Demystifying neuroblastoma malignancy through fractal dimension, entropy, and lacunarity.

PURPOSE: Neuroblastoma is a pediatric solid tumor with a prognosis associated with histology and age of the patient, which are the parameters of the well-established current classification (Shimada classification). Despite the development of new treatment options, the prognosis of high-risk neuroblastoma patients is still poor. Therefore, there is a continuous need to stratify the children suffering from this tumor. A mathematical and computational approach is proposed to enable automatic and precise cancer diagnosis on the histological slide. METHODS: We targeted the complexity of neuroblastoma by calculating its image entropy (S), fractal dimension (FD), and lacunarity (λ) in a combined mathematical code. First, we tested the proposed method for patient-derived glioma images. It allowed distinguishing between normal brain tissue, grade II, and grade III glioma, which harbor different outcomes. RESULTS: In neuroblastoma, our analysis of image's FD, S, and λ combined with a machine learning algorithm automatically predicted tumor malignancy with a receiver operating characteristic curve of 0.82. FD, S, and λ distinguish between neuroblastoma and ganglioneuroma, but they only partially differentiate between the normal samples and the other classes. Ganglioneuroma, the most differentiated form, and poorly-differentiated neuroblastoma display different values of FD, S, and λ. CONCLUSIONS: FD, S, and λ of imaging recognize groups in neuroblastic tumors. We suggest that future studies including these features may challenge the current Shimada classification of neuroblastoma with categories of favorable and unfavorable histology. It is expected that this methodology could trigger multicenter studies and potentially find practical use in the clinical setting of children's hospitals worldwide.

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.

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.

Topological Strata of Weighted Complex Networks.

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.