Direct Observation of Vibrational Energy Flow in Cytochrome c

Significance of the Double Bond in the Acyl Chain of Cardiolipin Revealed by the Partial Unfolding Dynamics of Cytochrome c Using Femtosecond Transient Absorption Spectroscopy

Cytochrome c (Cyt c) released from the mitochondrion acts as a trigger for the onset of apoptosis in which a double bond of cardiolipin (CL) is oxidized upon interaction with Cyt c. To understand the interaction dynamics of Cyt c with the double bond of CL, CLs having acyl chains with a systematic increase in the number of double bonds, 0 (18:0 CL), 1 (18:1 CL), and 2 (18,2 CL), were complexed with Cyt c, and their excited-state dynamics were studied using femtosecond time-resolved pump-probe spectroscopy. Steady-state and femtosecond transient absorption spectra revealed a systematic increase in the partial unfolding of Cyt c with an increase in double bonds in CL, as observed by the enhanced fluorescence intensity and lifetime of tryptophan due to variations in the resonance energy transfer and extended global conformational relaxation time constants. These studies reflect the significance of occurrence of global conformational changes of Cyt c by structural modification near the double bond of CL in the Cyt c-CL complex, which could be prerequisites for the apoptosis.

Temperature Dependence of Thermal Conductivity of Proteins: Contributions of Thermal Expansion and Grüneisen Parameter

The thermal conductivity of many materials depends on temperature due to several factors, including variation of heat capacity with temperature, changes in vibrational dynamics with temperature, and change in volume with temperature. For proteins some, but not all, of these influences on the variation of thermal conductivity with temperature have been investigated in the past. In this study, we examine the influence of change in volume, and corresponding changes in vibrational dynamics, on the temperature dependence of the thermal conductivity. Using a measured value for the coefficient of thermal expansion and recently computed values for the Grüneisen parameter of proteins we find that the thermal conductivity increases with increasing temperature due to change in volume with temperature. We compare the impact of thermal expansion on the variation of the thermal conductivity with temperature found in this study with contributions of heat capacity and anharmonic coupling examined previously. Using values of thermal transport coefficients computed for proteins we also model heating of water in a protein solution following photoexcitation.

Thermal Energy Transport through Nonbonded Native Contacts in Protein

Within the protein interior, where we observe various types of interactions, nonuniform flow of thermal energy occurs along the polypeptide chain and through nonbonded native contacts, leading to inhomogeneous transport efficiencies from one site to another. The folded native protein serves not merely as thermal transfer medium but, more importantly, as sophisticated molecular nanomachines in cells. Therefore, we are particularly interested in what sort of "communication" is mediated through native contacts in the folded proteins and how such features are quantitatively depicted in terms of local transport coefficients of heat currents. To address the issue, we introduced a concept of inter-residue thermal conductivity and characterized the nonuniform thermal transport properties of a small globular protein, HP36, using equilibrium molecular dynamics simulation and the Green-Kubo formula. We observed that the thermal transport of the protein was dominated by that along the polypeptide chain, while the local thermal conductivity of nonbonded native contacts decreased in the order of H-bonding > π-stacking > electrostatic > hydrophobic contacts. Furthermore, we applied machine learning techniques to analyze the molecular mechanism of protein thermal transport. As a result, the contact distance, variance in contact distance, and H-bonding occurrence probability during MD simulations are found to be the top three important determinants for predicting local thermal transport coefficients.

Iminothioindoxyl Donors with Exceptionally High Cross Section for Protein Vibrational Energy Transfer

Various protein functions are related to vibrational energy transfer (VET) as an important mechanism. The underlying transfer pathways can be experimentally followed by ultrafast Vis-pump/IR-probe spectroscopy with a donor-sensor pair of non-canonical amino acids (ncAAs) incorporated in a protein. However, so far only one donor ncAA, azulenylalanine (AzAla), exists, which suffers from a comparably low Vis extinction coefficient. Here, we introduce two novel donor ncAAs based on an iminothioindoxyl (ITI) chromophore. The dimethylamino-ITI (DMA-ITI) and julolidine-ITI (J-ITI) moieties overcome the limitation of AzAla with a 50 times higher Vis extinction coefficient. While ITI moieties are known for ultrafast photoswitching, DMA-ITI and J-ITI exclusively form a hot ground state on the sub-ps timescale instead, which is essential for their usage as vibrational energy donor. In VET measurements of donor-sensor dipeptides we investigate the performance of the new donors. We observe 20 times larger signals compared to the established AzAla donor, which opens unprecedented possibilities for the study of VET in proteins.

