Session N34: Focus Session: Brownian Motors in Physics, Chemistry, and Biology

Brownian Heat Engines -- from Leidenfrost Droplets to Nanowire Thermoelectrics

A Brownian heat engine is a system that rectifies the flow of Brownian particles to transform local temperature variations into directed motion (work). In the context of electronics, this is the principle of thermoelectric energy conversion. For a long time it was thought that Brownian heat engines (and thermoelectric devices) are inherently irreversible and would therefore necessarily fall short of the Carnot limit for the energy conversion efficiency. I will introduce the concept of a Brownian heat engine, and will discuss how quantum energy-filtering can in fact be used to design a Carnot efficient, Brownian heat engine [1]. I will then present two experimental systems. The first, heat-propelled Leidenfrost droplets [2], is not really `Brownian' but nevertheless a very entertaining and illustrative ratchet heat engine. The second is our experimental effort to demonstrate a near-Carnot efficient thermal-to-electric energy converter [3] based on a quantum dot embedded into a heterostructure nanowire [4]. The physics behind this novel thermoelectric system, and the status of experiments will be discussed. \newline \newline [1] T. E. Humphrey, R. Newbury, R. P. Taylor, H. Linke, \textit{Phys. Rev. Lett.} \textbf{89}, 116801 (2002). \newline [2] H. Linke\textit{ et al.}, \textit{Phys. Rev. Lett.} \textbf{96}, 154502 (2006). \newline [3] M. O'Dwyer, T. E. Humphrey, H. Linke, \textit{Nanotechnology} \textbf{17}, S338 (2006). \newline [4] M. T. Bj\"{o}rk\textit{ et al.}, \textit{Nano Letters} \textbf{2}, 87 (2002).   

Study of single flagellar propulsion with optical tweezers

Various theoretical models predict propulsion by the bacterial flagellum. Use of these models to calculate dynamical quantities of bacterial swimming are commonplace. However, direct verification of the various mathematical approaches has been difficult due to the lack of precise experimental data, which has been challenging to obtain. In this work we perform measurements on swimming bacterium which posses a single polar flagellum. Swimming with a single flagellum allows simpler parametrization as compared to a flagellar bundle. Bacteria are stably trapped in the bulk fluid (away from a surface) and perpendicular to the trapping axis with the aid of an imposed flow. This approach avoids hydrodynamic effects due to wall proximity, which were observed in previous measurements. The optical trap allows all dynamical quantities of a swimming bacterium to be determined. Flagellar dimensions are obtained by fluorescent imaging to obtain all pertinent information, required to put different theoretical models to test.   

The stochastic dynamics of filopodial growth

We build stochastic models for filopodial growth and retraction that combine mechanical and spatiotemporal signaling components to elucidate the mechanisms of filopodia dynamics. We explicitly model the tip signaling and diffusion process while the membrane and retrograde flow are modeled implicitly. The results are compared with experiments to verify the model effectivness.   

Swimming movements of filaments in a linearly viscoelastic medium

Motivated by the swimming of sperm in the non-Newtonian fluids of the female mammalian reproductive tract, we examine beating filaments in a linearly viscoelastic medium. The forces exerted by the medium are incorporated via a resistive force theory approriate for a Maxwell fluid, in which the force per unit length acting on a filament relaxes to the force per unit length exerted by a purely viscous fluid. We calculate the shapes of beating patterns of filaments with prescribed driving forces in two models: 1) an elastic passive filament forced from one end; 2) a simplified sliding-filament model for sperm flagellum with active internal sliding forces. We note that in a linearly viscoelastic model, for prescribed beating patterns, swimming velocity is the same in viscoelastic and viscous fluids, and there is a simple relation between the power dissipated in each fluid. In contrast, for prescribed driving forces, beating patterns may be different in viscoelastic and viscous fluids leading to changes in swimming velocities and power dissipated.   

Fusion versus endocytosis: the stochastic entry of enveloped viruses

Viral infection requires the binding of receptors on the target cell membrane to glycoproteins, or ``spikes,'' on the virus membrane. Fusion peptides that make up part of these spikes on the viral membrane may then be triggered by pH changes or binding of additional coreceptors. Thus, binding of virus envelope proteins to cell surface receptors not only initiates the viral adhesion and the wrapping process necessary for internalization, but also starts the direct fusion process. Both fusion and internalization may be viable pathways for some viruses, under appropriate conditions. We develop a stochastic model for viral entry that incorporates both receptor mediated fusion and endocytosis. The relative probabilities of fusion and endocytosis of a virus particle initially nonspecifically adsorbed on the host cell membrane are computed as functions of receptor concentration, binding strength, and number of spikes. We find the parameter regimes where each pathway is expected to arise and discuss possible experimental tuning of these parameters.   

Exact results for random deposition-driven ratcheting

We consider the discrete translocation of a polymer through a pore, across a wall, driven by the irreversible, random sequential adsorption of particles on one side of the pore. Although the kinetics of the wall motion and the deposition are coupled, we find the exact steady state distribution for the gap between the wall and the nearest deposited particle. From this exact result, the mean translocation velocity and variance are constructed. We explicitly show that translocation is faster and less variable when the adsorbing particles are smaller. The relative efficiencies of ratcheting using different sized deposition particles are also defined and compared.   

