Adaptive Response in Rat Retinal Cell Cultures Irradiated with γ-rays.

Retina can receive incidental γ-ray exposure from various sources. For example, although radiation therapy is a crucial tool for managing head and neck tumors, patients may develop ocular complications as collateral damage from accidental irradiation. Recently, there has been concern that retinal irradiation during space flight may compromise mission goals and long-term quality of life after space travel. Previously, in our in vitro model, we proved that immature retinal cells are more vulnerable to γ-radiation than differentiated neurons. Here, we investigate if a low-dose pre-irradiation (0.025 Gy), known to have a protective effect in various contexts, can affect DNA damage and oxidative stress in cells exposed to a high dose of γ-rays (2 Gy). Our results reveal that pre-irradiation reduces 2 Gy effects in apoptotic cell number, H2AX phosphorylation and oxidative stress. These defensive effects are also evident in glial cells (reduction in GFAP and ED1 levels) and antioxidant enzymes (catalase and CuZnSOD). Overall, our results confirm that rat retinal cultures can be an exciting tool to study γ-irradiation toxic effects on retinal tissue and speculate that low irradiation may enhance the skill of retinal cells to reduce damage induced by higher doses.

Synchronization in a system of Kuramoto oscillators with distributed Gaussian noise.

We consider a system of globally coupled phase-only oscillators with distributed intrinsic frequencies and evolving in the presence of distributed Gaussian white noise, namely, a Gaussian white noise whose strength for every oscillator is a specified function of its intrinsic frequency. In the absence of noise, the model reduces to the celebrated Kuramoto model of spontaneous synchronization. For two specific forms of the mentioned functional dependence and for a symmetric and unimodal distribution of the intrinsic frequencies, we unveil the rich long-time behavior that the system exhibits, which stands in stark contrast to the case in which the noise strength is the same for all the oscillators, namely, in the studied dynamics, the system may exist in either a synchronized, or an incoherent, or a time-periodic state; interestingly, all these states also appear as long-time solutions of the Kuramoto dynamics for the case of bimodal frequency distributions, but in the absence of any noise in the dynamics.

The study of the dynamics of the order parameter of coupled oscillators in the Ott-Antonsen scheme for generic frequency distributions.

The Ott-Antonsen ansatz shows that, for certain classes of distribution of the natural frequencies in systems of N globally coupled Kuramoto oscillators, the dynamics of the order parameter, in the limit N → ∞, evolves, under suitable initial conditions, in a manifold of low dimension. This is not possible when the frequency distribution, continued in the complex plane, has an essential singularity at infinity; this is the case, for example, of a Gaussian distribution. In this work, we propose a simple approximation scheme that allows one to extend also to this case the representation of the dynamics of the order parameter in a low dimensional manifold. Using the Gaussian frequency distribution as a working example, we compare the dynamical evolution of the order parameter of the system of oscillators, obtained by the numerical integration of the N equations of motion, with the analogous dynamics in the low dimensional manifold obtained with the application of the approximation scheme. The results confirm the validity of the approximation. The method could be employed for general frequency distributions, allowing the determination of the corresponding phase diagram of the oscillator system.

Erratum: Ensemble inequivalence in the Blume-Emery-Griffiths model near a fourth-order critical point [Phys. Rev. E 100, 052135 (2019)].

This corrects the article DOI: 10.1103/PhysRevE.100.052135.

Monte Carlo simulations in the unconstrained ensemble.

The unconstrained ensemble describes completely open systems whose control parameters are the chemical potential, pressure, and temperature. For macroscopic systems with short-range interactions, thermodynamics prevents the simultaneous use of these intensive variables as control parameters, because they are not independent and cannot account for the system size. When the range of the interactions is comparable with the size of the system, however, these variables are not truly intensive and may become independent, so equilibrium states defined by the values of these parameters may exist. Here, we derive a Monte Carlo algorithm for the unconstrained ensemble and show that simulations can be performed using the chemical potential, pressure, and temperature as control parameters. We illustrate the algorithm by applying it to physical systems where either the system has long-range interactions or is confined by external conditions. The method opens up an avenue for the simulation of completely open systems exchanging heat, work, and matter with the environment.