Mutual information analysis of mutation, nonlinearity, and triple interactions in proteins

Mutations are the cause of several diseases as well as the underlying force of evolution. A thorough understanding of their biophysical consequences is essential. We present a computational framework for evaluating different levels of mutual information (MI) and its dependence on mutation. We used molecular dynamics trajectories of the third PDZ domain and its different mutations. Nonlinear MI between all residue pairs are calculated by tensor Hermite polynomials up to the fifth order and compared with results from multivariate Gaussian distribution of joint probabilities. We show that MI is written as the sum of a Gaussian and a nonlinear component. Results for the PDZ domain show that the Gaussian term gives a sufficiently accurate representation of MI when compared with nonlinear terms up to the fifth order. Changes in MI between residue pairs show the characteristic patterns resulting from specific mutations. Emergence of new peaks in the MI versus residue index plots of mutated PDZ shows how mutation may change allosteric pathways. Triple correlations are characterized by evaluating MI between triplets of residues. We observed that certain triplets are strongly affected by mutation. Susceptibility of residues to perturbation is obtained by MI and discussed in terms of linear response theory.

Time-resolved spectroscopic mapping of vibrational energy flow in proteins: Understanding thermal diffusion at the nanoscale

Vibrational energy exchange between various degrees of freedom is critical to barrier-crossing processes in proteins. Hemeproteins are well suited for studying vibrational energy exchange in proteins because the heme group is an efficient photothermal converter. The released energy by heme following photoexcitation shows migration in a protein moiety on a picosecond timescale, which is observed using time-resolved ultraviolet resonance Raman spectroscopy. The anti-Stokes ultraviolet resonance Raman intensity of a tryptophan residue is an excellent probe for the vibrational energy in proteins, allowing the mapping of energy flow with the spatial resolution of a single amino acid residue. This Perspective provides an overview of studies on vibrational energy flow in proteins, including future perspectives for both methodologies and applications.

Energy Transport in Class B GPCRs: Role of Protein-Water Dynamics and Activation

We compute energy exchange networks (EENs) through glucagon-like peptide-1 receptor (GLP-1R), a class B G-protein-coupled receptor (GPCR), in inactive and two active states, one activated by a peptide ligand and the other by a small molecule agonist, from results of molecular dynamics simulations. The reorganized network upon activation contains contributions from structural as well as from dynamic changes and corresponding entropic contributions to the free energy of activation, which are estimated in terms of the change in rates of energy transfer across non-covalent contacts. The role of water in the EENs and in activation of GLP-1R is also investigated. The dynamics of water in contact with the central polar network of the transmembrane region is found to be significantly slower for both activated states compared to the inactive state. This result is consistent with the contribution of water molecules to activation of GLP-1R previously suggested and resembles water dynamics in parts of the transmembrane region found in earlier studies of rhodopsin-like GPCRs.

Prediction of Allosteric Communication Pathways in Proteins

MOTIVATION

Allostery in proteins is an essential phenomenon in biological processes. In this paper, we present a computational model to predict paths of maximum information transfer between active and allosteric sites. In this information theoretic study, we use mutual information as the measure of information transfer, where transition probability of information from one residue to its contacting neighbors is proportional to the magnitude of mutual information between the two residues. Starting from a given residue and using a Hidden Markov Model, we successively determine the neighboring residues that eventually lead to a path of optimum information transfer. The Gaussian approximation of mutual information between residue pairs is adopted. The limits of validity of this approximation are discussed in terms of a nonlinear theory of mutual information and its reduction to the Gaussian form.

