Probes bound to myosin Cys-707 rotate during length transients in contraction

It is widely conjectured that muscle shortens because portions of myosin molecules (the “cross-bridges”) impel the actin filament to which they transiently attach and that the impulses result from rotation of the cross-bridges. Crystallography indicates that a cross-bridge is articulated–consisting of a globular catalytic/actin-binding domain and a long lever arm that may rotate. Conveniently, a rhodamine probe with detectable attitude can be attached between the globular domain and the lever arm, enabling the observer to tell whether the anchoring region rotates. Well-established signature effects observed in shortening are tension changes resulting from the sudden release or quick stretch of active muscle fibers. In this investigation we found that closely correlated with such tension changes are changes in the attitude of the rhodamine probes. This correlation strongly supports the conjecture about how shortening is achieved.

Regular and stochastic dynamics in the real quadratic family

We prove the Regulat or Stochastic Conjecture for the real quadratic family which asserts that almost every real quadratic map Pc, c ∈ [−2, 1/4], has either an attracting cycle or an absolutely continuous invariant measure.

The α1 domain of HLA-G1 and HLA-G2 inhibits cytotoxicity induced by natural killer cells: Is HLA-G the public ligand for natural killer cell inhibitory receptors?

We have investigated the protective role of the membrane-bound HLA-G1 and HLA-G2 isoforms against natural killer (NK) cell cytotoxicity. For this purpose, HLA-G1 and HLA-G2 cDNAs were transfected into the HLA class I-negative human K562 cell line, a known reference target for NK lysis. The HLA-G1 protein, encoded by a full-length mRNA, presents a structure similar to that of classical HLA class I antigens. The HLA-G2 protein, deduced from an alternatively spliced transcript, consists of the α1 domain linked to the α3 domain. In this study we demonstrate that (i) HLA-G2 is present at the cell surface as a truncated class I molecule associated with β2-microglobulin; (ii) NK cytolysis, observed in peripheral blood mononuclear cells and in polyclonal CD3− CD16+ CD56+ NK cells obtained from 20 donors, is inhibited by both HLA-G1 and HLA-G2; this HLA-G-mediated inhibition is reversed by blocking HLA-G with a specific mAb; this led us to the conjecture that HLA-G is the public ligand for NK inhibitory receptors (NKIR) present in all individuals; (iii) the α1 domain common to HLA-G1 and HLA-G2 could mediate this protection from NK lysis; and (iv) when transfected into the K562 cell line, both HLA-G1 and HLA-G2 abolish lysis by the T cell leukemia NK-like YT2C2 clone due to interaction between the HLA-G isoform on the target cell surface and a membrane receptor on YT2C2. Because NKIR1 and NKIR2, known to interact with HLA-G, were undetectable on YT2C2, we conclude that a yet-unknown specific receptor for HLA-G1 and HLA-G2 is present on these cells.

A “midinfrared” scenario for cuprate superconductivity

I conjecture that the mechanism of superconductivity in the cuprates is a saving, due to the improved screening resulting from Cooper pair formation, of the part of the Coulomb energy associated with long wavelengths and midinfrared frequencies. This scenario is shown to provide a plausible explanation of the trend of transition temperature with layering structure in the Ca-spaced compounds and to predict a spectacularly large decrease in the electron-energy-loss spectroscopy cross-section in the midinfrared region on transition to the superconducting state, as well as less spectacular but still surprisingly large changes in the optical behavior. Existing experimental results appear to be consistent with this picture.

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.

