Modelling RNA folding under mechanical tension

We investigate the thermodynamics and kinetics of RNA unfolding and refolding under mechanical tension. The hierarchical nature of RNA structure and the existence of thermodynamic parameters for base pair formation based on nearest-neighbour interactions allows modelling of sequence-dependent folding dynamics for any secondary structure. We calculate experimental observables such as the transition force for unfolding, the end-to-end distribution function and its variance, as well as kinetic information, for a representative RNA sequence and for a sequence containing two homopolymer segments: A.U and G.C.     

钙离子调控微丝切割蛋白中A6亚基解折叠的单分子力谱研究

在生命活动中,金属离子扮演了非常重要的角色.微丝切割蛋白(adseverin)需要钙离子的活化才能行使其切割肌动蛋白微丝的功能.本文通过基于原子力显微镜的单分子力谱研究了微丝切割蛋白C端末的A6亚基在结合钙离子前后的力学解折叠机理.实验结果显示:在未结合钙离子时,A6的解折叠表现为两态过程;在结合钙离子后A6力学稳定性显著提高;同时,钙离子的结合使得A6解折叠过程中出现稳定的中间态.通过对中间态的链长的分析,我们推测了中间态对应着A6的N端部分解折叠.而这一部分的解折叠可以使得掩藏在该结构后的A5亚基中肌动蛋白微丝结合位点暴露,从而促使微丝切割蛋白执行功能.我们的实验结果为理解微丝切割蛋白的工作原理提供了新的实验证据.     

Equilibrium folding and unfolding dynamics to reveal detailed free energy landscape of src SH3 protein by magnetic tweezers

Src SH3 protein domain is a typical two-state protein which has been confirmed by research of denaturant-induced unfolding dynamics. Force spectroscopy experiments by optical tweezers and atomic force microscopy have measured the force-dependent unfolding rates with different kinds of pulling geometry. However, the equilibrium folding and unfolding dynamics at constant forces has not been reported. Here, using stable magnetic tweezers, we performed equilibrium folding and unfolding dynamic measurement and force-jump measurement of src SH3 domain with tethering points at its N-and C-termini. From the obtained force-dependent transition rates, a detailed two-state free energy landscape of src SH3 protein is constructed with quantitative information of folding free energy, transition state barrier height and position,which exemplifies the capability of magnetic tweezers to study protein folding and unfolding dynamics.     

Two state behavior in a solvable model of beta-hairpin folding

Understanding the mechanism of protein secondary structure formation is an essential part of the protein-folding puzzle. Here we describe a simple model for the formation of a beta hairpin, motivated by the fact that folding of a beta hairpin captures much of the basic physics of protein folding. The modeled hairpin is composed of two interacting Gaussian chains with one pairwise (two-body) and two many-body interactions. We show that these many-body interactions, arising from side chain packing effects, are responsible for producing an "all-or-none" folding transition. We also estimate the (single exponential) folding/unfolding rate via calculating the thermodynamic weight of the "critical" droplet/bubble.     

Unique features of animal mitochondrial translation systems: – The non-universal genetic code,unusual features of the translational apparatus and their relevance to human mitochondrial diseases –

In animal mitochondria, several codons are non-universal and their meanings differ depending on the species. In addition, the tRNA structures that decipher codons are sometimes unusually truncated. These features seem to be related to the shortening of mitochondrial (mt) genomes, which occurred during the evolution of mitochondria. These organelles probably originated from the endosymbiosis of an aerobic eubacterium into an ancestral eukaryote. It is plausible that these events brought about the various characteristic features of animal mt translation systems, such as genetic code variations, unusually truncated tRNA and rRNA structures, unilateral tRNA recognition mechanisms by aminoacyl-tRNA synthetases, elongation factors and ribosomes, and compensation for RNA deficits by enlarged proteins. In this article, we discuss molecular mechanisms for these phenomena. Finally, we describe human mt diseases that are caused by modification defects in mt tRNAs.     

过渡金属单硼化物TMB的第一性原理研究

基于密度泛函理论平面赝势波法的第一性原理计算,研究过渡金属单硼化物TMB（以3d系列中的TiB、VB和CrB;4d系列中的ZrB、NbB和MoB;5d系列中的HfB、TaB和WB为例）的热力学稳定性、力学性质和微观机制.发现过渡金属单硼化物的热力学稳定与硬度异常的规律.当价电子浓度为8 e·（f.u.）^-1时,热力学最稳定,且硬度最高.计算TMB的电子结构,发现TMB的价电子浓度为8 e·（f.u.）^-1时,pd共价键合,有效阻碍了金属双层之间的位错滑动,防止剪切变形,致使其具有高硬度.     

Protein folding as a stochastic process

In physiological conditions globular protein molecules assume a specific native conformation uniquely determined by its amino acid sequence. Upon environmental changes the protein molecules undergo reversible unfolding (order losing) and folding (order gaining) transitions, which is similar to the first-order phase transition. Pathways of folding have been intensively studied in the hope of deciphering the code that amino acid sequences carry as to the threedimensional structure of proteins. A strongly simplifiedlattice model of proteins has been found to be a powerful theoretical tool to simulate the dynamic process of the folding and unfolding transitions. The results of the simulation indicate the existence of stochastic pathways of folding.     

