Substrate stiffness tunes the dynamics of polyvalent rolling motors.

Nature has evolved many mechanisms for achieving directed motion on the subcellular level. The burnt-bridges ratchet (BBR) is one mechanism used to achieve superdiffusive molecular motion over long distances through the successive cleavage of surface-bound energy-rich substrate sites. This mechanism has been associated with both nanoscale and microscale movement, with the latter accomplished through polyvalent interactions between a large hub (e.g. influenza virus) and substrate (e.g. cell surface receptors). Experimental successes in achieving superdiffusive motion by synthetic polyvalent BBRs have raised questions about the dynamics of their motility, including whether rolling or translation is better able to direct motion of microscale spherical hubs. Here we simulate the three-dimensional dynamics of a polyvalent sphere moving on and cleaving an elastic substrate. We find that substrate stiffness plays an important role in controlling both the motor's mode of motility and its directional persistence. As we tune lateral substrate stiffness from soft to stiff we find there exists an intermediate value that optimizes rolling behaviour. We also find that there is an optimal substrate stiffness for maximizing persistence length, while stiffness does not influence as strongly the superdiffusive dynamics of the particle. Lastly, we examine the effect of substrate density, and show that softer landscapes are better able to buffer against decreases in substrate occupancy, with the spherical motor maintaining superdiffusive motion more on softer landscapes than on stiff landscapes as occupancy drops. Our results highlight the importance of surface in controlling the motion of polyvalent BBRs.

The Phase Behavior and Organization of Sphingomyelin/Cholesterol Membranes: A Deuterium NMR Study.

We have studied the dependence of the phase and domain characteristics of sphingomyelin (SM)/cholesterol model membranes on sterol content and temperature using deuterium nuclear magnetic resonance. NMR spectra of N-palmitoyl(D31)-D-erythro-sphingosylphosphorylcholine (PSM-d31) were taken for temperatures from 25 to 70°C and cholesterol concentrations of 0-40%. Analogous experiments were performed using 1-palmitoyl,2-palmitoyl(D31)-sn-glycero-3-phosphocholine (DPPC-d31)/cholesterol membranes to carefully compare the data obtained using palmitoyl chains that have similar "kinked" conformations. The constructed phase diagrams exhibit both solid-ordered (so) + liquid-ordered (lo) and liquid-disordered (ld) + lo phase-coexistence regions with a clear three-phase line. Macroscopic (micron-sized) coexistence of ld and lo phases was not observed; instead, line-broadening in the ld+lo region was characterized by intermediate exchange of lipids between the two types of domains. The length scales associated with the domains were estimated to be 75-150 nm for PSM-d31/cholesterol and DPPC-d31/cholesterol model membranes.

Effect of Sterol Structure on the Physical Properties of 1-Palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine Membranes Determined Using (2)H Nuclear Magnetic Resonance.

The effect of a series of phytosterols on lipid chain ordering in 1-palmitoyl((2)H31)-2-oleoyl-sn-glycero-3-phosphocholine (POPC-d31) multibilayer vesicles was examined by (2)H NMR spectroscopy at 25 °C. These results, along with existing data for other sterols, indicate that the ordering power of sterols in POPC-d31 depends on subtle aspects of sterol structure. Cholesterol, 7-dehydrocholesterol (7-DHC), campesterol, ß-sitosterol, ergosterol, brassicasterol, and stigmasterol all increase the lipid chain order as sterol concentration is increased. However, saturation of the ordering occurs at different sterol concentrations for ergosterol (as previously reported), brassicasterol, ß-sitosterol, and stigmasterol. Here our interest lies in finding which part of the sterol structure is responsible for the observed saturation of the palmitoyl chain order as a function of sterol concentration. In particular, we propose that the saturation of the ordering of POPC-d31/brassicasterol and POPC-d31/stigmasterol membranes at quite low sterol concentrations is due to the presence of a double bond at C22. We also discuss how the structural differences between the sterols affect their ability to intercalate between the POPC acyl chains. Furthermore, the effective solubility of sterols in POPC is discussed in relation to the dependence of maximum POPC-d31 chain order vs sterol concentration.

Design and construction of the lawnmower, an artificial burnt-bridges motor.

