Correlation analysis and its close variant principal component analysis are tools widely applied ... more Correlation analysis and its close variant principal component analysis are tools widely applied to predict the biological functions of macromolecules in terms of the relationship between fluctuation dynamics and structural properties. However, since this kind of analysis does not necessarily imply causation links among the elements of the system, its results run the risk of being biologically misinterpreted. By using as a benchmark the structure of ubiquitin, we report a critical comparison of correlation-based analysis with the analysis performed using two other indicators, response function and transfer entropy, that quantify the causal dependence. The use of ubiquitin stems from its simple structure and from recent experimental evidence of an allosteric control of its binding to target substrates. We discuss the ability of correlation, response and transfer-entropy analysis in detecting the role of the residues involved in the allosteric mechanism of ubiquitin as deduced by experiments. To maintain the comparison as much as free from the complexity of the modeling approach and the quality of time series, we describe the fluctuations of ubiquitin native state by the Gaussian network model which, being fully solvable, allows one to derive analytical expressions of the observables of interest. Our comparison suggests that a good strategy consists in combining correlation, response and transfer entropy, such that the preliminary information extracted from correlation analysis is validated by the two other indicators in order to discard those spurious correlations not associated with true causal dependencies.
Abstract. From the exact single step evolution equation of the two-point correlation function of ... more Abstract. From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field u(x), we derive different dynamical regimes when u(x) is iterated to build a stochastic velocity field. First we show that spatially uncorrelated fields u(x) lead to both standard and anomalous diffusion equations. When the field u(x) is spatially correlated each particle performs a simple free Brownian motion, but the trajectories of different particles result to be mutually correlated. The two-point statistical properties of the field u(x) induce two-point spatial correlations in the particle distribution satisfying a simple but non-trivial diffusion-like equation. These displacement–displacement correlations lead the system to three possible regimes: coalescence, simple clustering and a combination of the two. The existence of these different regimes is shown, in the one-dimensional system, through computer simulatio...
We study the dynamics of one-dimensional active particles confined in a double-well potential, fo... more We study the dynamics of one-dimensional active particles confined in a double-well potential, focusing on the escape properties of the system, such as the mean escape time from a well. We first consider a single-particle both in near and far-from-equilibrium regimes by varying the persistence time of the active force and the swim velocity. A non-monotonic behavior of the mean escape time is observed with the persistence time of the activity, revealing the existence of an optimal choice of the parameters favoring the escape process. For small persistence times, a Kramers-like formula with an effective potential obtained within the unified colored noise approximation is shown to hold. Instead, for large persistence times, we developed a simple theoretical argument based on the first passage theory, which explains the linear dependence of the escape time with the persistence of the active force. In the second part of the work, we consider the escape on two active particles mutually re...
We study the anomalous transport in systems of random walks on comblike lattices with fractal sid... more We study the anomalous transport in systems of random walks on comblike lattices with fractal sidebranches, showing subdiffusion, and in a system of Brownian particles driven by a random shear along the x direction, showing a superdiffusive behavior. In particular, we discuss whether scaling and universality are present or not in the shapes of the particle distribution along the preferential transport direction (x axis).
We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems.... more We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider strong anomalous diffusion characterized by the moment behaviour x(t) q ∼ t qν(q) , where ν(q) is a non constant function, and we discuss its consequences. Even in the apparently simple case ν(2) = 1/2, strong anomalous diffusion may correspond to non trivial features, such as non Gaussian probability distribution and peculiar scaling of large order moments. When a reactive term is added to a normal diffusion process, one has a propagating front with a constant velocity. The presence of anomalous diffusion by itself does not guarantee a changing in the front propagation scenario; a key factor to select linear in time or faster front propagation has been identified in the shape of the probability distribution tail in absence of reaction. In addition, we discuss the reaction spreading on graphs, underlying the major role of the connectivity properties of these structures, characterized by the connectivity dimension.
We present an analysis of the role of global topology on the structural stability of folded prote... more We present an analysis of the role of global topology on the structural stability of folded proteins in thermal equilibrium with a heat bath. For a large class of single domain proteins, we compute the harmonic spectrum within the Gaussian Network Model (GNM) and we determine the spectral dimension, a parameter describing the low frequency behaviour of the density of modes. We find a surprisingly strong correlation between the spectral dimension and the number of aminoacids of the protein. Considering that the larger the spectral dimension, the more topologically compact is the folded state, our results indicate that for a given temperature and length of the protein, the folded structure corresponds to the less compact folding compatible with thermodynamic stability.
