Cellular signaling networks function as generalized Wiener-Kolmogorov filters to suppress noise

Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity. Each stage of the cascade often takes the form of a kinase-phosphatase push-pull network, a basic unit of signaling pathways whose malfunction is linked with a host of cancers. We show this ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov (WK) optimal noise filter. Using concepts from umbral calculus, we generalize the linear WK theory, originally introduced in the context of communication and control engineering, to take nonlinear signal transduction and discrete molecule populations into account. This allows us to derive rigorous constraints for efficient noise reduction in this biochemical system. Our mathematical formalism yields bounds on filter performance in cases important to cellular function---like ultrasensitive response to stimuli. We highlight features of the system relevant for optimizing filter efficiency, encoded in a single, measurable, dimensionless parameter. Our theory, which describes noise control in a large class of signal transduction networks, is also useful both for the design of synthetic biochemical signaling pathways, and the manipulation of pathways through experimental probes like oscillatory input.

Design principles governing the motility of myosin V

The molecular motor myosin V exhibits a wide repertoire of pathways during the stepping process, which is intimately connected to its biological function. The best understood of these is hand-over-hand stepping by a swinging lever arm movement toward the plus-end of actin filaments, essential to its role as a cellular transporter. However, single-molecule experiments have also shown that the motor foot stomps, with one hand detaching and rebinding to the same site, and backsteps under sufficient load. Explaining the complete taxonomy of myosin Vs load-dependent stepping pathways, and the extent to which these are constrained by motor structure and mechanochemistry, are still open questions. Starting from a polymer model, we develop an analytical theory to understand the minimal physical properties that govern motor dynamics. In particular, we solve the first-passage problem of the head reaching the target binding site, investigating the competing effects of load pulling back at the motor, strain in the leading head that biases 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. The analytical approach yields a formula for the stall force, identifying the relative contributions of the chemical cycle rates and mechanical features like the bending rigidities of the lever arms. Most importantly, by fully exploring the design space of the motor, we predict that myosin V 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.

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 the 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 the 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, which is independent of the trap parameters.

Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder

For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire range of disorder. We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local magnetizations and local spin-glass order parameters, which turn out to exhibit, as function of temperature, complex and distinctive tulip patterns.