Topological Rearrangement Research Articles

Topological rearrangement-derived edge-sharing [MO6] motifs on perovskite oxide for optimizing O-O bonding in water oxidation

The connection configuration of active sites plays a crucial role in electrocatalytic O2 evolution. Reasonably integrating the advantages of different connection configurations can enhance the catalytic performance. Here, we report a Ba0.5Sr0.5Co0.8Fe0.2O3-δ electrocatalyst featuring edge-sharing [Co/FeO6] motifs surface, constructed through an innovative Cu+-assisted top-down topological rearrangement. Our study demonstrates that the edge-sharing [Co/FeO6] motifs exhibit high lattice oxygen redox activity as well as the abilities to stabilize high-oxidation-state Co3+/4+ species and accelerate hydroxyl aggregation, thereby facilitating intermolecular O-O coupling mechanism during O2 evolution. The inner corner-sharing [Co/FeO6] motifs function as a current collector to enhance conductivity. As-synthesized electrocatalyst with these excellet properties achieves a low overpotential of 298 mV and stable operation for 100 h at 10 mA cm−2 in 1 M KOH. This work clarifies the superiority of edge-sharing [Co/FeO6] motifs in oxygen evolution reaction and prove the precise manipulation of connection configuration as an effective approach for enhancing the catalytic performance.

Topological rearrangements activate the HerA-DUF anti-phage defense system.

Leveraging the rich structural information provided by AlphaFold, we used integrated experimental approaches to characterize the HerA-DUF4297 (DUF) anti-phage defense system, in which DUF is of unknown function. To infer the function of DUF, we performed structure-guided genomic analysis and found that DUF homologs are universally present in bacterial immune defense systems. One notable homolog of DUF is Cap4, a universal effector with nuclease activity in CBASS, the most prevalent anti-phage system in bacteria. To test the inferred nuclease function of DUF, we performed biochemical experiments and discovered that the DUF only exhibits activity against DNA substrates when it is bound by HerA. To understand how HerA activates DUF, we determined the structures of DUF and the HerA-DUF complex. DUF forms large oligomeric assemblies with or without HerA, suggesting that oligomerization per se is not sufficient for DUF activation. Instead, DUF activation requires dramatic topological rearrangements that propagate from HerA to the entire HerA-DUF complex, leading to reorganization of DUF for effective DNA cleavage. We further validated these structural insights by structure- guided mutagenesis. Together, these findings reveal dramatic topological rearrangements throughout the HerA-DUF complex, challenge the long-standing dogma that protein oligomerization alone activates immune signaling, and may inform the activation mechanism of CBASS.

A circularly permuted CasRx platform for efficient, site-specific RNA editing.

Inactive Cas13 orthologs have been fused to a mutant human ADAR2 deaminase domain at the C terminus to enable programmable adenosine-to-inosine (A-to-I) RNA editing in selected transcripts. Although promising, existing RNA-editing tools generally suffer from a trade-off between efficacy and specificity, and off-target editing remains an unsolved problem. Here we describe the development of an optimized RNA-editing platform by rational protein engineering, CasRx-based Programmable Editing of RNA Technology (xPERT). We demonstrate that the topological rearrangement of a CasRx K940L mutant by circular permutation results in a robust scaffold for the tethering of a deaminase domain. We benchmark our tool against the REPAIR system and show that xPERT exhibits strong on-target activity like REPAIRv1 but low off-target editing like REPAIRv2. Our xPERT platform can be used to alter RNA sequence information without risking genome damage, effect temporary cellular changes and customize protein function.

Synthesis and Characterization of Rebondable Polyurethane Adhesives Relying on Thermo-Activated Transcarbamoylation.

Dynamic polymer networks combine the noteworthy (thermo)mechanical features of thermosets with the processability of thermoplastics. They rely on externally triggered bond exchange reactions, which induce topological rearrangements and, at a sufficiently high rate, a macroscopic reflow of the polymer network. Due to this controlled change in viscosity, dynamic polymers are repairable, malleable, and reprocessable. Herein, several dynamic polyurethane networks were synthetized as model compounds, which were able to undergo thermo-activated transcarbamoylation for the use in rebondable adhesives. Ethylenediamine-N,N,N',N'-tetra-2-propanol (EDTP) was applied as a transcarbamoylation catalyst, which participates in the curing reaction across its four -OH groups and thus, is covalently attached within the polyurethane network. Both bond exchange rate and (thermo)mechanical properties of the dynamic networks were readily adjusted by the crosslink density and availability of -OH groups. In a last step, the most promising model compound was optimized to prepare an adhesive formulation more suitable for a real case application. Single-lap shear tests were carried out to evaluate the bond strength of this final formulation in adhesively bonded carbon fiber reinforced polymers (CFRP). Exploiting the dynamic nature of the adhesive layer, the debonded CFRP test specimens were rebonded at elevated temperature. The results clearly show that thermally triggered rebonding was feasible by recovering up to 79% of the original bond strength.

