arXiv subjects

Francesca Di Patti

Publications and source records attributed to Francesca Di Patti.

26 records · Page 2Linked to original sources

arXiv2010

Phase equilibria of polydisperse hydrocarbons: moment free energy method analysis

We analyze the phase equilibria of systems of polydisperse hydrocarbons by means of the recently introduced moment method. Hydrocarbons are modelled with the Soave-Redlick-Kwong and Peng-Robinson equations of states. Numerical results show no particular qualitative difference between the two equations of states. Furthermore, in general the moment method proves to be an excellent method for solving phase equilibria of polydisperse systems, showing excellent agreement with previous results and allowing a great improvement in generality of the numerical scheme and speed of computation.

cond-mat.dis-nn↗

arXiv2010

System size expansion for systems with an absorbing state

The well known van Kampen system size expansion, while of rather general applicability, is shown to fail to reproduce some qualitative features of the time evolution for systems with an absorbing state, apart from a transient initial time interval. We generalize the van Kampen ansatz by introducing a new prescription leading to non-Gaussian fluctuations around the absorbing state. The two expansion predictions are explicitly compared for the infinite range voter model with speciation as a paradigmatic model with an absorbing state. The new expansion, both for a finite size system in the large time limit and at finite time in the large size limit, converges to to the exact solution as obtained in a numerical implementation using the Gillespie algorithm. Furthermore, the predicted lifetime distribution is shown to have the correct asymptotic behavior.

cond-mat.stat-mech↗

arXiv2010

Deterministic and stochastic aspects of VEGF-A production and the cooperative behavior of tumoral cell colony

A model is proposed to study the process of hypoxia-induced angiogenesis in cancer cells. The model accounts for the role played by the vascular endothelial growth factor (VEGF)-A in regulating the oxygen intake. VEGF-A is dynamically controlled by the HIF-1alpha concentration. If not degraded, HIF-1alpha can bind to the subunit termed HIF-1beta and so experience translocation to the nucleus, to exert its proper transcriptional activity. The delicate balance between these opposing tendencies translates into the emergence of distinct macroscopic behaviors in terms of the associated molecular concentrations that we here trace back to normoxia, hypoxia and death regimes. These aspects are firstly analyzed with reference to the ideal mean-field scenario. Stochastic fluctuations are also briefly discussed and shown to seed a cooperative interaction among cellular units, competing for the same oxygen reservoir.

q-bio.CB↗

arXiv2010

Stochastic Turing patterns in the Brusselator model

A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining the Turing condition for instability, we pay particular attention to the role of cross diffusive terms, often neglected in the heuristic derivation of reaction diffusion schemes. Stochastic fluctuations are shown to give rise to spatially ordered solutions, sharing the same quantitative characteristic of the mean-field based Turing scenario, in term of excited wavelengths. Interestingly, the region of parameter yielding to the stochastic self-organization is wider than that determined via the conventional Turing approach, suggesting that the condition for spatial order to appear can be less stringent than customarily believed.

cond-mat.stat-mech↗

arXiv2010

A spatial model of autocatalytic reactions

Biological cells with all of their surface structure and complex interior stripped away are essentially vesicles - membranes composed of lipid bilayers which form closed sacs. Vesicles are thought to be relevant as models of primitive protocells, and they could have provided the ideal environment for pre-biotic reactions to occur. In this paper, we investigate the stochastic dynamics of a set of autocatalytic reactions, within a spatially bounded domain, so as to mimic a primordial cell. The discreteness of the constituents of the autocatalytic reactions gives rise to large sustained oscillations, even when the number of constituents is quite large. These oscillations are spatio-temporal in nature, unlike those found in previous studies, which consisted only of temporal oscillations. We speculate that these oscillations may have a role in seeding membrane instabilities which lead to vesicle division. In this way synchronization could be achieved between protocell growth and the reproduction rate of the constituents (the protogenetic material) in simple protocells.

cond-mat.stat-mech↗

arXiv2008

Can a microscopic stochastic model explain the emergence of pain cycles in patients?

A stochastic model is here introduced to investigate the molecular mechanisms which trigger the perception of pain. The action of analgesic drug compounds is discussed in a dynamical context, where the competition with inactive species is explicitly accounted for. Finite size effects inevitably perturb the mean-field dynamics: Oscillations in the amount of bound receptors spontaneously manifest, driven by the noise which is intrinsic to the system under scrutiny. These effects are investigated both numerically, via stochastic simulations and analytically, through a large-size expansion. The claim that our findings could provide a consistent interpretative framework to explain the emergence of cyclic behaviors in response to analgesic treatments, is substantiated.

cond-mat.stat-mech↗

arXiv2008

Enhanced stochastic oscillations in autocatalytic reactions

We study a simplified scheme of $k$ coupled autocatalytic reactions, previously introduced by Togashi and Kaneko. The role of stochastic fluctuations is elucidated through the use of the van Kampen system-size expansion and the results compared with direct stochastic simulations. Regular temporal oscillations are predicted to occur for the concentration of the various chemical constituents, with an enhanced amplitude resulting from a resonance which is induced by the intrinsic graininess of the system. The associated power spectra are determined and have a different form depending on the number of chemical constituents, $k$. We make detailed comparisons in the two cases $k=4$ and $k=8$. Agreement between the theoretical and numerical results for the power spectrum are good in both cases. The resulting spectrum is especially interesting in the $k=8$ system, since it has two peaks, which the system-size expansion is still able to reproduce accurately.

cond-mat.stat-mech↗

arXiv2007

A Biologically Inspired Classifier

We present a method for measuring the distance among records based on the correlations of data stored in the corresponding database entries. The original method (F. Bagnoli, A. Berrones and F. Franci. Physica A 332 (2004) 509-518) was formulated in the context of opinion formation. The opinions expressed over a set of topic originate a ``knowledge network'' among individuals, where two individuals are nearer the more similar their expressed opinions are. Assuming that individuals' opinions are stored in a database, the authors show that it is possible to anticipate an opinion using the correlations in the database. This corresponds to approximating the overlap between the tastes of two individuals with the correlations of their expressed opinions. In this paper we extend this model to nonlinear matching functions, inspired by biological problems such as microarray (probe-sample pairing). We investigate numerically the error between the correlation and the overlap matrix for eight sequences of reference with random probes. Results show that this method is particularly robust for detecting similarities in the presence of translocations.

cs.DB↗