Jacobson David R, Perkins Thomas T
JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309, USA.
Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder, Colorado 80309, USA.
Phys Rev E. 2020 Aug;102(2-1):022402. doi: 10.1103/PhysRevE.102.022402.
Equilibrium free-energy-landscape parameters governing biomolecular folding can be determined from nonequilibrium force-induced unfolding by measuring the rates k for transitioning back and forth between states as a function of force F. However, bias in the observed forward and reverse rates is introduced by limited effective temporal resolution, which includes the mechanical response time of the force probe and any smoothing used to improve the signal-to-noise ratio. Here we use simulations to characterize this bias, which is most prevalent when the ratio of forward and reverse rates is far from unity. We find deviations in k(F) at high rates, due to unobserved transitions from short- to long-lived states, and at low rates, due to the corresponding unobserved transitions from long- to short-lived states. These missing events introduce erroneous curvature in log(k) vs F that leads to incorrect landscape parameter determination. To correct the measured k(F), we derive a pair of model-independent analytical formulas. The first correction accounts for unobserved transitions from short- to long-lived states, but does surprisingly little to correct the erroneous energy-landscape parameters. Only by subsequently applying the second formula, which corrects the corresponding reverse process, do we recover the expected k(F) and energy-landscape quantities. Going forward, these corrections should be applied to transition-rate data whenever the highest measured rate is not at least an order of magnitude slower than the effective temporal resolution.
通过测量作为力F函数的状态之间来回转换的速率k，可以从非平衡力诱导的去折叠过程中确定控制生物分子折叠的平衡自由能景观参数。然而，有限的有效时间分辨率会引入观察到的正向和反向速率偏差，这包括力探针的机械响应时间以及用于提高信噪比的任何平滑处理。在这里，我们使用模拟来表征这种偏差，当正向和反向速率之比远离1时，这种偏差最为普遍。我们发现在高速率下k(F)存在偏差，这是由于未观察到从短寿命状态到长寿命状态的转变，而在低速率下，是由于从长寿命状态到短寿命状态的相应未观察到的转变。这些缺失的事件在log(k)与F的关系中引入了错误的曲率，导致景观参数的错误确定。为了校正测量的k(F)，我们推导了一对与模型无关的解析公式。第一个校正考虑了从短寿命状态到长寿命状态的未观察到的转变，但对校正错误的能量景观参数作用不大。只有随后应用校正相应反向过程的第二个公式，我们才能恢复预期的k(F)和能量景观量。展望未来，只要最高测量速率不比有效时间分辨率慢至少一个数量级，这些校正就应应用于转换速率数据。
