Paolo Malgaretti

Confined Brownian ratchets

We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the particles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases of a flashing ratchet, a two-state model, and a ratchet under the influence of a temperature gradient are analyzed in detail. We show the emergence of a strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may take place in situations where none of those mechanisms leads to rectification when acting individually. The combined rectification mechanisms may lead to bidirectional transport and to new routes to segregation phenomena. Confined Brownian ratchets could be used to control transport in mesostructures and to engineer new and more efficient devices for transport at the nanoscale.

Effective Interaction between Active Colloids and Fluid Interfaces Induced by Marangoni Flows

We show theoretically that near a fluid-fluid interface a single active colloidal particle generating, e.g., chemicals or a temperature gradient experiences an effective force of hydrodynamic origin. This force is due to the fluid flow driven by Marangoni stresses induced by the activity of the particle; it decays very slowly with the distance from the interface, and can be attractive or repulsive depending on how the activity modifies the surface tension. We show that, for typical systems, this interaction can dominate the dynamics of the particle as compared to Brownian motion, dispersion forces, or self-phoretic effects. In the attractive case, the interaction promotes the self-assembly of particles into a crystal-like monolayer at the interface.

Active colloids at fluid interfaces

If an active Janus particle is trapped at the interface between a liquid and a fluid, its self-propelled motion along the interface is affected by a net torque on the particle due to the viscosity contrast between the two adjacent fluid phases. For a simple model of an active, spherical Janus colloid we analyze the conditions under which translation occurs along the interface and we provide estimates of the corresponding persistence length. We show that under certain conditions the persistence length of such a particle is significantly larger than the corresponding one in the bulk liquid, which is in line with the trends observed in recent experimental studies.

Running faster together: huge speed up of thermal ratchets due to hydrodynamic coupling.

We present simulations that reveal a surprisingly large effect of hydrodynamic coupling on the speed of thermal ratchet motors. The model that we use considers particles performing thermal ratchet motion in a hydrodynamic solvent. Using particle-based, mesoscopic simulations that maintain local momentum conservation, we analyze quantitatively how the coupling to the surrounding fluid affects ratchet motion. We find that coupling can increase the mean velocity of the moving particles by almost 2 orders of magnitude, precisely because ratchet motion has both a diffusive and a deterministic component. The resulting coupling also leads to the formation of aggregates at longer times. The correlated motion that we describe increases the efficiency of motor-delivered cargo transport and we speculate that the mechanism that we have uncovered may play a key role in speeding up molecular motor-driven intracellular transport.

Model microswimmers in channels with varying cross section

We study different types of microswimmers moving in channels with varying cross section and thereby interacting hydrodynamically with the channel walls. Starting from the Smoluchowski equation for a dilute suspension, for which interactions among swimmers can be neglected, we derive analytic expressions for the lateral probability distribution between plane channel walls. For weakly corrugated channels, we extend the Fick-Jacobs approach to microswimmers and thereby derive an effective equation for the probability distribution along the channel axis. Two regimes arise dominated either by entropic forces due to the geometrical confinement or by the active motion. In particular, our results show that the accumulation of microswimmers at channel walls is sensitive to both the underlying swimming mechanism and the geometry of the channels. Finally, for asymmetric channel corrugation, our model predicts a rectification of microswimmers along the channel, the strength and direction of which strongly depends on the swimmer type.

Collective dynamics of chemically active particles trapped at a fluid interface

Chemically active colloids generate changes in the chemical composition of their surrounding solution and thereby induce flows in the ambient fluid which affect their dynamical evolution. Here we study the many-body dynamics of a monolayer of spherically symmetric active particles trapped at a fluid-fluid interface. To this end we consider a model for the large-scale spatial distribution of particles which incorporates the direct pair interaction (including also the capillary interaction which is caused specifically by the interfacial trapping) as well as the effect of hydrodynamic interactions (including the Marangoni flow induced by the response of the interface to the chemical activity). The values of the relevant physical parameters for typical experimental realizations of such systems are estimated and various scenarios, which are predicted by our approach for the dynamics of the monolayer, are discussed. In particular, we show that the chemically-induced Marangoni flow can prevent the clustering instability driven by the capillary attraction.