Adjoint modular Galois representations and their Selmer groups

In the last 15 years, many class number formulas and main conjectures have been proven. Here, we discuss such formulas on the Selmer groups of the three-dimensional adjoint representation ad(φ) of a two-dimensional modular Galois representation φ. We start with the p-adic Galois representation φ0 of a modular elliptic curve E and present a formula expressing in terms of L(1, ad(φ0)) the intersection number of the elliptic curve E and the complementary abelian variety inside the Jacobian of the modular curve. Then we explain how one can deduce a formula for the order of the Selmer group Sel(ad(φ0)) from the proof of Wiles of the Shimura–Taniyama conjecture. After that, we generalize the formula in an Iwasawa theoretic setting of one and two variables. Here the first variable, T, is the weight variable of the universal p-ordinary Hecke algebra, and the second variable is the cyclotomic variable S. In the one-variable case, we let φ denote the p-ordinary Galois representation with values in GL2(Zp[[T]]) lifting φ0, and the characteristic power series of the Selmer group Sel(ad(φ)) is given by a p-adic L-function interpolating L(1, ad(φk)) for weight k + 2 specialization φk of φ. In the two-variable case, we state a main conjecture on the characteristic power series in Zp[[T, S]] of Sel(ad(φ) ⊗ ν−1), where ν is the universal cyclotomic character with values in Zp[[S]]. Finally, we describe our recent results toward the proof of the conjecture and a possible strategy of proving the main conjecture using p-adic Siegel modular forms.

The structure of Selmer groups

The purpose of this article is to describe certain results and conjectures concerning the structure of Galois cohomology groups and Selmer groups, especially for abelian varieties. These results are analogues of a classical theorem of Iwasawa. We formulate a very general version of the Weak Leopoldt Conjecture. One consequence of this conjecture is the nonexistence of proper Λ-submodules of finite index in a certain Galois cohomology group. Under certain hypotheses, one can prove the nonexistence of proper Λ-submodules of finite index in Selmer groups. An example shows that some hypotheses are needed.

On degree 2 Galois representations over

We discuss proofs of some new special cases of Serre’s conjecture on odd, degree 2 representations of Gℚ.

Dynamic friction and the origin of the complexity of earthquake sources.

We study a simple antiplane fault of finite length embedded in a homogeneous isotropic elastic solid to understand the origin of seismic source heterogeneity in the presence of nonlinear rate- and state-dependent friction. All the mechanical properties of the medium and friction are assumed homogeneous. Friction includes a characteristic length that is longer than the grid size so that our models have a well-defined continuum limit. Starting from a heterogeneous initial stress distribution, we apply a slowly increasing uniform stress load far from the fault and we simulate the seismicity for a few 1000 events. The style of seismicity produced by this model is determined by a control parameter associated with the degree of rate dependence of friction. For classical friction models with rate-independent friction, no complexity appears and seismicity is perfectly periodic. For weakly rate-dependent friction, large ruptures are still periodic, but small seismicity becomes increasingly nonstationary. When friction is highly rate-dependent, seismicity becomes nonperiodic and ruptures of all sizes occur inside the fault. Highly rate-dependent friction destabilizes the healing process producing premature healing of slip and partial stress drop. Partial stress drop produces large variations in the state of stress that in turn produce earthquakes of different sizes. Similar results have been found by other authors using the Burridge and Knopoff model. We conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity.

Seven newly discovered intron positions in the triose-phosphate isomerase gene: evidence for the introns-late theory.

The gene encoding the glycolytic enzyme triose-phosphate isomerase (TPI; EC 5.3.1.1) has been central to the long-standing controversy on the origin and evolutionary significance of spliceosomal introns by virtue of its pivotal support for the introns-early view, or exon theory of genes. Putative correlations between intron positions and TPI protein structure have led to the conjecture that the gene was assembled by exon shuffling, and five TPI intron positions are old by the criterion of being conserved between animals and plants. We have sequenced TPI genes from three diverse eukaryotes--the basidiomycete Coprinus cinereus, the nematode Caenorhabditis elegans, and the insect Heliothis virescens--and have found introns at seven novel positions that disrupt previously recognized gene/protein structure correlations. The set of 21 TPI introns now known is consistent with a random model of intron insertion. Twelve of the 21 TPI introns appear to be of recent origin since each is present in but a single examined species. These results, together with their implication that as more TPI genes are sequenced more intron positions will be found, render TPI untenable as a paradigm for the introns-early theory and, instead, support the introns-late view that spliceosomal introns have been inserted into preexisting genes during eukaryotic evolution.