Optical tweezers as a mathematically driven spatio-temporal potential generator.

The ability to create and manipulate spatio-temporal potentials is essential in the diverse fields of science and technology. Here, we introduce an optical feedback trap system based on high precision position detection and ultrafast feedback control of a Brownian particle in the optical tweezers to generate spatio-temporal virtual potentials of the desired shape in a controlled manner. As an application, we study the nonequilibrium fluctuation dynamics of the particle in a time-varying virtual harmonic potential and validate the Crooks fluctuation theorem in the highly nonequilibrium condition.

The structural kinetics of switch-1 and the neck linker explain the functions of kinesin-1 and Eg5.

Kinesins perform mechanical work to power a variety of cellular functions, from mitosis to organelle transport. Distinct functions shape distinct enzymologies, and this is illustrated by comparing kinesin-1, a highly processive transport motor that can work alone, to Eg5, a minimally processive mitotic motor that works in large ensembles. Although crystallographic models for both motors reveal similar structures for the domains involved in mechanochemical transduction--including switch-1 and the neck linker--how movement of these two domains is coordinated through the ATPase cycle remains unknown. We have addressed this issue by using a novel combination of transient kinetics and time-resolved fluorescence, which we refer to as "structural kinetics," to map the timing of structural changes in the switch-1 loop and neck linker. We find that differences between the structural kinetics of Eg5 and kinesin-1 yield insights into how these two motors adapt their enzymologies for their distinct functions.

Microtubule C-Terminal Tails Can Change Characteristics of Motor Force Production.

Control of intracellular transport is poorly understood, and functional ramifications of tubulin isoform differences between cell types are mostly unexplored. Motors' force production and detachment kinetics are critical for their group function, but how microtubule (MT) details affect these properties--if at all--is unknown. We investigated these questions using both a vesicular transport human kinesin, kinesin-1, and also a mitotic kinesin likely optimized for group function, kinesin-5, moving along either bovine brain or MCF7(breast cancer) MTs. We found that kinesin-1 functioned similarly on the two sets of MTs--in particular, its mean force production was approximately the same, though due to its previously reported decreased processivity, the mean duration of kinesin-1 force production was slightly decreased on MCF7 MTs. In contrast, kinesin-5's function changed dramatically on MCF7 MTs: its average detachment force was reduced and its force-velocity curve was different. In spite of the reduced detachment force, the force-velocity alteration surprisingly improved high-load group function for kinesin-5 on the cancer-cell MTs, potentially contributing to functions such as spindle-mediated chromosome separation. Significant differences were previously reported for C-terminal tubulin tails in MCF7 versus bovine brain tubulin. Consistent with this difference being functionally important, elimination of the tails made transport along the two sets of MTs similar.

Comprehensive structural model of the mechanochemical cycle of a mitotic motor highlights molecular adaptations in the kinesin family.

Kinesins are responsible for a wide variety of microtubule-based, ATP-dependent functions. Their motor domain drives these activities, but the molecular adaptations that specify these diverse and essential cellular activities are poorly understood. It has been assumed that the first identified kinesin--the transport motor kinesin-1--is the mechanistic paradigm for the entire superfamily, but accumulating evidence suggests otherwise. To address the deficits in our understanding of the molecular basis of functional divergence within the kinesin superfamily, we studied kinesin-5s, which are essential mitotic motors whose inhibition blocks cell division. Using cryo-electron microscopy and determination of structure at subnanometer resolution, we have visualized conformations of microtubule-bound human kinesin-5 motor domain at successive steps in its ATPase cycle. After ATP hydrolysis, nucleotide-dependent conformational changes in the active site are allosterically propagated into rotations of the motor domain and uncurling of the drug-binding loop L5. In addition, the mechanical neck-linker element that is crucial for motor stepping undergoes discrete, ordered displacements. We also observed large reorientations of the motor N terminus that indicate its importance for kinesin-5 function through control of neck-linker conformation. A kinesin-5 mutant lacking this N terminus is enzymatically active, and ATP-dependent neck-linker movement and motility are defective, although not ablated. All these aspects of kinesin-5 mechanochemistry are distinct from kinesin-1. Our findings directly demonstrate the regulatory role of the kinesin-5 N terminus in collaboration with the motor's structured neck-linker and highlight the multiple adaptations within kinesin motor domains that tune their mechanochemistries according to distinct functional requirements.

CK2 activates kinesin via induction of a conformational change.