Molecular motors of the cell are protein-based, nanoscale machines, which use a variety of strategies to transduce chemical energy into mechanical work in the presence of a large thermal background. The design and construction of artificial molecular motors is one approach to better understand their basic physical principles. Here, we propose the concept of a protein-based, burnt-bridges ratchet, inspired by biological examples. Our concept, the lawnmower, utilizes protease blades to cleave peptide substrates, and uses the asymmetric substrate-product interface arising from productive cleavage to bias subsequent diffusion on the track (lawn). Following experimental screening to select a protease to act as the motor's blades, we chemically couple trypsin to quantum dots and demonstrate activity of the resulting lawnmower construct in solution. Accompanying Brownian dynamics simulations illustrate the importance for processivity of correct protease density on the quantum dot and spacing of substrates on the track. These results lay the groundwork for future tests of the protein-based lawnmower's motor performance characteristics.

Fluidic switching in nanochannels for the control of Inchworm: a synthetic biomolecular motor with a power stroke.

Synthetic molecular motors typically take nanometer-scale steps through rectification of thermal motion. Here we propose Inchworm, a DNA-based motor that employs a pronounced power stroke to take micrometer-scale steps on a time scale of seconds, and we design, fabricate, and analyze the nanofluidic device needed to operate the motor. Inchworm is a kbp-long, double-stranded DNA confined inside a nanochannel in a stretched configuration. Motor stepping is achieved through externally controlled changes in salt concentration (changing the DNA's extension), coordinated with ligand-gated binding of the DNA's ends to the functionalized nanochannel surface. Brownian dynamics simulations predict that Inchworm's stall force is determined by its entropic spring constant and is ∼ 0.1 pN. Operation of the motor requires periodic cycling of four different buffers surrounding the DNA inside a nanochannel, while keeping constant the hydrodynamic load force on the DNA. We present a two-layer fluidic device incorporating 100 nm-radius nanochannels that are connected through a few-nm-wide slit to a microfluidic system used for in situ buffer exchanges, either diffusionally (zero flow) or with controlled hydrodynamic flow. Combining experiment with finite-element modeling, we demonstrate the device's key performance features and experimentally establish achievable Inchworm stepping times of the order of seconds or faster.

Time-dependent motor properties of multipedal molecular spiders.

Molecular spiders are synthetic biomolecular walkers that use the asymmetry resulting from cleavage of their tracks to bias the direction of their stepping motion. Using Monte Carlo simulations that implement the Gillespie algorithm, we investigate the dependence of the biased motion of molecular spiders, along with binding time and processivity, on tunable experimental parameters, such as number of legs, span between the legs, and unbinding rate of a leg from a substrate site. We find that an increase in the number of legs increases the spiders' processivity and binding time but not their mean velocity. However, we can increase the mean velocity of spiders with simultaneous tuning of the span and the unbinding rate of a spider leg from a substrate site. To study the efficiency of molecular spiders, we introduce a time-dependent expression for the thermodynamic efficiency of a molecular motor, allowing us to account for the behavior of spider populations as a function of time. Based on this definition, we find that spiders exhibit transient motor function over time scales of many hours and have a maximum efficiency on the order of 1%, weak compared to other types of molecular motors.

Tuning the performance of an artificial protein motor.

The Tumbleweed (TW) is a concept for an artificial, tri-pedal, protein-based motor designed to move unidirectionally along a linear track by a diffusive tumbling motion. Artificial motors offer the unique opportunity to explore how motor performance depends on design details in a way that is open to experimental investigation. Prior studies have shown that TW's ability to complete many successive steps can be critically dependent on the motor's diffusional step time. Here, we present a simulation study targeted at determining how to minimize the diffusional step time of the TW motor as a function of two particular design choices: nonspecific motor-track interactions and molecular flexibility. We determine an optimal nonspecific interaction strength and establish a set of criteria for optimal molecular flexibility as a function of the nonspecific interaction. We discuss our results in the context of similarities to biological, linear stepping diffusive molecular motors with the aim of identifying general engineering principles for protein motors.

Biased motion and molecular motor properties of bipedal spiders.

