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The human neurotensin receptor 1 (NTSR1) is a G protein-coupled receptor. The receptor is activated by a small peptide ligand neurotensin. NTSR1 can be expressed in HEK cells by stable transfection. Previously we used the fluorescent protein markers mRuby3 or mNeonGreen fused to NTSR1 for EMCCD-based structured illumination microscopy (SIM) in living HEK cells. Ligand binding induced conformational changes in NTSR1 which triggered the intracellular signaling processes. Recent single-molecule studies revealed a dynamic monomer/dimer equilibrium of this receptor in artificial lipid bilayers. Here we report on the oligomerization state of human NTSR1 from living cells by trapping them into lipid nanodiscs. Briefly, SMALPs (styrene-maleic acid copolymer lipid nanoparticles) were produced directly from the plasma membranes of living HEK293T FlpIn cells. SMALPs with a diameter of 15 nm were soluble and stable. NTSR1 in SMALPs were analyzed by single-molecule intensity measurements one membrane patch at a time using a custom-built confocal anti-Brownian electrokinetic trap (ABEL trap) microscope. We found oligomerization changes before and after stimulation of the receptor with its ligand neurotensin., Comment: 13 pages, 4 figures

We calculate the singular instanton homology with local coefficients for the simplest n-strand braids in $S^1 \times S^2$ for all odd n, describing these homology groups and their module structures in terms of the coordinate rings of explicit algebraic curves. The calculation is expected to be equivalent to computing the quantum cohomology ring of a certain Fano variety, namely a moduli space of stable parabolic bundles on a sphere with n marked points., Comment: 88 pages, 5 figures

Ruberman gave the first examples of self-diffeomorphisms of four-manifolds that are isotopic to the identity in the topological category but not smoothly so. We give another example of this phenomenon, using the Dehn twist along a 3-sphere in the connected sum of two K3 surfaces., Comment: 15 pages. Corrected with additional remarks about prior work in the higher-dimensional case

Concordance invariants of knots are derived from the instanton homology groups with local coefficients, as introduced in earlier work of the authors. These concordance invariants include a 1-parameter family of homomorphisms $f_{r}$, from the knot concordance group to the reals. Prima facie, these concordance invariants have the potential to provide independent bounds on the genus and number of double points for immersed surfaces with boundary a given knot., Comment: This paper, together with a companion paper "Instantons and Bar-Natan homology", supersedes the authors' earlier preprint, "Instantons, Bar-Natan homology and some concordance invariants of knots"

A spectral sequence is established, whose $E_{2}$ page is Bar-Natan's variant of Khovanov homology and which abuts to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence whose $E_{2}$ page is a characteristic-2 version of $F_{5}$ homology, in Khovanov's classification., Comment: 60 pages. This paper, together with a companion, supersedes the authors' earlier preprint "Instantons, Bar-Natan homology and some concordance invariants of knots" (arXiv:1905.00828)

A spectral sequence is established, from Bar-Natan's variant of Khovanov homology to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence from a characteristic-2 version of $F_5$ homology, in Khovanov'sclassification. Concordance invariants of knots are derived from the corresponding instanton homology groups, including a 1-parameter family of homomorphisms $f_r$ from the concordance group to the reals, having the potential to provide independent bounds on the genus and number of double points for immersed surfaces with boundary a given knot., Comment: This paper has been withdrawn as its content is superseded by two more recent papers. The newer papers are arXiv:1910.11128 and arXiv:1910.11129, which separately treat the previous material relating instanton homology to Bar-Natan homology, and concordance invariants respectively

G protein-coupled receptors (GPCRs) are a large superfamily of membrane proteins that are activated by extracellular small molecules or photons. Neurotensin receptor 1 (NTSR1) is a GPCR that is activated by neurotensin, i.e. a 13 amino acid peptide. Binding of neurotensin induces conformational changes in the receptor that trigger the intracellular signaling processes. While recent single-molecule studies have reported a dynamic monomer - dimer equilibrium of NTSR1 in vitro, a biophysical characterization of the oligomerization status of NTSR1 in living mammalian cells is complicated. Here we report on the oligomerization state of the human NTSR1 tagged with mRuby3 by dissolving the plasma membranes of living HEK293T cells into 10 nm-sized soluble lipid nanoparticles by addition of styrene-maleic acid copolymers (SMALPs). Single SMALPs were analyzed one after another in solution by multi-parameter single molecule spectroscopy including brightness, fluorescence lifetime and anisotropy for homoFRET. Brightness analysis was improved using single SMALP detection in a confocal ABELtrap for extended observation times in solution. A bimodal brightness distribution indicated a significant fraction of dimeric NTSR1 in SMALPs or in the plasma membrane, respectively, before addition of neurotensin., Comment: 12 pages, 6 figures

