An Analytic Study of Pursuit Strategies

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 differential extension in dsDNA bound to Rad51 filaments may play important roles in homology recognition and strand exchange

RecA and Rad51 proteins play an important role in DNA repair and homologous recombination. For RecA, X-ray structure information and single molecule force experiments have indicated that the differential extension between the complementary strand and its Watson–Crick pairing partners promotes the rapid unbinding of non-homologous dsDNA and drives strand exchange forward for homologous dsDNA. In this work we find that both effects are also present in Rad51 protein. In particular, pulling on the opposite termini (3′ and 5′) of one of the two DNA strands in a dsDNA molecule allows dsDNA to extend along non-homologous Rad51-ssDNA filaments and remain stably bound in the extended state, but pulling on the 3′5′ ends of the complementary strand reduces the strand-exchange rate for homologous filaments. Thus, the results suggest that differential extension is also present in dsDNA bound to Rad51. The differential extension promotes rapid recognition by driving the swift unbinding of dsDNA from non-homologous Rad51-ssDNA filaments, while at the same time, reducing base pair tension due to the transfer of the Watson–Crick pairing of the complementary strand bases from the highly extended outgoing strand to the slightly less extended incoming strand, which drives strand exchange forward

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

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

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

Integrated electrophoretic cytometry separations and immunoassays for proteins and their complexes

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

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

Effect of Polymer Hydration State on In-Gel Immunoassays.

Applications as diverse as drug delivery and immunoassays require hydrogels to house high concentration macromolecular solutions. Yet, thermodynamic partitioning acts to lower the equilibrium concentration of macromolecules in the hydrogel, as compared to the surrounding liquid phase. For immunoassays that utilize a target antigen immobilized in the hydrogel, partitioning hinders introduction of detection antibody into the gel and, consequently, reduces the in-gel concentration of detection antibody, adversely impacting assay sensitivity. Recently, we developed a single-cell targeted proteomic assay with polyacrylamide gel electrophoresis of single cell lysates followed by an in-gel immunoassay. In the present work, we overcome partitioning that both limits analytical sensitivity and increases consumption of costly detection antibody by performing the immunoassay step after dehydrating the antigen-containing polyacrylamide gel. Gels are rehydrated with a solution of detection antibody. We hypothesized that matching the volume of detection antibody solution with the hydrogel water volume fraction would ensure that, at equilibrium, the detection antibody mass resides in the gel and not in the liquid surrounding the gel. Using this approach, we observe (compared with antibody incubation of hydrated gels): (i) 4-11 fold higher concentration of antibody in the dehydrated gels and in the single-cell assay (ii) higher fluorescence immunoassay signal, with up to 5-fold increases in signal-to-noise-ratio and (iii) reduced detection antibody consumption. We also find that detection antibody signal may be less well-correlated with target protein levels (GFP) using this method, suggesting a trade-off between analytical sensitivity and variation in immunoprobe signal. Our volume-matching approach for introducing macromolecular solutions to hydrogels increases the local in-gel concentration of detection antibody without requiring modification of the hydrogel structure, and thus we anticipate broad applicability to hydrogel-based assays, diagnostics, and drug delivery