Neutral space analysis for a Boolean network model of the fission yeast cell cycle network

Background

Interactions between genes and their products give rise to complex circuits known as gene regulatory networks (GRN) that enable cells to process information and respond to external stimuli. Several important processes for life, depend of an accurate and context-specific regulation of gene expression, such as the cell cycle, which can be analyzed through its GRN, where deregulation can lead to cancer in animals or a directed regulation could be applied for biotechnological processes using yeast. An approach to study the robustness of GRN is through the neutral space. In this paper, we explore the neutral space of a Schizosaccharomyces pombe (fission yeast) cell cycle network through an evolution strategy to generate a neutral graph, composed of Boolean regulatory networks that share the same state sequences of the fission yeast cell cycle.

Results

Through simulations it was found that in the generated neutral graph, the functional networks that are not in the wildtype connected component have in general a Hamming distance more than 3 with the wildtype, and more than 10 between the other disconnected functional networks. Significant differences were found between the functional networks in the connected component of the wildtype network and the rest of the network, not only at a topological level, but also at the state space level, where significant differences in the distribution of the basin of attraction for the G₁ fixed point was found for deterministic updating schemes.

Conclusions

In general, functional networks in the wildtype network connected component, can mutate up to no more than 3 times, then they reach a point of no return where the networks leave the connected component of the wildtype. The proposed method to construct a neutral graph is general and can be used to explore the neutral space of other biologically interesting networks, and also formulate new biological hypotheses studying the functional networks in the wildtype network connected component.     

Concurrent Neutral Evolution of mRNA Secondary Structures and Encoded Proteins

Messenger RNA sequences often have to preserve functional secondary structure elements in addition to coding for proteins. We present a statistical analysis of retroviral mRNA which supports the hypothesis that the natural genetic code is adapted to such complementary coding. These sequences are still able to explore efficiently the space of possible proteins by point mutations. This is borne out by the observation that, in stem regions of retroviral mRNA foldings, silent mutations on one strand are preferentially accompanied by conservative mutations on the other. Distances between amino acids based on physicochemical properties are used to quantify the conservation of protein function under the constraint of maintained RNA secondary structure. We find that preservation of RNA secondary structure by compensatory mutations is evolutionary compatible with the efficient search for new variants on the protein level. Received: 4 June 1999 / Accepted: 12 October 1999     

Gene surfing in expanding populations

Large scale genomic surveys are partly motivated by the idea that the neutral genetic variation of a population may be used to reconstruct its migration history. However, our ability to trace back the colonization pathways of a species from their genetic footprints is limited by our understanding of the genetic consequences of a range expansion. Here, we study, by means of simulations and analytical methods, the neutral dynamics of gene frequencies in an asexual population undergoing a continual range expansion in one dimension. During such a colonization period, lineages can fix at the wave front by means of a "surfing" mechanism [Edmonds, C.A., Lillie, A.S., Cavalli-Sforza, L.L., 2004. Mutations arising in the wave front of an expanding population. Proc. Natl. Acad. Sci. 101, 975-979]. We quantify this phenomenon in terms of (i) the spatial distribution of lineages that reach fixation and, closely related, (ii) the continual loss of genetic diversity (heterozygosity) at the wave front, characterizing the approach to fixation. Our stochastic simulations show that an effective population size can be assigned to the wave that controls the (observable) gradient in heterozygosity left behind the colonization process. This effective population size is markedly higher in the presence of cooperation between individuals ("pushed waves") than when individuals proliferate independently ("pulled waves"), and increases only sub-linearly with deme size. To explain these and other findings, we develop a versatile analytical approach, based on the physics of reaction-diffusion systems, that yields simple predictions for any deterministic population dynamics. Our analytical theory compares well with the simulation results for pushed waves, but is less accurate in the case of pulled waves when stochastic fluctuations in the tip of the wave are important.     

