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Updated: Feb 24, 2026

A Direct Force Probe for Measuring Mechanical Integration Between the Nucleus and the Cytoskeleton
Published on: July 29, 2018
Critical length of a one-dimensional nucleus
Mark N Joswiak1, Michael F Doherty1, Baron Peters1
1Department of Chemical Engineering, University of California-Santa Barbara, Santa Barbara, California 93106, USA.
Abstract:
One-dimensional (1D) nucleation is important in crystal growth, amyloid fibril formation, and supramolecular polymerization. The nucleation rate can be readily calculated, but there is no consensus on the critical length. In this work, we employ a splitting probability to derive an analytical expression for the critical length, which corresponds to a 50% survival probability. For a 1D nucleus on a crystal step, this critical length depends on the supersaturation (driving force) and is nearly independent of the kink (surface) energy.
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