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The acid-unfolded state of equine beta-lactoglobulin was characterized by means of circular dichroism, nuclear magnetic resonance, analytical gel-filtration chromatography, and analytical centrifugation. The acid-unfolded state of equine beta-lactoglobulin has a substantial secondary structure as shown by the far-ultraviolet circular dichroism spectrum but lacks persistent tertiary packing of the side chains as indicated by the near-ultraviolet circular dichroism and nuclear magnetic resonance spectra. It is nearly as compact as the native conformation as shown by the gel filtration and sedimentation experiments, and it has the exposed hydrophobic surface as indicated by its tendency to aggregate. All of these characteristics indicate that the acid-unfolded state of equine beta-lactoglobulin is a molten globule state. The alpha helix content in the acid-unfolded state, which has been estimated from the circular dichroism spectrum, is larger than that in the native state, suggesting the presence of nonnative alpha helices in the molten globule state. This result suggests the generality of the intermediate with nonnative alpha helices during the folding of proteins having the beta-clam fold.

The purpose of this paper is to give a q-analogue of Kostant's weight multiplicity formula for irreducible representations of complex semisimple Lie algebras, conjectured by Lusztig [6] quite recently. To prove this, we use the theory of spherical functions on p-adic groups (or on Hecke algebras) developed by Satake, Macdonald et al. extensively. In the course of the proof of the above result, we give a short proof of the theorem of Lusztig [6] which describes the weight multiplicities in terms of intersection homology (or Kazhdan-Lusztig polynomials Py, w).

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