Chemistry. Following the flow of energy in biomolecules

Deconvolution of dynamic heterogeneity in protein structure

Heterogeneity is intrinsic to the dynamic process of a chemical reaction. As reactants are converted to products via intermediates, the nature and extent of heterogeneity vary temporally throughout the duration of the reaction and spatially across the molecular ensemble. The goal of many biophysical techniques, including crystallography and spectroscopy, is to establish a reaction trajectory that follows an experimentally provoked dynamic process. It is essential to properly analyze and resolve heterogeneity inevitably embedded in experimental datasets. We have developed a deconvolution technique based on singular value decomposition (SVD), which we have rigorously practiced in diverse research projects. In this review, we recapitulate the motivation and challenges in addressing the heterogeneity problem and lay out the mathematical foundation of our methodology that enables isolation of chemically sensible structural signals. We also present a few case studies to demonstrate the concept and outcome of the SVD-based deconvolution. Finally, we highlight a few recent studies with mechanistic insights made possible by heterogeneity deconvolution.

Influence of pump laser fluence on ultrafast myoglobin structural dynamics

High-intensity femtosecond pulses from an X-ray free-electron laser enable pump-probe experiments for the investigation of electronic and nuclear changes during light-induced reactions. On timescales ranging from femtoseconds to milliseconds and for a variety of biological systems, time-resolved serial femtosecond crystallography (TR-SFX) has provided detailed structural data for light-induced isomerization, breakage or formation of chemical bonds and electron transfer1,2. However, all ultrafast TR-SFX studies to date have employed such high pump laser energies that nominally several photons were absorbed per chromophore3-17. As multiphoton absorption may force the protein response into non-physiological pathways, it is of great concern18,19 whether this experimental approach20 allows valid conclusions to be drawn vis-à-vis biologically relevant single-photon-induced reactions18,19. Here we describe ultrafast pump-probe SFX experiments on the photodissociation of carboxymyoglobin, showing that different pump laser fluences yield markedly different results. In particular, the dynamics of structural changes and observed indicators of the mechanistically important coherent oscillations of the Fe-CO bond distance (predicted by recent quantum wavepacket dynamics21) are seen to depend strongly on pump laser energy, in line with quantum chemical analysis. Our results confirm both the feasibility and necessity of performing ultrafast TR-SFX pump-probe experiments in the linear photoexcitation regime. We consider this to be a starting point for reassessing both the design and the interpretation of ultrafast TR-SFX pump-probe experiments20 such that mechanistically relevant insight emerges.

Energy Transport and Its Function in Heptahelical Transmembrane Proteins

Photoproteins such as bacteriorhodopsin (bR) and rhodopsin (Rho) need to effectively dissipate photoinduced excess energy to prevent themselves from damage. Another well-studied seven transmembrane (TM) helices protein is the β₂ adrenergic receptor (β₂AR), a G protein-coupled receptor for which energy dissipation paths have been linked with allosteric communication. To study the vibrational energy transport in the active and inactive states of these proteins, a master equation approach [J. Chem. Phys.2020, 152, 045103] is employed, which uses scaling rules that allow us to calculate energy transport rates solely based on the protein structure. Despite their overall structural similarity, the three 7TM proteins reveal quite different strategies to redistribute excess energy. While bR quickly removes the energy using the TM7 helix as a "lightning rod", Rho exhibits a rather poor energy dissipation, which might eventually require the hydrolysis of the Schiff base between the protein and the retinal chromophore to prevent overheating. Heating the ligand adrenaline of β₂AR, the resulting energy transport network of the protein is found to change significantly upon switching from the active state to the inactive state. While the energy flow may highlight aspects of the inter-residue couplings of β₂AR, it seems not particularly suited to explain allosteric phenomena.

