Myasthenia gravis (MG) is an autoimmune disorder characterized by a defect in synaptic transmission at the neuromuscular junction causing fluctuating muscle weakness with a decremental response to repetitive nerve stimulation or altered jitter in single-fiber electromyography (EMG). Approximately 80% of all myasthenia gravis patients have autoantibodies against the nicotinic acetylcholine receptor in their serum. Autoantibodies against the tyrosine kinase muscle-specific kinase (MuSK) are responsible for 5-10% of all myasthenia gravis cases. The autoimmune target in the remaining cases is unknown. Recently, low-density lipoprotein receptor-related protein (LRP4) has been identified as the agrin receptor. LRP4 interacts with agrin, and the binding of agrin activates MuSK, which leads to the formation of most if not all postsynaptic specializations, including aggregates containing acetylcholine receptors (AChRs) in the junctional plasma membrane. In the present study we tested if autoantibodies against LRP4 are detectable in patients with myasthenia gravis. To this end we analyzed 13 sera from patients with generalized myasthenia gravis but without antibodies against AChR or MuSK. The results showed that 12 out of 13 antisera from double-seronegative MG patients bound to proteins concentrated at the neuromuscular junction of adult mouse skeletal muscle and that approximately 50% of the tested sera specifically bound to HEK293 cells transfected with human LRP4. Moreover, 4 out of these 13 sera inhibited agrin-induced aggregation of AChRs in cultured myotubes by more than 50%, suggesting a pathogenic role regarding the dysfunction of the neuromuscular endplate. These results indicate that LRP4 is a novel target for autoantibodies and is a diagnostic marker in seronegative MG patients.

Working in a polynomial ring S = k[x1, . . . , xn] where k is an arbitrary commutative ring with 1, we consider the d th Veronese subalgebras R = S (d) , as well as natural R-submodules M = S (≥r,d) inside S. We develop and use characteristic-free theory of Schur functors associated to ribbon skew diagrams as a tool to construct simple GLn(k)-equivariant minimal free R-resolutions for the quotient ring k = R/R+ and for these modules M . These also lead to elegant descriptions of Tor R i (M, M ′ ) for all i and HomR(M, M ′ ) for any pair of these modules M, M ′ .

Given a representation of a finite group G over some commutative base ring k, the cofixed space is the largest quotient of the representation on which the group acts trivially. If G acts by k-algebra automorphisms, then the cofixed space is a module over the ring of G-invariants. When the order of G is not invertible in the base ring, little is known about this module structure. We study the cofixed space in the case that G is the symmetric group on n letters acting on a polynomial ring by permuting its variables. When k has characteristic 0, the cofixed space is isomorphic to an ideal of the ring of symmetric polynomials in n variables. Localizing k at a prime integer p while letting n vary reveals striking behavior in these ideals. As n grows, the ideals stay stable in a sense, then jump in complexity each time n reaches a multiple of p.