Modelling cytoskeletal traffic: an interplay between passive diffusion and active transport

We introduce the totally asymmetric exclusion process with Langmuir kinetics (TASEP-LK) on a network as a microscopic model for active motor protein transport on the cytoskeleton, immersed in the diffusive cytoplasm. We discuss how the interplay between active transport along a network and infinite diffusion in a bulk reservoir leads to a heterogeneous matter distribution on various scales. We find three regimes for steady state transport, corresponding to the scale of the network, of individual segments or local to sites. At low exchange rates strong density heterogeneities develop between different segments in the network. In this regime one has to consider the topological complexity of the whole network to describe transport. In contrast, at moderate exchange rates the transport through the network decouples, and the physics is determined by single segments and the local topology. At last, for very high exchange rates the homogeneous Langmuir process dominates the stationary state. We introduce effective rate diagrams for the network to identify these different regimes. Based on this method we develop an intuitive but generic picture of how the stationary state of excluded volume processes on complex networks can be understood in terms of the single-segment phase diagram.Comment: 5 pages, 7 figure

Motor proteins traffic regulation by supply-demand balance of resources

In cells and in vitro assays the number of motor proteins involved in biological transport processes is far from being unlimited. The cytoskeletal binding sites are in contact with the same finite reservoir of motors (either the cytosol or the flow chamber) and hence compete for recruiting the available motors, potentially depleting the reservoir and affecting cytoskeletal transport. In this work we provide a theoretical framework to study, analytically and numerically, how motor density profiles and crowding along cytoskeletal filaments depend on the competition of motors for their binding sites. We propose two models in which finite processive motor proteins actively advance along cytoskeletal filaments and are continuously exchanged with the motor pool. We first look at homogeneous reservoirs and then examine the effects of free motor diffusion in the surrounding medium. We consider as a reference situation recent in vitro experimental setups of kinesin-8 motors binding and moving along microtubule filaments in a flow chamber. We investigate how the crowding of linear motor proteins moving on a filament can be regulated by the balance between supply (concentration of motor proteins in the flow chamber) and demand (total number of polymerised tubulin heterodimers). We present analytical results for the density profiles of bound motors, the reservoir depletion, and propose novel phase diagrams that present the formation of jams of motor proteins on the filament as a function of two tuneable experimental parameters: the motor protein concentration and the concentration of tubulins polymerized into cytoskeletal filaments. Extensive numerical simulations corroborate the analytical results for parameters in the experimental range and also address the effects of diffusion of motor proteins in the reservoir.Comment: 31 pages, 10 figure

Exclusion processes on networks as models for cytoskeletal transport

We present a study of exclusion processes on networks as models for complex transport phenomena and in particular for active transport of motor proteins along the cytoskeleton. We argue that active transport processes on networks spontaneously develop density heterogeneities at various scales. These heterogeneities can be regulated through a variety of multi-scale factors, such as the interplay of exclusion interactions, the non-equilibrium nature of the transport process and the network topology. We show how an effective rate approach allows to develop an understanding of the stationary state of transport processes through complex networks from the phase diagram of one single segment. For exclusion processes we rationalize that the stationary state can be classified in three qualitatively different regimes: a homogeneous phase as well as inhomogeneous network and segment phases. In particular, we present here a study of the stationary state on networks of three paradigmatic models from non-equilibrium statistical physics: the totally asymmetric simple exclusion process, the partially asymmetric simple exclusion process and the totally asymmetric simple exclusion process with Langmuir kinetics. With these models we can interpolate between equilibrium (due to bi-directional motion along a network or infinite diffusion) and out-of-equilibrium active directed motion along a network. The study of these models sheds further light on the emergence of density heterogeneities in active phenomena.Comment: 55 pages, 26 figure

Collective Effects in Models for Interacting Molecular Motors and Motor-Microtubule Mixtures

Three problems in the statistical mechanics of models for an assembly of molecular motors interacting with cytoskeletal filaments are reviewed. First, a description of the hydrodynamical behaviour of density-density correlations in fluctuating ratchet models for interacting molecular motors is outlined. Numerical evidence indicates that the scaling properties of dynamical behavior in such models belong to the KPZ universality class. Second, the generalization of such models to include boundary injection and removal of motors is provided. In common with known results for the asymmetric exclusion processes, simulations indicate that such models exhibit sharp boundary driven phase transitions in the thermodynamic limit. In the third part of this paper, recent progress towards a continuum description of pattern formation in mixtures of motors and microtubules is described, and a non-equilibrium ``phase-diagram'' for such systems discussed.Comment: Proc. Int. Workshop on "Common Trends in Traffic Systems", Kanpur, India, Feb 2006; to be published in Physica

Instabilities and shape variation phase transitions in tubular lipid membranes

Changes of external parameters in proximity of critical point can increase thermal fluctuations of tubular lipid membrane (TLM) and result in variation of the membrane shape. The phase transitions in the system are shown to be controlled by a single effective parameter, which depends on the pressure difference between inner and outer regions of membrane and the applied stretching force. We determine an interval of the parameter values corresponding to the stability region of the cylindrical shape of TLM and investigate the behavior of the system in the vicinity of critical instabilities, where the cylindrical shape of membrane becomes unstable with respect to thermal fluctuations. The applied boundary conditions strongly influence the behavior of TLM. For example, small negative effective parameter corresponds to chiral shape of TLM only in the case of periodic boundary conditions. We also discuss other three types of phase transitions emerging in the system.Comment: 15 pages, 6 figures, in Russia

