Kinetic equations for diffusion in the presence of entropic barriers

The interplay of shape and catalyst distribution in the yield of compressible flow microreactors

We develop a semi-analytical model for transport in structured catalytic microreactors, where both reactant and product are compressible fluids. Using lubrication and Fick-Jacobs approximations, we reduce the three-dimensional governing equations to an effective one-dimensional set of equations. Our model captures the effect of compressibility, corrugations in the shape of the reactor, and an inhomogeneous catalytic coating of the reactor walls. We show that in the weakly compressible limit (e.g., liquid-phase reactors), the distribution of catalyst does not influence the reactor yield, which we verify experimentally. Beyond this limit, we show that introducing inhomogeneities in the catalytic coating and corrugations to the reactor walls can improve the yield.

Entropy Production in Reaction-Diffusion Systems Confined in Narrow Channels

This work analyzes the effect of wall geometry when a reaction-diffusion system is confined to a narrow channel. In particular, we study the entropy production density in the reversible Gray-Scott system. Using an effective diffusion equation that considers modifications by the channel characteristics, we find that the entropy density changes its value but not its qualitative behavior, which helps explore the structure-formation space.

Entropic stochastic resonance of finite-size particles in confined Brownian transport

We demonstrate the existence of entropic stochastic resonance (ESR) of passive Brownian particles with finite size in a double- or triple-circular confined cavity, and compare the similarities and differences of ESR in the double-circular cavity and triple-circular cavity. When the diffusion of Brownian particles is constrained to the double- or triple-circular cavity, the presence of irregular boundaries leads to entropic barriers. The interplay between the entropic barriers, a periodic input signal, the gravity of particles, and intrinsic thermal noise may give rise to a peak in the spectral amplification factor and therefore to the appearance of the ESR phenomenon. It is shown that ESR can occur in both a double-circular cavity and a triple-circular cavity, and by adjusting some parameters of the system, the response of the system can be optimized. The differences are that the spectral amplification factor in a triple-circular cavity is significantly larger than that in a double-circular cavity, and compared with the ESR in a double-circular cavity, the ESR effect in a triple-circular cavity occurs within a wider range of external force parameters. In addition, the strength of ESR also depends on the particle radius, and smaller particles can induce more obvious ESR, indicating that the size effect cannot be safely neglected. The ESR phenomenon usually occurs in small-scale systems where confinement and noise play an important role. Therefore, the mechanism that is found could be used to manipulate and control nanodevices and biomolecules.

In biased and soft-walled channels: Insights into transport phenomena and damped modulation

The motion of a particle along a channel of finite width is known to be affected by either the presence of energy barriers or changes in the bias forces along the channel direction. By using the lateral equilibrium hypothesis, we have successfully derived the effective diffusion coefficient for soft-walled channels, and the diffusion is found to be influenced by the curvature profile of the potential. A typical phenomenon of diffusion enhancement is observed under the appropriate parameter conditions. We first discovered an anomalous phenomenon of quasi-periodic enhancement of oscillations, which cannot be captured by the one-dimensional effective potential, under the combination of sub-Ohmic damping with two-dimensional restricted channels. We innovatively develop the effective potential and the formation mechanism of velocity variance under super-Ohmic and ballistic damping, and meanwhile, ergodicity is of concern. The theoretical framework of a ballistic system can be reinterpreted through the folding acceleration theory. This comprehensive analysis significantly enhances our understanding of diffusion processes in constrained geometries.

Optimizing Work Extraction in the Presence of an Entropic Potential: An Entropic Stochastic Resonance

We study the nontrivial thermodynamic responses of an overdamped Brownian system driven by an unbiased driving force when the particle is confined inside a bilobal irregular structure. The spatial irregularity of the confinement results in an effective entropic bistable potential along the direction of transport. We calculate the thermodynamic response functions in terms of the averaged work done and the absorbed heat over a cycle of driving. We find that the thermodynamic responses are influenced by the nonlinearity of the effective entropic potential, the frequency of the external periodic driving force, and the random thermal fluctuations in a nontrivial way. In the presence of an optimal amount of thermal noise and a favoring driving frequency, the process exhibits a resonance-like precedent in terms of both output work and absorbed heat. We explore the conditions to get best synchronized work extraction (or absorbed heat), which can be utilized as a potential quantifier of an entropic stochastic resonance phenomenon. Finally, we identify a hallmark of entropy dominance over an analogous energy-driven scenario in terms of output work.

Local electroneutrality breakdown for electrolytes within varying-section nanopores

We determine the local charge dynamics of a [Formula: see text] electrolyte embedded in a varying-section channel. By means of an expansion based on the length scale separation between the axial and transverse direction of the channel, we derive closed formulas for the local excess charge for both, dielectric and conducting walls, in 2D (planar geometry) as well as in 3D (cylindrical geometry). Our results show that, even at equilibrium, the local charge electroneutrality is broken whenever the section of the channel is not homogeneous for both dielectric and conducting walls as well as for 2D and 3D channels. Interestingly, even within our expansion, the local excess charge in the fluid can be comparable to the net charge on the walls. We critically discuss the onset of such local electroneutrality breakdown in particular with respect to the correction that it induces on the effective free energy profile experienced by tracer ions.

