Site-selective heat current analysis of α-helical protein with linear-homopolymer-like model.

Although thermal transport is among the essential biophysical properties of proteins, its relationship with protein structures, dynamics, and functions is still elusive. The structures of folded proteins are highly inhomogeneous, giving rise to an anisotropic and non-uniform flow of thermal energy during conformational fluctuations. To illustrate the nature of proteins, we developed a theoretical framework for analyzing local thermal transport properties based on the autocorrelation function formalism, constructed a linear-homopolymer-like model, and applied it to a small α-helical protein, the villin headpiece subdomain (HP36), using equilibrium molecular dynamics simulations. As a result, the model reproduced the exact value of the protein's thermal conductivity with an error of less than 1%. Interestingly, the site-selective analysis of the local, residue-wise, thermal conductivity demonstrated its distinct residue-type dependence, i.e., its magnitude decreased in the order of charged, polar, and hydrophobic residues. In addition, the local density dependence of the residue-wise thermal transport property was also discussed.

Computational Study on the Thermal Conductivity of a Protein.

Protein molecules are thermally fluctuating and tightly packed amino acid residues strongly interact with each other. Such interactions are characterized in terms of heat current at the atomic level. We calculated the thermal conductivity of a small globular protein, villin headpiece subdomain, based on the linear response theory using equilibrium molecular dynamics simulation. The value of its thermal conductivity was 0.3 ± 0.01 [W m-1 K-1], which is in good agreement with experimental and computational studies on the other proteins in the literature. Heat current along the main chain was dominated by local vibrations in the polypeptide bonds, with amide I, II, III, and A bands on the Fourier transform of the heat current autocorrelation function.

Energy Transfer across Nonpolar and Polar Contacts in Proteins: Role of Contact Fluctuations.

Molecular dynamics simulations of the villin headpiece subdomain HP36 have been carried out to examine relations between rates of vibrational energy transfer across non-covalently bonded contacts and equilibrium structural fluctuations, with focus on van der Waals contacts. Rates of energy transfer across van der Waals contacts vary inversely with the variance of the contact length, with the same constant of proportionality for all nonpolar contacts of HP36. A similar relation is observed for hydrogen bonds, but the proportionality depends on contact pairs, with hydrogen bonds stabilizing the α-helices all exhibiting the same constant of proportionality, one that is distinct from those computed for other polar contacts. Rates of energy transfer across van der Waals contacts are found to be up to 2 orders of magnitude smaller than rates of energy transfer across polar contacts.

Recent developments in the computational study of protein structural and vibrational energy dynamics.

Recent developments in the computational study of energy transport in proteins are reviewed, including advances in both methodology and applications. The concept of energy exchange network (EEN) is discussed, and a recent calculation of EENs for the allosteric protein FixL is reviewed, which illustrates how residues and protein regions involved in the allosteric transition can be identified. Recent work has examined relations between EENs and protein dynamics as well as structure. We review some of the computational studies carried out on several proteins that explore connections between energy conductivity across polar contacts in proteins and between proteins and water and equilibrium dynamics of the contacts, and we discuss some of the recent experimental work that addresses this topic.

Variation of Energy Transfer Rates across Protein-Water Contacts with Equilibrium Structural Fluctuations of a Homodimeric Hemoglobin.

Molecular dynamics simulations of the homodimeric hemoglobin from Scapharca inaequivalvis (HbI) have been carried out to examine relations between rates of vibrational energy transfer across nonbonded contacts and equilibrium structural fluctuations, with emphasis on protein-water contacts. The scaling of rates of energy transfer with equilibrium fluctuations of the contact length is found to hold up well for contacts between residues and hemes at the interface and the cluster of 17 interface water molecules in the unliganded state of HbI, as well as for the liganded state, for which the cluster contains on average 11 water molecules. In both states, the rate of energy transfer is also found to satisfy a diffusion relation. Within each globule, the scaling for polar contacts is similar to that found in an earlier analysis of myoglobin. Entropy associated with dynamics of polar contacts within each globule and with contacts between the hemes and water cluster is found to increase upon ligation. Energy exchange networks (EENs) for liganded and unliganded states obtained from the simulations are also presented and discussed. Energy transport networks through which nonbonded contacts transport energy in HbI, referred to as nonbonded networks (NBNs), are determined from the EENs and compared for the two states.

Energy Exchange Network Model Demonstrates Protein Allosteric Transition: An Application to an Oxygen Sensor Protein.

