Evolutionary Branching in a Finite Population: Deterministic Branching vs. Stochastic Branching

Adaptive dynamics formalism demonstrates that, in a constant environment, a continuous trait may first converge to a singular point followed by spontaneous transition from a unimodal trait distribution into a bimodal one, which is called “evolutionary branching.” Most previous analyses of evolutionary branching have been conducted in an infinitely large population. Here, we study the effect of stochasticity caused by the finiteness of the population size on evolutionary branching. By analyzing the dynamics of trait variance, we obtain the condition for evolutionary branching as the one under which trait variance explodes. Genetic drift reduces the trait variance and causes stochastic fluctuation. In a very small population, evolutionary branching does not occur. In larger populations, evolutionary branching may occur, but it occurs in two different manners: in deterministic branching, branching occurs quickly when the population reaches the singular point, while in stochastic branching, the population stays at singularity for a period before branching out. The conditions for these cases and the mean branching-out times are calculated in terms of population size, mutational effects, and selection intensity and are confirmed by direct computer simulations of the individual-based model.     

Branching out

正All hormone receptors have been thought to start action by binding their active hormone molecules reversibly.However,a novel perception mechanism for the plant branching hormone strigolactones(SLs)has unexpectedly branched out from this classic model:the receptor D14 generates and irreversibly binds active SL molecule CLIM,suggesting that SL perception surprisingly integrates bothsubstrate-enzymeandhormone-receptorinteractions(Yao et al.,2016).     

水稻籽粒淀粉分支酶活性的遗传分析

用由247个株系组成的珍汕97B/密阳46重组自交系群体及其含207个分子标记的连锁图谱,在2002年和2003年分别测定亲本和重组自交系群体开花后10 d和20 d籽粒的淀粉分支酶的活性,检测到3个控制开花后10 d Q酶活性的主效应QTL(qnantitative trait loci),联合贡献率为10%,其中qQ10-6与环境发生显著的互作;分别检测到5对和2对染色体区间对开花后10 d、20 d Q酶活性的影响具有加性×加性上位性作用,其中开花后10 d的3对染色体区间具有显著的上位性×环境互作效应.由此可见,水稻籽粒Q酶活性相关基因的表达,受到环境因子的极大影响.     

Parametric Analysis of Alignment and Phylogenetic Uncertainty

To infer a phylogenetic tree from a set of DNA sequences, typically a multiple alignment is first used to obtain homologous bases. The inferred phylogeny can be very sensitive to how the alignment was created. We develop tools for analyzing the robustness of phylogeny to perturbations in alignment parameters in the NW algorithm. Our main tool is parametric alignment, with novel improvements that are of general interest in parametric inference. Using parametric alignment and a Gaussian distribution on alignment parameters, we derive probabilities of optimal alignment summaries and inferred phylogenies. We apply our method to analyze intronic sequences from Drosophila flies. We show that phylogeny estimates can be sensitive to the choice of alignment parameters, and that parametric alignment elucidates the relationship between alignment parameters and reconstructed trees.     

Absolute Configurations of Marmelo Oxides

Our interest on engineering non-ribosomal synthetase responsible for SW-163 biosynthesis prompted us to determine the relative and absolute configuration of antitumor cyclic depsipeptide SW-163s. We first isolated and identified SW-163 homologs D, F and G as known compounds UK-63598, UK-65662 and UK-63052, respectively. Both enantiomers of the unusual constitutive amino acid, N-methylnorcoromic acid, were synthesized in chiral forms starting from (R)- and (S)-1,2-propanediol. The hydrolyzate of SW-163D, a major constituent of this family, was converted with Marfey’s reagent, 1-fluoro-2,4-dinitrophenyl-5-L-alanine-amide (L-FDAA), and the resulting mixture of amino acid derivatives was subjected to an LC/MS analysis. Compared with authentic samples, the analytical data unambiguously show that SW-163D consisted of L-Ala, D-Ser and (1S, 2S)-N-methylnorcoronamic acid. The remaining stereochemistry of the N-methylcysteine moieties was determined from NOE data.     

