Do vibrational spectroscopies uniquely describe protein dynamics? The case for myoglobin

Vibrational Energy in Proteins Correlates with Topology

The exchange of vibrational energy in proteins is crucial for their function. Here, we establish a connection between quantities related to it with geometry-based properties such as the proteins' residues coordination number. This relation is proven by molecular simulation in a neuro-pharmacologically relevant transmembrane receptor. The connection demonstrated here paves the way to studies of protein allostery and conformational changes based solely on protein structure.

Hydration, slaving and protein function

Protein dynamics is crucial for protein function. Proteins in living systems are not isolated, but operate in networks and in a carefully regulated environment. Understanding the external control of protein dynamics is consequently important. Hydration and solvent viscosity are among the salient properties of the environment. Dehydrated proteins and proteins in a rigid environment do not function properly. It is consequently important to understand the effect of hydration and solvent viscosity in detail. We discuss experiments that separate the two effects. These experiments have predominantly been performed with wild-type horse and sperm whale myoglobin, using the binding of carbon monoxide over a broad range of temperatures as a tool. The experiments demonstrate that data taken only in the physiological temperature range are not sufficient to understand the effect of hydration and solvent on protein relaxation and function. While the actual data come from myoglobin, it is expected that the results apply to most or all globular proteins.

Thermal excitations of hydrated macromolecules: the effects of hydration on the Mössbauer absorption and scattering spectra

The spectra of Rayleigh scattering of Mössbauer radiation (RSMR) and Mössbauer absorption by globular macromolecules are calculated. The dependence of the spectra parameters on hydration is modeled with the account for thermal low-frequency vibrations of the particles constituting the globule. Deformational motions of the macromolecule fragments leading to deviations from its equilibrium spherical shape are considered introducing collective dynamical variables governed by Langevin equations with random sources of external forces. The macromolecule is modeled by a double-layered sphere: a rigid (elastic) core is surrounded by a porous hydration shell filled with fluid. The dynamical properties of the bound water inside the shell are described by the Debye-Brinkman equations. The degree of hydration is introduced by means of a combination of the mass coefficients of the porous shell with fluid and the mass coefficients in the limiting cases when the flow inside the shell is "frozen" and in the case of free flow. The hydration-dependent Lamb-Mössbauer factor and the elastic fraction of the RSMR are calculated and compared with experimental data from the literature.

Structural fluctuations of myoglobin from normal-modes, Mössbauer, Raman, and absorption spectroscopy

A normal-mode analysis of carbon monoxymyoglobin (MbCO) and deoxymyoglobin (Mb) with 170 water molecules is performed for (54)Fe and (57)Fe. A projection is defined that extracts iron out-of-plane vibrational modes and is used to calculate spectra that can be compared with those from resonance Raman scattering. The calculated spectra and the isotopic shift (57)Fe versus (54)Fe agree with the experimental data. At low temperatures the average mean square fluctuations (MSFs) of the protein backbone atoms agree with molecular dynamics simulation. Below 180 K the MSFs of the heme iron agree with the data from Mossbauer spectroscopy. The MSFs of the iron atom relative to the heme are an order of magnitude smaller than the total MSFs of the iron atom. They agree with the data from optical absorption spectroscopy. Thus the MSFs of the iron atom as measured by Mossbauer spectroscopy can be used to probe the overall motion of the heme within the protein matrix, whereas the Gaussian thermal line broadening of the Soret band and the resonance Raman bands can be used to detect local intramolecular iron-porphyrin motions.

Dynamics of protein relaxation in site-specific mutants of human myoglobin

We have recently reported spectroscopic evidence for structural relaxation of myoglobin (Mb) following photodissociation of MbCO [Lambright, D. G., Balasubramanian, S., & Boxer, S. G. (1991) Chem. Phys. 158, 249-260]. In this paper we report measurements for a series of single amino acid mutants of human myoglobin on the distal side of the heme pocket (positions 45, 64, and 68) in order to examine specific structural determinants involved in this conformational relaxation and to determine the nature of the coupling between relaxation and the functional process of ligand binding. The kinetics of ligand binding and conformational relaxation were monitored by transient absorption spectroscopy in the Soret spectral region, and the results are analyzed using a four-state ligand binding model. Two principal results emerge: (1) amino acid substitutions in the distal heme pocket affect the kinetics of the nonequilibrium conformational relaxation and (2) the rate of ligand escape from the protein matrix is not significantly perturbed by the distal heme pocket mutations.

