Human lineage mutations regulate RNA-protein binding of conserved genes NTRK2 and ITPR1 involved in human evolution

Background The role of human lineage mutations(HLMs)in human evolution through post-transcriptional modification is unclear.Aims To investigate the contribution of HLMs to human evolution through post-transcriptional modification.Methods We applied a deep learning model Seqweaver to predict how HLMs impact RNA-binding protein affinity.Results We found that only 0.27%of HLMs had significant impacts on RNA-binding proteins at the threshold of the top 1%of human common variations.These HLMs enriched in a set of conserved genes highly expressed in adult excitatory neurons and prenatal Purkinje neurons,and were involved in synapse organisation and the GTPase pathway.These genes also carried excess damaging coding mutations that caused neurodevelopmental disorders,ataxia and schizophrenia.Among these genes,NTRK2 and ITPR1 had the most aggregated evidence of functional importance,suggesting their essential roles in cognition and bipedalism.Conclusions Our findings suggest that a small subset of human-specific mutations have contributed to human speciation through impacts on post-transcriptional modification of critical brain-related genes.

Lie Symmetries and Conserved Quantities for the Singular Lagrange System

The invariance of the ordinary differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities for the singular Lagrange system. The determining equations, the restriction equations of the Lie symmetries and the form of conserved quantities of the system are obtained.

Conserved quantities from Lie symmetries for nonholonomic systems

This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

Lie Symmetries and Conserved Quantities of Holonomic Mechanical Systems in Terms of Quasi-Coordinatee

Aim To study the Lie symmetries and conserved quantities of holonomic mechanical systems in terms of qnasi-coordinates. Methods The definition of an infinitesimal generator for the holonomic mechanical systems in terms of quasi-coordinates was given. Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equations of the Lie symmetries of holonomic mechanical systems in terms of quassi-coordinates are established. The structure equation and the form of conserved quantities are obtained. An example to illustrate the applicaiton of the result is given.

Cloning and Expression of Conserved Sequences of cry Gene in E.coli Strain Rosetta(DE3)

[Objective] The aim was to clone the conserved sequences of cry gene and express them in Rosetta （DE3）. [Method] Specific primers were designed according to NCBI database information and the conserved sequences of cry gene were amplified by PCR from Bt transgenic cotton. Then recombinant plasmids were constructed and expressed in E. coil strain Rosetta （DE3）. Finally, the effects of different concentrations and inducing time of IPTG on the expression level of protein were investigated. [Result] Two conserved sequences （304 and 853 bp respectively） of cry gene were amplified. The result of SDS-PAGE confirmed that the recombinant plasmids pGEX-4t-I-304 and pGEX-4t-1-853 could express fusion proteins by IPTG induction and the molecular weight of protein products was 39 and 62.4 kDa respectively, which was in accordance with predicted result. The optimal protein ex- pression conditions were confirmed as induction with 0.15 mmol/L IPTG for 7 h. [Conclusion] This study prepared the ground for the further detection of Bt transgenic crops.

Symmetries and conserved quantities of generalized Birkhoffian systems

Three kinds of symmetries and their corresponding conserved quantities of a generalized Birkhoffian system are studied. First, by using the invariance of the Pfaffian action under the infinitesimal transformations, the Noether theory of the generalized Birkhoffian system is established. Secondly, on the basis of the invariance of differential equations under infinitesimal transformations, the definition and the criterion of the Lie symmetry of the generalized Birkhoffian system are established, and the Hojman conserved quantity directly derived from the Lie symmetry of the system is given. Finally, by using the invariance that the dynamical functions in the differential equations of the motion of mechanical systems still satisfy the equations after undergoing the infinitesimal transformations, the definition and the criterion of the Mei symmetry of the generalized Birkhoffian system are presented, and the Mei conserved quantity directly derived from the Mei symmetry of the system is obtained. Some examples are given to illustrate the application of the results.

Lie Symmetry and Conserved Quantities for Nonholonomic Vacco Dynamical Systems

In this paper the Lie symmetry and conserved quantities for nonholonomic Vacco dynamical systems are studied. The determining equation of the Lie symmetry for the system is given. The general Hojman conserved quantity and the Lutzky conserved quantity deduced from the symmetry are obtained.

Lie Symmetries and Conserved Quantities of Holonomic Systems with Remainder Coordinates

Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.

Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems

This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non- conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invaxiance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.

Lie symmetries and conserved quantities for generalized Birkhoff system

To study Lie symmetry and the conserved quantity of a generalized Birkhoff system with additional terms, the determining equations of the Lie symmetry of the system is derived. A con- served quantity of Hojman＇ s type and a Noether＇ s conserved quantity are deduced by the Lie symme- try under some conditions. One example is given to illustrate the application of the result.

Lie Symmetries and Conserved Quantities of Systems of Relative Motion Dynamics

Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given.

Mei Symmetry and Conserved Ouantity of Tzénoff Equations for Nonholonomic Systems of Non-Chetaev's Type

Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained.

Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales

This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.

Symmetry and Hojman Conserved Quantity of Tznoff Equations for Unilateral Holonomic System

Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzénoffequations are given.Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given.Hojman conserved quantity of Tzénoff equations for the system above through special Lie symmetry and Lie symmetryin the condition of special Mei symmetry respectively is obtained.

A symmetry and a conserved quantity for the Birkhoff system

A symmetry and a conserved quantity of the Birkhoff system are studied. The symmetry is called the Birkhoff symmetry. Its definition and criterion are given in this paper. A conserved quantity can be deduced by using the symmetry. An example is given to illustrate the application of the result.

Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style

This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.

A new type of conserved quantity of Mei symmetry for the motion of mechanico electrical coupling dynamical systems

We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results.

Lie Symmetries and Conserved Quantities of Arbitrary Order Nonholonomic Systems

The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, the restriction equations, the structure equation and the form of the conserved quantities were obtained.

Conformal invariance and Hojman conserved quantities of first order Lagrange systems

In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

Detection of hyper-conserved regions in hepatitis B virus X gene potentially useful for gene therapy

AIM To detect hyper-conserved regions in the hepatitis B virus(HBV) X gene(HBX) 5' region that could be candidates for gene therapy.METHODS The study included 27 chronic hepatitis B treatmentnaive patients in various clinical stages(from chronic infection to cirrhosis and hepatocellular carcinoma, both HBeA g-negative and HBeA g-positive), and infected with HBV genotypes A-F and H. In a serum sample from each patient with viremia > 3.5 log IU/m L, the HBX 5' end region [nucleotide(nt) 1255-1611] was PCRamplified and submitted to next-generation sequencing(NGS). We assessed genotype variants by phylogenetic analysis, and evaluated conservation of this region by calculating the information content of each nucleotide position in a multiple alignment of all unique sequences(haplotypes) obtained by NGS. Conservation at the HBx protein amino acid(aa) level was also analyzed.RESULTS NGS yielded 1333069 sequences from the 27 samples, with a median of 4578 sequences/sample(2487-9279, IQR 2817). In 14/27 patients(51.8%), phylogenetic analysis of viral nucleotide haplotypes showed a complex mixture of genotypic variants. Analysis of the information content in the haplotype multiple alignments detected 2 hyper-conserved nucleotide regions, one in the HBX upstream non-coding region(nt 1255-1286) and the other in the 5' end coding region(nt 1519-1603). This last region coded for a conserved amino acid region(aa 63-76) that partially overlaps a Kunitz-like domain.CONCLUSION Two hyper-conserved regions detected in the HBX 5' end may be of value for targeted gene therapy, regardless of the patients' clinical stage or HBV genotype.