M.A. Despósito

Subdiffusive behavior in a trapping potential: Mean square displacement and velocity autocorrelation function

A theoretical framework for analyzing stochastic data from single-particle tracking in viscoelastic materials and under the influence of a trapping potential is presented. Starting from a generalized Langevin equation, we found analytical expressions for the two-time dynamics of a particle subjected to a harmonic potential. The mean-square displacement and the velocity autocorrelation function of the diffusing particle are given in terms of the time lag. In particular, we investigate the subdiffusive case. Using a power-law memory kernel, exact expressions for the mean-square displacement and the velocity autocorrelation function are obtained in terms of Mittag-Leffler functions and their derivatives. The behaviors for short-, intermediate-, and long-time lags are investigated in terms of the involved parameters. Finally, the validity of usual approximations is examined.

Mechanical Properties of Organelles Driven by Microtubule-Dependent Molecular Motors in Living Cells

The organization of the cytoplasm is regulated by molecular motors which transport organelles and other cargoes along cytoskeleton tracks. Melanophores have pigment organelles or melanosomes that move along microtubules toward their minus and plus end by the action of cytoplasmic dynein and kinesin-2, respectively. In this work, we used single particle tracking to characterize the mechanical properties of motor-driven organelles during transport along microtubules. We tracked organelles with high temporal and spatial resolutions and characterized their dynamics perpendicular to the cytoskeleton track. The quantitative analysis of these data showed that the dynamics is due to a spring-like interaction between melanosomes and microtubules in a viscoelastic microenvironment. A model based on a generalized Langevin equation explained these observations and predicted that the stiffness measured for the motor complex acting as a linker between organelles and microtubules is ∼ one order smaller than that determined for motor proteins in vitro. This result suggests that other biomolecules involved in the interaction between motors and organelles contribute to the mechanical properties of the motor complex. We hypothesise that the high flexibility observed for the motor linker may be required to improve the efficiency of the transport driven by multiple copies of motor molecules.

Anomalous Dynamics of Melanosomes Driven by Myosin-V in Xenopus laevis Melanophores

The organization of the cytoplasm is regulated by molecular motors, which transport organelles and other cargoes along cytoskeleton tracks. In this work, we use single particle tracking to study the in vivo regulation of the transport driven by myosin-V along actin filaments in Xenopus laevis melanophores. Melanophores have pigment organelles or melanosomes, which, in response to hormones, disperse in the cytoplasm or aggregate in the perinuclear region. We followed the motion of melanosomes in cells treated to depolymerize microtubules during aggregation and dispersion, focusing the analysis on the dynamics of these organelles in a time window not explored before to our knowledge. These data could not be explained by previous models that only consider active transport. We proposed a transport-diffusion model in which melanosomes may detach from actin tracks and reattach to nearby filaments to resume the active motion after a given time of diffusion. This model predicts that organelles spend approximately 70% and 10% of the total time in active transport during dispersion and aggregation, respectively. Our results suggest that the transport along actin filaments and the switching from actin to microtubule networks are regulated by changes in the diffusion time between periods of active motion driven by myosin-V.

Lateral Motion and Bending of Microtubules Studied with a New Single-Filament Tracking Routine in Living Cells

The cytoskeleton is involved in numerous cellular processes such as migration, division, and contraction and provides the tracks for transport driven by molecular motors. Therefore, it is very important to quantify the mechanical behavior of the cytoskeletal filaments to get a better insight into cell mechanics and organization. It has been demonstrated that relevant mechanical properties of microtubules can be extracted from the analysis of their motion and shape fluctuations. However, tracking individual filaments in living cells is extremely complex due, for example, to the high and heterogeneous background. We introduce a believed new tracking algorithm that allows recovering the coordinates of fluorescent microtubules with ∼9 nm precision in in vitro conditions. To illustrate potential applications of this algorithm, we studied the curvature distributions of fluorescent microtubules in living cells. By performing a Fourier analysis of the microtubule shapes, we found that the curvatures followed a thermal-like distribution as previously reported with an effective persistence length of ∼20 μm, a value significantly smaller than that measured in vitro. We also verified that the microtubule-associated protein XTP or the depolymerization of the actin network do not affect this value; however, the disruption of intermediate filaments decreased the persistence length. Also, we recovered trajectories of microtubule segments in actin or intermediate filament-depleted cells, and observed a significant increase of their motion with respect to untreated cells showing that these filaments contribute to the overall organization of the microtubule network. Moreover, the analysis of trajectories of microtubule segments in untreated cells showed that these filaments presented a slower but more directional motion in the cortex with respect to the perinuclear region, and suggests that the tracking routine would allow mapping the microtubule dynamical organization in cells.

The role of the reservoir correlations in the relaxation rates for different coupling models

A quantal system is assumed to interact with a thermal environment. The fully coupled (FC) and the rotating wave approximation (RWA) models are considered to derive a generalized master equation for the reduced density operator in terms of the spectral density of the correlation function of the thermal environment. The parameters of the irreversible motion are compared for different reservoir models. In particular, we examine the case of normal and odd heat baths and work out specific examples for both coupling mechanisms.

Extension of the quantal Brownian motion model to bosonic reservoirs

We formulate an extension of the Quantal Brownian Motion (QBM) model for collective mode damping designed to include coupling to other normal modes of the system. We derive the equations of motion of the macroscopic coordinates and of the fermionic and bosonic degrees of freedom and investigate their exact solution in the thermodynamic limit of the heat reservoir. We examine the properties of the microscopic transition rates and their dependence on the macroscopic parameters as well as on the coupling strengths. The characteristic times of the damping process are extracted and their trend is analyzed.

Memory effects in the spin relaxation within and without rotating wave approximation

In the frame of the time-convolutionless generalized master equation approach, an analysis of a spin relaxation is made within and without the rotating wave approximation. The non-Markovian reduced dynamics is investigated, giving explicit expressions for the time-dependent involved coefficients, and numerical results are presented for the Ohmic reservoir model. The comparisons between these results and those obtained with the Markovian approximation are developed, analyzing the positivity of the reduced dynamics in the short transient time.

Expansion method for nonlinear quantum master equations

We are interested in the solutions of those master equations which appear when we consider a nonlinear coupling between an oscillator and an arbitrary thermal bath. For this purpose we implement a power series expansion in the parameter Ω = kT/hω0. After observing that the master equation is of the diffusion type, we obtain a nonlinear Fokker-Planck equation for the probability density. Solving this equation we find that the relaxation becomes non-exponential. Going beyond lowest order in the expansion we deal again with a nonlinear Fokker-Plank equation which is equivalent to the obtained equation to first order in the case of a linear-plus-quadratic coupling. Finally, we transform the obtained equations to Schrodingers ones and analyze the corresponding eigenvalue spectrum.