General theory of the long-range interactions in protein folding

The process of the globular structure formation from a long molecular chain is examined in a general sense. In the course of this process various regions of the chain interact with each other. The bonds formed during this process are classified as native and non-native ones. Native bonds are formed in native globular structure. All other bonds are “incorrect” (non-native). It is demonstrated that the globule formation can occur actually without production and subsequent decay of non-native contacts. The proposed model allows to avoid a search of numerous non-native variants since long-distance interactions with a high selectivity take place between the chain regions that form native bonds. The presence of these interactions prompts the chain regions which yield native contacts start to draw together and to interact. The databank data analysis shows that the developed model can be applied not only to the abstract structures but also to real polypeptide chains which are able to form both globular structures and helical fibrils.     

Quantum theory on protein folding

The conformational change of biological macromolecule is investigated from the point of quantum transition. A quantum theory on protein folding is proposed. Compared with other dynamical variables such as mobile electrons, chemical bonds and stretching-bending vibrations the molecular torsion has the lowest energy and can be looked as the slow variable of the system. Simultaneously, from the multi-minima property of torsion potential the local conformational states are well defined. Following the idea that the slow variables slave the fast ones and using the nonadiabaticity operator method we deduce the Hamiltonian describing conformational change. It is shown that the influence of fast variables on the macromolecule can fully be taken into account through a phase transformation of slow variable wave function. Starting from the conformation-transition Hamiltonian the nonradiative matrix element was calculated and a general formulas for protein folding rate was deduced. The analytical form of the formula was utilized to study the temperature dependence of protein folding rate and the curious non-Arrhenius temperature relation was interpreted. By using temperature dependence data the multi-torsion correlation was studied. The decoherence time of quantum torsion state is estimated. The proposed folding rate formula gives a unifying approach for the study of a large class problems of biological conformational change.     

朗之万方程及其在蛋白质折叠动力学中的应用

研究了朗之万方程的动力学性质,并用它模拟了蛋白质分子的折叠过程.首先在相空间中对朗之万方程做连续映射,发现做布朗运动的粒子在位置坐标上存在明显的概率分布,这表明蛋白质折叠过程中分子空间构型是非遍历的.此外,本文还通过数值模拟得到了去折叠态蛋白质的紧密度指标,并验证了它与实验结果以及其他理论方法的一致性.本文还提出了一种利用重整化方法研究熔球体状态蛋白质的理论模型,并提供了考虑疏水基影响的蛋白质折叠过程的模拟思路. 关键词： 朗之万方程 蛋白质折叠非遍历性 紧密度指标 重整化     

Improvement of the relative entropy based protein folding method

The “relative entropy” has been used as a minimization function to predict the tertiary structure of a protein backbone, and good results have been obtained. However, in our previous work, the ensemble average of the contact potential was estimated by an approximate calculation. In order to improve the theoretical integrity of the relative-entropy-based method, a new theoretical calculation method of the ensemble average of the contact potential was presented in this work, which is based on the thermodynamic perturbation theory. Tests of the improved algorithm were performed on twelve small proteins. The root mean square deviations of the predicted versus the native structures from Protein Data Bank range from 0.40 to 0.60 nm. Compared with the previous approximate values, the average prediction accuracy is improved by 0.04 nm. Contributed equally to this work Supported by the National Natural Science Foundation of China (Grant No. 30670497), the Beijing Natural Science Foundation (Grant No. 5072002), and the Specialized Research Foundation for the Doctoral Program of Higher Education (Grant No. 200800050003)     

获得蛋白质激光脉冲升温光源方法的比较研究

触发蛋白质开折叠可以使用激光脉冲升温溶剂产生温跳的方法。红外光谱研究中常用的激光波长为1.9μm,可以通过钬激光器、半导体激光器和光参量振荡(OPO)等非线性光学的方法来实现频率转换。在拥有Nd∶YAG激光光源的情况下,对由LiNbO3晶体差频、临界相位匹配(CPM)的KTP OPO和高压氢气受激拉曼散射所获得的1.9μm激光输出的实验方法进行了比较。结果表明,受激拉曼散射是获得频率转换最有效而便捷的方法。     

Protein structural codes and nucleation sites for protein folding

One of the long-standing controversial arguments in protein folding is Levinthal's paradox. We have recently proposed a new nucleation hypothesis and shown that the nucleation residues are the most conserved sequences in protein. To avoid the complicated effect of tertiary interactions, we limit our search for structural codes to the nucleation residues. Starting with the hypotheses of secondary structure nucleation and conservation of residues important for folding, we have analysed 762 folds classified as unique by SCOP. Segments of 17 residues around the top 20% conserved amino acids are analysed, resulting in approximately 100 clusters each for the main secondary structure classes of helix, sheet and coil. Helical clusters have the longest correlation range, coils the shortest (four residues). Strong specific sequence-structure correlation is observed for coil but not for helix and sheet, suggesting a mapping relationship between the sequence and the structure for coil. We propose that the central sequences in these clusters form `structural codes', a useful basis set for identifying nucleation sites, protein fragments stable in isolation, and secondary structural patterns in proteins (particularly turns and loops).     

