Pollak Eli
Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel.
Phys Chem Chem Phys. 2016 Oct 19;18(41):28872-28882. doi: 10.1039/c6cp05052b.
The recent experimental measurement of the transition path time distributions of proteins presents several challenges to theory. Firstly, why do the fits of the experimental data to a theoretical expression lead to barrier heights which are much lower than the free energies of activation of the observed transitions? Secondly, there is the theoretical question of determining the transition path time distribution, without invoking the Smoluchowski limit. In this paper, we derive an exact expression for a transition path time distribution which is valid for arbitrary memory friction using the normal mode transformation which underlies Kramers' rate theory. We then recall that for low barriers, there is a noticeable difference between the transition path time distribution obtained with absorbing boundary conditions and free boundary conditions. For the former, the transition times are shorter, since recrossings of the boundaries are disallowed. As a result, if one uses the distribution based on absorbing boundary conditions to fit the experimental data, one will find that the transition path barrier will be larger than the values found based on a theory with free boundary conditions. We then introduce the paradigm of a transition path barrier height, and show that one should always expect it to be much smaller than the activation energy.
近期对蛋白质跃迁路径时间分布的实验测量给理论带来了诸多挑战。首先，为何将实验数据拟合到理论表达式会得出比观测到的跃迁活化自由能低得多的势垒高度？其次，存在一个理论问题，即在不引入斯莫卢霍夫斯基极限的情况下确定跃迁路径时间分布。在本文中，我们利用作为克莱默斯速率理论基础的正则模式变换，推导出了一个对任意记忆摩擦均有效的跃迁路径时间分布的精确表达式。然后我们回顾，对于低势垒，采用吸收边界条件和自由边界条件得到的跃迁路径时间分布存在显著差异。对于前者，跃迁时间更短，因为不允许再次穿过边界。因此，如果使用基于吸收边界条件的分布来拟合实验数据，就会发现跃迁路径势垒将大于基于自由边界条件理论得出的值。接着我们引入跃迁路径势垒高度的范例，并表明应始终预期其远小于活化能。
