Optical measurements of long-range protein vibrations

Tubulin Vibration Modes Are in the Subterahertz Range, and Their Electromagnetic Absorption Is Affected by Water

Many proteins are thought to coordinate distant sites in their structures through a concerted action of global structural vibrations. However, the direct experimental spectroscopic detection of these vibration modes is rather elusive. We used normal-mode analysis to explore the dominant vibration modes of an all-atom model of the tubulin protein and described their characteristics using a large ensemble of tubulin structures. We quantified the frequency range of the normal vibrational modes to be in the subterahertz band, specifically between ∼40 and ∼160 GHz. Adding water layers to the model increases the frequencies of the low-frequency modes and narrows the frequency variations of the modes among the protein ensemble. We also showed how the electromagnetic absorption of tubulin vibration modes is affected by vibrational damping. These results contribute to our understanding of tubulin's vibrational and electromagnetic properties and provide a foundation for future attempts to control protein behavior via external electromagnetic fields.

A handheld polarimetric imaging device and calibration technique for accurate mapping of terahertz Stokes vectors

In recent years, handheld and portable terahertz instruments have been in rapid development for various applications ranging from non-destructive testing to biomedical imaging and sensing. For instance, we have deployed our Portable Handheld Spectral Reflection (PHASR) Scanners for in vivo full-spectroscopic imaging of skin burns in large animal models in operating room settings. In this paper, we debut the polarimetric version of the PHASR Scanner, and describe a generalized calibration technique to map the spatial and spectral dependence of the Jones matrix of an imaging scanner across its field of view. Our design is based on placement of two orthogonal photoconductive antenna (PCA) detectors separated by a polarizing beam splitter in the PHASR Scanner housing. We show that as few as three independent measurements of a well-characterized polarimetric calibration target are sufficient to determine the polarization state of the incident beam at the sample location, as well as to extract the Jones propagation matrix from the sample location to the detectors. We have tested the accuracy of our scanner by validating polarimetric measurements obtained from a birefringent crystal rotated to various angles, as compared to the theoretically predicted response of the sample. This new version of our PHASR scanner can be used for high-speed imaging and investigation of heterogeneity of polarization-sensitive samples in the field.

Sound Matrix Shaping of Living Matter: From Macrosystems to Cell Microenvironment, Where Mitochondria Act as Energy Portals in Detecting and Processing Sound Vibrations

Vibration and sound are the shaping matrix of the entire universe. Everything in nature is shaped by energy vibrating and communicating through its own sound trail. Every cell within our body vibrates at defined frequencies, generating its peculiar "sound signature". Mitochondria are dynamic, energy-transforming, biosynthetic, and signaling organelles that actively transduce biological information. Novel research has shown that the mitochondrial function of mammalian cells can be modulated by various energetic stimuli, including sound vibrations. Regarding acoustic vibrations, definite types of music have been reported to produce beneficial impacts on human health. In very recent studies, the effects of different sound stimuli and musical styles on cellular function and mitochondrial activity were evaluated and compared in human cells cultured in vitro, investigating the underlying responsible molecular mechanisms. This narrative review will take a multilevel trip from macro to intracellular microenvironment, discussing the intimate vibrational sound activities shaping living matter, delving deeper into the molecular mechanisms underlying the sound modulation of biological systems, and mainly focusing our discussion on novel evidence showing the competence of mitochondria in acting as energy portals capable of sensing and transducing the subtle informational biofields of sound vibration.

Frequency-domain terahertz optoacoustics for non-contact quantitative detection of gas, liquid, and solid samples

Terahertz optoacoustics (THz-OA) combines the advantages of abundant molecular characteristic absorptions in a terahertz band and the low attenuation through ultrasonic detection. Frequency-domain THz-OA, benefiting from the compact and the low cost of a continuous-wave THz source, has been used in gas detection and sensing. However, liquid and solid detections are hard to achieve due to the sensitivity limitation of existing technologies. Here we present a high-sensitivity frequency-domain THz-OA system with customized optoacoustic cells to accomplish non-contact quantitative detection of gas, liquid, and solid samples. The relationships between signal amplitudes and sample concentration, volume and temperature are discussed separately, revealing a potential application of this technology.

High specificity THz metamaterial-based biosensor for label-free transcription factor detection in melanoma diagnostics

In this work, we present a promising diagnostic tool for melanoma diagnosis. With the proposed terahertz biosensor, it was possible to selectively and sensitively detect the early growth response protein 2, a transcription factor with an increased activity in melanoma cells, from a complex sample of cellular proteins. Fundamentally, the sensor belongs to the frequency selective surface type metamaterials and consists of a two-dimensional array of asymmetrically, doubly split ring resonator unit cells. The single elements are slits in a metallic layer and are complemented by an undercut etch. This allows a selective functionalization of the active area of the sensor and increases the sensitivity towards the target analyte. Hereby, specific detection of a defined transcription factor is feasible.

Intra-protein interacting collective modes in the terahertz frequency region

Understanding how proteins work requires a thorough understanding of their internal dynamics. Proteins support a wide range of motions, from the femtoseconds to seconds time scale, relevant to crucial biological functions. In this context, the term "protein collective dynamics" refers to the complex patterns of coordinated motions of numerous atoms throughout the protein in the sub-picosecond time scale (terahertz frequency region). It is hypothesized that these dynamics have a substantial impact on the regulation of functional dynamical mechanisms, including ligand binding and allosteric signalling, charge transport direction, and the regulation of thermodynamic and thermal transport properties. Using the theoretical framework of hydrodynamics, the collective dynamics of proteins had previously been described in a manner akin to that of simple liquids, i.e. in terms of a single acoustic-like excitation, related to intra-protein vibrational motions. Here, we employ an interacting-mode model to analyse the results from molecular dynamics simulations and we unveil that the vibrational landscape of proteins is populated by multiple acoustic-like and low-frequency optic-like modes, with mixed symmetry and interfering with each other. We propose an interpretation at the molecular level of the observed scenario that we relate to the side-chains and the hydrogen-bonded networks dynamics. The present insights provide a perspective for understanding the molecular mechanisms underlying the energy redistribution processes in the interior of proteins.