Different pathways in mechanical unfolding/folding cycle of a single semiflexible polymer

Kinetics of conformational change of a semiflexible polymer under mechanical external field were investigated with Langevin dynamics simulations. It is found that a semiflexible polymer exhibits large hysteresis in mechanical folding/unfolding cycle even with a slow operation, whereas in a flexible polymer, the hysteresis almost disappears at a sufficiently slow operation. This suggests that the essential features of the structural transition of a semiflexible polymer should be interpreted at least on a two-dimensional phase space. The appearance of such large hysteresis is discussed in relation to different pathways in the loading and unloading processes. By using a minimal two-variable model, the hysteresis loop is described in terms of different pathways on the transition between two stable states.     

Interaction between human telomeric G-quadruplexes characterized by single molecule magnetic tweezers

Human telomeric G-quadruplex plays a crucial role in regulating the genome stability. Despite extensive studies on structures and kinetics of monomeric G-quadruplex, the interaction between G-quadruplexes is still in debate. In this work,we employ magnetic tweezers to investigate the folding and unfolding kinetics of two contiguous G-quadruplexes in 100-mM K~+buffer. The interaction between G-quadruplexes and the consequent effect on the kinetics of G-quadruplex are revealed. The linker sequence between G-quadruplexes is further found to play an important role in the interaction between two G-quadruplexes. Our results provide a high-resolution insight into kinetics of multimeric G-quadruplexes and genome stability.     

Folding/unfolding kinetics of lattice proteins studied using a simple statistical mechanical model for protein folding, I: Dependence on native structures and amino acid sequences

The folding/unfolding kinetics of a three-dimensional lattice protein was studied using a simple statistical mechanical model for protein folding that we developed earlier. We calculated a characteristic relaxation rate for the free energy profile starting from a completely unfolded structure (or native structure) that is assumed to be associated with a folding rate (or an unfolding rate). The chevron plot of these rates as a function of the inverse temperature was obtained for four lattice proteins, namely, proteins a1, a2, b1, and b2, in order to investigate the dependency of the folding and unfolding rates on their native structures and amino acid sequences. Proteins a1 and a2 fold to the same native conformation, but their amino acid sequences differ. The same is the case for proteins b1 and b2, but their native conformation is different from that of proteins a1 and a2. However, the chevron plots of proteins a1 and a2 are very similar to each other, and those of proteins b1 and b2 differ considerably. Since the contact orders of proteins b1 and b2 are identical, the differences in their kinetics should be attributed to the amino acid sequences and consequently to the interactions between the amino acid residues. A detailed analysis revealed that long-range interactions play an important role in causing the difference in the folding rates. The chevron plots for the four proteins exhibit a chevron rollover under both strongly folding and strongly unfolding conditions. The slower relaxation time on the broad and flat free energy surfaces of the unfolding conformations is considered to be the main origin of the chevron rollover, although the free energy surfaces have features that are rather complicated to be described in detail here. Finally, in order to concretely examine the relationship between changes in the free energy profiles and the chevron plots, we illustrate some examples of single amino acid substitutions that increase the folding rate.     

Reconstructing the free-energy landscape of a mechanically unfolded model protein

The equilibrium free-energy landscape of an off-lattice model protein as a function of an internal (reaction) coordinate is reconstructed from out-of-equilibrium mechanical unfolding manipulations. This task is accomplished via two independent methods: by employing an extended version of the Jarzynski equality (EJE) and the protein inherent structures (ISs). In a range of temperatures around the "folding transition" we find a good quantitative agreement between the free energies obtained via EJE and IS approaches. This indicates that the two methodologies are consistent and able to reproduce equilibrium properties of the examined system. Moreover, for the studied model the structural transitions induced by pulling can be related to thermodynamical aspects of folding.     

A review of direct numerical simulations of astrophysical detonations and their implications

Multi-dimensional direct numerical simulations (DNS) of astrophysical detonations in degenerate matter have revealed that the nuclear burning is typically characterized by cellular structure caused by transverse instabilities in the detonation front. Type Ia supernova modelers often use onedimensional DNS of detonations as inputs or constraints for their whole star simulations.While these one-dimensional studies are useful tools, the true nature of the detonation is multi-dimensional. The multi-dimensional structure of the burning influences the speed, stability, and the composition of the detonation and its burning products, and therefore, could have an impact on the spectra of Type Ia supernovae. Considerable effort has been expended modeling Type Ia supernovae at densities above 1×10⁷ g·cm^-3 where the complexities of turbulent burning dominate the flame propagation. However, most full star models turn the nuclear burning schemes off when the density falls below 1×10⁷ g·cm^-3 and distributed burning begins. The deflagration to detonation transition (DDT) is believed to occur at just these densities and consequently they are the densities important for studying the properties of the subsequent detonation. This work will review the status of DNS studies of detonations and their possible implications for Type Ia supernova models. It will cover the development of Detonation theory from the first simple Chapman–Jouguet (CJ) detonation models to the current models based on the time-dependent, compressible, reactive flow Euler equations of fluid dynamics.     

