查看“︁希尔方程 (生物化学)”︁的源代码

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[[File:Hill Curves for Increasing Hill Coefficients.jpg|thumb|370x370px|Biochemical binding curves showing the characteristically sigmoidal curves generated by using the Hill equation to model cooperative binding. Each curve corresponds to a different Hill coefficient, labeled to the curve's right. The vertical axis displays the fraction of occupied ligand-binding sites on a protein receptor (<math>\theta</math>), equal to ratio of the concentration of ligand-bound protein ([<math>\left[ P L_n \right]</math>) to the total concentration of protein receptor (<math>\left[ P_{\text{Total}} \right]</math>). The horizontal axis is the ratio of the ligand concentration producing half occupation (<math>K_A</math>) to the free ligand concentration (<math>\left[L\right]</math>).]]

在[[生物化学]]中，若已经有配体分子结合在一个高分子上，那么新的[[配体 (生物化学)|配体]]分子与这个[[高分子]]的结合作用就常常会被增强（亦被称作[[协同结合]]）。以[[阿奇博爾德·希爾]]命名的'''希尔系数'''（{{lang|en|Hill coefficient}}）提供了量化这种效应的方法。

'''希尔方程'''（{{lang-en|Hill equation}}）描述了高分子被[[配体 (生物化学)|配体]]饱和的分数，是一个关于配体[[浓度]]的函数；被用于确定受体结合到酶或受体上的合同性程度。此方程首次于1910年由[[阿奇博爾德·希爾]]阐释出来以表述为何血红蛋白的氧气结合曲线会呈现S型<ref>{{cite journal|title=The possible effects of the aggregation of the molecules of hæmoglobin on its dissociation curves|journal=[[J. Physiol.]]|date=1910-01-22|first=A. V.|last=Hill|coauthors=|volume=40|issue=Suppl|pages=iv-vii|id=|url=http://jp.physoc.org/cgi/reprint/40/Suppl/i|format=PDF|accessdate=2009-03-18|author=|archive-url=https://web.archive.org/web/20081201212329/http://jp.physoc.org/cgi/reprint/40/Suppl/i|archive-date=2008-12-01|dead-url=yes}}</ref>。

当系数为1时，表明结合作用是完全独立的，而不取决于已经有多少配体已经结合上去。大于一的数表示正协同，而小于一的数表示负协同。希尔系数最初被设计出来是用于解释氧气协同地结合到[[血红蛋白]]上的过程（此系统的希尔系数为2.8～3）。

希尔方程：

<math> \theta = {[L]^n \over K_d + [L]^n} = {[L]^n \over (K_A)^n + [L]^n} </math>

<math> \theta </math> - 占用位点的分数，在占用位点处[[配体 (生物化学)|配体]]可以结合到[[受体 (生物化学)|受体蛋白的活性位点]]。

<math>[L]</math> - 游离的（未结合的）[[配体 (生物化学)|配体]]浓度

<math>K_d</math> - 表观[[解离常数]]来源于[[质量作用定律]]（对于解离的平衡常数）

<math>K_A</math> - 产生半数占用时的配体浓度（配体浓度足以占用结合位点的一半数目），亦为微观的[[解离常数]]。

<math>n</math> - 希尔系数，描述了协同性（或亦可能是其他生物化学性质，取决于使用希尔方程时的讨论背景）

对两边同时取倒数，重整，再取倒数，接下来对等式两边取对数，导出一个与希尔方程等价的方程：

<math> \log\left( {\theta\over 1-\theta} \right) = n\log{[L]} - \log{K_d}.</math> 

在适当的情况下，希尔常数的值描述了配体以下列几种方式结合时的协同性：

* <math> n>1 </math> - '''正协同反应'''：一旦一个配体分子结合到酶上，酶对其他配体的亲和力就会增加。

* <math> n<1 </math> - '''负协同反应'''：一旦一个配体分子结合到酶上，酶对其他配体的亲和力就会减小。

* <math> n=1 </math> - '''非协同反应'''：酶对于一个配体分子的亲和力并不取决于是否有配体分子已结合到其上。

希尔方程（作为描述吸附到结合位点上的化合物浓度与结合位点的被占分数之间的关系式）是等价于[[朗谬尔方程]]的。

==另见==
希尔方程与[[逻辑斯谛函数]]相关，且在某些方面是它的对数变换，例如在对数标尺上作出希尔函数时，它看起来就等于逻辑斯谛函数。如果达到饱和状态时的浓度变化范围未达到数量级时，这就显得尤其重要。在这种情况下，逻辑斯谛函数将会变成一个更可靠的描述该生化行为的模型。

* [[逻辑斯谛函数]]
* {{le|冈波茨曲线|Gompertz function}}
* [[S型函数]]

==参考文献==
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==延伸閱讀==
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{{refend}}

==外部連結==
* [http://www.fxsolver.com/browse/formulas/Hill+equation Hill equation calculator] {{Wayback|url=http://www.fxsolver.com/browse/formulas/Hill+equation |date=20210117023902 }}

[[Category:酶动力学]]
[[Category:藥理學]]