@article{CaetanodeCarvalhoMetzleretal.2017,
  author    = {Caetano, Daniel L. Z. and de Carvalho, Sidney J. and Metzler, Ralf and Cherstvy, Andrey G.},
  title     = {Critical adsorption of periodic and random polyampholytes onto charged surfaces},
  series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  volume    = {19},
  journal   = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c7cp04040g},
  pages     = {23397 -- 23413},
  year      = {2017},
  abstract  = {How different are the properties of critical adsorption of polyampholytes and polyelectrolytes onto charged surfaces? How important are the details of polyampholyte charge distribution on the onset of critical adsorption transition? What are the scaling relations governing the dependence of critical surface charge density on salt concentration in the surrounding solution? Here, we employ Metropolis Monte Carlo simulations and uncover the scaling relations for critical adsorption for quenched periodic and random charge distributions along the polyampholyte chains. We also evaluate and discuss the dependence of the adsorbed layer width on solution salinity and details of the charge distribution. We contrast our findings to the known results for polyelectrolyte adsorption onto oppositely charged surfaces, in particular, their dependence on electrolyte concentration.},
  language  = {en}
}
@article{Cherstvy2017,
  author    = {Cherstvy, Andrey G.},
  title     = {Shape Morphologies of Icosahedral Two-Component Vesicles},
  series = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry},
  volume    = {121},
  journal   = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry},
  publisher = {American Chemical Society},
  address   = {Washington},
  issn      = {1520-6106},
  doi       = {10.1021/acs.jpcb.7b02440},
  pages     = {7484 -- 7491},
  year      = {2017},
  abstract  = {What are the features of partitioning of crystalline materials on the surface of a two-component icosahedral vesicle? We model the response of the rigid hardly stretchable crystalline icosahedra upon addition of a softer component on its surface. We demonstrate how the soft phase "invades" the shell regions with the highest elastic energy density around 12 5-fold topological defects. We explore the phase diagram of these inhomogeneous shells as a function of the soft material fraction, shell radius, and elastic moduli of the two phases. The findings are compared with the recent computer simulation findings, and their biological relevance, for example, for the structure of icosahedral viruses, is also discussed.},
  language  = {en}
}
@article{HouCherstvyMetzleretal.2018,
  author    = {Hou, Ru and Cherstvy, Andrey G. and Metzler, Ralf and Akimoto, Takuma},
  title     = {Biased continuous-time random walks for ordinary and equilibrium cases},
  series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  volume    = {20},
  journal   = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  number    = {32},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c8cp01863d},
  pages     = {20827 -- 20848},
  year      = {2018},
  abstract  = {We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent alpha are considered for the WTD psi(t) similar to 1/t(1+alpha). We treat continuous-time random walks (CTRWs) with 0 < alpha < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < alpha < 2 and alpha > 2. We demonstrate that in the presence of a drift CTRWs with alpha < 1 are ageing and non-ergodic in the sense of the non-equivalence of their ensemble and time averaged displacement characteristics in the limit of lag times much shorter than the trajectory length. In the sense of the equivalence of ensemble and time averages, CTRW processes with 1 < alpha < 2 are ergodic for the equilibrium and non-ergodic for the ordinary situation. Lastly, CTRW renewal processes with alpha > 2-both for the equilibrium and ordinary situation-are always ergodic. For the situations 1 < alpha < 2 and alpha > 2 the variance of the diffusion process, however, depends on the initial ensemble. For biased CTRWs with alpha > 1 we also investigate the behaviour of the ergodicity breaking parameter. In addition, we demonstrate that for biased CTRWs the Einstein relation is valid on the level of the ensemble and time averaged displacements, in the entire range of the WTD exponent alpha.},
  language  = {en}
}
@article{CherstvyThapaMardoukhietal.2018,
  author    = {Cherstvy, Andrey G. and Thapa, Samudrajit and Mardoukhi, Yousof and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Time averages and their statistical variation for the Ornstein-Uhlenbeck process},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {98},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.98.022134},
  pages     = {15},
  year      = {2018},
  abstract  = {How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and outof-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed.},
  language  = {en}
}
@article{AydinerCherstvyMetzler2018,
  author    = {Aydiner, Ekrem and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Wealth distribution, Pareto law, and stretched exponential decay of money},
  series = {Physica : europhysics journal ; A, Statistical mechanics and its applications},