RESULTS

Predictions of the model are tested on six widely studied cases, CheY Bacterial Chemotaxis, B-cell Lymphoma extra-large Bcl-xL, Human proline isomerase cyclophilin A (CypA), Dihydrofolate reductase DHFR, HRas GTPase, and Caspase-1. The communication transmission rendering the propagation of local fluctuations from the active sites throughout the structure in multiple paths correlate well with the known experimental data. Distinct paths originating from the active site may likely represent a multi functionality such as involving more than one allosteric site and/or preexistence of some other functional states. Our model is computationally fast and simple, and can give allosteric communication pathways, which are crucial for the understanding and control of protein functionality.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Enhanced Mobility during Diels-Alder Reaction: Results of Molecular Simulations

Recent measurements indicate enhanced mobility of solvent molecules during Diels-Alder (DA) and other common chemical reactions. We present results of molecular dynamics simulations of the last stages of the DA cycloaddition reaction, from the transition state configuration to product, of furfurylamine and maleimide in acetonitrile at reactant concentrations studied experimentally. We find enhanced mobility of solvent and reactant molecules up to at least a nanometer from the DA product over hundreds of picoseconds. Local heating is ruled out as a factor in the enhanced mobility observed in the simulations, which is instead found to be due to solvent relaxation following the formation of the DA product.

Dependence of Vibrational Energy Transfer on Distance in a Four-Helix Bundle Protein: Equidistant Increments with the Periodicity of α Helices

Vibrational energy exchanges between various degrees of freedom are critical to barrier-crossing processes in proteins. Heme proteins are highly suitable for studies of the vibrational energy exchanges in proteins. The migration of excess energy released by heme in a protein moiety can be observed using time-resolved anti-Stokes ultraviolet resonance Raman spectroscopy. The anti-Stokes resonance Raman intensity of a tryptophan residue is an excellent probe for the excess energy and the spatial resolution of a single amino acid residue can be achieved. Here, we studied dependence of vibrational energy transfer on the distance in cytochrome b₅₆₂, which is a heme-containing, four-helix bundle protein. The vibrational energy transfer from the heme group to a single tryptophan residue introduced by site-directed mutagenesis was examined for different heme-tryptophan distances by a quasi-constant length with the periodicity of α helices. Taken together with structural data obtained by molecular dynamics simulations, the energy transfer could be well described by the model of classical thermal diffusion, which suggests that continuum media provide a good approximation of the protein interior, of which the atomic packing density is very high.

Information Flow and Allosteric Communication in Proteins

Based on Schreiber's work on transfer entropy, a molecular theory of nonlinear information transfer in proteins is developed. The joint distribution function for residue fluctuations is expressed in terms of tensor Hermite polynomials which conveniently separate harmonic and nonlinear contributions to information transfer. The harmonic part of information transfer is expressed as the difference between time dependent and independent mutual information. Third order nonlinearities are discussed in detail. Amount and speed of information transfer between residues, important for understanding allosteric activity in proteins, are discussed. While mutual information shows the maximum amount of information that may be transferred between two residues, it does not explain the actual amount of transfer nor the transfer rate of information. For this, dynamic equations of the system are needed. The solution of the Langevin equation and molecular dynamics trajectories are used in the present work for this purpose. Allosteric communication in Human NAD-dependent isocitrate dehydrogenase is studied as an example. Calculations show that several paths contribute collectively to information transfer. Important residues on these paths are identified. Time resolved information transfer between these residues, their amplitudes and transfer rates, which are in agreement with time resolved ultraviolet resonance Raman measurements in general, are estimated. Estimated transfer rates are in the order of 1-20 megabits per second. Information transfer from third order contributions are one to two orders of magnitude smaller than the harmonic terms, showing that harmonic analysis is a good approximation to information transfer.