Versatile Vibrational Energy Sensors for Proteins

Vibrational energy transfer (VET) is emerging as key mechanism for protein functions, possibly playing an important role for energy dissipation, allosteric regulation, and enzyme catalysis. A deep understanding of VET is required to elucidate its role in such processes. Ultrafast VIS-pump/IR-probe spectroscopy can detect pathways of VET in proteins. However, the requirement of having a VET donor and a VET sensor installed simultaneously limits the possible target proteins and sites; to increase their number we compare six IR labels regarding their utility as VET sensors. We compare these labels in terms of their FTIR, and VET signature in VET donor-sensor dipeptides in different solvents. Furthermore, we incorporated four of these labels in PDZ3 to assess their capabilities in more complex systems. Our results show that different IR labels can be used interchangeably, allowing for free choice of the right label depending on the system under investigation and the methods available.

Through bonds or contacts? Mapping protein vibrational energy transfer using non-canonical amino acids

Vibrational energy transfer (VET) is essential for protein function. It is responsible for efficient energy dissipation in reaction sites, and has been linked to pathways of allosteric communication. While it is understood that VET occurs via backbone as well as via non-covalent contacts, little is known about the competition of these two transport channels, which determines the VET pathways. To tackle this problem, we equipped the β-hairpin fold of a tryptophan zipper with pairs of non-canonical amino acids, one serving as a VET injector and one as a VET sensor in a femtosecond pump probe experiment. Accompanying extensive non-equilibrium molecular dynamics simulations combined with a master equation analysis unravel the VET pathways. Our joint experimental/computational endeavor reveals the efficiency of backbone vs. contact transport, showing that even if cutting short backbone stretches of only 3 to 4 amino acids in a protein, hydrogen bonds are the dominant VET pathway.

The hydrogen-bond configuration modulates the energy transfer efficiency in helical protein nanotubes

Energy transport in proteins is critical to a variety of physical, chemical, and biological processes in living organisms. While strenuous efforts have been made to study vibrational energy transport in proteins, thermal transport processes across the most fundamental building blocks of proteins, i.e. helices, are not well understood. This work studies energy transport in a group of "isomer" helices. The π-helix is shown to have the highest thermal conductivity, 110% higher than that of the α-helix and 207% higher than that of the 310-helix. The H-bond connectivity is found to govern thermal transport mechanisms including the phonon spectral energy density, dispersion, mode-specific transport, group velocity, and relaxation time. The energy transport is strongly correlated with the H-bond strength which is also modulated by the H-bond connectivity. These fundamental insights provide a novel perspective for understanding energy transfer in proteins and guiding a rational molecule-level design of novel materials with configurable H-bonds.

Mapping Structural Dynamics of Proteins with Femtosecond Stimulated Raman Spectroscopy

The structure-function relationships of biomolecules have captured the interest and imagination of the scientific community and general public since the field of structural biology emerged to enable the molecular understanding of life processes. Proteins that play numerous functional roles in cellular processes have remained in the forefront of research, inspiring new characterization techniques. In this review, we present key theoretical concepts and recent experimental strategies using femtosecond stimulated Raman spectroscopy (FSRS) to map the structural dynamics of proteins, highlighting the flexible chromophores on ultrafast timescales. In particular, wavelength-tunable FSRS exploits dynamic resonance conditions to track transient-species-dependent vibrational motions, enabling rational design to alter functions. Various ways of capturing excited-state chromophore structural snapshots in the time and/or frequency domains are discussed. Continuous development of experimental methodologies, synergistic correlation with theoretical modeling, and the expansion to other nonequilibrium, photoswitchable, and controllable protein systems will greatly advance the chemical, physical, and biological sciences.

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.

