The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally defined quantities of nodes and edges, such as node degrees, edge weights and –more recently– correlations between neighboring nodes. However, statistical methods quickly become cumbersome when dealing with many-body properties and do not capture the precise mesoscopic structure of complex networks. Here we introduce a novel method, based on persistent homology, to detect particular non-local structures, akin to weighted holes within the link-weight network fabric, which are invisible to existing methods. Their properties divide weighted networks in two broad classes: one is characterized by small hierarchically nested holes, while the second displays larger and longer living inhomogeneities. These classes cannot be reduced to known local or quasilocal network properties, because of the intrinsic non-locality of homological properties, and thus yield a new classification built on high order coordination patterns. Our results show that topology can provide novel insights relevant for many-body interactions in social and spatial networks. Moreover, this new method creates the first bridge between network theory and algebraic topology, which will allow to import the toolset of algebraic methods to complex systems.

In the first part of the present paper (theoretical), the activation of out-of-equilibrium collective oscillations of a macromolecule is described as a classical phonon condensation phenomenon. If a macromolecule is modeled as an open system, that is, it is subjected to an external energy supply and is in contact with a thermal bath to dissipate the excess energy, the internal nonlinear couplings among the normal modes make the system undergo a non-equilibrium phase transition when the energy input rate exceeds a threshold value. This transition takes place between a state where the energy is incoherently distributed among the normal modes, to a state where the input energy is channeled into the lowest frequency mode entailing a coherent oscillation of the entire molecule.The model put forward in the present work is derived as the classical counterpart of a quantum model proposed long time ago by H. Fröhlich in the attempt to explain the huge speed of enzymatic reactions. In the second part of the present paper (experimental), we show that such a phenomenon is actually possible. Two different and complementary THz near-field spectroscopic techniques, a plasmonic rectenna, and a micro-wire near-field probe, have been used in two different labs to get rid of artefacts. By considering a aqueous solution of a model protein, the BSA (Bovine Serum Albumin), we found that this protein displays a remarkable absorption feature around 0.314 THz, when driven in a stationary out-of-thermal equilibrium state by means of optical pumping. The experimental outcomes are in very good qualitative agreement with the theory developed in the first part, and in excellent quantitative agreement with a theoretical result allowing to identify the observed spectral feature with a collective oscillation of the entire molecule. * Electronic address: i.

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.

The present paper deals with an experimental feasibility study concerning the detection of longrange intermolecular interactions through molecular diffusion behavior in solution. This follows previous analyses, theoretical and numerical, where it was found that inter-biomolecular long-range force fields of electrodynamic origin could be detected through deviations from Brownian diffusion. The suggested experimental technique was Fluorescence Correlation Spectroscopy (FCS). By considering two oppositely charged molecular species in watery solution, that is, Lysozyme protein and a fluorescent dye molecule (Alexa488), the diffusion coefficient of the dye has been measured by means of the FCS technique at different values of the concentration of Lysozyme molecules, that is, at different average distances between the oppositely charged molecules. For the model considered long-range interactions are built-in as electrostatic forces, the action radius of which 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.

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BackgroundThis 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.MethodBy 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.ResultsThe 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.ConclusionsThe 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.

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.

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