Molecular motors driven by asymmetric nucleation

We study a one dimensional model of asymmetric nucleation where the phase boundaries are coupled to a load particle. Sites on the one-dimensional lattice are either empty or filled. Empty sites get filled faster if the is a filled site immediately preceding it. This model has applicability to nucleation problems where the substrate is directional. Examples include nucleation of proteins on filamentary substrates such as nucleic acids and microtubules. The hydrolysis of ATP or GTP in microfilaments such as RecA has been proposed as a mechanism of moving Halliday junctions, and can also be described qualitatively by our model. Using Monte Carlo simulations, we find mean velocities and of a load particle as function of the nucleation rates and the asymmetry parameter. Our results are compared with simple mean field approximations.   

Free boundaries and confinement in driven diffusive systems

We study the dynamics of a load wall confining an asymmetric exclusion process with Langmuir kinetics. Results from Monte Carlo simulations and mean field approximations are compared. We find that the mean position of the wall depends not only on the load on the wall and the injection, adsorption, and desorption rates, but also on the intrinsic fluctuations of the wall. Our results are discussed in the context of nonequilirium phases of the system, fluctuating boundary layers, and particle densities in the lab frame versus the frame of the fluctuating wall.   

Slow axonal transport: Neurofilaments switch between distinct mobile and stationary states during their transport along axons

According to the stop-and-go hypothesis of slow axonal transport, cytoskeletal and cytosolic proteins are transported along axons at fast rates but the average velocity of movement is slow because the movements are infrequent and bidirectional. To test whether this hypothesis can explain the kinetics of slow axonal transport in vivo, we have developed a stochastic model of neurofilament (NF) transport in axons based on tracking of single NF molecules. Based on this model, we propose that NFs in vivo move in both, anterograde and retrograde directions along cytoskeletal tracks switching between mobile and a stationary states. To verify the proposed stationary state we have developed a novel pulse-escape fluorescence photoactivation technique. We find that on average, the NFs spent 92{\%} of their time in the stationary state and 97{\%} of their time pausing. We speculate that the relative proportion of the time that NFs spend in the stationary state may be a principal determinant of their transport rate and distribution along axons, and a potential target of mechanisms that lead to abnormal NF accumulations in disease.   

A Geometric Mechanism for Asymmetric Diffusion and Membrane Rectification

Biological membranes commonly conduct ions freely in one direction while clogging in the other. Existing theories emphasize electrostatic binding of blocking ions in pores as a mechanism for rectification. Here we show that rectification can have a purely geometric origin, based on the interaction of shapes of diffusing particles and pore geometry. The two possibilities can be experimentally distinguished. Blocker binding based on confinement in a potential well will have a strong Arrhenius temperature dependence, whereas ``geometric binding'' will have a much smaller dependence on temperature. We present both Hamiltonian and Brownian-based computer simulations which demonstrate this effect. A rectifying membrane can maintain different concentrations on either side, resulting in a long-lived metastable state. We derive a dynamic equation of state describing the decay of this metastable system.   

Untying molecular friction knots

Molecular knots tied in individual polymer strands have fascinated researchers from many fields. Recently, laser tweezers have been used to tie knots in individual DNA and protein molecules and to observe their dynamics. Unlike their macroscopic counterparts, knots in tensioned polymer strands undergo rapid diffusion caused by thermal fluctuations. Here, we use computer simulations to study the dynamics of a ``friction knot'' joining a pair of polymer strands. While a friction knot splicing two ropes is jammed when the ropes are pulled apart, molecular friction knots eventually become undone by thermal motion. We show that depending on the knot type and on the polymer structure, a friction knot between polymer strands can be strong (the time $\tau$ the knot stays tied increases with the force \textit{F} applied to separate the strands) or weak ($\tau$ decreases with increasing \textit{F}). We further propose a simple model explaining these behaviors.   

Exact Solutions of Burnt-Bridge Models for Molecular Motor Transport

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called ``bridges''), is investigated theoretically by analyzing discrete-state stochastic ``burnt-bridge'' models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (``burned'') with a probability $p$, creating a biased directed motion for the particle. It is shown that for probability of burning $p=1$ the system can be mapped into one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For general case of $p<1$ a new theoretical method is developed, and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics, periodic and random distribution of bridges and different burning dynamics are analyzed and compared. Theoretical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.   

Molecular Dynamics simulation of Buttiker-Landauer Refrigerator

A position dependent temperature profile in presence of a periodic potential leads to directed current of Brownian particles, commonly known as Buttiker-Landauer ratchet. Onsager symmetry tells us that inhomogeneous temperature profile can be generated by reversing the Buttiker-Landauer ratchet. When Brownian particles driven by a constant external force cross over the potential barrier, they carry heat from one side to the other. Hence, starting with uniform temperature the flow of Brownian particles induces inhomogeneous temperature profile. We investigate this phenomenon using first principles molecular dynamics simulations as well as the phenomenologial Langevin equation.