43 research outputs found

    Statistical properties of multistep enzyme-mediated reactions

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    Enzyme-mediated reactions may proceed through multiple intermediate conformational states before creating a final product molecule, and one often wishes to identify such intermediate structures from observations of the product creation. In this paper, we address this problem by solving the chemical master equations for various enzymatic reactions. We devise a perturbation theory analogous to that used in quantum mechanics that allows us to determine the first () and the second (variance) cumulants of the distribution of created product molecules as a function of the substrate concentration and the kinetic rates of the intermediate processes. The mean product flux V=d/dt (or "dose-response" curve) and the Fano factor F=variance/ are both realistically measurable quantities, and while the mean flux can often appear the same for different reaction types, the Fano factor can be quite different. This suggests both qualitative and quantitative ways to discriminate between different reaction schemes, and we explore this possibility in the context of four sample multistep enzymatic reactions. We argue that measuring both the mean flux and the Fano factor can not only discriminate between reaction types, but can also provide some detailed information about the internal, unobserved kinetic rates, and this can be done without measuring single-molecule transition events.Comment: 8 pages, 3 figure

    Synchronization of Coupled Rotators: Josephson Junction Ladders and the locally coupled Kuramoto Model

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    We show that the resistively shunted junction (RSJ) equations describing a ladder array of overdamped, critical-current disordered Josephson junctions that are current biased along the rungs of the ladder can be mapped onto a Kuramoto model with nearest neighbor, sinusoidal couplings. This result is obtained by an averaging method, in which the fast dynamics of the RSJ equations are integrated out, leaving the dynamics which describe the time scale over which neighboring junctions along the rungs of the ladder phase and frequency synchronize. We quantify the degree of frequency synchronization of the rung junctions by calculating the standard deviation of their time-averaged voltages, σω, and the phase synchronization is quantified by calculating the time average of the modulus of the Kuramoto order parameter, ⟨|r|⟩. We test the results of our averaging process by comparing the values of σω and ⟨|r|⟩ for the original RSJ equations and our veraged equations. We find excellent agreement for dc bias currents of IB/⟨Ic⟩≳3, where ⟨Ic⟩ is the average critical current of the rung junctions, and critical current disorders of up to 10%. We also study the effects of thermal noise on the synchronization properties of the overdamped ladder. Finally, we find that including the ffects of junction capacitance can lead to a discontinuous synchronization transition as the strength of the coupling between neighboring junctions is smoothly varied

    Proximal junctional failure prevention in adult spinal deformity surgery utilizing interlaminar fixation constructs

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    Proximal junctional kyphosis (PJK) is a common complication following fusion for Adult Spinal Deformity. PJK and proximal junctional failure (PJF) may lead to pain, neurological injury, reoperation, and increased healthcare costs. Efforts to prevent PJK and PJF have aimed to preserve or reconstruct the posterior spinal tension band and/or modifying instrumentation to allow for more gradual transitions in stiffness at the cranial end of long spinal constructs. We describe placement of an interlaminar fixation construct at the upper instrumented vertebra which may decrease PJK/PJF severity, and is placed with little additional operative time and minimal posterior soft tissue trauma
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