Spectral division of conformational states of spin-labeled tRNA Phe from Escherichia coli

A spectral division method of two conformational states of spin-labeled macromolecules is presented. The method is suitable in conditions of highly anisotropic motion of spin label and is based on titration of experimental spectra of spin-labeled macromolecule by theoretical ones. Theoretical spectra simulation uses the Freed theory and spin-Hamiltonian parameters, derived from independent experiments. Nomogrammes and formula for calculation of order parameter Sz and correlation time tau c in temperature-viscosity experiment are available. The method was applied to spectral division of two conformational states of spin-labeled tRNAPhe from E. coli and spectral parameters Sz and tau c were obtained for both states. ESR spectra of these conformational states at t degree = 20 degrees differ strongly from one another by order parameter Sz. The first conformer, that is characterised by a greater order parameter has no globular conformational transition (in terms of changes of the hydrodynamic macromolecule radius) between 2 degrees and 20 degrees, but local conformational changes take place in this temperature region.     

The calculated free energy effects of 5-methyl cytosine on the B to Z transition in DNA

We have examined the free energy effects of 5-methylation of cytosine on the B in equilibrium Z conformational equilibrium in DNA. Free energy differences were calculated using the free energy perturbation approach, which uses an easily derived equation from classical statistical mechanics to relate the free energy difference between two states to the ensemble average of the potential energy difference between the states. Calculations were carried both in explicit solvent and (for comparison) in vacuo. The free energy values obtained for the explicit solvent systems are total free energies, with contributions from all parts of the system (solvent + solute), and so are relevant to the B in equilibrium Z transitions observed under real (physiological) conditions. We calculate that in solution, methylation makes the B in equilibrium Z transition more favorable by about -0.4 kcal/mole base pair (bp) in free energy. This value compares well with approximate experimentally derived values of about -0.3 kcal/mole-bp. We also discuss a method for determining the free energy difference between conformational states poorly maintained by a potential energy model. Finally, the effects of methylation on the melting temperature of DNA are examined.     

Cooperative transition between two helical conformations in a linear system: Poly-L-proline I ⇌ II. I. Equilibrium studies

The solvent-induced conformational transition between the two helical forms of poly-L -proline is studied as a model for cooperative order ? order transitions. The chain length dependent equilibrium data in two solvent systems are described by Schwarz's theory, which is based upon the most general formulation of the linear Ising model with nearest neighbor interactions. The parameter σ which describes the difficulty of nucleation of a I (II) residue in an uninterrupted II (I)-helix is 10^?5 in both solvent systems. The ratios of the nucleation difficulties of states I and II at the ends of the chains β′ and β″ are very different in the two systems. Nucleation difficulty within the chain is interpreted as being due to unfavorable excess interaction energies at the I–II and II–I junctions, which add up to 7 kcal/mole of nuclei as calculated from the σ value. A similar value is computed from the atomic interactions at the junctions. In contrast to this intrinsic properly of poly-L -proline, the energies of I and II residues at the ends are heavily influenced by interactions of the endgroups with the solvent. The above values of the nucleation parameters are determined by a new least-square fitting procedure which does not necessitate the assumption of the dependence of the equilibrium constant s for propagation upon the external parameters, but yields this function from the experimental transition data. A quantitative explanation of this experimental s function through the binding of solvent is attempted. In the transition region a very small free energy change (about 0.1 kcal/mole), arising from a preferential binding of solvent molecules to one of the conformational states, is sufficient for a complete conversion from one helical form to the other.     

Structure and thermodynamics of RNA-protein binding: using molecular dynamics and free energy analyses to calculate the free energies of binding and conformational change

An adaptive binding mechanism, requiring large conformational rearrangements, occurs commonly with many RNA-protein associations. To explore this process of reorganization, we have investigated the conformational change upon spliceosomal U1A-RNA binding with molecular dynamics (MD) simulations and free energy analyses. We computed the energetic cost of conformational change in U1A-hairpin and U1A-internal loop binding using a hybrid of molecular mechanics and continuum solvent methods. Encouragingly, in all four free energy comparisons (two slightly different proteins, two different RNAs), the free macromolecule was more stable than the bound form by the physically reasonable value of approximately 10 kcal/mol. We calculated the absolute binding free energies for both complexes to be in the same range as that found experimentally.     