Mechanisms of Side Branching and Tip Splitting in a Model of Branching Morphogenesis

Recent experimental work in lung morphogenesis has described an elegant pattern of branching phenomena. Two primary forms of branching have been identified: side branching and tip splitting. In our previous study of lung branching morphogenesis, we used a 4 variable partial differential equation (PDE), due to Meinhardt, as our mathematical model to describe the reaction and diffusion of morphogens creating those branched patterns. By altering key parameters in the model, we were able to reproduce all the branching styles and the switch between branching modes. Here, we attempt to explain the branching phenomena described above, as growing out of two fundamental instabilities, one in the longitudinal (growth) direction and the other in the transverse direction. We begin by decoupling the original branching process into two semi-independent sub-processes, 1) a classic activator/inhibitor system along the growing stalk, and 2) the spatial growth of the stalk. We then reduced the full branching model into an activator/inhibitor model that embeds growth of the stalk as a controllable parameter, to explore the mechanisms that determine different branching patterns. We found that, in this model, 1) side branching results from a pattern-formation instability of the activator/inhibitor subsystem in the longitudinal direction. This instability is far from equilibrium, requiring a large inhomogeneity in the initial conditions. It successively creates periodic activator peaks along the growing stalk, each of which later on migrates out and forms a side branch; 2) tip splitting is due to a Turing-style instability along the transversal direction, that creates the spatial splitting of the activator peak into 2 simultaneously-formed peaks at the growing tip, the occurrence of which requires the widening of the growing stalk. Tip splitting is abolished when transversal stalk widening is prevented; 3) when both instabilities are satisfied, tip bifurcation occurs together with side branching.     

DNA-dependent RNA polymerase subunit B as a tool for phylogenetic reconstructions: Branching topology of the archaeal domain

The branching topology of the archaeal (archaebacterial) domain was inferred from sequence comparisons of the largest subunit (B) of DNA-dependent RNA polymerases (RNAP). Both the nucleic acid sequences of the genes coding for RNAP subunit B and the amino acid sequences of the derived gene products were used for phylogenetic reconstructions. Individual analysis of the three nucleotide positions of codons revealed significant inequalities with respect to guanosine and cytosine (GC) content and evolutionary rates. Only the nucleotides at the second codon positions were found to be unbiased by varied GC contents and sufficiently conserved for reliable phylogenetic reconstructions. A decision matrix was used for the combination of the results of distance matrix, maximum parsimony, and maximum likelihood methods. For this purpose the original results (sums of squares, steps, and logarithms of likelihoods) were transformed into comparable effective values and analyzed with methods known from the theory of statistical decisions. Phylogenetic invariants and statistical analysis with resampling techniques (bootstrap and jackknife) confirmed the preferred branching topology, which is significantly different from the topology known from phylogenetic trees based on 16S rRNA sequences. The preferred topology reconstructed by this analysis shows a common stem for the Methanococcales and Methanobacteriales and a separation of the thermophilic sulfur archaea from the methanogens and halophiles. The latter coincides with a unique phylogenetic location of a characteristic splitting event replacing the largest RNAP subunit of thermophilic sulfur archaea by two fragments in methanogens and halophiles. This topology is in good agreement with physiological and structural differences between the various archaea and demonstrates RNAP to be a suitable phylogenetic marker molecule. Correspondence to: H.-P. Klenk     

Polyglucan Branching Isoenzymes of Algae

The cyanophyte, Oscillatoria princeps, and the enigmatic hot-spring alga, Cyanidium caldarium, contain two branching isoenzymes which can act on amylose and amylopectin, converting these polyglucans into highly branched phytoglycogens. The red alga, Rhodymenia pertusa contains three branching isoenzymes, only one of which is capable of the dual activity of the other algal branching isoenzymes. The other two red algal branching isoenzymes are Q enzymes and can only act on amylose, forming moderately branched amylopectìns. However, when the isoenzymes of all three algae are separated on different concentrations of polyacrylamide gel via electrophoresis, the mobilities of the isoenzymes show that the Q enzymes and the branching enzymes are related and true isoenzymic molecules. They differ only in electrical charges, probably caused by the substitution of amino acid residues in their active peptides. It is possible that if these charge isomers are due merely to amino acid substitutions, the enzymes may have been originally derived from a common catalytic molecule. The study indicates the identity of the branching isoenzymes of Oscillatoria and Cyanidium, and lends further supporting evidence to the cyanophyte origin of the enigmatic alga.     