Molecular spiders are synthetic molecular motors featuring multiple legs that each can interact with a substrate through binding and cleavage. Experimental studies suggest the motion of the spider in a matrix is biased toward uncleaved substrates and that spider properties such as processivity can be altered by changing the binding strength of the legs to substrate [R. Pei, S. K. Taylor, D. Stefanovic, S. Rudchenko, T. E. Mitchell, and M. N. Stojanovic, J. Am. Chem. Soc. 128, 12693 (2006)]. We investigate the origin of biased motion and molecular motor properties of bipedal spiders using Monte Carlo simulations. Our simulations combine a realistic chemical kinetic model, hand-over-hand or inchworm modes of stepping, and the use of a one-dimensional track. We find that stronger binding to substrate, cleavage and spider detachment from the track are contributing mechanisms to population bias. We investigate the contributions of stepping mechanism to speed, randomness parameter, processivity, coupling, and efficiency, and comment on how these molecular motor properties can be altered by changing experimentally tunable kinetic parameters.

Dynamics of a polymer in a Brownian ratchet.

We have used Brownian dynamics simulations to study the dynamics of a bead-and-spring polymer subject to a flashing ratchet potential. To elucidate the role of hydrodynamic (HD) interactions, simulations were carried out for the cases where HD interactions are present and when they are absent. The average speed of the polymer and its conformational properties were examined upon variation in the polymer length, N, and the ratchet spatial period, L. Two distinct dynamical regimes were evident. In the low-N/high-L regime, the velocity decreases with increasing N, and center-of-mass diffusion is a key part of the motional mechanism. By contrast, in the high-N /low-L regime, the velocity is insensitive to variation in N, and motion is achieved via the coupling of internal modes to the cycling of the ratchet potential. The location of the regimes is correlated with the average conformational state of the polymer. Incorporating HD interactions increases the average polymer velocity for all polymer lengths and ratchet spatial periods considered. The dynamical behavior of polymers in the low-N/high-L regime can be understood using simple a theoretical model that yields quantitatively reasonable predictions of the polymer velocity.

The Tumbleweed: towards a synthetic proteinmotor.

Biomolecular motors have inspired the design and construction of artificial nanoscale motors and machines based on nucleic acids, small molecules, and inorganic nanostructures. However, the high degree of sophistication and efficiency of biomolecular motors, as well as their specific biological function, derives from the complexity afforded by protein building blocks. Here, we discuss a novel bottom-up approach to understanding biological motors by considering the construction of synthetic protein motors. Specifically, we present a design for a synthetic protein motor that moves along a linear track, dubbed the "Tumbleweed." This concept uses three discrete ligand-dependent DNA-binding domains to perform cyclically ligand-gated, rectified diffusion along a synthesized DNA molecule. Here we describe how de novo peptide design and molecular biology could be used to produce the Tumbleweed, and we explore the fundamental motor operation of such a design using numerical simulations. The construction of this and more sophisticated protein motors is an exciting challenge that is likely to enhance our understanding of the structure-function relationship in biological motors.

Pore formation in a lipid bilayer under a tension ramp: modeling the distribution of rupture tensions.

The rupture of fluid membrane vesicles with a steady ramp of micropipette suction has been shown to produce a distribution of breakage tensions, with a mean that rises rapidly with tension rate. Starting from a lattice model that incorporates the essential features of the lipid bilayers held together with hydrophobic forces, and developing it to handle varying tension rates, we reproduce the main features of the experimental results. In essence, we show that the rupture kinetics are driven by the nucleation and growth of pores, with two limiting kinetics-growth-limited and nucleation-limited. The model has been extended to address the role of peptides in solution that can adsorb and insert themselves into the bilayer. At concentrations below those required to spontaneously rupture the membrane, the effect of the peptides is to lower the rupture tensions systematically for all tension rates.

Mechanical coupling in flashing ratchets.

We consider the transport of rigid objects with internal structure in a flashing ratchet potential by investigating the overdamped behavior of a rodlike chain of evenly spaced point particles. In one dimension, analytical arguments show that the velocity can reverse direction multiple times in response to changing the size of the chain or the temperature of the heat bath. The physical reason is that the effective potential experienced by the mechanically coupled objects can have a different symmetry than that of individual objects. All analytical predictions are confirmed by Brownian dynamics simulations. These results may provide a route to simple, coarse-grained models of molecular motor transport that incorporate an object's size and rotational degrees of freedom into the mechanism of transport.

Single-polymer Brownian motor: a simulation study.