The human neurotensin receptor 1 (NTSR1) is a G protein-coupled receptor that can be expressed in HEK293T cells by stable transfection. Its ligand is a 13-amino-acid peptide that binds with nanomolar affinity from the extracellular side to NTSR1. Ligand binding induces conformational changes that trigger the intracellular signaling processes. Recent single-molecule studies revealed a dynamic monomer - dimer equilibrium of the receptor in vitro. Here we report on the oligomerization state of the human NTSR1 in the plasma membrane of HEK293T cells in vivo. We fused different fluorescent marker proteins mRuby3 or mNeonGreen to the C-terminus of NTSR1 and mutated a tetracysteine motif into intracellular loop 3 (ICL3) for subsequent FlAsH labeling. Oligomerization of NTSR1 was monitored before and after stimulation of the receptor with its ligand by FLIM and homoFRET microscopy (i.e. Forster resonance energy transfer between identical fluorophores detected by fluorescence anisotropy), by colocalization microscopy and by time-lapse imaging using structured illumination microscopy (SIM)., Comment: 12 pages, 5 figures

A deformation of the authors' instanton homology for webs is constructed by introducing a local system of coefficients. In the case that the web is planar, the rank of the deformed instanton homology is equal to the number of Tait colorings of the web., Comment: 48 pages, 6 figures

Cytochrome C oxidase and FoF1-ATP synthase constitute complex IV and V, respectively, of the five membrane-bound enzymes in mitochondria comprising the respiratory chain. These enzymes are located in the inner mitochondrial membrane (IMM), which exhibits large invaginations called cristae. According to recent cryo-tomography, FoF1-ATP synthases are located predominantly at the rim of the cristae, while cytochrome C oxidases are likely distributed in planar membrane areas of the cristae. Previous FLIM measurements (K. Busch and coworkers) of complex II and III unravelled differences in the local environment of the membrane enzymes in the cristae. Here, we tagged complex IV and V with mNeonGreen and investigated their mitochondrial nano-environment by FLIM and superresolution microscopy in living human cells. Different lifetimes and anisotropy values were found and will be discussed., Comment: 14 pages, 5 figures

The SO(3) instanton homology recently introduced by the authors associates a finite-dimensional vector space over the field of two elements to every embedded trivalent graph (or "web"). The present paper establishes a skein exact triangle for this instanton homology, as well as a realization of the octahedral axiom. From the octahedral diagram, one can derive equivalent reformulations of the authors' conjecture that, for planar webs, the rank of the instanton homology is equal to the number of Tait colorings.

We use SO(3) gauge theory to define a functor from a category of unoriented webs and foams to the category of finite-dimensional vector spaces over the field of two elements. We prove a non-vanishing theorem for this SO(3) instanton homology of webs, using Gabai's sutured manifold theory. It is hoped that the non-vanishing theorem may support a program to provide a new proof of the four-color theorem.

We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover X' \to X. The completion of this complex in exponentially weighted L^2-norms is Fredholm for all but finitely many exceptional weights determined by the eigenvalues of the covering translation map H_*(X') \to H_*(X'). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones.

A previous paper of the authors' contained an error in the proof of a key claim, that Rasmussen's knot-invariant s(K) is equal to its gauge-theory counterpart. The original paper is included here together with a corrigendum, indicating which parts still stand and which do not. In particular, the gauge-theory counterpart of s(K) is not additive for connected sums., Comment: This version bundles the original submission with a 1-page corrigendum, indicating the error. The new version of the corrigendum points out that the invariant is not additive for connected sums. 23 pages, 3 figures

In earlier work of the authors, the Khovanov complex of a knot or link appeared as the first page in a spectral sequence abutting to the instanton homology. The quantum and (co)homological gradings on Khovanov homology do not survive as gradings, but we show that they survive as filtrations., Comment: 40 pages, 4 figures. Revised version, with corrected typos and extended introduction

