Molecular cloning and expression analysis of Ch-penaeidin, an antimicrobial peptide from Chinese shrimp, Fenneropenaeus chinensis

A new member of antimicrobial peptide genes of the penaeidin family, Ch-penaeidin, has been cloned from the haemocytes of Chinese shrimp, Fenneropenaeus chinensis, by reverse transcription PCR (RT-PCR), 3'-rapid amplification of cDNA end (3'-RACE) and smart cDNA methods. The Ch-penaeidin cDNA was 655 bp and the open reading frame of the cDNA encoded a 71 amino acid peptide. Ch-penaeidin contained a putative NH2-terminal signal Sequence (1-19) followed by a mature peptide (20-71). The sequence identify with other penaeidins from Litopenaeus vannamei and Litopenaeus setiferus is between 48% and 71%. The signal sequence of Ch-penaeidin is almost completely identical to that of other penaeidins, while differing relatively in the N-terminal domain of the mature peptide. Ch-penaeidin was designated as a novel member of class penaeidin 3 according to phylogenetic analysis. The Mature peptide. with a predicted molecular weight of 5589.32 Da, and a pI of 9.77, has eight positively charged amino acids and no negatively charged amino acids. The expression and distribution of Ch-penaeidin in Unchallenged shrimps were studied by RT-PCR, Northern blot and in situ hybridisation. The results showed that the Ch-penaeidin transcripts were detected in haemocytes (granular haemocytes), heart, gill, intestine, and subcuticular epithelia of the shrimp. and that Ch-penaeidin was constitutively expressed mainly in haemocytes. (C) 2003 Elsevier Ltd. All rights reserved.

Amphi-Eomes/Tbr1: An amphioxus cognate of vertebrate Eomesodermin and T-Brain1 genes whose expression reveals evolutionarily distinct domain in amphioxus development

A cDNA for a novel T-box containing gene was isolated from the amphioxus Branchiostoma belcheri. A molecular phylogenetic tree constructed from the deduced amino acid sequence of the isolated cDNA indicates that this gene belongs to the T-Brain subfamily. In situ hybridization reveals that the expression is first detected in the invaginating archenteron at the early gastrula stage and this expression is down-regulated at the neurula stage. In early larvae, the expression appears again and transcripts are detected exclusively in the pre-oral pit (wheel organ-Hatschek's pit of the adult). In contrast to the vertebrate counterparts, no transcripts are detected in the brain vesicle or nerve cord throughout the development. These results are interpreted to mean that a role of T-Brain products in vertebrate forebrain development was acquired after the amphioxus was split from the lineage leading to the vertebrates. On the other hand, comparison of the tissue-specific expression domain of T-Brain genes and other genes between amphioxus and vertebrates revealed that the pre-oral pit of amphioxus has several molecular features which are comparable to those of the vertebrate olfactory and hypophyseal placode. (C) 2002 Wiley-Liss, Inc.

Molecular cloning and expression of a novel Kazal-type serine proteinase inhibitor gene from Zhikong scallop Chlamys farreri, and the inhibitory activity of its recombinant domain

Serine proteinase inhibitors (SPIs) play important roles in host physiological and immunological processes in all multicellular organisms. A novel Kazal-type SPI gene was cloned from the Zhikong scallop Chlamys farreri (designated as CfKZSPI) by expressed sequence tag (EST) and rapid amplification of cDNA ends (RACE) approaches. The full-length cDNA of CfKZSPI was of 1788 nucleotides with a canonical polyadenylation signal sequence AATAAA and a polyA tail, and an open reading frame (ORF) encoding a polypeptide of 509 amino acids with a putative signal peptide of 22 amino acids. The deduced amino acid sequence of CfKZSPI contained 12 tandem Kazal domains with high similarity to other Kazal-type SPIs. The temporal expression of CfKZSPI in hemocytes after Vibrio anguillorum challenge was recorded by quantitative real-time RT-PCR. The relative mRNA expression level of CfKZSPI was up-regulated and reached 43.6-fold at 3 h post-challenge. After a decrease at 6 h, the expression Level increased again and reached 207.8-fold at 12 h post-challenge. The 12th Kazal domain of CfKZSPI was recombined into pET-32a(+) and expressed in Escherichia coli Rosetta-gami (DE3) to investigate its inhibitory activity. The purified recombinant protein (rCf KZSPI-1 2) showed significant inhibitory activity against trypsin but no activity against thrombin. When the molar ratio of inhibitor to trypsin reached 1:1, almost 90% of the enzyme activity could be inhibited, which suggested that one molecule of rCfKZSPI-12 was able to inhibit one molecule of trypsin. Kinetics analysis with Dixon plot showed that the inhibition constant (K-i) of rCfKZSPI-12 to trypsin was 173 nmol L-1. These results indicated that CfKZSPI was a novel Kazal-type SPI with significant inhibitory activity against trypsin, and was suspected to be involved in scallop immune response. (c) 2008 Elsevier Ltd. All rights reserved.