Numerical simulation is used to study a single polymer chain in a flashing ratchet potential to determine how the mechanism of this Brownian motor system is affected by the presence of internal degrees of freedom. The polymer is modeled by a freely jointed chain with N monomers in which the monomers interact via a repulsive Lennard-Jones potential and neighboring monomers on the chain are connected by finite extensible nonlinear elastic bonds. Each monomer is acted upon by a 1D asymmetric, piecewise linear potential of spatial period L comparable to the radius of gyration of the polymer. This potential is also characterized by a localization time, t(on), and by a free diffusion time, t(off). We characterize the average motor velocity as a function of L, t(off), and N to determine optimal parameter ranges, and we evaluate motor performance in terms of finite dispersion, Peclet number, rectification efficiency, stall force, and transportation of a load against a viscous drag. We find that the polymer motor performs qualitatively better than a single particle in a flashing ratchet: with increasing N, the polymer loses velocity much more slowly than expected in the absence of internal degrees of freedom, and the motor stall force increases linearly with N. To understand these cooperative aspects of motor operation, we analyze relevant Rouse modes. The experimental feasibility is analyzed and the parameters of the model are scaled to those of lambda-DNA. Finally, in the context of experimental realization, we present initial modeling results for a 2D flashing ratchet constructed using an electrode array, and find good agreement with the results of 1D simulations although the polymer in the 2D potential sometimes briefly "detaches" from the electrode surface.

Performance characteristics of Brownian motors.

Brownian motors are nonequilibrium systems that rectify thermal fluctuations to achieve directed motion, using spatial or temporal asymmetry. We provide a tutorial introduction to this basic concept using the well-known example of a flashing ratchet, discussing the micro- to nanoscopic scale on which such motors can operate. Because of the crucial role of thermal noise, the characterization of the performance of Brownian motors must include their fluctuations, and we review suitable performance measures for motor coherency and efficiency. Specifically, we highlight that it is possible to determine the energy efficiency of Brownian motors by measuring their velocity fluctuations, without detailed knowledge of the motor function and its energy input. Finally, we exemplify these concepts using a model for an artificial single-molecule motor with internal degrees of freedom.

What's so special about cholesterol?

Cholesterol (or other higher sterols such as ergosterol and phytosterols) is universally present in large amounts (20-40 mol%) in eukaryotic plasma membranes, whereas it is universally absent in the membranes of prokaryotes. Cholesterol has a unique ability to increase lipid order in fluid membranes while maintaining fluidity and diffusion rates. Cholesterol imparts low permeability barriers to lipid membranes and provides for large mechanical coherence. A short topical review is given of these special properties of cholesterol in relation to the structure of membranes, with results drawn from a variety of theoretical and experimental studies. Particular focus is put on cholesterol's ability to promote a special membrane phase, the liquid-ordered phase, which is unique for cholesterol (and other higher sterols like ergosterol) and absent in membranes containing the cholesterol precursor lanosterol. Cholesterol's role in the formation of special membrane domains and so-called rafts is discussed.

From lanosterol to cholesterol: structural evolution and differential effects on lipid bilayers.

Cholesterol is an important molecular component of the plasma membranes of mammalian cells. Its precursor in the sterol biosynthetic pathway, lanosterol, has been argued by Konrad Bloch (Bloch, K. 1965. Science. 150:19-28; 1983. CRC Crit. Rev. Biochem. 14:47-92; 1994. Blonds in Venetian Paintings, the Nine-Banded Armadillo, and Other Essays in Biochemistry. Yale University Press, New Haven, CT.) to also be a precursor in the molecular evolution of cholesterol. We present a comparative study of the effects of cholesterol and lanosterol on molecular conformational order and phase equilibria of lipid-bilayer membranes. By using deuterium NMR spectroscopy on multilamellar lipid-sterol systems in combination with Monte Carlo simulations of microscopic models of lipid-sterol interactions, we demonstrate that the evolution in the molecular chemistry from lanosterol to cholesterol is manifested in the model lipid-sterol membranes by an increase in the ability of the sterols to promote and stabilize a particular membrane phase, the liquid-ordered phase, and to induce collective order in the acyl-chain conformations of lipid molecules. We also discuss the biological relevance of our results, in particular in the context of membrane domains and rafts.