35 research outputs found

    An Analytic Study of Pursuit Strategies

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    The Two-on-One pursuit-evasion differential game is revisited where the holonomic players have equal speed, and the two pursuers are endowed with a circular capture range ℓ \u3e 0. Then, the case where the pursuers\u27 capture ranges are unequal, ℓ1 \u3e ℓ2 ≥ 0, is analyzed. In both cases, the state space region where capture is guaranteed is delineated and the optimal feedback strategies are synthesized. Next, pure pursuit is considered whereupon the terminal separation between a pursuer and an equal-speed evader less than the pursuer\u27s capture range ℓ \u3e 0. The case with two pursuers employing pure pursuit is considered, and the conditions for capturability are presented. The pure pursuit strategy is applied to a target-defense scenario and conditions are given that determine if capture of the attacker before he reaches the target is possible. Lastly, three-on-one pursuit-evasion is considered where the three pursuers are initially positioned in a fully symmetric configuration. The evader, situated at the circumcenter of the three pursuers, is slower than the pursuers. We analyze collision course and pure pursuit guidance and provide evidence that conventional strategy for “optimal” evasive maneuver is incorrect

    The Tension on dsDNA Bound to ssDNA/RecA Filaments May Play an Important Role in Driving Efficient and Accurate Homology Recognition and Strand Exchange

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    It is well known that during homology recognition and strand exchange the double stranded DNA (dsDNA) in DNA/RecA filaments is highly extended, but the functional role of the extension has been unclear. We present an analytical model that calculates the distribution of tension in the extended dsDNA during strand exchange. The model suggests that the binding of additional dsDNA base pairs to the DNA/RecA filament alters the tension in dsDNA that was already bound to the filament, resulting in a non-linear increase in the mechanical energy as a function of the number of bound base pairs. This collective mechanical response may promote homology stringency and underlie unexplained experimental results

    RecA homology search is promoted by mechanical stress along the scanned duplex DNA

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    A RecA–single-stranded DNA (RecA–ssDNA) filament searches a genome for sequence homology by rapidly binding and unbinding double-stranded DNA (dsDNA) until homology is found. We demonstrate that pulling on the opposite termini (3′ and 5′) of one of the two DNA strands in a dsDNA molecule stabilizes the normally unstable binding of that dsDNA to non-homologous RecA–ssDNA filaments, whereas pulling on the two 3′, the two 5′, or all four termini does not. We propose that the ‘outgoing’ strand in the dsDNA is extended by strong DNA–protein contacts, whereas the ‘complementary’ strand is extended by the tension on the base pairs that connect the ‘complementary’ strand to the ‘outgoing’ strand. The stress resulting from different levels of tension on its constitutive strands causes rapid dsDNA unbinding unless sufficient homology is present

    Effect of Polymer Hydration State on In-Gel Immunoassays.

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    Integrated electrophoretic cytometry separations and immunoassays for proteins and their complexes

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    Protein complexes, such as filamentous actin (F-actin) complexes, regulate key cell processes such as cell motility and division. Disruption of F-actin result in highly motile and invasive cancer cells. Cancer therapeutics have thus aimed to maintain F-actin, but cell-to-cell variation in F-actin levels in response to such therapeutics necessitate single-cell measurements of dynamic actin protein complexes, including the binding actin binding proteins that determine actin polymerization state. Protein complex levels cannot be inferred from an immunoassay, as most lack selective antibodies. Size-based separations of such protein species provide selectivity when coupled with an immunoassay for protein detection and quantitation. While this selectivity has been demonstrated at the single-cell level by the introduction of electrophoretic (EP) cytometry in our lab, we sought to establish a single-cell electrophoretic assay for protein complex identification and quantitation. In order to understand the regulation of actin polymerization and depolymerization in heterogeneous cells requires four key separation assay features: i) quantifiable technical variation to discern biological variation in the cell population ii) sufficient analytical sensitivity to detect F-actin bound actin binding proteins, iii) high-selectivity separations to detect actin and its binding proteins, and iv) sample preparation with assay stage-optimized buffers to isolate dynamic complexes without disrupting the complexes. We will share our studies to elucidate chemical and physical underpinnings of each of these needed features. First, we will describe algorithm development and applications to establish a technical variation threshold and protein sizing standards for electrophoretic (EP) cytometry to distinguish biological variation of protein expression and size in single cells. Next, we will discuss the impact of in-gel immunoassay performance and open microfluidic device design on analytical sensitivity. Given fundamental tradeoffs between in-gel immunoassay sensitivity and separation performance, we consider alternative sieving matrices tuned to separate proteins in specific molecular weight ranges. We then describe unique impacts of Joule heating on separation performance in open microfluidic electrophoresis. Joule heating is mitigated with a buffer exchange approach that reduces variation in separation performance and introduces assay stage-optimized buffers without further protein loss. Finally, we will discuss the design of EP cytometry to fractionate actin protein complexes from single cells with assay stage-optimized buffers. The microscale device achieves rapid, arrayed on-chip sample preparation and EP fractionation without perturbing complexes. We demonstrated F-actin separations from monomeric actin, and the measurement of F-actin binding proteins that regulate actin polymerization. We anticipate the single-cell protein complex measurements described here will be broadly applicable to protein complexes that drive human health

    Two-On-One Pursuit When the Pursuers Have the Same Speed as the Evader

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    A two-on-one pursuit-evasion differential game is considered. The setup is akin to Isaacs\u27 Two Cutters and Fugitive Ship differential game. In this paper it is however assumed that the three players have equal speeds and the two cutters/pursuers have a non-zero capture radius. The case where just one of the Pursuers is endowed with a circular capture set is also considered. The state space region where capture is guaranteed is delineated, thus providing the solution of the Game of Kind, and the players\u27 optimal state feedback strategies and the attendant value function are synthesized, thus providing the solution of the Game of Degree
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