RNA分子折叠的统计力学

RNA分子折叠对决定分子(基因)水平上的生命活动是至关重要的.文章对RNA分子折叠(特别是二级结构的折叠)的热力学和动力学性质作一简单回顾与介绍.因为静电相互作用在RNA折叠过程中的特殊重要作用, 文章作者对RNA(与DNA)折叠的电相互作用单独作较为详细的讨论.     

RNA分子折叠的统计力学

RNA分子折叠对决定分子（基因）水平上的生命活动是至关重要的．文章对RNA分子折叠（特别是二级结构的折叠）的热力学和动力学性质作一简单回顾与介绍．因为静电相互作用在RNA折叠过程中的特殊重要作用，文章作者对RNA（与DNA）折叠的电相互作用单独作较为详细的讨论．     

The characteristics of molten globule states and folding pathways strongly depend on the sequence of a protein

ABSTRACT

The majority of proteins perform their cellular function after folding into a specific and stable native structure. Additionally, for many proteins less compact ‘molten globule’ states have been observed. Current experimental observations show that the molten globule state can show varying degrees of compactness and solvent accessibility; the underlying molecular cause for this variation is not well understood. While the specificity of protein folding can be studied using protein lattice models, current design procedures for these models tend to generate sequences without molten globule-like behaviour. Here we alter the design process so the distance between the molten globule ensemble and the native structure can be steered; this allows us to design protein sequences with a wide range of folding pathways, and sequences with well-defined heat-induced molten globules. Simulating these sequences we find that (1) molten globule states are compact, but have less specific configurations compared to the folded state, (2) the nature of the molten globule state is highly sequence dependent, (3) both two-state and multi-state folding proteins may show heat-induced molten globule states, as observed in heat capacity curves. The varying nature of the molten globules and typical heat capacity curves associated with the transitions closely resemble experimental observations.     

Protein folding – simplicity in complexity

Understanding and predicting protein folding would elucidate how misfolded proteins cause aggregation and amyloid formation, for example in Alzheimer's disease. Despite the seemingly bewildering complexity of protein biology, simple analytic models can still capture the basic physics and predict the fundamental limits for protein domain size and folding speed.     

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.     

Functional structures and folding dynamics of two peptides

The folding dynamics and structural characteristics of peptides RTKAWNRQLYPEW (P1) and RTKQLYPEW (P2) are investigated by using all-atomic simulation procedure CHARMM in this work. The results show that P1, a segment of an antigen, has a folding motif of α-helix, whereas P2, which is derived by deleting four residues AWNR from peptide P1, prevents the formation of helix and presents a β-strand. And peptide P1 experiences a more rugged energy landscape than peptide P2. From our results, it is inferred that the antibody CD8 cytolytic T lymphocyte prefers an antigen with a β-folding structure to that with an α-helical one.     

Ultraviolet resonance Raman spectroscopy of a β‐sheet peptide: a model for membrane protein folding

The partitioning of a hydrophobic hexapeptide, N‐acetyl‐tryptophan‐pentaleucine (AcWL5), into self‐associated β‐sheets within a vesicle membrane was studied as a model for integral membrane protein folding and insertion via vibrational and electronic spectroscopy. Ultraviolet resonance Raman spectroscopy allows selective examination of the structures of amino acid side chains and the peptide backbone and provides information about local environment and molecular conformation. The secondary structure of AcWL5 within a vesicle membrane was investigated using 207.5‐nm excitation and found to consist of β‐sheets, in agreement with previous studies. The β‐sheet peptide shows enhanced Raman scattering cross‐sections for all amide modes as well as extensive hydrogen‐bonding networks. Tryptophan vibrational structure was probed using 230‐nm excitation. Increases in Raman cross‐sections of tryptophan modes W1, W3, W7, W10, W16, W17, and W18 of membrane‐incorporated AcWL5 are primarily attributed to greater resonance enhancement with the B_b electronic transition. The W17 mode, however, undergoes a much greater enhancement than is expected for a simple resonance effect, and this observation is discussed in terms of hydrogen bonding of the indole ring in a hydrophobic environment. The observed tryptophan mode frequencies and intensities overall support a hydrophobic environment for the indole ring within a vesicle, and these results have implications for the location of tryptophan in membrane protein systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Simple off-lattice model to study the folding and aggregation of peptides

