Protein dynamics: Rotational diffusion of rigid and fluctuating three dimensional structures

The optimized Rouse-Zimm approximation to the local dynamics (ORZLD theory) is extended to treat three-dimensional structures. Rigid model chains of different dimensionality are considered. The local dynamics of random peptides are compared to the rotational correlation times of rigid three-dimensional protein structures. The treatment of these rigid limits is a necessary step in a more advanced ORZLD theory of the dynamics of proteins including fluctuations relative to the three-dimensional structure. © 1995 John Wiley & Sons, Inc.     

Smoluchowski dynamics of the vnd/NK‐2 homeodomain from Drosophila melanogaster: First‐order mode‐coupling approximation

This work is the first in a series devoted to applying mode coupling diffusion theory to the derivation of local dynamics properties of proteins in solution. The first‐order mode‐coupling approximation, or optimized Rouse–Zimm local dynamics (ORZLD), is applied here to derive the rotational dynamics of the bonds and compare the calculated with the experimental nmr ¹⁵N spin–lattice relaxation time behavior of the vnd/NK‐2 homeodomain from Drosophila melanogaster. The starting point for the calculations is the experimental three‐dimensional structure of the homeodomain determined by multidimensional nmr spectroscopy. The results of the computations are compared with experimentally measured ¹⁵N spin–lattice relaxation times T₁, at 34.5 and 60.8 MHz, to check the first‐order approximation. To estimate the relative importance of internal and overall rotation, both rigid and fluctuating dynamic models are examined, with fluctuations evaluated using molecular dynamics (MD) simulations. The correlation times for the fundamental bond vector time correlation function and for the second‐order bond orientational TCF are obtained as a function of the residue number for vnd/NK‐2. The stability of the corresponding local dynamics pattern for the fluctuating structure as a function of the length of the MD trajectory is presented. Diffusive dynamics, which is essentially free of model parameters even at first order in the mode‐coupling diffusion approach, confirm that local dynamics of proteins can be described in terms of rotational diffusion of a fluctuating quasi‐rigid structure. The comparison with the nmr data shows that the first‐order mode coupling diffusion approximation accounts for the correct order of magnitude of the results and of important qualitative aspects of the data sensitive to conformational changes. Indications are obtained from this study to efficiently extend the theory to higher order in the mode‐coupling expansion. These results demonstrate the promise of the mode‐coupling approach, where the local dynamics of proteins is described in terms of rotational diffusion of a fluctuating quasi‐rigid structure, to analyze nmr spin–lattice relaxation behavior. © 1999 John Wiley & Sons, Inc. Biopoly 49: 235–254, 1999     

Determination of rotational correlation times from deconvoluted fluorescence anisotropy decay curves. Demonstration with 6,7-dimethyl-8-ribityllumazine and lumazine protein from Photobacterium leiognathi as fluorescent indicators

The experimental and analytical protocols required for obtaining rotational correlation times of biological macromolecules from fluorescence anisotropy decay measurements are described. As an example, the lumazine protein from Photobacterium leiognathi was used. This stable protein (Mr 21 200) contains the noncovalently bound, natural fluorescent marker 6,7-dimethyl-8-ribityllumazine, which has in the bound state a long fluorescence lifetime (tau = 14 ns). Shortening of the fluorescence lifetime to 2.6 ns at room temperature was achieved by addition of the collisional fluorescence quencher potassium iodide. The shortening of tau had virtually no effect on the rotational correlation time of the lumazine protein (phi = 9.4 ns, 19 degrees C). The ability to measure biexponential anisotropy decay was tested by the addition of Photobacterium luciferase (Mr 80 000), which forms an equilibrium complex with lumazine protein. Under the experimental conditions used (2 degrees C) the biexponential anisotropy decay can best be described with correlation times of 20 and 60 ns, representing the uncomplexed and luciferase-associated lumazine proteins, respectively. The unbound 6,7-dimethyl-8-ribityllumazine itself (tau = 9 ns) was used as a model compound for determining correlation times in the picosecond time range. In the latter case rigorous deconvolution from the excitation profile was required to recover the correlation time, which was shorter (100-200 ps) than the measured laser excitation pulse width (500 ps).     