Ensemble inequivalence in the Blume-Emery-Griffiths model near a fourth-order critical point.

The canonical phase diagram of the Blume-Emery-Griffiths model with infinite-range interactions is known to exhibit a fourth-order critical point at some negative value of the biquadratic interaction K<0. Here we study the microcanonical phase diagram of this model for K<0, extending previous studies which were restricted to positive K. A fourth-order critical point is found to exist at coupling parameters which are different from those of the canonical ensemble. The microcanonical phase diagram of the model close to the fourth-order critical point is studied in detail revealing some distinct features from the canonical counterpart.

Concavity, Response Functions and Replica Energy.

In nonadditive systems, like small systems or like long-range interacting systems even in the thermodynamic limit, ensemble inequivalence can be related to the occurrence of negative response functions, this in turn being connected with anomalous concavity properties of the thermodynamic potentials associated with the various ensembles. We show how the type and number of negative response functions depend on which of the quantities E, V and N (energy, volume and number of particles) are constrained in the ensemble. In particular, we consider the unconstrained ensemble in which E, V and N fluctuate, which is physically meaningful only for nonadditive systems. In fact, its partition function is associated with the replica energy, a thermodynamic function that identically vanishes when additivity holds, but that contains relevant information in nonadditive systems.

Exposing primary rat retina cell cultures to γ-rays: An in vitro model for evaluating radiation responses.

Retinal tissue can receive incidental γ-rays exposure during radiotherapy either of tumors of the eye and optic nerve or of head-and-neck tumors, and during medical diagnostic procedures. Healthy retina is therefore at risk of suffering radiation-related side effects and the knowledge of pathophysiological response of retinal cells to ionizing radiations could be useful to design possible strategies of prevention and management of radiotoxicity. In this study, we have exploited an in vitro model (primary rat retinal cell culture) to study an array of biological effects induced on retinal neurons by γ-rays. Most of the different cell types present in retinal tissue - either of the neuronal or glial lineages - are preserved in primary rat retinal cultures. Similar to the retina in situ, neuronal cells undergo in vitro a maturational development shown by the formation of polarized neuritic trees and operating synapses. Since 2 Gy is the incidental dose received by the healthy retina per fraction when the standard treatment is delivered to the brain, retina cell cultures have been exposed to 1 or 2 Gy of γ-rays at different level of neuronal differentiation in vitro: days in vitro (DIV)2 or DIV8. At DIV9, retinal cultures were analyzed in terms of viability, apoptosis and characterized by immunocytochemistry to identify alterations in neuronal differentiation. After irradiation at DIV2, MTT assay revealed an evident loss of cell viability and ßIII-tubulin immunostaining highlighted a marked neuritic damage, indicating that survived neurons showed an impaired differentiation. Differentiated cultures (DIV8) appeared to be more resistant with respect to undifferentiated, DIV2 cultures, both in terms of cell viability and differentiation. Apoptosis evaluated with TUNEL assay showed that irradiation at both DIV2 and DIV8 induced a significant increase in the apoptotic rate. To further investigate the effects of γ-rays on retinal neurons, we evaluated the expression of synaptic proteins, such as SNAP25 and synaptophysin. WB and immunofluorescence analysis showed an altered expression of these proteins in particular when cultures were irradiated at DIV2. To evaluate the effect of γ-rays on photoreceptors, we studied the expression of rhodopsin in WB analysis and immunofluorescence. Our results confirm data from the literature that differentiated photoreceptors appear to be more resistant to irradiation respect to other retinal cell types present in cultures. The results obtained suggest that γ-rays exposure of primary retinal cultures may contribute to shed further light on the mechanisms involved in γ-radiation-induced neurodegeneration.

Long-range interacting systems in the unconstrained ensemble.

