Second quantization of many-body dispersion interactions for chemical and biological systems.

The many-body dispersion (MBD) framework is a successful approach for modeling the long-range electronic correlation energy and optical response of systems with thousands of atoms. Inspired by field theory, here we develop a second-quantized MBD formalism (SQ-MBD) that recasts a system of atomic quantum Drude oscillators in a Fock-space representation. SQ-MBD provides: (i) tools for projecting observables (interaction energy, transition multipoles, polarizability tensors) on coarse-grained representations of the atomistic system ranging from single atoms to large structural motifs, (ii) a quantum-information framework to analyze correlations and (non)separability among fragments in a given molecular complex, and (iii) a path toward the applicability of the MBD framework to molecular complexes with even larger number of atoms. The SQ-MBD approach offers conceptual insights into quantum fluctuations in molecular systems and enables direct coupling of collective plasmon-like MBD degrees of freedom with arbitrary environments, providing a tractable computational framework to treat dispersion interactions and polarization response in intricate systems.

Examining the origins of observed terahertz modes from an optically pumped atomistic model protein in aqueous solution.

The microscopic origins of terahertz (THz) vibrational modes in biological systems are an active and open area of current research. Recent experiments [Phys Rev X. 8, 031061 (2018)] have revealed the presence of a pronounced mode at ∼0.3 THz in fluorophore-decorated bovine serum albumin (BSA) protein in aqueous solution under nonequilibrium conditions induced by optical pumping. This result was heuristically interpreted as a collective elastic fluctuation originating from the activation of a low-frequency phonon mode. In this work, we show that the sub-THz spectroscopic response emerges in a statistically significant manner (>2σ) from such collective behavior, illustrating how photoexcitation can alter specific THz vibrational modes. We revisit the theoretical analysis with proof-of-concept molecular dynamics that introduce optical excitations into the simulations. Using information theory techniques, we show that these excitations can give rise to a multiscale response involving two optically excited chromophores (tryptophans), other amino acids in the protein, ions, and water. Our results motivate new experiments and fully nonequilibrium simulations to probe these phenomena, as well as the refinement of atomistic models of Fröhlich condensates that are fundamentally determined by nonlinear interactions in biology.

Experimental evidence for long-distance electrodynamic intermolecular forces.

Both classical and quantum electrodynamics predict the existence of dipole-dipole long-range electrodynamic intermolecular forces; however, these have never been hitherto experimentally observed. The discovery of completely new and unanticipated forces acting between biomolecules could have considerable impact on our understanding of the dynamics and functioning of the molecular machines at work in living organisms. Here, using two independent experiments, on the basis of different physical effects detected by fluorescence correlation spectroscopy and terahertz spectroscopy, respectively, we demonstrate experimentally the activation of resonant electrodynamic intermolecular forces. This is an unprecedented experimental proof of principle of a physical phenomenon that, having been observed for biomacromolecules and with long-range action (up to 1000 Å), could be of importance for biology. In addition to thermal fluctuations that drive molecular motion randomly, these resonant (and thus selective) electrodynamic forces may contribute to molecular encounters in the crowded cellular space.

Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions.

Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of energy level submanifolds of the phase space. However, the sufficiency conditions are still a wide open question. In this study, a first important step forward was performed in this direction; in fact, a differential equation was worked out which describes how entropy varies as a function of total energy, and this variation is driven by the total energy dependence of a topology-related quantity of the relevant submanifolds of the phase space. Hence, general conditions can be in principle defined for topology-driven loss of differentiability of the entropy.

Fine-Structure Constant Connects Electronic Polarizability and Geometric van-der-Waals Radius of Atoms.

The fine-structure constant (FSC) measures the coupling strength between photons and charged particles and is more strongly associated with quantum electrodynamics than with atomic and molecular physics. Here we present an elementary derivation that accurately predicts the electronic polarizability of atoms A from their geometric van-der-Waals (vdW) radius RvdW and the FSC α through the compact formula A = (4πε0/a04) × α4/3RvdW7, where ε0 is the permittivity of free space and a0 is the Bohr radius. The validity of this formula is empirically confirmed by estimating the value of α from nonrelativistic quantum calculations of atomic polarizabilities and atomic vdW radii obtained from both theory and experiment. Our heuristic derivation based on empirical data extends the influence of FSC from quantum electrodynamics and specific materials properties such as the visual transparency of graphene to atomic electronic properties throughout the periodic table of elements.

Geometrical Aspects in the Analysis of Microcanonical Phase-Transitions.