Molecular basis of cooperativity in protein folding IV. Core: A general cooperative folding model

The cooperative nature of the protein folding process is independent of the characteristic fold and the specific secondary structure attributes of a globular protein. A general folding/unfolding model should, therefore, be based upon structural features that transcend the peculiarities of α-helices, β-sheets, and other structural motifs found in proteins. The studies presented in this paper suggest that a single structural characteristic common to all globular proteins is essential for cooperative folding. The formation of a partly folded state from the native state results in the exposure to solvent of two distinct regions: (1) the portions of the protein that are unfolded; and (2) the “complementary surfaces,” located in the regions of the protein that remain folded. The cooperative character of the folding/unfolding transition is determined largely by the energetics of exposing complementary surface regions to the solvent. By definition, complementary regions are present only in partly folded states; they are absent from the native and unfolded states. An unfavorable free energy lowers the probability of partly folded states and increases the cooperativity of the transition. In this paper we present a mathematical formulation of this behavior and develop a general cooperative folding/unfolding model, termed the “complementary region” (CORE) model. This model successfully reproduces the main properties of folding/unfolding transitions without limiting the number of partly folded states accessible to the protein, thereby permitting a systematic examination of the structural and solvent conditions under which intermediates become populated. It is shown that the CORE model predicts two-state folding/unfolding behavior, even though the two-state character is not assumed in the model. © 1993 Wiley-Liss, Inc.     

Kinetics of allosteric conformational transition of a macromolecule prior to ligand binding

Two fundamentally different mechanisms of ligand binding are commonly encountered in biological kinetics. One mechanism is a sequential multistep reaction in which the bimolecular binding step is followed by first-order steps. The other mechanism includes the conformational transition of the macromolecule, before the ligand binding, followed by the ligand binding process to one of the conformational states. In stopped-flow kinetic studies, the reaction mechanism is established by examining the behavior of relaxation times and amplitudes as a function of the reactant concentrations. A major diagnostic tool for detecting the presence of a conformational equilibrium of the macromolecule, before the ligand binding, is the decreasing value of one of the reciprocal relaxation times with the increasing [ligand]. The sequential mechanism cannot generate this behavior for any of the relaxation times. Such dependence is intuitively understood on the basis of approximate expressions for the relaxation times that can be comprehensively derived, using the characteristic equation of the coefficient matrix and polynomial theory. Generally, however, the used approximations may not be fulfilled. On the other hand, the two kinetic mechanisms can always be distinguished, using the approach based on the combined application of pseudo-first-order conditions, with respect to the ligand and the macromolecule. The two experimental conditions differ profoundly in the extent of the effect of the ligand on the protein conformational equilibrium. In a large excess of the ligand, the conformational equilibrium of the macromolecule, before the ligand binding, is strongly affected by the binding process. However, in a large excess of the macromolecule, ligand binding does not perturb the internal equilibrium of the macromolecule. As a result, the normal mode, affected by the conformational transition, is absent in the observed relaxation process. In the case of a sequential mechanism, the number of relaxation times is not altered by different pseudo-first-order conditions. Thus, the approach provides a strong diagnostic criterion for detecting the presence of the conformational transition of the macromolecule and establishing the correct mechanism. Application of this approach is illustrated for the binding of 3'-O-(N-methylantraniloyl)-5'-diphosphate to the E. coli DnaC protein.     