There and back again: Two views on the protein folding puzzle

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10–11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: “U-to-N” and “N-to-U”. In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the “N-to-U” transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical “detailed balance” principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the “N-to-U” transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the “U-to-N” transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the side of the native state; and both theories agree with experiment. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control and explain the observed maximal size of the “foldable” protein domains.     

Ashkin-Teller Formalism for Elastic Response of DNA Molecule to External Force and Torque

We propose an Ashkin-Teller-like model for elastic response of DNA molecule to external force and torque. The base-stacking interaction is described in a simple and uniform way. We obtain the phase diagram of dsDNA, and in particular, the transition from 13 form to the S state induced by stretching and twisting. The elastic response of the ssDNA is presented also in a unified formalism. The close relation of dsDNA molecule structure with elastic response is shown clearly. The calculated folding angle of the dsDNA molecule is 59.2°.     

Eu3+掺杂钛酸钇晶态薄膜的制备与高效红色荧光发射

采用溶胶-凝胶法制备了Eu³⁺掺杂的钛酸钇晶态发光薄膜。通过X射线衍射(XRD)对薄膜的结构和结晶过程进行了分析,利用荧光分光光度计对薄膜的发光性质开展了测试和研究。XRD结果表明,薄膜包含立方相Y_xTi_1-xO_1-0.5x晶粒,该晶粒属立方晶系,Fm3m(225)空间群,晶胞参数a=0.530nm,晶粒尺寸约为17nm。荧光光谱表明,Eu³⁺掺杂的Y_xTi_1-xO_1-0.5x薄膜显示了强的红光发射,其中Eu³⁺的⁵D₀→⁷F₂超灵敏跃迁为最强一组。紫外氙灯、准分子激光器、汞灯等是这种发光薄膜的有效激发源。     

Folding transitions of the square-diagonal lattice

We address the problem of “phantom” folding of the tethered membrane modeled by the two-dimensional square lattice, with bonds on the edges and diagonals of each face. Introducing bending rigidities K₁ and K₂ for respectively long and short bonds, we derive the complete phase diagram of the model, using transfer matrix calculations. The latter displays two transition curves, one corresponding to a first-order (ferromagnetic) folding transition, and the other to a continuous (anti-ferromagnetic) unfolding transition.     

以液体核磁共振波谱分析与帕金森氏病相关的I93M 突变对人类泛素碳端水解酶结构的影响

人类泛素碳端水解酶（UCH-L1）是涉及帕金森氏病并且在神经元高度表达的蛋白．UCH-L1 的家族性突变与转译后修饰会引起聚集倾向增加与去泛素活性损失,这二者都可能成为致病因素．作者所在实验室之前的研究指出与帕金森氏病相关的突变I93M 显著降低UCH-L1 的折叠稳定性并且加速其构型展开动力学．该研究使用液体核磁共振分析方法,包括侧链甲基化学位移,松弛骨干动力学和残余偶极耦合,以进一步阐明I93M 突变如何影响UCH-L1 的结构和动态．结果显示I93M 显著影响突变位点周围的疏水核心侧链构型．然而,这样的结构扰动并不会影响在纳秒时间尺度的快速骨干动力学．透过残余偶极耦合分析显示UCH-L1 在水溶液中的结构与之前报道的晶体结构有相当显著的偏离,另外I93M 突变也导致超出突变位点的远距离结构扰动．这一系列水溶液结构的分析结果可补充之前已知的晶体学数据,并对UCH-L1 在帕金森氏病相关的基因突变影响并提供详细的见解．     

Modeling the temperature-dependent peptide vibrational spectra based on implicit-solvent model and enhance sampling technique

We herein review our studies on simulating the thermal unfolding Fourier transform infrared and two-dimensional infrared spectra of peptides. The peptide–water configuration ensembles, required forspectrum modeling, aregenerated at a series of temperatures using the GBOBCimplicit solvent model and the integrated tempering sampling technique.The fluctuating vibrational Hamiltonians of the amide I vibrational band are constructed using the Frenkel exciton model.The signals are calculated using nonlinear exciton propagation. The simulated spectral features such as the intensity and ellipticity are consistent with the experimental observations. Comparing the signals for two beta-hairpin polypeptides with similar structures suggests that this technique is sensitive to peptide folding landscapes.     

Probing DNA and RNA single molecules with a double optical tweezer

A double-tweezer setup is used to induce mechanical stress in systems of molecular biology. A double strand of DNA is first stretched and the data is compared to precedent experiments to check the experimental setup. Then a short foldable fragment of RNA is probed; the typical unfolding/refolding hysteresis behaviour of this kind of construction is shown and followed by a study of its elasticity and a comparison to a worm-like chain model. Eventually, we describe the unfolding of a larger RNA structure, which unfolds by multiple steps. We show that this unfolding is not reversible and that it presents numerous unfolding pathways.