Fractal analysis of photolysis of nitrosyl haemoglobin at low temperatures

Photolysis of nitrosyl haemoglobin (HbNO) has been studied from 5.9 K to 20 K for R, T and RT conformations. It was observed that the experimental curves have two different behaviours at a given temperature in a particular conformation. At shorter time scales the data are well reproduced by a model based on fractal concepts, where the relevant parameter is the difference between the fractal dimension and the fraction. For simplicity at longer time scales a simple exponential was used to fit the curves.

The low-temperature heat capacity of solid proteins

Several harmonic models of protein fluctuations are used to calculate the heat capacity. They get the spectral density of conformational modes from inelastic neutron scattering, normal mode calculations, or macroscopic elasticity (Debye model). It is assumed that the low-frequency spectral density depends only weakly on temperature and protein species. The Debye model predicts temperatures below which modes are primarily in their ground states: 10 and 80 K for the lattice and conformational modes, respectively. The models differ most below 100 K. The mode calculations yield the most accurate predictions, though all three models are within twofold of the data. The heat capacity has the power law form aTb for T less than 30 K. The experimental b's of proteins are 1.6-1.8, and the theoretical, 1.1-1.3. One possible explanation for the discrepancy is the occurrence of transitions between discrete conformations. All of the models approach the measured data in the range 100-200 K. They are very similar above 200 K, where the heat capacity includes significant contributions from bond stretching and bending. This masks the possible anharmonic behavior of the conformational modes. Hydration substantially increases the heat capacity above 200 K. This effect seems to be a consequence of conformational transitions that have higher energy than the ones seen with low hydration. The analysis also predicts that denaturation with constant hydration produces a negligible increase of heat capacity. The larger increment in solution arises from the different hydration of the folded and unfolded states, and is responsible for the existence of cold denaturation. This phenomenon is thus predicted not to occur when the hydration is constant.

Protein dynamics: comparison of simulations with inelastic neutron scattering experiments

To deepen our understanding of the principles determining the folding and functioning of globular proteins the determination of their three-dimensional structures must be supplemented with the characterization of their internal motions. Although dynamical events in proteins occur on time-scale ranging from femtoseconds to at least seconds, the physical properties of globular proteins are such that picosecond (ps) time-scale motions make a particularly important contribution to the internal fluctuations of the atoms from their mean positions.

Possible mechanism for the influence of weak magnetic fields on biological systems

A physical mechanism is suggested for a resonant interaction of weak magnetic fields with biological systems. An ion inside a Ca(2+)-binding protein is approximated by a charged oscillator. A shift in the probability of ion transition between different vibrational energy levels occurs when a combination of static and alternating magnetic fields is applied. This in turn affects the interaction of the ion with the surrounding ligands. The effect reaches its maximum when the frequency of the alternating field is equal to the cyclotron frequency of this ion or to some of its harmonics or sub-harmonics. A resonant response of the biosystem to the magnetic field results. The proposed theory permits a quantitative explanation for the main characteristics of experimentally observed effects.

Temperature dependence of the structure and dynamics of myoglobin. A simulation approach

The results of simulations of the structure and internal motions of carbonomonoxymyoglobin (MbCO) at two different temperatures (325 and 80 K) are presented and compared with experimental data. Properties calculated from the 120 ps trajectory at 325 K are used as a reference in the analysis of the motion of the protein at 80 K. Three separate 80 K molecular dynamics trajectories were calculated; they were started with different coordinate sets from the 325 K simulation and the lower temperature was achieved by scaling the velocities. The simulations yield results for the structural changes between 325 and 80 K that are in general accord with those from X-ray data. Both the experimental and calculated radii of gyration, distances from the center of mass and main-chain difference distance matrices show that there is a significant but inhomogeneous shrinkage with decreasing temperature. For the atomic fluctuations, by contrast, the calculated temperature dependence is very different from the X-ray results; i.e. the calculated root-mean-square backbone fluctuations decrease to 0.11 A at 80 K from 0.51 A at 325 K, while the fluctuations obtained from the X-ray B factors go from 0.56 A at 260 K to 0.47 A at 80 K. The smaller temperature dependence of the B factors suggests that there is significant conformational disorder in MbCO crystals at lower temperatures. This is in accord with the simulation results, which show that the protein is trapped in restricted regions of conformational space at 80 K, while at 325 K a much larger region is accessible to the protein. Analysis of the fluctuations at 325 K and 80 K shows that the room temperature flexibility of the protein is determined by the mobility of the loop regions and by side-chain torsional motions (in accord with earlier simulation results), while the low temperature fluctuations involve motion within a single well. Examination of the calculated iron atom fluctuations and comparison with Mossbauer data show good agreement. It is found that the dominant contribution to the iron motion arises from heme sliding; motion of the iron relative to the heme are much smaller.