Investigations on Na+, K+-ATPase energy consumption in ion flow of hydrophilic pores by THz unipolar stimulation

Terahertz science and technology has recently shown new application prospects in artificial intelligence. It is found that terahertz unipolar stimulation can activate cell membrane hydrophilic pores. However, the behaviors of Na+, K+-ATPase and energy consumption during this period remain unknown. This paper investigates these behaviors by Na+, K+-ATPase and electroporation models, based on the interaction theory between terahertz fields and ions at the cellular level. The effective diameters of life ions are considered in the aqueous solution. From results, Na+, K+-ATPases can be activated and stay for a while before close after the stimulation. Their life ion flows are far lower than the flows via the pores. And their power dissipation is as low as 10-11 W in both rat neostriatal neurons and guinea pig ventricular myocytes. The results keep tenable in 0.1-1.2 THz. These lay the basis for investigations of information communication mechanisms in cells under terahertz stimulation.

Frequency-Selective Anharmonic Mode Analysis of Thermally Excited Vibrations in Proteins

Low-frequency molecular vibrations at far-infrared frequencies are thermally excited at room temperature. As a consequence, thermal fluctuations are not limited to the immediate vicinity of local minima on the potential energy surface, and anharmonic properties cannot be ignored. The latter is particularly relevant in molecules with multiple conformations, such as proteins and other biomolecules. However, existing theoretical and computational frameworks for the analysis of molecular vibrations have so far been limited by harmonic or quasi-harmonic approximations, which are ill-suited to describe anharmonic low-frequency vibrations. Here, we introduce a fully anharmonic analysis of molecular vibrations based on a time correlation formalism that eliminates the need for harmonic or quasi-harmonic approximations. We use molecular dynamics simulations of a small protein to demonstrate that this new approach, in contrast to harmonic and quasi-harmonic normal modes, correctly identifies the collective degrees of freedom associated with molecular vibrations at any given frequency. This allows us to unambiguously characterize the anharmonic character of low-frequency vibrations in the far-infrared spectrum.

Phonon Polaritonics in Broad Terahertz Frequency Range with Quantum Paraelectric SrTiO3

Photonics in the frequency range of 5-15 terahertz (THz) potentially open a new realm of quantum materials manipulation and biosensing. This range, sometimes called "the new terahertz gap", is traditionally difficult to access due to prevalent phonon absorption bands in solids. Low-loss phonon-polariton materials may realize sub-wavelength, on-chip photonic devices, but typically operate in mid-infrared frequencies with narrow bandwidths and are difficult to manufacture on a large scale. Here, for the first time, quantum paraelectric SrTiO3 enables broadband surface phonon-polaritonic devices in 7-13 THz. As a proof of concept, polarization-independent field concentrators are designed and fabricated to locally enhance intense, multicycle THz pulses by a factor of 6 and increase the spectral intensity by over 90 times. The time-resolved electric field inside the concentrators is experimentally measured by THz-field-induced second harmonic generation. Illuminated by a table-top light source, the average field reaches 0.5 GV m-1 over a large volume resolvable by far-field optics. These results potentially enable scalable THz photonics with high breakdown fields made of various commercially available phonon-polariton crystals for studying driven phases in quantum materials and nonlinear molecular spectroscopy.

Permeability enhancement of Kv1.2 potassium channel by a terahertz electromagnetic field

As biomolecules vibrate and rotate in the terahertz band, the biological effects of terahertz electromagnetic fields have drawn considerable attention from the physiological and medical communities. Ion channels are the basis of biological electrical signals, so studying the effect of terahertz electromagnetic fields on ion channels is significant. In this paper, the effect of a terahertz electromagnetic field with three different frequencies, 6, 15, and 25 THz, on the Kv1.2 potassium ion channel was investigated by molecular dynamics simulations. The results show that an electromagnetic field with a 15 THz frequency can significantly enhance the permeability of the Kv1.2 potassium ion channel, which is 1.7 times higher than without an applied electric field. By analyzing the behavior of water molecules, it is found that the electromagnetic field with the 15 THz frequency shortens the duration of frozen and relaxation processes when potassium ions pass through the channel, increases the proportion of the direct knock-on mode, and, thus, enhances the permeability of the Kv1.2 potassium ion channel.

Effect of Terahertz Electromagnetic Field on the Permeability of Potassium Channel Kv1.2

In this paper, the influence of external terahertz electromagnetic fields with different frequencies of 4 THz, 10 THz, 15 THz, and 20 THz on the permeability of the Kv1.2 voltage-gated potassium ion channel on the nerve cell membrane was studied using the combined model of the "Constant Electric Field-Ion Imbalance" method by molecular dynamics. We found that although the applied terahertz electric field does not produce strong resonance with the -C=O groups of the conservative sequence T-V-G-Y-G amino acid residue of the selective filter (SF) of the channel, it would affect the stability of the electrostatic bond between potassium ions and the carbonyl group of T-V-G-Y-G of SF, and it would affect the stability of the hydrogen bond between water molecules and oxygen atoms of the hydroxyl group of the 374THR side chain at the SF entrance, changing the potential and occupied states of ions in the SF and the occurrence probability of the permeation mode of ions and resulting in the change in the permeability of the channel. Compared with no external electric field, when the external electric field with 15 THz frequency is applied, the lifetime of the hydrogen bond is reduced by 29%, the probability of the "soft knock on" mode is decreased by 46.9%, and the ion flux of the channel is activated by 67.7%. Our research results support the view that compared to "direct knock-on", "soft knock-on" is a slower permeation mode.

Selectivity of Protein Interactions Stimulated by Terahertz Signals

It has been established that Terahertz (THz) band signals can interact with biomolecules through resonant modes. Specifically, of interest here, protein activation. Our research goal is to show how directing the mechanical signaling inside protein molecules using THz signals can control changes in their structure and activate associated biochemical and biomechanical events. To establish that, we formulate a selectivity metric that quantifies the system performance and captures the capability of the nanoantenna to induce a conformational change in the desired protein molecule/population. The metric provides a score between -1 and 1 that indicates the degree of control we have over the system to achieve targeted protein interactions. To develop the selectivity measure, we first use the Langevin stochastic equation driven by an external force to model the protein behavior. We then determine the probability of protein folding by computing the steady-state energy of the driven protein and then generalize our model to account for protein populations. Our numerical analysis results indicate that a maximum selectivity score is attained when only the targeted population experiences a folding behavior due to the impinging THz signal. From the achieved selectivity values, we conclude that the system response not only depends on the resonant frequency but also on the system controlling parameters namely, the nanoantenna force, the damping constant, and the abundance of each protein population. Based on the selectivity metric, the nanoantenna must be tuned to a frequency that is not necessarily the resonant frequency of the protein. The presented work sheds light on the potential associated with the electromagnetic-based control of protein networks, which could lead to a plethora of applications in the medical field ranging from bio-sensing to targeted therapy.