Lineage-specific domain fusion in the evolution of purine nucleotide cyclases in cyanobacteria

Cyclic nucleotides (both cAMP and cGMP) play extremely important roles in cyanobacteria, such as regulating heterocyst formation, respiration, or gliding. Catalyzing the formation of cAMP and cGMP from ATP and GTP is a group of functionally important enzymes named adenylate cyclases and guanylate cyclases, respectively. To understand their evolutionary patterns, in this study, we presented a systematic analysis of all the cyclases in cyanobacterial genomes. We found that different cyanobacteria had various numbers of cyclases in view of their remarkable diversities in genome size and physiology. Most of these cyclases exhibited distinct domain architectures, which implies the versatile functions of cyanobacterial cyclases. Mapping the whole set of cyclase domain architectures from diverse prokaryotic organisms to their phylogenetic tree and detailed phylogenetic analysis of cyclase catalytic domains revealed that lineage-specific domain recruitment appeared to be the most prevailing pattern contributing to the great variability of cyanobacterial cyclase domain architectures. However, other scenarios, such as gene duplication, also occurred during the evolution of cyanobacterial cyclases. Sequence divergence seemed to contribute to the origin of putative guanylate cyclases which were found only in cyanobacteria. In conclusion, the comprehensive survey of cyclases in cyanobacteria provides novel insight into their potential evolutionary mechanisms and further functional implications.

A novel C1q-domain-containing protein from Zhikong scallop Chlamys farreri with lipopolysaccharide binding activity

The C1q-domain-containing (C1qDC) proteins are a family of proteins characterized by a globular C1q (gC1q) domain in their C-terminus. They are involved in various processes of vertebrates and supposed to be an important pattern recognition receptor in innate immunity of invertebrates. In this study, a novel member of C1q-domain-containing protein family was identified from Zhikong scallop Chlamys farreri (designated as CfC1qDC) by expressed sequence tag (EST) and rapid amplification of cDNA ends (RACE) approaches. The full-length cDNA of CfC1qDC was of 777 bp, consisting of a T-terminal untranslated region (UTR) of 62 bp and a 3' UTR of 178 bp with a polyadenylation signal sequence AATAAA and a poly (A) tail. The CfC1qDC cDNA encoded a polypeptide of 178 amino acids, including a signal peptide and a C1q-domain of 158 amino acids with the theoretical isoelectric point of 5.19 and the predicted molecular weight of 17.2 kDa. The C1q-domain in CfC1qDC exhibited homology with those in sialic acid binding lectin from mollusks and C1qDC proteins from higher vertebrates. The typical 10 beta-strand jelly-roll folding topology structure of C1q-domain and the residues essential for effective packing of the hydrophobic core were well conserved in CfC1qDC. By fluorescent quantitative real-time PCR, mRNA transcripts of CfC1qDC were mainly detected in kidney, mantle, adductor muscle and gill, and also marginally detectable in hemocytes. In the bacterial challenge experiment, after the scallops were challenged by Listonella anguillarum, there was a significant up-regulation in the relative expression level of CfC1qDC and at 6 h post-injection, the mRNA expression reached the maximum level and was 4.55-fold higher than that of control scallops. Similarly, the expression of CfC1qDC mRNA in mixed primary cultures of hemocytes stimulated by lipopolysaccharides (LPS) was up-regulated and reached the maximum level at 6 h post-stimulation, and then dropped back to the original level gradually. In order to investigate its function, the cDNA fragment encoding the mature peptide of CfC1qDC was recombined and expressed in Escherichia coli BL21 (DE3). The recombinant CfC1qDC protein displayed a significantly strong activity to bind LIDS from E. coli, although no obvious antibacterial or agglutinating activity toward Gram-negative bacteria E. coli JM109, L. anguillarum and Gram-positive bacteria Micrococcus luteus was observed. These results suggested that CfC1qDC was absolutely a novel member of the C1qDC protein family and was involved in the recognition of invading microorganisms probably as a pattern recognition molecule in mollusk. (c) 2008 Elsevier Ltd. All rights reserved.