In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the energy level sets of the Hamiltonian of a system under investigation. In particular, it turns out that peculiar behaviours of thermodynamic observables at a phase transition point are rooted in more fundamental changes of the geometry of the energy level sets in phase space. More specifically, we discuss how microcanonical and geometrical descriptions of phase-transitions are shaped in the special case of ϕ 4 models with either nearest-neighbours and mean-field interactions.

Publisher Correction: Collective behavior of oscillating electric dipoles.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Coherent Riemannian-geometric description of Hamiltonian order and chaos with Jacobi metric.

By identifying Hamiltonian flows with geodesic flows of suitably chosen Riemannian manifolds, it is possible to explain the origin of chaos in classical Newtonian dynamics and to quantify its strength. There are several possibilities to geometrize Newtonian dynamics under the action of conservative potentials and the hitherto investigated ones provide consistent results. However, it has been recently argued that endowing configuration space with the Jacobi metric is inappropriate to consistently describe the stability/instability properties of Newtonian dynamics because of the nonaffine parametrization of the arc-length with physical time. On the contrary, in the present paper, it is shown that there is no such inconsistency and that the observed instabilities in the case of integrable systems using the Jacobi metric are artifacts.

Collective behavior of oscillating electric dipoles.

We investigate the dynamics of a population of identical biomolecules mimicked as electric dipoles with random orientations and positions in space and oscillating with their intrinsic frequencies. The biomolecules, beyond being coupled among themselves via the dipolar interaction, are also driven by a common external energy supply. A collective mode emerges by decreasing the average distance among the molecules as testified by the emergence of a clear peak in the power spectrum of the total dipole moment. This is due to a coherent vibration of the most part of the molecules at a frequency definitely larger than their own frequencies corresponding to a partial cluster synchronization of the biomolecules. These results can be verified experimentally via spectroscopic investigations of the strength of the intermolecular electrodynamic interactions, thus being able to test the possible biological relevance of the observed macroscopic mode.

Detection of long-range electrostatic interactions between charged molecules by means of fluorescence correlation spectroscopy.

In the present paper, an experimental feasibility study on the detection of long-range intermolecular interactions through three-dimensional molecular diffusion in solution is performed. This follows recent theoretical and numerical analyses reporting that long-range electrodynamic forces between biomolecules could be identified through deviations from Brownian diffusion. The suggested experimental technique was fluorescence correlation spectroscopy (FCS). By considering two oppositely charged molecular species in aqueous solution, namely, lysozymes and fluorescent dye molecules (Alexa488), the diffusion coefficient of the dyes has been measured for different values of the concentration of lysozyme, that is, for different average distances between the oppositely charged molecules. For our model, long-range interactions are of electrostatic origin, suggesting that their action radius can be varied by changing the ionic strength of the solution. The experimental outcomes clearly prove the detectability of long-range intermolecular interactions by means of the FCS technique. Molecular dynamics simulations provide a clear and unambiguous interpretation of the experimental results.

Persistent homology analysis of phase transitions.

Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called mean-field XY model and by the ϕ^{4} lattice model, respectively. For both models the relationship between phase transitions and the topological properties of certain submanifolds of configuration space are exactly known. It turns out that these a priori known facts are clearly retrieved by persistent homology analysis of dynamically sampled submanifolds of configuration space.

Random walk of passive tracers among randomly moving obstacles.

BACKGROUND: This study is mainly motivated by the need of understanding how the diffusion behavior of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target. METHOD: By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle among randomly moving and interacting obstacles. RESULTS: The relevant physical quantity which is worked out is the diffusion coefficient of the passive tracer which is computed as a function of the average inter-obstacles distance. CONCLUSIONS: The results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its motion can be considerably slowed down.

Experimental detection of long-distance interactions between biomolecules through their diffusion behavior: numerical study.

The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is shown that when the particles are uniformly distributed throughout the accessible space, the self-diffusion coefficient is always lowered by the considered interparticle interactions, irrespective of their attractive or repulsive character. This fact is also confirmed by a simple model to compute the correction to the Brownian diffusion coefficient due to the interactions among the particles. These interactions are also responsible for the onset of dynamical chaos and an associated chaotic diffusion which still follows an Einstein-Fick-like law for the mean-square displacement as a function of time. Transitional phenomena are observed for Coulomb-electrostatic (repulsive) and dipole-electrodynamic (attractive) interactions considered both separately and in competition. The outcomes reported in this paper clearly indicate a feasible experimental method to probe the activation of resonant electrodynamic interactions among biomolecules.