Computation of Minimal Uniform Transmission Range in Ad Hoc Wireless Networks

Power conservation is a critical issue for ad hoc wireless networks. The main objective of the paper is to find the minimum uniform transmission range of an ad hoc wireless network, where each node uses the same transmission power, while maintaining network connectivity. Three different algorithms, Prims Minimum Spanning Tree (MST), its extension with Fibonacci heap implementation, and an area-based binary search are developed to solve the problem. Their performance is compared by simulation study together with Kruskals MST, a known solution proposed by Ramanathan and Rosales-Hain for topology control by transmission power adjustment, and an edge-based binary search used by the same study in order to find the per-node-minimality after Kruskals algorithm is applied. Our results show that Prims MST outperforms both Kruskals MST and the two binary searches. The performance between Prims MST implemented with binary heap and Fibonacci heap is fairly close, with the Fibonacci implementation slightly outperforming the other.Qing Dai received her M.S. degree in Computer Science from Florida Atlantic University on August 2003, and M.S. degree in Microbiology from Upstate University on July 2000. She is currently a software engineer at Motorola, Plantation, FL.Jie Wu is a Professor at Department of Computer Science and Engineering, Florida Atlantic University. He has published over 200 papers in various journals and conference proceedings. His research interests are in the areas of wireless networks and mobile computing, routing protocols, fault-tolerant computing, and interconnection networks. He served on many conference organization committees. Dr. Wu is on the editorial board of IEEE Transactions on Parallel and Distributed Systems and was a co-guest-editor of IEEE Computer and Journal of Parallel and Distributed Computing. He is the author of the text Distributed System Design published by the CRC press. He was also the recipient of the 1996–97 and 2001–2002 Researcher of the Year Award at Florida Atlantic University. Dr. Wu has served as an IEEE Computer Society Distinguished Visitor. He is a Member of ACM and a Senior Member of IEEE.     

Simulation of protein evolution by random fixation of allowed codons

Summary Computer simulation of protein evolution is based on a simple model consisting of random fixation of allowed codons (RFAC). Random replacement of single nucleotides occurs in a DNA sequence. If this results in any of the synonomous codons for allowed amino acids the mutation is fixed, if not, there is no change in the DNA and the cycle is repeated. Multiple fixations at the same nucleotide site, back mutations, degenerate fixations and coincidental identity of amino acids all occur. RFAC simulation begins with a single DNA sequence and follows a phylogeny based on the fossil record. The rate of fixation at the level of DNA is constant. The model upon which RFAC simulation is based is the same as the neutral theory of molecular evolution. The simulation is therefore a test of this theory. The results of simulated and real evolution are compared for fibrinopeptides A in mammals and cytochromes C and hemoglobin and chains in vertebrates. In each case the allowed variation at each site has been set equal to that observed, twice that observed and all protein amino acids. Rates of fixation vary from 2.4 × 10^–10 to 10^–5 accepted nucleotide fixations per codon per year. There is some, although never excellent, agreement between real and simulated evolution, the better fits are obtained in the cases of fibrinopeptides A and cytochromes C. The major source of discrepancy between real evolution and simulation is irregularities in the rates of real evolution. RFAC simulation is compared with the random evolutionary hit (REH) model, augmented maximum parsimony and the accepted point mutations (PAM) approach.     

Purification and Characterization of Neutral and Acid Sphingomyelinases from Rat Brain