Design and Evaluation of a Reprocessable Bismaleimide Thermoset: Enhancing Functionality and Sustainability Compatibility.

Bismaleimide (BMI) resins are high-performance thermosets that are primarily used in aerospace because of their exceptional heat resistance and physical properties. However, their growing demand has led to significant environmentally unfriendly waste. To address this, our research proposes a reprocessable BMI system using a newly synthesized BMI vitrimer (BMIV) with functional groups that form covalent adaptable networks (CANs). To enhance the properties, a symmetrical BMI with two ester groups introduced into the rigid rod molecule was designed as a CAN component. After confirming the structure using various spectroscopic techniques, BMIV was coupled with aromatic diamines via an additional aza-Michael reaction to obtain the cured resins. Subsequently, the mechanical properties and reprocessing behavior of the thermally stable and optimized thermosetting material with the best performance were evaluated, and the evidence, mechanism, and activation energy of the topology rearrangement are reported in detail.

Thermadapt shape memory AB-copolymer networks exhibiting tunable properties and kinetics of topological rearrangement

Polycaprolactone (PCL) based thermadapt shape memory polymers (SMPs) have exhibited superiority over traditional analogues by allowing shape-editing to reconfigure permanent shapes into more complex geometrical shapes, driven by the pursuit of advanced functionalities for high-value applications. Nevertheless, although transesterification-based PCL networks exhibit impressive shape reconfigurability as prototypical thermadapt SMPs, there are still constraints in terms of the need for significant flexibility in architectural adjustment and property modulation without compromising reconfigurability, which would be relevant for practical applications. Here, we present a simple yet efficient strategy to create PCL-based thermadapt SMPs that possess a highly tunable structure and properties, as well as exceptional reconfigurability. The family of SMPs, called thermadapt shape memory AB copolymer networks (AB-CPNs), was synthesized by UV-initiated free radical polymerization between PCL diacrylate as crosslinker and 4-hydroxybutyl acrylate (HBA) as comonomer. The thermadapt AB-CPNs allow for significant structural alterations with 0 wt% to 70 wt% HBA while maintaining excellent shape memory and shape reconfigurability effects. The insertion of the polymer segment containing free hydroxyls not only promises tunable material properties but also makes network rearrangement easier since dynamic hydroxy-ester bonds are more active than dynamic ester-ester bonds. It is envisioned that the thermadapt shape memory AB-CPNs with widely tunable macroscopic properties will drive progress in the real-world applications of SMP devices with complicated geometric structures.

Rejuvenating liquid crystal elastomers for self-growth

To date, only one polymer can self-grow to an extended length beyond its original size at room temperature without external stimuli or energy input. This breakthrough paves the way for significant advancements in untethered autonomous soft robotics, eliminating the need for the energy input or external stimuli required by all existing soft robotics systems. However, only freshly prepared samples in an initial state can self-grow, while non-fresh ones cannot. The necessity of synthesizing from monomers for each use imposes significant limitations on practical applications. Here, we propose a strategy to rejuvenate non-fresh samples to their initial state for on-demand self-growth through the synergistic effects of solvents and dynamic covalent bonds during swelling. The solvent used for swelling physically transforms the non-fresh LCEs from the liquid crystal phase to the isotropic phase. Simultaneously, the introduction of the transesterification catalyst through swelling facilitates topological rearrangements through exchange reactions of dynamic covalent bonds. The rejuvenation process can also erase growth history, be repeated several times, and be regulated by selective swelling. This strategy provides a post-modulation method for the rejuvenation and reuse of self-growing LCEs, promising to offer high-performance materials for cutting-edge soft growing robotics.

A Biobased Vitrimer: Self-Healing, Shape Memory, and Recyclability Induced by Dynamic Covalent Bond Exchange.

