Formation of collective conformational degrees of freedom during macromolecular chain folding dynamics in a viscous medium

Computational methods were used to study the dynamics of the formation of the collective conformational degrees of freedom in the relaxation folding of a model biopolymer chain of 50 nodes in a viscous medium; the model has been described previously. Collective conformational motions of the nodes were shown to arise due to friction forces in a viscous medium. The collective motions have several typical forms, including a wave of differently directed motions of chain nodes that propagates from one end of the chain to another (like a soliton) in response to a pertubation in terminal group position. Individual nodes located at the middle of the chain make approximately equal contributions to the total energy dissipation rate. The end nodes contribute approximately 2–4 times more than internal nodes to the total energy dissipation. The results of numerical experiments are consistent with the theoretical concept developed earlier to describe the dynamics of linear macromolecular chains in a viscous medium in the limit of a very large number of nodes.     

Distribution of the energy dissipation rates among degrees of freedom during conformational movements and folding of a macromolecular chain in a viscous medium

The principle of the minimum rate of energy dissipation for conformational movements in a viscous medium formulated in an earlier study (K.V. Shaitan, Biophysics, 2015, Vol. 60, p. 692) has been applied for a theoretical estimation of the distribution functions of the energy dissipation rates for selected elements of a macromolecule. Equipartition of energy dissipation rates among the nodes of the chain upon conformational movements in the statistical limit of the process is obtained. The uniform distribution of energy dissipation rates along the chain does affect on the formation of the collective conformational degrees of freedom and the folding dynamics.     

Relaxation folding and the principle of the minimum rate of energy dissipation for conformational motions in a viscous medium

A numerical simulation of the folding of a model polymer chain of 50 units with valence bonds of a fixed length and fixed valence angle values has been performed using the strong friction approximation. The rate of energy dissipation in the system has been analyzed for conformational motions along a trajectory determined by the equations of mechanics and the trajectories characterized by random and variable deviations from the mechanical path. The validity of the principle of the minimum average rate of the energy dissipation for the conformational relaxation of a macromolecule in a viscous medium has been demonstrated. A profile of the relaxation energy funnel for the folding of a macromolecular chain has been constructed. Slow and rapid stages of folding could be distinguished in the energy funnel profile; the final state was separated from the nearest conformations of the folded chain by an energy gap.     

Conformational motion correlations in the formation of polypeptide secondary structure in a viscous medium

The Langevin dynamics method and statistical correlation analysis were used to study the α-helical structure folding dynamics of the (Ala)₅₀, (AlaGly)₂₅, and (AlaGly)₇₅ polypeptides depending on the viscosity of the medium. Friction forces that arise when the effective viscosity of the medium is similar to the viscosity of water were found to result in strong correlations between the backbone torsion angles. The polypeptides under study folded mainly to produce α-helical structures. A structure of two contacting α-helices that were approximately equal in length and had a loop between them was observed for a longer chain of 150 residues. A method to visualize the correlation matrix of the dihedral angles of a polypeptide chain was developed for analyzing the effects of the dynamic correlation of conformational degrees of freedom. The analysis of the dynamics of the correlation matrix showed that rotations involving angles of the same type (φ–φ and ψ–ψ) occur predominantly in one direction. Rotations invoving different angles (φ–ψ) occur predominantly in opposite directions, so that the total macromolecule does not rotate. A significant reduction in the effective viscosity of the medium disrupts the correlation and makes the rotations stochastic, thus distorting the formation of the regular (helical) structure. The effects of correlated conformational motions are consequences of viscous friction forces. This conclusion agrees with our previous results that outlined the principle of the minimum rate of energy dissipation and the equipartition of energy dissipation rate between conformational degrees of freedom.     

Tunnelling of electrons in biological processes

A new mechanism of energy conversion in biological systems (particularly for phosphorylation on intracellular membranes) is proposed. This mechanism involves electron tunnelling accompanied by relaxation type conformational changes in enzyme macromolecules. The membrane potential may be considered as a regulator of this process.Electron tunnelling is the most important mechanism of electron transfer between electron carriers in electron transport chains of chloroplasts and mitochondria. The requirements of energy balance are met due to excitation or changing of the normal vibrations of carriers or molecules in the medium.     

Dynamics of electron-conformational transitions in proteins and physical mechanisms of biomacromolecule function]

The proteins can be considered as a microheterogeneous structured media possessing memory and feedback properties. The conformational energy surface depends on the chemical states of protein groups. Conformational motions are local diffusion with relaxation times much longer than vibrational relaxation times in condensed media. Owing to the hierarchy of relaxation times chemical reaction rates depend on conformation parametrically. Regulation of functional activity by conformational mobility is accomplished via transmission of information in the form of changes in the distribution functions of separate groups along the conformational substates. The interpretation of drastic effects on conformational mobility needs super-stochastic approaches. A possible mechanism of sharp conformational change are discussed in terms of the catastrophe theory.     

