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.     

3-D maps and coupling numbers for protein sequences

Based on a five-letter model of the 20 amino acids, we propose a new 3-D graphical representation of protein sequence. Then we derive from the graphical representation, numerical indices called 3-D coupling numbers, to characterize protein sequences. The examination of the similarities/dissimilarities among the β-globin proteins of 15 species illustrates the utility of the approach.     

UV photoinduced dynamics in protonated aromatic amino acid

UV photoinduced fragmentation of protonated aromatic amino acids has emerged the last few years, coming from a situation where nothing was known to what we think a good understanding of the optical properties. We will mainly focus this review on the tryptophan case. Three groups have mostly done spectroscopic studies and one has mainly been involved in dynamics studies of the excited states in the femtosecond/picosecond range and also in the fragmentation kinetics from nanosecond to millisecond. All these data, along with high level ab initio calculations, have shed light on the role of the different electronic states of the protonated molecules upon the fragmentation mechanisms.     

Structural class tendency of polypeptide: A new conception in predicting protein structural class

Prediction of protein domain structural classes is an important topic in protein science. In this paper, we proposed a new conception: structural class tendency of polypeptides (SCTP), which is based on the fact that a given amino acid fragment tends to be presented in certain type of proteins. The SCTP is obtained from an available training data set PDB40-B. When using the SCTP to predict protein structural classes by Intimate Sorting predictive method, we got the predictive accuracy (jackknife test) with 93.7%, 96.5%, and 78.6% for the testing data set PDB40-j, Chou&Maggiora and CHOU. These results indicate that the SCTP approach is quite encouraging and promising. This new conception provides an effective tool to extract valuable information from protein sequences.     

Analysis of the local conformation of proteins with two-dimensional fluorescence techniques

Two 2D fluorescence techniques are described which allow the study of conformational changes in proteins in their native form in μM solutions using aromatic amino acids (tryptophan, tyrosine) as intrinsic fluorescence markers. Simultaneous time- and wavelength-resolved fluorescence spectra are measured using a 80 ps laser source in conjunction with streak detection in the exit plane of an astigmatism-corrected spectrometer. This approach allows identification of different photophysical processes by their associated lifetime and spectral intensity distribution; errors due to the more common integration over a wider spectral range are avoided. Time-resolved spectra are sensitive to changes in the collisional environment (dynamic quenching) and can thus be used to monitor local conformation changes close to the respective fluorophors. This is demonstrated for the Ras protein which undergoes a drastic conformation change while binding to different nucleotides. Excitation-emission spectra are two-dimensional fluorescence images with one axis corresponding to the excitation and the other to the emission wavelength. Thus, they contain all conventional excitation and fluorescence spectra of a given substance. The 2D structure facilitates the interpretation of these spectra and allows the direct identification of resonance effects, scattering and the isolation of the contribution of different fluorophors to the complete spectrum. This is demonstrated for mixtures of tyrosine and tryptophan. In this case, both wavelength-resolved spectra and temporal decays are affected by energy transfer processes between the two amino acids. In a last example, both static and time-resolved spectral methods are combined to determine the respective contribution of static and dynamic quenching in calsequestrin. Evaluation of the fluorescence data is in good agreement with a recent crystallographic analysis which shows that all tryptophans are located in a conserved domain of the protein. Addition of Ca²⁺ ions leads to a more compact form of calsequestrin and to polymers. This information would not be obtainable from either of the two techniques alone. Received: 10 February 2000 / Published online: 13 September 2000     

Changing the fragmentation pattern of molecules in helium nanodroplets by co-embedding with water

Individual amino acid molecules embedded in helium nanodroplets fragment extensively when the beam is ionized by electron bombardment. However, we find that when glycine and tryptophan are picked up right after, or right before, a small amount of water, the mass spectra become significantly altered. For glycine, the detected ions consist almost entirely of intact protonated amino acids, with or without a few water molecules attached. In other words, the presence of water exerts a striking “buffering” effect on the ionization-induced fragmentation. For tryptophan the effect is weaker but also present. In both cases, the hydroxyl group lost upon ionization overwhelmingly comes from the water partner (in strong contrast to the situation observed when amino acids are picked up by neat water clusters). A complementary experiment involving DCl molecules co-embedded with water shows that in this case Cl and/or DCl invariably leave the droplet upon ionization. The observed patterns may be steered by the analytes' dipole moments or by solvation effects.     

Signal propagation in stem-cell niches

Stem cells, maintaining tissue homeostasis, are nurtured in microscopic niches formed of so-called environmental cells. The kinetics of proliferation and differentiation of stem cells in such niches depend on their interaction with the messenger proteins secreted by environmental cells. We propose a generic mean-field kinetic model of the propagation of such signals. To motivate our study, we briefly describe a stem-cell niche in the Drosophila ovary. Our model is however applicable to other niches as well. In particular, it helps one to understand the necessary conditions for the niche function. For example, the model predicts that in the case of the Drosophila ovary each germline stem cell should have in the external membrane at least 700 receptors interacting with the signaling Dpp and Gpp proteins emanating from the cap cells.     

