Konkoli Zoran
Chalmers University of Technology, Department of Microtechnology and Nanoscience, Bionano Systems Laboratory, Sweden.
Theor Biol Med Model. 2010 Nov 1;7:40. doi: 10.1186/1742-4682-7-40.
A dose-response curve depicts the fraction of bound proteins as a function of unbound ligands. Dose-response curves are used to measure the cooperativity degree of a ligand binding process. Frequently, the Hill function is used to fit the experimental data. The Hill function is parameterized by the value of the dissociation constant and the Hill coefficient, which describes the cooperativity degree. The use of Hill's model and the Hill function has been heavily criticised in this context, predominantly the assumption that all ligands bind at once, which resulted in further refinements of the model. In this work, the validity of the Hill function has been studied from an entirely different point of view. In the limit of low copy numbers the dynamics of the system becomes noisy. The goal was to asses the validity of the Hill function in this limit, and to see in what ways the effects of the fluctuations change the form of the dose-response curves.
Dose-response curves were computed taking into account effects of fluctuations. The effects of fluctuations were described at the lowest order (the second moment of the particle number distribution) by using the previously developed Pair Approach Reaction Noise EStimator (PARNES) method. The stationary state of the system is described by nine equations with nine unknowns. To obtain fluctuation-corrected dose-response curves the equations have been investigated numerically.
The Hill function cannot describe dose-response curves in a low particle limit. First, dose-response curves are not solely parameterized by the dissociation constant and the Hill coefficient. In general, the shape of a dose-response curve depends on the variables that describe how an experiment (ensemble) is designed. Second, dose-response curves are multi-valued in a rather non-trivial way.
剂量反应曲线描绘了结合蛋白的分数作为未结合配体的函数。剂量反应曲线用于测量配体结合过程的协同程度。通常，希尔函数用于拟合实验数据。希尔函数由解离常数的值和描述协同程度的希尔系数进行参数化。在这种情况下，希尔模型和希尔函数的使用受到了严厉批评，主要是因为假设所有配体同时结合，这导致了对该模型的进一步改进。在这项工作中，从一个完全不同的角度研究了希尔函数的有效性。在低拷贝数的极限情况下，系统的动力学变得有噪声。目标是评估希尔函数在这个极限下的有效性，并了解波动的影响以何种方式改变剂量反应曲线的形式。
计算了考虑波动影响的剂量反应曲线。波动的影响通过使用先前开发的对方法反应噪声估计器（PARNES）方法在最低阶（粒子数分布的二阶矩）进行描述。系统的稳态由九个方程和九个未知数来描述。为了获得经波动校正的剂量反应曲线，对方程进行了数值研究。
希尔函数无法描述低粒子数极限下的剂量反应曲线。首先，剂量反应曲线不仅仅由解离常数和希尔系数进行参数化。一般来说，剂量反应曲线取决于描述实验（总体）设计方式的变量。其次，剂量反应曲线以一种相当复杂的方式具有多值性。