On the mechanism of ligand binding to myoglobin. The role of structural fluctuations

The association reaction of CO and O2 with heme is expected to reflect the differences in the electronic structures of the two ligands. CO binding should be controlled by a high spin/low spin transition while oxygen binding is spin-allowed. Dioxygen should thus bind substantially faster than CO. The experimental association rates of the two ligands are, however, almost identical. We propose that the reaction is triggered in both cases by a fast structural intermediate which allows the CO molecule to bind adiabatically. A suitable structural transition has been identified recently by inelastic neutron scattering.

Analysis of fractal ion channel gating kinetics: kinetic rates, energy levels, and activation energies

Ion channels in the cell membranes of the corneal endothelium, hippocampal neurons, and fibroblasts, and gramicidin channels in lipid bilayers have open and closed times that can be fit, in whole or part, by power law distributions. That is, the gating is self-similar when viewed at different time scales. Hence, kinetic processes at slow and fast time scales are not independent but rather are interrelated. To study how such a relationship can arise we analyze a closed in equilibrium open channel with the fractal dimension for leaving the closed state DCO approximately 2 and the fractal dimension for leaving the open state DOC approximately 1. This special case can be analyzed because it can be represented by equivalent Markov processes. We show that it is equivalent to Markov chains with forward and backward kinetic rate constants approximately equal at each stage, and forming an approximate geometric progression along the different stages. These kinetic rates determine the energy levels and activation energy barriers separating those levels. We find that there are many conformational states (substates) separated by high activation energy barriers. This is similar to the energy structure found for globular proteins such as myoglobin. However, the novel feature reported here is that the activation energy barriers are not independent but are interrelated and form an arithmetic progression. Because of this relationship the fast processes across the low activation energy barriers are linked to slow processes across the high activation energy barriers.

Quantum and classical dynamics in biochemical reactions

The classic experiment of deVault and Chance touched off a long series of theoretical and experimental studies of the interplay between quantum and classical dynamics in photosynthetic electron transfer. More recently these issues have also been addressed in experiments on ligand binding reactions in heme proteins and through the study of kinetic isotope effects in enzymatic proton transfer. Theoretical effort has focused on a class of relatively simple models which display a surprisingly rich spectrum of dynamical behavior. Much less attention has been paid to a very important issue: Why are we allowed to use such simple models to describe such obviously complex molecules? Here we provide some tentative answers to this question, contrasting the cases of electron and proton transfer. We suggest that ideas based on simple models can inspire novel strategies for 'realistic' simulations, and that we can begin to think about the general problems of enzymatic catalysis in terms of dynamical pictures that previously have been applied only to the simpler case of electron transfer.

Energy distributions at the high-spin ferric sites in myoglobin crystals

The orientation and temperature dependence (4.2-2.5 K) of electron paramagnetic resonance (EPR) power saturation and spin-lattice relaxation rate, and the orientation dependence of signal linewidth, were measured in single crystals of the aquo complex of ferric sperm whale skeletal muscle myoglobin. The spin-packet linewidth was found to be temperature independent and to vary by a factor of seven within the heme plane. An analysis is presented which enables one to arrive at (a) hyperfine component line-widths and, from the in-plane angular variation of the latter, at (b) the widths of distributions in energy differences between low-lying electronic levels and (c) the angular spread in the in-plane principal g-directions. The values of the energy level distributions in crystals obtained from the measurements and analysis reported here are compared with those obtained by a different method for the same protein complex in frozen solution. The spread in the rhombic energy splitting is significantly greater in solution than in the crystal.

Linkage of functional and structural heterogeneity in proteins: dynamic hole burning in carboxymyoglobin

Inhomogeneous broadening of the 760-nanometer photoproduct band of carboxymyoglobin at cryogenic temperatures has been demonstrated with a dynamic hole burning technique. Line-shape changes and frequency shifts in this spectral band are generated by ligand recombination and are shown not to be the result of structural relaxation below 60 K. The observation of dynamic hole burning exposes the relation between the structural disorder responsible for the inhomogeneous broadening and the well-known distributed ligand rebinding kinetics. The findings provide direct evidence for the functional relevance of conformational substrates in myoglobin rebinding. In addition, a general protocol for evaluating the relative contributions of structural relaxation and hole burning to the spectral changes accompanying rebinding in hemeproteins is presented.