Melting of columnar hexagonal DNA liquid crystals

The persistence length DNA hexagonal-cholesteric phase transition upon dilution and/or increase in solvent ionic strength is investigated with polarized light microscopy. The ionic strength dependence of the transition follows Lindemann criterion , i.e., the hexagonal lattice melts when the root-mean-square fluctuations in transverse order exceed 10% of the interaxial spacing. The spacings are derived from density and the fluctuations are estimated with a theory of undulation enhanced electrostatic interactions. Additional support for this theory is given by the DNA equation of state and anisotropic neutron radiation scattering from magnetically aligned cholesteric samples just below the phase transition. Received: 17 November 1997 / Revised: 21 January 1998 / Accepted: 25 February 1998     

Coupled oscillator models with no scale separation

We consider a class of spatially discrete wave equations that describe the motion of a system of linearly coupled oscillators perturbed by a nonlinear potential. We show that the dynamical behavior of this system cannot be understood by considering the slowest modes only: there is an “inverse cascade” in which the effects of changes in small scales are felt by the largest scales and the mean-field closure does not work. Despite this, a one and a half degree of freedom model is derived that includes the influence of the small-scale dynamics and predicts global conformational changes accurately. Thus, we provide a reduced model for a system in which there is no separation of scales. We analyze a specific coupled-oscillator system that models global conformation change in biomolecules, introduced in [I. Mezi?, On the dynamics of molecular conformation, Proc. Natl. Acad. Sci. 103 (20) (2006) 7542-7547]. In this model, the conformational states are stable to random perturbations, yet global conformation change can be quickly and robustly induced by the action of a targeted control. We study the efficiency of small-scale perturbations on conformational change and show that “zipper” traveling wave perturbations provide an efficient means for inducing such change. A visualization method for the transport barriers in the reduced model yields insight into the mechanism by which the conformation change occurs.     

Distinct conformational properties determined by implicit and explicit representation of protein-solvent interactions. An analytical and computer simulation study

In the protein folding problem, solvent-mediated forces are commonly represented by intra-chain pairwise contact energy. Although this approximation has proven to be useful in several circumstances, it is limited in some other aspects of the problem. Here we show that it is possible to achieve two models to represent the chain-solvent system, one of them with implicit and other with explicit solvent, such that both reproduce the same thermodynamic results. Firstly, lattice models treated by analytical methods, were used to show that the implicit and explicitly representation of solvent effects can be energetically equivalent only if local solvent properties are time and spatially invariant. Following, applying the same reasoning used for the lattice models, two inter-consistent Monte Carlo off-lattice models for implicit and explicit solvent are constructed, being that now in the latter the solvent properties are allowed to fluctuate. Then, it is shown that the chain configurational evolution as well as the globule equilibrium conformation are significantly distinct for implicit and explicit solvent systems. Actually, strongly contrasting with the implicit solvent version, the explicit solvent model predicts: (i) a malleable globule, in agreement with the estimated large protein-volume fluctuations; (ii) thermal conformational stability, resembling the conformational heat resistance of globular proteins, in which radii of gyration are practically insensitive to thermal effects over a relatively wide range of temperatures; and (iii) smaller radii of gyration at higher temperatures, indicating that the chain conformational entropy in the unfolded state is significantly smaller than that estimated from random coil configurations. Finally, we comment on the meaning of these results with respect to the understanding of the folding process.     

基于太赫兹光谱的氨基酸检测

太赫兹是指频率从0.1到2.0 THz之间的远红外波。与傅里叶红外相比,太赫兹时域光谱能量低,信躁比高,并且无辐射损伤。氨基酸分子的低频振动模式(扭转,集体振动模式和氢键)处在 THz波段。氨基酸是一类重要的生物分子,是组成蛋白质最基本的物质。氨基酸分子以分子间氢键相互连接构成晶体。氨基酸在THz波段比在红外波段体现更多独特吸收特征。到目前为止,已经获得了20种氨基酸分子的太赫兹吸收谱,包括利用太赫兹技术对部分氨基酸的定量分析。氨基酸的太赫兹光谱研究,有利于深层次理解蛋白质/ DNA的低频振动模式及相关生物反应和活性。文章综述了20种氨基酸分子的太赫兹吸收光谱并建立了吸收光谱数据库。总结了太赫兹技术在氨基酸应用方面存在的问题,并对未来发展方向进行展望。     

Modeling of recognition sites of nucleic acid bases aaand amide side chains of amino acids. Combination of experimental and theoretical approaches

