Topological origin of the protein folding transition.

In this paper, a geometrical and thermodynamical analysis of the global properties of the potential energy landscape of a minimalistic model of a polypeptide is presented. The global geometry of the potential energy landscape is supposed to contain relevant information about the properties of a given sequence of amino acids, that is, to discriminate between a random heteropolymer and a protein. By considering the SH3 and PYP protein-sequences and their randomized versions it turns out that, in addition to the standard signatures of the folding transition-discriminating between protein sequences of amino acids and random heteropolymer sequences-also peculiar geometric signatures of the equipotential hypersurfaces in configuration space can discriminate between proteins and random heteropolymers. Interestingly, these geometric signatures are the "shadows" of deeper topological changes that take place in correspondence with the protein folding transition. The protein folding transition takes place in systems with a small number of degrees of freedom (very far from the Avogadro number) and in the absence of a symmetry-breaking phenomenon. Nevertheless, seen from the deepest level of topology changes of equipotential submanifolds of phase space, the protein folding transition fully qualifies as a phase transition.

Agent-based models for detecting the driving forces of biomolecular interactions.

Agent-based modelling and simulation have been effectively applied to the study of complex biological systems, especially when composed of many interacting entities. Representing biomolecules as autonomous agents allows this approach to bring out the global behaviour of biochemical processes as resulting from local molecular interactions. In this paper, we leverage the capabilities of the agent paradigm to construct an in silico replica of the glycolytic pathway; the aim is to detect the role that long-range electrodynamic forces might have on the rate of glucose oxidation. Experimental evidences have shown that random encounters and short-range potentials might not be sufficient to explain the high efficiency of biochemical reactions in living cells. However, while the latest in vitro studies are limited by present-day technology, agent-based simulations provide an in silico support to the outcomes hitherto obtained and shed light on behaviours not yet well understood. Our results grasp properties hard to uncover through other computational methods, such as the effect of electromagnetic potentials on glycolytic oscillations.

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.

Transition between Random and Periodic Electron Currents on a DNA Chain.

By resorting to a model inspired to the standard Davydov and Holstein-Fröhlich models, in the present paper we study the motion of an electron along a chain of heavy particles modeling a sequence of nucleotides proper to a DNA fragment. Starting with a model Hamiltonian written in second quantization, we use the Time Dependent Variational Principle to work out the dynamical equations of the system. It can be found that, under the action of an external source of energy transferred to the electron, and according to the excitation site, the electron current can display either a broad frequency spectrum or a sharply peaked frequency spectrum. This sequence-dependent charge transfer phenomenology is suggestive of a potentially rich variety of electrodynamic interactions of DNA molecules under the action of electron excitation. This could imply the activation of interactions between DNA and transcription factors, or between DNA and external electromagnetic fields.

Energy transfer to the phonons of a macromolecule through light pumping.

In the present paper we address the problem of the energy downconversion of the light absorbed by a protein into its internal vibrational modes. We consider the case in which the light receptors are fluorophores either naturally co-expressed with the protein or artificially covalently bound to some of its amino acids. In a recent work [Phys. Rev. X 8, 031061 (2018)], it has been experimentally found that by shining a laser light on the fluorophores attached to a protein the energy fed to it can be channeled into the normal mode of lowest frequency of vibration thus making the subunits of the protein coherently oscillate. Even if the phonon condensation phenomenon has been theoretically explained, the first step - the energy transfer from electronic excitation into phonon excitation - has been left open. The present work is aimed at filling this gap.

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.

Riemannian-geometric entropy for measuring network complexity.

A central issue in the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate with a-in principle, any-network a differentiable object (a Riemannian manifold) whose volume is used to define the entropy. The effectiveness of the latter in measuring network complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale-free networks, as well as of characterizing small exponential random graphs, configuration models, and real networks.

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.

Topology driven modeling: the IS metaphor.