Probing terahertz dynamics of multidomain protein in cell-like confinement

The development of meaningful descriptions of multidomain proteins exhibiting complex inter-domain dynamics modes is a key challenge for understanding their roles in molecular recognition and signalling processes. Here we developed a generally applicable approach for probing the low frequency collective hydration dynamics of multidomain proteins that uses terahertz spectroscopy of a protein molecule confined in a phospholipid reverse micelles environment (named Droplet THz). With the combination of normal mode analysis, we demonstrated the binding of calcium ions modulates the local inter-domain motion of the human coagulant factor VIII protein in a concentration-dependent manner. These findings highlight the Droplet THz as a valuable tool for dissecting the ultrafast dynamics of domain motion in the multidomain proteins and suggest a modulating mechanism of calcium ions on the structural flexibility and function of human coagulant proteins.

On Collective Molecular Dynamics in Biological Systems: A Review of Our Experimental Observations and Theoretical Modeling

We review processes by which different sounds, such as meditation music, mantra, kindness, or hatred expressions, and noises induce responses from cells and their components. We define ‘good’ or ‘bad’ sounds as those enhancing or inhibiting the cell’s biological activity, respectively. It is highlighted that the cellular dynamics results in a coherent organization with the formation of ordered patterns due to long-range correlations among the system constituents. Due to coherence, in the framework of quantum field theory, extended domains become independent of quantum fluctuations. Non-dissipative energy transfer on macromolecule chains is briefly discussed. Observed fractal features are analyzed by the fast Fourier transform and a linear relationship between logarithms of conjugate variables is observed. The fractal relation to the generation of forms (morphogenesis) and to the transition from form to form (metamorphosis) is commented. The review is also motivated by the suggestions coming from the cells’ responses, which show their ability to move from the syntactic level of the sound component frequencies to the semantic level of their collective envelope. The process by which sounds are selected to be good or bad sounds sheds some light on the problem of the construction of languages.

Length-dependent collective vibrational dynamics in alpha-helices

Functions of protein molecules in nature are closely associated with their well-defined three-dimensional structures and dynamics in body fluid. So far, many efforts have been made to reveal the relation of protein structure, dynamics, and function, but the structural origin of protein dynamics, especially for secondary structures as building blocks of conformation transition, is still ambiguous. Here we theoretically uncover the collective vibrations of elastic poly-alanine α-helices and find vibration patterns that are distinctively different over residue numbers ranging from 20 to 80. Contrary to the decreasing vibration magnitude from ends to the middle region for short helices, the vibration magnitude for long helices takes the minimum at approximately 1/5 of helix length from ends but reaches a peak at the center. Further analysis indicates that major vibrational modes of helical structures strongly depend on their residue numbers, where the twist mode dominates in the vibrations of short helices while the bend mode dominates the long ones analogous to an elastic Euler beam. The helix-coil transition pathway is also affected by the alternation of the first-order mode in helices with different lengths. The dynamic properties of the helical polypeptides are promising to be harnessed for de novo design of protein-based materials and artificial biomolecules in clinical treatments.

Infrared fingerprints of water collective dynamics indicate proton transport in biological systems

Recent publications on spectroscopy of water layers in water bridge structures revealed a significant enhancement of the proton mobility and the dielectric contribution of translational vibrations of water molecules in the interfacial layers compared to bulk water. Herewith, the results of long-term studies of proton dynamics in solid-state acids have shown that proton mobility increases significantly with the predominance of hydronium, but not Zundel, cations in the aqueous phase. In the present work, in the light of these data, we reanalyzed our previously published results on broadband dielectric spectroscopy of bovine heart cytochrome c, bovine serum albumin, and the extracellular matrix and filaments of Shewanella oneidensis MR-1. We revealed that, just as in water bridges, an increase in electrical conductivity in these systems correlates with an increase in the dielectric contribution of water molecular translational vibrations. In addition, the appearance of spectral signatures of the hydronium cations was observed only in those cases when the system revealed noticeable electrical conductivity due to delocalized charge carriers.

Response of Terahertz Protein Vibrations to Ligand Binding: Calmodulin-Peptide Complexes as a Case Study

Terahertz vibrations are sensitive reporters of the structure and interactions of proteins. Ligand binding alters the nature and distribution of these collective vibrations. The ligand-induced changes in the terahertz protein vibrations contribute to the binding entropy and to the overall thermodynamic stability of the resultant protein-ligand complexes. Here, we have examined the response of the low-frequency (below 6 terahertz) collective vibrations of the calcium-loaded calmodulin (CaM) to binding to five different ligands, both in the presence and absence of water, using normal-mode analysis and molecular dynamics simulations. A comparison of the vibrational spectra of hydrated and dry systems reveals that protein-solvent interactions stiffen the terahertz protein vibrations and that these solvent-coupled collective vibrations contribute significantly to the hydration-sensitive variation in the vibrational entropy of CaM. In the absence of water, the low-frequency vibrations of CaM are stiffened by ligand binding. On the contrary, the number and the cumulative vibrational entropy of low-frequency vibrational modes (ω < 200 cm^-1) of the hydrated CaM are increased noticeably after binding to the peptides, indicating binding-induced softening of collective vibrations of the protein. Although the calculated and experimental binding affinities of the chosen complexes correlated reasonably well, no systematic correlation was observed between the protein vibrational entropy and the binding affinity. The results underscored the importance of the interplay of protein-ligand and solvent interactions in modulating the low-frequency vibrations of proteins.

Cell Responsiveness to Physical Energies: Paving the Way to Decipher a Morphogenetic Code

We discuss emerging views on the complexity of signals controlling the onset of biological shapes and functions, from the nanoarchitectonics arising from supramolecular interactions, to the cellular/multicellular tissue level, and up to the unfolding of complex anatomy. We highlight the fundamental role of physical forces in cellular decisions, stressing the intriguing similarities in early morphogenesis, tissue regeneration, and oncogenic drift. Compelling evidence is presented, showing that biological patterns are strongly embedded in the vibrational nature of the physical energies that permeate the entire universe. We describe biological dynamics as informational processes at which physics and chemistry converge, with nanomechanical motions, and electromagnetic waves, including light, forming an ensemble of vibrations, acting as a sort of control software for molecular patterning. Biomolecular recognition is approached within the establishment of coherent synchronizations among signaling players, whose physical nature can be equated to oscillators tending to the coherent synchronization of their vibrational modes. Cytoskeletal elements are now emerging as senders and receivers of physical signals, "shaping" biological identity from the cellular to the tissue/organ levels. We finally discuss the perspective of exploiting the diffusive features of physical energies to afford in situ stem/somatic cell reprogramming, and tissue regeneration, without stem cell transplantation.

