DNA hybridization catalysts and catalyst circuits

Practically all of life's molecular processes, from chemical synthesis to replication, involve enzymes that carry out their functions through the catalysis of metastable fuels into waste products. Catalytic control of reaction rates will prove to be as useful and ubiquitous in DNA nanotechnology as it is in biology. Here we present experimental results on the control of the decay rates of a metastable DNA "fuel". We show that the fuel complex can be induced to decay with a rate about 1600 times faster than it would decay spontaneously. The original DNA hybridization catalyst [15] achieved a maximal speed-up of roughly 30. The fuel complex discussed here can therefore serve as the basic ingredient for an improved DNA hybridization catalyst. As an example application for DNA hybridization catalysts, we propose a method for implementing arbitrary digital logic circuits

Lattice Gauge Theories at the Energy Frontier

This White Paper has been prepared as a planning document for the Division of High Energy Physics of the U. S. Department of Energy. Recent progress in lattice-based studies of physics beyond the standard model is summarized, and major current goals of USQCD research in this area are presented. Challenges and opportunities associated with the recently discovered 126 GeV Higgs-like particle are highlighted. Computational resources needed for reaching important goals are described. The document was finalized on February 11, 2013 with references that are not aimed to be complete, or account for an accurate historical record of the field.Comment: Submitted for the Snowmass 2013 e-Proceedings with 44 pages, 10 figures, and 3 table

Allocating and splitting free energy to maximize molecular machine flux

Biomolecular machines transduce between different forms of energy. These machines make directed progress and increase their speed by consuming free energy, typically in the form of nonequilibrium chemical concentrations. Machine dynamics are often modeled by transitions between a set of discrete metastable conformational states. In general, the free energy change associated with each transition can increase the forward rate constant, decrease the reverse rate constant, or both. In contrast to previous optimizations, we find that in general flux is neither maximized by devoting all free energy changes to increasing forward rate constants nor by solely decreasing reverse rate constants. Instead the optimal free energy splitting depends on the detailed dynamics. Extending our analysis to machines with vulnerable states (from which they can break down), in the strong driving corresponding to in vivo cellular conditions, processivity is maximized by reducing the occupation of the vulnerable state.Comment: 22 pages, 7 figure

Robustness: a new SLIP model based criterion for gait transitions in bipedal locomotion

Bipedal locomotion is a phenomenon that still eludes a fundamental and concise mathematical understanding. Conceptual models that capture some relevant aspects of the process exist but their full explanatory power is not yet exhausted. In the current study, we introduce the robustness criterion which defines the conditions for stable locomotion when steps are taken with imprecise angle of attack. Intuitively, the necessity of a higher precision indicates the difficulty to continue moving with a given gait. We show that the spring-loaded inverted pendulum model, under the robustness criterion, is consistent with previously reported findings on attentional demand during human locomotion. This criterion allows transitions between running and walking, many of which conserve forward speed. Simulations of transitions predict Froude numbers below the ones observed in humans, nevertheless the model satisfactorily reproduces several biomechanical indicators such as hip excursion, gait duty factor and vertical ground reaction force profiles. Furthermore, we identify reversible robust walk-run transitions, which allow the system to execute a robust version of the hopping gait. These findings foster the spring-loaded inverted pendulum model as the unifying framework for the understanding of bipedal locomotion.Comment: unpublished, in preparatio

Catalyzed relaxation of a metastable DNA fuel

Practically all of life's molecular processes, from chemical synthesis to replication, involve enzymes that carry out their functions through the catalytic transformation of metastable fuels into waste products. Catalytic control of reaction rates will prove to be as useful and ubiquitous in nucleic-acid-based engineering as it is in biology. Here we report a metastable DNA "fuel" and a corresponding DNA "catalyst" that improve upon the original hybridization-based catalyst system (Turberfield et al. Phys. Rev. Lett. 90, 118102-1118102-4) by more than 2 orders of magnitude. This is achieved by identifying and purifying a fuel with a kinetically trapped metastable configuration consisting of a "kissing loop" stabilized by flanking helical domains; the catalyst strand acts by opening a helical domain and allowing the complex to relax to its ground state by a multistep pathway. The improved fuel/catalyst system shows a roughly 5000-fold acceleration of the uncatalyzed reaction, with each catalyst molecule capable of turning over in excess of 40 substrates. With k_(cat)/K_M ≈ 10^7/M/min, comparable to many protein enzymes and ribozymes, this fuel system becomes a viable component enabling future DNA-based synthetic molecular machines and logic circuits. As an example, we designed and characterized a signal amplifier based on the fuel-catalyst system. The amplifier uses a single strand of DNA as input and releases a second strand with unrelated sequence as output. A single input strand can catalytically trigger the release of more than 10 output strands

Dynamically Stable 3D Quadrupedal Walking with Multi-Domain Hybrid System Models and Virtual Constraint Controllers

Hybrid systems theory has become a powerful approach for designing feedback controllers that achieve dynamically stable bipedal locomotion, both formally and in practice. This paper presents an analytical framework 1) to address multi-domain hybrid models of quadruped robots with high degrees of freedom, and 2) to systematically design nonlinear controllers that asymptotically stabilize periodic orbits of these sophisticated models. A family of parameterized virtual constraint controllers is proposed for continuous-time domains of quadruped locomotion to regulate holonomic and nonholonomic outputs. The properties of the Poincare return map for the full-order and closed-loop hybrid system are studied to investigate the asymptotic stabilization problem of dynamic gaits. An iterative optimization algorithm involving linear and bilinear matrix inequalities is then employed to choose stabilizing virtual constraint parameters. The paper numerically evaluates the analytical results on a simulation model of an advanced 3D quadruped robot, called GR Vision 60, with 36 state variables and 12 control inputs. An optimal amble gait of the robot is designed utilizing the FROST toolkit. The power of the analytical framework is finally illustrated through designing a set of stabilizing virtual constraint controllers with 180 controller parameters.Comment: American Control Conference 201