In order to define a new method for analyzing the immune system within the realm of Big Data, we bear on the metaphor provided by an extension of Parisi's model, based on a mean field approach. The novelty is the multilinearity of the couplings in the configurational variables. This peculiarity allows us to compare the partition function [Formula: see text] with a particular functor of topological field theory-the generating function of the Betti numbers of the state manifold of the system-which contains the same global information of the system configurations and of the data set representing them. The comparison between the Betti numbers of the model and the real Betti numbers obtained from the topological analysis of phenomenological data, is expected to discover hidden n-ary relations among idiotypes and anti-idiotypes. The data topological analysis will select global features, reducible neither to a mere subgraph nor to a metric or vector space. How the immune system reacts, how it evolves, how it responds to stimuli is the result of an interaction that took place among many entities constrained in specific configurations which are relational. Within this metaphor, the proposed method turns out to be a global topological application of the S[B] paradigm for modeling complex systems.

Possible role of electrodynamic interactions in long-distance biomolecular recognition.

The issue of retarded long-range resonant interactions between two molecules with oscillating dipole moments is revisited within the framework of classical electrodynamics. By taking advantage of a theorem in complex analysis, we present a simple method to calculate the frequencies of the normal modes, which are then used to estimate the interaction potential. The possibility that such interactions play a non-negligible role in ensuring the effective functioning of the biomolecular functions is investigated. On the basis of experimental results reported in the literature and simple numerical estimates, it is found that long-range interactions involving electromagnetic fields of frequencies 0.1-1THz could be temporarily activated despite radiation losses and solvent dissipation. Moreover, the theoretical background used to derive the mentioned interactions sheds light on Fröhlich's theory of selective long-range forces between biomolecules. At variance with a long-standing belief, we show that sizable resonant long-range interactions may exist only if the interacting system is out of thermal equilibrium.

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.

Experimental assessment of the contribution of electrodynamic interactions to long-distance recruitment of biomolecular partners: Theoretical basis.

Highly specific spatiotemporal interactions between cognate molecular partners essentially sustain all biochemical transactions in living matter. That such an exquisite level of accuracy may result from encountering forces solely driven by thermal diffusive processes is unlikely. Here we propose a yet unexplored strategy to experimentally tackle the long-standing question of a possibly active recruitment at a distance of cognate partners of biomolecular reactions via the action of resonant electrodynamic interactions. We considered two simplified models for a preliminary feasibility investigation of the devised methodology. By taking advantage of advanced experimental techniques nowadays available, we propose to measure the characteristic encounter time scales of dually interacting biopartners and to compare them with theoretical predictions worked out in both the presence and absence of putative long-range electromagnetic forces.

Riemannian geometry of Hamiltonian chaos: hints for a general theory.

We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.

Hamiltonian dynamics of homopolymer chain models.

The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of observables numerically computed along dynamical trajectories are found to reproduce results given by the statistical mechanics of homopolymer models. The dynamical treatment, however, indicates a nontrivial transition between regimes of slow and fast phase space mixing. Such a transition is inaccessible to a statistical mechanical treatment and reflects a bimodality in the relaxation of time averages to corresponding ensemble averages. It is also found that a change in the energy dependence of the largest Lyapunov exponent indicates the Theta transition between filamentary and globular polymer configurations, clearly detecting the transition even for a finite number of particles.

Topology and phase transitions: from an exactly solvable model to a relation between topology and thermodynamics.

The elsewhere surmized topological origin of phase transitions is given here important evidence through the analytic study of an exactly solvable model for which both topology of submanifolds of configuration space and thermodynamics are worked out. The model is a mean-field one with a k-body interaction. It undergoes a second-order phase transition for k=2 and a first-order one for k >2 . This opens a perspective for the understanding of the deep origin of first and second-order phase transitions, respectively. In particular, a remarkable theoretical result consists of a mathematical characterization of first-order transitions. Moreover, we show that a "reduced" configuration space can be defined in terms of collective variables, such that the correspondence between phase transitions and topology changes becomes one-to-one, for this model. Finally, an unusual relationship is worked out between the microscopic description of a classical N -body system and its macroscopic thermodynamic behavior. This consists of a functional dependence of thermodynamic entropy upon the Morse indexes of the critical points (saddles) of the constant energy hypersurfaces of the microscopic 2N-dimensional phase space. Thus phase space (and configuration space) topology is directly related to thermodynamics.