A novel serine protease with clip domain from scallop Chlamys farreri

The serine proteases with clip domain are involved in various innate immune functions in invertebrate such as antimicrobial activity, cell adhesion, pattern recognition and regulation of the prophenoloxidase system. A serine protease with clip-domain cDNA (Cf SP) was obtained by Expressed sequence taggings (ESTs) method and rapid amplification of cDNA ends (RACE). The Cf SP full-length cDNA was of 1,152 bp, including a 5'-terminal untranslated region (UTR) of 63 bp, a 3'-terminal UTR of 81 bp with a canonical polyadenylation signal sequence AATAAA and a poly(A) tail, and an open reading frame of 1,008 bp encoding a polypeptide of 336 amino acids with a putative signal peptide of 19 amino acids. The deduced amino acid sequence of Cf SP contained an amino-terminal clip domain with three disulfide bonds formed six conserved Cys residues, a carboxyl-terminal trypsin-like domain with the conserved His-Asp-Ser catalytic triad, and a low complexity linker sequence. The Cf SP was strongly expressed in hemocytes and the mRNA expression of Cf SP was up-regulated and increased 3.2-fold and 2.6-fold at 16 h after injection of Vibrio anguillarum and Micrococcus luteus. The results suggested that Cf SP gene might be involved in immune response of Gram-negative and Gram-positive microbial infection in scallop.

Molecular cloning, characterization and expression of a serine protease with clip-domain homologue from scallop Chlamys farreri

Serine proteases play critical roles in a variety of invertebrate immune defense responses, including hemolymph coagulation, antimicrobial peptide synthesis, and melanization. The first mollusk serine protease with clip-domain (designated CFSP1) cDNA was obtained from the scallop Chlamys farreri challenged with Vibrio anguillarum by randomly sequencing a whole tissue cDNA library and rapid amplification of cDNA ends (RACE). The full-length cDNA of the C. farreri serine protease was 1211 bp, consisting of a 5-terminal untranslated region (UTR) of 72 bp, a 3'-terminal UTR of 77 bp with a canonical polyadenylation signal sequence AATAAA and a poly (A) tail, and an open reading frame of 1062 bp. The CFSP1 cDNA encoded a polypeptide of 354 amino acids with a putative signal peptide of 19 amino acids and a mature protein of 335 amino acids. The deduced amino acid sequence of CFSP1 contained an amino-terminal clip domain, a low complexity region, and a carboxyl-terminal serine protease domain. CFSP1 mRNA was mainly expressed constitutively in the hemocytes and was up-regulated and increased 2.9- and 1.9-fold at 16 h after injury and injection of bacteria. (c) 2006 Elsevier Ltd. All rights reserved.

Dissection and localization of the immunostimulating domain of Edwardsiella tarda FliC

