Exact solution of the Bernoulli matching model of sequence alignment

Through a series of exact mappings we reinterpret the Bernoulli model of sequence alignment in terms of the discrete-time totally asymmetric exclusion process with backward sequential update and step function initial condition. Using earlier results from the Bethe ansatz we obtain analytically the exact distribution of the length of the longest common subsequence of two sequences of finite lengths $X,Y$. Asymptotic analysis adapted from random matrix theory allows us to derive the thermodynamic limit directly from the finite-size result.Comment: 13 pages, 4 figure

Anodic oxidation of ethynylferrocene derivatives in homogeneous solution and following anodic deposition onto glassy carbon electrodes

Eight ferrocene derivatives linked by either an ether, amine, or phenylacetylene moiety to a terminal ethynyl group were covalently deposited on glassy carbon electrodes by anodic electrochemical methods. The lithio activation method, in which the terminal hydrogen of the ethynyl group is replaced by a lithium atom before anodic oxidation, was successfully employed in all cases. Direct oxidation of the unactivated ethynyl group also resulted in surface deposition. Surface coverages between 1 x 10 ‐10 mol cm ‐2 and 14 x 10 ‐10 mol cm ‐2 were achieved. Cyclic voltammetry scans of the modified electrodes in pure electrolytes differed depending on the size of the supporting electrolyte anion, as little as half the current being measured for a [B(C 6 F 5 ) 4 ] ‐ vs. [PF 6 ] ‐ solution, suggesting differences in ion transport near the electrode surface. An ether‐linked ethynylferrocenium ion ( 5 + ) was isolated after electrolytic and chemical oxidation of 5 and characterized by X‐Ray crystallography as its [SbCl 6 ] ‐ salt

Exact Asymptotic Results for a Model of Sequence Alignment

Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the distribution of the LCS in a simpler, yet nontrivial, variant of the original model called the Bernoulli matching (BM) model which reduces to the original model in the large c limit. We show that in the BM model, for all c, the distribution of the asymptotic length of the LCS, suitably scaled, is identical to the Tracy-Widom distribution of the largest eigenvalue of a random matrix whose entries are drawn from a Gaussian unitary ensemble. In particular, in the large c limit, this provides an exact expression for the asymptotic length distribution in the original LCS problem.Comment: 4 pages Revtex, 2 .eps figures include

Rac1-Dependent Phosphorylation and Focal Adhesion Recruitment of Myosin IIA Regulates Migration and Mechanosensing

SummaryBackgroundCell migration requires coordinated formation of focal adhesions (FAs) and assembly and contraction of the actin cytoskeleton. Nonmuscle myosin II (MII) is a critical mediator of contractility and FA dynamics in cell migration. Signaling downstream of the small GTPase Rac1 also regulates FA and actin dynamics, but its role in regulation of MII during migration is less clear.ResultsWe found that Rac1 promotes association of MIIA with FA. Live-cell imaging showed that, whereas most MIIA at the leading edge assembled into dorsal contractile arcs, a substantial subset assembled in or was captured within maturing FA, and this behavior was promoted by active Rac1. Protein kinase C (PKC) activation was necessary and sufficient for integrin- and Rac1-dependent phosphorylation of MIIA heavy chain (HC) on serine1916 (S1916) and recruitment to FA. S1916 phosphorylation of MIIA HC and localization in FA was enhanced during cell spreading and ECM stiffness mechanosensing, suggesting upregulation of this pathway during physiological Rac1 activation. Phosphomimic and nonphosphorylatable MIIA HC mutants demonstrated that S1916 phosphorylation was necessary and sufficient for the capture and assembly of MIIA minifilaments in FA. S1916 phosphorylation was also sufficient to promote the rapid assembly of FAs to enhance cell migration and for the modulation of traction force, spreading, and migration by ECM stiffness.ConclusionsOur study reveals for the first time that Rac1 and integrin activation regulates MIIA HC phosphorylation through a PKC-dependent mechanism that promotes MIIA association with FAs and acts as a critical modulator of cell migration and mechanosensing

Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment

For the Bernoulli Matching model of sequence alignment problem we apply the Bethe ansatz technique via an exact mapping to the 5--vertex model on a square lattice. Considering the terrace--like representation of the sequence alignment problem, we reproduce by the Bethe ansatz the results for the averaged length of the Longest Common Subsequence in Bernoulli approximation. In addition, we compute the average number of nucleation centers of the terraces.Comment: 14 pages, 5 figures (some points are clarified

A Structural Model for Vinculin Insertion into PIP 2 -Containing Membranes and the Effect of Insertion on Vinculin Activation and Localization

