{"id":3310,"date":"2021-10-12T13:00:56","date_gmt":"2021-10-12T04:00:56","guid":{"rendered":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/?p=3310"},"modified":"2026-01-06T09:42:48","modified_gmt":"2026-01-06T00:42:48","slug":"%e8%a7%a3%e9%9b%a2%e5%ae%9a%e6%95%b0%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e3%81%ae%e3%81%abscatchard-plot%e3%82%92%e4%bd%bf%e3%81%86%e3%81%b9%e3%81%8d%e3%81%a7%e3%81%af%e3%81%aa%e3%81%84%e3%81%a8","status":"publish","type":"post","link":"https:\/\/www.ag.kagawa-u.ac.jp\/charlesy\/2021\/10\/12\/%e8%a7%a3%e9%9b%a2%e5%ae%9a%e6%95%b0%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e3%81%ae%e3%81%abscatchard-plot%e3%82%92%e4%bd%bf%e3%81%86%e3%81%b9%e3%81%8d%e3%81%a7%e3%81%af%e3%81%aa%e3%81%84%e3%81%a8\/","title":{"rendered":"\u89e3\u96e2\u5b9a\u6570\u3092\u6c42\u3081\u308b\u306e\u306bScatchard plot\u3092\u4f7f\u3046\u3079\u304d\u3067\u306f\u306a\u3044\u3068\u3044\u3046\u8a71"},"content":{"rendered":"\n\n\n\n

\u975e\u7dda\u5f62\u306e\u5f0f\u3092\u5909\u5f62\u3057\u3066\u3001\u7dda\u5f62\u56de\u5e30\u3092\u9069\u7528\u3059\u308b\u306e\u306f\u3084\u3063\u3066\u306f\u3044\u3051\u306a\u3044\u3068\u3044\u3046\u8a71\u306f\u6614\u304b\u3089\u77e5\u3089\u308c\u3066\u3044\u308b\u3068\u601d\u3044\u307e\u3059\u3002\u975e\u7dda\u5f62\u306e\u5f0f\u3092\u3001\u7dda\u5f62\u306b\u5909\u63db\u3057\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u306b\u306f\u3001\u30ea\u30ac\u30f3\u30c9\u7d50\u5408\u8a66\u9a13\u306b\u304a\u3051\u308bScatchard\uff08\u30b9\u30ad\u30e3\u30c3\u30c1\u30e3\u30fc\u30c9\uff09plot\u3001\u9175\u7d20\u53cd\u5fdc\u901f\u5ea6\u8ad6\u306b\u304a\u3051\u308bLineweaver\u2013Burk\uff08\u30e9\u30a4\u30f3\u30a6\u30a3\u30fc\u30d0\u30fc\u30fb\u30d0\u30fc\u30af\uff09plot\u3001Eadie-Hofstee\uff08\u30a4\u30fc\u30c7\u30a3\u30fc\u30fb\u30db\u30d5\u30b9\u30c6\u30fc\uff09plot\u3001Hanes\u2013Woolf\uff08\u30d8\u30a4\u30f3\u30ba\u30fb\u30a6\u30eb\u30d5\uff09plot\u304c\u3042\u308a\u307e\u3059\u3002\u4eca\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u65b9\u6cd5\u306f\u306f\u308b\u304b\u306b\u6b63\u78ba\u306a\uff08\u304b\u3064\u7c21\u5358\u306b\u5229\u7528\u53ef\u80fd\u306b\u306a\u3063\u305f\uff09\u975e\u7dda\u5f62\u56de\u5e30\u306b\u7f6e\u304d\u63db\u3048\u3089\u308c\u3066\u304a\u308a\u3001\u30c7\u30fc\u30bf\u306e\u8996\u899a\u5316\u76ee\u7684\u4ee5\u5916\u3067\u306f\u4f7f\u7528\u3059\u308b\u3079\u304d\u3067\u306f\u306a\u3044\u3068\u3055\u308c\u3066\u3044\u307e\u3059\uff08\u81ea\u5206\u306e\u5352\u8ad6\u3067\u306f\u3001\u8a73\u3057\u304f\u306a\u304b\u3063\u305f\u306e\u3067\u3001Hanes\u2013Woolf\u30d7\u30ed\u30c3\u30c8\u304b\u3089\u9175\u7d20\u53cd\u5fdc\u306eK<\/em>m<\/sub>\u3068V<\/em>max<\/sub>\u3092\u6c42\u3081\u3066\u3044\u307e\u3057\u305f\uff09\u3002<\/p>\n\n\n\n

