Compression-induced buckling of a semiflexible filament in two and three dimensions

Compression can induce buckling and affect biological functions like actomyosin contractility or buckling inside filopodial protrusions can impede cell motility. A good understanding of the buckling process in semiflexible biomolecules is required that will have both experimentally accessible predictions as well as relevance to biological systems. In the zero-temperature limit, Euler buckling theory predicts a sudden transition from a compressed to a bent state, but the buckling of a thermally fluctuating filament remains poorly understood. In this talk, we use a mean-field theory and Monte Carlo simulations to show that if a semiflexible chain is compressed at a finite temperature with a fixed end-to-end distance, it exhibits a continuous phase transition to a buckled state at a critical level of compression. We find the scaling of the critical compression in three dimensions matches the Euler buckling theory, but in two dimensions we find the scaling of the transition does not match the Euler theory. This work may be useful in understanding the buckling of filamentous biomolecules compressed by fluctuating forces, relevant in a variety of biological contexts.