Neutral and acid sphingomyelinases were copurified from a rat brain P2 fraction by extraction with 1% Triton X-100, followed by (NH4)2SO4 fractionation, acetone powdering, extraction with 1% Triton X-100, (NH4)2SO4 fractionation, Sepharose CL-6B chromatography, and chromatofocusing. The neutral sphingomyelinase was eluted with buffer containing 0.4 M NaCl after the acid sphingomyelinase had been eluted with Polybuffer at pH 5.3. The neutral sphingomyelinase exhibited specific activity of 48,300 nmol/h/mg of protein, with 254-fold purification; the corresponding value for acid sphingomyelinase was 25,300 nmol/h/mg protein, with 668-fold purification from the P2 fraction. The purified neutral sphingomyelinase had no acid sphingomyelinase activity, and vice versa. The properties of the two enzymes were examined. A single band corresponding to a molecular weight of 67,000 was obtained on sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) for both enzymes. The pI was estimated to be 5.5 for both on isoelectric focusing. The native molecular weights of the neutral and acid sphingomyelinases were found to be 434,000 and 284,000, respectively, on gel filtration with Sepharose CL-6B. The single band obtained for each enzyme on SDS-PAGE was identified as an antigen with antibody raised against the purified neutral sphingomyelinase. Their amino acid compositions were very similar. The neutral and acid sphingomyelinases probably consist of common polypeptides and are immunologically cross-reactive.     

The impact of homologous recombination on the generation of diversity in bacteria

The imprint of demographic and selective processes on bacterial population structure needs to be evaluated as deviation from the expectations of an appropriate null neutral model. We explore the impact of varying the population mutation and recombination rates theta and rho on ideal populations, using a recently developed model of neutral drift at multiple loci. This model may be fitted to experimental data to provide estimates of these parameters, and we do so for seven bacterial species (Neisseria meningitidis, Streptococcus pneumoniae, Streptococcus pyogenes, Staphylococcus aureus, Helicobacter pylori, Burkholderia pseudomallei and Bacillus cereus), illustrating that bacterial species vary extensively in these fundamental parameters. Historically, the influence of recombination has often been estimated through its influence on the Index of Association I(A). We show that this may be relatively insensitive to changes in either mutation or recombination rates. It is known that biased sampling can lead to artificially high estimates of I(A). We therefore provide a method of precisely separating the effects of such bias and true linkage between alleles. We also demonstrate that by fitting the neutral model to experimental data, more informative and precise estimates of the relative roles of recombination and mutation may be obtained.     

Singular value decomposition analysis of the secondary structure features contributing to the circular dichroism spectra of model proteins

Amyloid fibril formation occurs in restricted environment, such as the interface between intercellular fluids and bio-membranes. Conformational interconversion from α-helix to β-structure does not progress in fluids; however, it can occur after sedimentary aggregation during amyloid fibril formation induced by heat treatment of hen egg white lysozyme (HEWL). Secondary structures of various proteins and denatured proteins titrated with 2,2,2-trifluoroethanol (TFE) were examined using their CD spectra. Gaussian peak/trough and singular value decompositions (SVD) showed that the spectral pattern of the α-helix comprised a sharp trough at wavelength 207 nm and a broad trough at 220 nm. Conversely, we distinguished two patterns for β-sheet—a spread barrel type, corresponding to ConA, and a tightly weaved type, corresponding to the soybean trypsin inhibitor. Herein, we confirmed that the spectral/conformational interconversion of the heat-treated HEWL was not observed in the dissolved fluid.     

The Origin and Evolution of tRNA Inferred from Phylogenetic Analysis of Structure

The evolutionary history of the two structural and functional domains of tRNA is controversial but harbors the secrets of early translation and the genetic code. To explore the origin and evolution of tRNA, we reconstructed phylogenetic trees directly from molecular structure. Forty-two structural characters describing the geometry of 571 tRNAs and three statistical parameters describing thermodynamic and mechanical features of molecules quantitatively were used to derive phylogenetic trees of molecules and molecular substructures. Trees of molecules failed to group tRNA according to amino acid specificity and did not reveal the tripartite nature of life, probably due to loss of phylogenetic signal or because tRNA diversification predated organismal diversification. Trees of substructures derived from both structural and statistical characters support the origin of tRNA in the acceptor arm and the hypothesis that the top half domain composed of acceptor and pseudouridine (TΨC) arms is more ancient than the bottom half domain composed of dihydrouridine (DHU) and anticodon arms. This constitutes the cornerstone of the genomic tag hypothesis that postulates tRNAs were ancient telomeres in the RNA world. The trees of substructures suggest a model for the evolution of the major functional and structural components of tRNA. In this model, short RNA hairpins with stems homologous to the acceptor arm of present day tRNAs were extended with regions homologous to TΨC and anticodon arms. The DHU arm was then incorporated into the resulting three-stemmed structure to form a proto-cloverleaf structure. The variable region was the last structural addition to the molecular repertoire of evolving tRNA substructures. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time

