Multiple Interacting Collective Modes and Phonon Gap in Phospholipid Membranes

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.

In-plane and out-of-plane gigahertz sound velocities of saturated and unsaturated phospholipid bilayers from cryogenic to room temperatures

Here, we examined the gigahertz sound velocities of hydrated multibilayers of saturated (1,2-dimyristoyl-sn-glycero-3-phosphocholine, DMPC) and unsaturated (1,2-dioleoyl-sn-glycero-3-phosphocholine, DOPC) phospholipids by Brillouin spectroscopy. Out-of-plane and in-plane (lateral) phonons were studied independently of each other. Similar strong temperature dependences of the sound velocities were found for phonons of both types. The sound velocities in the low-temperature limit were two-fold higher than that at physiological temperatures; a significant part of the changes in sound velocity occurs in the solid-like gel phase. The factors that may be involved in the peculiar behavior of sound velocity include changes in the chain conformational state, relaxation susceptibility, changes in the elastic modulus at infinite frequencies, and lateral packing of molecules.

Real Space and Time Imaging of Collective Headgroup Dipole Motions in Zwitterionic Lipid Bilayers

Lipid bilayers are supramolecular structures responsible for a range of processes, such as transmembrane transport of ions and solutes, and sorting and replication of genetic materials, to name just a few. Some of these processes are transient and currently, cannot be visualized in real space and time. Here, we developed an approach using 1D, 2D, and 3D Van Hove correlation functions to image collective headgroup dipole motions in zwitterionic phospholipid bilayers. We show that both 2D and 3D spatiotemporal images of headgroup dipoles are consistent with commonly understood dynamic features of fluids. However, analysis of the 1D Van Hove function reveals lateral transient and re-emergent collective dynamics of the headgroup dipoles-occurring at picosecond time scales-that transmit and dissipate heat at longer times, due to relaxation processes. At the same time, the headgroup dipoles also generate membrane surface undulations due a collective tilting of the headgroup dipoles. A continuous intensity band of headgroup dipole spatiotemporal correlations-at nanometer length and nanosecond time scales-indicates that dipoles undergo stretching and squeezing elastic deformations. Importantly, the above mentioned intrinsic headgroup dipole motions can be externally stimulated at GHz-frequency scale, enhancing their flexoelectric and piezoelectric capabilities (i.e., increased conversion efficiency of mechanical energy into electric energy). In conclusion, we discuss how lipid membranes can provide molecular-level insights about biological learning and memory, and as platforms for the development of the next generation of neuromorphic computers.

The Phonon Theory of Liquids and Biological Fluids: Developments and Applications

Among the three basic states of matter (solid, liquid, and gas), the liquid state has always eluded general theoretical approaches for describing liquid energy and heat capacity. In this Viewpoint, we derive the phonon theory of liquids and biological fluids stemming from Frenkel's microscopic picture of the liquid state. Specifically, the theory predicts the existence of phonon gaps in vibrational spectra of liquids and a thermodynamic boundary in the supercritical state. Direct experimental evidence reaffirming these theoretical predictions was achieved through a combination of techniques using static compression X-ray diffraction and inelastic X-ray scattering on deeply supercritical argon in a diamond anvil cell. Furthermore, these findings inspired and then led to the discovery of phonon gaps in liquid crystals (mesogens), block copolymers, and biological membranes. Importantly, phonon gaps define viscoelastic crossovers in cellular membranes responsible for lipid self-diffusion, lateral molecular-level stress propagation, and passive transmembrane transport of small molecules and solutes. Finally, molecular interactions mediated by external stimuli result in synaptic activity controlling biological membranes' plasticity resulting in learning and memory. Therefore, we also discuss learning and memory effects─equally important for neuroscience as well as for the development of neuromorphic devices─facilitated in biological membranes by external stimuli.

