Michael Hinczewski

Extreme sensitivity biosensing platform based on hyperbolic metamaterials.

Optical sensor technology offers significant opportunities in the field of medical research and clinical diagnostics, particularly for the detection of small numbers of molecules in highly diluted solutions. Several methods have been developed for this purpose, including label-free plasmonic biosensors based on metamaterials. However, the detection of lower-molecular-weight (<500 Da) biomolecules in highly diluted solutions is still a challenging issue owing to their lower polarizability. In this context, we have developed a miniaturized plasmonic biosensor platform based on a hyperbolic metamaterial that can support highly confined bulk plasmon guided modes over a broad wavelength range from visible to near infrared. By exciting these modes using a grating-coupling technique, we achieved different extreme sensitivity modes with a maximum of 30,000 nm per refractive index unit (RIU) and a record figure of merit (FOM) of 590. We report the ability of the metamaterial platform to detect ultralow-molecular-weight (244 Da) biomolecules at picomolar concentrations using a standard affinity model streptavidin-biotin.

Inverted Berezinskii-Kosterlitz-Thouless singularity and high-temperature algebraic order in an ising model on a scale-free hierarchical-lattice small-world network

We have obtained exact results for the Ising model on a hierarchical lattice incorporating three key features characterizing many real-world networks--a scale-free degree distribution, a high clustering coefficient, and the small-world effect. By varying the probability p of long-range bonds, the entire spectrum from an unclustered, non-small-world network to a highly clustered, small-world system is studied. Using the self-similar structure of the network, we obtain analytic expressions for the degree distribution P(k) and clustering coefficient C for all p, as well as the average path length l for p = 0 and 1. The ferromagnetic Ising model on this network is studied through an exact renormalization-group transformation of the quenched bond probability distribution, using up to 562,500 renormalized probability bins to represent the distribution. For p < 0.494, we find power-law critical behavior of the magnetization and susceptibility, with critical exponents continuously varying with p, and exponential decay of correlations away from Tc. For p > or = 0.494, in fact where the network exhibits small-world character, the critical behavior radically changes: We find a highly unusual phase transition, namely an inverted Berezinskii-Kosterlitz-Thouless singularity, between a low-temperature phase with nonzero magnetization and finite correlation length and a high-temperature phase with zero magnetization and infinite correlation length, with power-law decay of correlations throughout the phase. Approaching Tc from below, the magnetization and the susceptibility, respectively, exhibit the singularities of exp(-C/square root of Tc - T) and exp(D/square root of Tc - T), with C and D positive constants. With long-range bond strengths decaying with distance, we see a phase transition with power-law critical singularities for all p, and evaluate an unusually narrow critical region and important corrections to power-law behavior that depend on the exponent characterizing the decay of long-range interactions.

From mechanical folding trajectories to intrinsic energy landscapes of biopolymers

In single-molecule laser optical tweezer (LOT) pulling experiments, a protein or RNA is juxtaposed between DNA handles that are attached to beads in optical traps. The LOT generates folding trajectories under force in terms of time-dependent changes in the distance between the beads. How to construct the full intrinsic folding landscape (without the handles and beads) from the measured time series is a major unsolved problem. By using rigorous theoretical methods—which account for fluctuations of the DNA handles, rotation of the optical beads, variations in applied tension due to finite trap stiffness, as well as environmental noise and limited bandwidth of the apparatus—we provide a tractable method to derive intrinsic free-energy profiles. We validate the method by showing that the exactly calculable intrinsic free-energy profile for a generalized Rouse model, which mimics the two-state behavior in nucleic acid hairpins, can be accurately extracted from simulated time series in a LOT setup regardless of the stiffness of the handles. We next apply the approach to trajectories from coarse-grained LOT molecular simulations of a coiled-coil protein based on the GCN4 leucine zipper and obtain a free-energy landscape that is in quantitative agreement with simulations performed without the beads and handles. Finally, we extract the intrinsic free-energy landscape from experimental LOT measurements for the leucine zipper.

How the diffusivity profile reduces the arbitrariness of protein folding free energies

The concept of a protein diffusing in its free-energy folding landscape has been fruitful for both theory and experiment. Yet the choice of the reaction coordinate (RC) introduces an undesirable degree of arbitrariness into the problem. We analyze extensive simulation data of an alpha-helix in explicit water solvent as it stochastically folds and unfolds. The free-energy profiles for different RCs exhibit significant variations, some having an activation barrier, while others not. We show that this variation has little effect on the predicted folding kinetics if the diffusivity profiles are properly taken into account. This kinetic quasi-universality is rationalized by an RC rescaling, which, due to the reparameterization invariance of the Fokker-Planck equation, allows the combination of free-energy and diffusivity effects into a single function, the rescaled free-energy profile. This rescaled free energy indeed shows less variation among different RCs than the bare free energy and diffusivity profiles separately do, if we properly distinguish between RCs that contain knowledge of the native state and those that are purely geometric in nature. Our method for extracting diffusivity profiles is easily applied to experimental single molecule time series data and might help to reconcile conflicts that arise when comparing results from different experimental probes for the same protein.