  volume    = {490},
  journal   = {Physica : europhysics journal ; A, Statistical mechanics and its applications},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2017.08.017},
  pages     = {278 -- 288},
  year      = {2018},
  abstract  = {We study by Monte Carlo simulations a kinetic exchange trading model for both fixed and distributed saving propensities of the agents and rationalize the person and wealth distributions. We show that the newly introduced wealth distribution - that may be more amenable in certain situations - features a different power-law exponent, particularly for distributed saving propensities of the agents. For open agent-based systems, we analyze the person and wealth distributions and find that the presence of trap agents alters their amplitude, leaving however the scaling exponents nearly unaffected. For an open system, we show that the total wealth - for different trap agent densities and saving propensities of the agents - decreases in time according to the classical Kohlrausch-Williams-Watts stretched exponential law. Interestingly, this decay does not depend on the trap agent density, but rather on saving propensities. The system relaxation for fixed and distributed saving schemes are found to be different.},
  language  = {en}
}
@article{GhoshCherstvyPetrovetal.2016,
  author    = {Ghosh, Surya K. and Cherstvy, Andrey G. and Petrov, Eugene P. and Metzler, Ralf},
  title     = {Interactions of rod-like particles on responsive elastic sheets},
  series = {Soft matter},
  journal   = {Soft matter},
  publisher = {RSC},
  address   = {London},
  issn      = {1744-6848},
  doi       = {10.1039/C6SM01522K},
  year      = {2016},
  abstract  = {What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive-repulsive rod-rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed.},
  language  = {en}
}
@article{CherstvyMetzler2016,
  author    = {Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes},
  series = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies},
  volume    = {18},
  journal   = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies},
  publisher = {RSC Publ.},
  address   = {Cambridge},
  issn      = {1463-9084},
  doi       = {10.1039/C6CP03101C},
  pages     = {23840 -- 23852},
  year      = {2016},
  abstract  = {We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion.},
  language  = {en}
}
@article{deCarvalhoMetzlerCherstvy2016,
  author    = {de Carvalho, Sidney J. and Metzler, Ralf and Cherstvy, Andrey G.},
  title     = {Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {18},
  journal   = {New journal of physics : the open-access journal for physics},
  publisher = {IOP Publ.},
  address   = {London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/18/8/083037},
  year      = {2016},
  abstract  = {We study the adsorption-desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition—demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces—are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye-H{\"u}ckel approximation is often not feasible and the nonlinear Poisson-Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson-Boltzmann equation is smaller than the Debye-H{\"u}ckel result, such that the required critical surface charge density for polyelectrolyte adsorption σc increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical-chemical and biophysical systems.},
  language  = {en}
}
@article{LiuCherstvyMetzler2017,
  author    = {Liu, Lin and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Facilitated Diffusion of Transcription Factor Proteins with Anomalous Bulk Diffusion},
  series = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry},
  volume    = {121},
  journal   = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry},
  publisher = {American Chemical Society},
  address   = {Washington},
  issn      = {1520-6106},
  doi       = {10.1021/acs.jpcb.6b12413},
  pages     = {1284 -- 1289},
  year      = {2017},
  abstract  = {What are the physical laws of the diffusive search of proteins for their specific binding sites on DNA in the presence of the macromolecular crowding in cells? We performed extensive computer simulations to elucidate the protein target search on DNA. The novel feature is the viscoelastic non-Brownian protein bulk diffusion recently observed experimentally. We examine the influence of the protein-DNA binding affinity and the anomalous diffusion exponent on the target search time. In all cases an optimal search time is found. The relative contribution of intermittent three-dimensional bulk diffusion and one-dimensional sliding of proteins along the DNA is quantified. Our results are discussed in the light of recent single molecule tracking experiments, aiming at a better understanding of the influence of anomalous kinetics of proteins on the facilitated diffusion mechanism.},
  language  = {en}
}
@article{AkimotoCherstvyMetzler2018,
  author    = {Akimoto, Takuma and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Ergodicity, rejuvenation, enhancement, and slow relaxation of diffusion in biased continuous-time random walks},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {98},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.98.022105},