Mimicking Natural Photosynthesis: Designing Ultrafast Photosensitized Electron Transfer into Multiheme Cytochrome Protein Nanowires

Efficient nanomaterials for artificial photosynthesis require fast and robust unidirectional electron transfer (ET) from photosensitizers through charge-separation and accumulation units to redox-active catalytic sites. We explored the ultrafast time-scale limits of photo-induced charge transfer between a Ru(II)tris(bipyridine) derivative photosensitizer and PpcA, a 3-heme c-type cytochrome serving as a nanoscale biological wire. Four covalent attachment sites (K28C, K29C, K52C, and G53C) were engineered in PpcA enabling site-specific covalent labeling with expected donor-acceptor (DA) distances of 4-8 Å. X-ray scattering results demonstrated that mutations and chemical labeling did not disrupt the structure of the proteins. Time-resolved spectroscopy revealed three orders of magnitude difference in charge transfer rates for the systems with otherwise similar DA distances and the same number of covalent bonds separating donors and acceptors. All-atom molecular dynamics simulations provided additional insight into the structure-function requirements for ultrafast charge transfer and the requirement of van der Waals contact between aromatic atoms of photosensitizers and hemes in order to observe sub-nanosecond ET. This work demonstrates opportunities to utilize multi-heme c-cytochromes as frameworks for designing ultrafast light-driven ET into charge-accumulating biohybrid model systems, and ultimately for mimicking the photosynthetic paradigm of efficiently coupling ultrafast, light-driven electron transfer chemistry to multi-step catalysis within small, experimentally versatile photosynthetic biohybrid assemblies.

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.

Role of atomic contacts in vibrational energy transfer in myoglobin

Heme proteins are ideal systems to investigate vibrational energy flow at the atomic level. Upon photoexcitation, a large amount of excess vibrational energy is selectively deposited on heme due to extremely fast internal conversion. This excess energy is redistributed to the surrounding protein moiety and then to water. Vibrational energy flow in myoglobin (Mb) was examined using picosecond time-resolved anti-Stokes ultraviolet resonance Raman (UVRR) spectroscopy. We used the Trp residue directly contacting the heme group as a selective probe for vibrationally excited populations. Trp residues were placed at different position close to the heme by site-directed mutagenesis. This technique allows us to monitor the excess energy on residue-to-residue basis. Anti-Stokes UVRR measurements for Mb mutants suggest that the dominant channel for energy transfer in Mb is the pathway through atomic contacts between heme and nearby amino acid residues as well as that between the protein and solvent water. It is found that energy flow through proteins is analogous to collisional exchange processes in solutions.

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.

Modelling vibrational relaxation in complex molecular systems

In this paper we show how it is possible to treat the quantum vibrational relaxation of a chromophore, embedded in a complex atomic-molecular environment, via the explicit solution of the time-dependent Schroedinger equation once using a proper separation between quantum and semiclassical degrees of freedom. The rigorous theoretical framework derived, based on first principles and making use of well defined approximations/assumptions, is utilized to construct a general model for the kinetics of the vibrational relaxation as obtained by the direct evaluation of the density matrix for all the relevant quantum state transitions. Application to (deuterated) N-methylacetamide (the typical benchmark used as a model for the amino acids) shows that the obtained theoretical-computational approach captures the essential features of the experimental process, unveiling the basic relaxation mechanism involving several vibrational state transitions.

Anharmonic Vibrational Analysis of Biomolecules and Solvated Molecules Using Hybrid QM/MM Computations