Bacterial flagellin is known to induce potent immune response in vertebrate systems via the toll-like receptor (TLR) 5. As a result, flagellin has been studied extensively as a vaccine adjuvant. In a previous study, we examined the vaccine and adjuvant potentials of the flagellin (FliC) of the fish pathogen Edwardsiella tarda. We found that E. tarda FliC induced low protective immunity by itself but could function as a molecular adjuvant and potentiate the specific immune response induced by the E. tarda antigen Eta6. Since FliC is a large protein and organized into distinct structural domains, we wondered whether the immunostimulating effect observed with the full-length protein could be localized to a certain region. To investigate this question, we in the present study dissected the FliC protein into several segments according to its structural features: (i) N163, which consists of the conserved N-terminal 163 residues of FliC; (ii) M160, which consists of the variable middle 160 residues; (iii) C94, which consists of the conserved C-terminal 94 residues; (iv) NC257, which is an artificial fusion of N163 and C94. To examine the adjuvanticity of the FliC fragments, DNA vaccine plasmids expressing FliC fragments in fusion with Eta6 were constructed and used to immunize Japanese flounder. The results showed that N163 produced the best adjuvant effect, which, in respect to improvement in the relative percent survival of the vaccinated fish, was comparable to that of the full-length FliC. None of the other FliC fragments exhibited apparent immunopotentiating effect. Further analysis showed that N163 enhanced the production of serum specific antibodies and, like full-length FliC, significantly upregulated the expression of the genes that are possibly involved in innate and adaptive immunity. These results indicate that N163 is the immunodominant region of FliC and suggest that E. tarda FliC may induce immune responses in Japanese flounder via mechanisms alternative to that involving TLR5. (C) 2010 Elsevier Ltd. All rights reserved.

AiC1qDC-1, a novel gC1q-domain-containing protein from bay scallop Argopecten irradians with fungi agglutinating activity

The globular C1q-domain-containing (C1qDC) proteins are a family of versatile pattern recognition receptors via their globular C1q (gC1q) domain to bind various ligands including several PAMPs on pathogens. In this study, a new gC1q-domain-containing protein (AiC1qDC-1) gene was cloned from Argopecten irradians by rapid amplification of cDNA ends (RACE) approaches and expressed sequence tag (EST) analysis. The full-length cDNA of AiC1qDC-1 was composed of 733 bp, encoding a signal peptide of 19 residues and a typical gC1q domain of 137 residues containing all eight invariant amino acids in human C1qDC proteins and seven aromatic residues essential for effective packing of the hydrophobic core of AiC1qDC-1. The gC1q domain of AiC1qDC-1, which possessed the typical 10-stranded beta-sandwich fold with a jelly-roll topology common to all C1q family members, showed high homology not only to those of Cl qDC proteins in mollusk but also to those of C1qDC proteins in human. The AiC1qDC-1 transcripts were mainly detected in the tissue of hepatopancreas and also marginally detectable in adductor, heart, mantle, gill and hemocytes by fluorescent quantitative real-time PCR. In the microbial challenge experiment, there was a significant up-regulation in the relative expression level of AiC1qDC-1 in hepatopancreas and hemocytes of the scallops challenged by fungi Pichia pastoris GS115, Gram-positive bacteria Micrococcus luteus and Gram-negative bacteria Listonella anguillarum. The recombinant AiC1qDC-1 (rAiC1qDC-1) protein displayed no obvious agglutination against M. luteus and L. anguillarum, but it aggregated P. pastoris remarkably. This agglutination could be inhibited by D-mannose and PGN but not by LPS, glucan or D-galactose. These results indicated that AiC1qDC-1 functioned as a pattern recognition receptor in the immune defense of scallops against pathogens and provided clues for illuminating the evolution of the complement classical pathway. (C) 2010 Elsevier Ltd. All rights reserved.

SmC2P1, a C2 domain protein from Scophthalmus maximus that binds bacterial pathogen-infected lymphocytes and reduces bacterial survival

C2 domains are protein structural modules found in many eukaryotic proteins involved in signal transduction, membrane trafficking, and immune defense. Most of the studied C2 domain-containing proteins are multi-domained in structure, in which the C2 domain is an independently folded motif and plays an essential role in calcium-dependent membrane-targeting. Although C2 domains isolated from intact proteins have been studied for biological functions, no study on natural proteins containing C2 domain only has been documented. In this study, we identified a Scophthalmus maximus protein SmC2P1 that is comprised of a single C2 domain and lacks any other apparent domain structures. The deduced amino acid sequence of SmC2P1 contains 129 residues and shares 36-38% identities with the C2 domains of the perforins of several fish species. Like typical C2 domains, SmC2P1 is predicted to organize into eight beta-strands with a Ca2+-binding site located in inter-strand loops. SmC2P1 expression was detected, in deceasing order, in liver, spleen, blood, brain, muscle, kidney, gill, and heart. Experimental challenge of turbot with a bacterial pathogen significantly upregulated SmC2P1 expression in kidney in a time-dependent manner. Recombinant SmC2P1 purified from yeast exhibits no hemolytic activity but binds to pathogen-infected kidney lymphocytes in the presence of calcium. Furthermore, interaction of recombinant SmC2P1 with bacterium-infected lymphocytes reduced bacterial survival. These results indicate that SmC2P1 is a functional protein that is involved in host immune defense against bacterial infection. (C) 2010 Elsevier Ltd. All rights reserved.