Kinesin is the canonical plus-end microtubule motor and has been the focus of intense study since its discovery in 1985. We previously demonstrated a time-dependent inactivation of kinesin in vitro that was fully reversible by the addition of purified casein kinase 2 (CK2) and showed that this inactivation/reactivation pathway was relevant in cells. Here we show that kinesin inactivation results from a conformational change that causes the neck linker to be positioned closer to the motor domain. Furthermore, we show that treatment of kinesin with CK2 prevents and reverses this repositioning. Finally, we demonstrate that CK2 treatment facilitates ADP dissociation from the motor, resulting in a nucleotide-free state that promotes microtubule binding. Thus, we propose that kinesin inactivation results from neck-linker repositioning and that CK2-mediated reactivation results from CK2's dual ability to reverse this repositioning and to promote ADP release.

Distinctions between dynamic characteristics of the single EG5 motor protein along neural vs. cancerous microtubules.

The kinesin 5 motor contributes critically to mitosis, and is often upregulated in cancer. In vitro motility studies of kinesin 5 moving along bovine brain microtubules indicate that the motors have limited processivity. Cancer cells have abnormal mitotic behavior, so one might wonder whether the functional properties of kinesin 5 change in such a background. Because there could be multiple unknown changes in cancerous vs normal cells, we chose to address this question in a controlled in vitro environment. Specifically, through a series of parallel experiments along bovine brain vs. breast cancer microtubules, we quantified the in vitro motility characteristics of single Eg5 molecular motors along these two types of microtubules, combining the utilization of an optical trapping technique with a study of motion in the unloaded regime. The obtained values indicate that Eg5 processivity is 40% less along MCF7 microtubules, compared to that measured on bovine brain MTs. Interestingly, not all single-molecule properties are altered, as the velocity of the single motor doesn't show any significant changes on either track, though the binding time along MCF7 microtubules is almost 25% shorter. The current results, in conjunction with our previously reported outcomes of the evaluation of the Eg5's characteristics under external load, show that in transition from no-load to high-load regime, the Eg5 binding time has less sensitivity on MCF7 as compared to bovine brain MTs. This finding is intriguing, as it suggests that, potentially, groups of Eg5 motors function more effectively in the cancer background of a large ensemble, possibly contributing to faster mitosis in cancer cells.

Differential protein partitioning within the herpesvirus tegument and envelope underlies a complex and variable virion architecture.

The herpesvirus virion is a multilayered structure consisting of a DNA-filled capsid, tegument, and envelope. Detailed reconstructions of the capsid are possible based on its icosahedral symmetry, but the surrounding tegument and envelope layers lack regular architecture. To circumvent limitations of symmetry-based ultrastructural reconstruction methods, a fluorescence approach was developed using single-particle imaging combined with displacement measurements at nanoscale resolution. An analysis of 11 tegument and envelope proteins defined the composition and plasticity of symmetric and asymmetric elements of the virion architecture. The resulting virion protein map ascribes molecular composition to density profiles previously acquired by traditional ultrastructural methods, and provides a way forward to examine the dynamics of the virion architecture during infection.

Calibration of optical tweezers for in vivo force measurements: how do different approaches compare?

There is significant interest in quantifying force production inside cells, but since conditions in vivo are less well controlled than those in vitro, in vivo measurements are challenging. In particular, the in vivo environment may vary locally as far as its optical properties, and the organelles manipulated by the optical trap frequently vary in size and shape. Several methods have been proposed to overcome these difficulties. We evaluate the relative merits of these methods and directly compare two of them, a refractive index matching method, and a light-momentum-change method. Since in vivo forces are frequently relatively high (e.g., can exceed 15 pN for lipid droplets), a high-power laser is employed. We discover that this high-powered trap induces local temperature changes, and we develop an approach to compensate for uncertainties in the magnitude of applied force due to such temperature variations.

Kinesin-1 translocation: Surprising differences between bovine brain and MCF7-derived microtubules.

While there have been many single-molecule studies of kinesin-1, most have been done along microtubules purified from bovine or porcine brain, and relatively little is known about how variations in tubulin might alter motor function. Of particular interest is transport along microtubules polymerized from tubulin purified from MCF7 breast cancer cells, both because these cells are a heavily studied model system to help understand breast cancer, and also because the microtubules are already established to have interesting polymerization/stability differences from bovine tubulin, suggesting that perhaps transport along them is also different. Thus, we carried out paired experiments to allow direct comparison of in vitro kinesin-1 translocation along microtubules polymerized from either human breast cancer cells (MCF7) or microtubules from bovine brain. We found surprising differences: on MCF7 microtubules, kinesin-1's processivity is significantly reduced, although its velocity is only slightly altered.

High-precision test of Landauer's principle in a feedback trap.