Coarse-grained free energy functions for studying protein conformational changes: a double-well network model

In this work, a double-well network model (DWNM) is presented for generating a coarse-grained free energy function that can be used to study the transition between reference conformational states of a protein molecule. Compared to earlier work that uses a single, multidimensional double-well potential to connect two conformational states, the DWNM uses a set of interconnected double-well potentials for this purpose. The DWNM free energy function has multiple intermediate states and saddle points, and is hence a “rough” free energy landscape. In this implementation of the DWNM, the free energy function is reduced to an elastic-network model representation near the two reference states. The effects of free energy function roughness on the reaction pathways of protein conformational change is demonstrated by applying the DWNM to the conformational changes of two protein systems: the coil-to-helix transition of the DB-loop in G-actin and the open-to-closed transition of adenylate kinase. In both systems, the rough free energy function of the DWNM leads to the identification of distinct minimum free energy paths connecting two conformational states. These results indicate that while the elastic-network model captures the low-frequency vibrational motions of a protein, the roughness in the free energy function introduced by the DWNM can be used to characterize the transition mechanism between protein conformations.     

Thermodynamics of the first transition in writhe of a small circular DNA by Monte Carlo simulation

Monte Carlo simulations are employed to investigate the thermodynamics of the first transition in writhe of a circular model filament corresponding to a 468 base-pair DNA. Parameters employed in these simulations are the torsional rigidity, C = 2.0 × 10⁻¹⁹ dyne cm², and persistence length, P = 500 Å. Intersubunit interactions are modeled by a screened Coulomb potential. For a straight line of subunits this accurately approximates the nonlinear Poisson-Boltzmann potential of a cylinder with the linear charge density of DNA. Curves of relative free energy vs writhe at fixed linking difference (Δ1) exhibit two minima, one corresponding to slightly writhed circles and one to slightly underwrithed figure-8's, whenever Δ1 lies in the transition region. The free energies of the two minima are equal when Δ1_c = 1.35, which defines the midpoint of the transition. At this midpoint, the free energy barrier between the two minima is found to be ΔG_bar = (0.20) k_BT at 298 K. Curves of mean potential energy vs writhe at fixed linking difference similarly exhibit two minima for Δ1 values in the transition region, and the two minimum mean potential energies are equal when Δ1 = 1.50. At the midpoint writhe, Δ1_c = 1.35, the difference in mean potential energy between the minimum free energy figure-8 and circle states is (1.3) k_BT, and the difference in their entropies is 1.3 k_B. Thus, the entropy of the minimum free energy figure-8 state significantly exceeds that of the circle at the midpoint of the transition. The first transition in writhe is found to occur over a rather broad range of Δ1 values from 0.85 to 1.85. The twist energy parameter (E_T), which governs the overall free energy of supercoiling, undergoes a sigmoidal decrease, while the translational diffusion coefficient undergoes a sigmoidal increase, over this same range. The static structure factor exhibits an increase, which reflects a decrease in radius of gyration associated with the circle to figure-8 transition. © 1996 John Wiley & Sons, Inc.     

Conformational Exchange in a Membrane Transport Protein Is Altered in Protein Crystals

Successful macromolecular crystallography requires solution conditions that may alter the conformational sampling of a macromolecule. Here, site-directed spin labeling is used to examine a conformational equilibrium within BtuB, the Escherichia coli outer membrane transporter for vitamin B₁₂. Electron paramagnetic resonance (EPR) spectra from a spin label placed within the N-terminal energy coupling motif (Ton box) of BtuB indicate that this segment is in equilibrium between folded and unfolded forms. In bilayers, substrate binding shifts this equilibrium toward the unfolded form; however, EPR spectra from this same spin-labeled mutant indicate that this unfolding transition is blocked in protein crystals. Moreover, crystal structures of this spin-labeled mutant are consistent with the EPR result. When the free energy difference between substates is estimated from the EPR spectra, the crystal environment is found to alter this energy by 3 kcal/mol when compared to the bilayer state. Approximately half of this energy change is due to solutes or osmolytes in the crystallization buffer, and the remainder is contributed by the crystal lattice. These data provide a quantitative measure of how a conformational equilibrium in BtuB is modified in the crystal environment, and suggest that more-compact, less-hydrated substates will be favored in protein crystals.     