Quantification of solid-phase chemical reactions using the temperature-dependent terahertz pulsed spectroscopy, sum rule, and Arrhenius theory: thermal decomposition of α-lactose monohydrate

Transformations of the low-energy vibrational spectra are associated with structural changes in an analyte and closely related to the instability of weak chemical bounds. Terahertz (THz)/far-infrared optical spectroscopy is commonly used to probe such transformation, aimed at characterization of the underlying solid-phase chemical reactions in organic compounds. However, such studies usually provide quite qualitative information about the temperature- and time-dependent parameters of absorption peaks in dielectric spectra of an analyte. In this paper, an approach for quantitative analyses of the solid-phased chemical reactions based on the THz pulsed spectroscopy was developed. It involves studying an evolution of the sample optical properties, as a function of the analyte temperature and reaction time, and relies on the classical oscillator model, the sum rule, and the Arrhenius theory. The method allows one to determine the temperature-dependent reaction rate V₁(T) and activation energy E_a. To demonstrate the practical utility of this method, it was applied to study α-lactose monohydrate during its temperature-induced molecular decomposition. Analysis of the measured THz spectra revealed the increase of the reaction rate in the range of V₁ ≃ ~9 × 10^-4-10^-2 min^-1, when the analyte temperature rises from 313 to 393 K, while the Arrhenius activation energy is E_a ≃ ~45.4 kJ/mol. Thanks to a large number of obtained physical and chemical parameters, the developed approach expands capabilities of THz spectroscopy in chemical physics, analytical chemistry, and pharmaceutical industry.

The origin and impact of bound water around intrinsically disordered proteins

Proteins and water couple dynamically over a wide range of time scales. Motivated by their central role in protein function, protein-water dynamics and thermodynamics have been extensively studied for structured proteins, where correspondence to structural features has been made. However, properties controlling intrinsically disordered protein (IDP)-water dynamics are not yet known. We report results of megahertz-to-terahertz dielectric spectroscopy and molecular dynamics simulations of a group of IDPs with varying charge content along with structured proteins of similar size. Hydration water around IDPs is found to exhibit more heterogeneous rotational and translational dynamics compared with water around structured proteins of similar size, yielding on average more restricted dynamics around individual residues of IDPs, charged or neutral, compared with structured proteins. The on-average slower water dynamics is found to arise from excess tightly bound water in the first hydration layer, which is related to greater exposure to charged groups. The more tightly bound water to IDPs correlates with the smaller hydration shell found experimentally, and affects entropy associated with protein-water interactions, the contribution of which we estimate based on the dielectric measurements and simulations. Water-IDP dynamic coupling at terahertz frequencies is characterized by the dielectric measurements and simulations.

Low-frequency collective motion of DNA-binding domain defines p53 function

Most mutations in the DNA-binding domain (DBD) of p53 inactivate or rescue the protein function interacting with the minor groove of DNA. However, how the conformation changes propagating from the mutation sites result in distinct molecular recognition is still not well understood. As the protein mobility is an intrinsic property encrypted in its primary structure, we examined if different structures of wild-type and mutant p53 core domains display any unique patterns of intrinsic mobility. Normal mode calculation was employed to characterize the collective dynamics of DBD in p53 monomer and tetramer as well as their mutants. Intriguingly, the low-frequency collective motions of DBD show similar patterns between the wild-type protein and the rescued mutants. The analysis on atomic backbone fluctuations and low-frequency vibration mode statistics does further support the correlation between the intrinsic collective motion of DBD and the p53 protein function. The mutations in the DBD influence the low-frequency vibration of the p53 tetramer via the change of the collective motions among its four monomers. These findings thus provide new insights for understanding the physical mechanism of p53 protein structure-function relationship and help find the small molecule drug to modulate protein dynamic for disease therapy.

Probing the existence of non-thermal Terahertz radiation induced changes of the protein solution structure

During the last decades discussions were taking place on the existence of global, non-thermal structural changes in biological macromolecules induced by Terahertz (THz) radiation. Despite numerous studies, a clear experimental proof of this effect for biological particles in solution is still missing. We developed a setup combining THz-irradiation with small angle X-ray scattering (SAXS), which is a sensitive method for detecting the expected structural changes. We investigated in detail protein systems with different shape morphologies (bovine serum albumin, microtubules), which have been proposed to be susceptible to THz-radiation, under variable parameters (THz wavelength, THz power densities up to 6.8 mW/cm², protein concentrations). None of the studied systems and conditions revealed structural changes detectable by SAXS suggesting that the expected non-thermal THz-induced effects do not lead to alterations of the overall structures, which are revealed by scattering from dissolved macromolecules. This leaves us with the conclusion that, if such effects are present, these are either local or outside of the spectrum and power range covered by the present study.

Unveiling the morphogenetic code: A new path at the intersection of physical energies and chemical signaling

In this editorial, we discuss the remarkable role of physical energies in the control of cell signaling networks and in the specification of the architectural plan of both somatic and stem cells. In particular, we focus on the biological relevance of bioelectricity in the pattern control that orchestrates both developmental and regenerative pathways. To this end, the narrative starts from the dawn of the first studies on animal electricity, reconsidering the pioneer work of Harold Saxton Burr in the light of the current achievements. We finally discuss the most recent evidence showing that bioelectric signaling is an essential component of the informational processes that control pattern specification during embryogenesis, regeneration, or even malignant transformation. We conclude that there is now mounting evidence for the existence of a Morphogenetic Code, and that deciphering this code may lead to unprecedented opportunities for the development of novel paradigms of cure in regenerative and precision medicine.