We confirm Landauer's 1961 hypothesis that reducing the number of possible macroscopic states in a system by a factor of 2 requires work of at least kTln2. Our experiment uses a colloidal particle in a time-dependent, virtual potential created by a feedback trap to implement Landauer's erasure operation. In a control experiment, similar manipulations that do not reduce the number of system states can be done reversibly. Erasing information thus requires work. In individual cycles, the work to erase can be below the Landauer limit, consistent with the Jarzynski equality.

Gambling demon and stopping-time fluctuation relation of a Brownian particle under a time-dependent trapping potential.

A gambling demon is an external agent that can terminate a time-dependent driving protocol when a certain observable of the system exceeds a prescribed threshold. The gambling demon is examined in detail both theoretically and experimentally in a Brownian particle system under a compressing potential trap. Insight for choosing an appropriate work threshold for stopping is discussed. The energetics and the distributions of the stopping positions and stopping times are measured in simulations to gain further understanding of the process. Furthermore, the nonstationary and far-from-equilibrium stochastic process in the action of the gambling demon allows us to examine in detail some fundamental issues in stochastic thermodynamics, such as irreversibility and stopping-time fluctuation relation. Paradoxical violation of the stopping-time fluctuation relation can be reconciled in terms of the entropy production associated with fast hidden internal degrees of freedom. All the simulation or theoretical results are confirmed experimentally.

Stochastic currents and efficiency in an autonomous heat engine.

We experimentally demonstrate that a Brownian gyrator of a colloidal particle confined in a two-dimensional harmonic potential with different effective temperatures on orthogonal axes can work as an autonomous heat engine capable of extracting work from the heat bath, generated by an optical feedback trap. The results confirm the theoretically predicted thermodynamic currents and validate the attainability of Carnot efficiency as well as the trade-off relation between power and efficiency. We further show that current fluctuations and the entropy production rate are time independent in the steady state and their product near the Carnot efficiency is close to the lower bound of the thermodynamic uncertainty relation.

Generation of virtual potentials by controlled feedback in electric circuit systems.

Electric circuits influenced by thermal noise are analogous to confined Brownian particles and can be an alternative and convenient scheme for studying stochastic thermodynamics. Here we experimentally demonstrate an effective technique of generating tunable potentials for Brownian dynamics in an electric circuit, realized by external controlled feedback. We present two illustrative examples of one-dimensional virtual potentials: static harmonic potential and time-varying double-well potential. The thermal noises of both cases undergo equivalent Brownian dynamics as if they were in the authentic potentials as long as the feedback is fast enough to respond to the designed potentials. The results show that the electric circuit provides a simple, effective, and programmable scheme to study the feedback-controlled virtual potential.

Shift a laser beam back and forth to exchange heat and work in thermodynamics.

Although the equivalence of heat and work has been unveiled since Joule's ingenious experiment in 1845, they rarely originate from the same source in experiments. In this study, we theoretically and experimentally demonstrated how to use a high-precision optical feedback trap to combine the generation of virtual temperature and potential to simultaneously manipulate the heat and work of a small system. This idea was applied to a microscopic Stirling engine consisting of a Brownian particle under a time-varying confining potential and temperature. The experimental results justified the position and the velocity equipartition theorem, confirmed several theoretically predicted energetics, and revealed the engine efficiency as well as its trade-off relation with the output power. The small theory-experiment discrepancy and high flexibility of the swift change of the particle condition highlight the advantage of this optical technique and prove it to be an efficient way for exploring heat and work-related issues in the modern thermodynamics for small systems.

Invariance of Initiation Mass and Predictability of Cell Size in Escherichia coli.

It is generally assumed that the allocation and synthesis of total cellular resources in microorganisms are uniquely determined by the growth conditions. Adaptation to a new physiological state leads to a change in cell size via reallocation of cellular resources. However, it has not been understood how cell size is coordinated with biosynthesis and robustly adapts to physiological states. We show that cell size in Escherichia coli can be predicted for any steady-state condition by projecting all biosynthesis into three measurable variables representing replication initiation, replication-division cycle, and the global biosynthesis rate. These variables can be decoupled by selectively controlling their respective core biosynthesis using CRISPR interference and antibiotics, verifying our predictions that different physiological states can result in the same cell size. We performed extensive growth inhibition experiments, and we discovered that cell size at replication initiation per origin, namely the initiation mass or unit cell, is remarkably invariant under perturbations targeting transcription, translation, ribosome content, replication kinetics, fatty acid and cell wall synthesis, cell division, and cell shape. Based on this invariance and balanced resource allocation, we explain why the total cell size is the sum of all unit cells. These results provide an overarching framework with quantitative predictive power over cell size in bacteria.

tCRISPRi: tunable and reversible, one-step control of gene expression.