Solution conformation and dynamics of a fungal cell wall polysaccharide isolated from Microsporum gypseum

The conformational and dynamical features of a branched mannan isolated from a fungal cell wall have been analysed by homo and heteronuclear NMR methods, employing different magnetic fields. 1HNMR cross relaxation times have been obtained for this polysaccharide and have been interpreted qualitatively using different motional models. 13C NMR relaxation parameters (T1, T2, NOE) have also been measured and interpreted using different approximations based on the Lipari and Szabo model free approach. The analysis of the data indicate the existence of important flexibility for the different linkages of the polysaccharide. Motions in the range of 4–6 ns contribute to the relaxation of the macromolecule, although faster internal motions in the 500 ps and 100 ps timescales are also present. These time scales indicate that segmental motions as well as internal motions around the glycosidic linkages are the major sources of relaxation for this molecule at 318 K. Molecular dynamics simulations have also been performed. The obtained results also indicate that the polysaccharide possess a substantial amount of conformational freedom.     

Effects of Molecular Crowding on the Dynamics of Intrinsically Disordered Proteins

Inside cells, the concentration of macromolecules can reach up to 400 g/L. In such crowded environments, proteins are expected to behave differently than in vitro. It has been shown that the stability and the folding rate of a globular protein can be altered by the excluded volume effect produced by a high density of macromolecules. However, macromolecular crowding effects on intrinsically disordered proteins (IDPs) are less explored. These proteins can be extremely dynamic and potentially sample a wide ensemble of conformations under non-denaturing conditions. The dynamic properties of IDPs are intimately related to the timescale of conformational exchange within the ensemble, which govern target recognition and how these proteins function. In this work, we investigated the macromolecular crowding effects on the dynamics of several IDPs by measuring the NMR spin relaxation parameters of three disordered proteins (ProTα, TC1, and α-synuclein) with different extents of residual structures. To aid the interpretation of experimental results, we also performed an MD simulation of ProTα. Based on the MD analysis, a simple model to correlate the observed changes in relaxation rates to the alteration in protein motions under crowding conditions was proposed. Our results show that 1) IDPs remain at least partially disordered despite the presence of high concentration of other macromolecules, 2) the crowded environment has differential effects on the conformational propensity of distinct regions of an IDP, which may lead to selective stabilization of certain target-binding motifs, and 3) the segmental motions of IDPs on the nanosecond timescale are retained under crowded conditions. These findings strongly suggest that IDPs function as dynamic structural ensembles in cellular environments.     

The Topology of the Energy Landscapes of Macromolecules in the Torsion Angle Space and the Principle of the Minimum Energy Dissipation Rate in Conformational Relaxation

This article discusses some basic problems of structural biology and molecular dynamics simulation methods that need to be taken into account when considering, the protein folding problem, and prediction of 3D-structures for biopolymers. A multidimensional Fourier series expansions were formulated for the energy landscapes of the systems with conformational mobility, These energy landscape representations are correct from the viewpoint of the topology of the macromolecule configuration spaces. The problem of the single global minimum on the energy landscape for proteins is discussed and is formulated in tems of phase rules for the component of Fourier expansions. This rule is formally similar to the problem of diffraction on a multidimensional cubic lattice. The calibration of biopolymer force fields and their correspondence to topologically correct energy landscapes are discussed. Equations of motion were obtained in a matrix form for the relaxation of a representative point position on a multidimensional potential energy surface. The solutions of the equations for conformational relaxation were shown to obey the principle of the minimum energy dissipation rate at a given relaxation rate of potential energy (or folding rate).     

Molecular dynamics of oligopeptides 6. A comparative study of poincare cross-section of monopeptide frames in media with different hydrophobicity

A comparative study of the molecular dynamics of natural amino acid residues and their closest homologues and isomers was carried out. Molecular dynamics protocols not interfering with the principle of equidistribution of energy with respect to degrees of freedom were used. Poincare cross-sections, auto- and cross-correlation of complex exponential curves as a function of dihedrons were considered. The classification of dynamic properties of conformational degrees of freedom in the series of amino acid residues was carried out.     

