercaptoethanol.     

Cloning and sequencing of glutamate mutase component S from Clostridium tetanomorphum. Homologies with other cobalamin-dependent enzymes.

The gene encoding component S, the small subunit, of glutamate mutase, an adenosylcobalamin (coenzyme B12)-dependent enzyme from Clostridium tetanomorphum has been cloned and its nucleotide sequence determined. The mutS gene encodes a protein of 137 amino acid residues, with M(r) 14,748. The deduced amino acid sequence showed homology with the C-terminal portion of adenosylcobalamin-dependent methylmalonyl-CoA mutase [1989, Biochem. J. 260, 345-352] and a region of cobalamin-dependent methionine synthase which has been shown to bind cobalamin [1989, J. Biol. Chem 264, 13888-13895].     

The Drosophila genes CG14593 and CG30106 code for G-protein-coupled receptors specifically activated by the neuropeptides CCHamide-1 and CCHamide-2

Recently, a novel neuropeptide, CCHamide, was discovered in the silkworm Bombyx mori (L. Roller et al., Insect Biochem. Mol. Biol. 38 (2008) 1147–1157). We have now found that all insects with a sequenced genome have two genes, each coding for a different CCHamide, CCHamide-1 and -2. We have also cloned and deorphanized two Drosophila G-protein-coupled receptors (GPCRs) coded for by genes CG14593 and CG30106 that are selectively activated by Drosophila CCH-amide-1 (EC₅₀, 2 × 10⁻⁹ M) and CCH-amide-2 (EC₅₀, 5 × 10⁻⁹ M), respectively. Gene CG30106 (symbol synonym CG14484) has in a previous publication (E.C. Johnson et al., J. Biol. Chem. 278 (2003) 52172–52178) been wrongly assigned to code for an allatostatin-B receptor. This conclusion is based on our findings that the allatostatins-B do not activate the CG30106 receptor and on the recent findings from other research groups that the allatostatins-B activate an unrelated GPCR coded for by gene CG16752. Comparative genomics suggests that a duplication of the CCHamide neuropeptide signalling system occurred after the split of crustaceans and insects, about 410 million years ago, because only one CCHamide neuropeptide gene is found in the water flea Daphnia pulex (Crustacea) and the tick Ixodes scapularis (Chelicerata).     

Chemotaxis and chemokinesis in eukaryotic cells: The Keller-Segel equations as an approximation to a detailed model

More than 20 years after its proposal, Keller and Segel's model (1971,J. theor. Biol.,30, 235–248) remains by far the most popular model for chemical control of cell movement. However, before the Keller-Segel equations can be applied to a particular system, appropriate functional forms must be specified for the dependence on chemical concentration of the cell transport coefficients and the chemical degradation rate. In the vast majority of applications, these functional forms have been chosen using simple intuitive criteria. We focus on the particular case of eukaryotic cell movement, and derive an approximation to the detailed model of Sherrattet al. (1993,J. theor. Biol.,162, 23–40). The approximation consists of the Keller-Segel equations, with specific forms predicted for the cell transport coefficients and chemical degradation rate. Moreover, the parameter values in these functional forms can be directly measured experimentally. In the case of the much studied neutrophil-peptide system, we test our approximation using both the Boyden chamber and under-agarose assays. Finally, we show that for other cell-chemical interactions, a simple comparison of time scales provides a rapid check on the validity of our Keller-Segel approximation.     

On the prevalence of certain codons (“RNY”) in genes for proteins

J.C. Shepherd notes that codons of the type RNY (R = purine, N = any nucleotide base, Y = pyrimidine) predominate over RNR in the genes for proteins. He has hypothesized that RNY codons are the relics of “a primitive code” composed of repeating RNY triplets. He found that RNY codons predominated in fourfold RNN codon sets (family boxes). These family boxes code for valine, threonine, alanine, and glycine. We argue that the proposed “comma-less” code composed of RNY never existed, and that, in any case, survival of such a code would have long since been erased by mutations. The excess of RNY codons in family boxes is probably attributable to preference for the corresponding tRNAs.