The ability to control the level of gene expression is a major quest in biology. A widely used approach employs deletion of a nonessential gene of interest (knockout), or multi-step recombineering to move a gene of interest under a repressible promoter (knockdown). However, these genetic methods are laborious, and limited for quantitative study. Here, we report a tunable CRISPR-cas system, "tCRISPRi", for precise and continuous titration of gene expression by more than 30-fold. Our tCRISPRi system employs various previous advancements into a single strain: (1) We constructed a new strain containing a tunable arabinose operon promoter PBAD to quantitatively control the expression of CRISPR-(d)Cas protein over two orders of magnitude in a plasmid-free system. (2) tCRISPRi is reversible, and gene expression is repressed under knockdown conditions. (3) tCRISPRi shows significantly less than 10% leaky expression. (4) Most important from a practical perspective, construction of tCRISPRi to target a new gene requires only one-step of oligo recombineering. Our results show that tCRISPRi, in combination with recombineering, provides a simple and easy-to-implement tool for gene expression control, and is ideally suited for construction of both individual strains and high-throughput tunable knockdown libraries.

Large-scale intermittency in two-dimensional driven turbulence.

It is generally believed that two-dimensional turbulence is immune to intermittency possibly due to the absence of vortex stretching. However, in turbulence created in a freely suspended soap film by electromagnetic forcing, it is found that intermittency is not insignificant. We draw this conclusion based on the measured velocity structure function Sp(l) (identical to ) proportional to l(zeta(p)) on scales l greater than the energy injection scale l(inj) . The scaling exponent zeta(p) vs p deviates from the expected linear relation and shows intermittent behavior comparable to that observed in fully developed three-dimensional turbulence in wind tunnels. Our measurements demonstrate that intermittency can be accounted for by the nonuniform distribution of saddle points in the flow.

Real-time calibration of a feedback trap.

Feedback traps use closed-loop control to trap or manipulate small particles and molecules in solution. They have been applied to the measurement of physical and chemical properties of particles and to explore fundamental questions in the non-equilibrium statistical mechanics of small systems. These applications have been hampered by drifts in the electric forces used to manipulate the particles. Although the drifts are small for measurements on the order of seconds, they dominate on time scales of minutes or slower. Here, we show that a recursive maximum likelihood (RML) algorithm can allow real-time measurement and control of electric and stochastic forces over time scales of hours. Simulations show that the RML algorithm recovers known parameters accurately. Experimental estimates of diffusion coefficients are also consistent with expected physical properties.

Virtual potentials for feedback traps.

The recently developed feedback trap can be used to create arbitrary virtual potentials, to explore the dynamics of small particles or large molecules in complex situations. Experimentally, feedback traps introduce several finite time scales: There is a delay between the measurement of a particle's position and the feedback response, the feedback response is applied for a finite update time, and a finite camera exposure integrates motion. We show how to incorporate such timing effects into the description of particle motion. For the test case of a virtual quadratic potential, we give the first accurate description of particle dynamics, calculating the power spectrum and variance of fluctuations as a function of feedback gain, testing against simulations. We show that for small feedback gains, the motion approximates that of a particle in an ordinary harmonic potential. Moreover, if the potential is varied in time, for example by varying its stiffness, the work that is calculated approximates that done in an ordinary changing potential. The quality of the approximation is set by the ratio of the update time of the feedback loop to the relaxation time of motion in the virtual potential.

Elastic turbulence in a curvilinear channel flow.

We report detailed quantitative studies of elastic turbulence in a curvilinear channel flow in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent. Detailed studies of the average and rms velocity and velocity gradients profiles reveal the emergence of a boundary layer associated with the nonuniform distribution of the elastic stresses across the channel. The characteristic boundary width is independent of the Weissenberg number Wi and proportional to the channel width, which is consistent with the findings our early investigations of the boundary layer in elastic turbulence in different flow geometries. The nonuniform distribution of the elastic stresses across the channel and appearance of the characteristic spatial scales of the order of the boundary layer width of both velocity and velocity gradient in the correlation functions of the velocity and velocity gradient fields in a bulk flow may suggest that excessive elastic stresses, concentrated in the boundary layer, are ejected into the bulk flow similar to jets observed in passive scalar mixing in elastic turbulence observed recently. Finally, the experimental results show that one of the main predictions of the theory of elastic turbulence, namely, the saturation of the normalized rms velocity gradient in the bulk flow of elastic turbulence contradicts the experimental observations both qualitatively and quantitatively in spite of the fact that the theory explains well the observed sharp power-law decay of the velocity power spectrum. The experimental findings call for further development of theory of elastic turbulence in a bounded container, similar to what was done for a passive scalar problem.