A combined experimental-theoretical approach to modeling of building blocks of recognition complexes formed by nucleic acid bases and the amino-acids side-chain amino group is reviewed. The approach includes the temperature dependent field-ionization mass spectrometry and ab initio quantum chemical calculations. The mass spectrometric technique allows determination of interaction enthalpies of biomolecules in the gas phase, and the results it produces are directly comparable to the results obtained through theoretical modeling. In our works we have analyzed both thermodynamic and structural aspects of the recognition complexes of four canonical nucleic acid bases and acrylamide, which models the side chain of asparagine and glutamine. It has been shown that all bases can interact with amide group of the amino acids via their Watson-Crick sites when being incorporated into a single strand DNA or RNA. Stability of the complexes studied, expressed as - ΔH (kJ mole^-1) decreases as: m⁹Gua (- 59.5) > m ¹Cyt (- 57.0) > m ⁹Ade (- 52.0) ≫m ¹Ura (- 40.6). We have determined that in the double stranded DNA only purine bases can be recognized. Received 5 February 2002 and Received in final form 14 March 2002 Published online 13 September 2002     

Learning to design resistance proof drugs from folding

Learning how proteins fold will hardly have any impact on the way conventional — active site centered — drugs are designed. On the other hand, this knowledge is proving instrumental in defining a new paradigm for the identification of drugs against any target protein: folding inhibition. Targeting folding renders drugs less susceptible to spontaneous genetic mutations that in many cases, notably in connection with retroviruses like the Human Immunodeficiency Virus (HIV), can abrogate drug effect. The progress which has taken place during the last years to understand which are the sequences of amino acids which code for a protein, and how to read from these sequences the associated three-dimensional, biologically active, native structure, constitutes the main subject of the present paper. From this narrative the idea of folding inhibitors emerges both naturally and, to some extent, inescapably.     

A study of Barstar folding events using boundary value simulations

From extensive biophysical studies of protein folding, two competing mechanisms emerged: hydrophobic collapse and the framework model. Our protein of choice is Barstar—a barnase inhibitor. The approximation algorithm we used to study Barstar folding trajectories is called SDEL—stochastic difference equation in length. Using the native structure as the final boundary value and a collection of unfolded structures as the varying initial boundary value, SDEL calculates an ensemble of least action pathways between these boundaries. The results are atomically detailed folding pathways, with as many intermediate structures as you request in the input. We generated 12 pathways, starting from a structurally wide selection of unfolded conformations. Using the protein's radius of gyration as our primary reaction coordinate, we tracked H-bonds, dihedral angles, native and non-native contacts, and energy along the folding pathways. This paper will follow our findings, with special emphasis on pinpointing hydrophobic collapse as a more appropriate mechanism for Barstar. Comparison with pathway predictions for Barstar using experimental techniques will also be discussed.     

Nonlinear Schrödinger equation and DNA dynamics

We study a possible solitary wave solution of the nonlinear Schrödinger equation (NLSE). It is shown that the wave can be both modulated and nonmodulated depending on a ratio of the envelope and the carrier wave velocities. We also study the same type of the soliton solution in DNA dynamics. We show that the ratio of these two velocities is a measure of modulation and we conclude that the modulated wave is more stable than the nonmodulated one. Finally, we solved the problem concerning three parameters arising from the applied procedure for the solution of the NLSE.     

Ionisation and fragmentation of tetraphenyl iron (III) porphyrin chloride induced by slow multiply charged ion impact

Ionisation and ion-induced fragmentation of tetraphenyl iron (III) porphyrin chloride (FeTPPCl) molecules have been studied after slow collisions (v∼ 0.2 a.u.) with multiply charged ions (O³⁺, Ar⁸⁺). Intact molecules and large fragments are observed in charge states up to q=4. For q=1, the intact molecule is the most abundant species, in particular, when projectiles in higher charge states are used. When the internal energy of the singly charged ion is increased by the energy transfer during the collision, the singly charged system de-excites by the emission of a neutral Cl-atom, a free electron or possibly a negative Cl anion. The processes are observed as direct as well as delayed processes on a μs-time scale. For q=2 to 4 the loss of the Cl-atom and some phenyl groups becomes more likely due to the lower stability and the larger energy transfer. The charge state distribution of atomic fragments is found to be very different, in particular, when C^q+ and Cl^q+ ions are compared. In the first case mainly singly charged ions are detected, whereas in the second case ions in charge states up to q=6 are observed with high intensities. These phenomena are discussed in terms of the intramolecular charge mobility.     

Folding kinetics of two-state proteins based on the model of general random walk in native contact number space

We investigated the folding kinetics of a series of two-state proteins by using the model of general random walk in native contact number space, and derive the observed linear relationship between the logarithms of the folding rate constants and the numbers of native contacts from “kinetic viewpoint”. The protein folding speed limit and stability in this model are consistent with experimental observations.     

Vectorial representation of single- and multi-domain protein folds

We discuss a vectorial representation applicable to both single- and multi-domain protein folds. This generalized vectorial representation is essentially identical to the previously described vectorial representation for single-domain proteins folds when applied to these, but allows for the additional consistent representation of multi-domain structures. We show that the generalized vectorial representation enables the accurate analytical prediction of site-specific amino acid distributions for both single- and multi-domain protein folds, similarly as the previously described vectorial representation does for single-domain folds.