Functional-State Dependence of Picosecond Protein Dynamics

We examine temperature-dependent picosecond dynamics of two benchmarking proteins lysozyme and cytochrome c using temperature-dependent terahertz permittivity measurements. We find that a double Arrhenius temperature dependence with activation energies E₁ ∼ 0.1 kJ/mol and E₂ ∼ 10 kJ/mol fits the folded and ligand-free state response. The higher activation energy is consistent with the so-called protein dynamical transition associated with beta relaxations at the solvent-protein interface. The lower activation energy is consistent with correlated structural motions. When the structure is removed by denaturing, the lower-activation-energy process is no longer present. Additionally, the lower-activation-energy process is diminished with ligand binding but not for changes in the internal oxidation state. We suggest that the lower-energy activation process is associated with collective structural motions that are no longer accessible with denaturing or binding.

Complete Mapping of DNA‐Protein Interactions at the Single‐Molecule Level

DNA–protein interaction plays an essential role in the storage, expression, and regulation of genetic information. A 1D/3D facilitated diffusion mechanism has been proposed to explain the extraordinarily rapid rate of DNA‐binding protein (DBP) searching for cognate sequence along DNA and further studied by single‐molecule experiments. However, direct observation of the detailed chronological protein searching image is still a formidable challenge. Here, for the first time, a single‐molecule electrical monitoring technique is utilized to realize label‐free detection of the DBP–DNA interaction process based on high‐gain silicon nanowire field‐effect transistors (SiNW FETs). The whole binding process of WRKY domain and DNA has been visualized with high sensitivity and single‐base resolution. Impressively, the swinging of hydrogen bonds between amino acid residues and bases in DNA induce the dynamic collective motion of DBP–DNA. This in situ, label‐free electrical detection platform provides a practical experimental methodology for dynamic studies of various biomolecules.

Terahertz pump-probe of liquid water at 12.3 THz

The dynamical complexity of the hydrogen-bonded water network can be investigated with intense Terahertz (THz) spectroscopy, which can drive the liquid into the nonlinear response regime and probe anharmonicity effects. Here we report single-color and polarization-dependent pump–probe experiments at 12.3 THz on liquid water, exciting the librational mode. By comparing results obtained on a static sample and a free-flowing water jet, we are able to disentangle the distinct contributions by thermal, acoustic, and nonlinear optical effects. We show that the transient transmission by the static water layer on a time scale of hundreds of microseconds can be described by thermal (slow) and acoustic (temperature-dependent) effects. In addition, during pump probe overlap we observe an anisotropic nonlinear optical response. This nonlinear signal is more prominent in the liquid jet than in the static cell, where temperature and density perturbations are more pronounced. Our measurements confirm that the THz excitation resonates with the rotationally-damped motion of water molecules, resulting in enhanced transient anisotropy. This model can be used to explain the non-linear response of water in the frequency range between about 1 and 20 THz.

The excitation on the librational band of liquid water at 12.3 THz resonates with the rotationally-damped motion of water molecules.

A Review of THz Technologies for Rapid Sensing and Detection of Viruses including SARS-CoV-2

Virus epidemics such as Ebola virus, Zika virus, MERS-coronavirus, and others have wreaked havoc on humanity in the last decade. In addition, a coronavirus (SARS-CoV-2) pandemic and its continuously evolving mutants have become so deadly that they have forced the entire technical advancement of healthcare into peril. Traditional ways of detecting these viruses have been successful to some extent, but they are costly, time-consuming, and require specialized human resources. Terahertz-based biosensors have the potential to lead the way for low-cost, non-invasive, and rapid virus detection. This review explores the latest progresses in terahertz technology-based biosensors for the virus, viral particle, and antigen detection, as well as upcoming research directions in the field.

Cellular effects of terahertz waves

SIGNIFICANCE

An increasing interest in the area of biological effects at exposure of tissues and cells to the terahertz (THz) radiation is driven by a rapid progress in THz biophotonics, observed during the past decades. Despite the attractiveness of THz technology for medical diagnosis and therapy, there is still quite limited knowledge about safe limits of THz exposure. Different modes of THz exposure of tissues and cells, including continuous-wave versus pulsed radiation, various powers, and number and duration of exposure cycles, ought to be systematically studied.

AIM

We provide an overview of recent research results in the area of biological effects at exposure of tissues and cells to THz waves.

APPROACH

We start with a brief overview of general features of the THz-wave-tissue interactions, as well as modern THz emitters, with an emphasis on those that are reliable for studying the biological effects of THz waves. Then, we consider three levels of biological system organization, at which the exposure effects are considered: (i) solutions of biological molecules; (ii) cultures of cells, individual cells, and cell structures; and (iii) entire organs or organisms; special attention is devoted to the cellular level. We distinguish thermal and nonthermal mechanisms of THz-wave-cell interactions and discuss a problem of adequate estimation of the THz biological effects' specificity. The problem of experimental data reproducibility, caused by rareness of the THz experimental setups and an absence of unitary protocols, is also considered.

RESULTS

The summarized data demonstrate the current stage of the research activity and knowledge about the THz exposure on living objects.

CONCLUSIONS

This review helps the biomedical optics community to summarize up-to-date knowledge in the area of cell exposure to THz radiation, and paves the ways for the development of THz safety standards and THz therapeutic applications.

Nanoscale Terahertz Monitoring on Multiphase Dynamic Assembly of Nanoparticles under Aqueous Environment

Probing the kinetic evolution of nanoparticle (NP) growth in liquids is essential for understanding complex nano-phases and their corresponding functions. Terahertz (THz) sensing, an emerging technology for next-generation laser photonics, has been developed with unique photonic features, including label-free, non-destructive, and molecular-specific spectral characteristics. Recently, metasurface-based sensing platforms have helped trace biomolecules by overcoming low THz absorption cross-sectional limits. However, the direct probing of THz signals in aqueous environments remains difficult. Here, the authors report that vertically aligned nanogap-hybridized metasurfaces can efficiently trap traveling NPs in the sensing region, thus enabling us to monitor the real-time kinetic evolution of NP assemblies in liquids. The THz photonics approach, together with an electric tweezing technique via spatially matching optical hotspots to particle trapping sites with a nanoscale spatial resolution, is highly promising for underwater THz analysis, forging a route toward unraveling the physicochemical events of nature within an ultra-broadband wavelength regime.

Analytical Hessians for Ewald and particle mesh Ewald electrostatics

The particle mesh Ewald (PME) method has become ubiquitous in the molecular simulation community due to its ability to deliver long range electrostatics accurately with ON  ⁡log(N) complexity. Despite this widespread use, spanning more than two decades, second derivatives (Hessians) have not been available. In this work, we describe the theory and implementation of PME Hessians, which have applications in normal mode analysis, characterization of stationary points, phonon dispersion curve calculation, crystal structure prediction, and efficient geometry optimization. We outline an exact strategy that requires O(1) effort for each Hessian element; after discussing the excessive memory requirements of such an approach, we develop an accurate, efficient approximation that is far more tractable on commodity hardware.