Conformational transitions of antibodies induced by hapten binding

The conformational changes of antibody structure induced by hapten molecule binding were investigated by means of thermal perturbation difference spectroscopy. The studies of the free rabit anti-dinitrophenyl antibodies show the conformational transition at temperatures between 25 and 35 degrees C. The changes occurring at the higher temperature are accompanied by the screening of the significant part of exposed tyrosine residues. Binding of the hapten molecules induces a similar transition to that which occurs between the two temperature dependent states of the free antibody. In contrast to our previous results with anti-dansyl rabbit antibodies the dinitrophenyl lysine stabilizes the "low temperature" native state of the protein. The investigation of the MOPC-315 mouse immunoglobulin A myeloma protein possessing anti-dinitrophenyl activity indicates no conformational transition at temperatures between 25 and 35 degrees C and only a small decrease of tyrosine exposure induced by the hapten binding. Our present and previous results indicate that most of the free immunoglobulins exist in two native conformational states which have a small difference in free energy. Hapten binding causes the transition in equilibrium between the two states towards the one of better binding. It is possible that this transition is necessary but not sufficient step for inducing the effector function of antibodies.     

Interpretation of DSC data on protein denaturation complicated by kinetic and irreversible effects

Thermal denaturation of Kunitz soybean trypsin inhibitor (KTI) and ribulose-1,5-biphosphate carboxylase (RBPC) from tobacco leafs was studied by the method of high-sensitivity differential scanning calorimetry (HS-DSC). The dependence of the denaturation temperature on the heating rate reveals in the case of both proteins a non-equilibrium character of the denaturation transition in applied conditions. Developed kinetic approach allows the determination of an equilibrium transition temperature as well as the rate constants of denaturation and renaturation from the complex data of HS-DSC. This method was applied to the analysis of the pH-induced change of the conformational stability of KTI within pH range from 2.0 to 11.0. It allowed the determination of the pH dependencies: of the excess free energy of denaturation, of the activation enthalpy and entropy of denaturation as well as of the denaturation rate constant. Conclusions have been made suggesting the contribution of side-chain hydrogen bonds in the stabilisation of the native and activated states of KTI.     

Beyond the EX1 limit: probing the structure of high-energy states in protein unfolding

Hydrogen exchange kinetics in native solvent conditions have been used to explore the conformational fluctuations of an immunoglobulin domain (CD2.domain1). The global folding/unfolding kinetics of the protein are unaltered between pH 4.5 and pH 9.5, allowing us to use the pH-dependence of amide hydrogen/deuterium exchange to characterise conformational states with energies up to 7.2kcal/mol higher than the folded ground state. The study was intended to search for discreet unfolding intermediates in this region of the energy spectrum, their presence being revealed by the concerted exchange behaviour of subsets of amide groups that become accessible at a given free energy, i.e. the spectrum would contain discreet groupings. Protection factors for 58 amide groups were measured across the pH range and the hydrogen-exchange energy profile is described.More interestingly, exchange behaviour could be grouped into three categories; the first two unremarkable, the third unexpected. (1) In 33 cases, amide exchange was dominated by rapid fluctuation, i.e. the free energy difference between the ground state and the rapidly accessed open state is sufficiently low that the contribution from crossing the unfolding barrier is negligible. (2) In 18 cases exchange is dominated by the global folding transition barrier across the whole pH range measured. The relationship between hydroxyl ion concentration and observed exchange rate is hyperbolic, with the limiting rate being that for global unfolding; the so-called EX1 limit. For these, the free energy difference between the folded ground state and any rapidly-accessed open state is too great for the proton to be exchanged through such fluctuations, even at the highest pH employed in this study. (3) For the third group, comprising five cases, we observe a behaviour that has not been described. In this group, as in category 2, the rate of exchange reaches a plateau; the EX1 limit. However, as the intrinsic exchange rate (k(int)) is increased, this limit is breached and the rate begins to rise again. This unintuitive behaviour does not result from pH instability, rather it is a consequence of amide groups experiencing two processes; rapid fluctuation of structure and crossing the global barrier for unfolding. The boundary at which the EX1 limit is overcome is determined by the equilibrium distribution of the fluctuating open and closed states (K(O/C)) and the rate constant for unfolding (k(u)). This critical boundary is reached when k(int)K(O/C)=k(u). Given that, in a simple transition state formalism: k(u)=K(#)k' (where K(#) describes the equilibrium distribution between the transition and ground state and k' describes the rate of a barrierless rearrangement), it follows that if the pH is raised to a level where k(int)=k', then the entire free energy spectrum from ground state to transition state could be sampled.     