Analysis of RNA motifs

RNA motifs are directed and ordered stacked arrays of non-Watson-Crick base pairs forming distinctive foldings of the phosphodiester backbones of the interacting RNA strands. They correspond to the 'loops' - hairpin, internal and junction - that intersperse the Watson-Crick two-dimensional helices as seen in two-dimensional representations of RNA structure. RNA motifs mediate the specific interactions that induce the compact folding of complex RNAs. RNA motifs also constitute specific protein or ligand binding sites. A given motif is characterized by all the sequences that fold into essentially identical three-dimensional structures with the same ordered array of isosteric non-Watson-Crick base pairs. It is therefore crucial, when analyzing a three-dimensional RNA structure in order to identify and compare motifs, to first classify its non-Watson-Crick base pairs geometrically.     

Parametric Finite Element Analysis and Closed-formSolutions in Orthodontics

The goal and clinical relevance of this work was the development of closed formulas that are correct and simple enough for a fast decision making by the orthodontist in the daily praxis. This paper performs a parametric three-dimensional finite element linear analysis on a maxillary central incisor with a root of paraboloidal shape, which is subjected to typical orthodontic force-systems. Parameters of most importance, such as the tooth mobility in translation and in pure moment rotation including orthodontic centers, as well as the stresses inside the periodontal ligament are calculated for a large variety of over four hundred different couples of root lengths and root diameters around a nominal value. Regression analysis is afterwards performed and establishes closed-form solutions, which are also explained in terms of analytical strain energy and hydrostatic stress considerations within the periodontal ligament characterised by a small compressibility. The obtained expressions include both the root length as well as the root diameter.     

玉米淀粉分支酶基因启动子的克隆与功能分析

以玉米品种“吉糯1号”的基因组DNA为模板,通过PCR扩增得到玉米淀粉分支酶基因的启动子序列,克隆到pMD18-TVector上,经测序,该启动子大小为934bp。与已报道的序列比较仅有14个核苷酸发生改变,同源性为98.5%。用该启动子取代植物表达载体pBI121的35S启动子,与GUS基因编码区连接,构建成融合质粒pSBE-GUS。经农杆菌介导法转化烟草,获得了转基因植株。GUS活性检测结果表明,由该启动子序列引导的GUS基因能在种子中表达,而在其他组织中表达微弱或未表达,证实该启动子具有种子特异性表达的功能。     

农杆菌介导淀粉分支酶基因RNAi片段转化玉米的研究

以玉米自交系“178”和“R18红”的胚性愈伤组织为材料,通过愈伤组织对潮霉素的敏感性实验,确定了潮霉素15 mg/L~25 mg/L为愈伤组织适宜的选择压。利用农杆菌(Agrobacterium tum efaciens)介导将淀粉分支酶基因RNA干涉表达载体转入玉米自交系中,并对农杆菌转化系统的条件进行研究。结果表明:在感染液和共培培养基中分别都加入100μm ol/L乙酰丁香酮和50 mg/L抗坏血酸,农杆菌LBA4404的菌液OD600为0.6、侵染时间20 m in为农杆菌转化的最适条件。对转化的愈伤组织分化诱导出苗后进行PCR检测,证明外源目的基因已整合到玉米基因组中,转化率最高达到2.4%。     

The Unique Branching Patterns of Deinococcus Glycogen Branching Enzymes Are Determined by Their N-Terminal Domains