Dynamic response on a nanometer scale of binary phospholipid-cholesterol vesicles: Low-frequency Raman scattering insight

Low-frequency Raman spectroscopy was used to study the dynamic response on a nanometer scale of aqueous suspensions of two-component lipid vesicles. Binary mixtures of saturated phospholipid (1,2-dipalmitoyl-sn-glycero-3-phosphocholine, DPPC) and cholesterol are interesting for possible coexistence of solidlike and liquid-ordered phases, while the phase coexistence was not reported for unsaturated phospholipid (1,2-dioleoyl-sn-glycero-3-phosphocholine, DOPC) and cholesterol mixtures. The DOPC-DPPC mixtures represent the well-documented case of coexisting domains of solidlike and liquid-disordered phases. These three series of lipid mixtures are studied here. A broad peak with the maximum in the range of 30-50cm^{-1} and a narrow peak near 10cm^{-1} are observed in the Raman susceptibility of the binary mixtures and attributed to the acousticlike vibrational density of states and layer modes, respectively. Parameters of the broad and narrow peaks are sensitive to lateral and conformational hydrocarbon chain ordering. It was also demonstrated that the low-frequency Raman susceptibility of multicomponent lipid bilayers allows one to determine the phase state of lipid bilayers and distinguish the homogeneous distribution of molecular complexes from coexisting domains with sizes above several nanometers. Thus, the low-frequency Raman spectroscopy provides unique information in studying phase coexistence in lipid bilayers.

Modulation of Membrane Fluidity to Control Interfacial Water Structure and Dynamics in Saturated and Unsaturated Phospholipid Vesicles

The structure and dynamics of interfacial water in biological systems regulate the biochemical reactions. But, it is still enigmatic how the behavior of the interfacial water molecule is controlled. Here, we have investigated the effect of membrane fluidity on the structure and dynamics of interfacial water molecules in biologically relevant phopholipid vesicles. This study delineates that modulation of membrane fluidity through interlipid separation and unsaturation not only mitigate membrane rigidity but also disrupt the strong hydrogen bond (H-bond) network around the lipid bilayer interface. As a result, a disorder in H-bonding between water molecules arises several layers beyond the first hydration shell of the polar headgroup, which essentially modifies the interfacial water structure and dynamics. Furthermore, we have also provided evidence of increasing transportation through these modulated membranes, which enhance the membrane mediated isomerization reaction rate.

Phonon-mediated lipid raft formation in biological membranes

Short-wavelength collective molecular motions, also known as phonons, have recently attracted much interest in revealing dynamic properties of biological membranes through the use of neutron and X-ray scattering, infrared and Raman spectroscopies, and molecular dynamics simulations. Experimentally detecting unique vibrational patterns such as, shear phonon excitations, viscoelastic crossovers, transverse acoustic phonon gaps, and continuous and truncated optical phonon modes in cellular membranes, to name a few, has proven non-trivial. Here, we review recent advances in liquid thermodynamics that have resulted in the development of the phonon theory of liquids. The theory has important predictions regarding the shear vibrational spectra of fluids, namely the emergence of viscoelastic crossovers and transverse acoustic phonon gaps. Furthermore, we show that these vibrational patterns are common in soft (non-crystalline) materials, including, but not limited to liquids, colloids, liquid crystals (mesogens), block copolymers, and biological membranes. The existence of viscoelastic crossovers and acoustic phonon gaps define the self-diffusion properties of cellular membranes and provide a molecular picture of the transient nature of lipid rafts (Bolmatov et al., 2020). Importantly, the timescales (picoseconds) for the formation and dissolution of transient lipid rafts match the lifetime of the formation and breakdown of interfacial water hydrogen bonds. Apart from acoustic propagating phonon modes, biological membranes can also support more energetic non-propagating optical phonon excitations, also known as standing waves or breathing modes. Importantly, optical phonons can be truncated due to the existence of finite size nanodomains made up of strongly correlated lipid-cholesterol molecular pairs. These strongly coupled molecular pairs can serve as nucleation centers for the formation of stable rafts at larger length scales, due to correlations of spontaneous fluctuations (Onsager's regression hypothesis). Finally and importantly, molecular level viscoelastic crossovers, acoustic phonon gaps, and continuous and truncated optical phonon modes may offer insights as to how lipid-lipid and lipid-protein interactions enable biological function.