Completely open systems can exchange heat, work, and matter with the environment. While energy, volume, and number of particles fluctuate under completely open conditions, the equilibrium states of the system, if they exist, can be specified using the temperature, pressure, and chemical potential as control parameters. The unconstrained ensemble is the statistical ensemble describing completely open systems and the replica energy is the appropriate free energy for these control parameters from which the thermodynamics must be derived. It turns out that macroscopic systems with short-range interactions cannot attain equilibrium configurations in the unconstrained ensemble, since temperature, pressure, and chemical potential cannot be taken as a set of independent variables in this case. In contrast, we show that systems with long-range interactions can reach states of thermodynamic equilibrium in the unconstrained ensemble. To illustrate this fact, we consider a modification of the Thirring model and compare the unconstrained ensemble with the canonical and grand-canonical ones: The more the ensemble is constrained by fixing the volume or number of particles, the larger the space of parameters defining the equilibrium configurations.

Facility for gamma irradiations of cultured cells at low dose rates: design, physical characteristics and functioning.

We describe a low dose/dose rate gamma irradiation facility (called LIBIS) for in vitro biological systems, for the exposure, inside a CO2 cell culture incubator, of cells at a dose rate ranging from few µGy/h to some tens of mGy/h. Three different (137)Cs sources are used, depending on the desired dose rate. The sample is irradiated with a gamma ray beam with a dose rate uniformity of at least 92% and a percentage of primary 662keV photons greater than 80%. LIBIS complies with high safety standards.

Thermodynamics of Nonadditive Systems.

The usual formulation of thermodynamics is based on the additivity of macroscopic systems. However, there are numerous examples of macroscopic systems that are not additive, due to the long-range character of the interaction among the constituents. We present here an approach in which nonadditive systems can be described within a purely thermodynamics formalism. The basic concept is to consider a large ensemble of replicas of the system where the standard formulation of thermodynamics can be naturally applied and the properties of a single system can be consequently inferred. After presenting the approach, we show its implementation in systems where the interaction decays as 1/r(α) in the interparticle distance r, with α smaller than the embedding dimension d, and in the Thirring model for gravitational systems.

The complex interactions between radiation induced non-targeted effects and cancer.

Radiation induced non-targeted effects have been widely investigated in the last two decades for their potential impact on low dose radiation risk. In this paper we will give an overview of the most relevant aspects related to these effects, starting from the definition of the low dose scenarios. We will underline the role of radiation quality, both in terms of mechanisms of interaction with the biological matter and for the importance of charged particles as powerful tools for low dose effects investigation. We will focus on cell communication, representing a common feature of non-targeted effects, giving also an overview of cancer models that have explicitly considered such effects.

Nonequilibrium first-order phase transition in coupled oscillator systems with inertia and noise.

We study the dynamics of a system of coupled oscillators of distributed natural frequencies, by including the features of both thermal noise, parametrized by a temperature, and inertial terms, parametrized by a moment of inertia. For a general unimodal frequency distribution, we report here the complete phase diagram of the model in the space of dimensionless moment of inertia, temperature, and width of the frequency distribution. We demonstrate that the system undergoes a nonequilibrium first-order phase transition from a synchronized phase at low parameter values to an incoherent phase at high values. We provide strong numerical evidence for the existence of both the synchronized and the incoherent phase, treating the latter analytically to obtain the corresponding linear stability threshold that bounds the first-order transition point from below. In the limit of zero noise and inertia, when the dynamics reduces to the one of the Kuramoto model, we recover the associated known continuous transition. At finite noise and inertia but in the absence of natural frequencies, the dynamics becomes that of a well-studied model of long-range interactions, the Hamiltonian mean-field model. Close to the first-order phase transition, we show that the escape time out of metastable states scales exponentially with the number of oscillators, which we explain to be stemming from the long-range nature of the interaction between the oscillators.

DNA and cellular effects of charged particles.