It is now appreciated that condition-relevant information can be present within distributed patterns of functional magnetic resonance imaging (fMRI) brain activity, even for conditions with similar levels of univariate activation. Multi-voxel pattern (MVP) analysis has been used to decode this information with great success. FMRI investigators also often seek to understand how brain regions interact in interconnected networks, and use functional connectivity (FC) to identify regions that have correlated responses over time. Just as univariate analyses can be insensitive to information in MVPs, FC may not fully characterize the brain networks that process conditions with characteristic MVP signatures. The method described here, informational connectivity (IC), can identify regions with correlated changes in MVP-discriminability across time, revealing connectivity that is not accessible to FC. The method can be exploratory, using searchlights to identify seed-connected areas, or planned, between pre-selected regions-of-interest. The results can elucidate networks of regions that process MVP-related conditions, can breakdown MVPA searchlight maps into separate networks, or can be compared across tasks and patient groups.     

Transition Path Sampling Study of the Local Molecular Structure in the Aqueous Solvation of Sodium Chloride

Abstract

The aqueous solvation of sodium chloride has been investigated using the recently introduced technique of the transition path sampling. We performed a series of Monte Carlo simulations for each element of an ensemble of chains of states. The evolution of the local solvent structure during the dissociation process has been observed. The incoming of a couple of waters to the first coordination shell is responsible for the structural changes which allow the dissociation occur: waters which leave the second coordination shell produce voids and a local molecular reorganization in order to allocate the dissociated ion pair.     

Protein sequence design based on the topology of the native state structure

Computational design of sequences for a given structure is generally studied by exhaustively enumerating the sequence space or by searching in such a large space, which is prohibitively expensive. However, we point out that the protein topology has a wealth of information, which can be exploited to design sequences for a chosen structure. In this paper, we present a computationally efficient method for ranking the residue sites in a given native-state structure, which enables us to design sequences for a chosen structure. The premise for the method is that the topology of the graph representing the energetically interacting neighbours in a protein plays an important role in the inverse-folding problem. While our previous work (which was also based on topology) used eigenspectral analysis of the adjacency matrix of interactions for ranking the residue sites in a given chain, here we use a simple but effective way of assigning weights to the nodes on the basis of secondary connections, along with primary connections. This indirectly accounts for the edge weight in the graph and removes degeneracy in the degree. The new scheme needs only a few multiplications and additions to compute the preferred ranking of the residue sites even for structures of real proteins of sizes of a few hundred amino acid residues. We use HP lattice model examples (for which exhaustive enumeration of sequences is practical) to validate our ranking approach in obtaining sequences of lowest energy for any H-P residue composition for a given native-state structure. Some examples of native structures of real proteins are also included. Quantitative comparison of the efficacy of the new scheme with the earlier schemes is made. The new scheme consistently performs better and with much lower computational cost. An optimization procedure is added to work with the new scheme in a few rare cases wherein the new scheme fails to provide the best sequence, an optimization procedure is added to work with the new scheme.     

