TY - JOUR
T1 - Criticality and supradiffusion in biological membranes
T2 - The effect of transverse multiplicative fluctuations
AU - Rodrguez, R. F.
AU - Salinas-Rodrguez, E.
AU - Maldonado, A.
AU - Hernndez-Zapata, E.
AU - Cocho, G.
PY - 2011/3/15
Y1 - 2011/3/15
N2 - We suggest that the cytoskeleton in contact with the inner surface of biological membranes in cells exhibiting tensegrity, may be considered as a system near critical conditions. This feature will influence the dynamical processes, such as diffusion, associated with the membrane's fluctuations induced by the surrounding medium. In this work we analyze a model for the diffusion of particles attached to the membrane due to the transverse membrane fluctuations when the surrounding fluid is near a critical state. We describe these fluctuations by a multiplicative Langevin equation with colored noise which accounts for the rheological nature of the medium. From the associated FokkerPlanck equation we calculate analytically the mean square displacement (MSD) and the dynamic structure factor (DSF) of the particles. In the limit of additive white noise, it is well known that the MSD and the DSF exhibit sub-diffusive behavior with a scaling MSD∼t23 and DSF∼exp(ΓkAWt) 23. In contrast, we show that for the case of external fluctuations arising from criticality and modeled by an OrnsteinUhlenbeck multiplicative noise, the behavior of these quantities becomes supradiffusive, with scalings MSD∼t53 and DSF∼exp(ΓkMCt)53. We suggest that this supradiffusive behavior might be of importance for the biological functions of the cell and compare our work with other approaches which also predict the same transition from a sub-diffusive to a supra-diffusive regime.
AB - We suggest that the cytoskeleton in contact with the inner surface of biological membranes in cells exhibiting tensegrity, may be considered as a system near critical conditions. This feature will influence the dynamical processes, such as diffusion, associated with the membrane's fluctuations induced by the surrounding medium. In this work we analyze a model for the diffusion of particles attached to the membrane due to the transverse membrane fluctuations when the surrounding fluid is near a critical state. We describe these fluctuations by a multiplicative Langevin equation with colored noise which accounts for the rheological nature of the medium. From the associated FokkerPlanck equation we calculate analytically the mean square displacement (MSD) and the dynamic structure factor (DSF) of the particles. In the limit of additive white noise, it is well known that the MSD and the DSF exhibit sub-diffusive behavior with a scaling MSD∼t23 and DSF∼exp(ΓkAWt) 23. In contrast, we show that for the case of external fluctuations arising from criticality and modeled by an OrnsteinUhlenbeck multiplicative noise, the behavior of these quantities becomes supradiffusive, with scalings MSD∼t53 and DSF∼exp(ΓkMCt)53. We suggest that this supradiffusive behavior might be of importance for the biological functions of the cell and compare our work with other approaches which also predict the same transition from a sub-diffusive to a supra-diffusive regime.
KW - Diffusion
KW - Fluctuations
KW - Membranes
KW - Noise in biological systems
KW - Stochastic modeling
UR - http://www.scopus.com/inward/record.url?scp=78751569588&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2010.11.022
DO - 10.1016/j.physa.2010.11.022
M3 - Artículo
SN - 0378-4371
VL - 390
SP - 1198
EP - 1208
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 6
ER -