Ultrafast Dynamics and Vibrational Relaxation in Six-Coordinate Heme Proteins Revealed by Femtosecond Stimulated Raman Spectroscopy

Identifying the structural rearrangements during photoinduced reactions is a fundamental challenge for understanding from a microscopic perspective the dynamics underlying the functional mechanisms of heme proteins. Here, femtosecond stimulated Raman spectroscopy is applied to follow the ultrafast evolution of two different proteins, each bearing a six-coordinate heme with two amino acid axial ligands. By exploiting the sensitivity of Raman spectra to the structural configuration, we investigate the effects of photolysis and the binding of amino acid residues in cytochrome c and neuroglobin. By comparing the system response for different time delays and Raman pump resonances, we show how detailed properties of atomic motions and energy redistribution can be unveiled. In particular, we demonstrate substantially faster energy flow from the dissociated heme to the protein moiety in cytochrome c, which we assign to the presence of covalent heme–protein bonds.

Dual Illumination Enhances Transformation of an Engineered Green-to-Red Photoconvertible Fluorescent Protein

The molecular mechanisms for the photoconversion of fluorescent proteins remain elusive owing to the challenges of monitoring chromophore structural dynamics during the light-induced processes. We implemented time-resolved electronic and stimulated Raman spectroscopies to reveal two hidden species of an engineered ancestral GFP-like protein LEA, involving semi-trapped protonated and trapped deprotonated chromophores en route to photoconversion in pH 7.9 buffer. A new dual-illumination approach was examined, using 400 and 505 nm light simultaneously to achieve faster conversion and higher color contrast. Substitution of UV irradiation with visible light benefits bioimaging, while the spectral benchmark of a trapped chromophore with characteristic ring twisting and bridge-H bending motions enables rational design of functional proteins. With the improved H-bonding network and structural motions, the photoexcited chromophore could increase the photoswitching-aided photoconversion while reducing trapped species.

Unveiling coupled electronic and vibrational motions of chromophores in condensed phases

The quest for capturing molecular movies of functional systems has motivated scientists and engineers for decades. A fundamental understanding of electronic and nuclear motions, two principal components of the molecular Schrödinger equation, has the potential to enable the de novo rational design for targeted functionalities of molecular machines. We discuss the development and application of a relatively new structural dynamics technique, femtosecond stimulated Raman spectroscopy with broadly tunable laser pulses from the UV to near-IR region, in tracking the coupled electronic and vibrational motions of organic chromophores in solution and protein environments. Such light-sensitive moieties hold broad interest and significance in gaining fundamental knowledge about the intramolecular and intermolecular Hamiltonian and developing effective strategies to control macroscopic properties. Inspired by recent experimental and theoretical advances, we focus on the in situ characterization and spectroscopy-guided tuning of photoacidity, excited state proton transfer pathways, emission color, and internal conversion via a conical intersection.

Ultrafast Structural Changes Decomposed from Serial Crystallographic Data

Direct visualization of electronic and molecular events during biochemical reactions is essential to mechanistic insights. This Letter presents an in-depth analysis of the serial crystallographic data sets collected by Barends and Schlichting et al. ( Science 2015 , 350 , 445 ) that probe the ligand photodissociation in carbonmonoxy myoglobin. This analysis reveals electron density changes caused by the formation of high-spin 3d atomic orbitals of the heme iron upon photolysis and their dynamic behaviors within the first few picoseconds. The heme iron is found popping out of and recoiling back into the heme plane in succession. These findings provide long-awaited visual validations for previous works using ultrafast spectroscopy and molecular dynamics simulations. Electron density variations are also found largely in the solvent during the first period of a low-frequency oscillation. This work demonstrates the importance of the analytical methods in detecting and isolating weak, transient signals of electronic changes arising from chemical reactions.

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.

Probing the communication of deoxythymidine triphosphate in HIV-1 reverse transcriptase by communication maps and interaction energy studies

We calculate communication maps for HIV-1 Reverse Transcriptase (RT) to elucidate energy transfer pathways between deoxythymidine triphosphate (dTTP) and other parts of the protein.

