{
  "id": "math/0611119",
  "version": "v2",
  "published": "2006-11-05T16:51:23.000Z",
  "updated": "2010-03-21T18:41:33.000Z",
  "title": "Properties of the Michaelis-Menten Mechanism in Phase Space",
  "authors": [
    "Matt S. Calder",
    "David Siegel"
  ],
  "comment": "29 pages, 8 figures, corrected a few typos and incorporated reviewer suggestions",
  "journal": "J. Math. Anal. Appl. 339 (2008) 1044-1064",
  "doi": "10.1016/j.jmaa.2007.06.078",
  "categories": [
    "math.DS",
    "math.CA"
  ],
  "abstract": "We study the two-dimensional reduction of the Michaelis-Menten reaction of enzyme kinetics. First, we prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Second, we determine the concavity of all solutions in the first quadrant. Third, we establish the asymptotic behaviour of all solutions near the origin, which generally is not given by a Taylor series. Finally, we determine the asymptotic behaviour of the slow manifold at infinity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-21T18:41:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "92C45",
      "34C05",
      "34E05"
    ],
    "keywords": [
      "michaelis-menten mechanism",
      "phase space",
      "slow manifold",
      "properties",
      "asymptotic behaviour"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Mathematical Analysis and Applications",
      "year": 2008,
      "month": "Mar",
      "volume": 339,
      "number": 2,
      "pages": 1044
    },
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JMAA..339.1044C"
    }
  }
}