Biophysical limits of ultrafast cellular motility

Many single-celled organisms and specialized cell types can surprisingly achieve speed and acceleration significantly faster than multicellular counterparts. These remarkable cellular machines must integrate energy storage and amplification in actuation, latches for triggered release, and energy dissipation without failure -- all implemented in macro-molecular assemblies inside a single cell. However, a universal biophysical framework that can comparatively evaluate extreme cellular motility remains lacking. Scaling laws have long been recognized as powerful tools for revealing universal principles in physical systems. We map the atlas of ultrafast motility for single cells across the tree of life. We then introduce a new quantitative framework that can be used to evaluate and compare extreme acceleration, speed, area strain rate, volume expansion strain rate, and density changes in single cells. Recognizing that many single cells operate in low-Reynolds number environments, we introduce a new dimensionless number, the "cellular acceleration number," based on energy dissipation at this scale. Using this new framework, we discover a scaling law between the cellular acceleration number and the transient Reynolds number, valid across six orders of magnitude in a range of single-cell organisms. We further generalize these ideas by placing various trigger, actuation, and dissipation mechanisms within the same framework and estimating the fundamental limits of speed and acceleration at the cellular scale. We conclude with a detailed summary of the range of functions implemented via ultrafast cellular phenomena, laying down a quantitative foundation for extreme biophysics at the cellular scale.