Backbone dynamics of proteins as studied by 15N inverse detected heteronuclear NMR spectroscopy: application to staphylococcal nuclease

This paper describes the use of novel two-dimensional nuclear magnetic resonance (NMR) pulse sequences to provide insight into protein dynamics. The sequences developed permit the measurement of the relaxation properties of individual nuclei in macromolecules, thereby providing a powerful experimental approach to the study of local protein mobility. For isotopically labeled macromolecules, the sequences enable measurements of heteronuclear nuclear Overhauser effects (NOE) and spin-lattice (T1) and spin-spin (T2) 15N or 13C relaxation times with a sensitivity similar to those of many homonuclear 1H experiments. Because T1 values and heteronuclear NOEs are sensitive to high-frequency motions (10(8)-10(12) s-1) while T2 values are also a function of much slower processes, it is possible to explore dynamic events occurring over a large time scale. We have applied these techniques to investigate the backbone dynamics of the protein staphylococcal nuclease (S. Nase) complexed with thymidine 3',5'-bisphosphate (pdTp) and Ca2+ and labeled uniformly with 15N. T1, T2, and NOE values were obtained for over 100 assigned backbone amide nitrogens in the protein. Values of the order parameter (S), characterizing the extent of rapid 1H-15N bond motions, have been determined. These results suggest that there is no correlation between these rapid small amplitude motions and secondary structure for S. Nase. In contrast, 15N line widths suggest a possible correlation between secondary structure and motions on the millisecond time scale. In particular, the loop region between residues 42 and 56 appears to be considerably more flexible on this slow time scale than the rest of the protein.     

Fluorescence correlation spectroscopy and nonideal solutions

The information that may be obtained from a fluorescence correlation spectroscopic study of a nonideal solution is considered. If all of the macromolecules in a two-component solution are fluorescently labeled, the mutual diffusion coefficient will be measured. If only a few of the macromolecules in a solution are fluorescently labeled, the tracer diffusion coefficient will be obtained. Two nonideal systems that probably may usefully be studied with fluorescence correlation spectroscopy are proposed. The application of fluorescence correlation spectroscopy to studies of lateral diffusion in biological membranes is discussed; the form of the contribution to the fluorescence correlation spectrum of bulk motion within a membrane is noted.     

Characterization of dynamic behavior of side groups of globular proteins by spin-label, NMR and luminescence polarization methods

In this work we suggest a quantitative estimation of a complicated motion of side groups of globular proteins. In the general case, three basic parameters determine the motion: (a) rotational correlation time of a side unit under study, or covalently bound spin label, or dye, (b) parameter S that reflects sterical restrictions for re-orientation of the given unit (these two parameters depending on the side-chain structure and its conformational change within the immediate dynamic protein surrounding whereas correlation times of side units on microviscosity in addition), (c) rotational correlation time of protein globule. These parameters can be measured by spin-label, NMR and fluorescence polarization techniques. An attempt to describe a complicated dynamic behaviour of side units of protein macromolecules with a single dynamics parameter--rotational correlation time--not only leads to a loss of part of information about the local structural dynamics of macromolecules but also can diminish the tau value.     

On a possible biological spectroscopy

A new type of physical transition, denotedS→S ^*, has been detected in irradiated organic molecules (λ=546 nm) through their interaction with specific biological macromolecules. In a specific enzyme-substrate interaction, a clear enhancement of the reaction rate is observed, when the substrate is irradiated with sharply well defined times. These “efficient irradiation times” are always of the 5k sec type (k=1, 2, 3, …). They have been consistently revealed in a great number of specific biological interactions. The present note demonstrates an important property, i.e. that forevery irradiation time aS→S ^* transition is induced in organic molecules. It is shown that for any irradiation times different from the 5k sec type (k=1, 2, 3, …) states of theS ^* type may occur, but the biological macromolecules may “detect” only theS ^* states induced by irradiations of the 5k sec type.     

Structure-Activity Correlations with Compounds Related to Abscisic Acid

Inhibition of cell expansion of excised embryonic axes of Phaseolus vulgaris was used to evaluate the growth-inhibiting activity of abscisic acid and related compounds. None of the 13 compounds tested was as active as abscisic acid. 4-Hydroxyisophorone, a substance representative of the abscisic acid ring system was essentially inactive; cis, trans-3-methylsorbic acid, a compound resembling the side chain of abscisic acid, had low activity; and cis, trans-beta-ionylideneacetic acid was one-sixth as active. Loss of the ring double bond results in a drastic decrease in biological activity. Comparison of our results with those reported previously leads to the suggestion that the double bond of the cyclohexyl moiety may have an important function in determining the degree of activity of cis, trans-ionylideneacetic acids. Two modes of action are discussed. It seems possible that the ring double bond is involved in covalent bonding in binding of the abscisic acid analogue to macromolecules. This may require formation of an intermediate epoxide. It can also be argued that stereochemical differences between cyclohexane derivatives are important factors in determining the degree of biological activity.     

Detection of living cervical cancer cells by transient terahertz spectroscopy

The photonic energy of terahertz wave is in the same order of magnitude as the rotational and vibrational energy levels of organic and biological macromolecules, so it has unique advantages in detecting cells and biological macromolecules. However, in the life environment, the dynamic time scale of cell-environment interaction and structural conformation change of biological macromolecules are within picosecond to millisecond, and water has strong absorption to terahertz wave, which has become the bottleneck problem for the detection of cells and biological macromolecules by terahertz technology. In this article, we developed a set of terahertz single measurement system based on the tilt wave front of grating pulse technique. The system was employed for the terahertz detection of trace living cervical cancer cells. We achieved transient detection of the terahertz pulse time-domain waveform of the living HeLa cells. The characteristic absorption peaks were identified by Lambert-Beer law, respectively, at 0.49, 0.71, 1.04, 1.07, 1.26 and 1.37 THz. The absorbance is proportional to the cell concentration.     

