Kirmizialtin Serdal, Huang Lei, Makarov Dmitrii E
Department of Chemistry and Biochemistry and Institute for Theoretical Chemistry, University of Texas at Austin, Austin, Texas 78712, USA.
J Chem Phys. 2005 Jun 15;122(23):234915. doi: 10.1063/1.1931659.
Single-molecule experiments in which proteins are unfolded by applying mechanical stretching forces generally force unfolding to proceed along a reaction coordinate that is different from that in chemical or thermal denaturation. Here we simulate the mechanical unfolding and refolding of a minimalist off-lattice model of the protein ubiquitin to explore in detail the slice of the multidimensional free-energy landscape that is accessible via mechanical pulling experiments. We find that while the free-energy profile along typical "chemical" reaction coordinates may exhibit two minima, corresponding to the native and denatured states, the free energy G(z) is typically a monotonic function of the mechanical coordinate z equal to the protein extension. Application of a stretching force along z tilts the free-energy landscape resulting in a bistable (or multistable) free energy G(z)-fz probed in mechanical unfolding experiments. We construct a two-dimensional free-energy surface as a function of both chemical and mechanical reaction coordinates and examine the coupling between the two. We further study the refolding trajectories after the protein has been prestretched by a large force, as well as the mechanical unfolding trajectories in the presence of a large stretching force. We demonstrate that the stretching forces required to destabilize the native state thermodynamically are larger than those expected on the basis of previous experimental estimates of G(z). This finding is consistent with the recent experimental studies, indicating that proteins may refold even in the presence of a substantial stretching force. Finally, we show that for certain temperatures the free energy of a polyprotein chain consisting of multiple domains is a linear function of the chain extension. We propose that the recently observed "slow phase" in the refolding of proteins under mechanical tension may be viewed as downhill diffusion in such a linear potential.
在单分子实验中，通过施加机械拉伸力使蛋白质展开，通常会迫使展开过程沿着与化学或热变性不同的反应坐标进行。在这里，我们模拟了蛋白质泛素的极简非晶格模型的机械展开和重新折叠，以详细探索通过机械拉伸实验可访问的多维自由能景观的切片。我们发现，虽然沿着典型“化学”反应坐标的自由能分布可能呈现两个最小值，分别对应天然态和变性态，但自由能G(z)通常是与蛋白质延伸量相等的机械坐标z的单调函数。沿着z施加拉伸力会使自由能景观倾斜，从而在机械展开实验中产生一个双稳态（或多稳态）的自由能G(z)-fz。我们构建了一个作为化学和机械反应坐标函数的二维自由能表面，并研究两者之间的耦合。我们进一步研究了蛋白质在受到大力预拉伸后的重新折叠轨迹，以及在存在大拉伸力时的机械展开轨迹。我们证明，使天然态热力学不稳定所需的拉伸力大于基于先前对G(z)的实验估计所预期的力。这一发现与最近的实验研究一致，表明即使在存在相当大的拉伸力的情况下，蛋白质也可能重新折叠。最后，我们表明，对于某些温度，由多个结构域组成的多蛋白链的自由能是链延伸量的线性函数。我们提出，最近在机械张力下蛋白质重新折叠中观察到的“慢相”可以被视为在这样的线性势中的下坡扩散。