\n

Avoid Scatchard, Lineweaver-Burke and similar transforms<\/strong><\/p>\n\n\n\n

Before nonlinear regression was readily available, the best way to analyze nonlinear data was to transform the data to create a linear graph, and then analyze the transformed data with linear regression. Examples include Lineweaver-Burke plots of enzyme kinetic data, Scatchard plots of binding data, and logarithmic plots of kinetic data. These methods are outdated, and should not be used to analyze data.<\/p>\n\n\n\n

The problem with these methods is that the transformation distorts the experimental error. Linear regression assumes that the scatter of points around the line follows a Gaussian distribution and that the standard deviation is the same at every value of X. These assumptions are rarely true after transforming data. Furthermore, some transformations alter the relationship between X and Y. For example, in a Scatchard plot the value of X (bound) is used to calculate Y (bound\/free), and this violates the assumption of linear regression that all uncertainty is in Y while X is known precisely. It doesn’t make sense to minimize the sum of squares of the vertical distances of points from the line, if the same experimental error appears in both X and Y directions.<\/p>\n\n\n\n

\u975e\u7dda\u5f62\u56de\u5e30\u304c\u624b\u8efd\u306b\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u4ee5\u524d\u306f\u3001\u975e\u7dda\u5f62\u30c7\u30fc\u30bf\u3092\u89e3\u6790\u3059\u308b\u6700\u826f\u306e\u65b9\u6cd5\u306f\u3001\u30c7\u30fc\u30bf\u3092\u5909\u63db\u3057\u3066\u76f4\u7dda\u306e\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3057\u3001\u305d\u306e\u5909\u63db\u3055\u308c\u305f\u30c7\u30fc\u30bf\u3092\u7dda\u5f62\u56de\u5e30\u3067\u89e3\u6790\u3059\u308b\u3053\u3068\u3067\u3057\u305f\u3002\u305d\u306e\u4f8b\u3068\u3057\u3066\u306f\u3001\u9175\u7d20\u53cd\u5fdc\u901f\u5ea6\u30c7\u30fc\u30bf\u306e\u30e9\u30a4\u30f3\u30a6\u30a3\u30fc\u30d0\u30fc\u30fb\u30d0\u30fc\u30af\u30d7\u30ed\u30c3\u30c8\u3001\u7d50\u5408\u30c7\u30fc\u30bf\u306e\u30b9\u30ad\u30e3\u30c3\u30c1\u30e3\u30fc\u30c9\u30d7\u30ed\u30c3\u30c8\u3001\u53cd\u5fdc\u901f\u5ea6\u30c7\u30fc\u30bf\u306e\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8\u306a\u3069\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u65b9\u6cd5\u306f\u6642\u4ee3\u9045\u308c\u3067\u3042\u308a\u3001\u30c7\u30fc\u30bf\u89e3\u6790\u306b\u4f7f\u7528\u3059\u3079\u304d\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n

