Structure-function relationship of biological gels revealed by multiple-particle tracking and differential interference contrast microscopy: The case of human lamin networks

Porntula Panorchan, Denis Wirtz, and Yiider Tseng

Phys. Rev. E 70, 041906 – Published 27 October 2004

Abstract

Lamin $B 1$ filaments organize into a thin dense meshwork underlying the nucleoplasmic side of the nuclear envelope. Recent experiments in vivo suggest that lamin $B 1$ plays a key structural role in the nuclear envelope, but the intrinsic mechanical properties of lamin $B 1$ networks remain unknown. To assess the potential mechanical contribution of lamin $B 1$ in maintaining the integrity and providing structural support to the nucleus, we measured the micromechanical properties and examined the ultrastructural distribution of lamin $B 1$ networks in vitro using particle tracking methods and differential interference contrast (DIC) microscopy. We exploit various surface chemistries of the probe microspheres (carboxylated, polyethylene glycol-coated, and amine-modified) to differentiate lamin-rich from lamin-poor regions and to rigorously extract local viscoelastic moduli from the mean-squared displacements of noninteracting particles. Our results show that human lamin $B 1$ can, even in the absence of auxiliary proteins, form stiff and yet extremely porous networks that are well suited to provide structural strength to the nuclear lamina. Combining DIC microscopy and particle tracking allows us to relate directly the local organization of a material to its local mechanical properties, a general methodology that can be extended to living cells.

Received 3 May 2004

DOI:https://doi.org/10.1103/PhysRevE.70.041906

Authors & Affiliations

Porntula Panorchan¹, Denis Wirtz^1,2, and Yiider Tseng^1,*

¹Department of Chemical and Biomolecular Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
²Department of Materials Science and Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA

^*Corresponding author. Email address: yiider@jhu.edu

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Vol. 70, Iss. 4 — October 2004

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Images

Figure 1
Microstructure of lamin $B 1$ suspensions marked with fluorescent amine-modified and carboxylated microspheres. Lamin $B 1$ networks (3 mg∕mL) in polymerization buffer at 25 °C. Scale bar, 10 μm. (a) Carboxylated microspheres. (b) Amine-modified microspheres. (c) PEGylated microspheres. Microspheres embedded in lamin-rich regions remain in focus, while microspheres in lamin-poor regions are somewhat fuzzy because of Brownian motion. Panels (a)–(c) are differential interference contrast (DIC) micrographs. Insets in panels (a)–(c) are micrographs of the fluorescently labeled microspheres embedded in those lamin $B 1$ suspensions. The microspheres have a diameter of 1 μm.Reuse & Permissions
Figure 2
Tracking the spontaneous movements of amine-modified and PEGylated microspheres in lamin $B 1$ networks. Lamin $B 1$ networks (3 mg∕mL) in polymerization buffer at 25 °C for 60 min. (a) Typical trajectory of a freely moving amine-modified microsphere in a lamin-poor region of the network. (b) Typical trajectory of an amine-modified microsphere embedded in a lamin-rich region of the network. (c) Typical MSD profiles, $⟨ Δ r^{2} (τ) ⟩ vs τ$ , of amine-modified microspheres in lamin $B 1$ . (d) Typical MSD profiles of carboxylated microspheres. (e) Typical MSD profiles of PEGylated microspheres. All microspheres have a diameter of 1 μm.Reuse & Permissions
Figure 3
Lamin $B 1$ network heterogeneity assessed by tracking the spontaneous movements of individual carboxylated and PEGylated microspheres. Lamin $B 1$ networks (3 mg∕mL) in polymerization buffer at 25 °C for 60 min. (a) Proportions of restricted and free-moving microspheres for amine-modified, carboxylated, and PEGylated microspheres in a 3 mg∕mL lamin $B 1$ solution. (b) Degree of heterogeneity for all (restricted and free-moving) microspheres. These parameters are close to 10%, 25%, and 50% for a homogeneous material like glycerol and progressively higher than those values for more heterogeneous materials. (c) Distribution of MSD’s of PEGylated microspheres in a 3 mg∕mL lamin $B 1$ network at a time scale of 0.1 s. Inset: MSD distribution of the microspheres undergoing restricted motion. All microspheres have a diameter of 1 μm.Reuse & Permissions
Figure 4
Ensemble-averaged MSD of microspheres embedded in lamin $B 1$ suspensions and apparent microelastic moduli from MSD profiles. Lamin $B 1$ networks (3 mg∕mL) in polymerization buffer at 25 °C for 60 min. (a) Ensemble-averaged MSD profiles for different types of microspheres embedded in lamin-rich regions of a 3 mg∕mL lamin $B 1$ network. (b) Frequency-dependent elastic modulus, $G^{'} (ω)$ , of lamin $B 1$ networks calculated from the ensemble-averaged MSD of the PEGylated microspheres embedded in the lamin-rich regions of the gel. The mathematical transformation of MSD profiles into $G^{'} (ω)$ is detailed in Refs. 27, 32.Reuse & Permissions
Figure 5
Diffusion coefficient of PEGylated microspheres embedded in lamin $B 1$ gels. Mean diffusion coefficient of 1-μm-diam PEGylated PS microspheres suspended in lamin-poor regions of the gel (top curve) and embedded in lamin-rich regions (bottom curve).Reuse & Permissions

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