There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

Substantial research over the past two decades has established that extracellular matrix (ECM) elasticity, or stiffness, affects fundamental cellular processes, including spreading, growth, proliferation, migration, differentiation and organoid formation. Linearly elastic polyacrylamide hydrogels and polydimethylsiloxane (PDMS) elastomers coated with ECM proteins are widely used to assess the role of stiffness, and results from such experiments are often assumed to reproduce the effect of the mechanical environment experienced by cells in vivo. However, tissues and ECMs are not linearly elastic materials-they exhibit far more complex mechanical behaviours, including viscoelasticity (a time-dependent response to loading or deformation), as well as mechanical plasticity and nonlinear elasticity. Here we review the complex mechanical behaviours of tissues and ECMs, discuss the effect of ECM viscoelasticity on cells, and describe the potential use of viscoelastic biomaterials in regenerative medicine. Recent work has revealed that matrix viscoelasticity regulates these same fundamental cell processes, and can promote behaviours that are not observed with elastic hydrogels in both two- and three-dimensional culture microenvironments. These findings have provided insights into cell-matrix interactions and how these interactions differentially modulate mechano-sensitive molecular pathways in cells. Moreover, these results suggest design guidelines for the next generation of biomaterials, with the goal of matching tissue and ECM mechanics for in vitro tissue models and applications in regenerative medicine.

Effects of extracellular matrix viscoelasticity on cellular behaviour.

The extracellular matrix (ECM) is a dynamic environment that constantly provides physical and chemical cues to embedded cells. Much progress has been made in engineering hydrogels that can mimic the ECM, but hydrogel properties are, in general, static. To recapitulate the dynamic nature of the ECM, many reversible chemistries have been incorporated into hydrogels to regulate cell spreading, biochemical ligand presentation and matrix mechanics. For example, emerging trends include the use of molecular photoswitches or biomolecule hybridization to control polymer chain conformation, thereby enabling the modulation of the hydrogel between two states on demand. In addition, many non-covalent, dynamic chemical bonds have found increasing use as hydrogel crosslinkers or tethers for cell signalling molecules. These reversible chemistries will provide greater temporal control of adhered cell behaviour, and they allow for more advanced in vitro models and tissue-engineering scaffolds to direct cell fate.

/pdf/the-design-of-reversible-hydrogels-to-capture-extracellular-47corb5k1s.pdf

The design of reversible hydrogels to capture extracellular matrix dynamics

Hydrogels with tunable viscoelasticity hold promise as materials that can recapitulate many dynamic mechanical properties found in native tissues. Here, covalent adaptable boronate bonds are exploited to prepare hydrogels that exhibit fast relaxation, with relaxation time constants on the order of seconds or less, but are stable for long-term cell culture and are cytocompatible for 3D cell encapsulation. Using human mesenchymal stem cells (hMSC) as a model, the fast relaxation matrix mechanics are found to promote cell-matrix interactions, leading to spreading and an increase in nuclear volume, and induce yes-associated protein/PDZ binding domain nuclear localization at longer times. All of these effects are exclusively based on the hMSCs' ability to physically remodel their surrounding microenvironment. Given the increasingly recognized importance of viscoelasticity in controlling cell function and fate, it is expected that the synthetic strategies and material platform presented should provide a useful system to study mechanotransduction on and within viscoelastic environments and explore many questions related to matrix biology.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/advs.201800638

Adaptable Fast Relaxing Boronate-Based Hydrogels for Probing Cell-Matrix Interactions.

Natural and synthetic materials based on associating polymers possess diverse mechanical behavior, transport properties and responsiveness to external stimuli. Although much is known about their dynamics on the molecular and macroscopic level, knowledge of self-diffusive dynamics of the network-forming constituents remains limited. Using forced Rayleigh scattering, anomalous self-diffusion is observed in model associating protein hydrogels originating from the interconversion between species that diffuse in both the molecular and associated state. The diffusion can be quantitatively modeled using a two-state model for polymers in the gel, where diffusivity in the associated state is critical to the super diffusive behavior. The dissociation time from bulk rheology measurements was 2–3 orders of magnitude smaller than the one measured by diffusion, because the former characterizes submolecular dissociation dynamics, whereas the latter depicts single protein molecules completely disengaging from the network...

Anomalous Self-Diffusion and Sticky Rouse Dynamics in Associative Protein Hydrogels

Dynamic covalent hydrogels as biomaterials to mimic the viscoelasticity of soft tissues

Bioinspired brush polymers containing α-2,6-linked sialic acids at the side chain termini were synthesized by protection-group-free, ring-opening metathesis polymerization. Polymers showed strain-selective antiviral activity through multivalent presentation of the sialosides. The multivalent effect was further controlled by independently varying the degree of polymerization, the number density of sialic acids, and the length of side chains in the brush polymers. Optimizing the three-dimensional sialoside spacing for better binding to hemagglutinin trimers was of critical importance to enhance the multivalent effect and the antiviral activity determined by hemagglutination inhibition assays and in vitro infection assays. By taking advantage of their structural similarities with native mucins, these brush polymers can be used as model systems to dissect the intricate design principles in natural mucins.

Antiviral Agents from Multivalent Presentation of Sialyl Oligosaccharides on Brush Polymers

Understanding the quantitative relationship between the dynamic mechanical properties of associating polymer networks and the dynamics of sticker bonds represents an important problem in polymer science because materials mechanics is affected by not only the sticker bond chemistry but also the sticker position, the polymer structure, and the physical environment of the associating polymers such as concentration and solvent quality. In this study, associating networks formed by structurally well-defined linear poly(N,N-dimethylacrylamide) polymers with histidine side groups in complexation with Ni2+ ions are chosen as a model system. “Sticker diffusion and dissociation spectrometry” is developed as a new method to quantify the dissociation dynamics of stickers within the network environment where the stickers are covalently attached to polymers above their overlap concentration. The estimated time constants for junction dissociation in gels are shown to be substantially different than the ones measured by ...

Shengchang Tang

Papers

Adaptable Fast Relaxing Boronate-Based Hydrogels for Probing Cell-Matrix Interactions.

Anomalous Self-Diffusion and Sticky Rouse Dynamics in Associative Protein Hydrogels

Dynamic covalent hydrogels as biomaterials to mimic the viscoelasticity of soft tissues

Antiviral Agents from Multivalent Presentation of Sialyl Oligosaccharides on Brush Polymers

Relaxation Processes in Supramolecular Metallogels Based on Histidine–Nickel Coordination Bonds