The effects of ligand binding on an oxygen sensor protein, FixLH, were investigated by molecular dynamics simulation. To illustrate the network of residue interactions in the deoxy, oxy, and carbomonoxy states of FixLH, we employed the energy exchange network (EEN) model in which residue interactions were evaluated in terms of local transport coefficients of energy flow. As a result, the difference map of EEN between the deoxy and oxy (deoxy and carbomonooxy) states clearly demonstrated the allosteric transition, although the structural changes by ligand binding are small. It is known that the FixLH forms a homodimer in solution, although neither O2 nor CO binding exhibits cooperativity. Therefore, we conjectured that the primary event after ligand binding occurs essentially at the monomer level, and it is subsequently followed by quaternary structural changes. The difference EEN maps showed that two regions, (A) the junction between the coiled-coil linker and the sensor domain and (B) the potential dimer interface, experienced considerable change of the energy-transport coefficients, indicating that these two regions play important roles in quaternary structural changes and signal transduction in response to ligand binding.

Normal mode analysis and beyond.

Normal mode analysis provides a powerful tool in biophysical computations. Particularly, we shed light on its application to protein properties because they directly lead to biological functions. As a result of normal mode analysis, the protein motion is represented as a linear combination of mutually independent normal mode vectors. It has been widely accepted that the large amplitude motions throughout the entire protein molecule can be well described with a few low-frequency normal modes. Furthermore, it is possible to represent the effect of external perturbations, e.g., ligand binding, hydrostatic pressure, as the shifts of normal mode variables. Making use of this advantage, we are able to explore mechanical properties of proteins such as Young's modulus and compressibility. Within thermally fluctuating protein molecules under physiological conditions, tightly packed amino acid residues interact with each other through heat and energy exchanges. Since the structure and dynamics of protein molecules are highly anisotropic, the flow of energy and heat should also be anisotropic. Based on the harmonic approximation of the heat current operator, it is possible to analyze the communication map of a protein molecule. By using this method, the energy transfer pathways of photoactive yellow protein were calculated. It turned out that these pathways are similar to those obtained via the Green-Kubo formalism with equilibrium molecular dynamics simulations, indicating that normal mode analysis captures the intrinsic nature of the transport properties of proteins.

Scaling of Rates of Vibrational Energy Transfer in Proteins with Equilibrium Dynamics and Entropy.

Theoretical arguments and results of molecular dynamics (MD) simulations of myoglobin at 300 K are presented to relate rates of vibrational energy transfer across nonbonded contacts interacting via short-range potentials to dynamics of the contact. Both theory and the results of the simulations support a scaling relation between the energy transfer rate and the inverse of the variance in the distance between hydrogen-bonded contacts. The results of the MD simulations do not support such a relation for longer-range charged contacts. Instead, the energy transfer rate is found to scale as a power law in the distance between charged groups. The scaling between rates of vibrational energy transfer across nonbonded contacts interacting via short-range potentials and conformational dynamics suggests a relation between vibrational energy transfer rates and entropy associated with the dynamics of interacting residues. The use of time-resolved vibrational spectroscopy to determine change in conformational entropy with change in protein functional state is discussed, and an expression quantifying the connection is provided.

Electron Transfer Pathways of Cyclobutane Pyrimidine Dimer Photolyase Revisited.

The photoinduced electron transfer (ET) reaction of cyclobutane pyrimidine dimer (CPD) photolyase plays an essential role in its DNA repair reaction, and the molecular mechanism of the ET reaction has attracted a large number of experimental and theoretical studies. We investigated the quantum mechanical nature of their ET reactions, characterized by multiple ET pathways of the CPD photolyase derived from Anacystis nidulans. Using the generalized Mulliken-Hush (GMH) method and the bridge green function (GF) methods, we estimated the electronic coupling matrix element, TDA, to be 36 ± 30 cm-1 from the donor (FADH-) to the acceptor (CPD). The estimated ET time was 386 ps, in good agreement with the experimental value (250 ps) in the literature. Furthermore, we performed the molecular dynamics (MD) simulations and ab initio molecular orbital (MO) calculations, and explored the electron tunneling pathway. We examined 20 different structures during the MD trajectory and quantitatively evaluated the electron tunneling currents for each of them. As a result, we demonstrated that the ET route via Asn349 was the dominant pathway among the five major routes via (Adenine/Asn349), (Adenine/Glu283), (Adenine/Glu283/Asn349/Met353), (Met353/Asn349), and (Asn349), indicating that Asn349 is an essential amino acid residue in the ET reaction.

Forced Unfolding Mechanism of Bacteriorhodopsin as Revealed by Coarse-Grained Molecular Dynamics.