Direct observation of subpicosecond vibrational dynamics in photoexcited myoglobin

Determining the initial pathway for ultrafast energy redistribution within biomolecules is a challenge, and haem proteins, for which energy can be deposited locally in the haem moiety using short light pulses, are suitable model systems to address this issue. However, data acquired using existing experimental techniques that fail to combine sufficient structural sensitivity with adequate time resolution have resulted in alternative hypotheses concerning the interplay between energy flow among highly excited vibrational levels and potential concomitant electronic processes. By developing a femtosecond-stimulated Raman set-up, endowed with the necessary tunability to take advantage of different resonance conditions, here we visualize the temporal evolution of energy redistribution over different vibrational modes in myoglobin. We establish that the vibrational energy initially stored in the highly excited Franck-Condon manifold is transferred with different timescales into low- and high-frequency modes, prior to slow dissipation through the protein. These findings demonstrate that a newly proposed mechanism involving the population dynamics of specific vibrational modes settles the controversy on the existence of transient electronic intermediates.

Femtosecond structural dynamics drives the trans/cis isomerization in photoactive yellow protein

A variety of organisms have evolved mechanisms to detect and respond to light, in which the response is mediated by protein structural changes after photon absorption. The initial step is often the photoisomerization of a conjugated chromophore. Isomerization occurs on ultrafast time scales and is substantially influenced by the chromophore environment. Here we identify structural changes associated with the earliest steps in the trans-to-cis isomerization of the chromophore in photoactive yellow protein. Femtosecond hard x-ray pulses emitted by the Linac Coherent Light Source were used to conduct time-resolved serial femtosecond crystallography on photoactive yellow protein microcrystals over a time range from 100 femtoseconds to 3 picoseconds to determine the structural dynamics of the photoisomerization reaction.

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.

Protein Thermal Conductivity Measured in the Solid State Reveals Anharmonic Interactions of Vibrations in a Fractal Structure

Energy processes and vibrations in biological macromolecules such as proteins ultimately dictate biological, chemical, and physical functions in living materials. These energetic vibrations in the ribbon-like motifs of proteins interact on self-similar structures and fractal-like objects over a range of length scales of the protein (a few angstroms to the size of the protein itself, a few nanometers). In fact, the fractal geometries of protein molecules create a complex network of vibrations; therefore, proteins represent an ideal material system to study the underlying mechanisms driving vibrational thermal transport in a dense, fractal network. However, experimental studies of thermal energy transport in proteins have been limited to dispersive protein suspensions, which limits the knowledge that can be extracted about how vibrational energy is transferred in a pure protein solid. We overcome this by synthesizing solid, water-insoluble protein films for thermal conductivity measurements via time-domain thermoreflectance. We measure the thermal conductivity of bovine serum albumin and myoglobin solid films over a range of temperatures from 77 to 296 K. These temperature trends indicate that anharmonic coupling of vibrations in the protein is contributing to thermal conductivity. This first-ever observation of anharmonic-like trends in the thermal conductivity of a fully dense protein forms the basis of validation of seminal theories of vibrational energy-transfer processes in fractal objects.

Deep UV resonance Raman spectroscopy of β-sheet amyloid fibrils: a QM/MM simulation

We present a combined quantum mechanics and molecular mechanics study of the deep ultraviolet ππ* resonance Raman spectra of β-sheet amyloid fibrils Aβ(34-42) and Aβ(1-40). Effects of conformational fluctuations are described using a Ramachandran angle map, thus avoiding repeated ab initio calculations. Experimentally observed effects of hydrogen-deuterium exchange are reproduced. We propose that the AmIII band redshift upon deuteration is caused by the loss of coupling between C(α)-H bending and N-D bending modes, rather than by peptide bond hydration.

