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

On the imaginary parts of chromatic root

While much attention has been directed to the maximum modulus and maximum real part of chromatic roots of graphs of order $n$ (that is, with $n$ vertices), relatively little is known about the maximum imaginary part of such graphs. We prove that the maximum imaginary part can grow linearly in the order of the graph. We also show that for any fixed $p \in (0,1)$, almost every random graph $G$ in the Erd\"os-R\'enyi model has a non-real root.Comment: 4 figure

Protein kinase A regulation of P2X4 receptors: Requirement for a specific motif in the C-terminus

AbstractThe P2X purinergic receptor sub-family of ligand-gated ion channels are subject to protein kinase modulation. We have previously demonstrated that P2X4R signaling can be positively regulated by increasing intracellular cAMP levels. The molecular mechanism underlying this effect was, however, unknown. The present study initially addressed whether protein kinase A (PKA) activation was required. Subsequently a mutational approach was utilized to determine which region of the receptor was required for this potentiation. In both DT-40 3KO and HEK-293 cells transiently expressing P2X4R, forskolin treatment enhanced ATP-mediated signaling. Specific PKA inhibitors prevented the forskolin-induced enhancement of ATP-mediated inward currents in P2X4R expressing HEK-293 cells. To define which region of the P2X4R was required for the potentiation, mutations were generated in the cytoplasmic C-terminal tail. It was determined that a limited region of the C-terminus, consisting of a non-canonical tyrosine based sorting motif, was required for the effects of PKA. Of note, this region does not harbor any recognizable PKA phosphorylation motifs, and no direct phosphorylation of P2X4R was detected, suggesting that PKA phosphorylation of an accessory protein interacts with the endocytosis motif in the C-terminus of the P2X4R. In support of this notion, using Total Internal Reflection Fluorescence Microscopy (TIRF)\ P2X4-EGFP was shown to accumulate at/near the plasma membrane following forskolin treatment. In addition, disrupting the endocytosis machinery using a dominant-negative dynamin construct also prevented the PKA-mediated enhancement of ATP-stimulated Ca2+ signals. Our results are consistent with a novel mechanism of P2XR regulation, whereby PKA activity, without directly phosphorylating P2X4R, markedly enhances ATP-stimulated P2X4R currents and hence cytosolic Ca2+ signals. This may occur at least in part, by altering the trafficking of a population of P2X4R present at the plasma membrane

Dynamic Tracing: a graphical language for rewriting protocols

The category Set* of sets and partial functions is well-known to be traced monoidal, meaning that a partial function S+U -/-> T+U can be coherently transformed into a partial function S -/-> T. This transformation is generally described in terms of an implicit procedure that must be run. We make this procedure explicit by enriching the traced category in Cat#, the symmetric monoidal category of categories and cofunctors: each hom-category has such procedures as objects, and advancement through the procedures as arrows. We also generalize to traced Kleisli categories beyond Set*, providing a conjectural trace operator for the Kleisli category of any polynomial monad of the form t+1. The main motivation for this work is to give a formal and graphical syntax for performing sophisticated computations powered by graph rewriting, which is itself a graphical language for data transformation

Astronomical random numbers for quantum foundations experiments

Photons from distant astronomical sources can be used as a classical source of randomness to improve fundamental tests of quantum nonlocality, wave-particle duality, and local realism through Bell's inequality and delayed-choice quantum eraser tests inspired by Wheeler's cosmic-scale Mach-Zehnder interferometer gedankenexperiment. Such sources of random numbers may also be useful for information-theoretic applications such as key distribution for quantum cryptography. Building on the design of an "astronomical random-number generator" developed for the recent "cosmic Bell" experiment [Handsteiner et al., Phys. Rev. Lett. 118, 060401 (2017)], in this paper we report on the design and characterization of a device that, with 20-nanosecond latency, outputs a bit based on whether the wavelength of an incoming photon is greater than or less than 700 nm. Using the one-meter telescope at the Jet Propulsion Laboratory (JPL) Table Mountain Observatory, we generated random bits from astronomical photons in both color channels from 50 stars of varying color and magnitude, and from 12 quasars with redshifts up to $z = 3.9$. With stars, we achieved bit rates of $\sim 1 \times 10^6$ Hz / m$^2$, limited by saturation for our single-photon detectors, and with quasars of magnitudes between 12.9 and 16, we achieved rates between $\sim 10^2$ and $2 \times 10^3$ Hz /m$^2$. For bright quasars, the resulting bitstreams exhibit sufficiently low amounts of statistical predictability as quantified by the mutual information. In addition, a sufficiently high fraction of bits generated are of true astronomical origin in order to address both the locality and freedom-of-choice loopholes when used to set the measurement settings in a test of the Bell-CHSH inequality.Comment: 17 pages, 12 figures. References added and minor edits to match published versio

Allocating Dissipation Across a Molecular Machine Cycle to Maximize Flux

Biomolecular machines consume free energy to break symmetry and make directed progress. Nonequilibrium ATP concentrations are the typical free energy source, with one cycle of a molecular machine consuming a certain number of ATP, providing a fixed free energy budget. Since evolution is expected to favor rapid-turnover machines that operate efficiently, we investigate how this free energy budget can be allocated to maximize flux. Unconstrained optimization eliminates intermediate metastable states, indicating that flux is enhanced in molecular machines with fewer states. When maintaining a set number of states, we show that—in contrast to previous findings—the flux-maximizing allocation of dissipation is not even. This result is consistent with the coexistence of both “irreversible” and reversible transitions in molecular machine models that successfully describe experimental data, which suggests that, in evolved machines, different transitions differ significantly in their dissipation