Developments in atomic force microscopy have opened up a new path toward single-molecular phenomena; in particular, during the process of pulling a membrane protein out of a lipid bilayer. However, the characteristic features of the force-distance (F-D) curve of a bacteriorhodopsin in purple membrane, for instance, have not yet been fully elucidated in terms of physicochemical principles. To address the issue, we performed a computer simulation of bacteriorhodopsin with, to our knowledge, a novel coarse-grained (C-G) model. Peptide planes are represented as rigid spheres, while the surrounding environment consisting of water solvents and lipid bilayers is represented as an implicit continuum. Force-field parameters were determined on the basis of auxiliary simulations and experimental values of transfer free energy of each amino acid from water to membrane. According to Popot's two-stage model, we separated molecular interactions involving membrane proteins into two parts: I) affinity of each amino acid to the membrane and intrahelical hydrogen bonding between main chain peptide bonds; and II) interhelix interactions. Then, only part I was incorporated into the C-G model because we assumed that the part plays a dominant role in the forced unfolding process. As a result, the C-G simulation has successfully reproduced the key features, including peak positions, of the experimental F-D curves in the literature, indicating that the peak positions are essentially determined by the residue-lipid and intrahelix interactions. Furthermore, we investigated the relationships between the energy barrier formation on the forced unfolding pathways and the force peaks of the F-D curves.

Energy exchange network of inter-residue interactions within a thermally fluctuating protein molecule: A computational study.

Protein function is regulated not only by the structure but also by physical dynamics and thermal fluctuations. We have developed the computer program, CURrent calculation for proteins (CURP), for the flow analysis of physical quantities within thermally fluctuating protein media. The CURP program was used to calculate the energy flow within the third PDZ domain of the neuronal protein PSD-95, and the results were used to illustrate the energy exchange network of inter-residue interactions based on atomistic molecular dynamics simulations. The removal of the α3 helix is known to decrease ligand affinity by 21-fold without changing the overall protein structure; nevertheless, we demonstrated that the helix constitutes an essential part of the network graph.

Ligand migration in myoglobin: a combined study of computer simulation and x-ray crystallography.

A ligand-migration mechanism of myoglobin was studied by a multidisciplinary approach that used x-ray crystallography and molecular dynamics simulation. The former revealed the structural changes of the protein along with the ligand migration, and the latter provided the statistical ensemble of protein conformations around the thermal average. We developed a novel computational method, homogeneous ensemble displacement, and generated the conformational ensemble of ligand-detached species from that of ligand-bound species. The thermally averaged ligand-protein interaction was illustrated in terms of the potential of mean force. Although the structural changes were small, the presence of the ligand molecule in the protein matrix significantly affected the 3D scalar field of the potential of mean force, in accordance with the self-opening model proposed in the previous x-ray study.

Nonneutral evolution of volume fluctuations in lysozymes revealed by normal-mode analysis of compressibility.

The evolution of structural fluctuations of proteins was examined by calculating the isothermal compressibility (ß(T)) values of chicken lysozyme and its six evolutionary mutants at Thr40, Ile55, and Ser91 (a ternary mutant corresponding to bobwhite lysozyme) from their X-ray structures by normal-mode analysis at 300 K. The ß(T) values of the two extant lysozymes from chicken and bobwhite were 1.61 and 1.59 Mbar(-1), respectively, but five other evolutionary mutants showed larger ß(T) values of up to 2.17 Mbar(-1). These results suggest that ancestral lysozymes exhibit larger volume fluctuations than extant ones, and hence that the molecular evolution of lysozymes has followed a nonneutral evolutionary pathway. The evolutionary mutants contained large amount of cavities, although no change was visible in the X-ray structures. There was a linear correlation between ß(T) and total cavity volume, predicting that the cavity volume or atomic packing is an important factor regulating volume fluctuations during the molecular evolution of this protein.

Molecular mechanism of long-range synergetic color tuning between multiple amino acid residues in conger rhodopsin.

The synergetic effects of multiple rhodopsin mutations on color tuning need to be completely elucidated. Systematic genetic studies and spectroscopy have demonstrated an interesting example of synergetic color tuning between two amino acid residues in conger rhodopsin's ancestral pigment (p501): -a double mutation at one nearby and one distant residue led to a significant λ(max) blue shift of 13 nm, whereas neither of the single mutations at these two sites led to meaningful shifts.To analyze the molecular mechanisms of this synergetic color tuning, we performed homology modeling, molecular simulations, and electronic state calculations. For the double mutant, N195A/A292S, in silico mutation analysis demonstrated conspicuous structural changes in the retinal chromophore, whereas that of the single mutant, A292S, was almost unchanged. Using statistical ensembles of QM/MM optimized structures, the excitation energy of retinal chromophore was evaluated for the three visual pigments. As a result, the λ(max) shift of double mutant (DM) from p501 was -8 nm, while that of single mutant (SM) from p501 was +1 nm. Molecular dynamics simulation for DM demonstrated frequent isomerization between 6-s-cis and 6-s-trans conformers. Unexpectedly, however, the two conformers exhibited almost identical excitation energy, whereas principal component analysis (PCA) identified the retinal-counterion cooperative change of BLA (bond length alternation) and retinal-counterion interaction lead to the shift.