Quantum mechanics/molecular mechanics (QM/MM) calculations are applied for anharmonic vibrational analyses of biomolecules and solvated molecules. The QM/MM method is implemented into a molecular dynamics (MD) program, GENESIS, by interfacing with external electronic structure programs. Following the geometry optimization and the harmonic normal-mode analysis based on a partial Hessian, the anharmonic potential energy surface (PES) is generated from QM/MM energies and gradients calculated at grid points. The PES is used for vibrational self-consistent field (VSCF) and post-VSCF calculations to compute the vibrational spectrum. The method is first applied to a phosphate ion in solution. With both the ion and neighboring water molecules taken as a QM region, IR spectra of representative hydration structures are calculated by the second-order vibrational quasi-degenerate perturbation theory (VQDPT2) at the level of B3LYP/cc-pVTZ and TIP3P force field. A weight-average of IR spectra over the structures reproduces the experimental spectrum with a mean absolute deviation of 16 cm^–1. Then, the method is applied to an enzyme, P450 nitric oxide reductase (P450nor), with the NO molecule bound to a ferric (Fe^III) heme. Starting from snapshot structures obtained from MD simulations of P450nor in solution, QM/MM calculations have been carried out at the level of B3LYP-D3/def2-SVP(D). The spin state of Fe^III(NO) is likely a closed-shell singlet state based on a ratio of N–O and Fe–NO stretching frequencies (ν_N–O and ν_Fe–NO) calculated for closed- and open-shell singlet states. The calculated ν_N–O and ν_Fe–NO overestimate the experimental ones by 120 and 75 cm^–1, respectively. The electronic structure and solvation of Fe^III(NO) affect the structure around the heme of P450nor leading to an increase in ν_N–O and ν_Fe–NO.

Site-Resolved Observation of Vibrational Energy Transfer Using a Genetically Encoded Ultrafast Heater

Allosteric information transfer in proteins has been linked to distinct vibrational energy transfer (VET) pathways in a number of theoretical studies. Experimental evidence for such pathways, however, is sparse because site-selective injection of vibrational energy into a protein, that is, localized heating, is required for their investigation. Here, we solved this problem by the site-specific incorporation of the non-canonical amino acid β-(1-azulenyl)-l-alanine (AzAla) through genetic code expansion. As an exception to Kasha's rule, AzAla undergoes ultrafast internal conversion and heating after S₁ excitation while upon S₂ excitation, it serves as a fluorescent label. We equipped PDZ3, a protein interaction domain of postsynaptic density protein 95, with this ultrafast heater at two distinct positions. We indeed observed VET from the incorporation sites in the protein to a bound peptide ligand on the picosecond timescale by ultrafast IR spectroscopy. This approach based on genetically encoded AzAla paves the way for detailed studies of VET and its role in a wide range of proteins.

Infrared Laser Activation of Soluble and Membrane Protein Assemblies in the Gas Phase

Collision-induced dissociation (CID) is the dominant method for probing intact macromolecular complexes in the gas phase by means of mass spectrometry (MS). The energy obtained from collisional activation is dependent on the charge state of the ion and the pressures and potentials within the instrument: these factors limit CID capability. Activation by infrared (IR) laser radiation offers an attractive alternative as the radiation energy absorbed by the ions is charge-state-independent and the intensity and time scale of activation is controlled by a laser source external to the mass spectrometer. Here we implement and apply IR activation, in different irradiation regimes, to study both soluble and membrane protein assemblies. We show that IR activation using high-intensity pulsed lasers is faster than collisional and radiative cooling and requires much lower energy than continuous IR irradiation. We demonstrate that IR activation is an effective means for studying membrane protein assemblies, and liberate an intact V-type ATPase complex from detergent micelles, a result that cannot be achieved by means of CID using standard collision energies. Notably, we find that IR activation can be sufficiently soft to retain specific lipids bound to the complex. We further demonstrate that, by applying a combination of collisional activation, mass selection, and IR activation of the liberated complex, we can elucidate subunit stoichiometry and the masses of specifically bound lipids in a single MS experiment.

Importance of Atomic Contacts in Vibrational Energy Flow in Proteins

Vibrational energy flow in proteins was studied by monitoring the time-resolved anti-Stokes ultraviolet resonance Raman scattering of three myoglobin mutants in which a Trp residue substitutes a different amino acid residue near heme. The anti-Stokes Raman intensities of the Trp residue in the three mutants increased with similar rates after depositing excess vibrational energy at heme, despite the difference in distance between heme and each substituted Trp residue along the main chain of the protein. This indicates that vibrational energy is not transferred through the main chain of the protein but rather through atomic contacts between heme and the Trp residue. Distinct differences were observed in the amplitude of the band intensity change between the Trp residues at different positions, and the amplitude of the band intensity change exhibits a correlation with the extent of exposure of the Trp residue to solvent water. This correlation indicates that atomic contacts between an amino acid residue and solvent water play an important role in vibrational energy flow in a protein.