The Free Energy Barrier for Arginine Gating Charge Translation Is Altered by Mutations in the Voltage Sensor Domain

The gating of voltage-gated ion channels is controlled by the arginine-rich S4 helix of the voltage-sensor domain moving in response to an external potential. Recent studies have suggested that S4 moves in three to four steps to open the conducting pore, thus visiting several intermediate conformations during gating. However, the exact conformational changes are not known in detail. For instance, it has been suggested that there is a local rotation in the helix corresponding to short segments of a 3-helix moving along S4 during opening and closing. Here, we have explored the energetics of the transition between the fully open state (based on the X-ray structure) and the first intermediate state towards channel closing (C), modeled from experimental constraints. We show that conformations within 3 Å of the X-ray structure are obtained in simulations starting from the C model, and directly observe the previously suggested sliding 3-helix region in S4. Through systematic free energy calculations, we show that the C state is a stable intermediate conformation and determine free energy profiles for moving between the states without constraints. Mutations indicate several residues in a narrow hydrophobic band in the voltage sensor contribute to the barrier between the open and C states, with F233 in the S2 helix having the largest influence. Substitution for smaller amino acids reduces the transition cost, while introduction of a larger ring increases it, largely confirming experimental activation shift results. There is a systematic correlation between the local aromatic ring rotation, the arginine barrier crossing, and the corresponding relative free energy. In particular, it appears to be more advantageous for the F233 side chain to rotate towards the extracellular side when arginines cross the hydrophobic region.     

Mechanism of chaperone function in small heat shock proteins. Two-mode binding of the excited states of T4 lysozyme mutants by alphaA-crystallin

To elucidate the mechanism of alphaA-crystallin chaperone function, a detailed thermodynamic analysis of its binding to destabilized, site-directed mutants of T4 lysozyme was carried out. The selected mutants form a ladder of stabilities spanning the 5-10 kcal/mol range of free energy of unfolding. The crystal structures of the majority of the mutants have been previously determined and found to be similar to that of the wild type with no evidence of static local unfolding. Complex formation between alphaA-crystallin and T4 lysozyme was observed directly via the changes in the electron paramagnetic resonance lineshape of a nitroxide introduced at a non-destabilizing, solvent exposed site in T4 lysozyme. AlphaA-crystallin differentially interacts with the mutants, binding the more destabilized ones to a larger extent despite the similar structure of their native states. Our results suggest that the states recognized by alphaA-crystallin are non-native excited states distinct from the unfolded state. Stable complexes are formed when the free energy of binding to alphaA-crystallin is on the order of the free energy associated with the transition from the excited state to the native state. Biphasic binding isotherms reveal two modes of interactions with distinct affinities and stoichiometries. Highly destabilized mutants preferentially bind to the high capacity mode, suggesting conformational preference in the use of each mode. Furthermore, binding can be enhanced by increased temperature and pH, which may be reflecting conformational changes in alphaA-crystallin oligomeric structure.     

Intramolecular conformational transitions "random coil-helix-folded structure" in polypeptides.

A general theory has been developed for conformational intramolecular transitions in a single macromolecule with a high degree of polymerization (an infinite length model) capable of forming two types of ordered structures: the α-helix and the folded β-structure, as well as acquiring the random coil conformation. The phase diagram analysis of this system has shown that the regular β-structure state is separated from all other states of the chain by the phase boundary line. Any intersection of the phase boundary is a phase transition which can be either of the first order or second order, depending on values of the energy parameters of the system. Mechanisms of intramolecular rearrangements: β-structure–random coil and α-helix–β-structure have been discussed. It has been shown that there exist two different mechanisms for each of these rearrangements, and the regions of parameter variation corresponding to each mechanism have been specified.     

