Force spectrum microscopy

FSM was developed by Ming Guo and David A. Weitz to probe stochastic intracellular forces generated by motor proteins.[1] Far from a liquid void, the cytoplasm contains a complex meshwork of actin and myosin conferring structural support to the cell, as well as harbouring vesicles and mitochondria among other organelles.[2] Recent research on the macromolecular crowding inside the cytoplasm raises concerns whether diffusive-like motion of large molecules have been mistakenly attributed to Brownian forces.[3] Instead, there are suspicions that myosin motor proteins, which tug randomly on the actin filaments embedded with large molecules, give rise to diffusive-like motion of molecules inside cells.[3][4] Guo et al. developed an assay to distinguish whether particle motion inside cells are driven by thermal diffusion or by repercussions from active motor proteins like non-muscle myosin II shaking the cellular cytoskeleton.

FSM relies on injecting tracer particles coated with polyethylene glycol (PEG) larger than the cytoskeletal mesh size (>50 nm),[5] settling in between an internetwork of actin filaments and myosin motor proteins. As myosin motor proteins tug on actin filaments to perform cellular work, these actin fluctuations invariably oscillate neighboring PEGylated particles. The magnitude of tracer fluctuation is proportional to the magnitude of aggregate active motor forces. Thus, by recording the displacement of tracer oscillations, FSM can gauge and derive the magnitude of forces exerted by active motor proteins.[1]

The fluctuations of PEGylated tracers coupled to aggregate myosin motor forces can be likened to a Hookean spring,

${\displaystyle F=kx}$

where the force ${\displaystyle F}$ applied to generate the oscillation displacement ${\displaystyle x}$ is proportional to the effective spring constant ${\displaystyle k}$ of the intracellular environment. The displacement during oscillation is a spatial function of time, which can be directly measured using optical microscopy.[1] A Fourier transform then maps information in the temporal domain to the frequency domain to derive a useful dimension as a function of frequency,

${\displaystyle \langle \left(F(v)\right)^{2}\rangle =\langle \left(K(v)\right)^{2}\rangle *\langle \left(x(v)\right)^{2}\rangle }$

where ${\displaystyle \langle \left(F(v)\right)^{2}\rangle }$, ${\displaystyle \langle \left(K(v)\right)^{2}\rangle }$ and ${\displaystyle \langle \left(x(v)\right)^{2}\rangle }$ are quadratic forms of averaged force, elasticity and displacement used to account for stochastic forces.[1] Time-averaged Mean squared displacement, ${\displaystyle MSD=\langle \left(X(t)\right)^{2}\rangle }$ can be retrieved by a Fourier Transform from the frequency domain back to the temporal domain. In the context of oscillation frequency, the higher the force frequency spectrum, the greater the metabolic activity of the cell.[6] Independent micromechanical measurements can calculate the elasticity of the cytoplasm. By using an optical tweezer to apply a prescribed force to a tracer particle, FSM can measure the resulting displacement in order to estimate the elastic spring constant.[7][8]