Hydrodynamic screening near planar boundaries: Effects on semiflexible polymer dynamics

The influence of hydrodynamic screening near a surface on the dynamics of a single semiflexible polymer is studied by means of Brownian dynamics simulations and hydrodynamic mean field theory. The polymer motion is characterized in terms of the mean squared displacements of the end-monomers, the end-to-end vector, and the scalar end-to-end distance. In order to control hydrodynamic screening effects, the polymer is confined to a plane at a fixed separation from the wall. When gradually decreasing this separation, a crossover from Zimm-type towards Rouse (free-draining) polymer dynamics is induced. However, this crossover is rather slow and the free-draining limit is not completely reached--substantial deviations from Rouse-like dynamics are registered in both simulations and theory--even at distances of the polymer from the wall on the order of the monomer size. Remarkably, the effect of surface-induced screening of hydrodynamic interactions sensitively depends on the type of dynamic observable considered. For vectorial quantities such as the end-to-end vector, hydrodynamic interactions are important and therefore surface screening effects are sizeable. For a scalar quantity such as the end-to-end distance, on the other hand, hydrodynamic interactions are less important, but a pronounced dependence of dynamic scaling exponents on the persistence length to contour length ratio becomes noticeable. Our findings are discussed against the background of single-molecule experiments on f-actin [L. Le Goff et al., Phys. Rev. Lett. 89, 258101 (2002)].

Compaction and tensile forces determine the accuracy of folding landscape parameters from single molecule pulling experiments.

We establish a framework for assessing whether the transition state location of a biopolymer, which can be inferred from single molecule pulling experiments, corresponds to the ensemble of structures that have equal probability of reaching either the folded or unfolded states (P(fold)=0.5). Using results for the forced unfolding of a RNA hairpin, an exactly soluble model, and an analytic theory, we show that P(fold) is solely determined by s, an experimentally measurable molecular tensegrity parameter, which is a ratio of the tensile force and a compaction force that stabilizes the folded state. Applications to folding landscapes of DNA hairpins and a leucine zipper with two barriers provide a structural interpretation of single molecule experimental data. Our theory can be used to assess whether molecular extension is a good reaction coordinate using measured free energy profiles.

End-Monomer Dynamics in Semiflexible Polymers

Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) 〈r(2)(t)〉 ~ t(1/2) at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; another study claimed the more conventional Zimm scaling 〈r(2)(t)〉 ~ t(2/3) in the same time range. Using hydrodynamic simulations, analytical and scaling theories, we find a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, α(t) = d log〈r(2)(t)〉/d log t, drops below the Zimm value of 2/3 for sufficiently long chains. The deviation from the Zimm prediction increases with chain length, though it does not reach the Rouse limit of 1/2. The qualitative features of this intermediate regime, found in simulations and in an improved mean-field theory for semiflexible polymers, in particular the variation of α(t) with chain and persistence lengths, can be reproduced through a heuristic scaling argument. Anomalously low values of the effective exponent α are explained by hydrodynamic effects related to the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger length scales.

Force-dependent switch in protein unfolding pathways and transition-state movements

Significance Single-domain proteins with symmetrical arrangement of secondary structural elements in the native state are expected to fold by diverse pathways. However, understanding the origins of pathway diversity, and the experimental signatures for identifying it, are major challenges, especially for small proteins with no obvious symmetry in the folded states. We show rigorously that upward curvature in the logarithm of unfolding rates as a function of force (or denaturants) implies that the folding occurs by diverse pathways. The theoretical concepts are illustrated using simulations of src SH3 domain, which explain the emergence of parallel pathways in single-molecule pulling experiments and provide structural description of the routes to the unfolded state. We make testable predictions illustrating the generality of the theory. Although it is known that single-domain proteins fold and unfold by parallel pathways, demonstration of this expectation has been difficult to establish in experiments. Unfolding rate, ku(f), as a function of force f, obtained in single-molecule pulling experiments on src SH3 domain, exhibits upward curvature on a log⁡ku(f) plot. Similar observations were reported for other proteins for the unfolding rate ku([C]). These findings imply unfolding in these single-domain proteins involves a switch in the pathway as f or [C] is increased from a low to a high value. We provide a unified theory demonstrating that if log⁡ku as a function of a perturbation (f or [C]) exhibits upward curvature then the underlying energy landscape must be strongly multidimensional. Using molecular simulations we provide a structural basis for the switch in the pathways and dramatic shifts in the transition-state ensemble (TSE) in src SH3 domain as f is increased. We show that a single-point mutation shifts the upward curvature in log⁡ku(f) to a lower force, thus establishing the malleability of the underlying folding landscape. Our theory, applicable to any perturbation that affects the free energy of the protein linearly, readily explains movement in the TSE in a β-sandwich (I27) protein and single-chain monellin as the denaturant concentration is varied. We predict that in the force range accessible in laser optical tweezer experiments there should be a switch in the unfolding pathways in I27 or its mutants.