Non-monotonous polymer translocation time across corrugated channels: Comparison between Fick-Jacobs approximation and numerical simulations

We study the translocation of polymers across varying-section channels. Using systematic approximations, we derive a simplified model that reduces the problem of polymer translocation through varying-section channels to that of a point-like particle under the action of an effective potential. Such a model allows us to identify the relevant parameters controlling the polymers dynamics and, in particular, their translocation time. By comparing our analytical results with numerical simulations we show that, under suitable conditions, our model provides reliable predictions of the dynamics of both Gaussian and self-avoiding polymers, in two- and three-dimensional confinement. Moreover, both theoretical predictions, as well Brownian dynamic results, show a non-monotonous dependence of polymer translocation velocity as a function of polymer size, a feature that can be exploited for polymer separation.

Self-diffusiophoresis induced by fluid interfaces

The influence of a fluid-fluid interface on self-phoresis of chemically active, axially symmetric, spherical colloids is analyzed. Distinct from the studies of self-phoresis for colloids trapped at fluid interfaces or in the vicinity of hard walls, here we focus on the issue of self-phoresis close to a fluid-fluid interface. In order to provide physically intuitive results highlighting the role played by the interface, the analysis is carried out for the case that the symmetry axis of the colloid is normal to the interface; moreover, thermal fluctuations are not taken into account. Similarly to what has been observed near hard walls, we find that such colloids can be set into motion even if their whole surface is homogeneously active. This is due to the anisotropy along the direction normal to the interface owing to the partitioning by diffusion, among the coexisting fluid phases, of the product of the chemical reaction taking place at the colloid surface. Different from results corresponding to hard walls, in the case of a fluid interface the direction of motion, i.e., towards the interface or away from it, can be controlled by tuning the physical properties of one of the two fluid phases. This effect is analyzed qualitatively and quantitatively, both by resorting to a far-field approximation and via an exact, analytical calculation which provides the means for a critical assessment of the approximate analysis.

Mechanical stability of bipolar spindle assembly

Assembly and stability of mitotic spindle is governed by the interplay of various intra-cellular forces, e.g. the forces generated by motor proteins by sliding overlapping anti-parallel microtubules (MTs) polymerized from the opposite centrosomes, the interaction of kinetochores with MTs, and the interaction of MTs with the chromosomes arms. We study the mechanical behavior and stability of spindle assembly within the framework of a minimal model which includes all these effects. For this model, we derive a closed--form analytical expression for the force acting between the centrosomes as a function of their separation distance and we show that an effective potential can be associated with the interactions at play. We obtain the stability diagram of spindle formation in terms of parameters characterizing the strength of motor sliding, repulsive forces generated by polymerizing MTs, and the forces arising out of interaction of MTs with kinetochores. The stability diagram helps in quantifying the relative effects of the different interactions and elucidates the role of motor proteins in formation and inhibition of spindle structures during mitotic cell division. We also predict a regime of bistability for certain parameter range, wherein the spindle structure can be stable for two different finite separation distances between centrosomes. This occurrence of bistability also suggests mechanical versatility of such self-assembled spindle structures.

Bistability, Oscillations, and Bidirectional Motion of Ensemble of Hydrodynamically Coupled Molecular Motors

We analyze the collective behavior of hydrodynamically coupled molecular motors. We show that the local fluxes induced by motor displacement can induce the experimentally observed bidirectional motion of cargoes and vesicles. By means of a mean-field approach we show that sustained oscillations as well as bistable collective motor motion arise even for very large collection of motors, when thermal noise is irrelevant. The analysis clarifies the physical mechanisms responsible for such dynamics by identifying the relevant coupling parameter and its dependence on the geometry of the hydrodynamic coupling as well as on system size. We quantify the phase diagram for the different phases that characterize the collective motion of hydrodynamically coupled motors and show that sustained oscillations can be reached for biologically relevant parameters, hence, demonstrating the relevance of hydrodynamic interactions in intracellular transport.