Conformational Changes of Trialanine in Water Induced by Vibrational Relaxation of the Amide I Mode

Most of the protein-based diseases are caused by anomalies in the functionality and stability of these molecules. Experimental and theoretical studies of the conformational dynamics of proteins are becoming in this respect essential to understand the origin of these anomalies. However, a description of the conformational dynamics of proteins based on mechano-energetic principles still remains elusive because of the intrinsic high flexibility of the peptide chains, the participation of weak noncovalent interactions, and the role of the ubiquitous water solvent. In this work, the conformational dynamics of trialanine dissolved in water (D2O) is investigated through Molecular Dynamics (MD) simulations combined with instantaneous normal modes (INMs) analysis both at equilibrium and after the vibrational excitation of the C-terminal amide I mode. The conformational equilibrium between α and pPII conformers is found to be altered by the intramolecular relaxation of the amide I mode as a consequence of the different relaxation pathways of each conformer which modify the amount of vibrational energy stored in the torsional motions of the tripeptide, so the α → pPII and pPII → α conversion rates are increased differently. The selectivity of the process comes from the shifts of the vibrational frequencies with the conformational changes that modify the resonance conditions driving the intramolecular energy flows.

Anisotropic energy flow and allosteric ligand binding in albumin

Allosteric interactions in proteins generally involve propagation of local structural changes through the protein to a remote site. Anisotropic energy transport is thought to couple the remote sites, but the nature of this process is poorly understood. Here, we report the relationship between energy flow through the structure of bovine serum albumin and allosteric interactions between remote ligand binding sites of the protein. Ultrafast infrared spectroscopy is used to probe the flow of energy through the protein backbone following excitation of a heater dye, a metalloporphyrin or malachite green, bound to different binding sites in the protein. We observe ballistic and anisotropic energy flow through the protein structure following input of thermal energy into the flexible ligand binding sites, without local heating of the rigid helix bundles that connect these sites. This efficient energy transport mechanism enables the allosteric propagation of binding energy through the connecting helix structures.

Observing Vibrational Energy Flow in a Protein with the Spatial Resolution of a Single Amino Acid Residue

One of the challenges in physical chemistry has been understanding how energy flows in a condensed phase from the microscopic viewpoint. To address this, space-resolved information at the molecular scale is required but has been lacking due to experimental difficulties. We succeeded in the real-time mapping of the vibrational energy flow in a protein with the spatial resolution of a single amino acid residue by combining time-resolved resonance Raman spectroscopy and site-directed single-Trp mutagenesis. Anti-Stokes Raman intensities of the Trp residues at different sites exhibited different temporal evolutions, reflecting propagation of the energy released by the heme group. A classical heat transport model was not able to reproduce the entire experimental data set, showing that we need a molecular-level description to explain the energy flow in a protein. The systematic application of our general methodology to proteins with different structural motifs may provide a greatly increased understanding of the energy flow in proteins.

Communication maps of vibrational energy transport through Photoactive Yellow Protein

We calculate communication maps for Photoactive Yellow Protein (PYP) from the purple phototropic eubacterium Halorhodospira halophile and use them to elucidate energy transfer pathways from the chromophore through the rest of the protein in the ground and excited state. The calculations reveal that in PYP excess energy from the chromophore flows mainly to regions of the surrounding residues that hydrogen bond to the chromophore. In addition, quantum mechanics/molecular mechanics and molecular dynamics (MD) simulations of the dielectric response of the protein and solvent environment due to charge rearrangement on the chromophore following photoexcitation are also presented, with both approaches yielding similar time constants for the response. Results of MD simulations indicate that the residues hydrogen bonding to the chromophore make the largest contribution to the response.