Mechanics and buckling of biopolymeric shells and cell nuclei

Abstract

We study a Brownian dynamics simulation model of a biopolymeric shell deformed by axial forces exerted at opposing poles. The model exhibits two distinct linear force-extension regimes, with the response to small tensions governed by linear elasticity and the response to large tensions governed by an effective spring constant that scales with radius as R −0.25 . When extended beyond the initial linear elastic regime, the shell undergoes a hysteretic, temperature-dependent buckling transition. We experimentally observe this buckling transition by stretching and imaging the lamina of isolated cell nuclei. Furthermore, the interior contents of the shell can alter mechanical response and buckling, which we show by simulating a model for the nucleus that quantitatively agrees with our micromanipulation experiments stretching individual nuclei.

Chromatin’s physical properties shape the nucleus and its functions

“…This is consistent with experiments revealing that lamins comprise a thin (10-30 nm) peripheral meshwork of highly bendable intermediate filaments with a short (few hundred nm) persistence length [43][44][45]. In turn, lamin networks can unfold during cell and nuclear spreading [46], but resist large stretching deformations [13,42,47]. Chromatin is a variably compacted polymer filling the nucleus [48] that interacts both with both itself (e.g., compartments and topologically associating domains, TADs seen in Hi-C [14]) and the nuclear periphery (e.g., lamin associated domains, LADs [49]).…”

“…Chromatin and lamins have distinct contributions to nuclear mechanics, as detailed by micromanipulation force measurements [13]. Chromatin acts as an elastic spring that dominates the force response to small deformations (few µm), while the lamin A meshwork deforms easily for small extensions and stiffens to resist large deformations ( Figure 1B) [13,42]. These two regimes reflect the geometry of the cell nucleus [42].…”

“…Chromatin and lamin A are the two major resistive elements that protect the nucleus, as shown by atomic force microscopy [10,11,38], micropipette aspiration [39,40], substrate stretching [41], and micromanipulation [12,13]. However, experiments with nuclei treated with the chromatindegrading enzyme MNase [13,42] show that lamins alone cannot maintain nuclear shape. Instead, the lamina buckles under mechanical stress when it is unsupported by chromatin.…”

“…Chromatin acts as an elastic spring that dominates the force response to small deformations (few µm), while the lamin A meshwork deforms easily for small extensions and stiffens to resist large deformations ( Figure 1B) [13,42]. These two regimes reflect the geometry of the cell nucleus [42]. Differential force response is biologically important because almost all cell nuclei undergo small deformations which are resisted by chromatin, while generally only nuclei in mechanically demanding tissues and microenvironments have high lamin A levels [5].…”

“…Several existing models for nuclear shape and rupture focus exclusively on the role of lamins [111,112], consider only osmotic pressure associated with the nucleoplasm [113], or treat chromatin as a viscoelastic material that is secondary to the lamina [114]. Other studies incorporate more robust models for chromatin but primarily apply to specific experimental conditions [42,115] or do not extensively explore the physical role of chromatin and its linkages to the lamina [115]. Most of these models omit the cytoskeleton.…”