Roy Ranjita Dutta, Rosenmund Christian, Stefan Melanie I
Department of Medicine Solna, Karolinska Institutet, Stockholm, Sweden.
NWFZ, Charité Crossover, Charite Universitätsmedizin, Berlin, Germany.
BMC Syst Biol. 2017 Aug 14;11(1):74. doi: 10.1186/s12918-017-0447-8.
The high-dose hook effect (also called prozone effect) refers to the observation that if a multivalent protein acts as a linker between two parts of a protein complex, then increasing the amount of linker protein in the mixture does not always increase the amount of fully formed complex. On the contrary, at a high enough concentration range the amount of fully formed complex actually decreases. It has been observed that allosterically regulated proteins seem less susceptible to this effect. The aim of this study was two-fold: First, to investigate the mathematical basis of how allostery mitigates the prozone effect. And second, to explore the consequences of allostery and the high-dose hook effect using the example of calmodulin, a calcium-sensing protein that regulates the switch between long-term potentiation and long-term depression in neurons.
We use a combinatorial model of a "perfect linker protein" (with infinite binding affinity) to mathematically describe the hook effect and its behaviour under allosteric conditions. We show that allosteric regulation does indeed mitigate the high-dose hook effect. We then turn to calmodulin as a real-life example of an allosteric protein. Using kinetic simulations, we show that calmodulin is indeed subject to a hook effect. We also show that this effect is stronger in the presence of the allosteric activator Ca /calmodulin-dependent kinase II (CaMKII), because it reduces the overall cooperativity of the calcium-calmodulin system. It follows that, surprisingly, there are conditions where increased amounts of allosteric activator actually decrease the activity of a protein.
We show that cooperative binding can indeed act as a protective mechanism against the hook effect. This will have implications in vivo where the extent of cooperativity of a protein can be modulated, for instance, by allosteric activators or inhibitors. This can result in counterintuitive effects of decreased activity with increased concentrations of both the allosteric protein itself and its allosteric activators.
高剂量钩状效应（也称为前带效应）是指这样一种观察结果：如果一种多价蛋白作为蛋白质复合物两部分之间的连接物，那么增加混合物中连接蛋白的量并不总是会增加完全形成的复合物的量。相反，在足够高的浓度范围内，完全形成的复合物的量实际上会减少。据观察，变构调节蛋白似乎对这种效应不太敏感。本研究的目的有两个：第一，研究变构如何减轻前带效应的数学基础。第二，以钙调蛋白为例，探讨变构和高剂量钩状效应的后果，钙调蛋白是一种钙传感蛋白，可调节神经元中长时程增强和长时程抑制之间的转换。
我们使用“完美连接蛋白”（具有无限结合亲和力）的组合模型来数学描述钩状效应及其在变构条件下的行为。我们表明变构调节确实减轻了高剂量钩状效应。然后我们以钙调蛋白作为变构蛋白的实际例子。通过动力学模拟，我们表明钙调蛋白确实存在钩状效应。我们还表明，在变构激活剂钙/钙调蛋白依赖性激酶II（CaMKII）存在的情况下，这种效应更强，因为它降低了钙 - 钙调蛋白系统的整体协同性。因此，令人惊讶的是，在某些情况下，变构激活剂数量的增加实际上会降低蛋白质的活性。
我们表明协同结合确实可以作为一种针对钩状效应的保护机制。这在体内具有重要意义，因为蛋白质的协同程度可以通过变构激活剂或抑制剂等进行调节。这可能导致变构蛋白本身及其变构激活剂浓度增加时活性降低的反直觉效应。