Visualizing breathing motion of internal cavities in concert with ligand migration in myoglobin.

Proteins harbor a number of cavities of relatively small volume. Although these packing defects are associated with the thermodynamic instability of the proteins, the cavities also play specific roles in controlling protein functions, e.g., ligand migration and binding. This issue has been extensively studied in a well-known protein, myoglobin (Mb). Mb reversibly binds gas ligands at the heme site buried in the protein matrix and possesses several internal cavities in which ligand molecules can reside. It is still an open question as to how a ligand finds its migration pathways between the internal cavities. Here, we report on the dynamic and sequential structural deformation of internal cavities during the ligand migration process in Mb. Our method, the continuous illumination of native carbonmonoxy Mb crystals with pulsed laser at cryogenic temperatures, has revealed that the migration of the CO molecule into each cavity induces structural changes of the amino acid residues around the cavity, which results in the expansion of the cavity with a breathing motion. The sequential motion of the ligand and the cavity suggests a self-opening mechanism of the ligand migration channel arising by induced fit, which is further supported by computational geometry analysis by the Delaunay tessellation method. This result suggests a crucial role of the breathing motion of internal cavities as a general mechanism of ligand migration in a protein matrix.

Theoretical modeling of the O-intermediate structure of bacteriorhodopsin.

Bacteriorhodopsin is a prototype of efficient molecular machinery functioning as a light-activated proton pump. Among the five distinct intermediates (K, L, M, N, and O) of the photocycle, there is less structural information on the later stages compared with the early intermediates. Here, we report the structural modeling of the O-intermediate for which the determination of experimental structure remains difficult. Hypothetical conformational change of the molecule from the light-adapted state to the O-intermediate state was simulated by gradually changing the protonation state of two residues. To achieve accurate molecular modeling, we carefully constructed a realistic system of the native purple membrane. The modeled structure of the O-intermediate has some implications about proton transfer in the later stages of the photocycle and the structural response of bacteriorhodopsin to the inner charge distribution.

Stress tensor analysis of the protein quake of photoactive yellow protein.

Immediately after photon absorption, the photoenergy is converted to local stress energy via the ultrafast photoisomerization reaction of the p-coumaric acid (pCA) chromophore in a small water-soluble blue light receptor, photoactive yellow protein (PYP), derived from the halophilic bacterium, Halorhodospira halophila. A series of conformational changes are then induced, which are intimately related with the relaxation process on the energy landscape of PYP. In order to understand the signaling function of PYP in atomic detail, the characterization of the physical mechanism of the protein quake of PYP is important, as is the atomic description of the series of conformational changes associated with the photocycle. Here, we report a theoretical/computational study for the analysis of the intramolecular stress tensor for the dark state and three intermediate states, pR, pB1 and pB2, of PYP. As a result, we found that the magnitude of the stress released during the change from the pR to the pB1 state is significantly large at the hydroxyl oxygen atom of Tyr42, suggesting that this atom is the focus of the protein quake of PYP. This is consistent with previous experimental observations.

Discrimination of class I cyclobutane pyrimidine dimer photolyase from blue light photoreceptors by single methionine residue.

DNA photolyase recognizes ultraviolet-damaged DNA and breaks improperly formed covalent bonds within the cyclobutane pyrimidine dimer by a light-activated electron transfer reaction between the flavin adenine dinucleotide, the electron donor, and cyclobutane pyrimidine dimer, the electron acceptor. Theoretical analysis of the electron-tunneling pathways of the DNA photolyase derived from Anacystis nidulans can reveal the active role of the protein environment in the electron transfer reaction. Here, we report the unexpectedly important role of the single methionine residue, Met-353, where busy trafficking of electron-tunneling currents is observed. The amino acid conservation pattern of Met-353 in the homologous sequences perfectly correlates with experimentally verified annotation as photolyases. The bioinformatics sequence analysis also suggests that the residue plays a pivotal role in biological function. Consistent findings from different disciplines of computational biology strongly suggest the pivotal role of Met-353 in the biological function of DNA photolyase.