Fluorescent bacterial biosensor E. coli/pTdcR-TurboYFP sensitive to terahertz radiation

A fluorescent biosensor E. coli/pTdcR-TurboYFP sensitive to terahertz (THz) radiation was developed via transformation of Escherichia coli (E. coli) cells with plasmid, in which the promotor of the tdcR gene controls the expression of yellow fluorescent protein TurboYFP. The biosensor was exposed to THz radiation in various vessels and nutrient media. The threshold and dynamics of fluorescence were found to depend on irradiation conditions. Heat shock or chemical stress yielded the absence of fluorescence induction. The biosensor is applicable to studying influence of THz radiation on the activity of tdcR promotor that is involved in the transport and metabolism of threonine and serine in E. coli.

Low-Frequency Protein Motions Coupled to Catalytic Sites

This review examines low-frequency vibrational modes of proteins and their coupling to enzyme catalytic sites. That protein motions are critical to enzyme function is clear, but the kinds of motions present in proteins and how they are involved in function remain unclear. Several models of enzyme-catalyzed reaction suggest that protein dynamics may be involved in the chemical step of the catalyzed reaction, but the evidence in support of such models is indirect. Spectroscopic studies of low-frequency protein vibrations consistently show that there are underdamped modes of the protein with frequencies in the tens of wavenumbers where overdamped behavior would be expected. Recent studies even show that such underdamped vibrations modulate enzyme active sites. These observations suggest that increasingly sophisticated spectroscopic methods will be able to unravel the link between low-frequency protein vibrations and enzyme function.

Modal Analysis of the Lysozyme Protein Considering All-Atom and Coarse-Grained Finite Element Models

Proteins are the fundamental entities of several organic activities. They are essential for a broad range of tasks in a way that their shapes and folding processes are crucial to achieving proper biological functions. Low-frequency modes, generally associated with collective movements at terahertz (THz) and sub-terahertz frequencies, have been appointed as critical for the conformational processes of many proteins. Dynamic simulations, such as molecular dynamics, are vastly applied by biochemical researchers in this field. However, in the last years, proposals that define the protein as a simplified elastic macrostructure have shown appealing results when dealing with this type of problem. In this context, modal analysis based on different modelization techniques, i.e., considering both an all-atom (AA) and coarse-grained (CG) representation, is proposed to analyze the hen egg-white lysozyme. This work presents new considerations and conclusions compared to previous analyses. Experimental values for the B-factor, considering all the heavy atoms or only one representative point per amino acid, are used to evaluate the validity of the numerical solutions. In general terms, this comparison allows the assessment of the regional flexibility of the protein. Besides, the low computational requirements make this approach a quick method to extract the protein’s dynamic properties under scrutiny.

Persistent Protein Motions in a Rugged Energy Landscape Revealed by Normal Mode Ensemble Analysis

Proteins are allosteric machines that couple motions at distinct, often distant, sites to control biological function. Low-frequency structural vibrations are a mechanism of this long-distance connection and are often used computationally to predict correlations, but experimentally identifying the vibrations associated with specific motions has proved challenging. Spectroscopy is an ideal tool to explore these excitations, but measurements have been largely unable to identify important frequency bands. The result is at odds with some previous calculations and raises the question what methods could successfully characterize protein structural vibrations. Here we show the lack of spectral structure arises in part from the variations in protein structure as the protein samples the energy landscape. However, by averaging over the energy landscape as sampled using an aggregate 18.5 μs of all-atom molecular dynamics simulation of hen egg white lysozyme and normal-mode analyses, we find vibrations with large overlap with functional displacements are surprisingly concentrated in narrow frequency bands. These bands are not apparent in either the ensemble averaged vibrational density of states or isotropic absorption. However, in the case of the ensemble averaged anisotropic absorption, there is persistent spectral structure and overlap between this structure and the functional displacement frequency bands. We systematically lay out heuristics for calculating the spectra robustly, including the need for statistical sampling of the protein and inclusion of adequate water in the spectral calculation. The results show the congested spectrum of these complex molecules obscures important frequency bands associated with function and reveal a method to overcome this congestion by combining structurally sensitive spectroscopy with robust normal mode ensemble analysis.

Sounds Stimulation on In Vitro HL1 Cells: A Pilot Study and a Theoretical Physical Model

Mechanical vibrations seem to affect the behaviour of different cell types and the functions of different organs. Pressure waves, including acoustic waves (sounds), could affect cytoskeletal molecules via coherent changes in their spatial organization and mechano-transduction signalling. We analyzed the sounds spectra and their fractal features. Cardiac muscle HL1 cells were exposed to different sounds, were stained for cytoskeletal markers (phalloidin, beta-actin, alpha-tubulin, alpha-actinin-1), and studied with multifractal analysis (using FracLac for ImageJ). A single cell was live-imaged and its dynamic contractility changes in response to each different sound were analysed (using Musclemotion for ImageJ). Different sound stimuli seem to influence the contractility and the spatial organization of HL1 cells, resulting in a different localization and fluorescence emission of cytoskeletal proteins. Since the cellular behaviour seems to correlate with the fractal structure of the sound used, we speculate that it can influence the cells by virtue of the different sound waves’ geometric properties that we have photographed and filmed. A theoretical physical model is proposed to explain our results, based on the coherent molecular dynamics. We stress the role of the systemic view in the understanding of the biological activity.

Terahertz pulse-altered gene networks in human induced pluripotent stem cells

Terahertz (THz) irradiation has been exploited in biomedical applications involving non-invasive manipulation of living cells. We developed an apparatus for studying the effects of THz pulse irradiation on living human induced pluripotent stem cells. The THz pulse of the maximum electric field reached 0.5 MV/cm and was applied for one hour with 1 kHz repetition to the entire cell-culture area, a diameter of 1 mm. RNA sequencing of global gene-expression revealed that many THz-regulated genes were driven by zinc-finger transcription factors. Combined with a consideration of the interactions of metal ions and a THz electric field, these results imply that the local intracellular concentration of metal ions, such as Zn²⁺, was changed by the effective electrical force of our THz pulse.