Identification, expression, function and localization of a DUF985 domain-containing hypothetical gene from amphioxus Branchiostoma belcheri

The progress in genome sequencing has led to an increasing submission of uncharacterized hypothetical genes with the domain of unknown function, DUF985, in GenBank, and none of these genes is related to a known protein. We therefore underwent an experimental study to identify the function of a DUF985 domain-containing hypothetical gene BbDUF985 (GenBank Accession No. AY273818) isolated from amphioxus Branchiostoma belcheri (B. belcheri). BbDUF985 was successfully expressed in both prokaryotic and eukaryotic systems, and its recombinant proteins expressed in both systems definitely exhibited an activity of phosphoglucose isomerase (PGI). Both tissue-section in situ hybridization and immunohistochemistry demonstrated that BbDUF985 was expressed in a tissue-specific manner, with most abundant levels in the hepatic caecum and ovary. In CHO cells transfected with the expression plasmid pEGFP-N1/BbDUF985, the fusion protein was targeted in the cytoplasm of CHO cells, suggesting that BbDUF985 is a cytosolic protein. In contrast, Western blotting indicated that BbDUF985 was also present in amphioxus humoral fluids, suggesting that it exists as a secreted protein as well. Our study provided a framework for further understanding the biochemical properties and physiological function of DUF985-containing hypothetical proteins in other species. (c) 2008 Elsevier Inc. All rights reserved.

裂隙/孔隙型弹性介质中地震波场模拟与叠前逆时偏移

With the development of oil/gas seismic exploration, seismic survey for fracture/porosity type reservoir is becoming more and more important. As for China, since it has over 60% store of low porosity and low permeability oil/gas reservoir, it’s more urgent to validly describe fracture/porosity type oil/gas trap and proposing the related, developed seismic technique. To achieve mapping fracture/porosity region and its development status, it demands profound understanding of seismic wave propagation discipline in complex fractured/pored media. Meanwhile, it has profound scientific significance and applied worth to study forward modeling of fracture/porosity type media and pre-stacked reverse time migration. Especially, pre-stacked reverse-time migration is the lead edge technique in the field of seismology and seismic exploration. In this paper, the author has summarized the meaning, history and the present state of numerical simulation of seismic propagation in fractured/pored media and seismic exploration of fractured/pored reservoirs. Extensive Dilatancy Anisotropy (EDA) model is selected as media object in this work. As to forward modeling, due to local limitation of solving spatial partial derivative when using finite-difference and finite-element method, the author turns to pseudo-spectral method (PSM), which is based on the global characteristic of Fourier transform to simulate three-component elastic wave-field. Artifact boundary effect reduction and simulation algorithm stability are also discussed in the work. The author has completed successfully forward modeling coding of elastic wave-field and numerical simulation of two-dimensional and three-dimensional EDA models with different symmetric axis. Seismic dynamic and kinematical properties of EDA media are analyzed from time slices and seismic records of wave propagation. As to pre-stacked reverse-time migration for elastic wave-field in fractured/pored media, based on the successful experience in forward modeling results with PSM, the author has studied pre-stacked reverse-time depth-domain migration technique using PSM of elastic wave-field in two dimensional EDA media induced by preferred fracture/pore distribution. At the same time, different image conditions will bring up what kind of migration result is detailed in this paper. The author has worded out software for pre-stacked reverse-time depth-domain migration of elastic wave-field in EDA media. After migration processing of a series of seismic shot gathers, influences to migration from different isotropic and anisotropy models are described in the paper. In summary, following creative research achievements are obtained:  Realizing two-dimensional and three-dimensional elastic wave-field modeling for fractured/pored media and related software has been completed.  Proposed pre-stacked reverse-time depth-domain migration technique using PSM of elastic wave-field.  Through analysis of the seismic dynamic and kinematical properties of EDA media, the author made a conclusion that collection of multi-component seismic data can provide important data basis for locating and describing the fracture/pore regions and their magnitudes and the preferred directions.  Pre-stacked reverse-time depth-domain migration technique has the ability to reconstruct complex geological object with steep formations and tilt fracture distribution. Neglecting seismic anisotropy induced by the preferred fracture/pore distribution, will lead to the disastrous imaging results.