Turning catalytically active pores into active pumps

We develop a semi-analytical model of self-diffusioosmotic transport in active pores, which includes advective transport and the inverse chemical reaction that consumes solute. In previous work [Antunes et al., Phys. Rev. Lett. 129, 188003 (2022)], we have demonstrated the existence of a spontaneous symmetry breaking in fore-aft symmetric pores that enables them to function as a micropump. We now show that this pumping transition is controlled by three timescales. Two timescales characterize advective and diffusive transport. The third timescale corresponds to how long a solute molecule resides in the pore before being consumed. Introducing asymmetry to the pore (either via the shape or the catalytic coating) reveals a second type of advection-enabled transition. In asymmetric pores, the flow rate exhibits discontinuous jumps and hysteresis loops upon tuning the parameters that control the asymmetry. This work demonstrates the interconnected roles of shape and catalytic patterning in the dynamics of active pores and shows how to design a pump for optimum performance.

Predicting cancer stages from tissue energy dissipation

Understanding cancer staging in order to predict its progression is vital to determine its severity and to plan the most appropriate therapies. This task has attracted interest from different fields of science and engineering. We propose a computational model that predicts the evolution of cancer in terms of the intimate structure of the tissue, considering that this is a self-organised structure that undergoes transformations governed by non-equilibrium thermodynamics laws. Based on experimental data on the dependence of tissue configurations on their elasticity and porosity, we relate the cancerous tissue stages with the energy dissipated, showing quantitatively that tissues in more advanced stages dissipate more energy. The knowledge of this energy allows us to know the probability of observing the tissue in its different stages and the probability of transition from one stage to another. We validate our results with experimental data and statistics from the World Health Organisation. Our quantitative approach provides insights into the evolution of cancer through its different stages, important as a starting point for new and integrative research to defeat cancer.

Diffusion Resistance of Segmented Channels

The geometry of ion and metabolite channels in membranes of biological cells and organelles is usually far from that of a regular right cylinder. Rather, the channels have complex shapes that are characterized by the so-called vestibules and constriction zones which play roles of molecular filters determining the channel selectivity. In the present paper we discuss several channel structures with varying radius that approximate most of the cases found in nature, specifically, channels of smoothly varying radius and channels composed of multiple cylindrical sections of different lengths and radii including channels containing very thin circular constrictions. We consider diffusive transport of electrically neutral molecules driven by the concentration gradient and derive analytical expressions for the diffusion resistance - the integral parameter that describes steady-state transport properties of membrane channels.

Diffusion coefficients and MSD measurements on curved membranes and porous media

We study some geometric aspects that influence the transport properties of particles that diffuse on curved surfaces. We compare different approaches to surface diffusion based on the Laplace-Beltrami operator adapted to predict concentration along entire membranes, confined subdomains along surfaces, or within porous media. Our goal is to summarize, firstly, how diffusion in these systems results in different types of diffusion coefficients and mean square displacement measurements, and secondly, how these two factors are affected by the concavity of the surface, the shape of the possible barriers or obstacles that form the available domains, the sinuosity, tortuosity, and constrictions of the trajectories and even how the observation plane affects the measurements of the diffusion. In addition to presenting a critical and organized comparison between different notions of MSD, in this review, we test the correspondence between theoretical predictions and numerical simulations by performing finite element simulations and illustrate some situations where diffusion theory can be applied. We briefly reviewed computational schemes for understanding surface diffusion and finally, discussed how this work contributes to understanding the role of surface diffusion transport properties in porous media and their relationship to other transport processes.

Transport theory up to second-order scattering for reaction-diffusion-phonon systems with applications to active transport in catalysis, explosions, and biological membranes

A Boltzmann transport equation approach is developed for reaction-diffusion systems which incorporates phonon transport in addition to the traditional approach. Scattering processes up to second order are taken into account. Two forces emerge from this analysis when a spatial gradient exists, one force on reactants and products, the other force on phonons. The forces are equal and opposite and have the tendency for separation of the phonons away from the reactants and products. These forces are capable of creating the types of instabilities that can lead to the formation of Turing patterns. The existence of these forces allows for exergonic conversion where not all of the released energy from reactions and diffusion becomes heat. When applied to homogeneous catalysis, one finds that reactants and products are pushed toward regions of greater catalytic activity. In the realm of high-energy explosions, calculations show that reactants and products can be accelerated laterally to the direction of a TNT reaction front up to speeds near 1000 m/s. This acceleration is in opposition to diffusion and represents active transport. Calculations also show that active transport observed in biological systems such as bacteria, mitochondria, and chloroplasts may be explained by this second-order transport theory. Using reasonable values for key parameters, calculations show that up to one-third of the available chemical energy can be converted toward pumping protons uphill to a potential of 50 mV.

Ratchet effect in an asymmetric two-dimensional system of Janus particles

We consider a disk-like Janus particle self-driven by a force of constant magnitude f, but an arbitrary direction depending on the stochastic rotation of the disk. The particle diffuses in a two-dimensional channel of varying width 2h(x). We applied the procedure mapping the 2+1-dimensional Fokker-Planck equation onto the longitudinal coordinate x; the result is the Fick-Jacobs equation extended by the spatially dependent effective diffusion constant D(x) and an additional effective potential -γ(x), derived recursively within the mapping procedure. Unlike the entropic potential ∼lnh(x), γ(x) becomes an increasing or decreasing function also in periodic channels, depending on the asymmetry of h(x) and thus it visualizes the net force driving the ratchet current. We demonstrate the appearance of the ratchet effect on a trial asymmetric channel; our theory is verified by a numerical solution of the corresponding Fokker-Planck equation. Isotropic driving force f results in the monotonic decrease of the ratchet current with a growing ratio α=D_{R}/D_{T} of the rotation and the translation diffusion constants; asymptotically going ∼1/α^{2}. If we allow anisotropy of the force, we can observe the current reversal depending on α.