  pages     = {6},
  year      = {2018},
  abstract  = {Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we report on an interesting phenomenon for the enhancement of diffusion by the start of the measurement in a random energy landscape. When the variance of the waiting time diverges, in contrast to the bias-free case, the dynamics with bias becomes superdiffusive. In the superdiffusive regime, we find a distinct initial ensemble dependence of the diffusivity. Moreover, the diffusivity can be increased by the aging time when the initial ensemble is not in equilibrium. We show that the time-averaged variance converges to the corresponding ensemble-averaged variance; i.e., ergodicity is preserved. However, trajectory-to-trajectory fluctuations of the time-averaged variance decay unexpectedly slowly. Our findings provide a rejuvenation phenomenon in the superdiffusive regime, that is, the diffusivity for a nonequilibrium initial ensemble gradually increases to that for an equilibrium ensemble when the start of the measurement is delayed.},
  language  = {en}
}
@article{AydinerCherstvyMetzler2019,
  author    = {Aydiner, Ekrem and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Money distribution in agent-based models with position-exchange dynamics},
  series = {The European physical journal : B, Condensed matter and complex systems},
  volume    = {92},
  journal   = {The European physical journal : B, Condensed matter and complex systems},
  number    = {5},
  publisher = {Springer},
  address   = {New York},
  issn      = {1434-6028},
  doi       = {10.1140/epjb/e2019-90674-0},
  pages     = {4},
  year      = {2019},
  abstract  = {Wealth and income distributions are known to feature country-specific Pareto exponents for their long power-law tails. To propose a rationale for this, we introduce an agent-based dynamic model and use Monte Carlo simulations to unveil the wealth distributions in closed and open economical systems. The standard money-exchange scenario is supplemented with the position-exchange agent dynamics that vitally affects the Pareto law. Specifically, in closed systems with position-exchange dynamics the power law changes to an exponential shape, while for open systems with traps the Pareto law remains valid.},
  language  = {en}
}
@article{CherstvyThapaWagneretal.2019,
  author    = {Cherstvy, Andrey G. and Thapa, Samudrajit and Wagner, Caroline E. and Metzler, Ralf},
  title     = {Non-Gaussian, non-ergodic, and non-Fickian diffusion of tracers in mucin hydrogels},
  series = {Soft matter},
  volume    = {15},
  journal   = {Soft matter},
  number    = {12},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1744-683X},
  doi       = {10.1039/c8sm02096e},
  pages     = {2526 -- 2551},
  year      = {2019},
  abstract  = {Native mucus is polymer-based soft-matter material of paramount biological importance. How non-Gaussian and non-ergodic is the diffusive spreading of pathogens in mucus? We study the passive, thermally driven motion of micron-sized tracers in hydrogels of mucins, the main polymeric component of mucus. We report the results of the Bayesian analysis for ranking several diffusion models for a set of tracer trajectories [C. E. Wagner et al., Biomacromolecules, 2017, 18, 3654]. The models with "diffusing diffusivity', fractional and standard Brownian motion are used. The likelihood functions and evidences of each model are computed, ranking the significance of each model for individual traces. We find that viscoelastic anomalous diffusion is often most probable, followed by Brownian motion, while the model with a diffusing diffusion coefficient is only realised rarely. Our analysis also clarifies the distribution of time-averaged displacements, correlations of scaling exponents and diffusion coefficients, and the degree of non-Gaussianity of displacements at varying pH levels. Weak ergodicity breaking is also quantified. We conclude that-consistent with the original study-diffusion of tracers in the mucin gels is most non-Gaussian and non-ergodic at low pH that corresponds to the most heterogeneous networks. Using the Bayesian approach with the nested-sampling algorithm, together with the quantitative analysis of multiple statistical measures, we report new insights into possible physical mechanisms of diffusion in mucin gels.},
  language  = {en}
}
@article{ThapaLukatSelhuberUnkeletal.2019,
  author    = {Thapa, Samudrajit and Lukat, Nils and Selhuber-Unkel, Christine and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Transient superdiffusion of polydisperse vacuoles in highly motile amoeboid cells},
  series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  volume    = {150},
  journal   = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  number    = {14},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0021-9606},
  doi       = {10.1063/1.5086269},
  pages     = {18},
  year      = {2019},