Vibrational energy transport in the presence of intrasite vibrational energy redistribution

The mechanism of vibrational energy flow is studied in a regime where a diffusion equation is likely to break down, i.e., on length scales of a few chemical bonds and time scales of a few picoseconds. This situation occurs, for example, during photochemical reactions in protein environment. To that end, a toy model is introduced that on the one hand mimics the vibrational normal mode distribution of proteins, and on the other hand is small enough to numerically time propagate the system fully quantum mechanically. Comparing classical and quantum-mechanical results, the question is addressed to what extent the classical nature of the molecular dynamics simulations (which would be the only choice for the modeling of a real molecular system) affects the vibrational energy flow mechanism. Small differences are found which are due to the different ways classical and quantum mechanics distribute thermal energy over vibrational modes. In either case, a ballistic and a diffusive phase can be identified. For these small length and time scales, the latter is governed by intrasite vibrational energy redistribution, since vibrational energy does not necessarily thermalize completely within individual peptide units. Overall, the model suggests a picture that unifies many of the observations made recently in experiments.

Low-frequency mode activity of heme: femtosecond coherence spectroscopy of iron porphine halides and nitrophorin

The low-frequency mode activity of metalloporphyrins has been studied for iron porphine-halides (Fe(P)(X), X = Cl, Br) and nitrophorin 4 (NP4) using femtosecond coherence spectroscopy (FCS) in combination with polarized resonance Raman spectroscopy and density functional theory (DFT). It is confirmed that the mode symmetry selection rules for FCS are the same as for Raman scattering and that both Franck-Condon and Jahn-Teller mode activities are observed for Fe(P)(X) under Soret resonance conditions. The DFT-calculated low-frequency (20-400 cm (-1)) modes, and their frequency shifts upon halide substitution, are in good agreement with experimental Raman and coherence data, so that mode assignments can be made. The doming mode is located at approximately 80 cm (-1) for Fe(P)(Cl) and at approximately 60 cm (-1) for Fe(P)(Br). NP4 is also studied with coherence techniques, and the NO-bound species of ferric and ferrous NP4 display a mode at approximately 30-40 cm (-1) that is associated with transient heme doming motion following NO photolysis. The coherence spectra of three ferric derivatives of NP4 with different degrees of heme ruffling distortion are also investigated. We find a mode at approximately 60 cm (-1) whose relative intensity in the coherence spectra depends quadratically on the magnitude of the ruffling distortion. To quantitatively account for this correlation, a new "distortion-induced" Raman enhancement mechanism is presented. This mechanism is unique to low-frequency "soft modes" of the molecular framework that can be distorted by environmental forces. These results demonstrate the potential of FCS as a sensitive probe of dynamic and functionally important nonplanar heme vibrational excitations that are induced by the protein environmental forces or by the chemical reactions in the aqueous phase.

Femtobiology

Functions of biologically active molecules are frequently initiated by elementary chemical reactions such as energy and electron transfer, cis-trans isomerizations, and proton transfer. The nature of these reactions generally makes them very fast and efficient, occurring on picosecond and femtosecond timescales. Ultrafast spectroscopy has played an important role in the study of a number of biological processes and has provided unique information about several of nature's responses to light. Here I review the current understanding of light-energy collection and conversion in photosynthesis, the function of carotenoid molecules in photosynthesis, and the primary light-initiated reactions of the photoreceptors rhodopsin, bacteriorhodopsin, photoactive yellow protein, phytochrome, and a new type of blue-light receptor based on flavin chromophores.

Coherence spectroscopy investigations of the low-frequency vibrations of heme: effects of protein-specific perturbations