基于波动方程的层间多次波预测方法研究

In exploration geophysics，velocity analysis and migration methods except reverse time migration are based on ray theory or one-way wave-equation. So multiples are regarded as noise and required to be attenuated. It is very important to attenuate multiples for structure imaging, amplitude preserving migration. So it is an interesting research in theory and application about how to predict and attenuate internal multiples effectively. There are two methods based on wave-equation to predict internal multiples for pre-stack data. One is common focus point method. Another is inverse scattering series method. After comparison of the two methods, we found that there are four problems in common focus point method: 1. dependence of velocity model; 2. only internal multiples related to a layer can be predicted every time; 3. computing procedure is complex; 4. it is difficult to apply it in complex media. In order to overcome these problems, we adopt inverse scattering series method. However, inverse scattering series method also has some problems: 1. computing cost is high; 2. it is difficult to predict internal multiples in the far offset; 3. it is not able to predict internal multiples in complex media. Among those problems, high computing cost is the biggest barrier in field seismic processing. So I present 1D and 1.5D improved algorithms for reducing computing time. In addition, I proposed a new algorithm to solve the problem which exists in subtraction, especially for surface related to multiples. The creative results of my research are following: 1. derived an improved inverse scattering series prediction algorithm for 1D. The algorithm has very high computing efficiency. It is faster than old algorithm about twelve times in theory and faster about eighty times for lower spatial complexity in practice; 2. derived an improved inverse scattering series prediction algorithm for 1.5D. The new algorithm changes the computing domain from pseudo-depth wavenumber domain to TX domain for predicting multiples. The improved algorithm demonstrated that the approach has some merits such as higher computing efficiency, feasibility to many kinds of geometries, lower predictive noise and independence to wavelet； 3. proposed a new subtraction algorithm. The new subtraction algorithm is not used to overcome nonorthogonality, but utilize the nonorthogonality's distribution in TX domain to estimate the true wavelet with filtering method. The method has excellent effectiveness in model testing. Improved 1D and 1.5D inverse scattering series algorithms can predict internal multiples. After filtering and subtracting among seismic traces in a window time, internal multiples can be attenuated in some degree. The proposed 1D and 1.5D algorithms have demonstrated that they are effective to the numerical and field data. In addition, the new subtraction algorithm is effective to the complex theoretic models.

地震波模拟：非规则网格离散的数值解法、吸收边界及其实际应用

This dissertation presents a series of irregular-grid based numerical technique for modeling seismic wave propagation in heterogeneous media. The study involves the generation of the irregular numerical mesh corresponding to the irregular grid scheme, the discretized version of motion equations under the unstructured mesh, and irregular-grid absorbing boundary conditions. The resulting numerical technique has been used in generating the synthetic data sets on the realistic complex geologic models that can examine the migration schemes. The motion equation discretization and modeling are based on Grid Method. The key idea is to use the integral equilibrium principle to replace the operator at each grid in Finite Difference scheme and variational formulation in Finite Element Method. The irregular grids of complex geologic model is generated by the Paving Method, which allow varying grid spacing according to meshing constraints. The grids have great quality at domain boundaries and contain equal quantities of nodes at interfaces, which avoids the interpolation of parameters and variables. The irregular grid absorbing boundary conditions is developed by extending the Perfectly Matched Layer method to the rotated local coordinates. The splitted PML equations of the first-order system is derived by using integral equilibrium principle. The proposed scheme can build PML boundary of arbitrary geometry in the computational domain, avoiding the special treatment at corners in a standard PML method and saving considerable memory and computation cost. The numerical implementation demonstrates the desired qualities of irregular grid based modeling technique. In particular, (1) smaller memory requirements and computational time are needed by changing the grid spacing according to local velocity; (2) Arbitrary surfaces and interface topographies are described accurately, thus removing the artificial reflection resulting from the stair approximation of the curved or dipping interfaces; (3) computational domain is significantly reduced by flexibly building the curved artificial boundaries using the irregular-grid absorbing boundary conditions. The proposed irregular grid approach is apply to reverse time migration as the extrapolation algorithm. It can discretize the smoothed velocity model by irregular grid of variable scale, which contributes to reduce the computation cost. The topography. It can also handle data set of arbitrary topography and no field correction is needed.