  abstract  = {We perform a detailed statistical analysis of diffusive trajectories of membrane-enclosed vesicles (vacuoles) in the supercrowded cytoplasm of living Acanthamoeba castellanii cells. From the vacuole traces recorded in the center-of-area frame of moving amoebae, we examine the statistics of the time-averaged mean-squared displacements of vacuoles, their generalized diffusion coefficients and anomalous scaling exponents, the ergodicity breaking parameter, the non-Gaussian features of displacement distributions of vacuoles, the displacement autocorrelation function, as well as the distributions of speeds and positions of vacuoles inside the amoeba cells. Our findings deliver novel insights into the internal dynamics of cellular structures in these infectious pathogens. Published under license by AIP Publishing.},
  language  = {en}
}
@article{FernandezCharcharCherstvyetal.2020,
  author    = {Fernandez, Amanda Diez and Charchar, Patrick and Cherstvy, Andrey G. and Metzler, Ralf and Finnis, Michael W.},
  title     = {The diffusion of doxorubicin drug molecules in silica nanoslits is non-Gaussian, intermittent and anticorrelated},
  series = {Physical chemistry, chemical physics},
  volume    = {22},
  journal   = {Physical chemistry, chemical physics},
  number    = {48},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/d0cp03849k},
  pages     = {27955 -- 27965},
  year      = {2020},
  abstract  = {In this study we investigate, using all-atom molecular-dynamics computer simulations, the in-plane diffusion of a doxorubicin drug molecule in a thin film of water confined between two silica surfaces. We find that the molecule diffuses along the channel in the manner of a Gaussian diffusion process, but with parameters that vary according to its varying transversal position. Our analysis identifies that four Gaussians, each describing particle motion in a given transversal region, are needed to adequately describe the data. Each of these processes by itself evolves with time at a rate slower than that associated with classical Brownian motion due to a predominance of anticorrelated displacements. Long adsorption events lead to ageing, a property observed when the diffusion is intermittently hindered for periods of time with an average duration which is theoretically infinite. This study presents a simple system in which many interesting features of anomalous diffusion can be explored. It exposes the complexity of diffusion in nanoconfinement and highlights the need to develop new understanding.},
  language  = {en}
}
@article{WangCherstvyChechkinetal.2020,
  author    = {Wang, Wei and Cherstvy, Andrey G. and Chechkin, Aleksei V. and Thapa, Samudrajit and Seno, Flavio and Liu, Xianbin and Metzler, Ralf},
  title     = {Fractional Brownian motion with random diffusivity},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {53},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {47},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/aba467},
  pages     = {34},
  year      = {2020},
  abstract  = {Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time tau characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on tau and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments.},
  language  = {en}
}
@article{WangCherstvyLiuetal.2020,
  author    = {Wang, Wei and Cherstvy, Andrey G. and Liu, Xianbin and Metzler, Ralf},
  title     = {Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {102},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {1},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.102.012146},
  pages     = {012146-1 -- 012146-16},
  year      = {2020},
  abstract  = {Heterogeneous diffusion processes (HDPs) feature a space-dependent diffusivity of the form D(x) = D-0|x|(alpha). Such processes yield anomalous diffusion and weak ergodicity breaking, the asymptotic disparity between ensemble and time averaged observables, such as the mean-squared displacement. Fractional Brownian motion (FBM) with its long-range correlated yet Gaussian increments gives rise to anomalous and ergodic diffusion. Here, we study a combined model of HDPs and FBM to describe the particle dynamics in complex systems with position-dependent diffusivity driven by fractional Gaussian noise. This type of motion is, inter alia, relevant for tracer-particle diffusion in biological cells or heterogeneous complex fluids. We show that the long-time scaling behavior predicted theoretically and by simulations for the ensemble-and time-averaged mean-squared displacements couple the scaling exponents alpha of HDPs and the Hurst exponent H of FBM in a characteristic way. Our analysis of the simulated data in terms of the rescaled variable y similar to |x|(1/(2/(2-alpha)))/t(H) coupling particle position x and time t yields a simple, Gaussian probability density function (PDF), PHDP-FBM(y) = e(-y2)/root pi. Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions.},
  language  = {en}
}
@article{ThapaLomholtKrogetal.2018,
  author    = {Thapa, Samudrajit and Lomholt, Michael Andersen and Krog, Jens and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Bayesian analysis of single-particle tracking data using the nested-sampling algorithm: maximum-likelihood model selection applied to stochastic-diffusivity data},
  series = {Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies},
  volume    = {20},
  journal   = {Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies},