Molecular Picture of the Transient Nature of Lipid Rafts

In biological membranes, lipid rafts are now thought to be transient and nanoscopic. However, the mechanism responsible for these nanoscopic assemblies remains poorly understood, even in the case of model membranes. As a result, it has proven extremely challenging to probe the physicochemical properties of lipid rafts at the molecular level. Here, we use all-atom molecular dynamics (MD) simulations and inelastic X-ray scattering (IXS), an intrinsically nanoscale technique, to directly probe the energy transfer and collective short-wavelength dynamics (phonons) of biologically relevant model membranes. We show that the nanoscale propagation of stress in lipid rafts takes place in the form of collective motions made up of longitudinal (compression waves) and transverse (shear waves) molecular vibrations. Importantly, we provide a molecular picture for the so-called van der Waals mediated "force from lipid" [Anishkin, A. et al. Proc. Natl. Acad. Sci. U.S.A. 2014, 111, 7898], a key parameter for the ionic channel mechano-transduction and the mechanism for the lipid transfer of molecular level stress [Aponte-Santamarı́a, C. et al. J. Am. Chem. Soc. 2017, 139, 13588]. Specifically, we describe how lipid rafts are formed and maintained through the propagation of molecular stress, lipid raft rattling dynamics, and a relaxation process. Eventually, the rafts dissipate through the self-diffusion of lipids making up the rafts. We also show that the molecular stress and viscoelastic properties of transient lipid rafts can be modulated through the use of hydrophobic biomolecules such as melatonin and tryptophan. Ultimately, the herein proposed mechanism describing the molecular interactions for the formation and dissolution of lipid rafts may offer insights as to how lipid rafts enable biological function.

Functional lipid pairs as building blocks of phase-separated membranes

Biological membranes exhibit a great deal of compositional and phase heterogeneity due to hundreds of chemically distinct components. As a result, phase separation processes in cell membranes are extremely difficult to study, especially at the molecular level. It is currently believed that the lateral membrane heterogeneity and the formation of domains, or rafts, are driven by lipid-lipid and lipid-protein interactions. Nevertheless, the underlying mechanisms regulating membrane heterogeneity remain poorly understood. In the present work, we combine inelastic X-ray scattering with molecular dynamics simulations to provide direct evidence for the existence of strongly coupled transient lipid pairs. These lipid pairs manifest themselves experimentally through optical vibrational (a.k.a. phononic) modes observed in binary (1,2-dipalmitoyl-sn-glycero-3-phosphocholine [DPPC]-cholesterol) and ternary (DPPC-1,2-dioleoyl-sn-glycero-3-phosphocholine/1-palmitoyl-2-oleoyl-glycero-3-phosphocholine [DOPC/POPC]-cholesterol) systems. The existence of a phononic gap in these vibrational modes is a direct result of the finite size of patches formed by these lipid pairs. The observation of lipid pairs provides a spatial (subnanometer) and temporal (subnanosecond) window into the lipid-lipid interactions in complex mixtures of saturated/unsaturated lipids and cholesterol. Our findings represent a step toward understanding the lateral organization and dynamics of membrane domains using a well-validated probe with a high spatial and temporal resolution.

Dynamic structure factor of a lipid bilayer in the presence of a high electric field

The influence of a high average electric field (∼1 V/nm) in the hydrophobic interior of a bilayer lipid membrane on short-wavelength in-plane phononic motions of lipid chains is considered. The average electric field is assumed to be nearly constant on a picosecond time scale and a nanometer length scale. This field may be induced, for instance, by externally applied subnanosecond electric pulses or the membrane dipole potential. Using a generalized hydrodynamic approach, we derive a corresponding electrohydrodynamic model generalized to high wave numbers. In the considered approximation, all electric field effects are reduced only to a constant contribution to the generalized isothermal compressibility modulus. The corresponding dynamic structure factor for a lipid bilayer is derived. We show that due to polarization effects, the high field can critically impact the dynamics of longitudinal acousticlike modes at wave numbers near the major peak of the static structure factor. We estimate quantitatively that for typical lipid bilayers, transverse high electric fields can cause strong phonon energy softening, enhancement of phonon population, and formation of a gap in the dispersion of excitation frequency. The results obtained agree with simulations of the initiation of lipid bilayer electropores, suggesting that the proposed model reproduces the essential features of the field's impact on atomic density fluctuations. The proposed mechanism may have significant implications for the understanding of electroporation, passive molecular transport, and spontaneous pore formation in lipid bilayers.