\u3053\u308c\u3089\u306e\u65b9\u6cd5\u306e\u554f\u984c\u70b9\u306f\u3001\u5909\u63db\u306b\u3088\u3063\u3066\u5b9f\u9a13\u8aa4\u5dee\u304c\u6b6a\u3081\u3089\u308c\u3066\u3057\u307e\u3046\u3053\u3068\u3067\u3059\u3002\u7dda\u5f62\u56de\u5e30\u306f\u3001\u76f4\u7dda\u306e\u5468\u56f2\u306b\u304a\u3051\u308b\u70b9\u306e\u3070\u3089\u3064\u304d\u304c\u30ac\u30a6\u30b9\u5206\u5e03\u306b\u5f93\u3046\u3053\u3068\u3001\u305d\u3057\u3066X\u306e\u3059\u3079\u3066\u306e\u5024\u306b\u304a\u3044\u3066\u6a19\u6e96\u504f\u5dee\u304c\u540c\u3058\u3067\u3042\u308b\u3053\u3068\u3092\u4eee\u5b9a\u3057\u3066\u3044\u307e\u3059\u3002\u30c7\u30fc\u30bf\u3092\u5909\u63db\u3057\u305f\u5f8c\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u4eee\u5b9a\u304c\u6210\u7acb\u3059\u308b\u3053\u3068\u306f\u3081\u3063\u305f\u306b\u3042\u308a\u307e\u305b\u3093\u3002\u3055\u3089\u306b\u3001\u5909\u63db\u306e\u4e2d\u306b\u306fX\u3068Y\u306e\u95a2\u4fc2\u3092\u5909\u3048\u3066\u3057\u307e\u3046\u3082\u306e\u3082\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30b9\u30ad\u30e3\u30c3\u30c1\u30e3\u30fc\u30c9\u30d7\u30ed\u30c3\u30c8\u3067\u306fX\u306e\u5024\uff08\u7d50\u5408\u91cf\uff09\u3092\u7528\u3044\u3066Y\u306e\u5024\uff08\u7d50\u5408\u91cf\uff0f\u904a\u96e2\u91cf\uff09\u3092\u7b97\u51fa\u3059\u308b\u305f\u3081\u3001\u3053\u308c\u306f\u300c\u3059\u3079\u3066\u306e\u4e0d\u78ba\u5b9f\u6027\u306fY\u306b\u3042\u308a\u3001X\u306f\u6b63\u78ba\u306b\u308f\u304b\u3063\u3066\u3044\u308b\u300d\u3068\u3059\u308b\u7dda\u5f62\u56de\u5e30\u306e\u4eee\u5b9a\u306b\u9055\u53cd\u3057\u307e\u3059\u3002\u3082\u3057\u540c\u3058\u5b9f\u9a13\u8aa4\u5dee\u304cX\u3068Y\u306e\u4e21\u65b9\u5411\u306b\u73fe\u308c\u308b\u306e\u3067\u3042\u308c\u3070\u3001\u70b9\u304b\u3089\u76f4\u7dda\u307e\u3067\u306e\u5782\u76f4\u8ddd\u96e2\u306e\u4e8c\u4e57\u548c\u3092\u6700\u5c0f\u5316\u3059\u308b\u3053\u3068\u306f\u7406\u306b\u304b\u306a\u3044\u307e\u305b\u3093\u3002<\/p>\n\n\n\n

\u2014 Motulsky, Harvey. Linear Regression. In: Analyzing Data with GraphPad Prism. 1999. GraphPad Software, Inc.<\/a><\/p>\n<\/blockquote>\n\n\n\n

\u3053\u3053\u3067\u306f\u5b9f\u969b\u306b\u5f97\u3089\u308c\u308b\u5024\u306b\u3069\u308c\u304f\u3089\u3044\u5dee\u304c\u3042\u308b\u306e\u304b\u3092\u8abf\u3079\u305f\u3053\u3068\u306f\u306a\u304b\u3063\u305f\u306e\u3067\u3084\u3063\u3066\u307f\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

Scatchard\u65b9\u7a0b\u5f0f\u3068\u30d7\u30ed\u30c3\u30c8<\/h2>\n\n\n\n

\u5c0e\u51fa<\/h3>\n\n\n\n

\u53d7\u5bb9\u4f53\u3068\u30ea\u30ac\u30f3\u30c9\u306e\u9593\u3067\u4ee5\u4e0b\u306e\u5e73\u8861\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\\[ [R] + [L] \\rightleftharpoons [RL] \\]\n\n\n\n