A structural and dynamic model for the nicotinic acetylcholine receptor

Folding of the five polypeptide subunits (alpha 2 beta gamma delta) of the nicotinic acetylcholine receptor (AChR) into a functional structural model is described. The principles used to arrange the sequences into a structure include: (1) hydrophobicity----membrane-crossing segments; (2) amphipathic character----ion-carrying segments (ion channel with single group rotations); (3) molecular shape (elongated, pentagonal cylinder)----folding dimensions of exobilayer portion; (4) choice of acetylcholine binding sites----specific folding of exobilayer segments; (5) location of reducible disulfides (near agonist binding site)----additional specification of exobilayer arrangement; (6) genetic homology----consistency of functional group choices; (7) noncompetitive antagonist labeling----arrangement of bilayer helices. The AChR model is divided into three parts: (a) exobilayer consisting of 11 antiparallel beta-strands from each subunit; (b) bilayer consisting of four hydrophobic and one amphiphilic alpha-helix from each subunit; (c) cytoplasmic consisting of one (folded) loop from each subunit. The exobilayer strands can form a closed 'flower' (the 'resting state') which is opened ('activated') by agonists bound perpendicular to the strands. Rearrangement of the agonists to a strand-parallel position and partial closing of the 'flower' leads to a desensitized receptor. The actions of acetylcholine and succinoyl and suberoyl bis-cholines are clarified by the model. The opening and closing of the exobilayer 'flower' controls access to the ion channel which is composed of the five amphiphilic bilayer helices. A molecular mechanism for ion flow in the channel is given. Openings interrupted by short duration closings (50 microseconds) depend upon channel group motions. The unusual photolabeling of intrabilayer serines in alpha, beta and delta subunits but not in gamma subunits near the binding site for non-competitive antagonists is explained along with a mechanism for the action of these antagonists such as phencyclidine. The unusual alpha 192Cys-193Cys disulfide may have a special peptide arrangement, such as a cis-peptide bond to a following proline (G.A. Petsko and E.M. Kosower, unpublished results). The position of phosphorylatable sites and proline-rich segments are noted for the cytoplasmic loops. The dynamic behavior of the AChR channel and many different experimental results can be interpreted in terms of the model. An example is the lowering of ionic conductivity on substitution of bovine for Torpedo delta M2 segment. The model represents a useful construct for the design of experiments on AChR.

Influence of specific contacts on the stability and structure of proteins. Theory for the perturbation of a harmonic system

The question of how specific contacts within a protein influence its stability and structure is examined within a formal theoretical framework. A mathematical model is developed in which the potential energy of a protein is taken as a harmonic expansion of all of its internal or normal coordinates. With classical statistical mechanics the properties of the system can be derived from this potential energy function. A few new contacts are then introduced as additional energy terms, each having a quadratic dependence on a single internal coordinate. These terms are added as perturbations to the original potential energy, and the attendant changes in the properties of the system are obtained. Exact expressions can be derived for changes in the enthalpy, entropy, and for any arbitrary internal degree of freedom. These quantities are expressed in terms of the parameters of the potential energy functions of the new contacts, and the mean square displacements and positional correlation functions of the internal coordinates. These results provide qualitative insights into the role of contacts in stabilizing a particular conformation. Estimates are given for the entropy of formation of a hydrogen bond in a protein. A criterion is proposed for determining whether a contact is essential to the stability of a protein conformation. This model may be applicable to many experimental systems in which mutant or modified proteins are available that differ by one or a few amino acids. The results may also be useful in thermodynamic analyses of computer simulations.

Multiple conformational states of proteins: a molecular dynamics analysis of myoglobin

A molecular dynamics simulation of myoglobin provides the first direct demonstration that the potential energy surface of a protein is characterized by a large number of thermally accessible minima in the neighborhood of the native structure (for example, approximately 2000 minima were sampled in a 300-picosecond trajectory). This is expected to have important consequences for the interpretation of the activity of transport proteins and enzymes. Different minima correspond to changes in the relative orientation of the helices coupled with side-chain rearrangements that preserve the close packing of the protein interior. The conformational space sampled by the simulation is similar to that found in the evolutionary development of the globins. Glasslike behavior is expected at low temperatures. The minima obtained from the trajectory do not satisfy certain criteria for ultrametricity.