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The end-plate species of acetylcholinesterase (AChE) is an asymmetric enzyme consisting of a collagenic tail subunit composed of three collagenic strands (ColQ), each attached to a tetramer of the T isoform of the catalytic subunit (AChE(T)) via a proline-rich attachment domain. The principal function of the tail subunit is to anchor asymmetric AChE in the synaptic basal lamina. Human end-plate AChE deficiency was recently shown to be caused by mutations in COLQ. We here report nine novel COLQ mutations in 7 patients with end-plate AChE deficiency. We examine the effects of the mutations on the assembly of asymmetric AChE by coexpressing each genetically engineered COLQ mutant with ACHE(T) in COS cells. We classify the newly recognized and previously reported COLQ mutations into four classes according to their position in ColQ and their effect on AChE expression. We find that missense mutations in the proline-rich attachment domain abrogate attachment of catalytic subunits, that truncation mutations in the ColQ collagen domain prevent the assembly of asymmetric AChE, that hydrophobic missense residues in the C-terminal domain prevent triple helical assembly of the ColQ collagen domain, and that other mutations in the C-terminal region produce asymmetric species of AChE that are likely insertion incompetent.

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Abstract. We present a computational approach for finding all integral solutions of the equation y 2 = 1 k + 2 k + · · · + x k for even values of k. By reducing this problem to that of finding integral solutions of a certain class of quartic equations closely related to the Pell equations, we are able to apply the powerful computational machinery related to quadratic number fields. Using our approach, we determine all integral solutions for 2 ≤ k ≤ 70 assuming the Generalized Riemann Hypothesis, and for 2 ≤ k ≤ 58 unconditionally.