\u89e3\u96e2\u5b9a\u6570K<\/em>d<\/sub>\u306f<\/p>\n\n\n\n

\\[ K_{\\mathrm d} = \\frac{[R][L]}{[RL]} \\]\n\n\n\n

\u3067\u3001<\/p>\n\n\n\n

\\[ [R_{\\mathrm T}] = [R] + [RL] \\]\n\n\n\n

\u304b\u3089\u3001<\/p>\n\n\n\n

\\[ [RL] = \\frac{[R_{\\mathrm T}][L]}{K_{\\mathrm d} + [L]} \\]\n\n\n\n

\u3068\u306a\u308b\u3002\u3053\u306e\u5f0f\u306f\u9175\u7d20\u53cd\u5fdc\u901f\u5ea6\u8ad6\u306e\u30df\u30ab\u30a8\u30ea\u30b9\u30fb\u30e1\u30f3\u30c6\u30f3\uff08Michaelis\u2013Menten\uff09\u5f0f\u306b\u76f8\u5f53\u3059\u308b\u975e\u7dda\u5f62\u306e\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n

\u4e00\u65b9\u3067\u3001\u540c\u3058\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3068\u3001<\/p>\n\n\n\n

\\[ \\frac{K_{\\mathrm d}[RL]}{[L]} = -[RL] + [R_{\\mathrm T}] \\]\n\n\n\n

\u3068\u306a\u308a\u3001\u4e21\u8fba\u3092K<\/em>d<\/sub>\u3067\u5272\u308b\u3068\u3001<\/p>\n\n\n\n

\\[ \\frac{[RL]}{[L]} = -\\frac{1}{K_{\\mathrm d}}[RL] + \\frac{[R_{\\mathrm T}]}{K_{\\mathrm d}} \\]\n\n\n\n

\u3068\u306a\u308a\u3001Scatchard\uff08\u30b9\u30ad\u30e3\u30c3\u30c1\u30e3\u30fc\u30c9\uff09\u65b9\u7a0b\u5f0f\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u5f0f\u306f\u30df\u30ab\u30a8\u30ea\u30b9\u30fb\u30e1\u30f3\u30c6\u30f3\u5f0f\u306e\u7dda\u5f62\u8868\u73fe\u306e1\u3064\u3067\u3042\u308b\u30a4\u30fc\u30c7\u30a3\u30fc\u2013\u30db\u30d5\u30b9\u30c6\u30fc\uff08Eadie\u2013Hofstee\uff09\u56f3\u306b\u76f8\u5f53\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u3053\u306e\u5f0f\u304b\u3089\u3001[RL]\uff08x\u8ef8\uff09\u306b\u5bfe\u3057\u3066 [RL]\/[L]\uff08y\u8ef8\uff09\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u7dda\u5f62\u56de\u5e30\u3059\u308b\u3068\u3001\u50be\u304d\u304c\u22121\/K<\/em>d<\/sub>\u3001x\u8ef8\u5207\u7247\u304c [RT<\/sub>] \u306e\u76f4\u7dda\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u30d7\u30ed\u30c3\u30c8\u306e\u7279\u5fb4\u3068\u3057\u3066\u3001\u30ea\u30ac\u30f3\u30c9\u306b\u5bfe\u3059\u308b\u89aa\u548c\u6027\u304c\u7570\u306a\u308b\u8907\u6570\u306e\u7d50\u5408\u90e8\u4f4d\u304c\u5b58\u5728\u3059\u308b\u6642\u306f\u3001\u30d7\u30ed\u30c3\u30c8\u306f\u76f4\u7dda\u3067\u306f\u306a\u304f\u3001\u4e0b\u306b\u51f8\u306e\u66f2\u7dda\u306b\u306a\u308a\u307e\u3059\uff08\u30b9\u30ad\u30e3\u30c3\u30c1\u30e3\u30fc\u30c9\u89e3\u6790<\/strong>\uff09\u3002<\/p>\n\n\n\n

\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6c42\u3081\u308b\u305f\u3081\u3067\u3042\u308c\u3070\u3001Scatchard plot\u3088\u308a\u3082Hanes-Woolf plot\u578b\u306e<\/p>\n\n\n\n