Prediction and comparison of the secondary structure of legume lectins

Secondary structure prediction for the 4 legume lectins: Concanavalin A, soybean agglutinin, favabean lectin and lentil lectin, was done by the method of Chou and Fasman. This prediction shows that these four lectins fall into a structurally distinct class of proteins, containing high amounts of β-sheet and β-turns. There is a notable similarity in the gross structure of these proteins; all four of them contain about 40–50% of β-sheet, 35–45 % β-turn and 0–10% of α-helix. When the secondary structure of corresponding residues in each pair of these lectins was compared, there was a striking similarity in the Concanavalin A-soybean agglutinin and favabean lectin-lentil lectin pairs, and considerably less similarity in the other pairs, suggesting that these legume lectins have probably evolved in a divergent manner from a common ancestor. A comparison of the predicted potential β-turn sites also supports the hypothesis of divergent evolution in this class of lectins.     

An RNA foldability metric; implications for the design of rapidly foldable RNA sequences

Evidence is presented suggesting, for the first time, that the protein foldability metric σ = (T_θ − T_f) / T_θ, where T_θ and T_f are, respectively, the collapse and folding transition temperatures, could be used also to measure the foldability of RNA sequences. These results provide further evidence of similarities between the folding energy landscapes of proteins and RNA. The importance of σ is discussed in the context of the in silico design of rapidly foldable RNA sequences.     

Characterisation of Neutral Endopeptidase 3.4.24.11 (NEP) in the Kidney: Comparison Between Normotensive,Genetically Hypertensive and Experimentally Hypertensive Rats

Abstract

Neutral endopeptidase 3.4.24.11 (NEP) has been identified as the major atrial natriuretic factor (ANF) degrading enzyme in rat kidney, therefore, suggesting a possible role for this enzyme in blood volume and pressure regulation. Various experimentally induced and genetically hypertensive rat models have been used to test NEP inhibitors. The presence of different isoforms of NEP in the various hypertensive rat models would have relevance when searching for novel NEP inhibitors. Therefore, we compared the properties of NEP in kidney cortex homogenates in order to test for possible differences in the following hypertensive rat models and their appropriate controls: spontaneously hypertensive rats (SHR), Wistar Kyoto strain (WKY). DOCA-salt hypertensive rats, and Sprague Dawley control rats (SD). No relevant differences were found when comparing the following parameters,: (1) specific activity (mean: 204 U/mg protein), (2) Michaelis constant (mean: 280μM), (3) IC₅₀ of thiorphan (mean: 6.5 nM) and phosphoramidon (mean: 54 nM), (4) pH profiles (optimum at pH8.0), (5) heat inactivation profiles (half-life 20min at 65°C), (6) immunotitration of kidney cortex homogenates, (7) molecular weight as determined by gel filtration (92,000 Dalton) and (8) affinity chromatography with concanavalin A. Without evidence for the presence of different NEP isoforms, it is unlikely that divergent findings in DOCA-salt rats and SHR using a given NEP inhibitor are due to isoforms of NEP.     

Analysis of proton chemical shifts in regular secondary structure of proteins

Summary The contribution of peptide groups to H and H proton chemical shifts can be modeled with empirical equations that represent magnetic anisotropy and electrostatic interactions [Ösapay, K. and Case, D.A. (1991) J. Am. Chem. Soc., 113, 9436–9444]. Using these, a model for the random coil reference state can be generated by averaging a dipeptide over energetically allowed regions of torsion-angle space. Such calculations support the notion that the empirical constant used in earlier studies arises from neighboring peptide contributions in the reference state, and suggest that special values be used for glycine and proline residues, which differ significantly from other residues in their allowed ,-ranges. New constants for these residues are reported that provide significant improvements in predicted backbone shifts. To illustrate how secondary structure affects backbone chemical shifts we report calculations on oligopeptide models for helices, sheets and turns. In addition to suggesting a physical mechanism for the widely recognized average difference between and secondary structures, these models suggest several additional regularities that should be expected: (a) H protons at the edges of -sheets will have a two-residue periodicity; (b) the H² and H³ protons of glycine residues will exhibit different shifts, particularly in sheets; (c) H protons will also be sensitive to local secondary structure, but in different directions and to a smaller extent than H protons; (d) H protons in turns will generally be shifted upfield, except those in position 3 of type I turns. Examples of observed shift patterns in several proteins illustrate the application of these ideas.     

