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Gelation Kinetics and Mechanical Properties of Thiol-Tetrazole Methylsulfone Hydrogels Designed for Cell Encapsulation
Hydrogel precursors that crosslink within minutes are essential for the development of cell encapsulation matrices and their implementation in automated systems. Such timescales allow sufficient mixing of cells and hydrogel precursors under low shear forces and the achievement of homogeneous networks and cell distributions in the 3D cell culture. The previous work showed that the thiol-tetrazole methylsulfone (TzMS) reaction crosslinks star-poly(ethylene glycol) (PEG) hydrogels within minutes at around physiological pH and can be accelerated or slowed down with small pH changes. The resulting hydrogels are cytocompatible and stable in cell culture conditions. Here, the gelation kinetics and mechanical properties of PEG-based hydrogels formed by thiol-TzMS crosslinking as a function of buffer, crosslinker structure and degree of TzMS functionality are reported. Crosslinkers of different architecture, length and chemical nature (PEG versus peptide) are tested, and degree of TzMS functionality is modified by inclusion of RGD cell-adhesive ligand, all at concentration ranges typically used in cell culture. These studies corroborate that thiol/PEG-4TzMS hydrogels show gelation times and stiffnesses that are suitable for 3D cell encapsulation and tunable through changes in hydrogel composition. The results of this study guide formulation of encapsulating hydrogels for manual and automated 3D cell culture.
Bilinear coagulation equations
We consider coagulation equations of Smoluchowski or Flory type where the total merge rate has a bilinear form π(y) · Aπ (x) for a vector of conserved quantities π, generalising the multiplicative kernel. For these kernels, a gelation transition occurs at a finite time tg ∈ (0,∞), which can be given exactly in terms of an eigenvalue problem in finite dimensions. We prove a hydrodynamic limit for a stochastic coagulant, including a corresponding phase transition for the largest particle, and exploit a coupling to random graphs to extend analysis of the limiting process beyond the gelation time.
Gelation kinetics of thiol-methylsulfone (MS) hydrogel formulations for 3D cell culture
Crosslinking chemistries that allow hydrogel formation within minutes are essential to achieve homogeneous networks and cell distributions in 3D cell culture. Thiol-methylsulfone (MS) crosslinking chemistry offers minutes-scale gelation under near-physiological conditions showing many desirable attributes for 3D cell encapsulation. Here we investigate the gelation kinetics and mechanical properties of PEG-based hydrogels formed by thiol-tetrazole methylsulfone (TzMS) crosslinking as a function of buffer, crosslinker structure, and degree of TzMS functionalization. Appropriate buffer selection ensured constant pH throughout crosslinking. The formulation containing cell adhesive ligand RGD and enzymatically-degradable peptide VPM gelled in ca. 4 min at pH 7.5, and stiffness could be increased from hundreds of Pascals to > 1 kPa by using excess VPM. The gelation times and stiffnesses for these hydrogels are highly suitable for 3D cell encapsulations, and pave the way for reliable 3D cell culture workflows in pipetting robots.
A large-deviations principle for all the cluster sizes of a sparse Erdős-Rényi graph
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A large-deviations approach to gelation
A @large-deviations principle (LDP) is derived for the state, at fixed time, of the multiplicative coalescent in the large particle number limit. The rate function is explicit and describes each of the three parts of the state: microscopic, mesoscopic and macroscopic. In particular, it clearly captures the well known gelation phase transition given by the formation of a particle containing a positive fraction of the system mass at time t = 1. Via a standard map of the multiplicative coalescent onto a time-dependent version of the Erdos-Rényi random graph, our results can also be rephrased as an LDP for the component sizes in that graph. Our proofs rely on estimates and asymptotics for the probability that smaller Erdos-Rényi graphs are connected.