\\[ \\frac{[L]}{[RL]} = \\frac{1}{[R_{\\mathrm T}]}[L] + \\frac{K_{\\mathrm d}}{[R_{\\mathrm T}]} \\]\n\n\n\n

\u306e\u65b9\u304c\u6b63\u78ba\u3067\u3059\u304c\u3001\u3053\u306e\u30d7\u30ed\u30c3\u30c8\u304b\u3089\u306f\u89aa\u548c\u6027\u306e\u7570\u306a\u308b\u8907\u6570\u306e\u7d50\u5408\u90e8\u4f4d\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u8aad\u307f\u53d6\u308b\u306e\u306f\u56f0\u96e3\u3067\u3059\u3002<\/p>\n\n\n\n

\u554f\u984c\u70b9<\/h3>\n\n\n\n

Scatchard plot\u306e\u554f\u984c\u70b9\u3068\u3057\u3066\u306f\u3001x\u5ea7\u6a19\uff08[RL]\uff09\u3068y\u5ea7\u6a19\uff08[RL]\/[L]\uff09\u304c\u72ec\u7acb\u5909\u6570\u306b\u306a\u3063\u3066\u3044\u306a\u3044\uff08\u3069\u3061\u3089\u306b\u3082 [RL] \u304c\u542b\u307e\u308c\u3066\u3044\u308b\uff09\u305f\u3081\u3001\u6700\u5c0f\u4e8c\u4e57\u6cd5\u304c\u672c\u6765\u9069\u7528\u3067\u304d\u306a\u3044\u3053\u3068\uff08\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306fx\u5ea7\u6a19\u304c\u8aac\u660e\u5909\u6570\u3008\u5b9f\u9a13\u8aa4\u5dee\u3092\u542b\u307e\u306a\u3044\u3009\u3001y\u5ea7\u6a19\u304c\u76ee\u7684\u5909\u6570\u3008\u5b9f\u9a13\u8aa4\u5dee\u3092\u542b\u3080\u3009\u3067\u3042\u308b\u3053\u3068\u3092\u60f3\u5b9a\u3057\u3066\u3044\u308b\uff09\u3084\u9069\u5408\u5ea6\u306e\u6307\u6a19\u3067\u3042\u308b\u76f8\u95a2\u4fc2\u6570\u3092\u9069\u7528\u3067\u304d\u306a\u3044\u3053\u3068\u3001\u305d\u3082\u305d\u3082\u76f4\u63a5\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u63a8\u5b9a\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u9593\u63a5\u7684\u3001\u5916\u633f\u3067\u6c42\u3081\u3066\u3044\u308b\u3053\u3068\u306a\u3069\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

\u305d\u306e\u305f\u3081\u3001\u8ad6\u6587\u3067\u306f\u5927\u62b5\u3001\u7d50\u5408\u98fd\u548c\u30d7\u30ed\u30c3\u30c8\u306e\u6a2a\u304b\u4e2d\u306b\u5c0f\u3055\u304fScatchard plot\u3092\u8f09\u305b\u3066\u3042\u308a\u307e\u3059\uff08\u4f8b: Braun (2005)\uff09\u3002<\/p>\n\n\n\n

\u7df4\u7fd2\u554f\u984c<\/h2>\n\n\n\n

\u4ee5\u4e0b\u306eURL\u306b\u30a2\u30fc\u30ab\u30a4\u30d6\u3055\u308c\u3066\u3044\u308b\u8b1b\u7fa9\u8cc7\u6599\u306e\u7df4\u7fd2\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

https:\/\/web.archive.org\/web\/20091007171045\/http:\/\/www.biochem.oulu.fi\/Biocomputing\/juffer\/Teaching\/PhysicalBiochemistry\/PhysBiochem-protein-ligand.pdf<\/a><\/p>\n\n\n\n

