Patch-clamp and amperometric recordings from norepinephrine transporters: Channel activity and voltage-dependent uptake

Transporters for the biogenic amines dopamine, norepinephrine, epinephrine and serotonin are largely responsible for transmitter inactivation after release. They also serve as high-affinity targets for a number of clinically relevant psychoactive agents, including antidepressants, cocaine, and amphetamines. Despite their prominent role in neurotransmitter inactivation and drug responses, we lack a clear understanding of the permeation pathway or regulation mechanisms at the single transporter level. The resolution of radiotracer-based flux techniques limits the opportunities to dissect these problems. Here we combine patch-clamp recording techniques with microamperometry to record the transporter-mediated flux of norepinephrine across isolated membrane patches. These data reveal voltage-dependent norepinephrine flux that correlates temporally with antidepressant-sensitive transporter currents in the same patch. Furthermore, we resolve unitary flux events linked with bursts of transporter channel openings. These findings indicate that norepinephrine transporters are capable of transporting neurotransmitter across the membrane in discrete shots containing hundreds of molecules. Amperometry is used widely to study neurotransmitter distribution and kinetics in the nervous system and to detect transmitter release during vesicular exocytosis. Of interest regarding the present application is the use of amperometry on inside-out patches with synchronous recording of flux and current. Thus, our results further demonstrate a powerful method to assess transporter function and regulation.

Voltage-induced membrane displacement in patch pipettes activates mechanosensitive channels

The patch-clamp technique allows currents to be recorded through single ion channels in patches of cell membrane in the tips of glass pipettes. When recording, voltage is typically applied across the membrane patch to drive ions through open channels and to probe the voltage-sensitivity of channel activity. In this study, we used video microscopy and single-channel recording to show that prolonged depolarization of a membrane patch in borosilicate pipettes results in delayed slow displacement of the membrane into the pipette and that this displacement is associated with the activation of mechanosensitive (MS) channels in the same patch. The membrane displacement, ≈1 μm with each prolonged depolarization, occurs after variable delays ranging from tens of milliseconds to many seconds and is correlated in time with activation of MS channels. Increasing the voltage step shortens both the delay to membrane displacement and the delay to activation. Preventing depolarization-induced membrane displacement by applying positive pressure to the shank of the pipette or by coating the tips of the borosilicate pipettes with soft glass prevents the depolarization-induced activation of MS channels. The correlation between depolarization-induced membrane displacement and activation of MS channels indicates that the membrane displacement is associated with sufficient membrane tension to activate MS channels. Because membrane tension can modulate the activity of various ligand and voltage-activated ion channels as well as some transporters, an apparent voltage dependence of a channel or transporter in a membrane patch in a borosilicate pipette may result from voltage-induced tension rather than from direct modulation by voltage.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Twist fields, the elliptic genus, and hidden symmetry

We combine infinite dimensional analysis (in particular a priori estimates and twist positivity) with classical geometric structures, supersymmetry, and noncommutative geometry. We establish the existence of a family of examples of two-dimensional, twist quantum fields. We evaluate the elliptic genus in these examples. We demonstrate a hidden SL(2,ℤ) symmetry of the elliptic genus, as suggested by Witten.

Parametrizations of elliptic curves by Shimura curves and by classical modular curves

Fix an isogeny class

Euler characteristics and elliptic curves

Let E be a modular elliptic curve over ℚ, without complex multiplication; let p be a prime number where E has good ordinary reduction; and let F∞ be the field obtained by adjoining to ℚ all p-power division points on E. Write G∞ for the Galois group of F∞ over ℚ. Assume that the complex L-series of E over ℚ does not vanish at s = 1. If p ⩾ 5, we make a precise conjecture about the value of the G∞-Euler characteristic of the Selmer group of E over F∞. If one makes a standard conjecture about the behavior of this Selmer group as a module over the Iwasawa algebra, we are able to prove our conjecture. The crucial local calculations in the proof depend on recent joint work of the first author with R. Greenberg.

Mutagenesis in the C-terminal region of human interleukin 5 reveals a central patch for receptor alpha chain recognition.

Cassette mutagenesis was used to identify side chains in human interleukin 5 (hIL-5) that mediate binding to hIL-5 receptor alpha chain (hIL-5R alpha). A series of single alanine substitutions was introduced into a stretch of residues in the C-terminal region, including helix D, which previously had been implicated in receptor alpha chain recognition and which is aligned on the IL-5 surface so as to allow the topography of receptor binding residues to be examined. hIL-5 and single site mutants were expressed in COS cells, their interactions with hIL-5R alpha were measured by a sandwich surface plasmon resonance biosensor method, and their biological activities were measured by an IL-5-dependent cell proliferation assay. A pattern of mutagenesis effects was observed, with greatest impact near the interface between the two four-helix bundles of IL-5, in particular at residues Glu-110 and Trp-111, and least at the distal ends of the D helices. This pattern suggests the possibility that residues near the interface of the two four-helix bundles in hIL-5 comprise a central patch or hot spot, which constitutes an energetically important alpha chain recognition site. This hypothesis suggests a structural explanation for the 1:1 stoichiometry observed for the complex of hIL-5 with hIL-5R alpha.