Collective excitations in α-helical protein structures interacting with the water environment

Low-frequency vibrational excitations of protein macromolecules in the terahertz frequency region are suggested to contribute to many biological processes such as enzymatic catalysis, intra-protein energy/charge transport, recognition, and allostery. To explain high effectiveness of these processes, two possible mechanisms of the long-lived excitation were proposed by H. Fröhlich and A.S. Davydov, which relate to either vibrational modes or solitary waves, respectively. In this paper, we developed a quantum dynamic model of vibrational excitation in α-helical proteins interacting with the aqueous environment. In the model, we distinguished three coupled subsystems, i.e., (i) a chain of hydrogen-bonded peptide groups (PGs), interacting with (ii) the subsystem of the side-chain residuals which in turn interact with (iii) the environment, surrounding water responsible for dissipation and fluctuation in the system. It was shown that the equation of motion for phonon variables of the PG chain can be transformed to nonlinear Schrodinger equation which admits bifurcation into the solution corresponding to the weak-damped vibrational modes (Fröhlich-type regime) and Davydov solitons. A bifurcation parameter is derived through the strength of phonon-phonon interaction between the side-chains and hydration-shell water molecules. As shown, the energy of these excited states is pumped through the interaction of the side-chains with fluctuating water environment of the proteins. The suggested mechanism of the collective vibrational mode excitation is discussed in connection with the recent experiments on the long-lived collective protein excitations in the terahertz frequency region and vibrational energy transport pathways in proteins.

Detection of boson peak and fractal dynamics of disordered systems using terahertz spectroscopy

The boson peak is a largely unexplained excitation found universally in the terahertz vibrational spectra of disordered systems; the so-called fracton is a vibrational excitation associated with the self-similar structure of monomers in polymeric glasses. We demonstrate that such excitations can be detected using terahertz spectroscopy. In the case of fractal structures, we determine the infrared light-vibration coupling coefficient for the fracton region and show that information concerning the fractal and fracton dimensions appears in the exponent of the absorption coefficient. Finally, using terahertz time-domain spectroscopy and low-frequency Raman scattering, we experimentally observe these universal excitations in a protein (lysozyme) system that has an intrinsically disordered and fractal structure and argue that the system should be considered a single supramolecule. These findings are applicable to amorphous and fractal objects in general and will be valuable for understanding universal dynamics of disordered systems via terahertz light.

A THz transparent 3D printed microfluidic cell for small angle x-ray scattering

Excitation frequencies in the terahertz (THz) range are expected to lead to functionally relevant domain movements within the biological macromolecules such as proteins. The possibility of examining such movements in an aqueous environment is particularly valuable since here proteins are not deprived of any motional degrees of freedom. Small angle x-ray scattering (SAXS) is a powerful method to study the structure and domain movements of proteins in solution. Here, we present a microfluidic cell for SAXS experiments, which is also transparent for THz radiation. Specifically, cell dimensions and material were optimized for both radiation sources. In addition, the polystyrene cell can be 3D printed and easily assembled. We demonstrate the practicality of our design for SAXS measurements on several proteins in solution.

Optomechanical detection of vibration modes of a single bacterium

Low-frequency vibration modes of biological particles, such as proteins, viruses and bacteria, involve coherent collective vibrations at frequencies in the terahertz and gigahertz domains. These vibration modes carry information on their structure and mechanical properties, which are good indicators of their biological state. In this work, we harnessed a particular regime in the physics of coupled mechanical resonators to directly measure these low-frequency mechanical resonances of a single bacterium. We deposit the bacterium on the surface of an ultrahigh frequency optomechanical disk resonator in ambient conditions. The vibration modes of the disk and bacterium hybridize when their associated frequencies are similar. We developed a general theoretical framework to describe this coupling, which allows us to retrieve the eigenfrequencies and mechanical loss of the bacterium low-frequency vibration modes (quality factor). Additionally, we analysed the effect of hydration on these vibrational modes. This work demonstrates that ultrahigh frequency optomechanical resonators can be used for vibrational spectrometry with the unique capability to obtain information on single biological entities.

First demonstration of coherent resonant backward diffraction radiation for a quasi-monochromatic terahertz-light source

We proposed coherent resonant backward diffraction radiation (CRBDR), which generates wavelength-tunable quasi-monochromatic lights using a compact diffractor assembly in an accelerator facility of high-energy electron beams, as a unique intense terahertz (THz) light source. Superimposing the coherent backward diffracted radiation emitted by periodically arranged hollow diffractors, it is possible to amplify the frequency components satisfying a resonant condition, and make the radiation monochromatic. We demonstrated the CRBDR using the L-band linac at the Institute for Integrated Radiation and Nuclear Science at Kyoto University. It was observed that the coherent backward diffraction radiation was amplified more than three times at a frequency which was the fundamental resonant frequency in the CRBDR theory. Moreover, the number of diffractors at the saturation of the radiation power was consistent with the number estimated from the electron distribution in a bunch. The experimental results show that the CRBDR is useful as a quasi-monochromatic light source in the THz band.

Terahertz time-domain polarimetry (THz-TDP) based on the spinning E-O sampling technique: determination of precision and calibration

We have developed a terahertz time-domain polarimetry (THz-TDP) system by applying frequency modulation to electro-optic sampling detection in a nonlinear crystal. We characterized the precision of this system in determining the polarization angles to be 1.3° for fixed time delay, and 0.5° for complete time-domain waveform. Furthermore, we calculated the Jones matrix of the optical components used for beam propagation to calibrate the induced systematic error. The advantages of employing this calibration approach are demonstrated on a sapphire crystal investigated at different sample test positions in transmission configuration, and using high resistivity Si, AlN and quartz in reflection geometry. The new THz-TDP technique has the advantage of not using any external polarizers, and therefore is not constrained by their optical performance limitations, such as restricted bandwidths and frequency-dependent extinction ratio. Finally, the THz-TDP technique can be easily implemented on existing time-domain spectroscopy (TDS) systems.