Plant oil-based vitrimer is an innovative and sustainable polymer with wide-ranging potential applications in the field of advanced materials. However, its restricted application is caused by the poor mechanical properties and the need for catalysts during preparation. Using renewable cardanol as the raw material, epoxy cardanol glycidyl ether (ECGE) with an end epoxide group was obtained by the clicking reaction and epoxidation reaction. After the application of citric acid (CA), ECGE was successfully cured, resulting in the production of fully biobased ECGE-CA vitrimers. This material does not require a catalyst, possesses self-healing properties, and exhibits high mechanical strength. On account of the introduction of hydroxyl groups in citric acid, plenty of hydrogen bonds are formed, allowing the topological network rearrangement of the material in the absence of a catalyst. Recyclable adhesives and repairable materials, vitrimer polymers have good shape memory, self-healing, and recyclability since of their dynamic ester and hydroxyl bonds.

Highly Ionic Conductive, Self-Healing, Li10GeP2S12-Filled Composite Solid Electrolytes Based on Reversibly Interlocked Macromolecule Networks for Lithium Metal Batteries with Improved Cycling Stability.

Ceramic-polymer composite solid electrolytes (CSEs) have attracted great attention by combining the advantages of polymer electrolytes and inorganic ceramic electrolytes. Herein, Li10GeP2S12 (LGPS) particles are incorporated into poly(ethylene oxide) (PEO)-based reversibly interlocked polymer networks (RILNs) derived from the topological rearrangement of two PEO networks cross-linked by reversible imine bonds and disulfide linkages. A series of highly ionic conductive, self-healing CSEs are obtained accordingly. The interlocking architecture successfully inhibits PEO crystallization, increasing the amorphous phase for Li ion transportation, and stabilizes the conductive pathways of LGPS particles by its unique confinement effect. Meanwhile, the LGPS particles cooperate with the RILN matrix, forming a filler-polymer interfacial phase for additional Li ion transportation and strengthening and toughening the resultant CSEs via the strong intermolecular Li+-O2- interactions. Furthermore, the dynamic characteristics of the included reversible bonds ensure a multiple intrinsic self-healing capability. Consequently, the CSEs containing 15 wt % LGPS deliver a high ionic conductivity (1.06 × 10-3 S cm-1) and high Li ion transference number (∼0.6) at 25 °C, a wide electrochemical stability window (>4.9 V), good mechanical properties (0.63 MPa, 377%), and a stable CSE/Li anode interface. The integrated Li/CSE/LiFePO4 battery exhibits a specific discharge capacity of 110.8 mAh g-1 at 1 C (25 °C) and a capacity retention of 76.9% after 200 cycles. Thanks to the healability, the damaged CSEs can regain the structural integrity, ion conductive capability, and cycling performance of the assembled cells. The present work provides an effective strategy to fabricate CSEs for lithium metal batteries that are workable at ambient temperature.

Auxetic Liquid Crystal Vitrimers with Adjustable Poisson's Ratios Enabled by Topological Rearrangements of Polymer Network

AbstractMetamaterials feature extraordinary physical properties that break the cognitive limitations of human beings on traditional materials. Auxetic materials and liquid crystal elastomers (LCEs) are representative of typical mechanical and thermal metamaterials. Their combination may introduce some unconventional and counterintuitive performances. Nevertheless, studies on LCEs with negative Poisson's ratio (v) are still rare. Herein, a liquid crystal vitrimer (Poly‐LCE) is developed that is a polydomain main‐chain LCE containing dynamic ester bonds. Its orientation process to monodomain (Mono‐LCE) is greatly simplified by transesterification reaction‐induced topological network rearrangement under mechanical alignment. By optimizing geometric parameters of re‐entrant (R) structures and orientation of liquid crystal units, all samples of R‐Poly‐LCE, R‐Mono‐LCE (//), and R‐Mono‐LCE (⊥) show negative Poisson's ratio (NPR) below 2% elongation (v = −0.22–0 for R‐Poly‐LCE, v = −0.12–0 for R‐Mono‐LCE (//) and v = −0.16–0 for R‐Mono‐LCE (⊥)). Interestingly, R‐Poly‐LCE presents v > 0 within 2%–10% axial elongation, while R‐Mono‐LCE (//) and R‐Mono‐LCE (⊥) exhibit v ≈ 0 under the same elongation. Materials with negative and zero Poisson's ratios are interesting in niche applications. This work develops a simple method to prepare these materials by liquid crystal vitrimers.