Integral equation theories for predicting water structure around molecules

Water plays a crucial role in the structure and function of proteins and other biological macromolecules; thus, theories of aqueous solvation for these molecules are of great importance. However, water is a complex solvent whose properties are still not completely understood. Statistical mechanical integral equation theories predict the density distribution of water molecules around a solute so that all particles are fully represented and thus potentially both molecular and macroscopic properties are included. Here we discuss how several theoretical tools we have developed have been integrated into an integral equation theory designed for globular macromolecular solutes such as proteins. Our approach predicts the three-dimensional spatial and orientational distribution of water molecules around a solute. Beginning with a three-dimensional Ornstein-Zernike equation, a separation is made between a reference part dependent only on the spatial distribution of solvent and a perturbation part dependent also on the orientational distribution of solvent. The spatial part is treated at a molecular level by a modified hypernetted chain closure whereas the orientational part is treated as a Boltzmann prefactor using a quasi-continuum theory we developed for solvation of simple ions. A potential energy function for water molecules is also needed and the sticky dipole models of water, such as our recently developed soft-sticky dipole (SSD) model, are ideal for the proposed separation. Moreover, SSD water is as good as or better than three point models typically used for simulations of biological macromolecules in structural, dielectric and dynamics properties and yet is seven times faster in Monte Carlo and four times faster in molecular dynamics simulations. Since our integral equation theory accurately predicts results from Monte Carlo simulations for solvation of a variety of test cases from a single water or ion to ice-like clusters and ion pairs, the application of this theory to biological macromolecules is promising.     

Information bounds and optimal analysis of dynamic single molecule measurements

Time-resolved single molecule fluorescence measurements may be used to probe the conformational dynamics of biological macromolecules. The best time resolution in such techniques will only be achieved by measuring the arrival times of individual photons at the detector. A general approach to the estimation of molecular parameters based on individual photon arrival times is presented. The amount of information present in a data set is quantified by the Fisher information, thereby providing a guide to deriving the basic equations relating measurement uncertainties and time resolution. Based on these information-theoretical considerations, a data analysis algorithm is presented that details the optimal analysis of single-molecule data. This method natively accounts and corrects for background photons and cross talk, and can scale to an arbitrary number of channels. By construction, and with corroboration from computer simulations, we show that this algorithm reaches the theoretical limit, extracting the maximal information out of the data. The bias inherent in the algorithm is considered and its implications for experimental design are discussed. The ideas underlying this approach are general and are expected to be applicable to any information-limited measurement.     

Preparation of pH‐stimuli‐responsive PEG–TGA/TGH‐capped CdTe QDs and their application in cell labeling

A pH‐sensitive and double functional nanoprobe was designed and synthesized in a water‐soluble system using thioglycolic acid (TGA) and mercapto‐acetohydrazide (TGH) as the stabilizers. TGA is biocompatible because the carboxyl group is easily linked to biological macromolecules. At the same time, the hydrazide on TGH reacts with the aldehyde on poly(ethylene glycol) (PEG) and forms a hydrazone bond. The hydrazone bond ruptured at specific pH values and exhibited pH‐stimuli‐responsive characteristics. As an optical imaging probe, the PEG–TGA/TGH‐capped CdTe quantum dots (QDs) had high quality, with a fluorescence efficiency of 25–30%, and remained stable for at least five months. This pH‐responsive factor can be used for the effective release of CdTe QDs under the acidic interstitial extracellular environment of tumor cells. This allows the prepared pH‐stimuli‐responsive nanoprobes to show fluorescence signals for use in cancer cell imaging. Copyright © 2014 John Wiley & Sons, Ltd.     

Ion-conformational interaction and charge transport through channels of biological membranes

This work proposes a theory of charge transport through channels in biological membranes, based on ion flow interaction with charged groups of protein macromolecules that form the channel. Displacements of the groups are due to conformational changes of the protein molecule, the relaxation times of which are much larger than the average time of ion ocurrence in the channel. Ion flow is assumed to depend on the conformational changes and vice-versa. The resulting self-organizing ion-conformational system is described by a set of nonlinear differential equations for conformational variables and average occupancy of the channel by ions. The system exhibits multistable behaviour in a certain range of control parameters (potential difference, input ion flow). The stationary states of the system may be identified with the states of discrete conductivity of the ionic channels.     

The mechanical properties of the abdominal cuticle of Rhodnius larvae.