  number    = {46},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c8cp04043e},
  pages     = {29018 -- 29037},
  year      = {2018},
  abstract  = {We employ Bayesian statistics using the nested-sampling algorithm to compare and rank multiple models of ergodic diffusion (including anomalous diffusion) as well as to assess their optimal parameters for in silico-generated and real time-series. We focus on the recently-introduced model of Brownian motion with "diffusing diffusivity'-giving rise to widely-observed non-Gaussian displacement statistics-and its comparison to Brownian and fractional Brownian motion, also for the time-series with some measurement noise. We conduct this model-assessment analysis using Bayesian statistics and the nested-sampling algorithm on the level of individual particle trajectories. We evaluate relative model probabilities and compute best-parameter sets for each diffusion model, comparing the estimated parameters to the true ones. We test the performance of the nested-sampling algorithm and its predictive power both for computer-generated (idealised) trajectories as well as for real single-particle-tracking trajectories. Our approach delivers new important insight into the objective selection of the most suitable stochastic model for a given time-series. We also present first model-ranking results in application to experimental data of tracer diffusion in polymer-based hydrogels.},
  language  = {en}
}
@article{CaetanoCarvalhoMetzleretal.2020,
  author    = {Caetano, Daniel L. Z. and Carvalho, Sidney Jurado de and Metzler, Ralf and Cherstvy, Andrey G.},
  title     = {Critical adsorption of multiple polyelectrolytes onto a nanosphere},
  series = {Interface : journal of the Royal Society},
  volume    = {17},
  journal   = {Interface : journal of the Royal Society},
  number    = {167},
  publisher = {Royal Society},
  address   = {London},
  issn      = {1742-5689},
  doi       = {10.1098/rsif.2020.0199},
  pages     = {10},
  year      = {2020},
  abstract  = {Employing extensive Monte Carlo computer simulations, we investigate in detail the properties of multichain adsorption of charged flexible polyelectrolytes (PEs) onto oppositely charged spherical nanoparticles (SNPs). We quantify the conditions of critical adsorption-the phase-separation curve between the adsorbed and desorbed states of the PEs-as a function of the SNP surface-charge density and the concentration of added salt. We study the degree of fluctuations of the PE-SNP electrostatic binding energy, which we use to quantify the emergence of the phase subtransitions, including a series of partially adsorbed PE configurations. We demonstrate how the phase-separation adsorption-desorption boundary shifts and splits into multiple subtransitions at low-salt conditions, thereby generalizing and extending the results for critical adsorption of a single PE onto the SNP. The current findings are relevant for finite concentrations of PEs around the attracting SNP, such as the conditions for PE adsorption onto globular proteins carrying opposite electric charges.},
  language  = {en}
}
@article{KarCherstvyMetzler2017,
  author    = {Kar, Prathitha and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Acceleration of bursty multiprotein target search kinetics on DNA by colocalisation},
  series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  volume    = {20},
  journal   = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  number    = {12},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c7cp06922g},
  pages     = {7931 -- 7946},
  year      = {2017},
  abstract  = {Proteins are capable of locating specific targets on DNA by employing a facilitated diffusion process with intermittent 1D and 3D search steps. Gene colocalisation and coregulation-i.e. the spatial proximity of two communicating genes-is one factor capable of accelerating the target search process along the DNA. We perform Monte Carlo computer simulations and demonstrate the benefits of gene colocalisation for minimising the search time in a model DNA-protein system. We use a simple diffusion model to mimic the search for targets by proteins, produced initially in bursts of multiple proteins and performing the first-passage search on the DNA chain. The behaviour of the mean first-passage times to the target is studied as a function of distance between the initial position of proteins and the DNA target position, as well as versus the concentration of proteins. We also examine the properties of bursty target search kinetics for varying physical-chemical protein-DNA binding affinity. Our findings underline the relevance of colocalisation of production and binding sites for protein search inside biological cells.},
  language  = {en}
}
@article{CherstvyMetzler2013,
  author    = {Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes},
  series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  volume    = {15},
  journal   = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  number    = {46},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c3cp53056f},
  pages     = {20220 -- 20235},
  year      = {2013},
  abstract  = {We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.},
  language  = {en}
}