Robust Epoxy Resins with Autonomous Visualization of Damaging‐Healing and Green Closed‐Loop Recycling

AbstractEpoxy resins‐based engineering plastics are indispensable in the global economy, but they have created a serious waste crisis caused by their chemical cross‐linked networks. To solve this problem, current strategies often require the assistance of catalysts or solvents at the expense of thermal and mechanical performance. In this work, a high‐performance epoxy resin featuring dynamic ester and disulfide bonds (TDS) is reported, which exhibits higher thermal and mechanical properties than common engineering plastics, i.e., tensile strength and modulus of 66.6 MPa and 2.63 GPa, flexural strength and modulus of 103.2 MPa and 3.52 GPa, and glass transition temperature (Tg) of 133 °C. Moreover, the reversible transformation between aromatic disulfide bonds and thiyl radicals endows TDS epoxy resin with autonomous visualization of damage and healing. In addition, the harmonious interplay between disulfide and ester bonds‐promoted by tertiary amine accelerated the topological network rearrangements, enabling TDS to easily reshape and weld. Specifically, TDS can be completely degraded in pure water at 200 °C without any catalyst, and the degraded products can be directly re‐polymerized to achieve green closed‐loop recycling. This work proposes a simple and economical strategy for the development of epoxy resin‐based cutting‐edge engineering plastics that are both functional and sustainable.

Self-healing and reprocessable biobased non-isocyanate polyurethane elastomer with dual dynamic covalent adaptive network for flexible strain sensor

Owing to the nontoxicity of monomers, non-isocyanate polyurethane elastomers have attracted considerable attention, yet the synthesis and functionalization are still challenging. Herein, self-healing and reprocessable biobased non-isocyanate polyurethane (NIPU) elastomers with dual dynamic covalent adaptive network (DDCAN) by disulfide bonds and dynamic imine bonds were synthesized as substrate for the construction of flexible strain sensor with MXene as conductive substance. The tensile strength and elongation at break of the NIPU elastomer were 3.22 MPa and 234 %, respectively. Thanks to the formation of DDCAN, the NIPU elastomer showed high healing efficiency of 97.5 % after healing at room temperature for 24 h. Interestingly, the NIPU elastomer possessed superior reprocessing capability and the tensile strength after three reprocessing cycles reached 136.1 % of the original one, which was attributed to the increase of crosslinking points caused by topological rearrangement. In addition, the NIPU elastomer-based flexible strain sensor exhibited fast response (response time = 60 ms) and excellent repeatability (1000 bending-releasing cycles) and was successfully applied for human motion detection and speech recognition. The findings in this work conceivably stand out as a new methodology for the preparation of biobased and functional elastomers, which will greatly promote the sustainable development and application of flexible electronics.

Mechanically Robust Photonic‐Ionic Skin Cross‐Linked by Metal–Imidazole Interactions

AbstractPhotonic‐ionic skins (PI‐skins) featuring multi‐signal synergistic outputs exhibit fascinating interactive sensing potential in flexible iononics. However, the existing ones are susceptible to irreversible damage in usage due to their poor toughness and deficiency in self‐healing. Herein, a novel tough mechanochromic PI‐skin is ingeniously constructed, from both molecular engineering and nanostructural engineering perspectives, via integrating the ordered photonic array and robust metal‐imidazole cross‐linked network. The PI‐skin displays synchronous structural color variation and sensitive electrical response under strain. Notably, the synergy of dense physical cross‐linking network and microphase‐separation structure achieved by strong metal‐imidazole coordination greatly promotes energy dissipation. PI‐skin possesses a combination of exceptional properties, including high fracture strength (8.22 MPa), remarkable toughness (10.23 MJ m−3), and robust adhesion behavior (2.30 MPa). Furthermore, favorable self‐healing capability at room temperature is realized thanks to the dynamic topological rearrangement of metal‐imidazole coordination. The PI‐skin demonstrates promising uses as a visually interactive wearable device for human motion monitoring and remote communication. This work not only broadens design considerations for the development of high‐performance artificial skins but also offers a general optical platform for high‐level interactive wearable devices.

