arXiv subjects

L. Giuggioli

Publications and source records attributed to L. Giuggioli.

7 recordsLinked to original sources

arXiv2008

Molecular motion in cell membranes: analytic study of fence-hindered random walks

A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G-protein coupled mu-opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.

physics.bio-ph↗

arXiv2006

Study of transients in the propagation of nonlinear waves in some reaction diffusion systems

We study the transient dynamics of single species reaction diffusion systems whose reaction terms $f(u)$ vary nonlinearly near $u\approx 0$, specifically as $f(u)\approx u^{2}$ and $f(u)\approx u^{3}$. We consider three cases, calculate their traveling wave fronts and speeds \emph{analytically} and solve the equations numerically with different initial conditions to study the approach to the asymptotic front shape and speed. Observed time evolution is found to be quite sensitive to initial conditions and to display in some cases nonmonotonic behavior. Our analysis is centered on cases with $f'(0)=0$, and uncovers findings qualitatively as well quantitatively different from the more familiar reaction diffusion equations with $f'(0)>0$. These differences are ascribable to the disparity in time scales between the evolution of the front interior and the front tail.

nlin.PS↗

arXiv2006

Diffusion and Home Range Parameters for Rodents: Peromyscus maniculatus in New Mexico

We analyze data from a long term field project in New Mexico, consisting of repeated sessions of mark-recaptures of Peromyscus maniculatus (Rodentia: Muridae), the host and reservoir of Sin Nombre Virus (Bunyaviridae: Hantavirus). The displacements of the recaptured animals provide a means to study their movement from a statistical point of view. We extract two parameters from the data with the help of a simple model: the diffusion constant of the rodents, and the size of their home range. The short time behavior shows the motion to be approximately diffusive and the diffusion constant to be 470+/-50m^2/day. The long time behavior provides an estimation of the diameter of the rodent home ranges, with an average value of 100+/-25m. As in previous investigations directed at Zygodontomys brevicauda observations in Panama, we use a box model for home range estimation. We also use a harmonic model in the present investigation to study the sensitivity of the conclusions to the model used and find that both models lead to similar estimates.

q-bio.PE↗

arXiv2005

Effect of Predators of Juvenile Rodents on the Spread of the Hantavirus Epidemic

Effects of predators of juvenile mice on the spread of the Hantavirus are analyzed in the context of a recently proposed model. Two critical values of the predation probability are identified. When the smaller of them is exceeded, the hantavirus infection vanishes without extinguishing the mice population. When the larger is exceeded, the entire mice population vanishes. These results suggest the possibility of control of the spread of the epidemic by introducing predators in areas of mice colonies in a suitable way so that such control does not kill all the mice but lowers the epidemic spread.

q-bio.PE↗

arXiv2005

Theory of Hantavirus Infection Spread Incorporating Localized Adult and Itinerant Juvenile Mice

A generalized model of the spread of the Hantavirus in mice populations is presented on the basis of recent observational findings concerning the movement characteristics of the mice that carry the infection. The factual information behind the generalization is based on mark-recapture observations reported in Giuggioli et al. [Bull. Math. Biol. 67, 1135 (2005)] that have necessitated the introduction of home ranges in the simple model of Hantavirus spread presented by Abramson and Kenkre [Phys. Rev. E 66, 11912 (2002)]. The essential feature of the model presented here is the existence of adult mice that remain largely confined to locations near their home ranges, and itinerant juvenile mice that are not so confined, and, during their search for their own homes, move and infect both other juveniles and adults that they meet during their movement. The model is presented at three levels of description: mean field, kinetic and configuration. Results of calculations are shown explicitly from the mean field equations and the simulation rules, and are found to agree in some respects and to differ in others. The origin of the differences is shown to lie in spatial correlations. It is indicated how mark-recapture observations in the field may be employed to verify the applicability of the theory.

q-bio.PE↗

arXiv2005

Diffusion and Home Range Parameters from Rodent Population Measurements in Panama

Simple random walk considerations are used to interpret rodent population data collected in Hantavirus-related investigations in Panama regarding the short-tailed cane mouse, \emph{Zygodontomys brevicauda}. The diffusion constant of mice is evaluated to be of the order of (and larger than) 200 meters squared per day. The investigation also shows that the rodent mean square displacement saturates in time, indicating the existence of a spatial scale which could, in principle, be the home range of the rodents. This home range is concluded to be of the order of 70 meters. Theoretical analysis is provided for interpreting animal movement data in terms of an interplay of the home ranges, the diffusion constant, and the size of the grid used to monitor the movement. The study gives impetus to a substantial modification of existing theory of the spread of the Hantavirus epidemic which has been based on simple diffusive motion of the rodents, and additionally emphasizes the importance for developing more accurate techniques for the measurement of rodent movement.

q-bio.PE↗

arXiv2005

Theory of Home Range Estimation from Mark-Recapture Measurements of Animal Populations

A theory is provided for the estimation of home ranges of animals from the standard mark-recapture technique in which data are collected by capturing, tagging and recapturing the animals. The theoretical tool used is the Fokker-Planck equation, its characteristic quantities being the diffusion constant which describes the motion of the animals, and the attractive potential which addresses their tendency to live near their burrows. The measurement technique is shown to correspond to the calculation of a certain kind of mean square displacement of the animals relevant to the specific probing window in space corresponding to the trapping region. The output of the theory is a sigmoid curve of the observable mean square displacement as a function of the ratio of distances characteristic of the home range and the trapping region, along with an explicit prescription to extract the home range form observations. Applications of the theory to rodent movement in Panama and New Mexico are pointed out. An analysis is given of the sensitivity of our theory to the choice of the confining potential via the use of various representative cases. A comparison is provided between home range size inferred from our method and from other procedures employed in the literature. Consequences of home range overlap are also discussed.

q-bio.PE↗