Correlation analysis and its close variant principal component analysis are tools widely applied ... more Correlation analysis and its close variant principal component analysis are tools widely applied to predict the biological functions of macromolecules in terms of the relationship between fluctuation dynamics and structural properties. However, since this kind of analysis does not necessarily imply causation links among the elements of the system, its results run the risk of being biologically misinterpreted. By using as a benchmark the structure of ubiquitin, we report a critical comparison of correlation-based analysis with the analysis performed using two other indicators, response function and transfer entropy, that quantify the causal dependence. The use of ubiquitin stems from its simple structure and from recent experimental evidence of an allosteric control of its binding to target substrates. We discuss the ability of correlation, response and transfer-entropy analysis in detecting the role of the residues involved in the allosteric mechanism of ubiquitin as deduced by experiments. To maintain the comparison as much as free from the complexity of the modeling approach and the quality of time series, we describe the fluctuations of ubiquitin native state by the Gaussian network model which, being fully solvable, allows one to derive analytical expressions of the observables of interest. Our comparison suggests that a good strategy consists in combining correlation, response and transfer entropy, such that the preliminary information extracted from correlation analysis is validated by the two other indicators in order to discard those spurious correlations not associated with true causal dependencies.
Abstract. From the exact single step evolution equation of the two-point correlation function of ... more Abstract. From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field u(x), we derive different dynamical regimes when u(x) is iterated to build a stochastic velocity field. First we show that spatially uncorrelated fields u(x) lead to both standard and anomalous diffusion equations. When the field u(x) is spatially correlated each particle performs a simple free Brownian motion, but the trajectories of different particles result to be mutually correlated. The two-point statistical properties of the field u(x) induce two-point spatial correlations in the particle distribution satisfying a simple but non-trivial diffusion-like equation. These displacement–displacement correlations lead the system to three possible regimes: coalescence, simple clustering and a combination of the two. The existence of these different regimes is shown, in the one-dimensional system, through computer simulatio...
We study the dynamics of one-dimensional active particles confined in a double-well potential, fo... more We study the dynamics of one-dimensional active particles confined in a double-well potential, focusing on the escape properties of the system, such as the mean escape time from a well. We first consider a single-particle both in near and far-from-equilibrium regimes by varying the persistence time of the active force and the swim velocity. A non-monotonic behavior of the mean escape time is observed with the persistence time of the activity, revealing the existence of an optimal choice of the parameters favoring the escape process. For small persistence times, a Kramers-like formula with an effective potential obtained within the unified colored noise approximation is shown to hold. Instead, for large persistence times, we developed a simple theoretical argument based on the first passage theory, which explains the linear dependence of the escape time with the persistence of the active force. In the second part of the work, we consider the escape on two active particles mutually re...
We study the anomalous transport in systems of random walks on comblike lattices with fractal sid... more We study the anomalous transport in systems of random walks on comblike lattices with fractal sidebranches, showing subdiffusion, and in a system of Brownian particles driven by a random shear along the x direction, showing a superdiffusive behavior. In particular, we discuss whether scaling and universality are present or not in the shapes of the particle distribution along the preferential transport direction (x axis).
We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems.... more We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider strong anomalous diffusion characterized by the moment behaviour x(t) q ∼ t qν(q) , where ν(q) is a non constant function, and we discuss its consequences. Even in the apparently simple case ν(2) = 1/2, strong anomalous diffusion may correspond to non trivial features, such as non Gaussian probability distribution and peculiar scaling of large order moments. When a reactive term is added to a normal diffusion process, one has a propagating front with a constant velocity. The presence of anomalous diffusion by itself does not guarantee a changing in the front propagation scenario; a key factor to select linear in time or faster front propagation has been identified in the shape of the probability distribution tail in absence of reaction. In addition, we discuss the reaction spreading on graphs, underlying the major role of the connectivity properties of these structures, characterized by the connectivity dimension.
We present an analysis of the role of global topology on the structural stability of folded prote... more We present an analysis of the role of global topology on the structural stability of folded proteins in thermal equilibrium with a heat bath. For a large class of single domain proteins, we compute the harmonic spectrum within the Gaussian Network Model (GNM) and we determine the spectral dimension, a parameter describing the low frequency behaviour of the density of modes. We find a surprisingly strong correlation between the spectral dimension and the number of aminoacids of the protein. Considering that the larger the spectral dimension, the more topologically compact is the folded state, our results indicate that for a given temperature and length of the protein, the folded structure corresponds to the less compact folding compatible with thermodynamic stability.
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Papers by fabio cecconi