Glycogen branching enzymes (GBE) or 1,4-α-glucan branching enzymes (EC 2.4.1.18) introduce α-1,6 branching points in α-glucans, e.g., glycogen. To identify structural features in GBEs that determine their branching pattern specificity, the Deinococcus geothermalis and Deinococcus radiodurans GBE (GBE_Dg and GBE_Dr, respectively) were characterized. Compared to other GBEs described to date, these Deinococcus GBEs display unique branching patterns, both transferring relatively short side chains. In spite of their high amino acid sequence similarity (88%) the D. geothermalis enzyme had highest activity on amylose while the D. radiodurans enzyme preferred amylopectin. The side chain distributions of the products were clearly different: GBE_Dg transferred a larger number of smaller side chains; specifically, DP5 chains corresponded to 10% of the total amount of transferred chains, versus 6.5% for GBE_Dr. GH13-type GBEs are composed of a central (β/α) barrel catalytic domain and an N-terminal and a C-terminal domain. Characterization of hybrid Deinococcus GBEs revealed that the N2 modules of the N domains largely determined substrate specificity and the product branching pattern. The N2 module has recently been annotated as a carbohydrate binding module (CBM48). It appears likely that the distance between the sugar binding subsites in the active site and the CBM48 subdomain determines the average lengths of side chains transferred.Glycogen is an energy reserve polymer of many animals and microorganisms. It is composed of a backbone of glucose residues linked by α-1,4 glycosidic bonds with α-1,6-linked side chains (7, 31). In bacteria, the linear α-1,4-glucan is synthesized from ADP-glucose by the enzyme glycogen synthase, which is thought to be involved in both initiation and elongation of the chain (40). Side chains are introduced by glycogen branching enzyme (GBE) or 1,4-α-glucan branching enzyme (EC 2.4.1.18). This enzyme catalyzes formation of α-1,6 branch points by cleaving an α-1,4 glycosidic linkage in the donor substrate and transferring the nonreducing end-terminal fragment of the chain to the C-6 hydroxyl position of an internal glucose residue that acts as the acceptor substrate (4). Depending on its source, GBEs have a preference for transferring different lengths of glucan chains (1, 23). Most GBEs are members of subfamily 8 (Eukaryota) or 9 (Bacteria) of glycoside hydrolase family 13 (GH13) (34). Recently, the first GBE from family GH57 was described (28) (http://www.cazy.org).GH13-type GBEs are composed of three major domains of secondary structure, a central (β/α) barrel catalytic domain or A domain, an N-terminal domain, and a C-terminal domain (1). Domain A is present in all members of family GH13 and consists of a highly symmetrical fold of eight parallel β-strands encircled by eight α-helices. However, some variations occur in GBEs (a missing α-helix 5 and insertion of extra α-helices) (1). Domain A contains the four conserved amino acid regions (I to IV) typical for enzymes of family GH13 (35). In most GH13 enzymes, an extra domain is present, inserted between β-strand 3 and α-helix 3 (domain B), which affects their catalysis and product specificity (16). In GBEs, the length of this loop is only 40 residues, not long enough to be considered a separate domain (1). Domain C is found in most GH13 enzymes and is believed to shield the hydrophobic residues of the catalytic domain from contacts with the solvent. Domain C has also been suggested to be involved in substrate binding (25).Domain N is typical for GH13 enzymes cleaving or forming endo-α-1,6 linkages (17), namely, isoamylase (EC 3.2.1.68; subfamily 11) (18), pullulanase (EC 3.2.1.41; subfamilies 12 to 14) (27), and both starch (subfamily 8) and glycogen branching enzymes (subfamilies 8 and 9). An exception is the 4-α-d-{(1→4)-α-d-glucano}trehalose trehalohydrolase (EC 3.2.1.141; subfamily 10), which hydrolyzes linear maltooligosaccharide-like substrates (6) (39). The crystal structures of most of these enzymes with their N domains (all or part) have been published previously (1, 6, 18, 27, 39). The exact function of this N domain has remained unclear, and the similarity between the N domains in these different enzymes is low. They vary in length, and some of them consist of two or three modules. However, they all possess one common module that was recently classified as a family 48 carbohydrate-binding-module (CBM48) (19) (http://www.cazy.org/).In GBEs domain N comprises a module of 150 amino acids, termed the N2 module, that contains the putative CBM48. In some branching enzymes, it is preceded by a module of 100 to 150 amino acids, termed the N1 module. It has been proposed that the N1 module has originated from a DNA duplication of the N2 module (24). Based on the architecture and length of the N domain, GBEs can be divided into group 1, containing both the N1 and the N2 modules, and group 2, containing only the N2 module (12). A 112-amino-acid truncation of the N1 module in E. coli GBE (group 1) resulted in a 40% reduction of enzyme activity (2) and an altered branching pattern (3). Further investigations of this N1 module, by sequential N-terminal deletions, showed that enzymes with the shorter N1 module transferred longer glucan chains (5). No studies have been reported thus far investigating the role of the N2 module (containing the putative CBM48 domain) in GBEs as well as in other GH13 members.Here, we report a detailed biochemical characterization of two GH13 GBEs from the extremophilic bacteria Deinococcus geothermalis and Deinococcus radiodurans. These two GBEs (GBE_Dg and GBE_Dr, respectively) generate unique branching patterns by transferring glucosidic chains that are shorter than those of other GBEs reported to date (9, 36, 38, 41). To investigate the role of the different domains in these enzymes, chimeras of GBE_Dg and GBE_Dr were constructed. Their characterization revealed that substrate and chain length specificity in these Deinococcus GH13 GBEs are largely determined by the putative CBM48 part of the N domain.