Optimal transport of active particles induced by substrate concentration oscillations

We show the existence of a stochastic resonant regime in the transport of active colloidal particles under confinement. The periodic addition of substrate to the system causes the spectral amplification to exhibit a maximum for an optimal noise level value. The consequence of this is that particles can travel longer distances with lower fuel consumption. The stochastic resonance phenomenon found allows the identification of optimal scenarios for the transport of active particles, enabling them to reach regions that are otherwise difficult to access, and may therefore find applications in transport in cell membranes and tissues for medical treatments and soil remediation.

Geometric Brownian information engine: Essentials for the best performance

We investigate a geometric Brownian information engine (GBIE) in the presence of an error-free feedback controller that transforms the information gathered on the state of Brownian particles entrapped in monolobal geometric confinement into extractable work. Outcomes of the information engine depend on the reference measurement distance x_{m}, the feedback site x_{f}, and the transverse force G. We determine the benchmarks for utilizing the available information in an output work and the optimum operating requisites for best achievable work. Transverse bias force (G) tunes the entropic contribution in the effective potential and hence the standard deviation (σ) of the equilibrium marginal probability distribution. We recognize that the amount of extractable work reaches a global maximum when x_{f}=2x_{m} with x_{m}∼0.6σ, irrespective of the extent of the entropic limitation. Because of the higher loss of information during the relaxation process, the best achievable work of a GBIE is lower in an entropic system. The feedback regulation also bears the unidirectional passage of particles. The average displacement increases with growing entropic control and is maximum when x_{m}∼0.81σ. Finally, we explore the efficacy of the information engine, a quantity that regulates the efficiency in utilizing the information acquired. With x_{f}=2x_{m}, the maximum efficacy reduces with increasing entropic control and shows a crossover from 2 to 11/9. We discover that the condition for the best efficacy depends only on the confinement lengthscale along the feedback direction. The broader marginal probability distribution accredits the increased average displacement in a cycle and the lower efficacy in an entropy-dominated system.

Boundary design regulates the diffusion of active matter in heterogeneous environments

Physical boundaries play a key role in governing the overall transport properties of nearby self-propelled particles. In this work, we develop dispersion theories and conduct Brownian dynamics simulations to predict the coupling between surface accumulation and effective diffusivity of active particles in boundary-rich media. We focus on three models that are well-understood for passive systems: particle transport in (i) an array of fixed volume-excluding obstacles; (ii) a pore with spatially heterogeneous width; and (iii) a tortuous path with kinks and corners. While the impact of these entropic barriers on passive particle transport is well established, we find that these classical models of porous media flows break down due to the unique interplay between activity and the microstructure of the internal geometry. We study the activity-induced slowdown of effective diffusivity by formulating a Smoluchowski description of long-time self diffusivity which contains contributions from the density and fluctuation fields of the active particles. Particle-based and finite element simulations corroborate this perspective and reveal important nonequilibrium considerations of active transport.

Closed Formula for Transport across Constrictions

In the last decade, the Fick-Jacobs approximation has been exploited to capture transport across constrictions. Here, we review the derivation of the Fick-Jacobs equation with particular emphasis on its linear response regime. We show that, for fore-aft symmetric channels, the flux of noninteracting systems is fully captured by its linear response regime. For this case, we derive a very simple formula that captures the correct trends and can be exploited as a simple tool to design experiments or simulations. Lastly, we show that higher-order corrections in the flux may appear for nonsymmetric channels.

Surface diffusion in narrow channels on curved domains

We study the transport properties of diffusing particles restricted to confined regions on curved surfaces. We relate particle mobility to the curvature of the surface where they diffuse and the constraint due to confinement. Applying the Fick-Jacobs procedure to diffusion in curved manifolds shows that the local diffusion coefficient is related to average geometric quantities such as constriction and tortuosity. Macroscopic experiments can record such quantities through an average surface diffusion coefficient. We test the accuracy of our theoretical predictions of the effective diffusion coefficient through finite-element numerical solutions of the Laplace-Beltrami diffusion equation. We discuss how this work contributes to understanding the link between particle trajectories and the mean-square displacement.

Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting

The transport of particles through channels is of paramount importance in physics, chemistry, and surface science due to its broad real world applications. Much insight can be gained by observing the transition paths of a particle through a channel and collecting statistics on the lifetimes in the channel or the escape probabilities from the channel. In this paper, we consider the diffusive transport through a narrow conical channel of a Brownian particle subject to intermittent dynamics, namely, stochastic resetting. As such, resetting brings the particle back to a desired location from where it resumes its diffusive phase. To this end, we extend the Fick-Jacobs theory of channel-facilitated diffusive transport to resetting-induced transport. Exact expressions for the conditional mean first passage times, escape probabilities, and the total average lifetime in the channel are obtained, and their behavior as a function of the resetting rate is highlighted. It is shown that resetting can expedite the transport through the channel-rigorous constraints for such conditions are then illustrated. Furthermore, we observe that a carefully chosen resetting rate can render the average lifetime of the particle inside the channel minimal. Interestingly, the optimal rate undergoes continuous and discontinuous transitions as some relevant system parameters are varied. The validity of our one-dimensional analysis and the corresponding theoretical predictions is supported by three-dimensional Brownian dynamics simulations. We thus believe that resetting can be useful to facilitate particle transport across biological membranes-a phenomenon that can spearhead further theoretical and experimental studies.