1. The mechanical properties of loops of cuticle cut from the abdomens of 5th instar Rhodnius have been investigated. The cuticle shows pronounced viscoelastic behaviour. 2. Stress-relaxation tests show a continuously falling modulus over a wide range of times after the imposition of a strain. 3. Plasticized samples of cuticle show stress-relaxation curves which are shifted along the time axis towards earlier times by up to times 10-3. The modulus at any particular time after the imposition of strain is about 10 times lower than that of the unplasticized cuticle. 4. It is concluded that the mechanical properties of this cuticle are determined, at least for maintained stresses, largely by the matrix material. Chitin microfibrils may act as a reinforcing filler for short-term, rapid stresses. The cuticular macromolecules are probably not extensively cross-linked by primary bonds, though secondary interactions between them are probably important in the viscoelastic properties of the cuticle. 5. Plasticization probably involves a change in either the number or the strength of secondary interactions between the cuticle macromolecules, or both.     

Virtual rigid body dynamics

An important direction in biological simulations is the development of methods that permit the study of larger systems and/or longer simulation time scales than is currently feasible by molecular dynamics. One such method designed with this objective in mind is stochastic boundary molecular dynamics (SBMD). SBMD was developed for the characterization of spatially localized processes in proteins, and has been shown to successfully reproduce structural and dynamical properties of these macromolecules, as compared to a molecular dynamics control simulation, when concerted or global motions are not present. The virtual rigid body dynamics method presented in this work extends the range of applicability of the SBMD method, by providing a framework to include these important long time scale conformational transitions. In this paper we describe the two-step implementation of the virtual rigid body model: first, the reduction of the full atomic representation to a reduced particle (virtual bond) model, and second, the propagation of the dynamics of flexibly connected rigid bodies containing virtual atom sites.     

生物大分子质谱电离技术的突破及核磁共振三维结构测定方法的建立——2002年诺贝尔化学奖简介

2002年诺贝尔化学奖授予了质谱和核磁共振领域的三位科学家以表彰他们对生物大分子鉴定及结构分析方法做出的贡献．其中两位科学家J．B．Fenn和K．Tanaka分别发展了生物大分子质谱分析的软解吸电离方法;另一科学家K．Wüthrich则将核磁共振技术成功地应用于生物大分子如蛋白质的溶液三维结构测定．他们的研究成果已使质谱和核磁共振技术成为生物大分子强有力的研究手段,极大地促进了生物大分子的研究进程,必将对整个生命科学研究产生深远的影响．     

Deconvolution can be used in electrooptic studies to correct for non-ideal electric excitation pulses only when the electric dipole moment of the studied molecules is predominantly induced

The electric field pulses used for most measurements of transient electrooptic properties such as birefringence and dichroism, are rectangular and assumed to be ideal, but in practice do all such pulses have non-zero rise and fall times. Claims have been made that this non-ideality may be taken into account by employing standard deconvolution techniques. We find that this approach yields exact results in the zero electric field limit when the electric dipole moment of the studied macromolecules is predominantly induced. However, for finite electric field strengths and/or macromolecules with partly or fully permanent electric dipole moments, we find that the deconvolution method yields erroneous estimates of the electrooptic relaxation times. When the decay time of the electric pulse and the electrooptic decay time are equal, and the system is operated in the Kerr domain, this systematic error for macromolecules with purely permanent electric dipole moment equals 37%. In a research field where the uncertainty of the reported relaxation times normally is assumed to be only a few percent this is an error that may seriously mislead unsuspecting users. We find that this systematic error can readily be avoided by employing standard numerical integration of a set of coupled first-order differential equations instead of the standard deconvolution techniques.     

基于设计的生物大分子成药性优化策略研究进展

目前生物药物正处在高速发展阶段,但生物大分子的一些固有特性限制了其成药性,使得很多具有良好治疗潜能的生物大分子 最终不能开发成药物,因而严重制约了生物药物的发展。生物药物开发的瓶颈已从“新分子的产生”转向“如何获得具有优良生理特性 和预期治疗效果的有效药物”。近年来,通过合理设计改造生物大分子高级结构以优化其成药性的研究获得了快速发展。综述基于设计 的生物大分子成药性优化策略研究进展。     

A Molecular Dynamics Simulation Study of Rigid and Non-rigid Hard Dumb-bells

Abstract

We present a comparative study, using molecular dynamics, of systems of diatomic, hard dumb-bell, molecules in which the interatomic distance is either constrained to a fixed value or is allowed to vary freely between preset limits. A significant improvement in simulation effciency can be attained by allowing the bond length to vary. We find that thermodynamic properties, and some time correlation functions, are only slightly affected by the removal of the rigid bond-length constraint. The atomic velocity correlation function responds dramatically at short times to changes in the degree of non-rigidity, but at long times these differences are much less important.