Development of new radiotherapy strategies based on the use of hadrons, as well as reduction of uncertainties associated with radiation health risk during long-term space flights, requires increasing knowledge of the mechanisms underlying the biological effects of charged particles. It is well known that charged particles are more effective in damaging biological systems than photons. This capability has been related to the production of spatially correlated and/or clustered DNA damage, in particular two or more double-strand breaks (DSB) in close proximity or DSB associated with other lesions within a localized DNA region. These kinds of complex damages are rarely induced by photons. They are difficult to repair accurately and are therefore expected to produce severe consequences at the cellular level. This paper provides a review of radiation-induced cellular effects and will discuss the dependence of cell death and mutation induction on the linear energy transfer of various light and heavy ions. This paper will show the inadequacy of a single physical parameter for describing radiation quality, underlining the importance of the characteristics of the track structure at the submicrometer level to determine the biological effects. This paper will give a description of the physical properties of the track structure that can explain the differences in the spatial distributions of DNA damage, in particular DSB, induced by radiation of different qualities. In addition, this paper will show how a combined experimental and theoretical approach based on Monte Carlo simulations can be useful for providing information on the damage distribution at the nanoscale level. It will also emphasize the importance, especially for DNA damage evaluation at low doses, of the more recent functional approaches based on the use of fluorescent antibodies against proteins involved in the cellular processing of DNA damage. Advantages and limitations of the different experimental techniques will be discussed with particular emphasis on the still unsolved problem of the clustered DNA damage resolution. Development of biophysical models aimed to describe the kinetics of the DNA repair process is underway, and it is expected to support the experimental investigation of the mechanisms underlying the cellular radiation response.

Track structure, radiation quality and initial radiobiological events: considerations based on the PARTRAC code experience.

PURPOSE: The role of track structures for understanding the biological effects of radiation has been the subject of research activities for decades. The physics that describes such processes is the core Monte Carlo codes, such as the biophysical PARTRAC (PARticle TRACks) code described in this review, which follow the mechanisms of radiation-matter interaction from the early stage. In this paper a review of the track structure theory (and of its possible extension concerning non-DNA targets) is presented. MATERIALS AND METHODS: The role of radiation quality and track structure is analyzed starting from the heavy ions results obtained with the biophysical Monte Carlo code PARTRAC (PARticles TRACks). PARTRAC calculates DNA damage in human cells based on the superposition of simulated track structures in liquid water to an 'atom-by-atom' model of human DNA. RESULTS: Calculations for DNA fragmentation compared with experimental data for different radiation qualities are illustrated. As an example, the strong dependence of the complexity of DNA damage on radiation track structure, and the very large production of very small DNA fragments (lower than 1 kbp (kilo base pairs) usually not detected experimentally) after high LET (high-Linear Energy Transfer) irradiation is shown. Furthermore the possible importance of non-nuclear/non-DNA targets is discussed in the particular case of cellular membrane and mitochondria. CONCLUSIONS: The importance of the track structure is underlined, in particular the dependence of a given late cellular effect on the spatial distribution of DNA double-strand breaks (DSB) along the radiation track. These results show that the relative biological effectiveness (RBE) for DSB production can be significantly larger than 1. Moreover the cluster properties of high LET radiation may determine specific initial targets and damage evolution.

Overdamped dynamics of long-range systems on a one-dimensional lattice: dominance of the mean-field mode and phase transition.

We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice and in the presence of thermal noise. The internal degree of freedom of each particle is a periodic variable that is coupled to those of other particles with an attractive XY-like interaction. The coupling strength decays with the interparticle separation r in space as 1/r^{α}; 0<α<1. We study the dynamics of the model in the continuum limit by considering the Fokker-Planck equation for the evolution of the spatial density of particles. We show that the equation allows a linearly stable stationary state, which is always uniform in space, being nonuniform in the internal degrees below a critical temperature T=1/2 and uniform above, with a phase transition between the two at T=1/2. The state is the same as the equilibrium state of the mean-field version of the model, obtained by considering α=0. Our analysis also allows us to compute the growth and decay rates of spatial Fourier modes of density fluctuations. The growth rates compare very well with numerical simulations.

An alpha-particle irradiator for radiobiological research and its implementation for bystander effect studies.