Synthesis of polypeptides by microwave heating I. Formation of polypeptides during repeated hydration-dehydration cycles and their characterization

Summary Amino acid amides effectively reacted to produce polypeptides in response to microwave heating during repeated hydration-dehydration cycles. The polypeptides, formed from a mixture of glycinamide, alaninamide, valinamide, and aspartic acid -amide, had molecular weights ranging from 1000 to 4000 daltons. Amino acids were incorporated into the polypeptides in proportion to the starting concentrations, with the exception of glycine whose incorporation was 1.5 times higher than that of the other amino acids. The polypeptides had some definite secondary structure, such as -helix and -sheet, in aqueous solution. This reaction provides not only a convenient method for abiotic peptide formation but also a convenient method for the chemical synthesis of peptides.     

Conservation Throughout Vertebrate Evolution of the Predicted β-Strands in Myelin Basic Protein

To identify functionally important parts of the 18.5-kDa myelin basic protein (MBP), the amino acid sequences from 10 species ranging from shark to human were aligned using the SEQHP computer program. The residues that are invariant or very conservatively substituted (Arg/Lys, Ser/Thr, Ile/Leu, Asp/Glu) among all 10 proteins were scored. Of the 72 conserved residues in the 170-residue human protein (42% conserved), 32 are found within the five beta-strands previously predicted (45 residues, 71% conserved), 23 within the small-loops region (42 residues, 55% conserved), but only 17 within the large-loops region (83 residues, 20% conserved). Of the 22 hydrophobic residues within the predicted beta-sheet of human MBP, 20 hydrophobic residues remain in the shark protein, 19 of them in the same positions. In contrast, there are 10 hydrophobic residues elsewhere in the human protein, but only 7 remain in the shark protein and only 1 of them is in the same position. The triprolyl sequence found in all mammalian MBPs and in the chicken MBP is not conserved in the shark protein. The four alternately spliced forms of mouse MBP can be accommodated by the beta-structural model, but not the 17-kDa human MBP, which lacks exon 5. These findings confirm the crucial role of the hydrophobic residues in the predicted beta-sheet for the structure and function of the protein. It seems likely that the conserved portions of the protein make an important contribution to the highly ordered lamellar structure of myelin.     

Neutral and selection-driven decay of sexual traits in asexual stick insects

Environmental shifts and lifestyle changes may result in formerly adaptive traits becoming non-functional or maladaptive. The subsequent decay of such traits highlights the importance of natural selection for adaptations, yet its causes have rarely been investigated. To study the fate of formerly adaptive traits after lifestyle changes, we evaluated sexual traits in five independently derived asexual lineages, including traits that are specific to males and therefore not exposed to selection. At least four of the asexual lineages retained the capacity to produce males that display normal courtship behaviours and are able to fertilize eggs of females from related sexual species. The maintenance of male traits may stem from pleiotropy, or from these traits only regressing via drift, which may require millions of years to generate phenotypic effects. By contrast, we found parallel decay of sexual traits in females. Asexual females produced altered airborne and contact signals, had modified sperm storage organs, and lost the ability to fertilize their eggs, impeding reversals to sexual reproduction. Female sexual traits were decayed even in recently derived asexuals, suggesting that trait changes following the evolution of asexuality, when they occur, proceed rapidly and are driven by selective processes rather than drift.     

祁连山森林生态环境与黑河流域径流量的灰色关联分析和拓扑预测

甘肃省河西走廊由于远离海洋和受高山阻隔而成为干旱区。但因特殊的地理环境而有南部祁连山水源涵养林调蓄降水和冰雪融水,形成了三大内陆河水系,灌溉河西走廊7.0×10~5