Flexible Solar Thermal Fuel Devices: Composites of Fabric and a Photoliquefiable Azobenzene Derivative

Controllable storage and release of solar energy has always been a highlighted scientific issue for its benefit of mankind. Solar thermal fuels (STFs) supply a closed cycle and renewable energy‐storage strategy by transforming solar energy into chemical energy stored in the conformation of molecular isomers, such as cis/trans‐azobenzene, and releasing it as heat under various stimuli. Although the potential high energy density of the STFs which are based on the hybrids of azobenzene derivatives and carbon nanomaterials has been reported the solvent‐assistant charging hinders their practicability. In this study, a solid‐state STF device is designed and fabricated by compositing one photoliquefiable azobenzene (PLAZ) derivative with a flexible fabric template. The photoinduced phase transition of the PLAZ derivative enables the charging of the flexible STFs to be totally solvent‐free. Interestingly, the energy‐storage capacity (energy density ≈201 J g^?1) of flexible PLAZ STFs has been improved by the soft fabric template. The exothermic situation is monitored with one infrared camera, which shows 4 °C temperature difference between charged and discharged samples under blue light stimulus. The flexible STFs are may be used in practice as heating equipment.     

Using UHF-dielectrometry to study protein structural transitions

UHF-dielectrometry method is based on the following facts: i) there is dispersion (i.e. dependence on frequency) of the dielectric permeability epsilon; ii) bound and free water have remarkable different epsilon, mobility and dispersion regions; iii) conformational changes in a macromolecule lead to redistribution of free and bound water and to change of the amount of free water molecules. Choosing the working frequency in the region of dispersion of free water molecules (9.2 GHz) we can detect conformational changes in proteins using free water as a marker. In this work the temperature dependencies of dielectric parameters of albumin and fibrinogen solutions were obtained in the temperature interval 5-40 degrees C. In contrast to dependencies for poor solvent, temperature dependencies of dielectric parameters for protein solutions are of non-monotonous character; they have a number of peculiarities in the temperature ranges of 8-10, 22-24 and 34-36 degrees C. At these temperatures redistribution of free and bound water in protein-water system occurs due to structural changes in protein molecules. In this work the mechanism of temperature changes of spatial organisation of protein molecules was proposed. Perhaps, this mechanism is responsible for maintenance of thermal stability of the functionally active conformation of native proteins.     

The role of the 132-160 region in prion protein conformational transitions

The native conformation of host-encoded cellular prion protein (PrP(C)) is metastable. As a result of a post-translational event, PrP(C) can convert to the scrapie form (PrP(Sc)), which emerges as the essential constituent of infectious prions. Despite thorough research, the mechanism underlying this conformational transition remains unknown. However, several studies have highlighted the importance of the N-terminal region spanning residues 90-154 in PrP folding. In order to understand why PrP folds into two different conformational states exhibiting distinct secondary and tertiary structure, and to gain insight into the involvement of this particular region in PrP transconformation, we studied the pressure-induced unfolding/ refolding of recombinant Syrian hamster PrP expanding from residues 90-231, and compared it with heat unfolding. By using two intrinsic fluorescent variants of this protein (Y150W and F141W), conformational changes confined to the 132-160 segment were monitored. Multiple conformational states of the Trp variants, characterized by their spectroscopic properties (fluorescence and UV absorbance in the fourth derivative mode), were achieved by tuning the experimental conditions of pressure and temperature. Further insight into unexplored conformational states of the prion protein, likely to mimic the in vivo structural change, was obtained from pressure-assisted cold unfolding. Furthermore, salt-induced conformational changes suggested a structural stabilizing role of Tyr150 and Phe141 residues, slowing down the conversion to a beta-sheet form.     

Fuzzy molecular surfaces.

Surface area of a macromolecule, accessible to a solvent, is defined and calculated, taking into account the probabilistic character of atomic positions due to the high frequency atomic vibrations. For a given a space point, we consider a probability of the event, that this point is covered by a macromolecule. A volume is defined as a space integral of this probability field. The envelope, accessible to a solvent molecule center, becomes fuzzy, existing only in a probabilistic sense. The accessible area is defined as a derivative of the envelope volume with respect to the probe size.