We extend the Atiyah, Patodi, and Singer index theorem for first order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes' Fredholm theory for general end-periodic operators. Our index theorem is expressed in terms of a new periodic eta-invariant that equals the Atiyah-Patodi-Singer eta-invariant in the cylindrical setting. We apply this periodic eta-invariant to the study of moduli spaces of Riemannian metrics of positive scalar curvature., Comment: 72 pages; extended and expanded from earlier versions. Introduction of twisted eta invariants with applications to moduli of metrics of positive scalar curvature

We show that instanton knot homology is mutation-invariant, as a consequence of earlier work of the third author., Comment: This paper has been withdrawn

We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is isomorphic to the instanton Floer homology of the sutured knot complement: an invariant that is already known to detect the unknot., Comment: 124 pages, 13 figures

We examine the $L^2$-topology of the gauge orbits over a closed Riemann surface. We prove a subtle local slice theorem based on the div-curl Lemma of harmonic analysis, and deduce local pathwise connectedness and local uniform quasiconvexity of the gauge orbits. Using these, we generalize compactness results for anti-self-dual instantons with Lagrangian boundary counditions to general gauge invariant Lagrangian submanifolds. This provides the foundation for the construction of instanton Floer homology for pairs of a $3$-manifold with boundary and a Lagrangian in the configuration space over the boundary.

Organic scintillators are widely used for fast neutron detection and spectroscopy. Several effects complicate the interpretation of results from detectors based upon these materials. First, fast neutrons will often leave a detector before depositing all of their energy within it. Second, fast neutrons will typically scatter several times within a detector, and there is a non-proportional relationship between the energy of, and the scintillation light produced by, each individual scatter; therefore, there is not a deterministic relationship between the scintillation light observed and the neutron energy deposited. Here we demonstrate a hardware technique for reducing both of these effects. Use of a segmented detector allows for the event-by-event correction of the light yield non-proportionality and for the preferential selection of events with near-complete energy deposition, since these will typically have high segment multiplicities., Comment: Accepted for publication in Nuclear Instruments and Methods in Physics Research Section A

The instanton Floer homology of a knot in the three-sphere is a vector space with a canonical mod 2 grading. It carries a distinguished endomorphism of even degree,arising from the 2-dimensional homology class represented by a Seifert surface. The Floer homology decomposes as a direct sum of the generalized eigenspaces of this endomorphism. We show that the Euler characteristics of these generalized eigenspaces are the coefficients of the Alexander polynomial of the knot. Among other applications, we deduce that instanton homology detects fibered knots., Comment: 25 pages, 6 figures. Revised version, correcting errors concerning mod 2 gradings in the skein sequence

We introduce a gauge-theoretic integer lift of the Rohlin invariant of a smooth 4-manifold X with the homology of $S^1 \times S^3$. The invariant has two terms; one is a count of solutions to the Seiberg-Witten equations on X, and the other is essentially the index of the Dirac operator on a non-compact manifold with end modeled on the infinite cyclic cover of X. Each term is metric (and perturbation) dependent, and we show that these dependencies cancel as the metric and perturbation vary in a 1-parameter family., Comment: Revision after referee report; section on negative definite manifolds revised. To appear in JDG

We develop monopole and instanton Floer homology groups for balanced sutured manifolds. Applications include a new proof of Property P for knots., Comment: 71 pages, 9 figures

For each partial flag manifold of SU(N), we define a Floer homology theory for knots in 3-manifolds, using instantons with codimension-2 singularities., Comment: 118 pages, 1 figure. v2: Further acknowledgements

We report on the experimental observation of an anomalous Hall effect (AHE) in highly oriented pyrolytic graphite samples. The overall data indicate that the AHE in graphite can be self-consistently understood within the frameworks of the magnetic-field-driven excitonic pairing models., Comment: 13 pages including 4 figures

We prove a generalization of Bennequin's inequality for Legendrian knots in a 3-dimensional contact manifold (Y,xi), under the assumption that Y is the boundary of a 4-dimensional manifold M and the version of Seiberg-Witten invariants introduced by Kronheimer and Mrowka [Invent. Math. 130 (1997) 209-255] is nonvanishing. The proof requires an excision result for Seiberg-Witten moduli spaces; then the Bennequin inequality becomes a special case of the adjunction inequality for surfaces lying inside M., Comment: This is the version published by Algebraic & Geometric Topology on 24 February 2006

Let K be a non-trivial knot in the 3-sphere and let Y(r) be the 3-manifold obtained by surgery on K with surgery-coefficient a rational number r. We show that there is a homomorphism from the fundamental group of Y(r) to SU(2) with non-cyclic image if r is less than or equal to 2., Comment: 15 pages