地震波场模拟及叠前深度偏移的李群方法

The processes of seismic wave propagation in phase space and one way wave extrapolation in frequency-space domain, if without dissipation, are essentially transformation under the action of one parameter Lie groups. Consequently, the numerical calculation methods of the propagation ought to be Lie group transformation too, which is known as Lie group method. After a fruitful study on the fast methods in matrix inversion, some of the Lie group methods in seismic numerical modeling and depth migration are presented here. Firstly the Lie group description and method of seismic wave propagation in phase space is proposed, which is, in other words, symplectic group description and method for seismic wave propagation, since symplectic group is a Lie subgroup and symplectic method is a special Lie group method. Under the frame of Hamiltonian, the propagation of seismic wave is a symplectic group transformation with one parameter and consequently, the numerical calculation methods of the propagation ought to be symplectic method. After discrete the wave field in time and phase space, many explicit, implicit and leap-frog symplectic schemes are deduced for numerical modeling. Compared to symplectic schemes, Finite difference (FD) method is an approximate of symplectic method. Consequently, explicit, implicit and leap-frog symplectic schemes and FD method are applied in the same conditions to get a wave field in constant velocity model, a synthetic model and Marmousi model. The result illustrates the potential power of the symplectic methods. As an application, symplectic method is employed to give synthetic seismic record of Qinghai foothills model. Another application is the development of Ray+symplectic reverse-time migration method. To make a reasonable balance between the computational efficiency and accuracy, we combine the multi-valued wave field & Green function algorithm with symplectic reverse time migration and thus develop a new ray+wave equation prestack depth migration method. Marmousi model data and Qinghai foothills model data are processed here. The result shows that our method is a better alternative to ray migration for complex structure imaging. Similarly, the extrapolation of one way wave in frequency-space domain is a Lie group transformation with one parameter Z and consequently, the numerical calculation methods of the extrapolation ought to be Lie group methods. After discrete the wave field in depth and space, the Lie group transformation has the form of matrix exponential and each approximation of it gives a Lie group algorithm. Though Pade symmetrical series approximation of matrix exponential gives a extrapolation method which is traditionally regarded as implicit FD migration, it benefits the theoretic and applying study of seismic imaging for it represent the depth extrapolation and migration method in a entirely different way. While, the technique of coordinates of second kind for the approximation of the matrix exponential begins a new way to develop migration operator. The inversion of matrix plays a vital role in the numerical migration method given by Pade symmetrical series approximation. The matrix has a Toepelitz structure with a helical boundary condition and is easy to inverse with LU decomposition. A efficient LU decomposition method is spectral factorization. That is, after the minimum phase correlative function of each array of matrix had be given by a spectral factorization method, all of the functions are arranged in a position according to its former location to get a lower triangular matrix. The major merit of LU decomposition with spectral factorization (SF Decomposition) is its efficiency in dealing with a large number of matrixes. After the setup of a table of the spectral factorization results of each array of matrix, the SF decomposition can give the lower triangular matrix by reading the table. However, the relationship among arrays is ignored in this method, which brings errors in decomposition method. Especially for numerical calculation in complex model, the errors is fatal. Direct elimination method can give the exact LU decomposition But even it is simplified in our case, the large number of decomposition cost unendurable computer time. A hybrid method is proposed here, which combines spectral factorization with direct elimination. Its decomposition errors is 10 times little than that of spectral factorization, and its decomposition speed is quite faster than that of direct elimination, especially in dealing with a large number of matrix. With the hybrid method, the 3D implicit migration can be expected to apply on real seismic data. Finally, the impulse response of 3D implicit migration operator is presented.