Towards Intense THz Spectroscopy on Water: Characterization of Optical Rectification by GaP, OH1, and DSTMS at OPA Wavelengths

Water is the most prominent solvent. The unique properties of water are rooted in the dynamical hydrogen-bonded network. While TeraHertz (THz) radiation can probe directly the collective molecular network, several open issues remain about the interpretation of these highly anharmonic, coupled bands. In order to address this problem, we need intense THz radiation able to drive the liquid into the nonlinear response regime. Firstly, in this study, we summarize the available brilliant THz sources and compare their emission properties. Secondly, we characterize the THz emission by Gallium Phosphide (GaP), 2-{3-(4-hydroxystyryl)-5,5-dimethylcyclohex-2-enylidene}malononitrile (OH1), and 4-N,N-dimethylamino-4'-N'-methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS) crystals pumped by an amplified near-infrared (NIR) laser with tunable wavelength. We found that both OH1 as well as DSTMS could convert NIR laser radiation between 1200 and 2500 nm into THz radiation with high efficiency (> 2 × 10-4), resulting in THz peak fields exceeding 0.1 MV/cm for modest pump excitation (~ mJ/cm2). DSTMS emits the broadest spectrum, covering the entire bandwidth of our detector from ca. 0.5 to ~7 THz, also at a laser wavelength of 2100 nm. Future improvements will require handling the photothermal damage of these delicate organic crystals, and increasing the THz frequency.

Gas-Phase Infrared Spectroscopy of Neutral Peptides: Insights from the Far-IR and THz Domain

Gas-phase, double resonance IR spectroscopy has proven to be an excellent approach to obtain structural information on peptides ranging from single amino acids to large peptides and peptide clusters. In this review, we discuss the state-of-the-art of infrared action spectroscopy of peptides in the far-IR and THz regime. An introduction to the field of far-IR spectroscopy is given, thereby highlighting the opportunities that are provided for gas-phase research on neutral peptides. Current experimental methods, including spectroscopic schemes, have been reviewed. Structural information from the experimental far-IR spectra can be obtained with the help of suitable theoretical approaches such as dynamical DFT techniques and the recently developed Graph Theory. The aim of this review is to underline how the synergy between far-IR spectroscopy and theory can provide an unprecedented picture of the structure of neutral biomolecules in the gas phase. The far-IR signatures of the discussed studies are summarized in a far-IR map, in order to gain insight into the origin of the far-IR localized and delocalized motions present in peptides and where they can be found in the electromagnetic spectrum.

Molecular dynamics simulations and linear response theories jointly describe biphasic responses of myoglobin relaxation and reveal evolutionarily conserved frequent communicators

In this study, we provide a time-dependent mechanical model, taking advantage of molecular dynamics simulations, quasiharmonic analysis of molecular dynamics trajectories, and time-dependent linear response theories to describe vibrational energy redistribution within the protein matrix. The theoretical description explained the observed biphasic responses of specific residues in myoglobin to CO-photolysis and photoexcitation on heme. The fast responses were found to be triggered by impulsive forces and propagated mainly by principal modes <40 cm⁻¹. The predicted fast responses for individual atoms were then used to study signal propagation within the protein matrix and signals were found to propagate ~8 times faster across helices (4076 m/s) than within the helices, suggesting the importance of tertiary packing in the sensitivity of proteins to external perturbations. We further developed a method to integrate multiple intramolecular signal pathways and discover frequent “communicators”. These communicators were found to be evolutionarily conserved including those distant from the heme.

Essential site scanning analysis: A new approach for detecting sites that modulate the dispersion of protein global motions

Despite the wealth of methods developed for exploring the molecular basis of allostery in biomolecular systems, there is still a need for structure-based predictive tools that can efficiently detect susceptible sites for triggering allosteric responses. Toward this goal, we introduce here an elastic network model (ENM)-based method, Essential Site Scanning Analysis (ESSA). Essential sites are here defined as residues that would significantly alter the protein's global dynamics if bound to a ligand. To mimic the crowding induced upon substrate binding, the heavy atoms of each residue are incorporated as additional network nodes into the α-carbon-based ENM, and the resulting shifts in soft mode frequencies are used as a metric for evaluating the essentiality of each residue. Results on a dataset of monomeric proteins indicate the enrichment of allosteric and orthosteric binding sites, as well as global hinge regions among essential residues, highlighting the significant role of these sites in controlling the overall structural dynamics. Further integration of ESSA with information on predicted pockets and their local hydrophobicity density enables successful predictions of allosteric pockets for both ligand-bound and -unbound structures. ESSA can be efficiently applied to large multimeric systems. Three case studies, namely (i) G-protein binding to a GPCR, (ii) heterotrimeric assembly of the Ser/Thr protein phosphatase PP2A, and (iii) allo-targeting of AMPA receptor, demonstrate the utility of ESSA for identifying essential sites and narrowing down target allosteric sites identified by druggability simulations.

Clustering of atomic displacement parameters in bovine trypsin reveals a distributed lattice of atoms with shared chemical properties

Low-frequency vibrations are crucial for protein structure and function, but only a few experimental techniques can shine light on them. The main challenge when addressing protein dynamics in the terahertz domain is the ubiquitous water that exhibit strong absorption. In this paper, we observe the protein atoms directly using X-ray crystallography in bovine trypsin at 100 K while irradiating the crystals with 0.5 THz radiation alternating on and off states. We observed that the anisotropy of atomic displacements increased upon terahertz irradiation. Atomic displacement similarities developed between chemically related atoms and between atoms of the catalytic machinery. This pattern likely arises from delocalized polar vibrational modes rather than delocalized elastic deformations or rigid-body displacements. The displacement correlation between these atoms were detected by a hierarchical clustering method, which can assist the analysis of other ultra-high resolution crystal structures. These experimental and analytical tools provide a detailed description of protein dynamics to complement the structural information from static diffraction experiments.

Quantum mechanics of proteins in explicit water: The role of plasmon-like solute-solvent interactions

Quantum-mechanical van der Waals dispersion interactions play an essential role in intraprotein and protein-water interactions-the two main factors affecting the structure and dynamics of proteins in water. Typically, these interactions are only treated phenomenologically, via pairwise potential terms in classical force fields. Here, we use an explicit quantum-mechanical approach of density-functional tight-binding combined with the many-body dispersion formalism and demonstrate the relevance of many-body van der Waals forces both to protein energetics and to protein-water interactions. In contrast to commonly used pairwise approaches, many-body effects substantially decrease the relative stability of native states in the absence of water. Upon solvation, the protein-water dispersion interaction counteracts this effect and stabilizes native conformations and transition states. These observations arise from the highly delocalized and collective character of the interactions, suggesting a remarkable persistence of electron correlation through aqueous environments and providing the basis for long-range interaction mechanisms in biomolecular systems.