“Mg2+<\/sup>\u3068ADP\u306f1\u5bfe1\u306e\u932f\u4f53\u3092\u5f62\u6210\u3059\u308b\u3002\u7d50\u5408\u5b9f\u9a13\u306b\u304a\u3044\u3066\u3001ADP\u306e\u7dcf\u6fc3\u5ea6\u306f80 \u00b5M\u306b\u4e00\u5b9a\u306b\u4fdd\u305f\u308c\u3066\u3044\u308b\u3002\u4ee5\u4e0b\u306e\u8868\u306e\u30c7\u30fc\u30bf\u304b\u3089\u89e3\u96e2\u5b9a\u6570K<\/em>d<\/sub>\u3092\u6c42\u3081\u306a\u3055\u3044\u3002”<\/p>\n\n\n\n

Total Mg2+<\/sup> (\u00b5M)<\/td>Mg2+<\/sup> bound to ADP (\u00b5M)<\/td><\/tr>
20<\/td>11.6<\/td><\/tr>
50<\/td>26.0<\/td><\/tr>
100<\/td>42.7<\/td><\/tr>
150<\/td>52.8<\/td><\/tr>
200<\/td>59.0<\/td><\/tr>
400<\/td>69.5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u307e\u305a\u3001[RL] = [RT<\/sub>][L]\/(K<\/em>d<\/sub> + [L]) \u304b\u3089\u3001[L] = K<\/em>d<\/sub> \u306e\u6642\u306b [RL] = [RT<\/sub>]\/2 = 40 \u00b5M\u3068\u306a\u308b\u306e\u3067\u3001\u304a\u304a\u3088\u305d\u306eK<\/em>d<\/sub>\u306e\u5024\u306e\u898b\u5f53\u304c\u4ed8\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

R\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f7f\u7528\u3057\u3066\u89e3\u6790\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