Irreversible and reversible modes of operation of deterministic ratchets

We discuss a problem of optimization of the energetic efficiency of a simple rocked ratchet. We concentrate on a low-temperature case in which the particle's motion in a ratchet potential is deterministic. We show that the energetic efficiency of a ratchet working adiabatically is bounded from above by a value depending on the form of ratchet potential. The ratchets with strongly asymmetric potentials can achieve ideal efficiency of unity without approaching reversibility. On the other hand we show that for any form of the ratchet potential a set of time-protocols of the outer force exist under which the operation is reversible and the ideal value of efficiency is also achieved. The mode of operation of the ratchet is still quasistatic but not adiabatic. The high values of efficiency can be preserved even under elevated temperatures

Tween® preserves enzyme activity and stability in PLGA nanoparticles

Enzymes, as natural and potentially long-term treatment options, have become one of the most sought-after pharmaceutical molecules to be delivered with nanoparticles (NPs); however, their instability during formulation often leads to underwhelming results. Various molecules, including the Tween® polysorbate series, have demonstrated enzyme activity protection but are often used uncontrolled without optimization. Here, poly(lactic-co-glycolic) acid (PLGA) NPs loaded with β-glucosidase (β-Glu) solutions containing Tween® 20, 60, or 80 were compared. Mixing the enzyme with Tween® pre-formulation had no effect on particle size or physical characteristics, but increased the amount of enzyme loaded. More importantly, NPs made with Tween® 20:enzyme solutions maintained significantly higher enzyme activity. Therefore, Tween® 20:enzyme solutions ranging from 60:1 to 2419:1 mol:mol were further analyzed. Isothermal titration calorimetry analysis demonstrated low affinity and unquantifiable binding between Tween® 20 and β-Glu. Incorporating these solutions in NPs showed no effect on size, zeta potential, or morphology. The amount of enzyme and Tween® 20 in the NPs was constant for all samples, but a trend towards higher activity with higher molar rapports of Tween® 20:β-Glu was observed. Finally, a burst release from NPs in the first hour with Tween®:β-Glu solutions was the same as free enzyme, but the enzyme remained active longer in solution. These results highlight the importance of stabilizers during NP formulation and how optimizing their use to stabilize an enzyme can help researchers design more efficient and effective enzyme loaded NPs

Microfluidic technology for the production of hybrid nanomedicines

Microfluidic technologies have recently been applied as innovative methods for the production of a variety of nanomedicines (NMeds), demonstrating their potential on a global scale. The capacity to precisely control variables, such as the flow rate ratio, temperature, total flow rate, etc., allows for greater tunability of the NMed systems that are more standardized and automated than the ones obtained by well-known benchtop protocols. However, it is a crucial aspect to be able to obtain NMeds with the same characteristics of the previously optimized ones. In this study, we focused on the transfer of a production protocol for hybrid NMeds (H-NMeds) consisting of PLGA, Cholesterol, and Pluronic® F68 from a benchtop nanoprecipitation method to a microfluidic device. For this aim, we modified parameters such as the flow rate ratio, the concentration of core materials in the organic phase, and the ratio between PLGA and Cholesterol in the feeding organic phase. Outputs analysed were the chemico–physical properties, such as size, PDI, and surface charge, the composition in terms of %Cholesterol and residual %Pluronic® F68, their stability to lyophilization, and the morphology via atomic force and electron microscopy. On the basis of the results, even if microfluidic technology is one of the unique procedures to obtain industrial production of NMeds, we demonstrated that the translation from a benchtop method to a microfluidic one is not a simple transfer of already established parameters, with several variables to be taken into account and to be optimized

Inattainability of Carnot efficiency in the Brownian heat engine

We discuss the reversibility of Brownian heat engine. We perform asymptotic analysis of Kramers equation on B\"uttiker-Landauer system and show quantitatively that Carnot efficiency is inattainable even in a fully overdamping limit. The inattainability is attributed to the inevitable irreversible heat flow over the temperature boundary.Comment: 5 pages, to appear in Phys. Rev.

Traffic of Molecular Motors

Molecular motors perform active movements along cytoskeletal filaments and drive the traffic of organelles and other cargo particles in cells. In contrast to the macroscopic traffic of cars, however, the traffic of molecular motors is characterized by a finite walking distance (or run length) after which a motor unbinds from the filament along which it moves. Unbound motors perform Brownian motion in the surrounding aqueous solution until they rebind to a filament. We use variants of driven lattice gas models to describe the interplay of their active movements, the unbound diffusion, and the binding/unbinding dynamics. If the motor concentration is large, motor-motor interactions become important and lead to a variety of cooperative traffic phenomena such as traffic jams on the filaments, boundary-induced phase transitions, and spontaneous symmetry breaking in systems with two species of motors. If the filament is surrounded by a large reservoir of motors, the jam length, i.e., the extension of the traffic jams is of the order of the walking distance. Much longer jams can be found in confined geometries such as tube-like compartments.Comment: 10 pages, latex, uses Springer styles (included), to appear in the Proceedings of "Traffic and Granular Flow 2005