Brownian particles in periodic potentials: Coarse-graining versus fine structure

We study the motion of an overdamped particle connected to a thermal heat bath in the presence of an external periodic potential in one dimension. When we coarse-grain, i.e., bin the particle positions using bin sizes that are larger than the periodicity of the potential, the packet of spreading particles, all starting from a common origin, converges to a normal distribution centered at the origin with a mean-squared displacement that grows as 2D^{*}t, with an effective diffusion constant that is smaller than that of a freely diffusing particle. We examine the interplay between this coarse-grained description and the fine structure of the density, which is given by the Boltzmann-Gibbs (BG) factor e^{-V(x)/k_{B}T}, the latter being nonnormalizable. We explain this result and construct a theory of observables using the Fokker-Planck equation. These observables are classified as those that are related to the BG fine structure, like the energy or occupation times, while others, like the positional moments, for long times, converge to those of the large-scale description. Entropy falls into a special category as it has a coarse-grained and a fine structure description. The basic thermodynamic formula F=TS-E is extended to this far-from-equilibrium system. The ergodic properties are also studied using tools from infinite ergodic theory.

Emergence of macroscopic directional motion of deformable active cells in confined structures

There is now growing evidence of collective turbulentlike motion of cells in dense tissues. However, how to control and harness this collective motion is an open question. We investigate the transport of deformable active cells in a periodically asymmetric channel by using a phase-field model. We demonstrate that collective turbulent-like motion of cells can power and steer the macroscopic directional motion through the ratchet channel. The active intercellular forces proportional to the deformation of cells can break thermodynamical equilibrium and induce the directional motion. This directional motion is caused by the ratchet effect rather than the spontaneous symmetry breaking. The motion direction is determined by the asymmetry of the channel. Remarkably, there exits an optimal nonequilibrium driving (depending on the active strength, the elasticity, and the packing fraction) at which the average velocity reaches the maximum. In addition, the optimized packing fraction and the optimized minimum width of the channel can facilitate the directional motion of cells. Our findings are relevant to understanding how macroscopic directional motion relates to the local force transmission mediated by cell-cell contacts in cellular monolayers.

Blockage coefficient of cylindrical blocker and diffusion resistance of membrane channels

This study deals with potential flow of ideal fluid in an infinite cylindrical tube in the presence of a blocking object. The blockage effect of the object on the flow can be characterized by a lump parameter, blockage coefficient, which accounts for the object shape and size. For a cylindrical blocking object, analytical results for the blockage coefficient are known only in three limiting cases: for a long thin cylinder and for small and large blocking disks. We propose a simple analytical expression for the blockage coefficient of a cylindrical blocker of arbitrary length and radius that reduces to the known asymptotic results in the corresponding limits.

First-passage times in conical varying-width channels biased by a transverse gravitational force: Comparison of analytical and numerical results

We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean first-passage time for such a system is derived under the assumption that the axial diffusion in a two-dimensional channel of smoothly varying geometry can be approximately described as a one-dimensional diffusion in an entropic potential with position-dependent effective diffusivity in terms of the modified Fick-Jacobs equation. We analyze the channel crossing dynamics in terms of the mean first-passage time, combining our analytical results with extensive two-dimensional Brownian dynamics simulations, allowing us to find the range of applicability of the one-dimensional approximation. We find that the effective particle diffusivity decreases with increasing amplitude of the external potential. Remarkably, the mean first-passage time for crossing the channel is shown to assume a minimum at finite values of the potential amplitude.

Pumping and Mixing in Active Pores

We show both numerically and analytically that a chemically patterned active pore can act as a micro- or nanopump for fluids, even if it is fore-aft symmetric. This is possible due to a spontaneous symmetry breaking which occurs when advection rather than diffusion is the dominant mechanism of solute transport. We further demonstrate that, for pumping and tuning the flow rate, a combination of geometrical and chemical inhomogeneities is required. For certain parameter values, the flow is unsteady, and persistent oscillations with a tunable frequency appear. Finally, we find that the flow exhibits convection rolls and hence promotes mixing in the low Reynolds number regime.

Parallel computing for mobilities in periodic geometries

We examine methods for calculating the effective mobilities of molecules driven through periodic geometries in the context of particle-based simulation. The standard formulation of the mobility, based on the long-time limit of the mean drift velocity, is compared to a formulation based on the mean first-passage time of molecules crossing a single period of the system geometry. The equivalence of the two definitions is derived under weaker assumptions than similar conclusions obtained previously, requiring only that the state of the system at subsequent period crossings satisfy the Markov property. Approximate theoretical analyses of the computational costs of estimating these two mobility formulations via particle simulations suggest that the definition based on first-passage times may be substantially better suited to exploiting parallel computation hardware. This claim is investigated numerically on an example system modeling the passage of nanoparticles through the slit-well device. In this case, the traditional mobility formulation is found to perform best when the Péclet number is small, whereas the mean first-passage time formulation is found to converge much more quickly when the Péclet number is moderate or large. The results suggest that, given relatively modest access to modern GPU hardware, this alternative mobility formulation may be an order of magnitude faster than the standard technique for computing effective mobilities of biomolecules through periodic geometries.

Transverse dichotomic ratchet in a two-dimensional corrugated channel

A particle diffusing in a two-dimensional channel of varying width h(x) is considered. It is driven by a force of constant magnitude f, but random orientation across the channel. We suggest the projection technique to study the ratchet effect appearing in this system. Reducing the transverse coordinate, as well as the orientation of the force in the full-dimensional Fokker-Planck equation, we arrive at the generalized Fick-Jacobs equation, describing dynamics of the system in the longitudinal coordinate x only. The additional effective potential -γ(x), calculated within the mapping procedure, exhibits an increasing or decreasing part in the channel shaped by an asymmetric periodic h(x), which determines the appearing ratchet current. As shown on a specific example, random driving in the transverse direction is much more effective than that in the longitudinal direction, at least for quickly flipping orientation of the force. Also, the transverse and the longitudinal driving push the rectified current in opposite directions along the same channel.