# R\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\n> TotalMg = c(20, 50, 100, 150, 200, 400) #Total Mg2+\n> B = c(11.6, 26.0, 42.7, 52.8, 59.0, 69.5) #Bound Mg2+\u3002\u5f0f\u4e2d\u306e [RL]\u3002\n> F = TotalMg - B #Free Mg2+\u3002\u5f0f\u4e2d\u306e [L]\u3002\n# \u975e\u7dda\u5f62\u56de\u5e30\n> result_nonlinear = nls(B ~ Rt*F/(Kd + F), start=c(Rt=10, Kd=10))\n> summary(result_nonlinear)\n\nFormula: B ~ Rt * F/(Kd + F)\n\nParameters:\n   Estimate Std. Error t value Pr(>|t|)    \nRt 79.92642    0.08296   963.5 6.96e-12 ***\nKd 49.86861    0.15975   312.2 6.32e-10 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.05816 on 4 degrees of freedom\n\nNumber of iterations to convergence: 5 \nAchieved convergence tolerance: 1.579e-06\n\n> confint(result_nonlinear)\nWaiting for profiling to be done...\n       2.5%    97.5%\nRt 79.69637 80.15752\nKd 49.42630 50.31459\n<\/pre>\n\n\n\n
\"\"<\/p>\n\n\n\n
\u975e\u7dda\u5f62\u56de\u5e30\u3067\u6c42\u3081\u305f\u89e3\u96e2\u5b9a\u6570K<\/em>d<\/sub> = 49.87 \u00b5M, [RT<\/sub>] = 79.93 \u00b5M\u3067\u3057\u305f\u3002Rt\u306b80\u3092\u4ee3\u5165\u3057\u3066\u975e\u7dda\u5f62\u56de\u5e30\u3059\u308b\u3068\u3001K<\/em>d<\/sub> = 49.99 \u00b5M\u3067\u3057\u305f\u3002<\/p>\n\n\n\n
\u6b21\u306b\u3001Scatchard plot\u304b\u3089K<\/em>d<\/sub> \u3068 [RT<\/sub>] \u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n
# R\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\n> result_linear = lm(B\/F ~ B)\n> summary(result_linear)\n\nCall:\nlm(formula = B\/F ~ B)\n\nResiduals:\n         1          2          3          4          5          6 \n 0.0038911 -0.0026571 -0.0032285 -0.0010654 -0.0005134  0.0035734 \n\nCoefficients:\n              Estimate Std. Error t value Pr(>|t|)    \n(Intercept)  1.6115350  0.0033919   475.1 1.18e-10 ***\nB           -0.0202132  0.0000709  -285.1 9.08e-10 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.00342 on 4 degrees of freedom\nMultiple R-squared:      1,\tAdjusted R-squared:  0.9999 \nF-statistic: 8.128e+04 on 1 and 4 DF,  p-value: 9.081e-10\n<\/pre>\n\n\n\n
\"\"<\/p>\n\n\n\n
\u56de\u5e30\u76f4\u7dda\u306e\u50be\u304d \u22121\/K<\/em>d<\/sub> = -0.0202132\u3001[RT<\/sub>]\uff08x\u5207\u7247\uff09= \u2212y\u5207\u7247\/\u50be\u304d = 1.6115350\/0.0202132 \u304b\u3089\u3001K<\/em>d<\/sub> = 49.47 \u00b5M\u3001[RT<\/sub>] = 79.72 \u00b5M \u3068\u6c42\u307e\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n
\u3053\u306e\u7df4\u7fd2\u554f\u984c\u306f\u89e3\u96e2\u5b9a\u6570K<\/em>d<\/sub> = 50 \u00b5M\u3092\u4f7f\u3063\u3066\u5404\u70b9\u306e\u5024\u304c\u51fa\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3059\u304c\u3001Bound Mg2+<\/sup> \u306e\u5024\u3092\u4e38\u3081\u305f\u6642\u306e\u8aa4\u5dee\u3067\u3001\u975e\u7dda\u5f62\u56de\u5e30\u3068Scatchard\u6cd5\u3067\u5f97\u3089\u308c\u305fK<\/em>d<\/sub>\u5024\u3068 [RT<\/sub>] \u5024\u306b\u5dee\u304c\u51fa\u3066\u3044\u308b\u3088\u3046\u3067\u3059\u3002\u5c0f\u6570\u70b9\u4ee5\u4e0b\u7b2c2\u4f4d\u307e\u3067\u4f7f\u3063\u3066\u8a08\u7b97\u3059\u308c\u3070\u3001\u975e\u7dda\u5f62\u56de\u5e30\u3067K<\/em>d<\/sub> = 49.99\u3001Scatchard\u6cd5\u3067K<\/em>d<\/sub> = 49.97\u3068\u7406\u8ad6\u901a\u308a\u306b\u5024\u304c\u6c42\u307e\u308a\u307e\u3059\u3002<\/p>\n\n\n\n
\u5b9f\u30c7\u30fc\u30bf<\/h2>\n\n\n\n