Exploring the dual dynamic synergy of transesterification and siloxane exchange in vitrimers

Despite the benefits of dynamic polymer networks with multiple dynamic bonds, identifying compatible combinations of dynamic chemistries that work synergistically to achieve desirable properties, remains a significant challenge. This work focuses on the potential of utilizing both siloxane and ester dynamic bonds in epoxy-acid cured vitrimers to finetune chemical exchange reactions. We identified to what extent a common basic catalyst (TBD) can simultaneously activate siloxane and ester exchange in the corresponding epoxy-based vitrimers. Our results showed that TBD is not only able to facilitate network formation but also improved the dynamic behavior of the resulting networks dramatically, with an overall exchange rate faster than the sum of the individual exchange chemistries, as shown by stress-relaxation studies. It has been demonstrated that the siloxane and ester dynamic bonds work together in a synergistic way to facilitate topology rearrangement. The relative increase or decrease in mobility of neighboring chains, located around a specific dynamic bond within the polymer network, was investigated in detail by adjusting the concentration of dynamic bonds and catalyst. The herein reported strategy allows the production of dual dynamic polymer networks that exhibit much shorter relaxation times and thus improved (re)processability in comparison to vitrimers with one type of dynamic bond.

Shape Memory Polyurethane Composite With Fast Response to Near-Infrared Light Based on Tannic Acid-Iron and Dynamic Phenol-Carbamate Network.

Intelligent materials derived from green and renewable bio-based materials garner widespread attention recently. Herein, shape memory polyurethane composite (PUTA/Fe) with fast response to near-infrared (NIR) light is successfully prepared by introducing Fe3+ into the tannic acid-based polyurethane (PUTA) matrix through coordination between Fe3+ and tannic acid. The results show that the excellent NIR light response ability is due to the even distribution of Fe3+ filler with good photo-thermal conversion ability. With the increase of Fe3+ content, the NIR light response shape recovery rate of PUTA/Fe composite films is significantly improved, and the shape recovery time is reduced from over 60 s to 40s. In addition, the mechanical properties of PUTA/Fe composite film are also improved. Importantly, owing to the dynamic phenol-carbamate network within the polymer matrix, the PUTA/Fe composite film can reshape its permanent shape through topological rearrangement and show its good NIR light response shape memory performance. Therefore, PUTA/Fe composites with high content of bio-based material (TA content of 15.1-19.4%) demonstrate the shape memory characteristics of fast response to NIR light; so, it will have great potential in the application of new intelligent materials including efficient and environmentally friendly smart photothermal responder.

Design of mechanically robust, recyclable, multi-stimuli-responsive shape memory elastomers based on biological phytic acid and cuttlefish ink

Facilitating the utilization of biomass in the rubber field is a facile strategy to reduce environmental pollution and the carbon emission. Herein, biological phytic acid (PA) was served as an eco-friendly curing agent, and cuttlefish ink (CI) was acted as a photothermal trigger switch to fabricate multi-stimuli-responsive shape memory biobased epoxidized natural rubber (ENR) with mechanical robustness and recyclable ability. ENR was vulcanized by PA via the ring-opening reaction between phosphate groups of PA and epoxy group of ENR, leading to the construction of an impeccable cross-linking network and an adjustable Tg gradient, which endowed the elastomers with improved mechanical properties and shape memory effect. Meanwhile, the topology rearrangement occurred at elevated temperatures relied on phosphate transesterification, leading to excellent thermo-activated recyclable ability and reconfigurable shape memory performance of the elastomers. Additionally, CI acted as reinforced filler to enhance the ENR matrix, enabling elastomers to achieve a robust tensile strength of 21.4 MPa and tensile toughness of 30.4 MJ/m3, which was nearly 26.8 times and 11.3 times of the neat ENR, respectively. Exhilaratingly, CI also acted as photothermal trigger switch for the response to near-infrared light and sun, which realized the remotely multistage shape memory performance, demonstrating the potential application of ENR in the field of actuators without environmental pollution.

A unified quasiparticle approach to the theory of strongly correlated electron liquids

Landau’s quasiparticle formalism is generalized to describe a wide class of strongly correlated Fermi systems, in addition to conventional Fermi liquids. This class includes (i) so-called marginal exemplars and (ii) systems that harbor interaction-driven flat bands, in both of which manifestations of non-Fermi-liquid behavior are well documented. Specifically, the advent of such flat bands is attributed to a spontaneous topological rearrangement of the Landau state that supplements the conventional Landau quasiparticle picture with a different set of quasiparticles, the so-called fermion condensate, whose single-particle spectrum is dispersionless. The celebrated Landau–Luttinger theorem is extended to marginal Fermi liquids, in which the density of the augmented quasiparticle system is shown to coincide with the particle density. On the other hand, the total density of a system hosting an interaction-driven flat band turns out to be the sum of the densities of the two quasiparticle subsystems: the Landau-like component and the fermion condensate. We demonstrate that within the framework of the scenario proposed, a long-standing problem faced by theories of D-wave superconductivity in cuprates, namely a consistent explanation of the so-called Uemera plot, can be naturally resolved.