Plasticity of hydrogen bond networks regulates mechanochemistry of cell adhesion complexes

Significance Selectins and integrins are receptor proteins on cell surfaces responsible for adhesion to extracellular biomolecules, a critical component of physiological processes like white blood cell localization at sites of inflammation. The bonds which the receptors form with their targets are regulated by mechanical forces (for example due to blood flow). The bond lifetimes before rupture increase with force before decreasing. Based on crystal structures of selectin and integrin, we created a general analytic theory which for the first time, to our knowledge, relates microscopic structural rearrangements at the receptor–ligand interface to macroscopic bond lifetimes. We quantitatively explain experimental data from diverse systems spanning four decades of lifetime scales, and also predict the outcome of mutations in specific residues. Mechanical forces acting on cell adhesion receptor proteins regulate a range of cellular functions by formation and rupture of noncovalent interactions with ligands. Typically, force decreases the lifetimes of intact complexes (“slip bonds”), making the discovery that these lifetimes can also be prolonged (“catch bonds”) a surprise. We created a microscopic analytic theory by incorporating the structures of selectin and integrin receptors into a conceptual framework based on the theory of stochastic equations, which quantitatively explains a wide range of experimental data (including catch bonds at low forces and slip bonds at high forces). Catch bonds arise due to force-induced remodeling of hydrogen bond networks, a finding that also accounts for unbinding in structurally unrelated integrin–fibronectin and actomyosin complexes. For the selectin family, remodeling of hydrogen bond networks drives an allosteric transition resulting in the formation of the maximum number of hydrogen bonds determined only by the structure of the receptor and independent of the ligand. A similar transition allows us to predict the increase in the number of hydrogen bonds in a particular allosteric state of α5β1 integrin–fibronectin complex, a conformation which is yet to be crystallized. We also make a testable prediction that a single point mutation (Tyr51Phe) in the ligand associated with selectin should dramatically alter the nature of the catch bond compared with the wild type. Our work suggests that nature uses a ductile network of hydrogen bonds to engineer function over a broad range of forces.

Design principles governing the motility of myosin V

Significance Myosin V, a two-headed motor protein, ferries cellular cargo by walking hand-over-hand on actin filaments. Interplay between ATP-driven conformational changes in the heads and stress due to load produces a variety of stepping dynamics: The motor can step forward or backward, or “stomp,” where one head detaches and rebinds to the same site. We created an analytically solvable theory capturing all these behaviors, quantitatively matching a wide array of single-molecule experiments. We describe the structural and chemical design principles underlying the motor’s robust function, providing a guide for how bioengineering might alter its dynamics. The molecular motor myosin V (MyoV) exhibits a wide repertoire of pathways during the stepping process, which is intimately connected to its biological function. The best understood of these is the hand-over-hand stepping by a swinging lever arm movement toward the plus end of actin filaments. Single-molecule experiments have also shown that the motor “foot stomps,” with one hand detaching and rebinding to the same site, and back-steps under sufficient load. The complete taxonomy of MyoV’s load-dependent stepping pathways, and the extent to which these are constrained by motor structure and mechanochemistry, are not understood. Using a polymer model, we develop an analytical theory to describe the minimal physical properties that govern motor dynamics. We solve the first-passage problem of the head reaching the target-binding site, investigating the competing effects of backward load, strain in the leading head biasing the diffusion in the direction of the target, and the possibility of preferential binding to the forward site due to the recovery stroke. The theory reproduces a variety of experimental data, including the power stroke and slow diffusive search regimes in the mean trajectory of the detached head, and the force dependence of the forward-to-backward step ratio, run length, and velocity. We derive a stall force formula, determined by lever arm compliance and chemical cycle rates. By exploring the MyoV design space, we predict that it is a robust motor whose dynamical behavior is not compromised by reasonable perturbations to the reaction cycle and changes in the architecture of the lever arm.