Percolation transition prescribes protein size-specific barrier to passive transport through the nuclear pore complex

Nuclear pore complexes (NPCs) control biomolecular transport in and out of the nucleus. Disordered nucleoporins in the complex's pore form a permeation barrier, preventing unassisted transport of large biomolecules. Here, we combine coarse-grained simulations of experimentally derived NPC structures with a theoretical model to determine the microscopic mechanism of passive transport. Brute-force simulations of protein transport reveal telegraph-like behavior, where prolonged diffusion on one side of the NPC is interrupted by rapid crossings to the other. We rationalize this behavior using a theoretical model that reproduces the energetics and kinetics of permeation solely from statistics of transient voids within the disordered mesh. As the protein size increases, the mesh transforms from a soft to a hard barrier, enabling orders-of-magnitude reduction in permeation rate for proteins beyond the percolation size threshold. Our model enables exploration of alternative NPC architectures and sets the stage for uncovering molecular mechanisms of facilitated nuclear transport.

Colloidal Stochastic Resonance in Confined Geometries

We investigate the dynamical properties of a colloidal particle in a double cavity. Without external driving, the particle hops between two free-energy minima with transition mean time depending on the system's entropic and energetic barriers. We then drive the particle with a periodic force. When the forcing period is set at twice the transition mean time, a statistical synchronization between particle motion and forcing phase marks the onset of a stochastic resonance mechanism. Comparisons between experimental results and predictions from the Fick-Jacobs theory and Brownian dynamics simulation reveal significant hydrodynamic effects, which change both resonant amplification and noise level. We further show that hydrodynamic effects can be incorporated into existing theory and simulation by using an experimentally measured particle diffusivity.

Blocker Effect on Diffusion Resistance of a Membrane Channel: Dependence on the Blocker Geometry

Being motivated by recent progress in nanopore sensing, we develop a theory of the effect of large analytes, or blockers, trapped within the nanopore confines, on diffusion flow of small solutes. The focus is on the nanopore diffusion resistance which is the ratio of the solute concentration difference in the reservoirs connected by the nanopore to the solute flux driven by this difference. Analytical expressions for the diffusion resistance are derived for a cylindrically symmetric blocker whose axis coincides with the axis of a cylindrical nanopore in two limiting cases where the blocker radius changes either smoothly or abruptly. Comparison of our theoretical predictions with the results obtained from Brownian dynamics simulations shows good agreement between the two.

Mitochondrial mRNA localization is governed by translation kinetics and spatial transport

For many nuclear-encoded mitochondrial genes, mRNA localizes to the mitochondrial surface co-translationally, aided by the association of a mitochondrial targeting sequence (MTS) on the nascent peptide with the mitochondrial import complex. For a subset of these co-translationally localized mRNAs, their localization is dependent on the metabolic state of the cell, while others are constitutively localized. To explore the differences between these two mRNA types we developed a stochastic, quantitative model for MTS-mediated mRNA localization to mitochondria in yeast cells. This model includes translation, applying gene-specific kinetics derived from experimental data; and diffusion in the cytosol. Even though both mRNA types are co-translationally localized we found that the steady state number, or density, of ribosomes along an mRNA was insufficient to differentiate the two mRNA types. Instead, conditionally-localized mRNAs have faster translation kinetics which modulate localization in combination with changes to diffusive search kinetics across metabolic states. Our model also suggests that the MTS requires a maturation time to become competent to bind mitochondria. Our work indicates that yeast cells can regulate mRNA localization to mitochondria by controlling mitochondrial volume fraction (influencing diffusive search times) and gene translation kinetics (adjusting mRNA binding competence) without the need for mRNA-specific binding proteins. These results shed light on both global and gene-specific mechanisms that enable cells to alter mRNA localization in response to changing metabolic conditions.

Enhanced diffusion in soft-walled channels with a periodically varying curvature

The motion of particles along channels of finite width is known to be hindered by either the presence of energy barriers along the channel direction or by variations in the width of the channel in the transverse direction (rugged channel). Remarkably, when both features are present, they can interact to produce a counterintuitive result: adding energy barriers to a rugged channel can enhance the rate of diffusion along it. This is the result of competing energetic and entropic effects. Under the approximation of particles instantaneously in equilibrium in the transverse direction, one can tailor the energy barriers to the ruggedness to recover free diffusion. However, such fine-tuning and potentially restrictive approximations are not necessary to observe an enhanced rate of diffusion as we demonstrate by adding a range of (non-fine-tuned) energy barriers to a channel of sinusoidally varying curvature. Furthermore, this was observed to hold for systems with a finite characteristic timescale for motion in the transverse direction, thus, suggesting that the phenomenon lends itself to be exploited for practical applications.

Mean first-passage time to a small absorbing target in three-dimensional elongated domains

We derive an approximate formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape inside an elongated domain of a slowly varying axisymmetric profile. For this purpose, the original Poisson equation in three dimensions is reduced to an effective one-dimensional problem on an interval with a semipermeable semiabsorbing membrane. The approximate formula captures correctly the dependence of the MFPT on the distance to the target, the radial profile of the domain, and the size and the shape of the target. This approximation is validated by Monte Carlo simulations.