Vinculin, a scaffolding protein that localizes to focal adhesions (FAs) and adherens junctions, links the actin cytoskeleton to the adhesive super-structure. While vinculin binds to a number of cytoskeletal proteins, it can also associate with phosphatidylinositol 4,5-bisphosphate (PIP2) to drive membrane association. To generate a structural model for PIP2-dependent interaction of vinculin with the lipid bilayer, we conducted lipid-association, nuclear magnetic resonance, and computational modeling experiments. We find that two basic patches on the vinculin tail drive membrane association: the basic collar specifically recognizes PIP2, while the basic ladder drives association with the lipid bilayer. Vinculin mutants with defects in PIP2-dependent liposome association were then expressed in vinculin knockout murine embryonic fibroblasts. Results from these analyses indicate that PIP2 binding is not required for localization of vinculin to FAs or FA strengthening, but is required for vinculin activation and turnover at FAs to promote its association with the force transduction FA nanodomain

Polarized light field under dynamic ocean surfaces: Numerical modeling compared with measurements

As part of the Radiance in a Dynamic Ocean (RaDyO) program, we have developed a numerical model for efficiently simulating the polarized light field under highly dynamic ocean surfaces. Combining the advantages of the three-dimensional Monte Carlo and matrix operator methods, this hybrid model has proven to be computationally effective for simulations involving a dynamic air-sea interface. Given water optical properties and ocean surface wave slopes obtained from RaDyO field measurements, model-simulated radiance and polarization fields under a dynamic surface are found to be qualitatively comparable to their counterparts from field measurements and should be quantitatively comparable if the light field measurement and the wave slope/water optical property measurements are appropriately collocated and synchronized. This model serves as a bridge to connect field measurements of water optical properties, wave slopes and polarized light fields. It can also be used as a powerful yet convenient tool to predict the temporal underwater polarized radiance in a real-world situation. When appropriate surface measurements are available, model simulation is shown to reveal more dynamic features in the underwater light field than direct measurements

Graph Reconstruction via Distance Oracles

We study the problem of reconstructing a hidden graph given access to a distance oracle. We design randomized algorithms for the following problems: reconstruction of a degree bounded graph with query complexity $\tilde{O}(n^{3/2})$; reconstruction of a degree bounded outerplanar graph with query complexity $\tilde{O}(n)$; and near-optimal approximate reconstruction of a general graph

Concerning P450 Evolution: Structural Analyses Support Bacterial Origin of Sterol 14α-Demethylases

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Lamb, D. C., Hargrove, T. Y., Zhao, B., Wawrzak, Z., Goldstone, J. V., Nes, W. D., Kelly, S. L., Waterman, M. R., Stegeman, J. J., & Lepesheva, G. I. Concerning P450 evolution: structural analyses support bacterial origin of sterol 14α-demethylases. Molecular Biology and Evolution, (2020): msaa260, doi:10.1093/molbev/msaa260.Sterol biosynthesis, primarily associated with eukaryotic kingdoms of life, occurs as an abbreviated pathway in the bacterium Methylococcus capsulatus. Sterol 14α-demethylation is an essential step in this pathway and is catalyzed by cytochrome P450 51 (CYP51). In M. capsulatus, the enzyme consists of the P450 domain naturally fused to a ferredoxin domain at the C-terminus (CYP51fx). The structure of M. capsulatus CYP51fx was solved to 2.7 Å resolution and is the first structure of a bacterial sterol biosynthetic enzyme. The structure contained one P450 molecule per asymmetric unit with no electron density seen for ferredoxin. We connect this with the requirement of P450 substrate binding in order to activate productive ferredoxin binding. Further, the structure of the P450 domain with bound detergent (which replaced the substrate upon crystallization) was solved to 2.4 Å resolution. Comparison of these two structures to the CYP51s from human, fungi, and protozoa reveals strict conservation of the overall protein architecture. However, the structure of an “orphan” P450 from nonsterol-producing Mycobacterium tuberculosis that also has CYP51 activity reveals marked differences, suggesting that loss of function in vivo might have led to alterations in the structural constraints. Our results are consistent with the idea that eukaryotic and bacterial CYP51s evolved from a common cenancestor and that early eukaryotes may have recruited CYP51 from a bacterial source. The idea is supported by bioinformatic analysis, revealing the presence of CYP51 genes in >1,000 bacteria from nine different phyla, >50 of them being natural CYP51fx fusion proteins.The study was supported by National Institutes of Health (Grant No. R01 GM067871 to G.I.L.) and by a UK-USA Fulbright Scholarship and the Royal Society (to D.C.L.)