Should we teach linear algebra through geometry?

AbstractCan geometry help students learn linear algebra? I study this question and demonstrate that there is no obvious clear answer: geometry can be an obstacle to learning linear algebra; or it can be helpful. Geometry is helpful only under certain conditions and with a specific use of drawings. These special requirements for using geometry are apparently not much recognized in our teaching of linear algebra courses, at least in France, where my educational studies have taken place

A new, simple assay for long-chain acyl-CoA dehydrogenase in cultured skin fibroblasts using stable isotopes and GC-MS

In this paper, we present a new method for measurement of long-chain acyl-CoA dehydrogenase (LCAD) activities in cultured skin fibroblasts. The method is based upon gas chromatographic/mass spectrometric determination of 3-OH-hexadecanoic acid formed during incubation of fibroblasts in a medium containing palmitoyl-CoA and crotonase, to convert the enoyl-CoA ester produced into the 3-hydroxyacyl-CoA ester. The validity of the method is demonstrated by the finding of a full deficiency of LCAD in fibroblasts from three patients with an established deficiency of LCAD

Determination of medium chain acyl-CoA dehydrogenase activity in cultured skin fibroblasts using mass spectrometry

Medium chain acyl-CoA dehydrogenase deficiency, a defect of mitochondrial beta-oxidation, is one of the most frequently occurring among inborn errors of metabolism. We describe a rapid and sensitive gas chromatographic/mass spectrometric method allowing reliable assessment of medium chain acyl-CoA dehydrogenase activity in cultured skin fibroblasts. We investigated MCAD activity in three presumed medium chain acyl-CoA dehydrogenase deficient (MCADD) patients and 10 control subjects. The medium chain acyl-CoA dehydrogenase activity determined in three patients was 1.0 +/- 0.4 nmol . min-1 . mg-1 protein (mean +/- SD; range: 0.6-1.4) and in controls it was 2.8 +/- 1.0 nmol . min-1 . mg-1 protein (mean +/- SD; range: 1.6-4.4)

Measurement of short-chain acyl-CoA dehydrogenase (SCAD) in cultured skin fibroblasts with hexanoyl-CoA as a competitive inhibitor to eliminate the contribution of medium-chain acyl-CoA dehydrogenase

Short-chain acyl-CoA dehydrogenase (SCAD) deficiency has so far been reported in only very few patients. This is due, in part, to the problems involved in measuring the activity of SCAD unequivocally. The main reason for this difficulty is that butyryl-CoA, the substrate preferably used for SCAD activity measurements, is also dehydrogenated by medium-chain acyl-CoA dehydrogenase (MCAD). Elimination of this contribution can be achieved by means of immune precipitation with a specific MCAD antibody. We now describe a relatively straightforward assay based on the use of gas chromatography/mass spectrometry for detection. The contribution of MCAD to overall butyryl-CoA dehydrogenation was eliminated by adding excess hexanoyl-CoA to the assay medium. The validity of the method developed was checked by SCAD-activity measurements in fibroblasts from an established SCAD-deficient patien

Type IIIb glycogen storage disease associated with end-stage cirrhosis and hepatocellular carcinoma. The Liver Transplant Group

Type III glycogen storage disease (GSD) is a disorder of carbohydrate metabolism caused by a deficiency of debranching enzyme. Different subtypes with different clinical pictures have been recognized. During childhood and early adulthood, the symptoms generally regress, and normal adulthood appears possible in most patients without symptoms or signs of cirrhosis. We report on an adult patient with GSD who developed endstage cirrhosis and a small hepatocellular carcinoma. She had GSD subtype IIIb, i.e., there were no signs of cardiomyopathy, myopathy, or neuropathy. She underwent a successful transplantation, representing the first case treated this way for this indication to our knowledge, and she is doing well after 1 year. Debranching enzyme activity was absent both in the liver and in the leukocytes before transplantation. The debranching enzyme activity remained absent in the leukocytes after transplantation. We conclude that patients with GSD type III may develop end-stage cirrhosis and hepatocellular carcinoma and therefore need hepatological follow-up during adulthood