First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry

We investigate the first passage properties of a Brownian particle diffusing freely inside a d-dimensional sphere with absorbing spherical surface subject to stochastic resetting. We derive the mean time to absorption (MTA) as functions of resetting rate γ and initial distance r of the particle to the center of the sphere. We find that when r>r_{c} there exists a nonzero optimal resetting rate γ_{opt} at which the MTA is a minimum, where r_{c}=sqrt[d/(d+4)]R and R is the radius of the sphere. As r increases, γ_{opt} exhibits a continuous transition from zero to nonzero at r=r_{c}. Furthermore, we consider that the particle lies between two two-dimensional or three-dimensional concentric spheres with absorbing boundaries, and obtain the domain in which resetting expedites the MTA, which is (R_{1},r_{c_{1}})∪(r_{c_{2}},R_{2}), with R_{1} and R_{2} being the radii of inner and outer spheres, respectively. Interestingly, when R_{1}/R_{2} is less than a critical value, γ_{opt} exhibits a discontinuous transition at r=r_{c_{1}}; otherwise, such a transition is continuous. However, at r=r_{c_{2}} the transition is always continuous.

Active microrheology in corrugated channels: Comparison of thermal and colloidal baths

HYPOTHESIS

The dynamics of colloidal suspension confined within porous materials strongly differs from that in the bulk. In particular, within porous materials, the presence of boundaries with complex shapes entangles the longitudinal and transverse degrees of freedom inducing a coupling between the transport of the suspension and the density inhomogeneities induced by the walls.

METHOD

Colloidal suspension confined within model porous media are characterized by means of active microrheology where a net force is applied on a single colloid (tracer particle) whose transport properties are then studied. The trajectories provided by active microrheology are exploited to determine the local transport coefficients. In order to asses the role of the colloid-colloid interactions we compare the case of a tracer embedded in a colloidal suspension to the case of a tracer suspended in an ideal bath.

FINDING

Our results show that the friction coefficient increases and the passage time distribution widens upon increasing the corrugation of the channel. These features are obtained for a tracer suspended in a (thermalized) colloidal bath as well as for the case of an ideal thermal bath. These results highlight the relevance of the confinement on the transport and show a mild dependence on the colloidal/thermal bath. Finally, we rationalize our numerical results with a semi-analytical model. Interestingly, the predictions of the model are quantitatively reliable for mild external forces, hence providing a reliable tool for predicting the transport across porous materials.

Geometric Brownian information engine: Upper bound of the achievable work under feedback control

We design a geometric Brownian information engine by considering overdamped Brownian particles inside a two-dimensional monolobal confinement with irregular width along the transport direction. Under such detention, particles experience an effective entropic potential which has a logarithmic form. We employ a feedback control protocol as an outcome of error-free position measurement. The protocol comprises three stages: measurement, feedback, and relaxation. We reposition the center of the confinement to the measurement distance (x_p) instantaneously when the position of the trapped particle crosses x_p for the first time. Then, the particle is allowed for thermal relaxation. We calculate the extractable work, total information, and unavailable information associated with the feedback control using this equilibrium probability distribution function. We find the exact analytical value of the upper bound of extractable work as (53-2ln2)k_BT. We introduce a constant force G downward to the transverse coordinate (y). A change in G alters the effective potential of the system and tunes the relative dominance of entropic and energetic contributions in it. The upper bound of the achievable work shows a crossover from (53-2ln2)k_BT to 12k_BT when the system changes from an entropy-dominated regime to an energy-dominated one. Compared to an energetic analog, the loss of information during the relaxation process is higher in the entropy-dominated region, which accredits the less value in achievable work. Theoretical predictions are in good agreement with the Langevin dynamics simulation studies.

Enhancing carrier flux for efficient drug delivery in cancer tissues

Ultrasound focused toward tumors in the presence of circulating microbubbles improves the delivery of drug-loaded nanoparticles and therapeutic outcomes; however, the efficacy varies among the different properties and conditions of the tumors. Therefore, there is a need to optimize the ultrasound parameters and determine the properties of the tumor tissue important for the successful delivery of nanoparticles. Here, we propose a mesoscopic model considering the presence of entropic forces to explain the ultrasound-enhanced transport of nanoparticles across the capillary wall and through the interstitium of tumors. The nanoparticles move through channels of variable shape whose irregularities can be assimilated to barriers of entropic nature that the nanoparticles must overcome to reach their targets. The model assumes that focused ultrasound and circulating microbubbles cause the capillary wall to oscillate, thereby changing the width of transcapillary and interstitial channels. Our analysis provides values for the penetration distances of nanoparticles into the interstitium that are in agreement with experimental results. We found that the penetration increased significantly with increasing acoustic intensity as well as tissue elasticity, which means softer and more deformable tissue (Young modulus lower than 50 kPa), whereas porosity of the tissue and pulse repetition frequency of the ultrasound had less impact on the penetration length. We also considered that nanoparticles can be absorbed into cells and to extracellular matrix constituents, finding that the penetration length is increased when there is a low absorbance coefficient of the nanoparticles compared with their diffusion coefficient (close to 0.2). The model can be used to predict which tumor types, in terms of elasticity, will successfully deliver nanoparticles into the interstitium. It can also be used to predict the penetration distance into the interstitium of nanoparticles with various sizes and the ultrasound intensity needed for the efficient distribution of the nanoparticles.

Dichotomic ratchet in a two-dimensional corrugated channel

We consider a particle diffusing in a two-dimensional (2D) channel of varying width h(x). It is driven by a force of constant magnitude f but random orientation there or back along the channel. We derive the effective generalized Fick-Jacobs equation for this system, which describes the dynamics of such a particle in the longitudinal coordinate x. Aside from the effective diffusion coefficient D(x), our mapping also generates an additional effective potential -γ(x) added to the entropic potential -log[h(x)]. It acquires an increasing or decreasing component in asymmetric periodic channels, and thus it explains appearance of the ratchet current. We study this effect on a trial example and compare the results of our true 2D theory with a commonly used effective one-dimensional description; the data are verified by the numerical solution of the full 2D problem.