An experimental system based on an improved version of an existing alpha-particle irradiator has been developed for radiobiological studies, in particular those investigating bystander effects. It consists of a 20-mm-diameter stainless steel chamber that can be equipped alternatively with 244Cm or 241Am sources of different activities. Mylar-based petri dishes 56 mm in diameter were specially designed to house adaptors for permeable membrane inserts that reproduce the geometry of commercial cell culture insert companion plates. Characterization of the radiation field at the cell level was performed by experimental measurements and calculations. The average incident LET was about 122 keV/microm for 244Cm and about 125 keV/microm for 241Am. Dose rates at the chosen source-sample distance were 2.8 and 88.6 mGy/min, respectively. These low dose rates are suitable for our planned experiments on low-dose effects. For both sources, the uniformity of the alpha-particle dose was better than +/-7%, and the photon dose calculated at the cell entrance was negligible compared to the alpha-particle dose. The irradiator is small enough to be inserted into a cell incubator for irradiation under physiological conditions or into a refrigerator to prevent metabolic processes during irradiation. Benchmark experiments using the 241Am source to examine DNA double-strand breaks in directly hit and bystander primary human fibroblasts have shown that the irradiator can be used successfully for bystander effect studies.

Dynamical phase transitions in long-range Hamiltonian systems and Tsallis distributions with a time-dependent index.

We study dynamical phase transitions in systems with long-range interactions, using the Hamiltonian mean field model as a simple example. These systems generically undergo a violent relaxation to a quasistationary state (QSS) before relaxing towards Boltzmann equilibrium. In the collisional regime, the out-of-equilibrium one-particle distribution function (DF) is a quasistationary solution of the Vlasov equation, slowly evolving in time due to finite- N effects. For subcritical energy densities, we exhibit cases where the DF is well fitted by a Tsallis q distribution with an index q(t) slowly decreasing in time from q approximately = 3 (semiellipse) to q=1 (Boltzmann). When the index q(t) reaches an energy-dependent critical value q_(crit) , the nonmagnetized (homogeneous) phase becomes Vlasov unstable and a dynamical phase transition is triggered, leading to a magnetized (inhomogeneous) state. While Tsallis distributions play an important role in our study, we explain this dynamical phase transition by using only conventional statistical mechanics. For supercritical energy densities, we report the existence of a magnetized QSS with a very long lifetime.

Long-time behavior of quasistationary states of the Hamiltonian mean-field model.

The Hamiltonian mean-field model has been investigated, since its introduction about a decade ago, to study the equilibrium and dynamical properties of long-range interacting systems. Here we study the long-time behavior of long-lived, out-of-equilibrium, quasistationary dynamical states, whose lifetime diverges in the thermodynamic limit. The nature of these states has been the object of a lively debate in the recent past. We introduce a numerical tool, based on the fluctuations of the phase of the instantaneous magnetization of the system. Using this tool, we study the quasistationary states that arise when the system is started from different classes of initial conditions, showing that the new observable can be exploited to compute the lifetime of these states. We also show that quasistationary states are present not only below, but also above the critical temperature of the second-order magnetic phase transition of the model. We find that at supercritical temperatures the lifetime is much larger than at subcritical temperatures.

DNA fragmentation induced in human fibroblasts by accelerated (56)fe ions of differing energies.

DNA fragmentation was studied in the fragment size range 0.023-5.7 Mbp after irradiation of human fibroblasts with iron-ion beams of four different energies, i.e., 200 MeV/nucleon, 500 MeV/nucleon, 1 GeV/nucleon and 5 GeV/nucleon, with gamma rays used as the reference radiation. The double-strand break (DSB) yield (and thus the RBE for DNA DSB induction) of the four iron-ion beams, which have LETs ranging from 135 to 442 keV/mum, does not vary greatly as a function of LET. As a consequence, the variation of the cross section for DSB induction mainly reflects the variation in LET. However, when the fragmentation spectra were analyzed with a simple theoretical tool that we recently introduced, the results showed that spatially correlated DSBs, which are absent after gamma irradiation, increased markedly with LET for the iron-ion beams. This occurred because iron ions produce DNA fragments smaller than 0.75 Mbp with a higher probability than gamma rays (a probability that increases with LET). These sizes include those expected from fragmentation of the chromatin loops with Mbp dimensions. This result does not exclude a correlation at distances smaller than the lower size analyzed here, i.e. 23 kbp. Moreover, the DSB correlation is dependent on dose, decreasing when dose increases; this can be explained with the argument that at increasing dose there is an increasing fraction of fragments produced by DSBs caused by separate, uncorrelated tracks.