Femtosecond coherence spectroscopy is used to probe the low-frequency (20-200 cm(-1)) vibrational modes of heme proteins in solution. Horseradish peroxidase (HRP), myoglobin (Mb), and Campylobacter jejuni globin (Cgb) are compared and significant differences in the coherence spectra are revealed. It is concluded that hydrogen bonding and ligand charge do not strongly affect the low-frequency coherence spectra and that protein-specific deformations of the heme group lower its symmetry and control the relative spectral intensities. Such deformations potentially provide a means for proteins to tune heme reaction coordinates, so that they can perform a broad array of specific functions. Native HRP displays complex spectral behavior above approximately 50 cm(-1) and very weak activity below approximately 50 cm(-1). Binding of the substrate analog, benzhydroxamic acid, leads to distinct changes in the coherence and Raman spectra of HRP that are consistent with the stabilization of a heme water ligand. The CN derivatives of the three proteins are studied to make comparisons under conditions of uniform heme coordination and spin-state. MbCN is dominated by a doming mode near 40 cm(-1), while HRPCN displays a strong oscillation at higher frequency (96 cm(-1)) that can be correlated with the saddling distortion observed in the X-ray structure. In contrast, CgbCN displays low-frequency coherence spectra that contain strong modes near 30 and 80 cm(-1), probably associated with a combination of heme doming and ruffling. HRPNO displays a strong doming mode near 40 cm(-1) that is activated by photolysis. The damping of the coherent motions is significantly reduced when the heme is shielded from solvent fluctuations by the protein material and reduced still further when T approximately < 50 K, as pure dephasing processes due to the protein-solvent phonon bath are frozen out.

Femtosecond Stimulated Raman Spectroscopy

Femtosecond stimulated Raman spectroscopy (FSRS) is a new ultrafast spectroscopic technique that provides vibrational structural information with high temporal (50-fs) and spectral (10-cm(1)) resolution. As a result of these unique capabilities, FSRS studies of chemical and biochemical reaction dynamics are expected to grow rapidly, giving previously unattainable insight into the structural dynamics of reactively evolving systems with atomic spatial and femtosecond temporal resolution. This review discusses the experimental and theoretical concepts behind FSRS, with an emphasis on the origins of its unique temporal and spectral capabilities. We illustrate these capabilities with vibrational studies of ultrafast electronic dynamics, as well as the direct structural observation of nonstationary vibrational wave-packet motion in small molecules and in complex biochemical reaction dynamics.

Time-resolved methods in biophysics. 4. Broadband pump–probe spectroscopy system with sub-20 fs temporal resolution for the study of energy transfer processes in photosynthesis

In this paper we discuss how to push the temporal resolution limits of transient absorption spectroscopy in order to detect very fast processes (energy relaxation, energy or charge transfer, vibrational coherence) taking place in molecules of biological relevance. After reviewing the main principles of femtosecond pump-probe spectroscopy, we describe an experimental setup based on two synchronized non-collinear optical parametric amplifiers (NOPAs). Each NOPA can be independently configured to generate ultra-broadband sub-10 fs visible pulses, tunable 10-15 fs visible pulses, tunable 15-40 fs near-infrared pulses (900-1500 nm). This system enables to perform pump-probe experiments over nearly two octaves of spectrum with sub-20 fs temporal resolution. We then present an application example highlighting the capability of this instrument to track excited state dynamics in biomolecules on the sub-100 fs timescale: the study of carotenoid-bacteriochlorophyll energy transfer processes in peripheral light-harvesting complexes (LH2) from purple bacteria. We show that, by comparing excited-state dynamics of the carotenoids in organic solvents and inside the LH2 complexes, it is possible to visualize in the time domain the primary events in photosynthesis.

Dynamics of clusters: from elementary to biological structures

Between isolated atoms or molecules and bulk materials there lies a class of unique structures, known as clusters, that consist of a few to hundreds of atoms or molecules. Within this range of "nanophase," many physical and chemical properties of the materials evolve as a function of cluster size, and materials may exhibit novel properties due to quantum confinement effects. Understanding these phenomena is in its own rights fundamental, but clusters have the additional advantage of being controllable model systems for unraveling the complexity of condensed-phase and biological structures, not to mention their vanguard role in defining nanoscience and nanotechnology. Over the last two decades, much progress has been made, and this short overview highlights our own involvement in developing cluster dynamics, from the first experiments on elementary systems to model systems in the condensed phase, and on to biological structures.