Conformational analysis and molecular dynamics simulations of maltose

Constrained conformational energy minimizations have been used to calculate an adiabatic (Φ, ψ) potential energy surface for the disaccharide β-maltose. The inclusion of molecular flexibility in the conformational energy analysis of the disaccharide was found to significantly lower the barriers to conformational transitions, as has been observed previously for other systems. Several low energy wells were identified on the adiabatic surface which differ in energy by small amounts and with low absolute barriers separating them, indicating the possibility of a non-negligible equilibrium population distribution in each well. If such a distribution of conformations existed in the physical system, the conformation observed by NMR NOE measurements would thus be a “virtual” conformation. Molecular dynamics simulations of the motions of this molecule in vacuum were also conducted and indicate that the rate of relaxation of the molecule to the adiabatic surface may be slower than the typical timescale of conformational fluctuations. This effect is apparently due to an unphysical persistence of hydrogen bond patterns in vacuum which does not occur in aqueous solution. Trajectories undergoing transitions between wells were calculated and the effects of such conformational transitions upon the ensemble mean structure, such as might be observed in an NMR experiment, were demonstrated.     

Conformational relaxation in hemoproteins: the cytochrome P-450cam case

Photodissociation of (CO)P-450(cam)(substrate) complexes was found to trigger a conformational relaxation process that interferes with ligand rebinding at temperatures as low as 140 K even though the protein conformational substates (CS(1)) remain frozen. To analyze the rebinding and relaxation kinetics, we developed a model that takes the distribution of relaxation rates explicitly into account and in which rebinding and relaxation rates are connected by a linear free energy relation. In all complexes heme relaxation occurs first and is probably faster than 100 ns even at 77 K. This is the only process found in substrate-free P-450(cam). Above 140 K and in the presence of a substrate, this initial, fast rebinding state (P) progressively relaxes to another state (P degrees ) in which rebinding is slower. The relaxation rate is independent of solvent rigidity and is governed by the protein's internal dynamics. Rebinding enthalpies in P and P degrees as well as the enthalpy shift brought about by relaxation correlate with the substrate propensity to block access to the iron site. In P degrees the barrier is higher because the substrate is closer to the heme normal and exerts more steric repulsion for CO binding. The relaxation process implies the return of substrate and heme to their ligand-free positions in which access to the heme is reduced.     

A model of the mechanism of enzyme action in terms of protein conformational relaxation

A theoretical model of enzymatic reaction is formulated in which the modulation of the reaction coordinates by low-frequency conformational motions of the enzyme molecule causes the lowering of the activation energy barriers until they completely disappear. If the rates of electron transitions in the enzyme-substrate complex exceed the characteristic frequencies of conformational motions then the rate of the elementary enzymatic reaction shows hysteresis dependence on temperature and substrate concentration.     

Triple Quantum Decoherence under Multiple Refocusing: Slow Correlated Chemical Shift Modulations of C′ and N Nuclei in Proteins

A new experiment allows the identification of residues that feature slow conformational exchange in macromolecules. Rotations about dihedral angles that are slower than the global correlation time tau(c) cause a modulation of the isotropic chemical shifts of the nuclei. If these fluctuations are correlated they induce a differential line broadening between three-spin single-quantum and triple-quantum coherences involving three nuclei such as the carbonyl C', the neighbouring amide nitrogen N and the amide proton H(N) belonging to a pair of consecutive amino acids. A cross-correlated relaxation rate R (CS/CS)(C'N) can be determined that corresponds to the sum of the isotropic and anisotropic contributions to the chemical shift modulations of the carbonyl carbon and nitrogen nuclei. Only the isotropic contributions depend on the pulse repetition rate of a multiple-refocusing sequence. An attenuation of the relaxation rate with increasing pulse repetition rate can therefore be attributed to slow motions. The asparagine N25 residue of ubiquitin, located in the first alpha-helix, is shown to feature significant slow conformational exchange.     

Internal motions in B- and Z-form poly(dG-dC).poly(dG-dC): 1H NMR relaxation studies