Two-dimensional diffusion biased by a transverse gravitational force in an asymmetric channel: Reduction to an effective one-dimensional description

We focus on the derivation of a general position-dependent effective diffusion coefficient to describe two-dimensional (2D) diffusion in a narrow and smoothly asymmetric channel of varying width under a transverse gravitational external field, a generalization of the symmetric channel case using the projection method introduced earlier by Kalinay and Percus [P. Kalinay and J. K. Percus, J. Chem. Phys. 122, 204701 (2005)10.1063/1.1899150]. To this end, we project the 2D Smoluchowski equation into an effective one-dimensional generalized Fick-Jacobs equation in the presence of constant force in the transverse direction. The expression for the diffusion coefficient given in Eq. (34) is our main result. This expression is a more general effective diffusion coefficient for narrow 2D channels in the presence of constant transverse force, which contains the well-known previous results for a symmetric channel obtained by Kalinay, as well as the limiting cases when the transverse gravitational external field goes to zero and infinity. Finally, we show that diffusivity can be described by the interpolation formula proposed by Kalinay, D_{0}/[1+(1/4)w^{'2}(x)]^{-η}, where spatial confinement, asymmetry, and the presence of a constant transverse force can be encoded in η, which is a function of channel width (w), channel centerline, and transverse force. The interpolation formula also reduces to well-known previous results, namely, those obtained by Reguera and Rubi [D. Reguera and J. M. Rubi, Phys. Rev. E 64, 061106 (2001)10.1103/PhysRevE.64.061106] and by Kalinay [P. Kalinay, Phys. Rev. E 84, 011118 (2011)10.1103/PhysRevE.84.011118].

Reduced dynamics of a one-dimensional Janus particle

A Janus particle diffusing on a line is considered. Aside from its own driving force f acting forward or backward according to its stochastic orientation, it moves in a position-dependent potential U(x). We propose here the mapping scheme generating the effective generalized Fick-Jacobs equation, describing motion of the particle in the spatial coordinate x only; the orientation is understood as the transverse coordinate. The self-propulsion, driving the system out of equilibrium, is reflected as an additional effective potential -γ(x) in the reduced picture. It enables us to understand peculiarities of this system in a handy way. The additionally corrected potential redistributes the confined particles in quasiequilibrium causing their piling at the walls. In periodic asymmetric channels, it acquires a growing contribution, responsible for driving the ratchet effect.

Antiresonant driven systems for particle manipulation

We report on the onset of antiresonant behavior of mass transport systems driven by time-dependent forces. Antiresonances arise from the coupling of a sufficiently high number of space-time modes of the force. The presence of forces having a wide space-time spectrum, a necessary condition for the formation of an antiresonance, is typical of confined systems with uneven and deformable walls that induce entropic forces dependent on space and time. We have analyzed, in particular, the case of polymer chains confined in a flexible channel and shown how they can be sorted and trapped. The presence of resonance-antiresonance pairs found can be exploited to design protocols able to engineer optimal transport processes and to manipulate the dynamics of nano-objects.

Effective diffusivity of a Brownian particle in a two-dimensional periodic channel of abruptly alternating width

We study diffusion of a Brownian particle in a two-dimensional periodic channel of abruptly alternating width. Our main result is a simple approximate analytical expression for the particle effective diffusivity, which shows how the diffusivity depends on the geometric parameters of the channel: lengths and widths of its wide and narrow segments. The result is obtained in two steps: first, we introduce an approximate one-dimensional description of particle diffusion in the channel, and second, we use this description to derive the expression for the effective diffusivity. While the reduction to the effective one-dimensional description is standard for systems of smoothly varying geometry, such a reduction in the case of abruptly changing geometry requires a new methodology used here, which is based on the boundary homogenization approach to the trapping problem. To test the accuracy of our analytical expression and thus establish the range of its applicability, we compare analytical predictions with the results obtained from Brownian dynamics simulations. The comparison shows excellent agreement between the two, on condition that the length of the wide segment of the channel is equal to or larger than its width.

Characterizing stochastic resonance in a triple cavity

Many biological systems possess confined structures, which produce novel influences on the dynamics. Here, stochastic resonance (SR) in a triple cavity that consists of three units and is subjected to noise, periodic force and vertical constance force is studied, by calculating the spectral amplification η numerically. Meanwhile, SR in the given triple cavity and differences from other structures are explored. First, it is found that the cavity parameters can eliminate or regulate the maximum of η and the noise intensity that induces this maximum. Second, compared to a double cavity with similar maximum/minimum widths and distances between two maximum widths as the triple cavity, η in the triple one shows a larger maximum. Next, the conversion of the natural boundary in the pure potential to the reflection boundary in the triple cavity will create the necessity of a vertical force to induce SR and lead to a decrease in the maximum of η. In addition, η monotonically decreases with the increase of the vertical force and frequency of the periodic force, while it presents several trends when increasing the periodic force's amplitude for different noise intensities. Finally, our studies are extended to the impact of fractional Gaussian noise excitations. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Resetting transition is governed by an interplay between thermal and potential energy

A dynamical process that takes a random time to complete, e.g., a chemical reaction, may either be accelerated or hindered due to resetting. Tuning system parameters, such as temperature, viscosity, or concentration, can invert the effect of resetting on the mean completion time of the process, which leads to a resetting transition. Although the resetting transition has been recently studied for diffusion in a handful of model potentials, it is yet unknown whether the results follow any universality in terms of well-defined physical parameters. To bridge this gap, we propose a general framework that reveals that the resetting transition is governed by an interplay between the thermal and potential energy. This result is illustrated for different classes of potentials that are used to model a wide variety of stochastic processes with numerous applications.