High strength, self-healing and hydrophobic fully bio-based polybenzoxazine reinforced pine oleoresin-based vitrimer and its application in carbon fiber reinforced polymers

The traditional carbon fiber reinforced polymers (CFRPs) matrix is a permanent 3D cross-linked network that is difficult to degrade and reprocess. In order to solve the closed-loop recycling of carbon fibers (CFs) and develop green economy. We synthesized aldehyde-containing bio-based benzoxazine (VD) from vanillin and 1,10-diaminodecane, the epoxy resin vitrimer matrix (P-AE-MV) was prepared by curing acrylpimaric acid diglycidyl ester (AE) with a Schiff base (MV) formed by 1,8-menthane diamine (MDA) and VD. Under the double dynamic covalent bond of Schiff base and β-hydroxy ester, P-AE-MV has a very low dynamic bond exchange activation energy Ea = 48.1 kJ mol−1, which can realize the rapid topological rearrangement of polymer network, and give P-AE-MV excellent self-healing, shape memory, reprocessability and degradability. In addition, the introduction of polybenzoxazine (PBz) structure greatly improved the mechanical properties, thermal decomposition temperature, carbon yield and hydrophobicity of epoxy resin vitrimer, which is very suitable for CFRPs matrix. The CFRP (P-AE-MV-CF) prepared with P-AE-MV as matrix resin have good mechanical properties, reprocessability, shape memory and self-adhesion. Especially, it can be rapidly ammonolysis with n-butylamine under mild conditions (60 °C), achieving efficient and non-destructive recycling of CFs. This work provides an effective solution to promote the closed-loop recycling of CFs and the sustainable development of CFRPs using fully bio-based resources as raw materials.

Catalyst-Free Cardanol-Based Epoxy Vitrimers for Self-Healing, Shape Memory, and Recyclable Materials.

Bio-based vitrimers present a promising solution to the issues associated with non-renewable and non-recyclable attributes of traditional thermosetting resins, showcasing extensive potential for diverse applications. However, their broader adoption has been hindered by the requirement for catalyst inclusion during the synthesis process. In this study, a cardanol-based curing agent with poly-hydroxy and tertiary amine structures was prepared by a clean synthetic method under the theory of click chemistry. The reaction of a cardanol-based curing agent with diglycidyl ether of bisphenol A formed catalyst-free, self-healing, and recyclable bio-based vitrimers. The poly-hydroxy and tertiary amine structures in the vitrimers promoted the curing of epoxy-carboxylic acid in the cross-linked network and served as internal catalysts of dynamic transesterification. In the absence of catalysts, the vitrimers network can achieve topological network rearrangement through dynamic transesterification, exhibiting excellent reprocessing performance. Moreover, the vitrimers exhibited faster stress relaxation (1500 s at 180 °C), lower activation energy (92.29 kJ·mol-1) and the tensile strength of the recycled material reached almost 100% of the original sample. This work offers a new method for preparing cardanol-based epoxy vitrimers that be used to make coatings, hydrogels, biomaterials, adhesives, and commodity plastics in the future.

Biomechanical models of living tissue

The evolution of living things has led to the emergence of multicellular organ-isms in which cells differentiate, specializing in performing various functions. Cells interact and unite into large groups, forming tissues and transferring the control func-tion to an organ or organism. In fact, the latter is a complex biomechanical system controlled by chemical and mechanical signals. The development of computer tech-nologies and high-speed computing systems gradually leads to the possibility of realistic modeling of the biomechanics of cellular tissue, which reproduces both the averaged dynamics of the tissue and the behavior of cells. Mathematical modeling allows us to study the historical aspects of the evolution of living things, describe the morphogenesis of specific organ-isms, understand the healing processes in organs when they are damaged, consider the appearance of tumors, and develop the tech-nology for artificial tissue growth. This pa-per presents an overview of works devoted to mathematical models of multicellular tissue of living organisms. Specifically, we focus on those models where the cell is a structural unit of a complex system. We classify biomechanical models according to the approach describing the tissue, the method of constructing cells, and the dimension of the tissue formed by the cells. We discuss the interaction forces between cells and topological rear-rangements in tissue during intense cell movement. Finally, we discuss the results of some selected ap-plied research.