\u4e0a\u306e\u7406\u60f3\u7684\u306a\u5024\u3092\u4f7f\u3063\u305f\u7df4\u7fd2\u554f\u984c\u3067\u306f\u975e\u7dda\u5f62\u56de\u5e30\u3068Scatchard plot\u3067\u307b\u3068\u3093\u3069\u9055\u3044\u306f\u3042\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u304c\u3001\u5b9f\u969b\u306e\u5b9f\u9a13\u30c7\u30fc\u30bf\u3067\u306f\u3069\u3046\u306a\u308b\u304b\u8a66\u3057\u3066\u307f\u307e\u3057\u305f\u3002<\/p>\n\n\n\n
> B = c(0.729,0.805,0.748,1.328,1.317,1.314,1.905,1.936,1.851,2.546,2.414,2.355) #\u5358\u4f4d\u306fnM\n> F = c(6.102,5.532,5.490,10.448,11.710,11.092,22.863,24.570,24.401,48.750,46.621,46.682) #\u5358\u4f4d\u306fnM\n> result = nls(B~Rt*F/(Kd+F),start=c(Rt=3,Kd=0.2))\n> summary(result)\n\nFormula: B ~ Rt * F/(Kd + F)\n\nParameters:\n   Estimate Std. Error t value Pr(>|t|)    \nRt   3.3825     0.1127   30.01 3.95e-11 ***\nKd  18.3799     1.4360   12.80 1.59e-07 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.06848 on 10 degrees of freedom\n\nNumber of iterations to convergence: 6 \nAchieved convergence tolerance: 1.785e-07\n\n> confint(result) #95%\u4fe1\u983c\u533a\u9593\nWaiting for profiling to be done...\n        2.5%     97.5%\nRt  3.148358  3.652665\nKd 15.470323 21.906326<\/pre>\n\n\n\n
\"\"<\/p>\n\n\n\n
\u975e\u7dda\u5f62\u56de\u5e30\u3067\u6c42\u3081\u305f\u89e3\u96e2\u5b9a\u6570K<\/em>d<\/sub> = 18.4 nM, [RT<\/sub>] = 3.38 nM\u3067\u3057\u305f\u3002<\/p>\n\n\n\n
> result_lm = lm(B/F ~ B)\n> summary(result_lm)\n\nCall:\nlm(formula = B/F ~ B)\n\nResiduals:\n       Min         1Q     Median         3Q        Max \n-0.0207551 -0.0043123  0.0007946  0.0048720  0.0171733 \n\nCoefficients:\n             Estimate Std. Error t value Pr(>|t|)    \n(Intercept)  0.177090   0.008028   22.06 8.21e-10 ***\nB           -0.050571   0.004659  -10.85 7.46e-07 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 0.01015 on 10 degrees of freedom\nMultiple R-squared:  0.9218,\tAdjusted R-squared:  0.9139 \nF-statistic: 117.8 on 1 and 10 DF,  p-value: 7.464e-07\n> confint(result_lm)\n                  2.5 %     97.5 %\n(Intercept)  0.15920357  0.1949766\nB           -0.06095189 -0.0401892\n> -1/result_lm$coefficients[2]\n       B \n19.77436 \n> -result_lm$coefficients[1]/result_lm$coefficients[2]\n(Intercept) \n   3.501842 \n<\/pre>\n\n\n\n
\"\"<\/p>\n\n\n\n
\u4f4e\u6fc3\u5ea6\u5074\u306e2\u3064\u306eB\/F\u5024\u306e\u7bc4\u56f2\u304c\u91cd\u306a\u3063\u3066\u3057\u307e\u3063\u3066\u3044\u307e\u3059\uff08F\u306e\u9006\u6570\u3092\u4f7f\u3046\u305f\u3081\u3001\u8aa4\u5dee\u304c\u5927\u304d\u304f\u5897\u5e45\u3055\u308c\u3066\u3044\u308b\uff09\u3002Scatchard plot\u304b\u3089\u6c42\u3081\u305f\u89e3\u96e2\u5b9a\u6570K<\/em>d<\/sub> = 19.8 nM, [RT<\/sub>] = 3.50 nM\u3067\u3057\u305f\u3002\u975e\u7dda\u5f62\u56de\u5e30\u3067\u6c42\u3081\u305f\u5024\u3068\u6bd4\u8f03\u3059\u308b\u3068K<\/em>d<\/sub> \u306f\u7d048%\u3001[RT<\/sub>] \u306f\u7d044%\u5927\u304d\u3044\u5024\u3067\u3057\u305f\u3002<\/p>\n\n\n\n
\u89e3\u96e2\u5b9a\u6570K<\/em>d<\/sub>\u306e95%\u4fe1\u983c\u533a\u9593\u3092\u6bd4\u3079\u308b\u3068\u3001\u975e\u7dda\u5f62\u56de\u5e30\u3067\u306fK<\/em>d<\/sub> = 18.4 (95% CI: 15.5\u201321.9)\u3001\u30b9\u30ad\u30e3\u30c3\u30c1\u30e3\u30fc\u30c9\u30d7\u30ed\u30c3\u30c8\u3067\u306fK<\/em>d<\/sub> = 19.8 (95% CI: 16.4\u201324.9) \u3067\u3057\u305f\u3002<\/p>\n\n\n\n
References<\/h2>\n\n\n\n