We present a numerical study of a new protein model. This off-lattice model takes into account both the hydrogen bonds and the amino-acid interactions. It reproduces the folding of a small protein (peptide): morphological analysis of the conformations at low temperature shows two well-known substructures α-helix and β-sheet depending on the chosen sequence. The folding pathway in the scope of this model is studied through a free-energy analysis. We then study the aggregation of proteins. Proteins in the aggregate are mainly bound via hydrogen bonds. Performing a free-energy analysis we show that the addition of a peptide to such an aggregate is not favourable. We qualitatively reproduce the abnormal aggregation of proteins in prion diseases.     

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.     

Physics of protein folding

Protein physics is grounded on three fundamental experimental facts: protein, this long heteropolymer, has a well defined compact three-dimensional structure; this structure can spontaneously arise from the unfolded protein chain in appropriate environment; and this structure is separated from the unfolded state of the chain by the “all-or-none” phase transition, which ensures robustness of protein structure and therefore of its action. The aim of this review is to consider modern understanding of physical principles of self-organization of protein structures and to overview such important features of this process, as finding out the unique protein structure among zillions alternatives, nucleation of the folding process and metastable folding intermediates. Towards this end we will consider the main experimental facts and simple, mostly phenomenological theoretical models. We will concentrate on relatively small (single-domain) water-soluble globular proteins (whose structure and especially folding are much better studied and understood than those of large or membrane and fibrous proteins) and consider kinetic and structural aspects of transition of initially unfolded protein chains into their final solid (“native”) 3D structures.     

Calculation of decay half-lives for superheavy elements using the double folding model

α decay half-lives of some new synthesized superheavy elements, possibly synthesized superheavy elements and decay products are calculated theoretically within the WKB approximation by using microscopic m-nucleus interaction potentials. These nuclear potentials between the α particle and daughter nuclei are obtained by using the double folding integral of the matter density distribution of the α particle and daughter nuclei with a density-dependent effective nucleon-nucleon interaction, in which the zero-range exchange term is supplemented. The calculated α decay half-lives are compared with those of the different models and experimental data. It is shown that the present calculation successfully provides the half-lives of the observed αdecays for some new superheavy elements and therefore gives reliable predictions for α decay of possibly synthesized superheavy elements in future experiments.     

Nucleon--nucleon interactions in the double folding model for fusion reactions

Nucleus--nucleus potentials are determined in the framework of double folding model for M3Y--Reid and M3Y--Paris effective nucleon--nucleon (NN) interactions. Both zero-range and finite-range exchange parts of NN interactions are considered in the folding procedure. In this paper the spherical projectile--spherical target system ¹⁶O+²⁰⁸Pb is selected for calculating the barrier energies, fusion cross sections and barrier distributions with the density-independent and density-dependent NN interactions on the basis of M3Y--Reid and M3Y--Paris NN interactions. The barrier energies become lower for Paris NN interactions in comparison with Reid NN interactions, and also for finite-range exchange part in comparison with zero-range exchange part. The density-dependent NN interactions give similar fusion cross sections and barrier distributions, and the density-independent NN interaction causes the barrier distribution moving to a higher position. However, the density-independent Reid NN interaction with zero-range exchange part gives the lowest fusion cross sections. We find that the calculated fusion cross sections and the barrier distributions are in agreement with the experimental data after renormalization of the nuclear potential due to coupled-channel effect.     

Nanosecond-time-resolved infrared spectroscopic study of fast relaxation kinetics of protein folding by means of laser-induced temperature-jump

Elucidating the initial kinetics of folding pathways is critical to the understanding of the protein folding mechanism. Transient infrared spectroscopy has proved a powerful tool to probe the folding kinetics. Herein we report the construction of a nanosecond laser-induced temperature-jump （T-jump） technique coupled to a nanosecond timeresolved transient mid-infrared （mid-IR） spectrometer system capable of investigating the protein folding kinetics with a temporal resolution of 50 ns after deconvolution of the instrumental response function. The mid-IR source is a liquid N2 cooled CO laser covering a spectral range of 5.0μm （2000 cm^-1）-6.5μm （1540 cm^-1）. The heating pulse was generated by a high pressure H2 Raman shifter at wavelength of 1.9μm. The maximum temperature-jump could reach as high as 26±1℃. The fast folding/unfolding dynamics of cytochrome C was investigated by the constructed system, providing an example.