Proton NMR relaxation measurements are used to compare the molecular dynamics of 60 base pair duplexes of B- and Z-form poly(dG-dC).poly(dG-dC). The relaxation rates of the exchangeable guanine imino protons (Gim) in H2O and in 90% D2O show that below 20 degrees C spin-lattice relaxation is exclusively from proton-proton magnetic dipolar interactions while proton-nitrogen interactions contribute about 30% to the spin-spin relaxation. The observation that the spin-lattice relaxation is nonexponential and that the initial spin-lattice relaxation rate of the Gim, G-H8 and C-H6 protons depends on the selectivity of the exciting pulse shows that spin-diffusion dominates the spin-lattice relaxation. The relaxation rates of the Gim, C-H5, and C-H6 in B- and Z-form poly(dG-dC).poly(dG-dC) cannot be explained by assuming the DNA behaves as a rigid rod. The data can be fit by assuming large-amplitude out of plane motions (+/- 30-40 degrees, tau = 1-100 ns) and fast, large-amplitude local torsional motions (+/- 25-90 degrees, tau = 0.1-1.5 ns) in addition to collective torsional motions. The results for the B and Z forms show that the rapid internal motions are similar and large in both conformations although backbone motions are slightly slower, or of lower amplitude, in Z DNA. At high temperatures (greater than 60 degrees C), imino proton exchange with solvent dominates the spin-lattice relaxation of B-form poly(dG-dC).poly(dG-dC), but in the Z form no exchange contribution (less than 2 s-1) is observed at temperatures as high as 85 degrees C. Conformational fluctuations that expose the imino protons to the solvent are strikingly different in the B and Z forms. The results obtained here are compared with those previously reported for poly(dA-dT).poly(dA-dT).     

Light-induced protein-matrix uncoupling and protein relaxation in dry samples of trehalose-coated MbCO at room temperature

In humid samples of trehalose-coated carboxy-myoglobin (MbCO), thermally driven conformational relaxation takes place after photodissociation of the carbon monoxide (CO) molecule at room temperature. In such samples, because of the extreme viscosity of the external matrix, photodissociated CO cannot diffuse out of the protein and explores the whole (proximal and distal side) heme pocket, experiencing averaged protein heme pocket structures, as a results of the presence of Brownian motions. At variance, in very dry samples, a lower portion of the photodissociated CO diffuses from the distal to the proximal heme pocket side probing in nonaveraged structures. We revisit here the flash photolysis data by Librizzi et al. (2002) and report on new, room temperature experiments in MbCO-trehalose samples, shortly illuminated prior the laser pulse. In dry samples, pre-illumination increased the diffusion of CO from the distal to the proximal heme pocket side, which resulted in less structure than in non-pre-illuminated samples. Such an effect, which is absent in humid samples, stems from a decoupling of the protein internal degrees of freedom from those of the external water-sugar matrix. We suggest that such a decoupling can be brought about by the continuous attempts performed by the protein during pre-illumination to undergo relaxation toward the photodissociated deoxy state. This, in turn, causes a collapse in the hydrogen bond network, which connects the protein surface to the water-sugar matrix, as reported by Cottone et al. (2002) and Giuffrida et al. (2003). In the conclusion section, we discuss the possible involvement of the processes invoked to rationalize the present data, in the function of macromolecules and interactions in living cells.     

Magnetic relaxation analysis of dynamic processes in macromolecules in the pico- to microsecond range.

A formalism based on the theory of Markov processes and suitable for the analysis of multiple internal motions in macromolecules is presented. Computer calculations of specific motional models for (13)C nuclear magnetic resonance (NMR) relaxation, treated as special cases of the proposed formalism, demonstrate the potential of this approach for discriminating between different motional models on the basis of NMR relaxation data.     

Time-dependent rotational rates of excited fluorophores. A linkage between fluorescence depolarization and solvent relaxation

It is generally assumed that the rotational diffusion coefficients of fluorophores are independent of time subsequent to excitation, and that the rotational diffusion coefficients of the ground and the excited states are the same. We now describe a linkage between the extent of solvent relaxation and the rate of fluorescence depolarization. Specifically, if a fluorophore displays time-dependent solvent relaxation it may also show a time-dependent decrease in its rotational rate. A decreased rate of rotation could result from the increased interaction with polar solvent molecules which occurs as a result of solvent relaxation. The decays of anisotropy predicted from our model closely mimic those often observed for fluorophores which are bound to macromolecules. For example, the decays are more complex than a single exponential, and the time-resolved anisotropy can display a limiting value which does not decay to zero. The effect of solvent relaxation upon the rates of rotational diffusion is expected to be most dramatic for solvent-sensitive fluorophores in a viscous environment. These conditions are frequently encountered for fluorophore-macromolecule complexes. Consideration of the linkage between solvent relaxation and rotational diffusion leads to two unusual predictions. First even spherical fluorophores in an isotropic environment could display multi- or nonexponential decays of fluorescence anisotropy. Secondly, for the special case in which the fluorophore dipole moment decreases upon excitation, the theory predicts that the anisotropy decay rate may increase with time subsequent to pulsed excitation. The predictions of this theory are consistent with published data on the effects of red-edge excitation upon the apparent rotational rates of fluorophores in polar solvents.