Real time observation of the interaction between aluminium salts and sweat under microfluidic conditions

Aluminium salts such as aluminium chlorohydrate (ACH) are the active ingredients of antiperspirant products. Their mechanism of action involves a temporary and superficial plugging of eccrine sweat pores at the skin surface. We developed a microfluidic system that allows the real time observation of the interactions between sweat and ACH in conditions mimicking physiological sweat flow and pore dimensions. Using artificial sweat containing bovine serum albumin as a model protein, we performed experiments under flowing conditions to demonstrate that pore clogging results from the aggregation of proteins by aluminium polycations at specific location in the sweat pore. Combining microfluidic experiments, confocal microscopy and numerical models helps to better understand the physical chemistry and mechanisms involved in pore plugging. The results show that plugging starts from the walls of sweat pores before expanding into the centre of the channel. The simulations aid in explaining the influence of ACH concentration as well as the impact of flow conditions on the localization of the plug. Altogether, these results outline the potential of both microfluidic confocal observations and numerical simulations at the single sweat pore level to understand why aluminium polycations are so efficient for sweat channel plugging.

Transport of neutral and charged nanorods across varying-section channels

We study the dynamics of neutral and charged rods embedded in varying-section channels. By means of systematic approximations, we derive the dependence of the local diffusion coefficient on both the geometry and charge of the rods. This microscopic insight allows us to provide predictions for the permeability of varying-section channels to rods with diverse lengths, aspect ratios and charge. Our analysis shows that the dynamics of charged rods is sensitive to the geometry of the channel and that their transport can be controlled by tuning both the shape of the confining walls and the charge of the rod. Interestingly, we find that the channel permeability does not depend monotonically on the charge of the rod. This opens the possibility of a novel mechanism to separate charged rods.

Computational Model for Membrane Transporters. Potential Implications for Cancer

To explain the increased transport of nutrients and metabolites and to control the movement of drug molecules through the transporters to the cancer cells, it is important to understand the exact mechanism of their structure and activity, as well as their biological and physical characteristics. We propose a computational model that reproduces the functionality of membrane transporters by quantifying the flow of substrates through the cell membrane. The model identifies the force induced by conformational changes of the transporter due to hydrolysis of ATP, in ABC transporters, or by an electrochemical gradient of ions, in secondary transporters. The transport rate is computed by averaging the velocity generated by the force along the paths followed by the substrates. The results obtained are in accordance with the experiments. The model provides an overall framework for analyzing the membrane transport proteins that regulate the flows of ions, nutrients and other molecules across the cell membranes, and their activities.

Trapping of particles diffusing in two dimensions by a hidden binding site

We study trapping of particles diffusing in a two-dimensional rectangular chamber by a binding site located at the end of a rectangular sleeve. To reach the site a particle first has to enter the sleeve. After that it has two options: to come back to the chamber or to diffuse to the site where it is trapped. The main result of the present work is a simple expression for the mean particle lifetime as a function of its starting position and geometric parameters of the system. This expression is obtained by an approximate reduction of the initial two-dimensional problem to the effective one-dimensional one which can be solved with relative ease. Our analytical predictions are tested against the results obtained from Brownian dynamics simulations. The test shows excellent agreement between the two for a wide range of the geometric parameters of the system.

Preferred penetration of active nano-rods into narrow channels and their clustering

In a channel connected to a reservoir, passive particles prefer staying in the reservoir than the channel due to the entropic effect, as the size of the particles is comparable to that of the channel. Self-propelled rods can exhibit out-of-equilibrium phenomena, and their partition behavior may differ from that of passive rods due to their persistent swimming ability. In this work, the distribution of active nano-rods between the nanoscale channel and reservoir is explored using dissipative particle dynamics. The ratio of the nano-rod concentration in the slit to that in the reservoir, defined as the partition ratio Ψ, is a function of active force, channel width, and rod length. Although passive nano-rods prefer staying in bulk (Ψ < 1), active rods can overcome the entropic barrier and show favorable partition toward narrow channels (Ψ > 1). As the slit width decreases to about the rod's width, active rods entering the slit behave like a quasi-two-dimensional system dynamically. At sufficiently high concentrations and Peclet numbers, nano-rods tend to align and move together in the same direction for a certain time. The distribution (PM) of the cluster size (M) follows a power law, PM ∝ M-2, for small clusters.

Colloid particles in microfluidic inertial hydrodynamic ratchet at moderate Reynolds number

The movement of spherical Brownian particle carried by an alternating fluid flow in a tube of periodically variable diameter is investigated. On the basis of our previous results [Phys. Rev. E 99, 012604 (2019)10.1103/PhysRevE.99.012604] on the hydrodynamics of the problem, we look at the competition of hydrodynamics and diffusion. We use the method of Fick-Jacobs mapping on an effective one-dimensional problem. We calculate the ratchet current and show that is is strictly related to finite size of the particles. The ratchet current grows quadratically with particle radius. We also show that the dominant contribution to the ratchet current is due to inertial hydrodynamic effects. This means that Reynolds number must be at least of order one. We discuss the possible use for separation of particles by size and perspectives of optimization of the tube shape.