Cellular adhesion via the formation of molecular bond clusters is a fundamental biological phenomenon. Cell adhesion forces can be measured by various advanced techniques with adjustable probe stiffness. To quantitatively understand how the stiffness of a loading device may influence the measurement of these forces, we consider an idealized theoretical model of a cluster of molecular bonds that are subjected to an applied tensile load by a Hookean spring. In this model, the rebinding and rupture of individual molecular bonds are governed by stochastic master equations. By deriving an exact expression of the rebinding rate and directly solving the master equation, we find that the conventional moment method provides incorrect predictions for this problem. Moreover, the measured adhesion strength of a molecular bond cluster exhibits strong dependence on the stiffness of the loading device and the bond number when the stiffness value is close to or smaller than the effective stiffness of the bond cluster. Thus, an improper selection of the stiffness value of the loading device may lead to measurement uncertainty. Monte Carlo simulations are performed to verify the proposed analytical results.

通过形成分子键簇的细胞粘附是一种基本的生物学现象。细胞粘附力可以通过各种先进技术和可调节的探针硬度进行测量。为了定量地了解加载设备的刚度如何影响这些力的测量，我们考虑了一个理想的分子模型簇的理论模型，该模型通过Hookean弹簧承受了施加的拉伸载荷。在该模型中，单个分子键的重新结合和断裂受随机主方程控制。通过得出结合率的精确表达式并直接求解主方程，我们发现常规矩量法为该问题提供了错误的预测。此外，当刚度值接近或小于键群的有效刚度时，测得的分子键群的粘附强度强烈依赖于加载装置的刚度和键数。因此，加载设备的刚度值选择不当可能导致测量不确定性。进行蒙特卡洛模拟以验证所提出的分析结果。